void lpx_get_col_info(glp_prob *lp, int j, int *tagx, double *vx,
double *dx)
{ /* obtain column solution information */
if (tagx != NULL) *tagx = lpx_get_col_stat(lp, j);
if (vx != NULL) *vx = lpx_get_col_prim(lp, j);
if (dx != NULL) *dx = lpx_get_col_dual(lp, j);
return;
}
int lpx_dual_ratio_test(LPX *lp, int len, const int ind[],
const double val[], int how, double tol)
{ int k, m, n, t, q, tagx;
double dir, alfa_j, abs_alfa_j, big, eps, cbar_j, temp, teta;
if (!lpx_is_b_avail(lp))
xfault("lpx_dual_ratio_test: LP basis is not available\n");
if (lpx_get_dual_stat(lp) != LPX_D_FEAS)
xfault("lpx_dual_ratio_test: current basic solution is not dua"
"l feasible\n");
if (!(how == +1 || how == -1))
xfault("lpx_dual_ratio_test: how = %d; invalid parameter\n",
how);
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
dir = (lpx_get_obj_dir(lp) == LPX_MIN ? +1.0 : -1.0);
/* compute the largest absolute value of the specified influence
coefficients */
big = 0.0;
for (t = 1; t <= len; t++)
{ temp = val[t];
if (temp < 0.0) temp = - temp;
if (big < temp) big = temp;
}
/* compute the absolute tolerance eps used to skip small entries
of the row */
if (!(0.0 < tol && tol < 1.0))
xfault("lpx_dual_ratio_test: tol = %g; invalid tolerance\n",
tol);
eps = tol * (1.0 + big);
/* initial settings */
q = 0, teta = DBL_MAX, big = 0.0;
/* walk through the entries of the specified row */
for (t = 1; t <= len; t++)
{ /* get ordinal number of non-basic variable */
k = ind[t];
if (!(1 <= k && k <= m+n))
xfault("lpx_dual_ratio_test: ind[%d] = %d; variable number "
"out of range\n", t, k);
if (k <= m)
tagx = lpx_get_row_stat(lp, k);
else
tagx = lpx_get_col_stat(lp, k-m);
if (tagx == LPX_BS)
xfault("lpx_dual_ratio_test: ind[%d] = %d; basic variable n"
"ot allowed\n", t, k);
/* determine unscaled reduced cost of the non-basic variable
x[k] = xN[j] in the current basic solution */
if (k <= m)
cbar_j = lpx_get_row_dual(lp, k);
else
cbar_j = lpx_get_col_dual(lp, k-m);
/* determine influence coefficient at the non-basic variable
x[k] = xN[j] in the explicitly specified row and turn to
the case of increasing the variable y in order to simplify
program logic */
alfa_j = (how > 0 ? +val[t] : -val[t]);
abs_alfa_j = (alfa_j > 0.0 ? +alfa_j : -alfa_j);
/* analyze main cases */
switch (tagx)
{ case LPX_NL:
/* xN[j] is on its lower bound */
if (alfa_j < +eps) continue;
temp = (dir * cbar_j) / alfa_j;
break;
case LPX_NU:
/* xN[j] is on its upper bound */
if (alfa_j > -eps) continue;
temp = (dir * cbar_j) / alfa_j;
break;
case LPX_NF:
/* xN[j] is non-basic free variable */
if (abs_alfa_j < eps) continue;
temp = 0.0;
break;
case LPX_NS:
/* xN[j] is non-basic fixed variable */
continue;
default:
xassert(tagx != tagx);
}
/* if the reduced cost of the variable xN[j] violates its zero
bound (slightly, because the current basis is assumed to be
dual feasible), temp is negative; we can think this happens
due to round-off errors and the reduced cost is exact zero;
this allows replacing temp by zero */
if (temp < 0.0) temp = 0.0;
/* apply the minimal ratio test */
if (teta > temp || teta == temp && big < abs_alfa_j)
q = k, teta = temp, big = abs_alfa_j;
}
/* return the ordinal number of the chosen non-basic variable */
return q;
}
double lpx_eval_degrad(LPX *lp, int len, int ind[], double val[],
int type, double rhs)
{ int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int dir = lpx_get_obj_dir(lp);
int q, k;
double y, delta;
if (lpx_get_dual_stat(lp) != LPX_D_FEAS)
fault("lpx_eval_degrad: LP basis is not dual feasible");
if (!(0 <= len && len <= n))
fault("lpx_eval_degrad: len = %d; invalid row length", len);
if (!(type == LPX_LO || type == LPX_UP))
fault("lpx_eval_degrad: type = %d; invalid row type", type);
/* compute value of the row auxiliary variable */
y = lpx_eval_row(lp, len, ind, val);
/* the inequalitiy constraint is assumed to be violated */
if (!(type == LPX_LO && y < rhs || type == LPX_UP && y > rhs))
fault("lpx_eval_degrad: y = %g, rhs = %g; constraint is not vi"
"olated", y, rhs);
/* transform the row in order to express y through only non-basic
variables: y = alfa[1] * xN[1] + ... + alfa[n] * xN[n] */
len = lpx_transform_row(lp, len, ind, val);
/* in the adjacent basis y would become non-basic, so in case of
'>=' it increases and in case of '<=' it decreases; determine
which non-basic variable x[q], 1 <= q <= m+n, should leave the
basis to keep dual feasibility */
q = lpx_dual_ratio_test(lp, len, ind, val,
type == LPX_LO ? +1 : -1, 1e-7);
/* q = 0 means no adjacent dual feasible basis exist */
if (q == 0) return dir == LPX_MIN ? +DBL_MAX : -DBL_MAX;
/* find the entry corresponding to x[q] in the list */
for (k = 1; k <= len; k++)
if (ind[k] == q) break;
insist(k <= len);
/* dy = alfa[q] * dx[q], so dx[q] = dy / alfa[q], where dy is a
change in y, dx[q] is a change in x[q] */
delta = (rhs - y) / val[k];
#if 0
/* Tomlin noticed that if the variable x[q] is of integer kind,
its change cannot be less than one in the magnitude */
if (q > m && lpx_get_col_kind(lp, q-m) == LPX_IV)
{ /* x[q] is structural integer variable */
if (fabs(delta - floor(delta + 0.5)) > 1e-3)
{ if (delta > 0.0)
delta = ceil(delta); /* +3.14 -> +4 */
else
delta = floor(delta); /* -3.14 -> -4 */
}
}
#endif
/* dz = lambda[q] * dx[q], where dz is a change in the objective
function, lambda[q] is a reduced cost of x[q] */
if (q <= m)
delta *= lpx_get_row_dual(lp, q);
else
delta *= lpx_get_col_dual(lp, q-m);
/* delta must be >= 0 (in case of minimization) or <= 0 (in case
of minimization); however, due to round-off errors and finite
tolerance used to choose x[q], this condition can be slightly
violated */
switch (dir)
{ case LPX_MIN: if (delta < 0.0) delta = 0.0; break;
case LPX_MAX: if (delta > 0.0) delta = 0.0; break;
default: insist(dir != dir);
}
return delta;
}