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;
}
int lpx_write_cpxlp(LPX *lp, const char *fname)
{ /* write problem data in CPLEX LP format */
FILE *fp;
int nrows, ncols, i, j, t, len, typx, flag, kind, *ind;
double lb, ub, temp, *val;
char line[1023+1], term[1023+1], rname[255+1], cname[255+1];
print("lpx_write_cpxlp: writing problem data to `%s'...", fname);
/* open the output text file */
fp = xfopen(fname, "w");
if (fp == NULL)
{ print("lpx_write_cpxlp: unable to create `%s' - %s", fname,
strerror(errno));
goto fail;
}
/* determine the number of rows and columns */
nrows = lpx_get_num_rows(lp);
ncols = lpx_get_num_cols(lp);
/* the problem should contain at least one row and one column */
if (!(nrows > 0 && ncols > 0))
fault("lpx_write_cpxlp: problem has no rows/columns");
/* write problem name */
{ const char *name = lpx_get_prob_name(lp);
if (name == NULL) name = "Unknown";
fprintf(fp, "\\* Problem: %s *\\\n", name);
fprintf(fp, "\n");
}
/* allocate working arrays */
ind = xcalloc(1+ncols, sizeof(int));
val = xcalloc(1+ncols, sizeof(double));
/* write the objective function definition and the constraints
section */
for (i = 0; i <= nrows; i++)
{ if (i == 0)
{ switch (lpx_get_obj_dir(lp))
{ case LPX_MIN:
fprintf(fp, "Minimize\n");
break;
case LPX_MAX:
fprintf(fp, "Maximize\n");
break;
default:
xassert(lp != lp);
}
}
else if (i == 1)
{ temp = lpx_get_obj_coef(lp, 0);
if (temp != 0.0)
fprintf(fp, "\\* constant term = %.*g *\\\n", DBL_DIG,
temp);
fprintf(fp, "\n");
fprintf(fp, "Subject To\n");
}
row_name(lp, i, rname);
if (i == 0)
{ len = 0;
for (j = 1; j <= ncols; j++)
{ temp = lpx_get_obj_coef(lp, j);
if (temp != 0.0)
len++, ind[len] = j, val[len] = temp;
}
}
else
{ lpx_get_row_bnds(lp, i, &typx, &lb, &ub);
if (typx == LPX_FR) continue;
len = lpx_get_mat_row(lp, i, ind, val);
}
flag = 0;
more: if (!flag)
sprintf(line, " %s:", rname);
else
sprintf(line, " %*s ", strlen(rname), "");
for (t = 1; t <= len; t++)
{ col_name(lp, ind[t], cname);
if (val[t] == +1.0)
sprintf(term, " + %s", cname);
else if (val[t] == -1.0)
sprintf(term, " - %s", cname);
else if (val[t] > 0.0)
sprintf(term, " + %.*g %s", DBL_DIG, +val[t], cname);
else if (val[t] < 0.0)
sprintf(term, " - %.*g %s", DBL_DIG, -val[t], cname);
else
xassert(lp != lp);
if (strlen(line) + strlen(term) > 72)
fprintf(fp, "%s\n", line), line[0] = '\0';
strcat(line, term);
}
if (len == 0)
{ /* empty row */
sprintf(term, " 0 %s", col_name(lp, 1, cname));
strcat(line, term);
}
if (i > 0)
{ switch (typx)
{ case LPX_LO:
case LPX_DB:
sprintf(term, " >= %.*g", DBL_DIG, lb);
break;
case LPX_UP:
sprintf(term, " <= %.*g", DBL_DIG, ub);
break;
case LPX_FX:
sprintf(term, " = %.*g", DBL_DIG, lb);
break;
default:
xassert(typx != typx);
}
if (strlen(line) + strlen(term) > 72)
fprintf(fp, "%s\n", line), line[0] = '\0';
