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

Input File: test_more/compare_c/det_by_minor.c