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library-> py_lib cpp_lib

py_lib-> py_fun py_sparse py_utility more_py

py_fun-> py_independent py_abort_recording py_fun_ctor py_fun_property py_fun_new_dynamic py_fun_jacobian py_fun_hessian py_fun_forward py_fun_reverse py_fun_optimize

py_fun_hessian-> fun_hessian_xam.py

fun_hessian_xam.py

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def fun_hessian_xam() :
     #
     import numpy
     import cppad_py
     #
     # initialize return variable
     ok = True
     # ---------------------------------------------------------------------
     # number of dependent and independent variables
     n_dep = 1
     n_ind = 3
     #
     # create the independent variables ax
     x = numpy.empty(n_ind, dtype=float)
     for i in range( n_ind  ) :
          x[i] = i + 2.0
     #
     ax = cppad_py.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   = numpy.empty(n_dep, dtype=cppad_py.a_double)
     ay[0] = ax_0 * ax_1 * ax_2
     #
     # define af corresponding to f(x) = x_0 * x_1 * x_2
     f  = cppad_py.d_fun(ax, ay)
     #
     # g(x) = w_0 * f_0 (x) = f(x)
     w = numpy.empty(n_dep, dtype=float)
     w[0] = 1.0
     #
     # compute Hessian
     fpp = f.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, 0] == 0.0
     ok = ok and fpp[0, 1] == x[2]
     ok = ok and fpp[0, 2] == x[1]
     #
     ok = ok and fpp[1, 0] == x[2]
     ok = ok and fpp[1, 1] == 0.0
     ok = ok and fpp[1, 2] == x[0]
     #
     ok = ok and fpp[2, 0] == x[1]
     ok = ok and fpp[2, 1] == x[0]
     ok = ok and fpp[2, 2] == 0.0
     # ---------------------------------------------------------------------
     af = cppad_py.a_fun(f)
     #
     # compute and check Hessian
     aw    = numpy.empty(n_dep, dtype=cppad_py.a_double)
     aw[0] = w[0]
     afpp  = af.hessian(ax, aw)
     ok    = ok and afpp.shape == fpp.shape
     (nr, nc) = fpp.shape
     for i in range(nr) :
          for j in range(nc) :
               ok = ok and afpp[i, j] == cppad_py.a_double( fpp[i, j] )
     #
     return( ok )
#