Task: LU decomposition

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;
}








VB: Option Base 1
Private Function pivotize(m As Variant) As Variant
    Dim n As Integer: n = UBound(m)
    Dim im() As Double
    ReDim im(n, n)
    For i = 1 To n
        For j = 1 To n
            im(i, j) = 0
        Next j
        im(i, i) = 1
    Next i
    For i = 1 To n
        mx = Abs(m(i, i))
        row_ = i
        For j = i To n
            If Abs(m(j, i)) > mx Then
                mx = Abs(m(j, i))
                row_ = j
            End If
        Next j
        If i <> Row Then
            For j = 1 To n
                tmp = im(i, j)
                im(i, j) = im(row_, j)
                im(row_, j) = tmp
            Next j
        End If
    Next i
    pivotize = im
End Function
 
Private Function lu(a As Variant) As Variant
    Dim n As Integer: n = UBound(a)
    Dim l() As Double
    ReDim l(n, n)
    For i = 1 To n
        For j = 1 To n
            l(i, j) = 0
        Next j
    Next i
    u = l
    p = pivotize(a)
    a2 = WorksheetFunction.MMult(p, a)
    For j = 1 To n
        l(j, j) = 1#
        For i = 1 To j
            sum1 = 0#
            For k = 1 To i
                sum1 = sum1 + u(k, j) * l(i, k)
            Next k
            u(i, j) = a2(i, j) - sum1
        Next i
        For i = j + 1 To n
            sum2 = 0#
            For k = 1 To j
                sum2 = sum2 + u(k, j) * l(i, k)
            Next k
            l(i, j) = (a2(i, j) - sum2) / u(j, j)
        Next i
    Next j
    Dim res(4) As Variant
    res(1) = a
    res(2) = l
    res(3) = u
    res(4) = p
    lu = res
End Function
 
Public Sub main()
    
    a = [{1, 3, 5; 2, 4, 7; 1, 1, 0}]
    Debug.Print "== a,l,u,p: =="
    result = lu(a)
    For i = 1 To 4
        For j = 1 To UBound(result(1))
            For k = 1 To UBound(result(1), 2)
                Debug.Print result(i)(j, k),
            Next k
            Debug.Print
        Next j
        Debug.Print
    Next i
    a = [{11, 9,24, 2; 1, 5, 2, 6; 3,17,18, 1; 2, 5, 7, 1}]
    Debug.Print "== a,l,u,p: =="
    result = lu(a)
    For i = 1 To 4
        For j = 1 To UBound(result(1))
            For k = 1 To UBound(result(1), 2)
                Debug.Print Format(result(i)(j, k), "0.#####"),
            Next k
            Debug.Print
        Next j
        Debug.Print
    Next i
End Sub