Gauss-Jordan elimination

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
typedef struct {
    int r, c;
    double *m;
} matrix;
//static matrix *matrix_new(int r, int c) {
//    matrix *m = (matrix *)calloc(sizeof(*m), 1);
//    m->r = r;
//    m->c = c;
//    m->m = (double *)calloc(sizeof(m->m), r * c);
//    return m;
//}
//static void matrix_delete(matrix *m) {
//    free(m->m);
//    free(m);
//}
static double matrix_at(matrix *m, int x, int y) {
    return m->m[m->c * x + y];
}
static void matrix_as(matrix *m, int x, int y, double v) {
    m->m[m->c * x + y] = v;
}
static void pivot(matrix *m, int k) {
    for (int i = k; i < m->r; ++i) {
        double row_i_max = matrix_at(m, i, k);
        for (int j = k + 1; j < m->c; ++j) {
            double e = matrix_at(m, i, j);
            if (fabs(row_i_max) < fabs(e)) {
                row_i_max = e;
            }
        }
        for (int j = k; j < m->c; ++j) {
            double e = matrix_at(m, i, j);
            matrix_as(m, i, j, e / row_i_max);
        }
    }
    double col_k_max = matrix_at(m, k, k);
    int x = k;
    for (int i = k; i < m->r; ++i) {
        double e = matrix_at(m, i, k);
        if (col_k_max < e) {
            col_k_max = e;
            x = i;
        }
    }
    if (x == k) {
        return;
    }
    for (int i = k; i < m->c; ++i) {
        double e = matrix_at(m, k, i);
        double f = matrix_at(m, x, i);
        matrix_as(m, k, i, f);
        matrix_as(m, x, i, e);
    }
}
static void gauss_jordan_elimination(matrix *m) {
    for (int k = 0; k < m->r; ++k) {
        pivot(m, k);
        double p = matrix_at(m, k, k);
        for (int j = 0; j < m->c; ++j) {
            double e = matrix_at(m, k, j);
            matrix_as(m, k, j, e / p);
        }
        for (int i = 0; i < m->r; ++i) {
            if (i == k) {
                continue;
            }
            double e = matrix_at(m, i, k);
            for (int j = 0; j < m->c; ++j) {
                double f = matrix_at(m, i, j);
                double g = matrix_at(m, k, j);
                matrix_as(m, i, j, f - e * g);
            }
        }
    }
}
static void matrix_print(matrix *m) {
    for (int i = 0; i < m->r; ++i) {
        for (int j = 0; j < m->c; ++j) {
            printf("%s%lf", ((j == 0) ? "" : " "), matrix_at(m, i, j));
        }
        puts("");
    }
}
int main() {
    double v[] = {
        2., 1., 3., 1., 0., 0.,
        1., 3., 2., 0., 1., 0.,
        3., 2., 1., 0., 0., 1.
    };
    matrix m = { 3, 6, v };
    matrix_print(&m);
    gauss_jordan_elimination(&m);
    matrix_print(&m);
}