void lpx_eval_b_dual(LPX *lp, double row_dual[], double col_dual[])
{ int i, j, k, m, n, len, *ind;
double dj, *cB, *pi, *val;
if (!lpx_is_b_avail(lp))
xfault("lpx_eval_b_dual: LP basis is not available\n");
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* store zero reduced costs of basic auxiliary and structural
variables and build the vector cB of objective coefficients at
basic variables */
cB = xcalloc(1+m, sizeof(double));
for (i = 1; i <= m; i++)
{ k = lpx_get_b_info(lp, i);
/* xB[i] is k-th original variable */
xassert(1 <= k && k <= m+n);
if (k <= m)
{ row_dual[k] = 0.0;
cB[i] = 0.0;
}
else
{ col_dual[k-m] = 0.0;
cB[i] = lpx_get_obj_coef(lp, k-m);
}
}
/* solve the system B'*pi = cB to compute the vector pi */
pi = cB, lpx_btran(lp, pi);
/* compute reduced costs of non-basic auxiliary variables */
for (i = 1; i <= m; i++)
{ if (lpx_get_row_stat(lp, i) != LPX_BS)
row_dual[i] = - pi[i];
}
/* compute reduced costs of non-basic structural variables */
ind = xcalloc(1+m, sizeof(int));
val = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ if (lpx_get_col_stat(lp, j) != LPX_BS)
{ dj = lpx_get_obj_coef(lp, j);
len = lpx_get_mat_col(lp, j, ind, val);
for (k = 1; k <= len; k++) dj += val[k] * pi[ind[k]];
col_dual[j] = dj;
}
}
xfree(ind);
xfree(val);
xfree(cB);
return;
}
static int mat(void *info, int k, int ndx[], double val[])
{ /* this auxiliary routine obtains a required row or column of the
original constraint matrix */
LPX *lp = info;
int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int i, j, len;
if (k > 0)
{ /* i-th row required */
i = +k;
xassert(1 <= i && i <= m);
len = lpx_get_mat_row(lp, i, ndx, val);
}
else
{ /* j-th column required */
j = -k;
xassert(1 <= j && j <= n);
len = lpx_get_mat_col(lp, j, ndx, val);
}
return len;
}
int lpx_print_prob(LPX *lp, const char *fname)
{ XFILE *fp;
int m, n, mip, i, j, len, t, type, *ndx;
double coef, lb, ub, *val;
char *str, name[255+1];
xprintf("lpx_write_prob: writing problem data to `%s'...\n",
fname);
fp = xfopen(fname, "w");
if (fp == NULL)
{ xprintf("lpx_write_prob: unable to create `%s' - %s\n",
fname, strerror(errno));
goto fail;
}
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
mip = (lpx_get_class(lp) == LPX_MIP);
str = (void *)lpx_get_prob_name(lp);
xfprintf(fp, "Problem: %s\n", str == NULL ? "(unnamed)" : str);
xfprintf(fp, "Class: %s\n", !mip ? "LP" : "MIP");
xfprintf(fp, "Rows: %d\n", m);
if (!mip)
xfprintf(fp, "Columns: %d\n", n);
else
xfprintf(fp, "Columns: %d (%d integer, %d binary)\n",
n, lpx_get_num_int(lp), lpx_get_num_bin(lp));
xfprintf(fp, "Non-zeros: %d\n", lpx_get_num_nz(lp));
xfprintf(fp, "\n");
xfprintf(fp, "*** OBJECTIVE FUNCTION ***\n");
xfprintf(fp, "\n");
switch (lpx_get_obj_dir(lp))
{ case LPX_MIN:
xfprintf(fp, "Minimize:");
break;
case LPX_MAX:
xfprintf(fp, "Maximize:");
break;
default:
xassert(lp != lp);
}
str = (void *)lpx_get_obj_name(lp);
xfprintf(fp, " %s\n", str == NULL ? "(unnamed)" : str);
coef = lpx_get_obj_coef(lp, 0);
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
"(constant term)");
for (i = 1; i <= m; i++)
#if 0
{ coef = lpx_get_row_coef(lp, i);
#else
{ coef = 0.0;
#endif
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
row_name(lp, i, name));
}
for (j = 1; j <= n; j++)
{ coef = lpx_get_obj_coef(lp, j);
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
col_name(lp, j, name));
}
xfprintf(fp, "\n");
xfprintf(fp, "*** ROWS (CONSTRAINTS) ***\n");
ndx = xcalloc(1+n, sizeof(int));
val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ xfprintf(fp, "\n");
xfprintf(fp, "Row %d: %s", i, row_name(lp, i, name));
lpx_get_row_bnds(lp, i, &type, &lb, &ub);
switch (type)
{ case LPX_FR:
xfprintf(fp, " free");
break;
case LPX_LO:
xfprintf(fp, " >= %.*g", DBL_DIG, lb);
break;
case LPX_UP:
xfprintf(fp, " <= %.*g", DBL_DIG, ub);
break;
case LPX_DB:
xfprintf(fp, " >= %.*g <= %.*g", DBL_DIG, lb, DBL_DIG,
ub);
break;
case LPX_FX:
xfprintf(fp, " = %.*g", DBL_DIG, lb);
break;
default:
xassert(type != type);
}
xfprintf(fp, "\n");
#if 0
coef = lpx_get_row_coef(lp, i);
#else
coef = 0.0;
#endif
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
"(objective)");
len = lpx_get_mat_row(lp, i, ndx, val);
for (t = 1; t <= len; t++)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, val[t],
col_name(lp, ndx[t], name));
}
xfree(ndx);
xfree(val);
xfprintf(fp, "\n");
xfprintf(fp, "*** COLUMNS (VARIABLES) ***\n");
ndx = xcalloc(1+m, sizeof(int));
val = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ xfprintf(fp, "\n");
xfprintf(fp, "Col %d: %s", j, col_name(lp, j, name));
if (mip)
{ switch (lpx_get_col_kind(lp, j))
{ case LPX_CV:
break;
case LPX_IV:
xfprintf(fp, " integer");
break;
default:
xassert(lp != lp);
}
}
lpx_get_col_bnds(lp, j, &type, &lb, &ub);
switch (type)
{ case LPX_FR:
xfprintf(fp, " free");
break;
case LPX_LO:
xfprintf(fp, " >= %.*g", DBL_DIG, lb);
break;
case LPX_UP:
xfprintf(fp, " <= %.*g", DBL_DIG, ub);
break;
case LPX_DB:
xfprintf(fp, " >= %.*g <= %.*g", DBL_DIG, lb, DBL_DIG,
ub);
break;
case LPX_FX:
xfprintf(fp, " = %.*g", DBL_DIG, lb);
break;
default:
xassert(type != type);
}
xfprintf(fp, "\n");
coef = lpx_get_obj_coef(lp, j);
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
"(objective)");
len = lpx_get_mat_col(lp, j, ndx, val);
for (t = 1; t <= len; t++)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, val[t],
row_name(lp, ndx[t], name));
}
xfree(ndx);
xfree(val);
xfprintf(fp, "\n");
xfprintf(fp, "End of output\n");
xfflush(fp);
if (xferror(fp))
{ xprintf("lpx_write_prob: write error on `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
xfclose(fp);
return 0;
fail: if (fp != NULL) xfclose(fp);
return 1;
}
#undef row_name
#undef col_name
/*----------------------------------------------------------------------
-- lpx_print_sol - write LP problem solution in printable format.
