gauher.c

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#include <math.h>
#define EPS 3.0e-14
#define PIM4 0.7511255444649425
#define MAXIT 10

void gauher(float x[], float w[], int n)
{
	void nrerror(char error_text[]);
	int i,its,j,m;
	double p1,p2,p3,pp,z,z1;

	m=(n+1)/2;
	for (i=1;i<=m;i++) {
		if (i == 1) {
			z=sqrt((double)(2*n+1))-1.85575*pow((double)(2*n+1),-0.16667);
		} else if (i == 2) {
			z -= 1.14*pow((double)n,0.426)/z;
		} else if (i == 3) {
			z=1.86*z-0.86*x[1];
		} else if (i == 4) {
			z=1.91*z-0.91*x[2];
		} else {
			z=2.0*z-x[i-2];
		}
		for (its=1;its<=MAXIT;its++) {
			p1=PIM4;
			p2=0.0;
			for (j=1;j<=n;j++) {
				p3=p2;
				p2=p1;
				p1=z*sqrt(2.0/j)*p2-sqrt(((double)(j-1))/j)*p3;
			}
			pp=sqrt((double)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];
	}
}
#undef EPS
#undef PIM4
#undef MAXIT