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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.
Complex case
*/
static char rcsid[] = "$Id: zsolve.c,v 1.1 1994/01/13 04:20:33 des Exp $";
#include <stdio.h>
#include "zmatrix2.h"
#include <math.h>
#define is_zero(z) ((z).re == 0.0 && (z).im == 0.0 )
/* Most matrix factorisation routines are in-situ unless otherwise specified */
/* zUsolve -- back substitution with optional over-riding diagonal
-- can be in-situ but doesn't need to be */
ZVEC *zUsolve(matrix,b,out,diag)
ZMAT *matrix;
ZVEC *b, *out;
double diag;
{
u_int dim /* , j */;
int i, i_lim;
complex **mat_ent, *mat_row, *b_ent, *out_ent, *out_col, sum;
if ( matrix==ZMNULL || b==ZVNULL )
error(E_NULL,"zUsolve");
dim = min(matrix->m,matrix->n);
if ( b->dim < dim )
error(E_SIZES,"zUsolve");
if ( out==ZVNULL || out->dim < dim )
out = zv_resize(out,matrix->n);
mat_ent = matrix->me; b_ent = b->ve; out_ent = out->ve;
for ( i=dim-1; i>=0; i-- )
if ( ! is_zero(b_ent[i]) )
break;
else
out_ent[i].re = out_ent[i].im = 0.0;
i_lim = i;
for ( i = i_lim; i>=0; i-- )
{
sum = b_ent[i];
mat_row = &(mat_ent[i][i+1]);
out_col = &(out_ent[i+1]);
sum = zsub(sum,__zip__(mat_row,out_col,i_lim-i,Z_NOCONJ));
/******************************************************
for ( j=i+1; j<=i_lim; j++ )
sum -= mat_ent[i][j]*out_ent[j];
sum -= (*mat_row++)*(*out_col++);
******************************************************/
if ( diag == 0.0 )
{
if ( is_zero(mat_ent[i][i]) )
error(E_SING,"zUsolve");
else
/* out_ent[i] = sum/mat_ent[i][i]; */
out_ent[i] = zdiv(sum,mat_ent[i][i]);
}
else
{
/* out_ent[i] = sum/diag; */
out_ent[i].re = sum.re / diag;
out_ent[i].im = sum.im / diag;
}
}
return (out);
}
/* zLsolve -- forward elimination with (optional) default diagonal value */
ZVEC *zLsolve(matrix,b,out,diag)
ZMAT *matrix;
ZVEC *b,*out;
double diag;
{
u_int dim, i, i_lim /* , j */;
complex **mat_ent, *mat_row, *b_ent, *out_ent, *out_col, sum;
if ( matrix==ZMNULL || b==ZVNULL )
error(E_NULL,"zLsolve");
dim = min(matrix->m,matrix->n);
if ( b->dim < dim )
error(E_SIZES,"zLsolve");
if ( out==ZVNULL || out->dim < dim )
out = zv_resize(out,matrix->n);
mat_ent = matrix->me; b_ent = b->ve; out_ent = out->ve;
for ( i=0; i<dim; i++ )
if ( ! is_zero(b_ent[i]) )
break;
else
out_ent[i].re = out_ent[i].im = 0.0;
i_lim = i;
for ( i = i_lim; i<dim; i++ )
{
sum = b_ent[i];
mat_row = &(mat_ent[i][i_lim]);
out_col = &(out_ent[i_lim]);
sum = zsub(sum,__zip__(mat_row,out_col,(int)(i-i_lim),Z_NOCONJ));
/*****************************************************
for ( j=i_lim; j<i; j++ )
sum -= mat_ent[i][j]*out_ent[j];
sum -= (*mat_row++)*(*out_col++);
******************************************************/
if ( diag == 0.0 )
{
if ( is_zero(mat_ent[i][i]) )
error(E_SING,"zLsolve");
else
out_ent[i] = zdiv(sum,mat_ent[i][i]);
}
else
{
out_ent[i].re = sum.re / diag;
out_ent[i].im = sum.im / diag;
}
}
