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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.
Complex version
*/
static char rcsid[] = "$Id: zhsehldr.c,v 1.2 1994/04/07 01:43:47 des Exp $";
#include <stdio.h>
#include <math.h>
#include "zmatrix.h"
#include "zmatrix2.h"
#define is_zero(z) ((z).re == 0.0 && (z).im == 0.0)
/* zhhvec -- calulates Householder vector to eliminate all entries after the
i0 entry of the vector vec. It is returned as out. May be in-situ */
ZVEC *zhhvec(vec,i0,beta,out,newval)
ZVEC *vec,*out;
int i0;
Real *beta;
complex *newval;
{
complex tmp;
Real norm, abs_val;
if ( i0 < 0 || i0 >= vec->dim )
error(E_BOUNDS,"zhhvec");
out = _zv_copy(vec,out,i0);
tmp = _zin_prod(out,out,i0,Z_CONJ);
if ( tmp.re <= 0.0 )
{
*beta = 0.0;
*newval = out->ve[i0];
return (out);
}
norm = sqrt(tmp.re);
abs_val = zabs(out->ve[i0]);
*beta = 1.0/(norm * (norm+abs_val));
if ( abs_val == 0.0 )
{
newval->re = norm;
newval->im = 0.0;
}
else
{
abs_val = -norm / abs_val;
newval->re = abs_val*out->ve[i0].re;
newval->im = abs_val*out->ve[i0].im;
} abs_val = -norm / abs_val;
out->ve[i0].re -= newval->re;
out->ve[i0].im -= newval->im;
return (out);
}
/* zhhtrvec -- apply Householder transformation to vector -- may be in-situ */
ZVEC *zhhtrvec(hh,beta,i0,in,out)
ZVEC *hh,*in,*out; /* hh = Householder vector */
int i0;
double beta;
{
complex scale, tmp;
/* unsigned int i; */
if ( hh==ZVNULL || in==ZVNULL )
error(E_NULL,"zhhtrvec");
if ( in->dim != hh->dim )
error(E_SIZES,"zhhtrvec");
if ( i0 < 0 || i0 > in->dim )
error(E_BOUNDS,"zhhvec");
tmp = _zin_prod(hh,in,i0,Z_CONJ);
scale.re = -beta*tmp.re;
scale.im = -beta*tmp.im;
out = zv_copy(in,out);
__zmltadd__(&(out->ve[i0]),&(hh->ve[i0]),scale,
(int)(in->dim-i0),Z_NOCONJ);
/************************************************************
for ( i=i0; i<in->dim; i++ )
out->ve[i] = in->ve[i] - scale*hh->ve[i];
************************************************************/
return (out);
}
/* zhhtrrows -- 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) */
ZMAT *zhhtrrows(M,i0,j0,hh,beta)
ZMAT *M;
int i0, j0;
ZVEC *hh;
double beta;
{
complex ip, scale;
int i /*, j */;
if ( M==ZMNULL || hh==ZVNULL )
error(E_NULL,"zhhtrrows");
if ( M->n != hh->dim )
error(E_RANGE,"zhhtrrows");
if ( i0 < 0 || i0 > M->m || j0 < 0 || j0 > M->n )
error(E_BOUNDS,"zhhtrrows");
if ( beta == 0.0 ) return (M);
/* for each row ... */
for ( i = i0; i < M->m; i++ )
{ /* compute inner product */
ip = __zip__(&(M->me[i][j0]),&(hh->ve[j0]),
(int)(M->n-j0),Z_NOCONJ);
/**************************************************
ip = 0.0;
for ( j = j0; j < M->n; j++ )
ip += M->me[i][j]*hh->ve[j];
**************************************************/
scale.re = -beta*ip.re;
scale.im = -beta*ip.im;
/* if ( scale == 0.0 ) */
if ( is_zero(scale) )
continue;
/* do operation */
__zmltadd__(&(M->me[i][j0]),&(hh->ve[j0]),scale,
(int)(M->n-j0),Z_CONJ);
/**************************************************
for ( j = j0; j < M->n; j++ )
M->me[i][j] -= scale*hh->ve[j];
**************************************************/
}
return (M);
}
/* zhhtrcols -- 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 _zhhtrcols() with the scratch vector w
-- Meschach internal routines should call _zhhtrcols() to
avoid excessive memory allocation/de-allocation
*/
ZMAT *zhhtrcols(M,i0,j0,hh,beta)
ZMAT *M;
int i0, j0;
ZVEC *hh;
double beta;
{
/* Real ip, scale; */
complex scale;
int i /*, k */;
STATIC ZVEC *w = ZVNULL;
if ( M==ZMNULL || hh==ZVNULL )
error(E_NULL,"zhhtrcols");
if ( M->m != hh->dim )
error(E_SIZES,"zhhtrcols");
if ( i0 < 0 || i0 > M->m || j0 < 0 || j0 > M->n )
error(E_BOUNDS,"zhhtrcols");
if ( beta == 0.0 ) return (M);
if ( ! w || w->dim < M->n )
w = zv_resize(w,M->n);
MEM_STAT_REG(w,TYPE_ZVEC);
M = _zhhtrcols(M,i0,j0,hh,beta,w);
#ifdef THREADSAFE
ZV_FREE(w);
#endif
return M;
}
/* _zhhtrcols -- 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 */
ZMAT *_zhhtrcols(M,i0,j0,hh,beta,w)
ZMAT *M;
int i0, j0;
ZVEC *hh;
double beta;
ZVEC *w;
{
/* Real ip, scale; */
complex scale;
int i /*, k */;
if ( M==ZMNULL || hh==ZVNULL )
error(E_NULL,"zhhtrcols");
if ( M->m != hh->dim )
error(E_SIZES,"zhhtrcols");
if ( i0 < 0 || i0 > M->m || j0 < 0 || j0 > M->n )
error(E_BOUNDS,"zhhtrcols");
if ( beta == 0.0 ) return (M);
if ( w->dim < M->n )
w = zv_resize(w,M->n);
zv_zero(w);
for ( i = i0; i < M->m; i++ )
/* if ( hh->ve[i] != 0.0 ) */
if ( ! is_zero(hh->ve[i]) )
__zmltadd__(&(w->ve[j0]),&(M->me[i][j0]),hh->ve[i],
(int)(M->n-j0),Z_CONJ);
for ( i = i0; i < M->m; i++ )
/* if ( hh->ve[i] != 0.0 ) */
if ( ! is_zero(hh->ve[i]) )
{
scale.re = -beta*hh->ve[i].re;
scale.im = -beta*hh->ve[i].im;
__zmltadd__(&(M->me[i][j0]),&(w->ve[j0]),scale,
(int)(M->n-j0),Z_CONJ);
}
return (M);
}
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