lines 232-303 of file: test_more/compare_c/det_by_minor.c

{xrst_begin det_by_minor_c app}

Compute Determinant using Expansion by Minors
#############################################

Syntax
******
*d* = ``det_by_minor`` ( *a* , *n* )

Purpose
*******
returns the determinant of the matrix :math:`A`
using expansion by minors.
The elements of the :math:`n \times n` minor :math:`M`
of the matrix :math:`A` are defined,
for :math:`i = 0 , \ldots , n-1` and :math:`j = 0 , \ldots , n-1`, by

.. math::

   M_{i,j} = A_{i, j}

a
*
The argument *a* has prototype

   ``const double`` * *a*

and is a vector with size :math:`m * m`.
The elements of the :math:`m \times m` matrix :math:`A` are defined,
for :math:`i = 0 , \ldots , m-1` and :math:`j = 0 , \ldots , m-1`, by

.. math::

   A_{i,j} = a[ i * m + j]

m
*
The argument *m* has prototype

   ``size_t`` *m*

and is the number of rows (and columns) in the square matrix :math:`A`.

Source Code
***********
{xrst_spell_off}
{xrst_code cpp} */
double det_by_minor(double* a, size_t m)
{  size_t *r, *c, i;
   double value;

   r = (size_t*) malloc( (m+1) * sizeof(size_t) );
   c = (size_t*) malloc( (m+1) * sizeof(size_t) );

   assert(m <= 100);
   for(i = 0; i < m; i++)
   {  r[i] = i+1;
      c[i] = i+1;
   }
   r[m] = 0;
   c[m] = 0;

   value = det_of_minor(a, m, m, r, c);

   free(r);
   free(c);
   return value;
}
/* {xrst_code}
{xrst_spell_on}

{xrst_end det_by_minor_c}