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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.
**
***************************************************************************/
/*
Matrix factorisation routines to work with the other matrix files.
*/
/* update.c 1.3 11/25/87 */
static char rcsid[] = "$Id: update.c,v 1.2 1994/01/13 05:26:06 des Exp $";
#include <stdio.h>
#include <math.h>
#include "matrix.h"
#include "matrix2.h"
/* Most matrix factorisation routines are in-situ unless otherwise specified */
/* LDLupdate -- updates a CHolesky factorisation, replacing LDL' by
MD~M' = LDL' + alpha.w.w' Note: w is overwritten
Ref: Gill et al Math Comp 28, p516 Algorithm C1 */
MAT *LDLupdate(CHmat,w,alpha)
MAT *CHmat;
VEC *w;
double alpha;
{
u_int i,j;
Real diag,new_diag,beta,p;
if ( CHmat==(MAT *)NULL || w==(VEC *)NULL )
error(E_NULL,"LDLupdate");
if ( CHmat->m != CHmat->n || w->dim != CHmat->m )
error(E_SIZES,"LDLupdate");
for ( j=0; j < w->dim; j++ )
{
p = w->ve[j];
diag = CHmat->me[j][j];
new_diag = CHmat->me[j][j] = diag + alpha*p*p;
if ( new_diag <= 0.0 )
error(E_POSDEF,"LDLupdate");
beta = p*alpha/new_diag;
alpha *= diag/new_diag;
for ( i=j+1; i < w->dim; i++ )
{
w->ve[i] -= p*CHmat->me[i][j];
CHmat->me[i][j] += beta*w->ve[i];
CHmat->me[j][i] = CHmat->me[i][j];
}
}
return (CHmat);
}
/* QRupdate -- updates QR factorisation in expanded form (seperate matrices)
Finds Q+, R+ s.t. Q+.R+ = Q.(R+u.v') and Q+ orthogonal, R+ upper triang
Ref: Golub & van Loan Matrix Computations pp437-443
-- does not update Q if it is NULL */
MAT *QRupdate(Q,R,u,v)
MAT *Q,*R;
VEC *u,*v;
{
int i,j,k;
Real c,s,temp;
if ( ! R || ! u || ! v )
error(E_NULL,"QRupdate");
if ( ( Q && ( Q->m != Q->n || R->m != Q->n ) ) ||
u->dim != R->m || v->dim != R->n )
error(E_SIZES,"QRupdate");
/* find largest k s.t. u[k] != 0 */
for ( k=R->m-1; k>=0; k-- )
if ( u->ve[k] != 0.0 )
break;
/* transform R+u.v' to Hessenberg form */
for ( i=k-1; i>=0; i-- )
{
/* get Givens rotation */
givens(u->ve[i],u->ve[i+1],&c,&s);
rot_rows(R,i,i+1,c,s,R);
if ( Q )
rot_cols(Q,i,i+1,c,s,Q);
rot_vec(u,i,i+1,c,s,u);
}
/* add into R */
temp = u->ve[0];
for ( j=0; j<R->n; j++ )
R->me[0][j] += temp*v->ve[j];
/* transform Hessenberg to upper triangular */
for ( i=0; i<k; i++ )
{
givens(R->me[i][i],R->me[i+1][i],&c,&s);
rot_rows(R,i,i+1,c,s,R);
if ( Q )
rot_cols(Q,i,i+1,c,s,Q);
}
return R;
}
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