lines 8-60 of file: cpp/xam/gradient/check_grad_ode.hpp

{xrst_begin check_grad_ode.hpp}

C++ Check Gradient of an_ode
############################

Syntax
******
| |tab| ``# include "check_grad_ode.hpp"``
| |tab| *ok* = check_grad_ode( *grad_ode* )


Prototype
*********
{xrst_literal
   // BEGIN PROTOTYPE
   // END PROTOTYPE
}

grad_ode
********
Is a :ref:`cpp_fun_obj-name`
object that computes the gradient for the ref:`cpp_an_ode-name` algorithm.

ok
**
is true (false) if the gradient passes (fails) the test.

Gradient
********
We use :math:`r` to denote
the range space component of the an_ode algorithm that we are
computing the gradient for.

.. math::

   y_r (t) = \frac{ t^{r+1} }{ (r+1)! }  \prod{j=0}^r x_j

.. math::

   \frac{ \partial y_r (t) }{  \partial x_j } = \begin{cases}
      y_r (t) / x_j   & \text{if} \; j \leq r  \\
      0               & \text{otherwise}
   \end{cases}


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

{xrst_end  check_grad_ode.hpp}