--
-- *Synopsis*
--
-- #include "glplpx.h"
-- int lpx_print_sol(LPX *lp, char *fname);
--
-- *Description*
--
-- The routine lpx_print_sol writes the current basic solution of an LP
-- problem, which is specified by the pointer lp, to a text file, whose
-- name is the character string fname, in printable format.
--
-- Information reported by the routine lpx_print_sol is intended mainly
-- for visual analysis.
--
-- *Returns*
--
-- If the operation was successful, the routine returns zero. Otherwise
-- the routine prints an error message and returns non-zero. */
int lpx_print_sol(LPX *lp, const char *fname)
{ XFILE *fp;
int what, round;
xprintf(
"lpx_print_sol: writing LP problem solution to `%s'...\n",
fname);
fp = xfopen(fname, "w");
if (fp == NULL)
{ xprintf("lpx_print_sol: can't create `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
/* problem name */
{ const char *name;
name = lpx_get_prob_name(lp);
if (name == NULL) name = "";
xfprintf(fp, "%-12s%s\n", "Problem:", name);
}
/* number of rows (auxiliary variables) */
{ int nr;
nr = lpx_get_num_rows(lp);
xfprintf(fp, "%-12s%d\n", "Rows:", nr);
}
/* number of columns (structural variables) */
{ int nc;
nc = lpx_get_num_cols(lp);
xfprintf(fp, "%-12s%d\n", "Columns:", nc);
}
/* number of non-zeros (constraint coefficients) */
{ int nz;
nz = lpx_get_num_nz(lp);
xfprintf(fp, "%-12s%d\n", "Non-zeros:", nz);
}
/* solution status */
{ int status;
status = lpx_get_status(lp);
xfprintf(fp, "%-12s%s\n", "Status:",
status == LPX_OPT ? "OPTIMAL" :
status == LPX_FEAS ? "FEASIBLE" :
status == LPX_INFEAS ? "INFEASIBLE (INTERMEDIATE)" :
status == LPX_NOFEAS ? "INFEASIBLE (FINAL)" :
status == LPX_UNBND ? "UNBOUNDED" :
status == LPX_UNDEF ? "UNDEFINED" : "???");
}
/* objective function */
{ char *name;
int dir;
double obj;
name = (void *)lpx_get_obj_name(lp);
dir = lpx_get_obj_dir(lp);
obj = lpx_get_obj_val(lp);
xfprintf(fp, "%-12s%s%s%.10g %s\n", "Objective:",
name == NULL ? "" : name,
name == NULL ? "" : " = ", obj,
dir == LPX_MIN ? "(MINimum)" :
dir == LPX_MAX ? "(MAXimum)" : "(" "???" ")");
}
/* main sheet */
for (what = 1; what <= 2; what++)
{ int mn, ij;
xfprintf(fp, "\n");
xfprintf(fp, " No. %-12s St Activity Lower bound Upp"
"er bound Marginal\n",
what == 1 ? " Row name" : "Column name");
xfprintf(fp, "------ ------------ -- ------------- -----------"
"-- ------------- -------------\n");
mn = (what == 1 ? lpx_get_num_rows(lp) : lpx_get_num_cols(lp));
for (ij = 1; ij <= mn; ij++)
{ const char *name;
int typx, tagx;
double lb, ub, vx, dx;
if (what == 1)
{ name = lpx_get_row_name(lp, ij);
if (name == NULL) name = "";
lpx_get_row_bnds(lp, ij, &typx, &lb, &ub);
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
lpx_get_row_info(lp, ij, &tagx, &vx, &dx);
lpx_set_int_parm(lp, LPX_K_ROUND, round);
}
else
{ name = lpx_get_col_name(lp, ij);
if (name == NULL) name = "";
lpx_get_col_bnds(lp, ij, &typx, &lb, &ub);
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
lpx_get_col_info(lp, ij, &tagx, &vx, &dx);
lpx_set_int_parm(lp, LPX_K_ROUND, round);
}
/* row/column ordinal number */
xfprintf(fp, "%6d ", ij);
/* row column/name */
if (strlen(name) <= 12)
xfprintf(fp, "%-12s ", name);
else
xfprintf(fp, "%s\n%20s", name, "");
/* row/column status */
xfprintf(fp, "%s ",
tagx == LPX_BS ? "B " :
tagx == LPX_NL ? "NL" :
tagx == LPX_NU ? "NU" :
tagx == LPX_NF ? "NF" :
tagx == LPX_NS ? "NS" : "??");
/* row/column primal activity */
xfprintf(fp, "%13.6g ", vx);
/* row/column lower bound */
if (typx == LPX_LO || typx == LPX_DB || typx == LPX_FX)
xfprintf(fp, "%13.6g ", lb);
else
xfprintf(fp, "%13s ", "");
/* row/column upper bound */
if (typx == LPX_UP || typx == LPX_DB)
xfprintf(fp, "%13.6g ", ub);
else if (typx == LPX_FX)
xfprintf(fp, "%13s ", "=");
else
xfprintf(fp, "%13s ", "");
/* row/column dual activity */
if (tagx != LPX_BS)
{ if (dx == 0.0)
xfprintf(fp, "%13s", "< eps");
else
xfprintf(fp, "%13.6g", dx);
}
/* end of line */
xfprintf(fp, "\n");
}
}
xfprintf(fp, "\n");
#if 1
if (lpx_get_prim_stat(lp) != LPX_P_UNDEF &&
lpx_get_dual_stat(lp) != LPX_D_UNDEF)
{ int m = lpx_get_num_rows(lp);
LPXKKT kkt;
xfprintf(fp, "Karush-Kuhn-Tucker optimality conditions:\n\n");
lpx_check_kkt(lp, 1, &kkt);
xfprintf(fp, "KKT.PE: max.abs.err. = %.2e on row %d\n",
kkt.pe_ae_max, kkt.pe_ae_row);
xfprintf(fp, " max.rel.err. = %.2e on row %d\n",
kkt.pe_re_max, kkt.pe_re_row);
switch (kkt.pe_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " PRIMAL SOLUTION IS WRONG\n");
break;
}
xfprintf(fp, "\n");
xfprintf(fp, "KKT.PB: max.abs.err. = %.2e on %s %d\n",
kkt.pb_ae_max, kkt.pb_ae_ind <= m ? "row" : "column",
kkt.pb_ae_ind <= m ? kkt.pb_ae_ind : kkt.pb_ae_ind - m);
xfprintf(fp, " max.rel.err. = %.2e on %s %d\n",
