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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.
*/
/* CHfactor.c 1.2 11/25/87 */
static char rcsid[] = "$Id: chfactor.c,v 1.2 1994/01/13 05:36:36 des Exp $";
#include <stdio.h>
#include "matrix.h"
#include "matrix2.h"
#include <math.h>
/* Most matrix factorisation routines are in-situ unless otherwise specified */
/* CHfactor -- Cholesky L.L' factorisation of A in-situ */
MAT *CHfactor(A)
MAT *A;
{
u_int i, j, k, n;
Real **A_ent, *A_piv, *A_row, sum, tmp;
if ( A==(MAT *)NULL )
error(E_NULL,"CHfactor");
if ( A->m != A->n )
error(E_SQUARE,"CHfactor");
n = A->n; A_ent = A->me;
for ( k=0; k<n; k++ )
{
/* do diagonal element */
sum = A_ent[k][k];
A_piv = A_ent[k];
for ( j=0; j<k; j++ )
{
/* tmp = A_ent[k][j]; */
tmp = *A_piv++;
sum -= tmp*tmp;
}
if ( sum <= 0.0 )
error(E_POSDEF,"CHfactor");
A_ent[k][k] = sqrt(sum);
/* set values of column k */
for ( i=k+1; i<n; i++ )
{
sum = A_ent[i][k];
A_piv = A_ent[k];
A_row = A_ent[i];
sum -= __ip__(A_row,A_piv,(int)k);
/************************************************
for ( j=0; j<k; j++ )
sum -= A_ent[i][j]*A_ent[k][j];
sum -= (*A_row++)*(*A_piv++);
************************************************/
A_ent[j][i] = A_ent[i][j] = sum/A_ent[k][k];
}
}
return (A);
}
/* CHsolve -- given a CHolesky factorisation in A, solve A.x=b */
VEC *CHsolve(A,b,x)
MAT *A;
VEC *b,*x;
{
if ( A==(MAT *)NULL || b==(VEC *)NULL )
error(E_NULL,"CHsolve");
if ( A->m != A->n || A->n != b->dim )
error(E_SIZES,"CHsolve");
x = v_resize(x,b->dim);
Lsolve(A,b,x,0.0);
Usolve(A,x,x,0.0);
return (x);
}
/* LDLfactor -- L.D.L' factorisation of A in-situ */
MAT *LDLfactor(A)
MAT *A;
{
u_int i, k, n, p;
Real **A_ent;
Real d, sum;
static VEC *r = VNULL;
if ( ! A )
error(E_NULL,"LDLfactor");
if ( A->m != A->n )
error(E_SQUARE,"LDLfactor");
n = A->n; A_ent = A->me;
r = v_resize(r,n);
MEM_STAT_REG(r,TYPE_VEC);
for ( k = 0; k < n; k++ )
{
sum = 0.0;
for ( p = 0; p < k; p++ )
{
r->ve[p] = A_ent[p][p]*A_ent[k][p];
sum += r->ve[p]*A_ent[k][p];
}
d = A_ent[k][k] -= sum;
if ( d == 0.0 )
error(E_SING,"LDLfactor");
for ( i = k+1; i < n; i++ )
{
sum = __ip__(A_ent[i],r->ve,(int)k);
/****************************************
sum = 0.0;
for ( p = 0; p < k; p++ )
sum += A_ent[i][p]*r->ve[p];
****************************************/
A_ent[i][k] = (A_ent[i][k] - sum)/d;
}
}
return A;
}
VEC *LDLsolve(LDL,b,x)
MAT *LDL;
VEC *b, *x;
{
if ( ! LDL || ! b )
error(E_NULL,"LDLsolve");
if ( LDL->m != LDL->n )
error(E_SQUARE,"LDLsolve");
if ( LDL->m != b->dim )
error(E_SIZES,"LDLsolve");
x = v_resize(x,b->dim);
Lsolve(LDL,b,x,1.0);
Dsolve(LDL,x,x);
LTsolve(LDL,x,x,1.0);
return x;
}
/* MCHfactor -- Modified Cholesky L.L' factorisation of A in-situ */
MAT *MCHfactor(A,tol)
MAT *A;
double tol;
{
u_int i, j, k, n;
Real **A_ent, *A_piv, *A_row, sum, tmp;
if ( A==(MAT *)NULL )
error(E_NULL,"MCHfactor");
if ( A->m != A->n )
error(E_SQUARE,"MCHfactor");
if ( tol <= 0.0 )
error(E_RANGE,"MCHfactor");
n = A->n; A_ent = A->me;
for ( k=0; k<n; k++ )
{
/* do diagonal element */
sum = A_ent[k][k];
A_piv = A_ent[k];
for ( j=0; j<k; j++ )
{
/* tmp = A_ent[k][j]; */
tmp = *A_piv++;
sum -= tmp*tmp;
}
if ( sum <= tol )
sum = tol;
A_ent[k][k] = sqrt(sum);
/* set values of column k */
for ( i=k+1; i<n; i++ )
{
sum = A_ent[i][k];
A_piv = A_ent[k];
A_row = A_ent[i];
sum -= __ip__(A_row,A_piv,(int)k);
/************************************************
for ( j=0; j<k; j++ )
sum -= A_ent[i][j]*A_ent[k][j];
sum -= (*A_row++)*(*A_piv++);
************************************************/
A_ent[j][i] = A_ent[i][j] = sum/A_ent[k][k];
}
}
return (A);
}
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