sparse_jac_fun: Example and test

sparse_jac_fun.cpp

Headings

@(@\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}} }@)@ sparse_jac_fun: Example and test

# include <cppad/speed/sparse_jac_fun.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/cppad.hpp>

bool sparse_jac_fun(void)
{     using CppAD::NearEqual;
     using CppAD::AD;

     bool ok = true;

     size_t j, k;
     double eps = CppAD::numeric_limits<double>::epsilon();
     size_t n   = 3;
     size_t m   = 4;
     size_t K   = 5;
     CppAD::vector<size_t>       row(K), col(K);
     CppAD::vector<double>       x(n),   yp(K);
     CppAD::vector< AD<double> > a_x(n), a_y(m);

     // choose x
     for(j = 0; j < n; j++)
          a_x[j] = x[j] = double(j + 1);

     // choose row, col
     for(k = 0; k < K; k++)
     {     row[k] = k % m;
          col[k] = (K - k) % n;
     }

     // declare independent variables
     Independent(a_x);

     // evaluate function
     size_t order = 0;
     CppAD::sparse_jac_fun< AD<double> >(m, n, a_x, row, col, order, a_y);

     // evaluate derivative
     order = 1;
     CppAD::sparse_jac_fun<double>(m, n, x, row, col, order, yp);

     // use AD to evaluate derivative
     CppAD::ADFun<double>   f(a_x, a_y);
     CppAD::vector<double>  jac(m * n);
     jac = f.Jacobian(x);

     for(k = 0; k < K; k++)
     {     size_t index = row[k] * n + col[k];
          ok &= NearEqual(jac[index], yp[k] , eps, eps);
     }
     return ok;
}

Input File: speed/example/sparse_jac_fun.cpp