Octave: Dense Hessian Using AD: Example and Test

a_fun_hessian_xam.m

Headings

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@Octave: Dense Hessian Using AD: Example and Test

function ok = a_fun_hessian_xam()
     %
     % load the Cppad Swig library
     m_cppad
     %
     % initialize return variable
     ok = true;
     % -----------------------------------------------------------------------
     % number of dependent and independent variables
     n_dep = 1;
     n_ind = 3;
     %
     % create the independent variables ax
     x = m_cppad.vec_double(n_ind);
     for i = [ 0 :(n_ind -1) ]
          x(i) = i + 2.0;
     end
     ax = m_cppad.independent(x);
     %
     % create dependent variables ay with ay0 = ax_0 * ax_1 * ax_2
     ax_0 = ax(0);
     ax_1 = ax(1);
     ax_2 = ax(2);
     ay = m_cppad.vec_a_double(n_dep);
     ay(0) = ax_0 * ax_1 * ax_2;
     %
     % define af corresponding to f(x) = x_0 * x_1 * x_2
     af = m_cppad.a_fun(ax, ay);
     %
     % g(x) = w_0 * f_0 (x) = f(x)
     w = m_cppad.vec_double(n_dep);
     w(0) = 1.0;
     %
     % compute Hessian
     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(0 * n_ind + 0) == 0.0 ;
     ok = ok && fpp(0 * n_ind + 1) == x(2) ;
     ok = ok && fpp(0 * n_ind + 2) == x(1) ;
     %
     ok = ok && fpp(1 * n_ind + 0) == x(2) ;
     ok = ok && fpp(1 * n_ind + 1) == 0.0 ;
     ok = ok && fpp(1 * n_ind + 2) == x(0) ;
     %
     ok = ok && fpp(2 * n_ind + 0) == x(1) ;
     ok = ok && fpp(2 * n_ind + 1) == x(0) ;
     ok = ok && fpp(2 * n_ind + 2) == 0.0 ;
     %
     return;
end

Input File: build/lib/example/octave/a_fun_hessian_xam.m