kkt.pb_re_max, kkt.pb_re_ind <= m ? "row" : "column",
kkt.pb_re_ind <= m ? kkt.pb_re_ind : kkt.pb_re_ind - m);
switch (kkt.pb_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " PRIMAL SOLUTION IS INFEASIBLE\n");
break;
}
xfprintf(fp, "\n");
xfprintf(fp, "KKT.DE: max.abs.err. = %.2e on column %d\n",
kkt.de_ae_max, kkt.de_ae_col);
xfprintf(fp, " max.rel.err. = %.2e on column %d\n",
kkt.de_re_max, kkt.de_re_col);
switch (kkt.de_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " DUAL SOLUTION IS WRONG\n");
break;
}
xfprintf(fp, "\n");
xfprintf(fp, "KKT.DB: max.abs.err. = %.2e on %s %d\n",
kkt.db_ae_max, kkt.db_ae_ind <= m ? "row" : "column",
kkt.db_ae_ind <= m ? kkt.db_ae_ind : kkt.db_ae_ind - m);
xfprintf(fp, " max.rel.err. = %.2e on %s %d\n",
kkt.db_re_max, kkt.db_re_ind <= m ? "row" : "column",
kkt.db_re_ind <= m ? kkt.db_re_ind : kkt.db_re_ind - m);
switch (kkt.db_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " DUAL SOLUTION IS INFEASIBLE\n");
break;
}
xfprintf(fp, "\n");
}
#endif
#if 1
if (lpx_get_status(lp) == LPX_UNBND)
{ int m = lpx_get_num_rows(lp);
int k = lpx_get_ray_info(lp);
xfprintf(fp, "Unbounded ray: %s %d\n",
k <= m ? "row" : "column", k <= m ? k : k - m);
xfprintf(fp, "\n");
}
#endif
xfprintf(fp, "End of output\n");
xfflush(fp);
if (xferror(fp))
{ xprintf("lpx_print_sol: can't write to `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
xfclose(fp);
return 0;
fail: if (fp != NULL) xfclose(fp);
return 1;
}
int lpx_interior(LPX *_lp)
{ /* easy-to-use driver to the interior-point method */
struct dsa _dsa, *dsa = &_dsa;
int ret, status;
double *row_pval, *row_dval, *col_pval, *col_dval;
/* initialize working area */
dsa->lp = _lp;
dsa->orig_m = lpx_get_num_rows(dsa->lp);
dsa->orig_n = lpx_get_num_cols(dsa->lp);
dsa->ref = NULL;
dsa->m = 0;
dsa->n = 0;
dsa->size = 0;
dsa->ne = 0;
dsa->ia = NULL;
dsa->ja = NULL;
dsa->ar = NULL;
dsa->b = NULL;
dsa->c = NULL;
dsa->x = NULL;
dsa->y = NULL;
dsa->z = NULL;
/* check if the problem is empty */
if (!(dsa->orig_m > 0 && dsa->orig_n > 0))
{ print("lpx_interior: problem has no rows and/or columns");
ret = LPX_E_FAULT;
goto done;
}
/* issue warning about dense columns */
if (dsa->orig_m >= 200)
{ int j, len, ndc = 0;
for (j = 1; j <= dsa->orig_n; j++)
{ len = lpx_get_mat_col(dsa->lp, j, NULL, NULL);
if ((double)len > 0.30 * (double)dsa->orig_m) ndc++;
}
if (ndc == 1)
print("lpx_interior: WARNING: PROBLEM HAS ONE DENSE COLUMN")
;
else if (ndc > 0)
print("lpx_interior: WARNING: PROBLEM HAS %d DENSE COLUMNS",
ndc);
}
/* determine dimension of transformed LP */
print("lpx_interior: original LP problem has %d rows and %d colum"
"ns", dsa->orig_m, dsa->orig_n);
calc_mn(dsa);
print("lpx_interior: transformed LP problem has %d rows and %d co"
"lumns", dsa->m, dsa->n);
/* transform original LP to standard formulation */
dsa->ref = ucalloc(1+dsa->orig_m+dsa->orig_n, sizeof(int));
dsa->size = lpx_get_num_nz(dsa->lp);
if (dsa->size < dsa->m) dsa->size = dsa->m;
if (dsa->size < dsa->n) dsa->size = dsa->n;
dsa->ne = 0;
dsa->ia = ucalloc(1+dsa->size, sizeof(int));
dsa->ja = ucalloc(1+dsa->size, sizeof(int));
dsa->ar = ucalloc(1+dsa->size, sizeof(double));
dsa->b = ucalloc(1+dsa->m, sizeof(double));
dsa->c = ucalloc(1+dsa->n, sizeof(double));
transform(dsa);
/* solve the transformed LP problem */
{ int *A_ptr = ucalloc(1+dsa->m+1, sizeof(int));
int *A_ind = ucalloc(1+dsa->ne, sizeof(int));
double *A_val = ucalloc(1+dsa->ne, sizeof(double));
int i, k, pos, len;
/* determine row lengths */
for (i = 1; i <= dsa->m; i++)
A_ptr[i] = 0;
for (k = 1; k <= dsa->ne; k++)
A_ptr[dsa->ia[k]]++;
/* set up row pointers */
pos = 1;
for (i = 1; i <= dsa->m; i++)
len = A_ptr[i], pos += len, A_ptr[i] = pos;
A_ptr[dsa->m+1] = pos;
insist(pos - 1 == dsa->ne);
/* build the matrix */
for (k = 1; k <= dsa->ne; k++)
{ pos = --A_ptr[dsa->ia[k]];
A_ind[pos] = dsa->ja[k];
A_val[pos] = dsa->ar[k];
}
ufree(dsa->ia), dsa->ia = NULL;
ufree(dsa->ja), dsa->ja = NULL;
ufree(dsa->ar), dsa->ar = NULL;
dsa->x = ucalloc(1+dsa->n, sizeof(double));
dsa->y = ucalloc(1+dsa->m, sizeof(double));
dsa->z = ucalloc(1+dsa->n, sizeof(double));
ret = ipm_main(dsa->m, dsa->n, A_ptr, A_ind, A_val, dsa->b,
dsa->c, dsa->x, dsa->y, dsa->z);
ufree(A_ptr);
ufree(A_ind);
ufree(A_val);
ufree(dsa->b), dsa->b = NULL;
ufree(dsa->c), dsa->c = NULL;
}
/* analyze return code reported by the solver */
switch (ret)
{
case 0:
/* optimal solution found */
ret = LPX_E_OK;
break;
case 1:
/* problem has no feasible (primal or dual) solution */
ret = LPX_E_NOFEAS;
break;
case 2:
/* no convergence */
ret = LPX_E_NOCONV;
break;
case 3:
/* iterations limit exceeded */
ret = LPX_E_ITLIM;
break;
case 4:
/* numerical instability on solving Newtonian system */
ret = LPX_E_INSTAB;
