A-M baby

Task/LU-decomposition/C/lu-decomposition.c

@@ -0,0 +1,129 @@
+#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;
+}