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solve.c
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solve.c
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/*
* Copyright (c) 2012, Richard P. Curnow
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the <organization> nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
* */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "tool.h"
static void reduce(Matrix m, int n, long double *r)
{
int i, j, k;
int ii;
long double t, scale;
for (i=0; i<n; i++) {
ii = -1;
for (j=i+1; j<n; j++) {
if (fabs(m[j][i] > fabs(m[i][i]))) {
ii = j;
}
}
if (ii > i) {
/* swap */
for (k=i; k<n; k++) {
t = m[ii][k];
m[ii][k] = m[i][k];
m[i][k] = t;
}
t = r[ii];
r[ii] = r[i];
r[i] = t;
}
/* Now subtract multiples of row i from the rows below */
for (j=i+1; j<n; j++) {
if (m[i][i] == 0.0) {
printf("scale is 0 at %d,%d\n", i, i);
exit(1);
}
scale = m[j][i] / m[i][i];
for (k=i; k<n; k++) {
m[j][k] -= scale * m[i][k];
}
r[j] -= scale * r[i];
}
}
}
static void backfill(Matrix m, int n, long double *l, long double *r)
{
int i, j;
for (i=n-1; i>=0; i--) {
long double t;
t = r[i];
for (j=i+1; j<n; j++) {
t -= m[i][j] * l[j];
}
l[i] = t / m[i][i];
}
}
void solve(Matrix m, int n, long double *l, long double *r)
{
/* Row reduction with partial pivot */
reduce(m, n, r);
backfill(m, n, l, r);
}