void glp_unscale_prob(glp_prob *lp)
{ int m = glp_get_num_rows(lp);
int n = glp_get_num_cols(lp);
int i, j;
for (i = 1; i <= m; i++) glp_set_rii(lp, i, 1.0);
for (j = 1; j <= n; j++) glp_set_sjj(lp, j, 1.0);
return;
}
static void scale_prob(glp_prob *lp, int flags)
{ static const char *fmt =
"%s: min|aij| = %10.3e max|aij| = %10.3e ratio = %10.3e\n";
double min_aij, max_aij, ratio;
xprintf("Scaling...\n");
/* cancel the current scaling effect */
glp_unscale_prob(lp);
/* report original scaling "quality" */
min_aij = min_mat_aij(lp, 1);
max_aij = max_mat_aij(lp, 1);
ratio = max_aij / min_aij;
xprintf(fmt, " A", min_aij, max_aij, ratio);
/* check if the problem is well scaled */
if (min_aij >= 0.10 && max_aij <= 10.0)
{ xprintf("Problem data seem to be well scaled\n");
/* skip scaling, if required */
if (flags & GLP_SF_SKIP) goto done;
}
/* perform iterative geometric mean scaling, if required */
if (flags & GLP_SF_GM)
{ gm_iterate(lp, 15, 0.90);
min_aij = min_mat_aij(lp, 1);
max_aij = max_mat_aij(lp, 1);
ratio = max_aij / min_aij;
xprintf(fmt, "GM", min_aij, max_aij, ratio);
}
/* perform equilibration scaling, if required */
if (flags & GLP_SF_EQ)
{ eq_scaling(lp, max_row_ratio(lp) > max_col_ratio(lp));
min_aij = min_mat_aij(lp, 1);
max_aij = max_mat_aij(lp, 1);
ratio = max_aij / min_aij;
xprintf(fmt, "EQ", min_aij, max_aij, ratio);
}
/* round scale factors to nearest power of two, if required */
if (flags & GLP_SF_2N)
{ int i, j;
for (i = 1; i <= lp->m; i++)
glp_set_rii(lp, i, round2n(glp_get_rii(lp, i)));
for (j = 1; j <= lp->n; j++)
glp_set_sjj(lp, j, round2n(glp_get_sjj(lp, j)));
min_aij = min_mat_aij(lp, 1);
max_aij = max_mat_aij(lp, 1);
ratio = max_aij / min_aij;
xprintf(fmt, "2N", min_aij, max_aij, ratio);
}
done: return;
}
static void gm_scaling(glp_prob *lp, int flag)
{ int i, j, pass;
double temp;
xassert(flag == 0 || flag == 1);
for (pass = 0; pass <= 1; pass++)
{ if (pass == flag)
{ /* scale rows */
for (i = 1; i <= lp->m; i++)
{ temp = min_row_aij(lp, i, 1) * max_row_aij(lp, i, 1);
glp_set_rii(lp, i, glp_get_rii(lp, i) / sqrt(temp));
}
}
else
{ /* scale columns */
for (j = 1; j <= lp->n; j++)
{ temp = min_col_aij(lp, j, 1) * max_col_aij(lp, j, 1);
glp_set_sjj(lp, j, glp_get_sjj(lp, j) / sqrt(temp));
}
}
}
return;
}