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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Reverse Mode Jacobian Sparsity: Example and Test
# include <cppad/cppad.hpp> bool rev_jac_sparsity(void) { bool ok = true; using CppAD::AD; typedef CPPAD_TESTVECTOR(size_t) SizeVector; typedef CppAD::sparse_rc<SizeVector> sparsity; // // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD<double>) ax(n); ax[0] = 0.; ax[1] = 1.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD<double>) ay(m); ay[0] = ax[0]; ay[1] = ax[0] * ax[1]; ay[2] = ax[1]; // create f: x -> y and stop tape recording CppAD::ADFun<double> f(ax, ay); // sparsity pattern for the identity matrix size_t nr = m; size_t nc = m; size_t nnz_in = m; sparsity pattern_in(nr, nc, nnz_in); for(size_t k = 0; k < nnz_in; k++) { size_t r = k; size_t c = k; pattern_in.set(k, r, c); } // compute sparsite pattern for J(x) = F'(x) bool transpose = false; bool dependency = false; bool internal_bool = false; sparsity pattern_out; f.rev_jac_sparsity( pattern_in, transpose, dependency, internal_bool, pattern_out ); size_t nnz = pattern_out.nnz(); ok &= nnz == 4; ok &= pattern_out.nr() == m; ok &= pattern_out.nc() == n; { // check results const SizeVector& row( pattern_out.row() ); const SizeVector& col( pattern_out.col() ); SizeVector col_major = pattern_out.col_major(); // ok &= row[ col_major[0] ] == 0 && col[ col_major[0] ] == 0; ok &= row[ col_major[1] ] == 1 && col[ col_major[1] ] == 0; ok &= row[ col_major[2] ] == 1 && col[ col_major[2] ] == 1; ok &= row[ col_major[3] ] == 2 && col[ col_major[3] ] == 1; } // note that the transpose of the identity is the identity transpose = true; internal_bool = true; f.rev_jac_sparsity( pattern_in, transpose, dependency, internal_bool, pattern_out ); nnz = pattern_out.nnz(); ok &= nnz == 4; ok &= pattern_out.nr() == n; ok &= pattern_out.nc() == m; { // check results const SizeVector& row( pattern_out.row() ); const SizeVector& col( pattern_out.col() ); SizeVector row_major = pattern_out.row_major(); // ok &= col[ row_major[0] ] == 0 && row[ row_major[0] ] == 0; ok &= col[ row_major[1] ] == 1 && row[ row_major[1] ] == 0; ok &= col[ row_major[2] ] == 1 && row[ row_major[2] ] == 1; ok &= col[ row_major[3] ] == 2 && row[ row_major[3] ] == 1; } return ok; } 
Input File: example/sparse/rev_jac_sparsity.cpp