strcat(line, term);
}
fprintf(fp, "%s\n", line);
if (i > 0 && typx == LPX_DB)
{ /* double-bounded row needs a copy for its upper bound */
flag = 1;
typx = LPX_UP;
goto more;
}
}
/* free working arrays */
xfree(ind);
xfree(val);
/* write the bounds section */
flag = 0;
for (j = 1; j <= ncols; j++)
{ col_name(lp, j, cname);
lpx_get_col_bnds(lp, j, &typx, &lb, &ub);
if (typx == LPX_LO && lb == 0.0) continue;
if (!flag)
{ fprintf(fp, "\n");
fprintf(fp, "Bounds\n");
flag = 1;
}
switch (typx)
{ case LPX_FR:
fprintf(fp, " %s free\n", cname);
break;
case LPX_LO:
fprintf(fp, " %s >= %.*g\n", cname, DBL_DIG, lb);
break;
case LPX_UP:
fprintf(fp, " %s <= %.*g\n", cname, DBL_DIG, ub);
break;
case LPX_DB:
fprintf(fp, " %.*g <= %s <= %.*g\n", DBL_DIG, lb, cname,
DBL_DIG, ub);
break;
case LPX_FX:
fprintf(fp, " %s = %.*g\n", cname, DBL_DIG, lb);
break;
default:
xassert(typx != typx);
}
}
/* write the general section */
if (lpx_get_class(lp) == LPX_MIP)
{ flag = 0;
for (j = 1; j <= ncols; j++)
{ kind = lpx_get_col_kind(lp, j);
if (kind == LPX_CV) continue;
xassert(kind == LPX_IV);
if (!flag)
{ fprintf(fp, "\n");
fprintf(fp, "Generals\n");
flag = 1;
}
fprintf(fp, " %s\n", col_name(lp, j, cname));
}
}
/* write the end keyword */
fprintf(fp, "\n");
fprintf(fp, "End\n");
/* close the output text file */
fflush(fp);
if (ferror(fp))
{ print("lpx_write_cpxlp: write error on `%s' - %s", fname,
strerror(errno));
goto fail;
}
xfclose(fp);
/* return to the calling program */
return 0;
fail: /* the operation failed */
if (fp != NULL) xfclose(fp);
return 1;
}
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;
}
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;
}
int lpx_integer(LPX *mip)
{ int m = lpx_get_num_rows(mip);
int n = lpx_get_num_cols(mip);
MIPTREE *tree;
LPX *lp;
int ret, i, j, stat, type, len, *ind;
double lb, ub, coef, *val;
#if 0
/* the problem must be of MIP class */
if (lpx_get_class(mip) != LPX_MIP)
{ print("lpx_integer: problem is not of MIP class");
ret = LPX_E_FAULT;
goto done;
}
#endif
/* an optimal solution of LP relaxation must be known */
if (lpx_get_status(mip) != LPX_OPT)
{ print("lpx_integer: optimal solution of LP relaxation required"
);
ret = LPX_E_FAULT;
goto done;
}
/* bounds of all integer variables must be integral */
for (j = 1; j <= n; j++)
{ if (lpx_get_col_kind(mip, j) != LPX_IV) continue;
type = lpx_get_col_type(mip, j);
if (type == LPX_LO || type == LPX_DB || type == LPX_FX)
{ lb = lpx_get_col_lb(mip, j);
if (lb != floor(lb))
{ print("lpx_integer: integer column %d has non-integer lo"
"wer bound or fixed value %g", j, lb);
ret = LPX_E_FAULT;
goto done;
}
}
if (type == LPX_UP || type == LPX_DB)
{ ub = lpx_get_col_ub(mip, j);
if (ub != floor(ub))
{ print("lpx_integer: integer column %d has non-integer up"
"per bound %g", j, ub);
