programming-examples/c/Numerical/C Program to Perform LU Decomposition of any Matrix.c

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define foreach(a, b, c) for (int a = b; a < c; a++)
#define for_i foreach(i, 0, n)
#define for_j foreach(j, 0, n)
#define for_k foreach(k, 0, n)
#define for_ij for_i for_j
#define for_ijk for_ij for_k
#define _dim int n
#define _swap(x, y) { typeof(x) tmp = x; x = y; y = tmp; }
#define _sum_k(a, b, c, s) { s = 0; foreach(k, a, b) s+= c; }

typedef double **mat;

#define _zero(a) mat_zero(a, n)
void mat_zero(mat x, int n)
{
    for_ij
    x[i][j] = 0;
}

#define _new(a) a = mat_new(n)
mat mat_new(_dim)
{
    mat x = malloc(sizeof(double*) * n);
    x[0] = malloc(sizeof(double) * n * n);
    for_i
    x[i] = x[0] + n * i;
    _zero(x);
    return x;
}

#define _copy(a) mat_copy(a, n)
mat mat_copy(void *s, _dim)
{
    mat x = mat_new(n);
    for_ij
    x[i][j] = ((double(*)[n]) s)[i][j];
    return x;
}

#define _del(x) mat_del(x)
void mat_del(mat x)
{
    free(x[0]);
    free(x);
}

#define _QUOT(x) #x
#define QUOTE(x) _QUOT(x)
#define _show(a) printf(QUOTE(a)" =");mat_show(a, 0, n)
void mat_show(mat x, char *fmt, _dim)
{
    if (!fmt)
        fmt = "%8.4g";
    for_i
    {
        printf(i ? "      " : " [ ");
        for_j {
            printf(fmt, x[i][j]);
            printf(j < n - 1 ? "  " : i == n - 1 ? " ]\n" : "\n");
        }
    }
}

#define _mul(a, b) mat_mul(a, b, n)
mat mat_mul(mat a, mat b, _dim)
{
    mat c = _new(c);
    for_ijk
    c[i][j] += a[i][k] * b[k][j];
    return c;
}

#define _pivot(a, b) mat_pivot(a, b, n)
void mat_pivot(mat a, mat p, _dim)
{
    for_ij
    {
        p[i][j] = (i == j);
    }
    for_i
    {
        int max_j = i;
        foreach(j, i, n)
            if (fabs(a[j][i]) > fabs(a[max_j][i]))
                max_j = j;

        if (max_j != i)
            for_k {
                _swap(p[i][k], p[max_j][k]);
            }
    }
}

#define _LU(a, l, u, p) mat_LU(a, l, u, p, n)
void mat_LU(mat A, mat L, mat U, mat P, _dim)
{
    _zero(L);
    _zero(U);
    _pivot(A, P);
    mat Aprime = _mul(P, A);
    for_i
    {
        L[i][i] = 1;
    }
    for_ij
    {
        double s;
        if (j <= i)
            {
                _sum_k(0, j, L[j][k] * U[k][i], s)
                U[j][i] = Aprime[j][i] - s;
            }
        if (j >= i)
            {
                _sum_k(0, i, L[j][k] * U[k][i], s);
                L[j][i] = (Aprime[j][i] - s) / U[i][i];
            }
    }
    _del(Aprime);
}

double A3[][3] = { { 1, 3, 5 }, { 2, 4, 7 }, { 1, 1, 0 } };
double A4[][4] = { { 11, 9, 24, 2 }, { 1, 5, 2, 6 }, { 3, 17, 18, 1 }, {
        2, 5,
        7, 1
    }
};

int main()
{
    int n = 3;
    mat A, L, P, U;
    _new(L);
    _new(P);
    _new(U);
    A = _copy(A3);
    _LU(A, L, U, P);
    _show(A);
    _show(L);
    _show(U);
    _show(P);
    _del(A);
    _del(L);
    _del(U);
    _del(P);
    printf("\n");
    n = 4;
    _new(L);
    _new(P);
    _new(U);
    A = _copy(A4);
    _LU(A, L, U, P);
    _show(A);
    _show(L);
    _show(U);
    _show(P);
    _del(A);
    _del(L);
    _del(U);
    _del(P);
    return 0;
}