break;
default:
insist(ret != ret);
}
/* recover solution of original LP */
row_pval = ucalloc(1+dsa->orig_m, sizeof(double));
row_dval = ucalloc(1+dsa->orig_m, sizeof(double));
col_pval = ucalloc(1+dsa->orig_n, sizeof(double));
col_dval = ucalloc(1+dsa->orig_n, sizeof(double));
restore(dsa, row_pval, row_dval, col_pval, col_dval);
ufree(dsa->ref), dsa->ref = NULL;
ufree(dsa->x), dsa->x = NULL;
ufree(dsa->y), dsa->y = NULL;
ufree(dsa->z), dsa->z = NULL;
/* store solution components into the problem object */
status = (ret == LPX_E_OK ? LPX_T_OPT : LPX_T_UNDEF);
lpx_put_ipt_soln(dsa->lp, status, row_pval, row_dval, col_pval,
col_dval);
ufree(row_pval);
ufree(row_dval);
ufree(col_pval);
ufree(col_dval);
done: /* return to the calling program */
return ret;
}
static void restore(struct dsa *dsa, double row_pval[],
double row_dval[], double col_pval[], double col_dval[])
{ /* restore solution of original LP */
LPX *lp = dsa->lp;
int orig_m = dsa->orig_m;
int orig_n = dsa->orig_n;
int *ref = dsa->ref;
int m = dsa->m;
double *x = dsa->x;
double *y = dsa->y;
int dir = lpx_get_obj_dir(lp);
int i, j, k, type, t, len, *ind;
double lb, ub, rii, sjj, temp, *val;
/* compute primal values of structural variables */
for (k = 1; k <= orig_n; k++)
{ j = ref[orig_m+k];
type = lpx_get_col_type(lp, k);
sjj = lpx_get_sjj(lp, k);
lb = lpx_get_col_lb(lp, k) / sjj;
ub = lpx_get_col_ub(lp, k) / sjj;
switch (type)
{
case LPX_FR:
/* source: -inf < x < +inf */
/* result: x = x' - x'', x' >= 0, x'' >= 0 */
col_pval[k] = x[j] - x[j+1];
break;
case LPX_LO:
/* source: lb <= x < +inf */
/* result: x = lb + x', x' >= 0 */
col_pval[k] = lb + x[j];
break;
case LPX_UP:
/* source: -inf < x <= ub */
/* result: x = ub - x', x' >= 0 */
col_pval[k] = ub - x[j];
break;
case LPX_DB:
/* source: lb <= x <= ub */
/* result: x = lb + x', x' + x'' = ub - lb */
col_pval[k] = lb + x[j];
break;
case LPX_FX:
/* source: x = lb */
/* result: just substitute */
col_pval[k] = lb;
break;
default:
insist(type != type);
}
}
/* compute primal values of auxiliary variables */
/* xR = A * xS */
ind = ucalloc(1+orig_n, sizeof(int));
val = ucalloc(1+orig_n, sizeof(double));
for (k = 1; k <= orig_m; k++)
{ rii = lpx_get_rii(lp, k);
temp = 0.0;
len = lpx_get_mat_row(lp, k, ind, val);
for (t = 1; t <= len; t++)
{ sjj = lpx_get_sjj(lp, ind[t]);
temp += (rii * val[t] * sjj) * col_pval[ind[t]];
}
row_pval[k] = temp;
}
ufree(ind);
ufree(val);
/* compute dual values of auxiliary variables */
for (k = 1; k <= orig_m; k++)
{ type = lpx_get_row_type(lp, k);
i = ref[k];
switch (type)
{
case LPX_FR:
insist(i == 0);
row_dval[k] = 0.0;
break;
case LPX_LO:
case LPX_UP:
case LPX_DB:
case LPX_FX:
insist(1 <= i && i <= m);
row_dval[k] = (dir == LPX_MIN ? +1.0 : -1.0) * y[i];
break;
default:
insist(type != type);
}
}
/* compute dual values of structural variables */
/* dS = cS - A' * (dR - cR) */
ind = ucalloc(1+orig_m, sizeof(int));
val = ucalloc(1+orig_m, sizeof(double));
for (k = 1; k <= orig_n; k++)
{ sjj = lpx_get_sjj(lp, k);
temp = lpx_get_obj_coef(lp, k) / sjj;
len = lpx_get_mat_col(lp, k, ind, val);
for (t = 1; t <= len; t++)
{ rii = lpx_get_rii(lp, ind[t]);
temp -= (rii * val[t] * sjj) * row_dval[ind[t]];
}
col_dval[k] = temp;
}
ufree(ind);
ufree(val);
/* unscale solution of original LP */
for (i = 1; i <= orig_m; i++)
{ rii = lpx_get_rii(lp, i);
row_pval[i] /= rii;
row_dval[i] *= rii;
}
for (j = 1; j <= orig_n; j++)
{ sjj = lpx_get_sjj(lp, j);
col_pval[j] *= sjj;
col_dval[j] /= sjj;
}
return;
}
static void transform(struct dsa *dsa)
{ /* transform original LP to standard formulation */
LPX *lp = dsa->lp;
int orig_m = dsa->orig_m;
int orig_n = dsa->orig_n;
int *ref = dsa->ref;
int m = dsa->m;
int n = dsa->n;
double *b = dsa->b;
double *c = dsa->c;
int i, j, k, type, t, ii, len, *ind;
double lb, ub, coef, rii, sjj, *val;
/* initialize components of transformed LP */
dsa->ne = 0;
for (i = 1; i <= m; i++) b[i] = 0.0;
c[0] = lpx_get_obj_coef(lp, 0);
for (j = 1; j <= n; j++) c[j] = 0.0;
/* i and j are, respectively, ordinal number of current row and
ordinal number of current column in transformed LP */
i = j = 0;
/* transform rows (auxiliary variables) */
for (k = 1; k <= orig_m; k++)
{ type = lpx_get_row_type(lp, k);
rii = lpx_get_rii(lp, k);
lb = lpx_get_row_lb(lp, k) * rii;
ub = lpx_get_row_ub(lp, k) * rii;
switch (type)
{
case LPX_FR:
/* source: -inf < (L.F.) < +inf */
/* result: ignore free row */
ref[k] = 0;
break;
case LPX_LO:
/* source: lb <= (L.F.) < +inf */
/* result: (L.F.) - x' = lb, x' >= 0 */
i++;
j++;
ref[k] = i;
new_coef(dsa, i, j, -1.0);
b[i] = lb;
break;
case LPX_UP:
/* source: -inf < (L.F.) <= ub */
/* result: (L.F.) + x' = ub, x' >= 0 */
i++;
j++;
ref[k] = i;
new_coef(dsa, i, j, +1.0);
b[i] = ub;
