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@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@
Perl: Dense Hessian Using AD: Example and Test
package a_fun_hessian_xam;
sub a_fun_hessian_xam() {
     # check for standard perl programming conventions
     use strict;
     use warnings;
     #
     # load the Cppad Swig library
     use pm_cppad;
     #
     # initilaize return variable
     my $ok = 1;
     # ---------------------------------------------------------------------
     # number of dependent and independent variables
     my $n_dep = 1;
     my $n_ind = 3;
     #
     # create the independent variables ax
     my $x = new pm_cppad::vec_double($n_ind);
     for(my $i = 0; $i < $n_ind ; $i++) {
          $x->set($i, $i + 2.0);
     }
     my $ax = pm_cppad::independent($x);
     #
     # create dependent variables ay with ay0 = ax_0 * ax_1 * ax_2
     my $ax_0 = $ax->get(0);
     my $ax_1 = $ax->get(1);
     my $ax_2 = $ax->get(2);
     my $ay = new pm_cppad::vec_a_double($n_dep);
     $ay->set(0, $ax_0 * $ax_1 * $ax_2);
     #
     # define af corresponding to f(x) = x_0 * x_1 * x_2
     my $af = new pm_cppad::a_fun($ax, $ay);
     #
     # g(x) = w_0 * f_0 (x) = f(x)
     my $w = new pm_cppad::vec_double($n_dep);
     $w->set(0, 1.0);
     #
     # compute Hessian
     my $fpp = $af->hessian($x, $w);
     #
     #          [ 0.0 , x_2 , x_1 ]
     # f''(x) = [ x_2 , 0.0 , x_0 ]
     #          [ x_1 , x_0 , 0.0 ]
     $ok = $ok && $fpp->get(0 * $n_ind + 0) == 0.0 ;
     $ok = $ok && $fpp->get(0 * $n_ind + 1) == $x->get(2) ;
     $ok = $ok && $fpp->get(0 * $n_ind + 2) == $x->get(1) ;
     #
     $ok = $ok && $fpp->get(1 * $n_ind + 0) == $x->get(2) ;
     $ok = $ok && $fpp->get(1 * $n_ind + 1) == 0.0 ;
     $ok = $ok && $fpp->get(1 * $n_ind + 2) == $x->get(0) ;
     #
     $ok = $ok && $fpp->get(2 * $n_ind + 0) == $x->get(1) ;
     $ok = $ok && $fpp->get(2 * $n_ind + 1) == $x->get(0) ;
     $ok = $ok && $fpp->get(2 * $n_ind + 2) == 0.0 ;
     #
     return( $ok );
}
Input File: build/lib/example/perl/a_fun_hessian_xam.pm