--------------------------------------------------
lines 8-83 of file: include/cppad/speed/det_33.hpp
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{xrst_begin det_33}

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

Syntax
******
| # ``include <cppad/speed/det_33.hpp>``
| *ok* = ``det_33`` ( *x* , *d* )

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

Inclusion
*********
The template function ``det_33`` is defined in the ``CppAD``
namespace by including
the file ``cppad/speed/det_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 ]

d
*
The argument *d* has prototype

   ``const`` *Vector* & *d*

.
It is tested to see if *d* [0] it is equal to :math:`\det ( X )`.

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* .
(Note that only the first element of the vector *d* is used.)

ok
**
The return value *ok* has prototype

   ``bool`` *ok*

It is true, if the determinant *d* [0]
passes the test and false otherwise.
{xrst_toc_hidden
   xrst/det_33_hpp.xrst
}

Source Code
***********
The file
:ref:`det_33.hpp-name`
contains the source code for this template function.

{xrst_end det_33}