ret = LPX_E_FAULT;
goto done;
}
}
}
/* it seems all is ok */
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 2)
print("Integer optimization begins...");
/* create the branch-and-bound tree */
tree = mip_create_tree(m, n, lpx_get_obj_dir(mip));
/* set up column kinds */
for (j = 1; j <= n; j++)
tree->int_col[j] = (lpx_get_col_kind(mip, j) == LPX_IV);
/* access the LP relaxation template */
lp = tree->lp;
/* set up the objective function */
tree->int_obj = 1;
for (j = 0; j <= tree->n; j++)
{ coef = lpx_get_obj_coef(mip, j);
lpx_set_obj_coef(lp, j, coef);
if (coef != 0.0 && !(tree->int_col[j] && coef == floor(coef)))
tree->int_obj = 0;
}
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 2 && tree->int_obj)
print("Objective function is integral");
/* set up the constraint matrix */
ind = xcalloc(1+n, sizeof(int));
val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ len = lpx_get_mat_row(mip, i, ind, val);
lpx_set_mat_row(lp, i, len, ind, val);
}
xfree(ind);
xfree(val);
/* set up scaling matrices */
for (i = 1; i <= m; i++)
lpx_set_rii(lp, i, lpx_get_rii(mip, i));
for (j = 1; j <= n; j++)
lpx_set_sjj(lp, j, lpx_get_sjj(mip, j));
/* revive the root subproblem */
mip_revive_node(tree, 1);
/* set up row attributes for the root subproblem */
for (i = 1; i <= m; i++)
{ type = lpx_get_row_type(mip, i);
lb = lpx_get_row_lb(mip, i);
ub = lpx_get_row_ub(mip, i);
stat = lpx_get_row_stat(mip, i);
lpx_set_row_bnds(lp, i, type, lb, ub);
lpx_set_row_stat(lp, i, stat);
}
/* set up column attributes for the root subproblem */
for (j = 1; j <= n; j++)
{ type = lpx_get_col_type(mip, j);
lb = lpx_get_col_lb(mip, j);
ub = lpx_get_col_ub(mip, j);
stat = lpx_get_col_stat(mip, j);
lpx_set_col_bnds(lp, j, type, lb, ub);
lpx_set_col_stat(lp, j, stat);
}
/* freeze the root subproblem */
mip_freeze_node(tree);
/* inherit some control parameters and statistics */
tree->msg_lev = lpx_get_int_parm(mip, LPX_K_MSGLEV);
if (tree->msg_lev > 2) tree->msg_lev = 2;
tree->branch = lpx_get_int_parm(mip, LPX_K_BRANCH);
tree->btrack = lpx_get_int_parm(mip, LPX_K_BTRACK);
tree->tol_int = lpx_get_real_parm(mip, LPX_K_TOLINT);
tree->tol_obj = lpx_get_real_parm(mip, LPX_K_TOLOBJ);
tree->tm_lim = lpx_get_real_parm(mip, LPX_K_TMLIM);
lpx_set_int_parm(lp, LPX_K_BFTYPE, lpx_get_int_parm(mip,
LPX_K_BFTYPE));
lpx_set_int_parm(lp, LPX_K_PRICE, lpx_get_int_parm(mip,
LPX_K_PRICE));
lpx_set_real_parm(lp, LPX_K_RELAX, lpx_get_real_parm(mip,
LPX_K_RELAX));
lpx_set_real_parm(lp, LPX_K_TOLBND, lpx_get_real_parm(mip,
LPX_K_TOLBND));
lpx_set_real_parm(lp, LPX_K_TOLDJ, lpx_get_real_parm(mip,
LPX_K_TOLDJ));
lpx_set_real_parm(lp, LPX_K_TOLPIV, lpx_get_real_parm(mip,
LPX_K_TOLPIV));
lpx_set_int_parm(lp, LPX_K_ITLIM, lpx_get_int_parm(mip,
LPX_K_ITLIM));
lpx_set_int_parm(lp, LPX_K_ITCNT, lpx_get_int_parm(mip,
