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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> namespace { // ------------------------------------------------------------- // define the template function BoolCases<Vector> template <typename Vector> // vector class, elements of type bool bool BoolCases(void) { bool ok = true; using CppAD::AD; // 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 Vector r(m * m); size_t i, j; for(i = 0; i < m; i++) { for(j = 0; j < m; j++) r[ i * m + j ] = (i == j); } // sparsity pattern for F'(x) Vector s(m * n); s = f.RevSparseJac(m, r); // check values ok &= (s[ 0 * n + 0 ] == true); // y[0] does depend on x[0] ok &= (s[ 0 * n + 1 ] == false); // y[0] does not depend on x[1] ok &= (s[ 1 * n + 0 ] == true); // y[1] does depend on x[0] ok &= (s[ 1 * n + 1 ] == true); // y[1] does depend on x[1] ok &= (s[ 2 * n + 0 ] == false); // y[2] does not depend on x[0] ok &= (s[ 2 * n + 1 ] == true); // y[2] does depend on x[1] // sparsity pattern for F'(x)^T, note R is the identity, so R^T = R bool transpose = true; Vector st(n * m); st = f.RevSparseJac(m, r, transpose); // check values ok &= (st[ 0 * m + 0 ] == true); // y[0] does depend on x[0] ok &= (st[ 1 * m + 0 ] == false); // y[0] does not depend on x[1] ok &= (st[ 0 * m + 1 ] == true); // y[1] does depend on x[0] ok &= (st[ 1 * m + 1 ] == true); // y[1] does depend on x[1] ok &= (st[ 0 * m + 2 ] == false); // y[2] does not depend on x[0] ok &= (st[ 1 * m + 2 ] == true); // y[2] does depend on x[1] return ok; } // define the template function SetCases<Vector> template <typename Vector> // vector class, elements of type std::set<size_t> bool SetCases(void) { bool ok = true; using CppAD::AD; // 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 Vector r(m); size_t i; for(i = 0; i < m; i++) { assert( r[i].empty() ); r[i].insert(i); } // sparsity pattern for F'(x) Vector s(m); s = f.RevSparseJac(m, r); // check values bool found; // y[0] does depend on x[0] found = s[0].find(0) != s[0].end(); ok &= (found == true); // y[0] does not depend on x[1] found = s[0].find(1) != s[0].end(); ok &= (found == false); // y[1] does depend on x[0] found = s[1].find(0) != s[1].end(); ok &= (found == true); // y[1] does depend on x[1] found = s[1].find(1) != s[1].end(); ok &= (found == true); // y[2] does not depend on x[0] found = s[2].find(0) != s[2].end(); ok &= (found == false); // y[2] does depend on x[1] found = s[2].find(1) != s[2].end(); ok &= (found == true); // sparsity pattern for F'(x)^T bool transpose = true; Vector st(n); st = f.RevSparseJac(m, r, transpose); // y[0] does depend on x[0] found = st[0].find(0) != st[0].end(); ok &= (found == true); // y[0] does not depend on x[1] found = st[1].find(0) != st[1].end(); ok &= (found == false); // y[1] does depend on x[0] found = st[0].find(1) != st[0].end(); ok &= (found == true); // y[1] does depend on x[1] found = st[1].find(1) != st[1].end(); ok &= (found == true); // y[2] does not depend on x[0] found = st[0].find(2) != st[0].end(); ok &= (found == false); // y[2] does depend on x[1] found = st[1].find(2) != st[1].end(); ok &= (found == true); return ok; } } // End empty namespace # include <vector> # include <valarray> bool RevSparseJac(void) { bool ok = true; // Run with Vector equal to four different cases // all of which are Simple Vectors with elements of type bool. ok &= BoolCases< CppAD::vectorBool >(); ok &= BoolCases< CppAD::vector <bool> >(); ok &= BoolCases< std::vector <bool> >(); ok &= BoolCases< std::valarray <bool> >(); // Run with Vector equal to two different cases both of which are // Simple Vectors with elements of type std::set<size_t> typedef std::set<size_t> set; ok &= SetCases< CppAD::vector <set> >(); ok &= SetCases< std::vector <set> >(); // Do not use valarray because its element access in the const case // returns a copy instead of a reference // ok &= SetCases< std::valarray <set> >(); return ok; } 
Input File: example/sparse/rev_sparse_jac.cpp