return (out);
}
/* zUAsolve -- forward elimination with (optional) default diagonal value
using UPPER triangular part of matrix */
ZVEC *zUAsolve(U,b,out,diag)
ZMAT *U;
ZVEC *b,*out;
double diag;
{
u_int dim, i, i_lim /* , j */;
complex **U_me, *b_ve, *out_ve, tmp;
Real invdiag;
if ( ! U || ! b )
error(E_NULL,"zUAsolve");
dim = min(U->m,U->n);
if ( b->dim < dim )
error(E_SIZES,"zUAsolve");
out = zv_resize(out,U->n);
U_me = U->me; b_ve = b->ve; out_ve = out->ve;
for ( i=0; i<dim; i++ )
if ( ! is_zero(b_ve[i]) )
break;
else
out_ve[i].re = out_ve[i].im = 0.0;
i_lim = i;
if ( b != out )
{
__zzero__(out_ve,out->dim);
/* MEM_COPY(&(b_ve[i_lim]),&(out_ve[i_lim]),
(dim-i_lim)*sizeof(complex)); */
MEMCOPY(&(b_ve[i_lim]),&(out_ve[i_lim]),dim-i_lim,complex);
}
if ( diag == 0.0 )
{
for ( ; i<dim; i++ )
{
tmp = zconj(U_me[i][i]);
if ( is_zero(tmp) )
error(E_SING,"zUAsolve");
/* out_ve[i] /= tmp; */
out_ve[i] = zdiv(out_ve[i],tmp);
tmp.re = - out_ve[i].re;
tmp.im = - out_ve[i].im;
__zmltadd__(&(out_ve[i+1]),&(U_me[i][i+1]),tmp,dim-i-1,Z_CONJ);
}
}
else
{
invdiag = 1.0/diag;
for ( ; i<dim; i++ )
{
out_ve[i].re *= invdiag;
out_ve[i].im *= invdiag;
tmp.re = - out_ve[i].re;
tmp.im = - out_ve[i].im;
__zmltadd__(&(out_ve[i+1]),&(U_me[i][i+1]),tmp,dim-i-1,Z_CONJ);
}
}
return (out);
}
/* zDsolve -- solves Dx=b where D is the diagonal of A -- may be in-situ */
ZVEC *zDsolve(A,b,x)
ZMAT *A;
ZVEC *b,*x;
{
u_int dim, i;
if ( ! A || ! b )
error(E_NULL,"zDsolve");
dim = min(A->m,A->n);
if ( b->dim < dim )
error(E_SIZES,"zDsolve");
x = zv_resize(x,A->n);
dim = b->dim;
for ( i=0; i<dim; i++ )
if ( is_zero(A->me[i][i]) )
error(E_SING,"zDsolve");
else
x->ve[i] = zdiv(b->ve[i],A->me[i][i]);
return (x);
}
/* zLAsolve -- back substitution with optional over-riding diagonal
using the LOWER triangular part of matrix
-- can be in-situ but doesn't need to be */
ZVEC *zLAsolve(L,b,out,diag)
ZMAT *L;
ZVEC *b, *out;
double diag;
{
u_int dim;
int i, i_lim;
complex **L_me, *b_ve, *out_ve, tmp;
Real invdiag;
if ( ! L || ! b )
error(E_NULL,"zLAsolve");
dim = min(L->m,L->n);
if ( b->dim < dim )
error(E_SIZES,"zLAsolve");
out = zv_resize(out,L->n);
L_me = L->me; b_ve = b->ve; out_ve = out->ve;
for ( i=dim-1; i>=0; i-- )
if ( ! is_zero(b_ve[i]) )
break;
i_lim = i;
if ( b != out )
{
__zzero__(out_ve,out->dim);
/* MEM_COPY(b_ve,out_ve,(i_lim+1)*sizeof(complex)); */
MEMCOPY(b_ve,out_ve,i_lim+1,complex);
}
if ( diag == 0.0 )
{
for ( ; i>=0; i-- )
{
tmp = zconj(L_me[i][i]);
if ( is_zero(tmp) )
error(E_SING,"zLAsolve");
out_ve[i] = zdiv(out_ve[i],tmp);
tmp.re = - out_ve[i].re;
tmp.im = - out_ve[i].im;
__zmltadd__(out_ve,L_me[i],tmp,i,Z_CONJ);
}
}
else
{
invdiag = 1.0/diag;
for ( ; i>=0; i-- )
{
out_ve[i].re *= invdiag;
out_ve[i].im *= invdiag;
tmp.re = - out_ve[i].re;
tmp.im = - out_ve[i].im;
__zmltadd__(out_ve,L_me[i],tmp,i,Z_CONJ);
}
}
return (out);
}
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