Python: Hessian Sparsity Patterns: Example and Test

sparse_hes_pattern_xam.py

Headings

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@ Python: Hessian Sparsity Patterns: Example and Test

def sparse_hes_pattern_xam() :
     #
     import numpy
     import cppad_py
     #
     # initialize return variable
     ok = True
     # ---------------------------------------------------------------------
     # number of dependent and independent variables
     n = 3
     #
     # create the independent variables ax
     x = numpy.empty(n, dtype=float)
     for i in range( n  ) :
          x[i] = i + 2.0
     #
     ax = cppad_py.independent(x)
     #
     # create dependent variables ay with ay[i] = ax[j] * ax[i]
     # where i = mod(j + 1, n)
     ay = numpy.empty(n, dtype=cppad_py.a_double)
     for j in range( n  ) :
          i = j+1
          if i >= n  :
               i = i - n
          #
          ay_i = ax[i] * ax[j]
          ay[i] = ay_i
     #
     #
     # define af corresponding to f(x)
     f  = cppad_py.d_fun(ax, ay)
     #
     # Set select_d (domain) to all true, initial select_r (range) to all false
     select_d = numpy.empty(n, dtype=bool)
     select_r = numpy.empty(n, dtype=bool)
     for i in range( n ) :
          select_d[i] = True
          select_r[i] = False
     #
     #
     # only select component 0 of the range function
     # f_0 (x) = x_0 * x_{n-1}
     select_r[0] = True
     #
     # loop over forward and reverse mode
     for mode in range( 2 ) :
          pat_out = cppad_py.sparse_rc()
          if mode == 0  :
               f.for_hes_sparsity(select_d, select_r, pat_out)
          #
          if mode == 1  :
               f.rev_hes_sparsity(select_d, select_r, pat_out)
          #
          #
          # check that result is sparsity pattern for Hessian of f_0 (x)
          ok = ok and pat_out.nnz() == 2
          row = pat_out.row()
          col = pat_out.col()
          for k in range( 2 ) :
               r = row[k]
               c = col[k]
               if r <= c  :
                    ok = ok and r == 0
                    ok = ok and c == n-1
               #
               if r >= c  :
                    ok = ok and r == n-1
                    ok = ok and c == 0
               #
          #
     #
     #
     return( ok )
#

Input File: lib/example/python/sparse_hes_pattern_xam.py