break;
case LPX_DB:
/* source: lb <= (L.F.) <= ub */
/* result: (L.F.) - x' = lb, x' + x'' = ub - lb */
i++;
j++;
ref[k] = i;
new_coef(dsa, i, j, -1.0);
b[i] = lb;
i++;
new_coef(dsa, i, j, +1.0);
j++;
new_coef(dsa, i, j, +1.0);
b[i] = ub - lb;
break;
case LPX_FX:
/* source: (L.F.) = lb */
/* result: (L.F.) = lb */
i++;
ref[k] = i;
b[i] = lb;
break;
default:
insist(type != type);
}
}
/* transform columns (structural variables) */
ind = ucalloc(1+orig_m, sizeof(int));
val = ucalloc(1+orig_m, sizeof(double));
for (k = 1; k <= orig_n; k++)
{ type = lpx_get_col_type(lp, k);
sjj = lpx_get_sjj(lp, k);
lb = lpx_get_col_lb(lp, k) / sjj;
ub = lpx_get_col_ub(lp, k) / sjj;
coef = lpx_get_obj_coef(lp, k) * sjj;
len = lpx_get_mat_col(lp, k, ind, val);
for (t = 1; t <= len; t++)
val[t] *= (lpx_get_rii(lp, ind[t]) * sjj);
switch (type)
{
case LPX_FR:
/* source: -inf < x < +inf */
/* result: x = x' - x'', x' >= 0, x'' >= 0 */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0) new_coef(dsa, ii, j, +val[t]);
}
c[j] = +coef;
j++;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0) new_coef(dsa, ii, j, -val[t]);
}
c[j] = -coef;
break;
case LPX_LO:
/* source: lb <= x < +inf */
/* result: x = lb + x', x' >= 0 */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0)
{ new_coef(dsa, ii, j, val[t]);
b[ii] -= val[t] * lb;
}
}
c[j] = +coef;
c[0] += c[j] * lb;
break;
case LPX_UP:
/* source: -inf < x <= ub */
/* result: x = ub - x', x' >= 0 */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0)
{ new_coef(dsa, ii, j, -val[t]);
b[ii] -= val[t] * ub;
}
}
c[j] = -coef;
c[0] -= c[j] * ub;
break;
case LPX_DB:
/* source: lb <= x <= ub */
/* result: x = lb + x', x' + x'' = ub - lb */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0)
{ new_coef(dsa, ii, j, val[t]);
b[ii] -= val[t] * lb;
}
}
c[j] = +coef;
c[0] += c[j] * lb;
i++;
new_coef(dsa, i, j, +1.0);
j++;
new_coef(dsa, i, j, +1.0);
b[i] = ub - lb;
break;
case LPX_FX:
/* source: x = lb */
/* result: just substitute */
ref[orig_m+k] = 0;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0) b[ii] -= val[t] * lb;
}
c[0] += coef * lb;
break;
default:
insist(type != type);
}
}
ufree(ind);
ufree(val);
/* end of transformation */
insist(i == m && j == n);
/* change the objective sign in case of maximization */
if (lpx_get_obj_dir(lp) == LPX_MAX)
for (j = 0; j <= n; j++) c[j] = -c[j];
return;
}
void lpx_check_kkt(LPX *lp, int scaled, LPXKKT *kkt)
{ int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
#if 0 /* 21/XII-2003 */
int *typx = lp->typx;
double *lb = lp->lb;
double *ub = lp->ub;
double *rs = lp->rs;
#else
int typx, tagx;
double lb, ub;
#endif
int dir = lpx_get_obj_dir(lp);
#if 0 /* 21/XII-2003 */
double *coef = lp->coef;
#endif
#if 0 /* 22/XII-2003 */
int *A_ptr = lp->A->ptr;
int *A_len = lp->A->len;
int *A_ndx = lp->A->ndx;
double *A_val = lp->A->val;
#endif
int *A_ndx;
double *A_val;
#if 0 /* 21/XII-2003 */
int *tagx = lp->tagx;
int *posx = lp->posx;
int *indx = lp->indx;
double *bbar = lp->bbar;
double *cbar = lp->cbar;
#endif
int beg, end, i, j, k, t;
double cR_i, cS_j, c_k, xR_i, xS_j, x_k, dR_i, dS_j, d_k;
double g_i, h_k, u_j, v_k, temp, rii, sjj;
if (lpx_get_prim_stat(lp) == LPX_P_UNDEF)
xfault("lpx_check_kkt: primal basic solution is undefined\n");
if (lpx_get_dual_stat(lp) == LPX_D_UNDEF)
xfault("lpx_check_kkt: dual basic solution is undefined\n");
/*--------------------------------------------------------------*/
/* compute largest absolute and relative errors and corresponding
row indices for the condition (KKT.PE) */
kkt->pe_ae_max = 0.0, kkt->pe_ae_row = 0;
kkt->pe_re_max = 0.0, kkt->pe_re_row = 0;
A_ndx = xcalloc(1+n, sizeof(int));
A_val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ /* determine xR[i] */
#if 0 /* 21/XII-2003 */
if (tagx[i] == LPX_BS)
xR_i = bbar[posx[i]];
else
xR_i = spx_eval_xn_j(lp, posx[i] - m);
#else
lpx_get_row_info(lp, i, NULL, &xR_i, NULL);
xR_i *= lpx_get_rii(lp, i);
#endif
/* g[i] := xR[i] */
g_i = xR_i;
/* g[i] := g[i] - (i-th row of A) * xS */
beg = 1;
end = lpx_get_mat_row(lp, i, A_ndx, A_val);
for (t = beg; t <= end; t++)
{ j = m + A_ndx[t]; /* a[i,j] != 0 */
/* determine xS[j] */
#if 0 /* 21/XII-2003 */
if (tagx[j] == LPX_BS)
xS_j = bbar[posx[j]];
else
xS_j = spx_eval_xn_j(lp, posx[j] - m);
#else
lpx_get_col_info(lp, j-m, NULL, &xS_j, NULL);
xS_j /= lpx_get_sjj(lp, j-m);
#endif
/* g[i] := g[i] - a[i,j] * xS[j] */
rii = lpx_get_rii(lp, i);
sjj = lpx_get_sjj(lp, j-m);
g_i -= (rii * A_val[t] * sjj) * xS_j;
}
/* unscale xR[i] and g[i] (if required) */
if (!scaled)
{ rii = lpx_get_rii(lp, i);
xR_i /= rii, g_i /= rii;
}
/* determine absolute error */
temp = fabs(g_i);
if (kkt->pe_ae_max < temp)
kkt->pe_ae_max = temp, kkt->pe_ae_row = i;
