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/* poly/balance.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
*
* 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
static void balance_companion_matrix (double *m, size_t n);
#define RADIX 2
#define RADIX2 (RADIX*RADIX)
static void
balance_companion_matrix (double *m, size_t nc)
{
int not_converged = 1;
double row_norm = 0;
double col_norm = 0;
while (not_converged)
{
size_t i, j;
double g, f, s;
not_converged = 0;
for (i = 0; i < nc; i++)
{
/* column norm, excluding the diagonal */
if (i != nc - 1)
{
col_norm = fabs (MAT (m, i + 1, i, nc));
}
else
{
col_norm = 0;
for (j = 0; j < nc - 1; j++)
{
col_norm += fabs (MAT (m, j, nc - 1, nc));
}
}
/* row norm, excluding the diagonal */
if (i == 0)
{
row_norm = fabs (MAT (m, 0, nc - 1, nc));
}
else if (i == nc - 1)
{
row_norm = fabs (MAT (m, i, i - 1, nc));
}
else
{
row_norm = (fabs (MAT (m, i, i - 1, nc))
+ fabs (MAT (m, i, nc - 1, nc)));
}
if (col_norm == 0 || row_norm == 0)
{
continue;
}
g = row_norm / RADIX;
f = 1;
s = col_norm + row_norm;
while (col_norm < g)
{
f *= RADIX;
col_norm *= RADIX2;
}
g = row_norm * RADIX;
while (col_norm > g)
{
f /= RADIX;
col_norm /= RADIX2;
}
if ((row_norm + col_norm) < 0.95 * s * f)
{
not_converged = 1;
g = 1 / f;
if (i == 0)
{
MAT (m, 0, nc - 1, nc) *= g;
}
else
{
MAT (m, i, i - 1, nc) *= g;
MAT (m, i, nc - 1, nc) *= g;
}
if (i == nc - 1)
{
for (j = 0; j < nc; j++)
{
MAT (m, j, i, nc) *= f;
}
}
else
{
MAT (m, i + 1, i, nc) *= f;
}
}
}
}
}
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