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a_fun_xam.py

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Python: Purpose of a_fun Objects: Example and Test

def a_fun_xam() :
   #
   import numpy
   import cppad_py
   #
   # initialize return variable
   ok = True
   # ---------------------------------------------------------------------
   # number of dependent and independent variables
   m = 1
   n = 3
   #
   # Record the function
   #   f(x) = 0.5 * ( x[0]^2 + ... + x[n-1]^2 )
   x = numpy.empty(n, dtype=float)
   for i in range(n) :
      x[i] = i
   ax   = cppad_py.independent(x)
   ay   = numpy.empty(m, dtype=cppad_py.a_double)
   asum = cppad_py.a_double(0.0)
   for i in range(n) :
      asum = asum + ax[i] * ax[i]
   ay[0] = cppad_py.a_double(0.5) * asum
   f     = cppad_py.d_fun(ax, ay)
   af    = cppad_py.a_fun(f)
   #
   # Record the function
   #   g(x) = f'(x) * v
   au   = numpy.empty(m, dtype=cppad_py.a_double)
   av   = numpy.empty(n, dtype=cppad_py.a_double)
   for i in range(n) :
      av[i] = cppad_py.a_double(i)
   ax   = cppad_py.independent(x)
   af.forward(0, ax)
   au = af.forward(1, av)
   g  = cppad_py.d_fun(ax, au)
   #
   # compute g(x)
   u  = g.forward(0, x)
   #
   # compute g'(x)
   uq       = numpy.empty( (m, 1), dtype=float )
   uq[0, 0] = 1.0
   xq       = g.reverse(1, uq)
   #
   # g'(x) = f''(x) * v = v
   for i in range(n) :
      ok = ok and cppad_py.a_double(xq[i, 0]) == av[i]
   return ok