add numerical recipes library

lib/nr/k_and_r/recipes/ludcmp.c

@@ -0,0 +1,58 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define TINY 1.0e-20
+
+void ludcmp(a,n,indx,d)
+float **a,*d;
+int *indx,n;
+{
+	int i,imax,j,k;
+	float big,dum,sum,temp;
+	float *vv;
+
+	vv=vector(1,n);
+	*d=1.0;
+	for (i=1;i<=n;i++) {
+		big=0.0;
+		for (j=1;j<=n;j++)
+			if ((temp=fabs(a[i][j])) > big) big=temp;
+		if (big == 0.0) nrerror("Singular matrix in routine ludcmp");
+		vv[i]=1.0/big;
+	}
+	for (j=1;j<=n;j++) {
+		for (i=1;i<j;i++) {
+			sum=a[i][j];
+			for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];
+			a[i][j]=sum;
+		}
+		big=0.0;
+		for (i=j;i<=n;i++) {
+			sum=a[i][j];
+			for (k=1;k<j;k++)
+				sum -= a[i][k]*a[k][j];
+			a[i][j]=sum;
+			if ( (dum=vv[i]*fabs(sum)) >= big) {
+				big=dum;
+				imax=i;
+			}
+		}
+		if (j != imax) {
+			for (k=1;k<=n;k++) {
+				dum=a[imax][k];
+				a[imax][k]=a[j][k];
+				a[j][k]=dum;
+			}
+			*d = -(*d);
+			vv[imax]=vv[j];
+		}
+		indx[j]=imax;
+		if (a[j][j] == 0.0) a[j][j]=TINY;
+		if (j != n) {
+			dum=1.0/(a[j][j]);
+			for (i=j+1;i<=n;i++) a[i][j] *= dum;
+		}
+	}
+	free_vector(vv,1,n);
+}
+#undef TINY