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@(@\newcommand{\B}[1]{{\bf #1}} \newcommand{\R}[1]{{\rm #1}}@)@
get_started: Example and Test

For our getting started example, we consider the Gaussian density for two independent random variables @(@ F : \B{R}^2 \rightarrow \B{R} @)@ and its partial derivatives : @[@ \begin{array}{rcl} F(x) & = & \exp \left[ - ( x_0^2 + x_1^2 ) / 2. \right] \\ \partial_{x(0)} F(x) & = & - F(x) * x_0 \\ \partial_{x(1)} F(x) & = & - F(x) * x_1 \end{array} @]@ The following Python code computes these derivatives using pycppad and then checks the results for correctness: 
 
from pycppad import *
def pycppad_test_get_started() :
  def F(x) :                                   # function to be differentiated
    return exp(-(x[0]**2. + x[1]**2.) / 2.)    # is Gaussian density
  x     = numpy.array( [ 1.,  2.] )
  a_x   = independent(x)
  a_y   = numpy.array( [ F(a_x) ] ) 
  f     = adfun(a_x, a_y)
  J     = f.jacobian(x)                        # J = F'(x)
  assert abs( J[0, 0] + F(x) * x[0] ) < 1e-10  # J[0,0] ~= - F(x) * x[0]
  assert abs( J[0, 1] + F(x) * x[1] ) < 1e-10  # J[0,1] ~= - F(x) * x[1]
Input File: example/get_started.py