vTridiag.c

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/*******************************************************
 *
 * Author: Shinsaku Hiura, Hirokazu Kato
 *
 *         shinsaku@sys.es.osaka-u.ac.jp
 *         kato@sys.im.hiroshima-cu.ac.jp
 *
 * Revision: 2.1
 * Date: 99/07/16
 *
*******************************************************/

#include <stdio.h>
#include <math.h>
#include <AR/matrix.h>

int arVecTridiagonalize( ARMat *a, ARVec *d, ARVec *e )
{
    ARVec     wv1, wv2;
    double  *v;
    double  s, t, p, q;
    int     dim;
    int     i, j, k;

    if( a->clm != a->row )   return(-1);
    if( a->clm != d->clm )   return(-1);
    if( a->clm != e->clm+1 ) return(-1);
    dim = a->clm;

    for( k = 0; k < dim-2; k++ ) {
        v = &(a->m[k*dim]);
        d->v[k] = v[k];

        wv1.clm = dim-k-1;
        wv1.v = &(v[k+1]);
        e->v[k] = arVecHousehold(&wv1);
        if( e->v[k] == 0.0 ) continue;

        for( i = k+1; i < dim; i++ ) {
            s = 0.0;
            for( j = k+1; j < i; j++ ) {
                s += a->m[j*dim+i] * v[j];
            }
            for( j = i; j < dim; j++ ) {
                s += a->m[i*dim+j] * v[j];
            }
            d->v[i] = s;
        }

        wv1.clm = wv2.clm = dim-k-1;
        wv1.v = &(v[k+1]);
        wv2.v = &(d->v[k+1]);
        t = arVecInnerproduct( &wv1, &wv2 ) / 2;
        for( i = dim-1; i > k; i-- ) {
            p = v[i];
            q = d->v[i] -= t*p;
            for( j = i; j < dim; j++ ) {
                a->m[i*dim+j] -= p*(d->v[j]) + q*v[j];
            }
        }
    }

    if( dim >= 2) {
        d->v[dim-2] = a->m[(dim-2)*dim+(dim-2)];
        e->v[dim-2] = a->m[(dim-2)*dim+(dim-1)];
    }

    if( dim >= 1 ) d->v[dim-1] = a->m[(dim-1)*dim+(dim-1)];

    for( k = dim-1; k >= 0; k-- ) {
        v = &(a->m[k*dim]);
        if( k < dim-2 ) {
            for( i = k+1; i < dim; i++ ) {
                wv1.clm = wv2.clm = dim-k-1;
                wv1.v = &(v[k+1]);
                wv2.v = &(a->m[i*dim+k+1]);
                t = arVecInnerproduct( &wv1, &wv2 );
                for( j = k+1; j < dim; j++ ) a->m[i*dim+j] -= t * v[j];
            }
        }
        for( i = 0; i < dim; i++ ) v[i] = 0.0;
        v[k] = 1;
    }

    return(0);
}