svd.c

su 的源代码库

/* Copyright (c) Colorado School of Mines, 2006.*/
/* All rights reserved.                       */

/***************************************************************************
SVD - Singular Value Decomposition related routines
****************************************************************************

compute_svd - perform singular value decomposition 
svd_backsubstitute - back substitute results of compute_svd
svd_sort - sort singular values in descending order

****************************************************************************
Credits: Ian Kay, Canadian Geological Survey, Ottawa, Ontario 1999.
This is a translation in C from an code written in Fortran that appeared
in NETLIB, EISPACK, and SLATEC collections that was itself a translation
from an original Algol code that appeared in:

Golub, G. and C. Reinsch (1971) Handbook for automatic computation II,
 linear algebra, p 134-151. SpringerVerlag, New York.

See also discussions of a similar code in Numerical Recipes in C.
svd_sort: Nils Maercklin, GeoForschungsZentrum (GFZ) Potsdam, Germany, 2001.
***************************************************************************/

#include <cwp.h>

#define SVD_SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
#define SVD_MAX_ITERATION 40

/* Function prototype of routine used internally */
float pythag(float a, float b);

float pythag(float a, float b)
/* pythagorean theorem */
{
    float absa,absb;
    absa=fabs(a);
    absb=fabs(b);
    if (absa > absb) 
    	return absa*sqrt(1.0+(absb/absa)*(absb/absa));
    else return 
    	(absb == 0.0 ? 0.0 : absb*sqrt(1.0+(absa/absb)*(absa/absb)));
}

void 
svd_backsubstitute(float **u, float w[], float **v, int m, int n, float b[], float x[])
/**************************************************************************
svd_backsubstitute - back substitute results of compute_svd
***************************************************************************
Credits: similar to code in Netlib's EISPACK and CLAPACK
see also discussions in NR in C
**************************************************************************/
{
	int jj,j,i;
	float s,*tmp;

	tmp=alloc1float(n);

	for (j=0;j<n;j++) {
		s=0.0;
		if (w[j]) {
			for (i=0;i<m;i++) 
				s += u[i][j]*b[i];
			s /= w[j];
		}
		tmp[j]=s;
	}
	for (j=0;j<n;j++) {
		s=0.0;
		for (jj=0;jj<n;jj++) 
			s += v[j][jj]*tmp[jj];
		x[j]=s;
	}
	free1float (tmp);
}


void 
compute_svd(float **a, int m, int n, float w[], float **v)
/*************************************************************************
compute_svd - perform singular value decomposition 
**************************************************************************
Credits: similar to code in Netlib's EISPACK and CLAPACK 
see also discussions in NR in C
*************************************************************************/
{
	float pythag(float a, float b);
	int flag,i,its,j,jj,k,l=0,nm=0;
	float anorm,c,f,g,h,s,scale,x,y,z,*rv1;
	int maxiter=SVD_MAX_ITERATION;

	rv1=alloc1float(n);
	g=scale=anorm=0.0;
	for (i=0;i<n;i++) {
		l=i+1;
		rv1[i]=scale*g;
		g=s=scale=0.0;
		if (i < m) {
			for (k=i;k<m;k++) 
				scale += fabs(a[k][i]);
			if (scale) {
				for (k=i;k<m;k++) {
					a[k][i] /= scale;
					s += a[k][i]*a[k][i];
				}
				f=a[i][i];
				g = -SVD_SIGN(sqrt(s),f);
				h=f*g-s;
				a[i][i]=f-g;
				for (j=l;j<n;j++) {
					for (s=0.0,k=i;k<m;k++) 
						s += a[k][i]*a[k][j];
					f=s/h;
					for (k=i;k<m;k++) 
						a[k][j] += f*a[k][i];
				}
				for (k=i;k<m;k++) 
					a[k][i] *= scale;
			}
		}
		w[i]=scale *g;
		g=s=scale=0.0;
		if (i < m && i != n-1) {
			for (k=l;k<n;k++) 
				scale += fabs(a[i][k]);
			if (scale) {
				for (k=l;k<n;k++) {
					a[i][k] /= scale;
					s += a[i][k]*a[i][k];
				}
				f=a[i][l];
				g = -SVD_SIGN(sqrt(s),f);
				h=f*g-s;
				a[i][l]=f-g;
				for (k=l;k<n;k++) 
					rv1[k]=a[i][k]/h;
				for (j=l;j<m;j++) {
					for (s=0.0,k=l;k<n;k++) 
						s += a[j][k]*a[i][k];
					for (k=l;k<n;k++) 
						a[j][k] += s*rv1[k];
				}
				for (k=l;k<n;k++) 
					a[i][k] *= scale;
			}
		}
		anorm=(anorm>(fabs(w[i])+fabs(rv1[i])) ? anorm : (fabs(w[i])+fabs(rv1[i])));
	}
	for (i=n-1;i>=0;i--) {
		if (i < n-1) {
			if (g) {
				for (j=l;j<n;j++)
					v[j][i]=(a[i][j]/a[i][l])/g;
				for (j=l;j<n;j++) {
					for (s=0.0,k=l;k<n;k++) 
						s += a[i][k]*v[k][j];
					for (k=l;k<n;k++) 
						v[k][j] += s*v[k][i];
				}
			}
			for (j=l;j<n;j++) 
				v[i][j]=v[j][i]=0.0;
		}
		v[i][i]=1.0;
		g=rv1[i];
		l=i;
	}

