#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;
}

Output

$ gcc LUDecomposition.cpp
$ ./a.out

A

1 3 5
2 4 7
1 1 0

L

1.00000 0.00000 0.00000
0.50000 1.00000 0.00000
0.50000 -1.00000 1.00000

U

2.00000 4.00000 7.00000
0.00000 1.00000 1.50000
0.00000 0.00000 -2.00000

P

0 1 0
1 0 0
0 0 1