lines 8-89 of file: include/cppad/speed/det_grad_33.hpp

{xrst_begin det_grad_33}

Check Gradient of Determinant of 3 by 3 matrix
##############################################

Syntax
******

   # ``include <cppad/speed/det_grad_33.hpp>``

*ok* = ``det_grad_33`` ( *x* , *g* )

Purpose
*******
This routine can be used to check a method for computing the
gradient of the determinant of a matrix.

Inclusion
*********
The template function ``det_grad_33`` is defined in the ``CppAD``
namespace by including
the file ``cppad/speed/det_grad_33.hpp``
(relative to the CppAD distribution directory).

x
*
The argument *x* has prototype

   ``const`` *Vector* & *x*

.
It contains the elements of the matrix :math:`X` in row major order; i.e.,

.. math::

   X_{i,j} = x [ i * 3 + j ]

g
*
The argument *g* has prototype

   ``const`` *Vector* & *g*

.
It contains the elements of the gradient of
:math:`\det ( X )` in row major order; i.e.,

.. math::

   \D{\det (X)}{X(i,j)} = g [ i * 3 + j ]

Vector
******
If *y* is a *Vector* object,
it must support the syntax

   *y* [ *i* ]

where *i* has type ``size_t`` with value less than 9.
This must return a ``double`` value corresponding to the *i*-th
element of the vector *y* .
This is the only requirement of the type *Vector* .

ok
**
The return value *ok* has prototype

   ``bool`` *ok*

It is true, if the gradient *g*
passes the test and false otherwise.
{xrst_toc_hidden
   xrst/det_grad_33_hpp.xrst
}

Source Code
***********
The file
:ref:`det_grad_33.hpp-name`
contains the source code for this template function.

{xrst_end det_grad_33}