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/*
* Matrix operations library
*
* Copyright (C) 1999-2000
* Thomas Sailer, <sailer@ife.ee.ethz.ch>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
/* AIX requires this to be the first thing in the file. */
#ifndef __GNUC__
# if HAVE_ALLOCA_H
# include <alloca.h>
# else
# ifdef _AIX
#pragma alloca
# else
# ifndef alloca /* predefined by HP cc +Olibcalls */
char *alloca ();
# endif
# endif
# endif
#endif
#include <math.h>
#include <string.h>
#include "mat.h"
/*
* Golub/van Loan, 3.1.3, p 112; PA=LU factorization with partial pivoting
*/
#define exch(x,y) do { float z; z = (x); (x) = (y); (y) = z; } while (0)
void frlufact(float *u, unsigned int *p, const float *a, unsigned int d)
{
unsigned int i, j, k, mu;
float f1, f2;
if (u != a)
memcpy(u, a, d*d*sizeof(u[0]));
for (k = 0; k < d-1; k++) {
/* search pivot index */
for (f1 = 0, i = mu = k; i < d; i++) {
f2 = fabs(u[i*d+k]);
if (f2 > f1) {
f1 = f2;
mu = i;
}
}
/* exchange rows */
p[k] = mu;
for (i = k; i < d; i++)
exch(u[k*d+i], u[mu*d+i]);
f1 = u[k*d+k];
if (f1 != 0) {
f1 = 1 / f1;
for (i = k+1; i < d; i++)
u[i*d+k] *= f1;
for (i = k+1; i < d; i++)
for (j = k+1; j < d; j++)
u[i*d+j] -= u[i*d+k] * u[k*d+j];
}
}
}
void frlusolve(float *x, const float *b, const float *u, const unsigned int *p, unsigned int d)
{
float *y, s;
unsigned int k, i;
y = alloca(d * sizeof(y[0]));
memcpy(y, b, d * sizeof(y[0]));
for (k = 0; k < d-1; k++) {
i = p[k];
if (i != k)
exch(y[k], y[i]);
if (y[k] == 0)
continue;
for (i = k+1; i < d; i++)
y[i] -= y[k] * u[i*d+k];
}
/* solve Ux=y */
for (k = d; k > 0; k--) {
s = y[k-1];
for (i = k; i < d; i++)
s -= u[(k-1)*d+i] * x[i];
x[k-1] = s / u[(k-1)*d+(k-1)];
}
}
void frinv(float *ainv, const float *a, unsigned d)
{
float *u, *y;
unsigned int *p;
unsigned int k;
u = alloca(d * d * sizeof(u[0]));
p = alloca((d-1) * sizeof(p[0]));
frlufact(u, p, a, d);
for (k = 0; k < d; k++) {
y = &ainv[k*d];
memset(y, 0, d * sizeof(y[0]));
y[k] = 1;
frlusolve(y, y, u, p, d);
}
frtranspose(ainv, ainv, d, d);
}
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