/* determine relative error */
temp /= (1.0 + fabs(xR_i));
if (kkt->pe_re_max < temp)
kkt->pe_re_max = temp, kkt->pe_re_row = i;
}
xfree(A_ndx);
xfree(A_val);
/* estimate the solution quality */
if (kkt->pe_re_max <= 1e-9)
kkt->pe_quality = 'H';
else if (kkt->pe_re_max <= 1e-6)
kkt->pe_quality = 'M';
else if (kkt->pe_re_max <= 1e-3)
kkt->pe_quality = 'L';
else
kkt->pe_quality = '?';
/*--------------------------------------------------------------*/
/* compute largest absolute and relative errors and corresponding
variable indices for the condition (KKT.PB) */
kkt->pb_ae_max = 0.0, kkt->pb_ae_ind = 0;
kkt->pb_re_max = 0.0, kkt->pb_re_ind = 0;
for (k = 1; k <= m+n; k++)
{ /* determine x[k] */
if (k <= m)
{ lpx_get_row_bnds(lp, k, &typx, &lb, &ub);
rii = lpx_get_rii(lp, k);
lb *= rii;
ub *= rii;
lpx_get_row_info(lp, k, &tagx, &x_k, NULL);
x_k *= rii;
}
else
{ lpx_get_col_bnds(lp, k-m, &typx, &lb, &ub);
sjj = lpx_get_sjj(lp, k-m);
lb /= sjj;
ub /= sjj;
lpx_get_col_info(lp, k-m, &tagx, &x_k, NULL);
x_k /= sjj;
}
/* skip non-basic variable */
if (tagx != LPX_BS) continue;
/* compute h[k] */
h_k = 0.0;
switch (typx)
{ case LPX_FR:
break;
case LPX_LO:
if (x_k < lb) h_k = x_k - lb;
break;
case LPX_UP:
if (x_k > ub) h_k = x_k - ub;
break;
case LPX_DB:
case LPX_FX:
if (x_k < lb) h_k = x_k - lb;
if (x_k > ub) h_k = x_k - ub;
break;
default:
xassert(typx != typx);
}
/* unscale x[k] and h[k] (if required) */
if (!scaled)
{ if (k <= m)
{ rii = lpx_get_rii(lp, k);
x_k /= rii, h_k /= rii;
}
else
{ sjj = lpx_get_sjj(lp, k-m);
x_k *= sjj, h_k *= sjj;
}
}
/* determine absolute error */
temp = fabs(h_k);
if (kkt->pb_ae_max < temp)
kkt->pb_ae_max = temp, kkt->pb_ae_ind = k;
/* determine relative error */
temp /= (1.0 + fabs(x_k));
if (kkt->pb_re_max < temp)
kkt->pb_re_max = temp, kkt->pb_re_ind = k;
}
/* estimate the solution quality */
if (kkt->pb_re_max <= 1e-9)
kkt->pb_quality = 'H';
else if (kkt->pb_re_max <= 1e-6)
kkt->pb_quality = 'M';
else if (kkt->pb_re_max <= 1e-3)
kkt->pb_quality = 'L';
else
kkt->pb_quality = '?';
/*--------------------------------------------------------------*/
/* compute largest absolute and relative errors and corresponding
column indices for the condition (KKT.DE) */
kkt->de_ae_max = 0.0, kkt->de_ae_col = 0;
kkt->de_re_max = 0.0, kkt->de_re_col = 0;
A_ndx = xcalloc(1+m, sizeof(int));
A_val = xcalloc(1+m, sizeof(double));
for (j = m+1; j <= m+n; j++)
{ /* determine cS[j] */
#if 0 /* 21/XII-2003 */
cS_j = coef[j];
#else
sjj = lpx_get_sjj(lp, j-m);
cS_j = lpx_get_obj_coef(lp, j-m) * sjj;
#endif
/* determine dS[j] */
#if 0 /* 21/XII-2003 */
if (tagx[j] == LPX_BS)
dS_j = 0.0;
else
dS_j = cbar[posx[j] - m];
#else
lpx_get_col_info(lp, j-m, NULL, NULL, &dS_j);
dS_j *= sjj;
#endif
/* u[j] := dS[j] - cS[j] */
u_j = dS_j - cS_j;
/* u[j] := u[j] + (j-th column of A) * (dR - cR) */
beg = 1;
end = lpx_get_mat_col(lp, j-m, A_ndx, A_val);
for (t = beg; t <= end; t++)
{ i = A_ndx[t]; /* a[i,j] != 0 */
/* determine cR[i] */
#if 0 /* 21/XII-2003 */
cR_i = coef[i];
#else
cR_i = 0.0;
#endif
/* determine dR[i] */
#if 0 /* 21/XII-2003 */
if (tagx[i] == LPX_BS)
dR_i = 0.0;
else
dR_i = cbar[posx[i] - m];
#else
lpx_get_row_info(lp, i, NULL, NULL, &dR_i);
rii = lpx_get_rii(lp, i);
dR_i /= rii;
#endif
/* u[j] := u[j] + a[i,j] * (dR[i] - cR[i]) */
rii = lpx_get_rii(lp, i);
sjj = lpx_get_sjj(lp, j-m);
u_j += (rii * A_val[t] * sjj) * (dR_i - cR_i);
}
/* unscale cS[j], dS[j], and u[j] (if required) */
if (!scaled)
{ sjj = lpx_get_sjj(lp, j-m);
cS_j /= sjj, dS_j /= sjj, u_j /= sjj;
}
/* determine absolute error */
temp = fabs(u_j);
if (kkt->de_ae_max < temp)
kkt->de_ae_max = temp, kkt->de_ae_col = j - m;
/* determine relative error */
temp /= (1.0 + fabs(dS_j - cS_j));
if (kkt->de_re_max < temp)
kkt->de_re_max = temp, kkt->de_re_col = j - m;
}
xfree(A_ndx);
xfree(A_val);
/* estimate the solution quality */
if (kkt->de_re_max <= 1e-9)
kkt->de_quality = 'H';
else if (kkt->de_re_max <= 1e-6)
kkt->de_quality = 'M';
else if (kkt->de_re_max <= 1e-3)
kkt->de_quality = 'L';
else
kkt->de_quality = '?';
/*--------------------------------------------------------------*/
/* compute largest absolute and relative errors and corresponding
variable indices for the condition (KKT.DB) */
kkt->db_ae_max = 0.0, kkt->db_ae_ind = 0;
kkt->db_re_max = 0.0, kkt->db_re_ind = 0;
for (k = 1; k <= m+n; k++)
{ /* determine c[k] */
#if 0 /* 21/XII-2003 */
c_k = coef[k];
#else
if (k <= m)
c_k = 0.0;
else
{ sjj = lpx_get_sjj(lp, k-m);
c_k = lpx_get_obj_coef(lp, k-m) / sjj;
}
#endif
/* determine d[k] */
#if 0 /* 21/XII-2003 */
d_k = cbar[j-m];
#else
if (k <= m)
{ lpx_get_row_info(lp, k, &tagx, NULL, &d_k);
rii = lpx_get_rii(lp, k);
d_k /= rii;
}
else
{ lpx_get_col_info(lp, k-m, &tagx, NULL, &d_k);
