add numerical recipes library

lib/nr/cpp/recipes/pade.cpp

@@ -0,0 +1,42 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::pade(Vec_IO_DP &cof, DP &resid)
+{
+	const DP BIG=1.0e30;
+	int j,k;
+	DP d,rr,rrold,sum;
+
+	int n=(cof.size()-1)/2;
+	Mat_DP q(n,n),qlu(n,n);
+	Vec_INT indx(n);
+	Vec_DP x(n),y(n),z(n);
+	for (j=0;j<n;j++) {
+		y[j]=x[j]=cof[n+j+1];
+		for (k=0;k<n;k++) {
+			q[j][k]=cof[j-k+n];
+			qlu[j][k]=q[j][k];
+		}
+	}
+	ludcmp(qlu,indx,d);
+	lubksb(qlu,indx,x);
+	rr=BIG;
+	do {
+		rrold=rr;
+		for (j=0;j<n;j++) z[j]=x[j];
+		mprove(q,qlu,indx,y,x);
+		for (rr=0.0,j=0;j<n;j++)
+			rr += SQR(z[j]-x[j]);
+	} while (rr < rrold);
+	resid=sqrt(rrold);
+	for (k=0;k<n;k++) {
+		for (sum=cof[k+1],j=0;j<=k;j++)
+			sum -= z[j]*cof[k-j];
+		y[k]=sum;
+	}
+	for (j=0;j<n;j++) {
+		cof[j+1]=y[j];
+		cof[j+1+n] = -z[j];
+	}
+}