lines 6-79 of file: python/cmpad/det_by_minor.py

{xrst_begin_parent py_det_by_minor}

Python Determinant Using Expansion by Minors
############################################

Syntax
******
| |tab| *det* = ``cmpad.det_by_minor()``
| |tab| *det* . ``setup`` ( *option* )
| |tab| *y* = *det* ( *x* )

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

Algorithm
*********
This is a Python implementation of the
det_by_minor :ref:`det_by_minor@Algorithm` .

Scalar
******
We use *Scalar* for the type of the elements of *x* and *y*.

det
***
The :ref:`py_fun_obj-name` *det* computes the determinant of a square matrix.

ell
***
see :ref:`det_by_minor@ell` .

n_arg
*****
see :ref:`det_by_minor@option@n_arg` .

n_other
=======
see :ref:`det_by_minor@option@n_other` .

x
*
The argument *x* has size *n_arg* = :math:`\ell * \ell` .
The elements of the matrix :math:`A(x)` is defined as follows:
for :math:`i = 0 , \ldots , \ell-1` and :math:`j = 0 , \ldots , \ell-1`, by

.. math::

   A(x)_{i,j} = x[ i * \ell + j]

y
*
The return value *y* has length one and its element
is equal to the determinant of :math:`A(x)`.

{xrst_toc_hidden after
   python/xam/det_by_minor.py
   python/cmpad/det_of_minor.py
}

Example
*******
The file
:ref:`xam_det_by_minor.py-name`
contains an example and test of ``det_by_minor`` .

Source Code
***********
:ref:`det_by_minor.py-name` displays the source code for this algorithm.

{xrst_end py_det_by_minor}