184 lines
3.4 KiB
C
184 lines
3.4 KiB
C
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#include <math.h>
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#include "nrutil.h"
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void dsvdcmp(a,m,n,w,v)
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double **a,**v,w[];
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int m,n;
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{
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double dpythag();
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int flag,i,its,j,jj,k,l,nm;
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double anorm,c,f,g,h,s,scale,x,y,z,*rv1;
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rv1=dvector(1,n);
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g=scale=anorm=0.0;
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for (i=1;i<=n;i++) {
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l=i+1;
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rv1[i]=scale*g;
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g=s=scale=0.0;
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if (i <= m) {
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for (k=i;k<=m;k++) scale += fabs(a[k][i]);
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if (scale) {
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for (k=i;k<=m;k++) {
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a[k][i] /= scale;
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s += a[k][i]*a[k][i];
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}
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f=a[i][i];
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g = -SIGN(sqrt(s),f);
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h=f*g-s;
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a[i][i]=f-g;
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for (j=l;j<=n;j++) {
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for (s=0.0,k=i;k<=m;k++) s += a[k][i]*a[k][j];
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f=s/h;
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for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
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}
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for (k=i;k<=m;k++) a[k][i] *= scale;
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}
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}
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w[i]=scale *g;
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g=s=scale=0.0;
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if (i <= m && i != n) {
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for (k=l;k<=n;k++) scale += fabs(a[i][k]);
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if (scale) {
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for (k=l;k<=n;k++) {
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a[i][k] /= scale;
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s += a[i][k]*a[i][k];
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}
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f=a[i][l];
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g = -SIGN(sqrt(s),f);
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h=f*g-s;
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a[i][l]=f-g;
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for (k=l;k<=n;k++) rv1[k]=a[i][k]/h;
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for (j=l;j<=m;j++) {
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for (s=0.0,k=l;k<=n;k++) s += a[j][k]*a[i][k];
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for (k=l;k<=n;k++) a[j][k] += s*rv1[k];
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}
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for (k=l;k<=n;k++) a[i][k] *= scale;
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}
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}
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anorm=DMAX(anorm,(fabs(w[i])+fabs(rv1[i])));
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}
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for (i=n;i>=1;i--) {
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if (i < n) {
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if (g) {
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for (j=l;j<=n;j++) v[j][i]=(a[i][j]/a[i][l])/g;
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for (j=l;j<=n;j++) {
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for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j];
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for (k=l;k<=n;k++) v[k][j] += s*v[k][i];
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}
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}
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for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0;
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}
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v[i][i]=1.0;
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g=rv1[i];
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l=i;
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}
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for (i=IMIN(m,n);i>=1;i--) {
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l=i+1;
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g=w[i];
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for (j=l;j<=n;j++) a[i][j]=0.0;
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if (g) {
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g=1.0/g;
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for (j=l;j<=n;j++) {
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for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j];
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f=(s/a[i][i])*g;
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for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
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}
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for (j=i;j<=m;j++) a[j][i] *= g;
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} else for (j=i;j<=m;j++) a[j][i]=0.0;
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++a[i][i];
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}
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for (k=n;k>=1;k--) {
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for (its=1;its<=30;its++) {
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flag=1;
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for (l=k;l>=1;l--) {
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nm=l-1;
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if ((double)(fabs(rv1[l])+anorm) == anorm) {
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flag=0;
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break;
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}
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if ((double)(fabs(w[nm])+anorm) == anorm) break;
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}
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if (flag) {
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c=0.0;
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s=1.0;
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for (i=l;i<=k;i++) {
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f=s*rv1[i];
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rv1[i]=c*rv1[i];
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if ((double)(fabs(f)+anorm) == anorm) break;
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g=w[i];
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h=dpythag(f,g);
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w[i]=h;
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h=1.0/h;
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c=g*h;
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s = -f*h;
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for (j=1;j<=m;j++) {
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y=a[j][nm];
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z=a[j][i];
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a[j][nm]=y*c+z*s;
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a[j][i]=z*c-y*s;
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}
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}
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}
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z=w[k];
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if (l == k) {
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if (z < 0.0) {
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w[k] = -z;
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for (j=1;j<=n;j++) v[j][k] = -v[j][k];
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}
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break;
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}
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if (its == 30) nrerror("no convergence in 30 dsvdcmp iterations");
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x=w[l];
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nm=k-1;
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y=w[nm];
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g=rv1[nm];
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h=rv1[k];
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f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
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g=dpythag(f,1.0);
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f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
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c=s=1.0;
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for (j=l;j<=nm;j++) {
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i=j+1;
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g=rv1[i];
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y=w[i];
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h=s*g;
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g=c*g;
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z=dpythag(f,h);
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rv1[j]=z;
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c=f/z;
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s=h/z;
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f=x*c+g*s;
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g = g*c-x*s;
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h=y*s;
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y *= c;
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for (jj=1;jj<=n;jj++) {
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x=v[jj][j];
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z=v[jj][i];
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v[jj][j]=x*c+z*s;
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v[jj][i]=z*c-x*s;
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}
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z=dpythag(f,h);
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w[j]=z;
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if (z) {
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z=1.0/z;
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c=f*z;
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s=h*z;
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}
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f=c*g+s*y;
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x=c*y-s*g;
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for (jj=1;jj<=m;jj++) {
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y=a[jj][j];
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z=a[jj][i];
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a[jj][j]=y*c+z*s;
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a[jj][i]=z*c-y*s;
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}
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}
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rv1[l]=0.0;
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rv1[k]=f;
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w[k]=x;
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}
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}
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free_dvector(rv1,1,n);
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}
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