gauleg.cpp

Numerical recipes in C++

#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];
	}
}