tred2.cpp

这是C++数值算法(第二版)的源代码,其中包含了目前一些比较常用的数值计算的算法.

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

void NR::tred2(Mat_IO_DP &a, Vec_O_DP &d, Vec_O_DP &e)
{
	int l,k,j,i;
	DP scale,hh,h,g,f;

	int n=d.size();
	for (i=n-1;i>0;i--) {
		l=i-1;
		h=scale=0.0;
		if (l > 0) {
			for (k=0;k<l+1;k++)
				scale += fabs(a[i][k]);
			if (scale == 0.0)
				e[i]=a[i][l];
			else {
				for (k=0;k<l+1;k++) {
					a[i][k] /= scale;
					h += a[i][k]*a[i][k];
				}
				f=a[i][l];
				g=(f >= 0.0 ? -sqrt(h) : sqrt(h));
				e[i]=scale*g;
				h -= f*g;
				a[i][l]=f-g;
				f=0.0;
				for (j=0;j<l+1;j++) {
				// Next statement can be omitted if eigenvectors not wanted
					a[j][i]=a[i][j]/h;
					g=0.0;
					for (k=0;k<j+1;k++)
						g += a[j][k]*a[i][k];
					for (k=j+1;k<l+1;k++)
						g += a[k][j]*a[i][k];
					e[j]=g/h;
					f += e[j]*a[i][j];
				}
				hh=f/(h+h);
				for (j=0;j<l+1;j++) {
					f=a[i][j];
					e[j]=g=e[j]-hh*f;
					for (k=0;k<j+1;k++)
						a[j][k] -= (f*e[k]+g*a[i][k]);
				}
			}
		} else
			e[i]=a[i][l];
		d[i]=h;
	}
	// Next statement can be omitted if eigenvectors not wanted
	d[0]=0.0;
	e[0]=0.0;
	// Contents of this loop can be omitted if eigenvectors not
	//	wanted except for statement d[i]=a[i][i];
	for (i=0;i<n;i++) {
		l=i;
		if (d[i] != 0.0) {
			for (j=0;j<l;j++) {
				g=0.0;
				for (k=0;k<l;k++)
					g += a[i][k]*a[k][j];
				for (k=0;k<l;k++)
					a[k][j] -= g*a[k][i];
			}
		}
		d[i]=a[i][i];
		a[i][i]=1.0;
		for (j=0;j<l;j++) a[j][i]=a[i][j]=0.0;
	}
}