lines 6-71 of file: example/atomic_four/forward.cpp

{xrst_begin atomic_four_forward.cpp}

Atomic Functions and Forward Mode: Example and Test
###################################################

Purpose
*******
This example demonstrates forward mode derivative calculation
using an :ref:`atomic_four-name` function.

Function
********
For this example, the atomic function
:math:`g : \B{R}^3 \rightarrow \B{R}^2` is defined by

.. math::

   g(x) = \left( \begin{array}{c}
      x_2 * x_2 \\
      x_0 * x_1
   \end{array} \right)

Jacobian
********
The corresponding Jacobian is

.. math::

   g^{(1)} (x) = \left( \begin{array}{ccc}
     0  &   0 & 2 x_2 \\
   x_1  & x_0 & 0
   \end{array} \right)

Hessian
*******
The Hessians of the component functions are

.. math::

   g_0^{(2)} ( x ) = \left( \begin{array}{ccc}
      0 & 0 & 0  \\
      0 & 0 & 0  \\
      0 & 0 & 2
   \end{array} \right)
   \W{,}
   g_1^{(2)} ( x ) = \left( \begin{array}{ccc}
      0 & 1 & 0 \\
      1 & 0 & 0 \\
      0 & 0 & 0
   \end{array} \right)

Define Atomic Function
**********************
{xrst_literal
   // BEGIN_DEFINE_ATOMIC_FUNCTION
   // END_DEFINE_ATOMIC_FUNCTION
}

Use Atomic Function
*******************
{xrst_literal
   // BEGIN_USE_ATOMIC_FUNCTION
   // END_USE_ATOMIC_FUNCTION
}

{xrst_end atomic_four_forward.cpp}