add numerical recipes library

lib/nr/ansi/recipes/pade.c

@@ -0,0 +1,56 @@
+
+#include <math.h>
+#define NRANSI
+#include "nrutil.h"
+#define BIG 1.0e30
+
+void pade(double cof[], int n, float *resid)
+{
+	void lubksb(float **a, int n, int *indx, float b[]);
+	void ludcmp(float **a, int n, int *indx, float *d);
+	void mprove(float **a, float **alud, int n, int indx[], float b[],
+		float x[]);
+	int j,k,*indx;
+	float d,rr,rrold,sum,**q,**qlu,*x,*y,*z;
+
+	indx=ivector(1,n);
+	q=matrix(1,n,1,n);
+	qlu=matrix(1,n,1,n);
+	x=vector(1,n);
+	y=vector(1,n);
+	z=vector(1,n);
+	for (j=1;j<=n;j++) {
+		y[j]=x[j]=cof[n+j];
+		for (k=1;k<=n;k++) {
+			q[j][k]=cof[j-k+n];
+			qlu[j][k]=q[j][k];
+		}
+	}
+	ludcmp(qlu,n,indx,&d);
+	lubksb(qlu,n,indx,x);
+	rr=BIG;
+	do {
+		rrold=rr;
+		for (j=1;j<=n;j++) z[j]=x[j];
+		mprove(q,qlu,n,indx,y,x);
+		for (rr=0.0,j=1;j<=n;j++)
+			rr += SQR(z[j]-x[j]);
+	} while (rr < rrold);
+	*resid=sqrt(rrold);
+	for (k=1;k<=n;k++) {
+		for (sum=cof[k],j=1;j<=k;j++) sum -= z[j]*cof[k-j];
+		y[k]=sum;
+	}
+	for (j=1;j<=n;j++) {
+		cof[j]=y[j];
+		cof[j+n] = -z[j];
+	}
+	free_vector(z,1,n);
+	free_vector(y,1,n);
+	free_vector(x,1,n);
+	free_matrix(qlu,1,n,1,n);
+	free_matrix(q,1,n,1,n);
+	free_ivector(indx,1,n);
+}
+#undef BIG
+#undef NRANSI