gaulag.cpp

这是数学计算上常用的计算方法

#include <cmath>
#include "nr.h"
using namespace std;

void NR::gaulag(Vec_O_DP &x, Vec_O_DP &w, const DP alf)
{
	const int MAXIT=10;
	const DP EPS=1.0e-14;
	int i,its,j;
	DP ai,p1,p2,p3,pp,z,z1;

	int n=x.size();
	for (i=0;i<n;i++) {
		if (i == 0) {
			z=(1.0+alf)*(3.0+0.92*alf)/(1.0+2.4*n+1.8*alf);
		} else if (i == 1) {
			z += (15.0+6.25*alf)/(1.0+0.9*alf+2.5*n);
		} else {
			ai=i-1;
			z += ((1.0+2.55*ai)/(1.9*ai)+1.26*ai*alf/
				(1.0+3.5*ai))*(z-x[i-2])/(1.0+0.3*alf);
		}
		for (its=0;its<MAXIT;its++) {
			p1=1.0;
			p2=0.0;
			for (j=0;j<n;j++) {
				p3=p2;
				p2=p1;
				p1=((2*j+1+alf-z)*p2-(j+alf)*p3)/(j+1);
			}
			pp=(n*p1-(n+alf)*p2)/z;
			z1=z;
			z=z1-p1/pp;
			if (fabs(z-z1) <= EPS) break;
		}
		if (its >= MAXIT) nrerror("too many iterations in gaulag");
		x[i]=z;
		w[i] = -exp(gammln(alf+n)-gammln(DP(n)))/(pp*n*p2);
	}
}