LPX_K_ITCNT));
/* reset the status of MIP solution */
lpx_put_mip_soln(mip, LPX_I_UNDEF, NULL, NULL);
/* try solving the problem */
ret = mip_driver(tree);
/* if an integer feasible solution has been found, copy it to the
MIP problem object */
if (tree->found)
lpx_put_mip_soln(mip, LPX_I_FEAS, &tree->mipx[0],
&tree->mipx[m]);
/* copy back statistics about spent resources */
lpx_set_real_parm(mip, LPX_K_TMLIM, tree->tm_lim);
lpx_set_int_parm(mip, LPX_K_ITLIM, lpx_get_int_parm(lp,
LPX_K_ITLIM));
lpx_set_int_parm(mip, LPX_K_ITCNT, lpx_get_int_parm(lp,
LPX_K_ITCNT));
/* analyze exit code reported by the mip driver */
switch (ret)
{ case MIP_E_OK:
if (tree->found)
{ if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("INTEGER OPTIMAL SOLUTION FOUND");
lpx_put_mip_soln(mip, LPX_I_OPT, NULL, NULL);
}
else
{ if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("PROBLEM HAS NO INTEGER FEASIBLE SOLUTION");
lpx_put_mip_soln(mip, LPX_I_NOFEAS, NULL, NULL);
}
ret = LPX_E_OK;
break;
case MIP_E_ITLIM:
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("ITERATIONS LIMIT EXCEEDED; SEARCH TERMINATED");
ret = LPX_E_ITLIM;
break;
case MIP_E_TMLIM:
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("TIME LIMIT EXCEEDED; SEARCH TERMINATED");
ret = LPX_E_TMLIM;
break;
case MIP_E_ERROR:
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 1)
print("lpx_integer: cannot solve current LP relaxation");
ret = LPX_E_SING;
break;
default:
xassert(ret != ret);
}
/* delete the branch-and-bound tree */
mip_delete_tree(tree);
done: /* return to the application program */
return ret;
}
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;
}
int lpx_warm_up(LPX *lp)
{ int m, n, j, k, ret, type, stat, p_stat, d_stat;
double lb, ub, prim, dual, tol_bnd, tol_dj, dir;
double *row_prim, *row_dual, *col_prim, *col_dual, sum;
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* reinvert the basis matrix, if necessary */
if (lpx_is_b_avail(lp))
ret = LPX_E_OK;
else
{ if (m == 0 || n == 0)
{ ret = LPX_E_EMPTY;
goto done;
}
#if 0
ret = lpx_invert(lp);
switch (ret)
{ case 0:
ret = LPX_E_OK;
break;
case 1:
case 2:
ret = LPX_E_SING;
goto done;
case 3:
ret = LPX_E_BADB;
goto done;
default:
xassert(ret != ret);
}
#else
switch (glp_factorize(lp))
{ case 0:
ret = LPX_E_OK;
break;
case GLP_EBADB:
ret = LPX_E_BADB;
goto done;
case GLP_ESING:
case GLP_ECOND:
ret = LPX_E_SING;
goto done;
default:
xassert(lp != lp);
}
#endif
}
/* allocate working arrays */
row_prim = xcalloc(1+m, sizeof(double));
row_dual = xcalloc(1+m, sizeof(double));
col_prim = xcalloc(1+n, sizeof(double));
col_dual = xcalloc(1+n, sizeof(double));
/* compute primal basic solution components */
lpx_eval_b_prim(lp, row_prim, col_prim);
/* determine primal status of basic solution */
tol_bnd = 3.0 * lpx_get_real_parm(lp, LPX_K_TOLBND);
