\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

sparse_jac_fun.cpp

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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;
}