sparse_hes_fun: Example and test

sparse_hes_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_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;
}

Input File: speed/example/sparse_hes_fun.cpp