p_stat = LPX_P_FEAS;
for (k = 1; k <= m+n; k++)
{ if (k <= m)
{ type = lpx_get_row_type(lp, k);
lb = lpx_get_row_lb(lp, k);
ub = lpx_get_row_ub(lp, k);
prim = row_prim[k];
}
else
{ type = lpx_get_col_type(lp, k-m);
lb = lpx_get_col_lb(lp, k-m);
ub = lpx_get_col_ub(lp, k-m);
prim = col_prim[k-m];
}
if (type == LPX_LO || type == LPX_DB || type == LPX_FX)
{ /* variable x[k] has lower bound */
if (prim < lb - tol_bnd * (1.0 + fabs(lb)))
{ p_stat = LPX_P_INFEAS;
break;
}
}
if (type == LPX_UP || type == LPX_DB || type == LPX_FX)
{ /* variable x[k] has upper bound */
if (prim > ub + tol_bnd * (1.0 + fabs(ub)))
{ p_stat = LPX_P_INFEAS;
break;
}
}
}
/* compute dual basic solution components */
lpx_eval_b_dual(lp, row_dual, col_dual);
/* determine dual status of basic solution */
tol_dj = 3.0 * lpx_get_real_parm(lp, LPX_K_TOLDJ);
dir = (lpx_get_obj_dir(lp) == LPX_MIN ? +1.0 : -1.0);
d_stat = LPX_D_FEAS;
for (k = 1; k <= m+n; k++)
{ if (k <= m)
{ stat = lpx_get_row_stat(lp, k);
dual = row_dual[k];
}
else
{ stat = lpx_get_col_stat(lp, k-m);
dual = col_dual[k-m];
}
if (stat == LPX_BS || stat == LPX_NL || stat == LPX_NF)
{ /* reduced cost of x[k] must be non-negative (minimization)
or non-positive (maximization) */
if (dir * dual < - tol_dj)
{ d_stat = LPX_D_INFEAS;
break;
}
}
if (stat == LPX_BS || stat == LPX_NU || stat == LPX_NF)
{ /* reduced cost of x[k] must be non-positive (minimization)
or non-negative (maximization) */
if (dir * dual > + tol_dj)
{ d_stat = LPX_D_INFEAS;
break;
}
}
}
/* store basic solution components */
p_stat = p_stat - LPX_P_UNDEF + GLP_UNDEF;
d_stat = d_stat - LPX_D_UNDEF + GLP_UNDEF;
sum = lpx_get_obj_coef(lp, 0);
for (j = 1; j <= n; j++)
sum += lpx_get_obj_coef(lp, j) * col_prim[j];
glp_put_solution(lp, 0, &p_stat, &d_stat, &sum,
NULL, row_prim, row_dual, NULL, col_prim, col_dual);
xassert(lpx_is_b_avail(lp));
/* free working arrays */
xfree(row_prim);
xfree(row_dual);
xfree(col_prim);
xfree(col_dual);
done: /* return to the calling program */
return ret;
}
int lpx_print_sens_bnds(LPX *lp, char *fname)
{ FILE *fp = NULL;
int what, round;
print("lpx_print_sens_bnds: writing LP problem solution bounds to"
" `%s'...", fname);
#if 1
/* added by mao */
/* this routine needs factorization of the current basis matrix
which, however, does not exist if the basic solution was
obtained by the lp presolver; therefore we should warm up the
basis to be sure that the factorization is valid (note that if
the factorization exists, lpx_warm_up does nothing) */
lpx_warm_up(lp);
#endif
#if 0 /* 21/XII-2003 by mao */
if (lp->b_stat == LPX_B_UNDEF)
#else
if (!lpx_is_b_avail(lp))
#endif
{ print("lpx_print_sens_bnds: basis information not available (m"
"ay be a presolve issue)");
goto fail;
}
fp = ufopen(fname, "w");
if (fp == NULL)
