/* $Id: matrix.c,v 1.8 2003/04/07 16:27:10 ukai Exp $ */
/*
* matrix.h, matrix.c: Liner equation solver using LU decomposition.
*
* by K.Okabe Aug. 1999
*
* LUfactor, LUsolve, Usolve and Lsolve, are based on the functions in
* Meschach Library Version 1.2b.
*/
/**************************************************************************
**
** 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.
**
***************************************************************************/
#include "config.h"
#include "matrix.h"
#include "alloc.h"
/*
* Macros from "fm.h".
*/
#define SWAPD(a,b) { double tmp = a; a = b; b = tmp; }
#define SWAPI(a,b) { int tmp = a; a = b; b = tmp; }
#ifdef HAVE_FLOAT_H
#include <float.h>
#endif /* not HAVE_FLOAT_H */
#if defined(DBL_MAX)
static double Tiny = 10.0 / DBL_MAX;
#elif defined(FLT_MAX)
static double Tiny = 10.0 / FLT_MAX;
#else /* not defined(FLT_MAX) */
static double Tiny = 1.0e-30;
#endif /* not defined(FLT_MAX */
/*
* LUfactor -- gaussian elimination with scaled partial pivoting
* -- Note: returns LU matrix which is A.
*/
int
LUfactor(Matrix A, int *indexarray)
{
int dim = A->dim, i, j, k, i_max, k_max;
Vector scale;
double mx, tmp;
scale = new_vector(dim);
for (i = 0; i < dim; i++)
indexarray[i] = i;
for (i = 0; i < dim; i++) {
mx = 0.;
for (j = 0; j < dim; j++) {
tmp = fabs(M_VAL(A, i, j));
if (mx < tmp)
mx = tmp;
}
scale->ve[i] = mx;
}
k_max = dim - 1;
for (k = 0; k < k_max; k++) {
mx = 0.;
i_max = -1;
for (i = k; i < dim; i++) {
if (fabs(scale->ve[i]) >= Tiny * fabs(M_VAL(A, i, k))) {
tmp = fabs(M_VAL(A, i, k)) / scale->ve[i];
if (mx < tmp) {
mx = tmp;
i_max = i;
}
}
}
if (i_max == -1) {
M_VAL(A, k, k) = 0.;
continue;
}
if (i_max != k) {
SWAPI(indexarray[i_max], indexarray[k]);
for (j = 0; j < dim; j++)
SWAPD(M_VAL(A, i_max, j), M_VAL(A, k, j));
}
for (i = k + 1; i < dim; i++) {
tmp = M_VAL(A, i, k) = M_VAL(A, i, k) / M_VAL(A, k, k);
for (j = k + 1; j < dim; j++)
M_VAL(A, i, j) -= tmp * M_VAL(A, k, j);
}
}
return 0;
}
/*
* LUsolve -- given an LU factorisation in A, solve Ax=b.
*/
int
LUsolve(Matrix A, int *indexarray, Vector b, Vector x)
{
int i, dim = A->dim;
for (i = 0; i < dim; i++)
x->ve[i] = b->ve[indexarray[i]];
if (Lsolve(A, x, x, 1.) == -1 || Usolve(A, x, x, 0.) == -1)
return -1;
return 0;
}
/* m_inverse -- returns inverse of A, provided A is not too rank deficient
* -- uses LU factorisation */
#if 0
Matrix
m_inverse(Matrix A, Matrix out)
{
int *indexarray = NewAtom_N(int, A->dim);
Matrix A1 = new_matrix(A->dim);
m_copy(A, A1);
LUfactor(A1, indexarray);
return LUinverse(A1, indexarray, out);
}
#endif /* 0 */
Matrix
LUinverse(Matrix A, int *indexarray, Matrix out)
{
int i, j, dim = A->dim;
Vector tmp, tmp2;
if (!out)
out = new_matrix(dim);
tmp = new_vector(dim);
tmp2 = new_vector(dim);
for (i = 0; i < dim; i++) {
for (j = 0; j < dim; j++)
tmp->ve[j] = 0.;
tmp->ve[i] = 1.;
if (LUsolve(A, indexarray, tmp, tmp2) == -1)
return NULL;
for (j = 0; j < dim; j++)
M_VAL(out, j, i) = tmp2->ve[j];
}
return out;
}
/*
* Usolve -- back substitution with optional over-riding diagonal
* -- can be in-situ but doesn't need to be.
*/
int
Usolve(Matrix mat, Vector b, Vector out, double diag)
{
int i, j, i_lim, dim = mat->dim;
double sum;
for (i = dim - 1; i >= 0; i--) {
if (b->ve[i] != 0.)
break;
else
out->ve[i] = 0.;
}
i_lim = i;
for (; i >= 0; i--) {
sum = b->ve[i];
for (j = i + 1; j <= i_lim; j++)
sum -= M_VAL(mat, i, j) * out->ve[j];
if (diag == 0.) {
if (fabs(M_VAL(mat, i, i)) <= Tiny * fabs(sum))
return -1;
else
out->ve[i] = sum / M_VAL(mat, i, i);
}
else
out->ve[i] = sum / diag;
}
return 0;
}
/*
* Lsolve -- forward elimination with (optional) default diagonal value.
*/
int
Lsolve(Matrix mat, Vector b, Vector out, double diag)
{
int i, j, i_lim, dim = mat->dim;
double sum;
for (i = 0; i < dim; i++) {
if (b->ve[i] != 0.)
break;
else
out->ve[i] = 0.;
}
i_lim = i;
for (; i < dim; i++) {
sum = b->ve[i];
for (j = i_lim; j < i; j++)
sum -= M_VAL(mat, i, j) * out->ve[j];
if (diag == 0.) {
if (fabs(M_VAL(mat, i, i)) <= Tiny * fabs(sum))
return -1;
else
out->ve[i] = sum / M_VAL(mat, i, i);
}
else
out->ve[i] = sum / diag;
}
return 0;
}
/*
* new_matrix -- generate a nxn matrix.
*/
Matrix
new_matrix(int n)
{
Matrix mat;
mat = New(struct matrix);
mat->dim = n;
mat->me = NewAtom_N(double, n * n);
return mat;
}
/*
* new_matrix -- generate a n-dimension vector.
*/
Vector
new_vector(int n)
{
Vector vec;
vec = New(struct vector);
vec->dim = n;
vec->ve = NewAtom_N(double, n);
return vec;
}
