hsehldr.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.
**
***************************************************************************/


/*
		Files for matrix computations

	Householder transformation file. Contains routines for calculating
	householder transformations, applying them to vectors and matrices
	by both row & column.
*/

/* hsehldr.c 1.3 10/8/87 */
static	char	rcsid[] = "$Id: hsehldr.c,v 1.2 1994/01/13 05:36:29 des Exp $";

#include	<stdio.h>
#include	<math.h>
#include	"matrix.h"
#include        "matrix2.h"


/* hhvec -- calulates Householder vector to eliminate all entries after the
	i0 entry of the vector vec. It is returned as out. May be in-situ */
#ifndef ANSI_C
VEC	*hhvec(vec,i0,beta,out,newval)
VEC	*vec,*out;
unsigned int	i0;
Real	*beta,*newval;
#else
VEC	*hhvec(const VEC *vec, unsigned int i0, Real *beta,
	       VEC *out, Real *newval)
#endif
{
	Real	norm;

	out = _v_copy(vec,out,i0);
	norm = sqrt(_in_prod(out,out,i0));
	if ( norm <= 0.0 )
	{
		*beta = 0.0;
		return (out);
	}
	*beta = 1.0/(norm * (norm+fabs(out->ve[i0])));
	if ( out->ve[i0] > 0.0 )
		*newval = -norm;
	else
		*newval = norm;
	out->ve[i0] -= *newval;

	return (out);
}

/* hhtrvec -- apply Householder transformation to vector 
	-- that is, out <- (I-beta.hh(i0:n).hh(i0:n)^T).in
	-- may be in-situ */
#ifndef ANSI_C
VEC	*hhtrvec(hh,beta,i0,in,out)
VEC	*hh,*in,*out;	/* hh = Householder vector */
unsigned int	i0;
double	beta;
#else
VEC	*hhtrvec(const VEC *hh, double beta, unsigned int i0,
		 const VEC *in, VEC *out)
#endif
{
	Real	scale;
	/* unsigned int	i; */

	if ( hh==VNULL || in==VNULL )
		error(E_NULL,"hhtrvec");
	if ( in->dim != hh->dim )
		error(E_SIZES,"hhtrvec");
	if ( i0 > in->dim )
		error(E_BOUNDS,"hhtrvec");

	scale = beta*_in_prod(hh,in,i0);
	out = v_copy(in,out);
	__mltadd__(&(out->ve[i0]),&(hh->ve[i0]),-scale,(int)(in->dim-i0));
	/************************************************************
	for ( i=i0; i<in->dim; i++ )
		out->ve[i] = in->ve[i] - scale*hh->ve[i];
	************************************************************/

	return (out);
}

/* hhtrrows -- transform a matrix by a Householder vector by rows
	starting at row i0 from column j0 -- in-situ
	-- that is, M(i0:m,j0:n) <- M(i0:m,j0:n)(I-beta.hh(j0:n).hh(j0:n)^T) */
#ifndef ANSI_C
MAT	*hhtrrows(M,i0,j0,hh,beta)
MAT	*M;
unsigned int	i0, j0;
VEC	*hh;
double	beta;
#else
MAT	*hhtrrows(MAT *M, unsigned int i0, unsigned int j0,
		  const VEC *hh, double beta)
#endif
{
	Real	ip, scale;
	int	i /*, j */;

	if ( M==MNULL || hh==VNULL )
		error(E_NULL,"hhtrrows");
	if ( M->n != hh->dim )
		error(E_RANGE,"hhtrrows");
	if ( i0 > M->m || j0 > M->n )
		error(E_BOUNDS,"hhtrrows");

	if ( beta == 0.0 )	return (M);