{ print("lpx_print_sens_bnds: can't create `%s' - %s", fname,
strerror(errno));
goto fail;
}
/* problem name */
{ char *name;
name = lpx_get_prob_name(lp);
if (name == NULL) name = "";
fprintf(fp, "%-12s%s\n", "Problem:", name);
}
/* number of rows (auxiliary variables) */
{ int nr;
nr = lpx_get_num_rows(lp);
fprintf(fp, "%-12s%d\n", "Rows:", nr);
}
/* number of columns (structural variables) */
{ int nc;
nc = lpx_get_num_cols(lp);
fprintf(fp, "%-12s%d\n", "Columns:", nc);
}
/* number of non-zeros (constraint coefficients) */
{ int nz;
nz = lpx_get_num_nz(lp);
fprintf(fp, "%-12s%d\n", "Non-zeros:", nz);
}
/* solution status */
{ int status;
status = lpx_get_status(lp);
fprintf(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" : "???");
}
/* explanation/warning */
{ fprintf(fp, "\nExplanation: This file presents amounts by whi"
"ch objective coefficients,\n");
fprintf(fp, "constraint bounds, and variable bounds may be cha"
"nged in the original problem\n");
fprintf(fp, "while the optimal basis remains the same. Note t"
"hat the optimal solution\n");
fprintf(fp, "and objective value may change even though the ba"
"sis remains the same.\n");
fprintf(fp, "These bounds assume that all parameters remain fi"
"xed except the one in\n");
fprintf(fp, "question. If more than one parameter is changed,"
" it is possible for the\n");
fprintf(fp, "optimal basis to change even though each paramete"
"r stays within its bounds.\n");
fprintf(fp, "For more details, consult a text on linear progra"
"mming.\n");
}
/* Sensitivity ranges if solution was optimal */
{ int status;
status = lpx_get_status(lp);
if (status == LPX_OPT)
{ int i,j,k,m,n;
int dir;
double max_inc, max_dec;
int *index;
double *val;
fprintf(fp, "\nObjective Coefficient Analysis\n");
fprintf(fp, " No. Column name St Value Max incr"
"ease Max decrease\n");
fprintf(fp, "------ ------------ -- ------------- ---------"
"---- ------------- \n");
n = lpx_get_num_cols(lp);
m = lpx_get_num_rows(lp);
dir = lpx_get_obj_dir(lp);
/* allocate memory for index and val arrays */
index = ucalloc(1+n+m, sizeof(int));
val = ucalloc(1+n+m, sizeof(double));
for (j = 1; j <= n; j++)
{ char *name;
int typx, tagx;
double lb, ub, vx, dx;
name = lpx_get_col_name(lp, j);
if (name == NULL) name = "";
lpx_get_col_bnds(lp, j, &typx, &lb, &ub);
#if 0 /* 21/XII-2003 by mao */
round = lp->round, lp->round = 1;
lpx_get_col_info(lp, j, &tagx, &vx, &dx);
lp->round = round;
#else
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
lpx_get_col_info(lp, j, &tagx, &vx, &dx);
lpx_set_int_parm(lp, LPX_K_ROUND, round);
#endif
/* row/column ordinal number */
fprintf(fp, "%6d ", j);
/* row column/name */
if (strlen(name) <= 12)
fprintf(fp, "%-12s ", name);
else
fprintf(fp, "%s\n%20s", name, "");
/* row/column status */
fprintf(fp, "%s ",
