add numerical recipes library

lib/nr/ansi/examples/xqrupdt.c

@@ -0,0 +1,159 @@
+
+/* Driver for routine qrdupd */
+
+#include <stdio.h>
+#include <stdlib.h>
+#define NRANSI
+#include "nr.h"
+#include "nrutil.h"
+
+#define NP 20
+#define MAXSTR 80
+
+int main(void)
+{
+	int i,j,k,l,m,n,sing;
+	float con,**a,**au,*c,*d,**q,**qt,**r,**s,*u,*v,**x;
+	char dummy[MAXSTR];
+	FILE *fp;
+
+	a=matrix(1,NP,1,NP);
+	au=matrix(1,NP,1,NP);
+	c=vector(1,NP);
+	d=vector(1,NP);
+	q=matrix(1,NP,1,NP);
+	qt=matrix(1,NP,1,NP);
+	r=matrix(1,NP,1,NP);
+	s=matrix(1,NP,1,NP);
+	u=vector(1,NP);
+	v=vector(1,NP);
+	x=matrix(1,NP,1,NP);
+	if ((fp = fopen("matrx1.dat","r")) == NULL)
+		nrerror("Data file matrx1.dat not found\n");
+	while (!feof(fp)) {
+		fgets(dummy,MAXSTR,fp);
+		fgets(dummy,MAXSTR,fp);
+		fscanf(fp,"%d %d ",&n,&m);
+		fgets(dummy,MAXSTR,fp);
+		for (k=1;k<=n;k++)
+			for (l=1;l<=n;l++) fscanf(fp,"%f ",&a[k][l]);
+		fgets(dummy,MAXSTR,fp);
+		for (l=1;l<=m;l++)
+			for (k=1;k<=n;k++) fscanf(fp,"%f ",&s[k][l]);
+		/* Print out a-matrix for comparison with product of
+		   Q and R decomposition matrices */
+		printf("Original matrix:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",a[k][l]);
+			printf("\n");
+		}
+		/* updated matrix we'll use later */
+		for (k=1;k<=n;k++)
+			for (l=1;l<=n;l++)
+				au[k][l]=a[k][l]+s[k][1]*s[l][2];
+		/* Perform the decomposition */
+		qrdcmp(a,n,c,d,&sing);
+		if (sing) fprintf(stderr,"Singularity in QR decomposition.\n");
+		/* find the Q and R matrices */
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) {
+				if (l > k) {
+					r[k][l]=a[k][l];
+					q[k][l]=0.0;
+				} else if (l < k) {
+					r[k][l]=q[k][l]=0.0;
+				} else {
+					r[k][l]=d[k];
+					q[k][l]=1.0;
+				}
+			}
+		}
+		for (i=n-1;i>=1;i--) {
+			for (con=0.0,k=i;k<=n;k++) con += a[k][i]*a[k][i];
+			con /= 2.0;
+			for (k=i;k<=n;k++) {
+				for (l=i;l<=n;l++) {
+					qt[k][l]=0.0;
+					for (j=i;j<=n;j++) {
+						qt[k][l] += q[j][l]*a[k][i]*a[j][i]/con;
+					}
+				}
+			}
+			for (k=i;k<=n;k++)
+				for (l=i;l<=n;l++) q[k][l] -= qt[k][l];
+		}
+		/* compute product of Q and R matrices for comparison
+		   with original matrix. */
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) {
+				x[k][l]=0.0;
+				for (j=1;j<=n;j++)
+					x[k][l] += q[k][j]*r[j][l];
+			}
+		}
+		printf("\nProduct of Q and R matrices:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",x[k][l]);
+			printf("\n");
+		}
+		printf("\nQ matrix of the decomposition:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",q[k][l]);
+			printf("\n");
+		}
+		printf("\nR matrix of the decomposition:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",r[k][l]);
+			printf("\n");
+		}
+		/* Q transpose */
+		for (k=1;k<=n;k++)
+			for (l=1;l<=n;l++)
+				qt[k][l]=q[l][k];
+		for (k=1;k<=n;k++) {
+			v[k]=s[k][2];
+			for (u[k]=0.0,l=1;l<=n;l++) u[k] += qt[k][l]*s[l][1];
+		}
+		qrupdt(r,qt,n,u,v);
+		for (k=1;k<=n;k++)
+			for (l=1;l<=n;l++)
+				for (x[k][l]=0.0,j=1;j<=n;j++) x[k][l] += qt[j][k]*r[j][l];
+		printf("Updated matrix:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",au[k][l]);
+			printf("\n");
+		}
+		printf("\nProduct of new Q and R matrices:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",x[k][l]);
+			printf("\n");
+		}
+		printf("\nNew Q matrix:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",qt[l][k]);
+			printf("\n");
+		}
+		printf("\nNew R matrix:\n");
+		for (k=1;k<=n;k++) {
+			for (l=1;l<=n;l++) printf("%12.6f",r[k][l]);
+			printf("\n");
+		}
+		printf("\n***********************************\n");
+		printf("press return for next problem:\n");
+		(void) getchar();
+	}
+	fclose(fp);
+	free_matrix(x,1,NP,1,NP);
+	free_vector(v,1,NP);
+	free_vector(u,1,NP);
+	free_matrix(s,1,NP,1,NP);
+	free_matrix(r,1,NP,1,NP);
+	free_matrix(qt,1,NP,1,NP);
+	free_matrix(q,1,NP,1,NP);
+	free_vector(d,1,NP);
+	free_vector(c,1,NP);
+	free_matrix(au,1,NP,1,NP);
+	free_matrix(a,1,NP,1,NP);
+	return 0;
+}
+#undef NRANSI