sjj = lpx_get_sjj(lp, k-m);
d_k *= sjj;
}
#endif
/* skip basic variable */
if (tagx == LPX_BS) continue;
/* compute v[k] */
v_k = 0.0;
switch (tagx)
{ case LPX_NL:
switch (dir)
{ case LPX_MIN:
if (d_k < 0.0) v_k = d_k;
break;
case LPX_MAX:
if (d_k > 0.0) v_k = d_k;
break;
default:
xassert(dir != dir);
}
break;
case LPX_NU:
switch (dir)
{ case LPX_MIN:
if (d_k > 0.0) v_k = d_k;
break;
case LPX_MAX:
if (d_k < 0.0) v_k = d_k;
break;
default:
xassert(dir != dir);
}
break;
case LPX_NF:
v_k = d_k;
break;
case LPX_NS:
break;
default:
xassert(tagx != tagx);
}
/* unscale c[k], d[k], and v[k] (if required) */
if (!scaled)
{ if (k <= m)
{ rii = lpx_get_rii(lp, k);
c_k *= rii, d_k *= rii, v_k *= rii;
}
else
{ sjj = lpx_get_sjj(lp, k-m);
c_k /= sjj, d_k /= sjj, v_k /= sjj;
}
}
/* determine absolute error */
temp = fabs(v_k);
if (kkt->db_ae_max < temp)
kkt->db_ae_max = temp, kkt->db_ae_ind = k;
/* determine relative error */
temp /= (1.0 + fabs(d_k - c_k));
if (kkt->db_re_max < temp)
kkt->db_re_max = temp, kkt->db_re_ind = k;
}
/* estimate the solution quality */
if (kkt->db_re_max <= 1e-9)
kkt->db_quality = 'H';
else if (kkt->db_re_max <= 1e-6)
kkt->db_quality = 'M';
else if (kkt->db_re_max <= 1e-3)
kkt->db_quality = 'L';
else
kkt->db_quality = '?';
/* complementary slackness is always satisfied by definition for
any basic solution, so not checked */
kkt->cs_ae_max = 0.0, kkt->cs_ae_ind = 0;
kkt->cs_re_max = 0.0, kkt->cs_re_ind = 0;
kkt->cs_quality = 'H';
return;
}
static int mat(void *info, int k, int ndx[])
{ /* this auxiliary routine returns the pattern of a given row or
a given column of the augmented constraint matrix A~ = (I|-A),
in which columns of fixed variables are implicitly cleared */
LPX *lp = info;
int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int typx, i, j, lll, len = 0;
if (k > 0)
{ /* the pattern of the i-th row is required */
i = +k;
xassert(1 <= i && i <= m);
#if 0 /* 22/XII-2003 */
/* if the auxiliary variable x[i] is non-fixed, include its
element (placed in the i-th column) in the pattern */
lpx_get_row_bnds(lp, i, &typx, NULL, NULL);
if (typx != LPX_FX) ndx[++len] = i;
/* include in the pattern elements placed in columns, which
correspond to non-fixed structural varables */
i_beg = aa_ptr[i];
i_end = i_beg + aa_len[i] - 1;
for (i_ptr = i_beg; i_ptr <= i_end; i_ptr++)
{ j = m + sv_ndx[i_ptr];
lpx_get_col_bnds(lp, j-m, &typx, NULL, NULL);
if (typx != LPX_FX) ndx[++len] = j;
}
#else
lll = lpx_get_mat_row(lp, i, ndx, NULL);
for (k = 1; k <= lll; k++)
{ lpx_get_col_bnds(lp, ndx[k], &typx, NULL, NULL);
if (typx != LPX_FX) ndx[++len] = m + ndx[k];
}
lpx_get_row_bnds(lp, i, &typx, NULL, NULL);
if (typx != LPX_FX) ndx[++len] = i;
#endif
}
else
{ /* the pattern of the j-th column is required */
j = -k;
xassert(1 <= j && j <= m+n);
/* if the (auxiliary or structural) variable x[j] is fixed,
the pattern of its column is empty */
if (j <= m)
lpx_get_row_bnds(lp, j, &typx, NULL, NULL);
else
lpx_get_col_bnds(lp, j-m, &typx, NULL, NULL);
if (typx != LPX_FX)
{ if (j <= m)
{ /* x[j] is non-fixed auxiliary variable */
ndx[++len] = j;
}
else
{ /* x[j] is non-fixed structural variables */
#if 0 /* 22/XII-2003 */
j_beg = aa_ptr[j];
j_end = j_beg + aa_len[j] - 1;
for (j_ptr = j_beg; j_ptr <= j_end; j_ptr++)
ndx[++len] = sv_ndx[j_ptr];
#else
len = lpx_get_mat_col(lp, j-m, ndx, NULL);
#endif
}
}
}
/* return the length of the row/column pattern */
return len;
}
void ipp_load_orig(IPP *ipp, LPX *orig)
{ IPPROW **row;
IPPCOL *col;
int i, j, k, type, len, *ind;
double lb, ub, *val;
/* save some information about the original problem */
ipp->orig_m = lpx_get_num_rows(orig);
ipp->orig_n = lpx_get_num_cols(orig);
ipp->orig_nnz = lpx_get_num_nz(orig);
ipp->orig_dir = lpx_get_obj_dir(orig);
/* allocate working arrays */
row = xcalloc(1+ipp->orig_m, sizeof(IPPROW *));
ind = xcalloc(1+ipp->orig_m, sizeof(int));
val = xcalloc(1+ipp->orig_m, sizeof(double));
/* copy rows of the original problem into the workspace */
for (i = 1; i <= ipp->orig_m; i++)
{ type = lpx_get_row_type(orig, i);
if (type == LPX_FR || type == LPX_UP)
lb = -DBL_MAX;
else
lb = lpx_get_row_lb(orig, i);
if (type == LPX_FR || type == LPX_LO)
ub = +DBL_MAX;
else
ub = lpx_get_row_ub(orig, i);
row[i] = ipp_add_row(ipp, lb, ub);
}
/* copy columns of the original problem into the workspace; each
column created in the workspace is assigned a reference number
which is its ordinal number in the original problem */
for (j = 1; j <= ipp->orig_n; j++)
{ type = lpx_get_col_type(orig, j);
if (type == LPX_FR || type == LPX_UP)
lb = -DBL_MAX;
else
lb = lpx_get_col_lb(orig, j);
if (type == LPX_FR || type == LPX_LO)
ub = +DBL_MAX;
else
ub = lpx_get_col_ub(orig, j);
col = ipp_add_col(ipp, lpx_get_col_kind(orig, j) == LPX_IV,
