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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Computing Reverse Mode on Subgraphs: Example and Test
# include <cppad/cppad.hpp> bool subgraph_reverse(void) { bool ok = true; // using CppAD::AD; using CppAD::NearEqual; using CppAD::sparse_rc; using CppAD::sparse_rcv; // typedef CPPAD_TESTVECTOR(AD<double>) a_vector; typedef CPPAD_TESTVECTOR(double) d_vector; typedef CPPAD_TESTVECTOR(bool) b_vector; typedef CPPAD_TESTVECTOR(size_t) s_vector; // double eps99 = 99.0 * std::numeric_limits<double>::epsilon(); // // domain space vector size_t n = 4; a_vector a_x(n); for(size_t j = 0; j < n; j++) a_x[j] = AD<double> (0); // // declare independent variables and starting recording CppAD::Independent(a_x); // size_t m = 3; a_vector a_y(m); a_y[0] = a_x[0] + a_x[1]; a_y[1] = a_x[2] + a_x[3]; a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 2.; // // create f: x -> y and stop tape recording CppAD::ADFun<double> f(a_x, a_y); // // new value for the independent variable vector d_vector x(n); for(size_t j = 0; j < n; j++) x[j] = double(j); f.Forward(0, x); /* [ 1 1 0 0 ] J(x) = [ 0 0 1 1 ] [ 1 1 1 x_3] */ double J[] = { 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0 }; J[11] = x[3]; // // exclude x[0] from the calculations b_vector select_domain(n); select_domain[0] = false; for(size_t j = 1; j < n; j++) select_domain[j] = true; // // initilaize for reverse mode derivatives computation on subgraphs f.subgraph_reverse(select_domain); // // compute the derivative for each range component for(size_t i = 0; i < m; i++) { d_vector dw; s_vector col; size_t q = 1; // derivative of one Taylor coefficient (zero order) f.subgraph_reverse(q, i, col, dw); // // check order in col for(size_t c = 1; c < size_t( col.size() ); c++) ok &= col[c] > col[c-1]; // // check that x[0] has been excluded by select_domain if( size_t( col.size() ) > 0 ) ok &= col[0] != 0; // // check derivatives for i-th row of J(x) // note that dw is only specified for j in col size_t c = 0; for(size_t j = 1; j < n; j++) { while( c < size_t( col.size() ) && col[c] < j ) ++c; if( c < size_t( col.size() ) && col[c] == j ) ok &= NearEqual(dw[j], J[i * n + j], eps99, eps99); else ok &= NearEqual(0.0, J[i * n + j], eps99, eps99); } } return ok; } 
Input File: example/sparse/subgraph_reverse.cpp