Dsvdcmp.cpp

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#include <math.h>
#include "Allocation.h"
 
static double dmaxarg1,dmaxarg2;
#define DMAX(a,b) (dmaxarg1=(a),dmaxarg2=(b),(dmaxarg1) > (dmaxarg2) ?\
        (dmaxarg1) : (dmaxarg2))
static int iminarg1,iminarg2;
#define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ?\
        (iminarg1) : (iminarg2))
 
#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
 
#include <stdio.h>
 
void dsvdcmp(double **a, int m, int n, double w[], double **v)
{
        double dpythag(double a, double b);
        int flag,i,its,j,jj,k,l,nm;
        double anorm,c,f,g,h,s,scale,x,y,z,*rv1;
 
        rv1=dvector(1,n);
        g=scale=anorm=0.0;
        for (i=1;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 = -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) {
                        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 = -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=DMAX(anorm,(fabs(w[i])+fabs(rv1[i])));
        }
        for (i=n;i>=1;i--) {
                if (i < n) {
                        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=IMIN(m,n);i>=1;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;k>=1;k--) {
                for (its=1;its<=30;its++) {
                        flag=1;
                        for (l=k;l>=1;l--) {
                                nm=l-1;
                                if ((double)(fabs(rv1[l])+anorm) == anorm) {
                                        flag=0;
                                        break;
                                }
                                if ((double)(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 ((double)(fabs(f)+anorm) == anorm) break;
                                        g=w[i];
                                        h=dpythag(f,g);
                                        w[i]=h;
                                        h=1.0/h;
                                        c=g*h;
                                        s = -f*h;
                                        for (j=1;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=1;j<=n;j++) v[j][k] = -v[j][k];
                                }
                                break;
                        }
                        if (its == 50) {fprintf(stderr,"no convergence in 30 dsvdcmp iterations");}
                        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=dpythag(f,1.0);
                        f=((x-z)*(x+z)+h*((y/(f+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=dpythag(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=1;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=dpythag(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=1;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;
                }
        }
        free_dvector(rv1,1,n);
}