lb, ub, lpx_get_obj_coef(orig, j));
len = lpx_get_mat_col(orig, j, ind, val);
for (k = 1; k <= len; k++)
ipp_add_aij(ipp, row[ind[k]], col, val[k]);
}
/* copy the constant term of the original objective function */
ipp->c0 = lpx_get_obj_coef(orig, 0);
/* if the original problem is maximization, change the sign of
the objective function, because the transformed problem to be
processed by the presolver must be minimization */
if (ipp->orig_dir == LPX_MAX)
{ for (col = ipp->col_ptr; col != NULL; col = col->next)
col->c = - col->c;
ipp->c0 = - ipp->c0;
}
/* free working arrays */
xfree(row);
xfree(ind);
xfree(val);
return;
}
void lpx_eval_b_prim(LPX *lp, double row_prim[], double col_prim[])
{ int i, j, k, m, n, stat, len, *ind;
double xN, *NxN, *xB, *val;
if (!lpx_is_b_avail(lp))
xfault("lpx_eval_b_prim: LP basis is not available\n");
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* store values of non-basic auxiliary and structural variables
and compute the right-hand side vector (-N*xN) */
NxN = xcalloc(1+m, sizeof(double));
for (i = 1; i <= m; i++) NxN[i] = 0.0;
/* walk through auxiliary variables */
for (i = 1; i <= m; i++)
{ /* obtain status of i-th auxiliary variable */
stat = lpx_get_row_stat(lp, i);
/* if it is basic, skip it */
if (stat == LPX_BS) continue;
/* i-th auxiliary variable is non-basic; get its value */
switch (stat)
{ case LPX_NL: xN = lpx_get_row_lb(lp, i); break;
case LPX_NU: xN = lpx_get_row_ub(lp, i); break;
case LPX_NF: xN = 0.0; break;
case LPX_NS: xN = lpx_get_row_lb(lp, i); break;
default: xassert(lp != lp);
}
/* store the value of non-basic auxiliary variable */
row_prim[i] = xN;
/* and add corresponding term to the right-hand side vector */
NxN[i] -= xN;
}
/* walk through structural variables */
ind = xcalloc(1+m, sizeof(int));
val = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ /* obtain status of j-th structural variable */
stat = lpx_get_col_stat(lp, j);
/* if it basic, skip it */
if (stat == LPX_BS) continue;
/* j-th structural variable is non-basic; get its value */
switch (stat)
{ case LPX_NL: xN = lpx_get_col_lb(lp, j); break;
case LPX_NU: xN = lpx_get_col_ub(lp, j); break;
case LPX_NF: xN = 0.0; break;
case LPX_NS: xN = lpx_get_col_lb(lp, j); break;
default: xassert(lp != lp);
}
/* store the value of non-basic structural variable */
col_prim[j] = xN;
/* and add corresponding term to the right-hand side vector */
if (xN != 0.0)
{ len = lpx_get_mat_col(lp, j, ind, val);
for (k = 1; k <= len; k++) NxN[ind[k]] += val[k] * xN;
}
}
xfree(ind);
xfree(val);
/* solve the system B*xB = (-N*xN) to compute the vector xB */
xB = NxN, lpx_ftran(lp, xB);
/* store values of basic auxiliary and structural variables */
for (i = 1; i <= m; i++)
{ k = lpx_get_b_info(lp, i);
xassert(1 <= k && k <= m+n);
if (k <= m)
row_prim[k] = xB[i];
else
col_prim[k-m] = xB[i];
}
xfree(NxN);
return;
}
int lpx_transform_row(LPX *lp, int len, int ind[], double val[])
{ int i, j, k, m, n, t, lll, *iii;
double alfa, *a, *aB, *rho, *vvv;
if (!lpx_is_b_avail(lp))
xfault("lpx_transform_row: LP basis is not available\n");
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* unpack the row to be transformed to the array a */
a = xcalloc(1+n, sizeof(double));
for (j = 1; j <= n; j++) a[j] = 0.0;
if (!(0 <= len && len <= n))
xfault("lpx_transform_row: len = %d; invalid row length\n",
len);
for (t = 1; t <= len; t++)
{ j = ind[t];
if (!(1 <= j && j <= n))
xfault("lpx_transform_row: ind[%d] = %d; column index out o"
"f range\n", t, j);
if (val[t] == 0.0)
xfault("lpx_transform_row: val[%d] = 0; zero coefficient no"
"t allowed\n", t);
if (a[j] != 0.0)
xfault("lpx_transform_row: ind[%d] = %d; duplicate column i"
"ndices not allowed\n", t, j);
a[j] = val[t];
}
/* construct the vector aB */
aB = xcalloc(1+m, sizeof(double));
for (i = 1; i <= m; i++)
{ k = lpx_get_b_info(lp, i);
/* xB[i] is k-th original variable */
xassert(1 <= k && k <= m+n);
aB[i] = (k <= m ? 0.0 : a[k-m]);
}
/* solve the system B'*rho = aB to compute the vector rho */
rho = aB, lpx_btran(lp, rho);
/* compute coefficients at non-basic auxiliary variables */
len = 0;
for (i = 1; i <= m; i++)
{ if (lpx_get_row_stat(lp, i) != LPX_BS)
{ alfa = - rho[i];
if (alfa != 0.0)
{ len++;
ind[len] = i;
val[len] = alfa;
}
}
}
/* compute coefficients at non-basic structural variables */
iii = xcalloc(1+m, sizeof(int));
vvv = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ if (lpx_get_col_stat(lp, j) != LPX_BS)
{ alfa = a[j];
lll = lpx_get_mat_col(lp, j, iii, vvv);
for (t = 1; t <= lll; t++) alfa += vvv[t] * rho[iii[t]];
if (alfa != 0.0)
{ len++;
ind[len] = m+j;
val[len] = alfa;
}
}
}
xassert(len <= n);
xfree(iii);
xfree(vvv);
xfree(aB);
xfree(a);
return len;
}