Prev Next Index-> contents reference index search external Up-> CppAD ADFun sparsity_pattern RevSparseHes sparsity_sub.cpp ADFun-> record_adfun drivers Forward Reverse sparsity_pattern sparse_derivative optimize abs_normal FunCheck check_for_nan sparsity_pattern-> for_jac_sparsity ForSparseJac rev_jac_sparsity RevSparseJac rev_hes_sparsity RevSparseHes for_hes_sparsity ForSparseHes dependency.cpp rc_sparsity.cpp subgraph_sparsity RevSparseHes-> rev_sparse_hes.cpp sparsity_sub.cpp sparsity_sub.cpp Headings-> See Also ForSparseJac RevSparseHes

$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Sparsity Patterns For a Subset of Variables: Example and Test

The routine ForSparseJac is used to compute the sparsity for both the full Jacobian (see s ) and a subset of the Jacobian (see s2 ).
The routine RevSparseHes is used to compute both sparsity for both the full Hessian (see h ) and a subset of the Hessian (see h2 ).  # include <cppad/cppad.hpp> bool sparsity_sub(void) { // C++ source code bool ok = true; // using std::cout; using CppAD::vector; using CppAD::AD; using CppAD::vectorBool; size_t n = 4; size_t m = n-1; vector< AD<double> > ax(n), ay(m); for(size_t j = 0; j < n; j++) ax[j] = double(j+1); CppAD::Independent(ax); for(size_t i = 0; i < m; i++) ay[i] = (ax[i+1] - ax[i]) * (ax[i+1] - ax[i]); CppAD::ADFun<double> f(ax, ay); // Evaluate the full Jacobian sparsity pattern for f vectorBool r(n * n), s(m * n); for(size_t j = 0 ; j < n; j++) { for(size_t i = 0; i < n; i++) r[i * n + j] = (i == j); } s = f.ForSparseJac(n, r); // evaluate the sparsity for the Hessian of f_0 + ... + f_{m-1} vectorBool t(m), h(n * n); for(size_t i = 0; i < m; i++) t[i] = true; h = f.RevSparseHes(n, t); // evaluate the Jacobian sparsity pattern for first n/2 components of x size_t n2 = n / 2; vectorBool r2(n * n2), s2(m * n2); for(size_t j = 0 ; j < n2; j++) { for(size_t i = 0; i < n; i++) r2[i * n2 + j] = (i == j); } s2 = f.ForSparseJac(n2, r2); // evaluate the sparsity for the subset of Hessian of // f_0 + ... + f_{m-1} where first partial has only first n/2 components vectorBool h2(n2 * n); h2 = f.RevSparseHes(n2, t); // check sparsity pattern for Jacobian for(size_t i = 0; i < m; i++) { for(size_t j = 0; j < n2; j++) ok &= s2[i * n2 + j] == s[i * n + j]; } // check sparsity pattern for Hessian for(size_t i = 0; i < n2; i++) { for(size_t j = 0; j < n; j++) ok &= h2[i * n + j] == h[i * n + j]; } return ok; }