lines 6-57 of file: example/python/numeric/simple_inv_xam.py

# {xrst_begin numeric_simple_inv_xam.py}
# {xrst_spell
#     cc
# }
# {xrst_comment_ch #}
#
# Example Computing Derivatives of Matrix Inversion
# #################################################
#
# Problem
# *******
# We define
#
# .. math::
#
#    A(x) = \left( \begin{array}{cc}
#    x_0 & x_1 \\
#    x_2 & x_3
#    \end{array} \right)
#
# It follows that
#
# .. math::
#
#    A^{-1}(x) =
#    \frac{1}{x_3 * x_0 - x_1 * x_2}
#    \left( \begin{array}{cc}
#    x_3 & - x_1 \\
#    - x_2 & x_0
#    \end{array} \right)
#
# We define
#
# .. math::
#
#    f(x) = (x_3 * x_0 - x_1 * x_2) [
#    A_{0,0}^{-1} (x),
#    A_{0,1}^{-1} (x),
#    A_{1,0}^{-1} (x),
#    A_{1,1}^{-1} (x)
#    ]
#    = [ x_3, -x_1, -x_2, x_0]
#
# The following example below check the derivative of :math:`f(x)`
#
# Source Code
# ***********
# {xrst_literal
#  # BEGIN_PYTHON
#  # END_PYTHON
# }
# {xrst_end numeric_simple_inv_xam.py}