tagx == LPX_BS ? "B " :
tagx == LPX_NL ? "NL" :
tagx == LPX_NU ? "NU" :
tagx == LPX_NF ? "NF" :
tagx == LPX_NS ? "NS" : "??");
/* objective coefficient */
fprintf(fp, "%13.6g ", lpx_get_obj_coef(lp, j));
if (tagx == LPX_NL)
{ if (dir==LPX_MIN)
{ /* reduced cost must be positive */
max_inc = DBL_MAX; /* really represents infinity */
max_dec = dx;
}
else
{ /* reduced cost must be negative */
max_inc = -dx;
max_dec = DBL_MAX; /* means infinity */
}
}
if (tagx == LPX_NU)
{ if (dir==LPX_MIN)
{ /* reduced cost must be negative */
max_inc = -dx;
max_dec = DBL_MAX;
}
else
{ max_inc = DBL_MAX;
max_dec = dx;
}
}
if (tagx == LPX_NF)
{ /* can't change nonbasic free variables' cost */
max_inc = 0.0;
max_dec = 0.0;
}
if (tagx == LPX_NS)
{ /* doesn't matter what happens to the cost */
max_inc = DBL_MAX;
max_dec = DBL_MAX;
}
if (tagx == LPX_BS)
{ int len;
/* We need to see how this objective coefficient
affects reduced costs of other variables */
len = lpx_eval_tab_row(lp, m+j, index, val);
max_inc = DBL_MAX;
max_dec = DBL_MAX;
for (i = 1; i <= len; i++)
{ /*int stat;*/
int tagx2;
double vx2, dx2;
double delta;
if (index[i]>m)
lpx_get_col_info(lp, index[i]-m, &tagx2, &vx2,
&dx2);
else
lpx_get_row_info(lp, index[i], &tagx2, &vx2,
&dx2);
if (tagx2 == LPX_NL)
{ if (val[i] != 0.0)
{ delta = dx2 / val[i];
if (delta < 0 && -delta < max_inc)
max_inc = -delta;
else if (delta >0 && delta < max_dec)
max_dec = delta;
}
}
if (tagx2 == LPX_NU)
{ if (val[i] != 0.0)
{ delta = dx2 / val[i];
if (delta < 0 && -delta < max_inc)
max_inc = -delta;
else if (delta > 0 && delta < max_dec)
max_dec = delta;
}
}
if (tagx2 == LPX_NF)
{ if (val[i] != 0.0)
{ max_inc = 0.0;
max_dec = 0.0;
}
}
}
}
if (max_inc == -0.0) max_inc = 0.0;
if (max_dec == -0.0) max_dec = 0.0;
if (max_inc == DBL_MAX)
fprintf(fp, "%13s ", "infinity");
else if (max_inc < 1.0e-12 && max_inc > 0)
fprintf(fp, "%13s ", "< eps");
else
fprintf(fp, "%13.6g ", max_inc);
if (max_dec == DBL_MAX)
fprintf(fp, "%13s ", "infinity");
else if (max_dec < 1.0e-12 && max_dec > 0)
fprintf(fp, "%13s ", "< eps");
else
fprintf(fp, "%13.6g ", max_dec);
fprintf(fp, "\n");
}
for (what = 1; what <= 2; what++)
{ int ij, mn;
fprintf(fp, "\n");
fprintf(fp, "%s Analysis\n",
what==1? "Constraint Bounds":"Variable Bounds");
fprintf(fp, " No. %12s St Value Max increase "
" Max decrease\n",
what==1 ? " Row name":"Column name");
fprintf(fp, "------ ------------ -- ------------- ------"
"------- ------------- \n");
mn = what==1 ? m : n;
for (ij = 1; ij <= mn; ij++)
{ char *name;
int typx, tagx;
double lb, ub, vx, dx;
if (what==1)
name = lpx_get_row_name(lp, ij);
else
name = lpx_get_col_name(lp, ij);
if (name == NULL) name = "";
#if 0 /* 21/XII-2003 by mao */
if (what==1)
{ lpx_get_row_bnds(lp, ij, &typx, &lb, &ub);
round = lp->round, lp->round = 1;
