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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.
**
***************************************************************************/
/*
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);
}
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