determinant_of_square_nxn_matrix.c

/*

    determinant_of_square_nxn_matrix.c

    n is rang of square matrix M[n][n].

    Calculate determinant of matrix M[n][n] by recursive function determinant().


    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

*/

#include <stdio.h>
#include <stdlib.h>     // for exit()
#include <math.h>       // for pow()

#define MAX_SIZE 10


// Displays a square double matrix M[n][n] that has n rows and n columns
void display_square_double_matrix( char *text, double M[][MAX_SIZE], int n )
{
    int i, j;

    printf("\n%s\n\n",text);

    for(i=0;i<n;i++) {                  // print matrix M[n][n]
        for(j=0;j<n;j++)
            printf("\t%.2lf", M[i][j]);

        printf("\n\n");                 // new row of matrix
    }
}


// Recursive definition of determinate using expansion by minors.
// http://paulbourke.net/miscellaneous/determinant/determinant.c
double determinant( double M[][MAX_SIZE], int n )
{
    int i, j, j1, j2;
    double det = 0;
    double Sub[MAX_SIZE][MAX_SIZE];

    if ( n < 1 )                // Error
    {
        printf("\n Error: rang of matrix M[][] is less than 1 !!! \n");
        exit(1);
    }
    else if ( n == 1 )      // Shouldn't get used
    {
        det = M[0][0];
    }
    else if ( n == 2 )
    {
        det = M[0][0] * M[1][1] - M[1][0] * M[0][1];
    }
    else
    {
        det = 0;

        for ( j1=0; j1<n; j1++ )
        {
            for ( i=1; i<n; i++ )
            {
                j2 = 0;

                for ( j=0; j<n; j++ )
                {
                    if ( j == j1 )
                        continue;

                    Sub[i-1][j2] = M[i][j];
                    j2++;
                }
            }

            det += pow(-1.0,1.0+j1+1.0) * M[0][j1] * determinant( Sub, n-1 );
        }
    }
    return( det );
} // determinant()


int main()
{
    int i, j, n=3;              // n is rang of square matrix M[n][n]
    double det;
    double M[MAX_SIZE][MAX_SIZE];
/*
    double M[MAX_SIZE][MAX_SIZE] = {
                                    { 1.0, 2.0, 3.0 },
                                    { 4.0, 5.0, 6.0 },
                                    { 7.0, 8.0, 1.0 },
                                                        };
*/

    printf("\n Enter number of rows and columns of square matrix M[n][n], rang n = ");
    scanf("%d", &n );

    for( i=0; i<n; i++ )                    // input matrix M[n][n]
    {
        for( j=0; j<n; j++ )
        {
            printf("\n Enter M[%d][%d] = ", i, j );
            scanf("%lf", &M[i][j] );
        }

        printf("\n");                       // new row of matrix
    }

    display_square_double_matrix("\n Square matrix M[n][n] is: ", M, n );

    det = determinant( M, n );

    printf("\n determinant = %.2lf \n", det );


    return 0;
}