add numerical recipes library

lib/nr/cpp/recipes/gauleg.cpp

@@ -0,0 +1,34 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::gauleg(const DP x1, const DP x2, Vec_O_DP &x, Vec_O_DP &w)
+{
+	const DP EPS=1.0e-14;
+	int m,j,i;
+	DP z1,z,xm,xl,pp,p3,p2,p1;
+
+	int n=x.size();
+	m=(n+1)/2;
+	xm=0.5*(x2+x1);
+	xl=0.5*(x2-x1);
+	for (i=0;i<m;i++) {
+		z=cos(3.141592654*(i+0.75)/(n+0.5));
+		do {
+			p1=1.0;
+			p2=0.0;
+			for (j=0;j<n;j++) {
+				p3=p2;
+				p2=p1;
+				p1=((2.0*j+1.0)*z*p2-j*p3)/(j+1);
+			}
+			pp=n*(z*p1-p2)/(z*z-1.0);
+			z1=z;
+			z=z1-p1/pp;
+		} while (fabs(z-z1) > EPS);
+		x[i]=xm-xl*z;
+		x[n-1-i]=xm+xl*z;
+		w[i]=2.0*xl/((1.0-z*z)*pp*pp);
+		w[n-1-i]=w[i];
+	}
+}