zsolve.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.
    Complex case
*/

static  char    rcsid[] = "zsolve.c,v 1.1 1997/12/04 17:56:17 hines 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);
}