spline.cpp

C++数值算法原书代码

#include "nr.h"

void NR::spline(Vec_I_DP &x, Vec_I_DP &y, const DP yp1, const DP ypn,
	Vec_O_DP &y2)
{
	int i,k;
	DP p,qn,sig,un;

	int n=y2.size();
	Vec_DP u(n-1);
	if (yp1 > 0.99e30)
		y2[0]=u[0]=0.0;
	else {
		y2[0] = -0.5;
		u[0]=(3.0/(x[1]-x[0]))*((y[1]-y[0])/(x[1]-x[0])-yp1);
	}
	for (i=1;i<n-1;i++) {
		sig=(x[i]-x[i-1])/(x[i+1]-x[i-1]);
		p=sig*y2[i-1]+2.0;
		y2[i]=(sig-1.0)/p;
		u[i]=(y[i+1]-y[i])/(x[i+1]-x[i]) - (y[i]-y[i-1])/(x[i]-x[i-1]);
		u[i]=(6.0*u[i]/(x[i+1]-x[i-1])-sig*u[i-1])/p;
	}
	if (ypn > 0.99e30)
		qn=un=0.0;
	else {
		qn=0.5;
		un=(3.0/(x[n-1]-x[n-2]))*(ypn-(y[n-1]-y[n-2])/(x[n-1]-x[n-2]));
	}
	y2[n-1]=(un-qn*u[n-2])/(qn*y2[n-2]+1.0);
	for (k=n-2;k>=0;k--)
		y2[k]=y2[k]*y2[k+1]+u[k];
}