source: proiecte/PPPP/eigenface/new/jacobi_vector.c @ 93

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define ROTATE(a,i,j,k,l) g=a[i*n + j];h=a[k*n + l];a[i*n + j]=g-s*(h+g*tau);\
a[k*n + l]=h+s*(g-h*tau);

/*
Computes all eigenvalues and eigenvectors of a real symmetric matrix a[1..n][1..n]. On
output, elements of a above the diagonal are destroyed. d[1..n] returns the eigenvalues of a.
v[1..n][1..n] is a matrix whose columns contain, on output, the normalized eigenvectors of
a. nrot returns the number of Jacobi rotations that were required.
*/
void jacobi(float *a, int n, float d[], float *v, int *nrot)
{
        int j,iq,ip,i;
        float tresh,theta,tau,t,sm,s,h,g,c,*b,*z;
        
        b = (float *) malloc(n * sizeof(float));
        z = (float *) malloc(n * sizeof(float));
        
        for (ip=0;ip<n;ip++) {                                                                                                                  // Initialize to the identity matrix.
                for (iq=0;iq<n;iq++) v[ip*n + iq]=0.0;
                        v[ip*n + ip]=1.0;
        }
        for (ip=0;ip<n;ip++) {                                                                                                                  // Initialize b and d to the diagonal of a.
                b[ip]=d[ip]=a[ip*n + ip];                                                                                                               
                z[ip]=0.0;                                                                                                                              // This vector will accumulate terms of the form t*a[pq] as in equation (11.1.14).
        }
        
        *nrot=0;
        for (i=1;i<=50;i++) {
                sm=0.0;
                for (ip=0;ip<n-1;ip++) {                                                                                                                // Sum off-diagonal elements.
                        for (iq=ip+1;iq<n;iq++)
                        sm += fabs(a[ip*n + iq]);
                }
                if (sm == 0.0) {                                                                                                                        // The normal return, which relies on quadratic convergence to machine underflow.
                        free(z);
                        free(b);
                        return;
                }
                if (i < 4)
                        tresh=0.2*sm/(n*n);                                                                                                             // ...on the first three sweeps.
                else
                        tresh=0.0;                                                                                                                      // ...thereafter.
                for (ip=0;ip<n-1;ip++) {
                        for (iq=ip+1;iq<n;iq++) {
                                g=100.0*fabs(a[ip*n + iq]);
                                if (i > 4 && (float)(fabs(d[ip])+g) == (float)fabs(d[ip])                                               // After four sweeps, skip the rotation if the off-diagonal element is small.
                                        && (float)(fabs(d[iq])+g) == (float)fabs(d[iq]))
                                        a[ip*n + iq]=0.0;
                                else if (fabs(a[ip*n + iq]) > tresh) {
                                        h=d[iq]-d[ip];
                                        if ((float)(fabs(h)+g) == (float)fabs(h))
                                                t=(a[ip*n + iq])/h;                                                                                     // t = 1/(2*theta)
                                        else {
                                                theta=0.5*h/(a[ip*n + iq]);                                                                     // Equation (11.1.10).
                                                t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
                                                if (theta < 0.0) t = -t;
                                        }
                                        
                                        c=1.0/sqrt(1+t*t);
                                        s=t*c;
                                        tau=s/(1.0+c);
                                        h=t*a[ip*n + iq];
                                        z[ip] -= h;
                                        z[iq] += h;
                                        d[ip] -= h;
                                        d[iq] += h;
                                        a[ip*n + iq]=0.0;
                                        
                                        for (j=0;j<=ip-1;j++) {                                                                                         // Case of rotations 1 <= j < p.
                                                ROTATE(a,j,ip,j,iq)
                                        }
                                        for (j=ip+1;j<=iq-1;j++) {                                                                              // Case of rotations p < j < q.
                                                ROTATE(a,ip,j,j,iq)
                                        }
                                        for (j=iq+1;j<n;j++) {                                                                                  // Case of rotations q < j <= n.
                                                ROTATE(a,ip,j,iq,j)
                                        }
                                        for (j=0;j<n;j++) {
                                                ROTATE(v,j,ip,j,iq)
                                        }
                                        
                                        ++(*nrot);
                                }
                        }
                }
                
                for (ip=0;ip<n;ip++) {
                        b[ip] += z[ip];
                        d[ip]=b[ip];                                                                                                                    // Updte d with the sum of t*a[pq],
                        z[ip]=0.0;                                                                                                                      // and reinitialize z.
                }
        }
        
        printf("Too many iterations in routine jacobi\n");
}

/* 
Given the eigenvalues d[1..n] and eigenvectors v[1..n][1..n] as output from jacobi
(x11.1) or tqli (x11.3), this routine sorts the eigenvalues into descending order, and rearranges
the columns of v correspondingly. The method is straight insertion. 
*/
void eigsrt(float d[], float **v, int n)        
{
        int k,j,i;
        float p;
        for (i=0;i<n-1;i++) {
                p=d[k=i];
                for (j=i+1;j<n;j++)
                        if (d[j] >= p) p=d[k=j];
                if (k != i) {
                        d[k]=d[i];
                        d[i]=p;
                        for (j=0;j<n;j++) {
                                p=v[j*n + i];
                                v[j*n + i]=v[j*n + k];
                                v[j*n + k]=p;
                        }
                }
        }
}