	for (i=(m<n?m:n)-1;i>=0;i--) {
		l=i+1;
		g=w[i];
		for (j=l;j<n;j++) 
			a[i][j]=0.0;
		if (g) {
			g=1.0/g;
			for (j=l;j<n;j++) {
				for (s=0.0,k=l;k<m;k++) 
					s += a[k][i]*a[k][j];
				f=(s/a[i][i])*g;
				for (k=i;k<m;k++) 
					a[k][j] += f*a[k][i];
			}
			for (j=i;j<m;j++) 
				a[j][i] *= g;
		} else 
			for (j=i;j<m;j++) 
				a[j][i]=0.0;
		++a[i][i];
	}
	for (k=n-1;k>=0;k--) {
		for (its=1;its<=maxiter;its++) {
			flag=1;
			for (l=k;l>=0;l--) {
				nm=l-1;
				if ((float)(fabs(rv1[l])+anorm) == anorm) {
					flag=0;
					break;
				}
				if ((float)(fabs(w[nm])+anorm) == anorm) break;
			}
			if (flag) {
				c=0.0;
				s=1.0;
				for (i=l;i<=k;i++) {
					f=s*rv1[i];
					rv1[i]=c*rv1[i];
					if ((float)(fabs(f)+anorm) == anorm) break;
					g=w[i];
					h=pythag(f,g);
					w[i]=h;
					h=1.0/h;
					c=g*h;
					s = -f*h;
					for (j=0;j<m;j++) {
						y=a[j][nm];
						z=a[j][i];
						a[j][nm]=y*c+z*s;
						a[j][i]=z*c-y*s;
					}
				}
			}
			z=w[k];
			if (l == k) {
				if (z < 0.0) {
					w[k] = -z;
					for (j=0;j<n;j++) v[j][k] = -v[j][k];
				}
				break;
			}
			if (its == 30) { fprintf(stderr,"no convergence in 30 compute_svd iterations\n");exit (-2);}
			x=w[l];
			nm=k-1;
			y=w[nm];
			g=rv1[nm];
			h=rv1[k];
			f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
			g=pythag(f,1.0);
			f=((x-z)*(x+z)+h*((y/(f+SVD_SIGN(g,f)))-h))/x;
			c=s=1.0;
			for (j=l;j<=nm;j++) {
				i=j+1;
				g=rv1[i];
				y=w[i];
				h=s*g;
				g=c*g;
				z=pythag(f,h);
				rv1[j]=z;
				c=f/z;
				s=h/z;
				f=x*c+g*s;
				g = g*c-x*s;
				h=y*s;
				y *= c;
				for (jj=0;jj<n;jj++) {
					x=v[jj][j];
					z=v[jj][i];
					v[jj][j]=x*c+z*s;
					v[jj][i]=z*c-x*s;
				}
				z=pythag(f,h);
				w[j]=z;
				if (z) {
					z=1.0/z;
					c=f*z;
					s=h*z;
				}
				f=c*g+s*y;
				x=c*y-s*g;
				for (jj=0;jj<m;jj++) {
					y=a[jj][j];
					z=a[jj][i];
					a[jj][j]=y*c+z*s;
					a[jj][i]=z*c-y*s;
				}
			}
			rv1[l]=0.0;
			rv1[k]=f;
			w[k]=x;
		}
	}
	free1float(rv1);
}

void svd_sort(float **u, float *w, float **v, int n, int m)
/**********************************************************************
svd_sort - sort singular values and corresponding eigenimages
           in descending order
**********************************************************************
Input:
u[][]	
**********************************************************************
Notes:
We assume input of the singular value decomposition of a matrix a[][]
of the form:
                    t
a[][] = u[][] w[] v[][]

**********************************************************************
Credits: Nils Maercklin, GeoForschungsZentrum (GFZ) Potsdam, Germany, 2001.
**********************************************************************/
{
        int k,j,i;
        float p;

        for (i=0;i<n-1;i++) {
                p=w[k=i];
                for (j=i+1;j<=n;j++)
                        if (w[j] >= p) p=w[k=j];
                if (k != i) {
                        w[k]=w[i];
                        w[i]=p;
                        for (j=0;j<n;j++) {
                                p=v[j][i];
                                v[j][i]=v[j][k];
                                v[j][k]=p;
                        }
                        for (j=0;j<m;j++) {
                                p=u[j][i];
                                u[j][i]=u[j][k];
                                u[j][k]=p;
                        }
                }
        }
}