add numerical recipes library

lib/nr/cpp/recipes/gauher.cpp

@@ -0,0 +1,45 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::gauher(Vec_O_DP &x, Vec_O_DP &w)
+{
+	const DP EPS=1.0e-14,PIM4=0.7511255444649425;
+	const int MAXIT=10;
+	int i,its,j,m;
+	DP p1,p2,p3,pp,z,z1;
+
+	int n=x.size();
+	m=(n+1)/2;
+	for (i=0;i<m;i++) {
+		if (i == 0) {
+			z=sqrt(DP(2*n+1))-1.85575*pow(DP(2*n+1),-0.16667);
+		} else if (i == 1) {
+			z -= 1.14*pow(DP(n),0.426)/z;
+		} else if (i == 2) {
+			z=1.86*z-0.86*x[0];
+		} else if (i == 3) {
+			z=1.91*z-0.91*x[1];
+		} else {
+			z=2.0*z-x[i-2];
+		}
+		for (its=0;its<MAXIT;its++) {
+			p1=PIM4;
+			p2=0.0;
+			for (j=0;j<n;j++) {
+				p3=p2;
+				p2=p1;
+				p1=z*sqrt(2.0/(j+1))*p2-sqrt(DP(j)/(j+1))*p3;
+			}
+			pp=sqrt(DP(2*n))*p2;
+			z1=z;
+			z=z1-p1/pp;
+			if (fabs(z-z1) <= EPS) break;
+		}
+		if (its >= MAXIT) nrerror("too many iterations in gauher");
+		x[i]=z;
+		x[n-1-i] = -z;
+		w[i]=2.0/(pp*pp);
+		w[n-1-i]=w[i];
+	}
+}