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

sparse_hes_fun.cpp

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sparse_hes_fun: Example and test

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

bool sparse_hes_fun(void)
{  using CppAD::NearEqual;
   bool ok = true;

   typedef CppAD::AD<double> ADScalar;

   size_t j, k;
   double eps = 10. * CppAD::numeric_limits<double>::epsilon();
   size_t n   = 5;
   size_t m   = 1;
   size_t K   = 2 * n;
   CppAD::vector<size_t>       row(K),  col(K);
   CppAD::vector<double>       x(n),    ypp(K);
   CppAD::vector<ADScalar>     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 % 3;
      col[k] = k / 3;
   }
   for(k = 0; k < K; k++)
   {  for(size_t k1 = 0; k1 < K; k1++)
         assert( k == k1 || row[k] != row[k1] || col[k] != col[k1] );
   }

   // declare independent variables
   Independent(a_x);

   // evaluate function
   size_t order = 0;
   CppAD::sparse_hes_fun<ADScalar>(n, a_x, row, col, order, a_y);

   // evaluate Hessian
   order = 2;
   CppAD::sparse_hes_fun<double>(n, x, row, col, order, ypp);

   // use AD to evaluate Hessian
   CppAD::ADFun<double>   f(a_x, a_y);
   CppAD::vector<double>  hes(n * n);
   // compoute Hessian of f_0 (x)
   hes = f.Hessian(x, 0);

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