update.c

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#include <../../nrnconf.h>

/**************************************************************************
**
** 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[] = "update.c,v 1.1 1997/12/04 17:56:01 hines Exp";

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