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lines 7-70 of file: example/chkpoint_two/get_started.cpp
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{xrst_begin chkpoint_two_get_started.cpp}

Get Started Checkpointing: Example and Test
###########################################

Purpose
*******
Break a large computation into pieces and only store values at the
interface of the pieces.
In actual applications, there may many uses of each function
and many more functions.

f
*
The function :math:`f : \B{R}^2 \rightarrow \B{R}^2`
is defined by

.. math::

   f(y) = \left( \begin{array}{c}
      y_0 + y_0 + y_0
      \\
      y_1 + y_1 + y_1
   \end{array} \right)

g
*
The function :math:`g : \B{R}^2 \rightarrow \B{R}^2`
defined by

.. math::

   g(x) = \left( \begin{array}{c}
      x_0 \cdot x_0 \cdot x_0
      \\
      x_1 \cdot x_1 \cdot x_1
   \end{array} \right)

f[g(x)]
*******
The function :math:`f[g(x)]` is given by

.. math::

   f[g(x)]
   =
   f \left[ \begin{array}{c}
      x_0^3 \\
      x_1^3
   \end{array} \right]
   =
   \left[ \begin{array}{c}
      3 x_0^3 \\
      3 x_1^3
   \end{array} \right]

Source Code
***********
{xrst_literal
   // BEGIN C++
   // END C++
}

{xrst_end chkpoint_two_get_started.cpp}