Data commit

Task/QR-decomposition/C/qr-decomposition.c

@@ -0,0 +1,192 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+typedef struct {
+	int m, n;
+	double ** v;
+} mat_t, *mat;
+
+mat matrix_new(int m, int n)
+{
+	mat x = malloc(sizeof(mat_t));
+	x->v = malloc(sizeof(double*) * m);
+	x->v[0] = calloc(sizeof(double), m * n);
+	for (int i = 0; i < m; i++)
+		x->v[i] = x->v[0] + n * i;
+	x->m = m;
+	x->n = n;
+	return x;
+}
+
+void matrix_delete(mat m)
+{
+	free(m->v[0]);
+	free(m->v);
+	free(m);
+}
+
+void matrix_transpose(mat m)
+{
+	for (int i = 0; i < m->m; i++) {
+		for (int j = 0; j < i; j++) {
+			double t = m->v[i][j];
+			m->v[i][j] = m->v[j][i];
+			m->v[j][i] = t;
+		}
+	}
+}
+
+mat matrix_copy(int n, double a[][n], int m)
+{
+	mat x = matrix_new(m, n);
+	for (int i = 0; i < m; i++)
+		for (int j = 0; j < n; j++)
+			x->v[i][j] = a[i][j];
+	return x;
+}
+
+mat matrix_mul(mat x, mat y)
+{
+	if (x->n != y->m) return 0;
+	mat r = matrix_new(x->m, y->n);
+	for (int i = 0; i < x->m; i++)
+		for (int j = 0; j < y->n; j++)
+			for (int k = 0; k < x->n; k++)
+				r->v[i][j] += x->v[i][k] * y->v[k][j];
+	return r;
+}
+
+mat matrix_minor(mat x, int d)
+{
+	mat m = matrix_new(x->m, x->n);
+	for (int i = 0; i < d; i++)
+		m->v[i][i] = 1;
+	for (int i = d; i < x->m; i++)
+		for (int j = d; j < x->n; j++)
+			m->v[i][j] = x->v[i][j];
+	return m;
+}
+
+/* c = a + b * s */
+double *vmadd(double a[], double b[], double s, double c[], int n)
+{
+	for (int i = 0; i < n; i++)
+		c[i] = a[i] + s * b[i];
+	return c;
+}
+
+/* m = I - v v^T */
+mat vmul(double v[], int n)
+{
+	mat x = matrix_new(n, n);
+	for (int i = 0; i < n; i++)
+		for (int j = 0; j < n; j++)
+			x->v[i][j] = -2 *  v[i] * v[j];
+	for (int i = 0; i < n; i++)
+		x->v[i][i] += 1;
+
+	return x;
+}
+
+/* ||x|| */
+double vnorm(double x[], int n)
+{
+	double sum = 0;
+	for (int i = 0; i < n; i++) sum += x[i] * x[i];
+	return sqrt(sum);
+}
+
+/* y = x / d */
+double* vdiv(double x[], double d, double y[], int n)
+{
+	for (int i = 0; i < n; i++) y[i] = x[i] / d;
+	return y;
+}
+
+/* take c-th column of m, put in v */
+double* mcol(mat m, double *v, int c)
+{
+	for (int i = 0; i < m->m; i++)
+		v[i] = m->v[i][c];
+	return v;
+}
+
+void matrix_show(mat m)
+{
+	for(int i = 0; i < m->m; i++) {
+		for (int j = 0; j < m->n; j++) {
+			printf(" %8.3f", m->v[i][j]);
+		}
+		printf("\n");
+	}
+	printf("\n");
+}
+
+void householder(mat m, mat *R, mat *Q)
+{
+	mat q[m->m];
+	mat z = m, z1;
+	for (int k = 0; k < m->n && k < m->m - 1; k++) {
+		double e[m->m], x[m->m], a;
+		z1 = matrix_minor(z, k);
+		if (z != m) matrix_delete(z);
+		z = z1;
+
+		mcol(z, x, k);
+		a = vnorm(x, m->m);
+		if (m->v[k][k] > 0) a = -a;
+
+		for (int i = 0; i < m->m; i++)
+			e[i] = (i == k) ? 1 : 0;
+
+		vmadd(x, e, a, e, m->m);
+		vdiv(e, vnorm(e, m->m), e, m->m);
+		q[k] = vmul(e, m->m);
+		z1 = matrix_mul(q[k], z);
+		if (z != m) matrix_delete(z);
+		z = z1;
+	}
+	matrix_delete(z);
+	*Q = q[0];
+	*R = matrix_mul(q[0], m);
+	for (int i = 1; i < m->n && i < m->m - 1; i++) {
+		z1 = matrix_mul(q[i], *Q);
+		if (i > 1) matrix_delete(*Q);
+		*Q = z1;
+		matrix_delete(q[i]);
+	}
+	matrix_delete(q[0]);
+	z = matrix_mul(*Q, m);
+	matrix_delete(*R);
+	*R = z;
+	matrix_transpose(*Q);
+}
+
+double in[][3] = {
+	{ 12, -51,   4},
+	{  6, 167, -68},
+	{ -4,  24, -41},
+	{ -1, 1, 0},
+	{ 2, 0, 3},
+};
+
+int main()
+{
+	mat R, Q;
+	mat x = matrix_copy(3, in, 5);
+	householder(x, &R, &Q);
+
+	puts("Q"); matrix_show(Q);
+	puts("R"); matrix_show(R);
+
+	// to show their product is the input matrix
+	mat m = matrix_mul(Q, R);
+	puts("Q * R"); matrix_show(m);
+
+	matrix_delete(x);
+	matrix_delete(R);
+	matrix_delete(Q);
+	matrix_delete(m);
+	return 0;
+}