\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

det_by_minor_c

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Compute Determinant using Expansion by Minors

Syntax

d = det_by_minor ( a , n )

Purpose

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

\[M_{i,j} = A_{i, j}\]

a

The argument a has prototype

const double * a

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

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

m

The argument m has prototype

size_t m

and is the number of rows (and columns) in the square matrix \(A\).

Source Code

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;
}