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/**************************************************************************
**
** Copyright (C) 1993 David E. Steward & Zbigniew Leyk, all rights reserved.
**
** Meschach Library
**
** This Meschach Library is provided "as is" without any express
** or implied warranty of any kind with respect to this software.
** In particular the authors shall not be liable for any direct,
** indirect, special, incidental or consequential damages arising
** in any way from use of the software.
**
** Everyone is granted permission to copy, modify and redistribute this
** Meschach Library, provided:
** 1. All copies contain this copyright notice.
** 2. All modified copies shall carry a notice stating who
** made the last modification and the date of such modification.
** 3. No charge is made for this software or works derived from it.
** This clause shall not be construed as constraining other software
** distributed on the same medium as this software, nor is a
** distribution fee considered a charge.
**
***************************************************************************/
/*
File containing routines for determining Hessenberg
factorisations.
*/
static char rcsid[] = "$Id: hessen.c,v 1.2 1994/01/13 05:36:24 des Exp $";
#include <stdio.h>
#include "matrix.h"
#include "matrix2.h"
/* Hfactor -- compute Hessenberg factorisation in compact form.
-- factorisation performed in situ
-- for details of the compact form see QRfactor.c and matrix2.doc */
#ifndef ANSI_C
MAT *Hfactor(A, diag, beta)
MAT *A;
VEC *diag, *beta;
#else
MAT *Hfactor(MAT *A, VEC *diag, VEC *beta)
#endif
{
STATIC VEC *hh = VNULL, *w = VNULL;
int k, limit;
if ( ! A || ! diag || ! beta )
error(E_NULL,"Hfactor");
if ( diag->dim < A->m - 1 || beta->dim < A->m - 1 )
error(E_SIZES,"Hfactor");
if ( A->m != A->n )
error(E_SQUARE,"Hfactor");
limit = A->m - 1;
hh = v_resize(hh,A->m);
w = v_resize(w,A->n);
MEM_STAT_REG(hh,TYPE_VEC);
MEM_STAT_REG(w, TYPE_VEC);
for ( k = 0; k < limit; k++ )
{
/* compute the Householder vector hh */
get_col(A,(unsigned int)k,hh);
/* printf("the %d'th column = "); v_output(hh); */
hhvec(hh,k+1,&beta->ve[k],hh,&A->me[k+1][k]);
/* diag->ve[k] = hh->ve[k+1]; */
v_set_val(diag,k,v_entry(hh,k+1));
/* printf("H/h vector = "); v_output(hh); */
/* printf("from the %d'th entry\n",k+1); */
/* printf("beta = %g\n",beta->ve[k]); */
/* apply Householder operation symmetrically to A */
_hhtrcols(A,k+1,k+1,hh,v_entry(beta,k),w);
hhtrrows(A,0 ,k+1,hh,v_entry(beta,k));
/* printf("A = "); m_output(A); */
}
#ifdef THREADSAFE
V_FREE(hh); V_FREE(w);
#endif
return (A);
}
/* makeHQ -- construct the Hessenberg orthogonalising matrix Q;
-- i.e. Hess M = Q.M.Q' */
#ifndef ANSI_C
MAT *makeHQ(H, diag, beta, Qout)
MAT *H, *Qout;
VEC *diag, *beta;
#else
MAT *makeHQ(MAT *H, VEC *diag, VEC *beta, MAT *Qout)
#endif
{
int i, j, limit;
STATIC VEC *tmp1 = VNULL, *tmp2 = VNULL;
if ( H==(MAT *)NULL || diag==(VEC *)NULL || beta==(VEC *)NULL )
error(E_NULL,"makeHQ");
limit = H->m - 1;
if ( diag->dim < limit || beta->dim < limit )
error(E_SIZES,"makeHQ");
if ( H->m != H->n )
error(E_SQUARE,"makeHQ");
Qout = m_resize(Qout,H->m,H->m);
tmp1 = v_resize(tmp1,H->m);
tmp2 = v_resize(tmp2,H->m);
MEM_STAT_REG(tmp1,TYPE_VEC);
MEM_STAT_REG(tmp2,TYPE_VEC);
for ( i = 0; i < H->m; i++ )
{
/* tmp1 = i'th basis vector */
for ( j = 0; j < H->m; j++ )
/* tmp1->ve[j] = 0.0; */
v_set_val(tmp1,j,0.0);
/* tmp1->ve[i] = 1.0; */
v_set_val(tmp1,i,1.0);
/* apply H/h transforms in reverse order */
for ( j = limit-1; j >= 0; j-- )
{
get_col(H,(unsigned int)j,tmp2);
/* tmp2->ve[j+1] = diag->ve[j]; */
v_set_val(tmp2,j+1,v_entry(diag,j));
hhtrvec(tmp2,beta->ve[j],j+1,tmp1,tmp1);
}
/* insert into Qout */
set_col(Qout,(unsigned int)i,tmp1);
}
#ifdef THREADSAFE
V_FREE(tmp1); V_FREE(tmp2);
#endif
return (Qout);
}
/* makeH -- construct actual Hessenberg matrix */
#ifndef ANSI_C
MAT *makeH(H,Hout)
MAT *H, *Hout;
#else
MAT *makeH(const MAT *H, MAT *Hout)
#endif
{
int i, j, limit;
if ( H==(MAT *)NULL )
error(E_NULL,"makeH");
if ( H->m != H->n )
error(E_SQUARE,"makeH");
Hout = m_resize(Hout,H->m,H->m);
Hout = m_copy(H,Hout);
limit = H->m;
for ( i = 1; i < limit; i++ )
for ( j = 0; j < i-1; j++ )
/* Hout->me[i][j] = 0.0;*/
m_set_val(Hout,i,j,0.0);
return (Hout);
}
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