add numerical recipes library

lib/nr/k_and_r/recipes/qrdcmp.c

@@ -0,0 +1,35 @@
+
+#include <math.h>
+#include "nrutil.h"
+
+void qrdcmp(a,n,c,d,sing)
+float **a,*c,*d;
+int *sing,n;
+{
+	int i,j,k;
+	float scale,sigma,sum,tau;
+
+	*sing=0;
+	for (k=1;k<n;k++) {
+		scale=0.0;
+		for (i=k;i<=n;i++) scale=FMAX(scale,fabs(a[i][k]));
+		if (scale == 0.0) {
+			*sing=1;
+			c[k]=d[k]=0.0;
+		} else {
+			for (i=k;i<=n;i++) a[i][k] /= scale;
+			for (sum=0.0,i=k;i<=n;i++) sum += SQR(a[i][k]);
+			sigma=SIGN(sqrt(sum),a[k][k]);
+			a[k][k] += sigma;
+			c[k]=sigma*a[k][k];
+			d[k] = -scale*sigma;
+			for (j=k+1;j<=n;j++) {
+				for (sum=0.0,i=k;i<=n;i++) sum += a[i][k]*a[i][j];
+				tau=sum/c[k];
+				for (i=k;i<=n;i++) a[i][j] -= tau*a[i][k];
+			}
+		}
+	}
+	d[n]=a[n][n];
+	if (d[n] == 0.0) *sing=1;
+}