zhessen.c

Meschach 可以解稠密或稀疏线性方程组、计算特征值和特征向量和解最小平方问题

/**************************************************************************
**
** 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.

	Complex version
*/

static	char	rcsid[] = "$Id: zhessen.c,v 1.2 1995/03/27 15:47:50 des Exp $";

#include	<stdio.h>
#include	"zmatrix.h"
#include        "zmatrix2.h"


/* zHfactor -- compute Hessenberg factorisation in compact form.
	-- factorisation performed in situ
	-- for details of the compact form see zQRfactor.c and zmatrix2.doc */
ZMAT	*zHfactor(A, diag)
ZMAT	*A;
ZVEC	*diag;
{
	STATIC	ZVEC	*tmp1 = ZVNULL, *w = ZVNULL;
	Real	beta;
	int	k, limit;

	if ( ! A || ! diag )
		error(E_NULL,"zHfactor");
	if ( diag->dim < A->m - 1 )
		error(E_SIZES,"zHfactor");
	if ( A->m != A->n )
		error(E_SQUARE,"zHfactor");
	limit = A->m - 1;

	tmp1 = zv_resize(tmp1,A->m);
	w    = zv_resize(w,   A->n);
	MEM_STAT_REG(tmp1,TYPE_ZVEC);
	MEM_STAT_REG(w,   TYPE_ZVEC);

	for ( k = 0; k < limit; k++ )
	{
	    zget_col(A,k,tmp1);
	    zhhvec(tmp1,k+1,&beta,tmp1,&A->me[k+1][k]);
	    diag->ve[k] = tmp1->ve[k+1];
	    /* printf("zHfactor: k = %d, beta = %g, tmp1 =\n",k,beta);
	    zv_output(tmp1); */
	    
	    _zhhtrcols(A,k+1,k+1,tmp1,beta,w);
	    zhhtrrows(A,0  ,k+1,tmp1,beta);
	    /* printf("# at stage k = %d, A =\n",k);	zm_output(A); */
	}

#ifdef	THREADSAFE
	ZV_FREE(tmp1);	ZV_FREE(w);
#endif

	return (A);
}

/* zHQunpack -- unpack the compact representation of H and Q of a
	Hessenberg factorisation
	-- if either H or Q is NULL, then it is not unpacked
	-- it can be in situ with HQ == H
	-- returns HQ
*/
ZMAT	*zHQunpack(HQ,diag,Q,H)
ZMAT	*HQ, *Q, *H;
ZVEC	*diag;
{
	int	i, j, limit;
	Real	beta, r_ii, tmp_val;
	STATIC	ZVEC	*tmp1 = ZVNULL, *tmp2 = ZVNULL;

	if ( HQ==ZMNULL || diag==ZVNULL )
		error(E_NULL,"zHQunpack");
	if ( HQ == Q || H == Q )
	    error(E_INSITU,"zHQunpack");
	limit = HQ->m - 1;
	if ( diag->dim < limit )
		error(E_SIZES,"zHQunpack");
	if ( HQ->m != HQ->n )
		error(E_SQUARE,"zHQunpack");


	if ( Q != ZMNULL )
	{
	    Q = zm_resize(Q,HQ->m,HQ->m);
	    tmp1 = zv_resize(tmp1,H->m);
	    tmp2 = zv_resize(tmp2,H->m);
	    MEM_STAT_REG(tmp1,TYPE_ZVEC);
	    MEM_STAT_REG(tmp2,TYPE_ZVEC);
	    
	    for ( i = 0; i < H->m; i++ )
	    {
		/* tmp1 = i'th basis vector */
		for ( j = 0; j < H->m; j++ )
		    tmp1->ve[j].re = tmp1->ve[j].im = 0.0;
		tmp1->ve[i].re = 1.0;
		
		/* apply H/h transforms in reverse order */
		for ( j = limit-1; j >= 0; j-- )
		{
		    zget_col(HQ,j,tmp2);
		    r_ii = zabs(tmp2->ve[j+1]);
		    tmp2->ve[j+1] = diag->ve[j];
		    tmp_val = (r_ii*zabs(diag->ve[j]));
		    beta = ( tmp_val == 0.0 ) ? 0.0 : 1.0/tmp_val;
		    /* printf("zHQunpack: j = %d, beta = %g, tmp2 =\n",
			   j,beta);
		    zv_output(tmp2); */
		    zhhtrvec(tmp2,beta,j+1,tmp1,tmp1);
		}
		
		/* insert into Q */
		zset_col(Q,i,tmp1);
	    }
	}

	if ( H != ZMNULL )
	{
	    H = zm_copy(HQ,zm_resize(H,HQ->m,HQ->n));
	    
	    limit = H->m;
	    for ( i = 1; i < limit; i++ )
		for ( j = 0; j < i-1; j++ )
		    H->me[i][j].re = H->me[i][j].im = 0.0;
	}

#ifdef	THREADSAFE
	ZV_FREE(tmp1);	ZV_FREE(tmp2);
#endif

	return HQ;
}