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@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@
Python: Dense Hessian Using AD: Example and Test
def a_fun_hessian_xam() :
     #
     # load the Cppad Swig library
     import py_cppad
     #
     # initialize return variable
     ok = True
     # ---------------------------------------------------------------------
     # number of dependent and independent variables
     n_dep = 1
     n_ind = 3
     #
     # create the independent variables ax
     x = py_cppad.vec_double(n_ind)
     for i in range( n_ind  ) :
          x[i] = i + 2.0
     #
     ax = py_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 = py_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 = py_cppad.a_fun(ax, ay)
     #
     # g(x) = w_0 * f_0 (x) = f(x)
     w = py_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 and fpp[0 * n_ind + 0] == 0.0 
     ok = ok and fpp[0 * n_ind + 1] == x[2] 
     ok = ok and fpp[0 * n_ind + 2] == x[1] 
     #
     ok = ok and fpp[1 * n_ind + 0] == x[2] 
     ok = ok and fpp[1 * n_ind + 1] == 0.0 
     ok = ok and fpp[1 * n_ind + 2] == x[0] 
     #
     ok = ok and fpp[2 * n_ind + 0] == x[1] 
     ok = ok and fpp[2 * n_ind + 1] == x[0] 
     ok = ok and fpp[2 * n_ind + 2] == 0.0 
     #
     return( ok )
#
Input File: build/lib/example/python/a_fun_hessian_xam.py