	/* for each row ... */
	for ( i = i0; i < M->m; i++ )
	{	/* compute inner product */
		ip = __ip__(&(M->me[i][j0]),&(hh->ve[j0]),(int)(M->n-j0));
		/**************************************************
		ip = 0.0;
		for ( j = j0; j < M->n; j++ )
			ip += M->me[i][j]*hh->ve[j];
		**************************************************/
		scale = beta*ip;
		if ( scale == 0.0 )
		    continue;

		/* do operation */
		__mltadd__(&(M->me[i][j0]),&(hh->ve[j0]),-scale,
							(int)(M->n-j0));
		/**************************************************
		for ( j = j0; j < M->n; j++ )
			M->me[i][j] -= scale*hh->ve[j];
		**************************************************/
	}

	return (M);
}

/* hhtrcols -- transform a matrix by a Householder vector by columns
	starting at row i0 from column j0 
	-- that is, M(i0:m,j0:n) <- (I-beta.hh(i0:m).hh(i0:m)^T)M(i0:m,j0:n)
	-- in-situ
	-- calls _hhtrcols() with the scratch vector w
	-- Meschach internal routines should call _hhtrcols() to
	avoid excessive memory allocation/de-allocation
*/
#ifndef ANSI_C
MAT	*hhtrcols(M,i0,j0,hh,beta)
MAT	*M;
unsigned int	i0, j0;
VEC	*hh;
double	beta;
#else
MAT	*hhtrcols(MAT *M, unsigned int i0, unsigned int j0,
		  const VEC *hh, double beta)
#endif
{
  STATIC VEC	*w = VNULL;

  if ( M == MNULL || hh == VNULL || w == VNULL )
    error(E_NULL,"hhtrcols");
  if ( M->m != hh->dim )
    error(E_SIZES,"hhtrcols");
  if ( i0 > M->m || j0 > M->n )
    error(E_BOUNDS,"hhtrcols");

  if ( ! w || w->dim < M->n )
    w = v_resize(w,M->n);
  MEM_STAT_REG(w,TYPE_VEC);

  M = _hhtrcols(M,i0,j0,hh,beta,w);

#ifdef THREADSAFE
  V_FREE(w);
#endif

  return M;
}

/* _hhtrcols -- transform a matrix by a Householder vector by columns
	starting at row i0 from column j0 
	-- that is, M(i0:m,j0:n) <- (I-beta.hh(i0:m).hh(i0:m)^T)M(i0:m,j0:n)
	-- in-situ
	-- scratch vector w passed as argument
	-- raises error if w == NULL
*/
#ifndef ANSI_C
MAT	*_hhtrcols(M,i0,j0,hh,beta,w)
MAT	*M;
unsigned int	i0, j0;
VEC	*hh;
double	beta;
VEC	*w;
#else
MAT	*_hhtrcols(MAT *M, unsigned int i0, unsigned int j0,
		   const VEC *hh, double beta, VEC *w)
#endif
{
	/* Real	ip, scale; */
	int	i /*, k */;
	/*  STATIC	VEC	*w = VNULL; */

	if ( M == MNULL || hh == VNULL || w == VNULL )
		error(E_NULL,"_hhtrcols");
	if ( M->m != hh->dim )
		error(E_SIZES,"_hhtrcols");
	if ( i0 > M->m || j0 > M->n )
		error(E_BOUNDS,"_hhtrcols");

	if ( beta == 0.0 )	return (M);

	if ( w->dim < M->n )
	  w = v_resize(w,M->n);
	/*  MEM_STAT_REG(w,TYPE_VEC); */
	v_zero(w);

	for ( i = i0; i < M->m; i++ )
	    if ( hh->ve[i] != 0.0 )
		__mltadd__(&(w->ve[j0]),&(M->me[i][j0]),hh->ve[i],
							(int)(M->n-j0));
	for ( i = i0; i < M->m; i++ )
	    if ( hh->ve[i] != 0.0 )
		__mltadd__(&(M->me[i][j0]),&(w->ve[j0]),-beta*hh->ve[i],
							(int)(M->n-j0));
	return (M);
}