lpx_get_row_info(lp, ij, &tagx, &vx, &dx);
lp->round = round;
}
else
{ lpx_get_col_bnds(lp, ij, &typx, &lb, &ub);
round = lp->round, lp->round = 1;
lpx_get_col_info(lp, ij, &tagx, &vx, &dx);
lp->round = round;
}
#else
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
if (what==1)
{ lpx_get_row_bnds(lp, ij, &typx, &lb, &ub);
lpx_get_row_info(lp, ij, &tagx, &vx, &dx);
}
else
{ lpx_get_col_bnds(lp, ij, &typx, &lb, &ub);
lpx_get_col_info(lp, ij, &tagx, &vx, &dx);
}
lpx_set_int_parm(lp, LPX_K_ROUND, round);
#endif
/* row/column ordinal number */
fprintf(fp, "%6d ", ij);
/* row column/name */
if (strlen(name) <= 12)
fprintf(fp, "%-12s ", name);
else
fprintf(fp, "%s\n%20s", name, "");
/* row/column status */
fprintf(fp, "%s ",
tagx == LPX_BS ? "B " :
tagx == LPX_NL ? "NL" :
tagx == LPX_NU ? "NU" :
tagx == LPX_NF ? "NF" :
tagx == LPX_NS ? "NS" : "??");
fprintf(fp, "\n");
/* first check lower bound */
if (typx == LPX_LO || typx == LPX_DB ||
typx == LPX_FX)
{ int at_lower;
at_lower = 0;
if (tagx == LPX_BS || tagx == LPX_NU)
{ max_inc = vx - lb;
max_dec = DBL_MAX;
}
if (tagx == LPX_NS)
{ max_inc = 0.0;
max_dec = 0.0;
if (dir == LPX_MIN && dx > 0) at_lower = 1;
if (dir == LPX_MAX && dx < 0) at_lower = 1;
}
if (tagx == LPX_NL || at_lower == 1)
{ int len;
/* we have to see how it affects basic
variables */
len = lpx_eval_tab_col(lp, what==1?ij:ij+m,
index, val);
k = lpx_prim_ratio_test(lp, len, index, val, 1,
10e-7);
max_inc = DBL_MAX;
if (k != 0)
{ /*int stat;*/
int tagx2, typx2;
double vx2, dx2, lb2, ub2;
/*double delta;*/
double alpha;
int l;
for (l = 1; l <= len; l++)
if (index[l] == k) alpha = val[l];
if (k>m)
{ lpx_get_col_info(lp, k-m, &tagx2, &vx2,
&dx2);
lpx_get_col_bnds(lp, k-m, &typx2, &lb2,
&ub2);
}
else
{ lpx_get_row_info(lp, k, &tagx2, &vx2,
&dx2);
lpx_get_row_bnds(lp, k, &typx2, &lb2,
&ub2);
}
/* Check which direction;
remember this is upper bound */
if (alpha > 0)
max_inc = (ub2 - vx2)/ alpha;
else
max_inc = (lb2 - vx2)/ alpha;
}
/* now check lower bound */
k = lpx_prim_ratio_test(lp, len, index, val, -1,
10e-7);
max_dec = DBL_MAX;
if (k != 0)
{ /*int stat;*/
int tagx2, typx2;
double vx2, dx2, lb2, ub2;
/*double delta;*/
double alpha;
int l;
for (l = 1; l <= len; l++)
if (index[l] == k) alpha = val[l];
if (k>m)
{ lpx_get_col_info(lp, k-m, &tagx2, &vx2,
&dx2);
lpx_get_col_bnds(lp, k-m, &typx2, &lb2,
&ub2);
}
else
{ lpx_get_row_info(lp, k, &tagx2, &vx2,
&dx2);
lpx_get_row_bnds(lp, k, &typx2, &lb2,
&ub2);
}
/* Check which direction;
remember this is lower bound */
if (alpha > 0)
max_dec = (vx2 - lb2)/ alpha;
else
max_dec = (vx2 - ub2)/ alpha;
}
}
/* bound */
if (typx == LPX_DB || typx == LPX_FX)
{ if (max_inc > ub - lb)
max_inc = ub - lb;
}
fprintf(fp, " LOWER %13.6g ", lb);
if (max_inc == -0.0) max_inc = 0.0;
if (max_dec == -0.0) max_dec = 0.0;
if (max_inc == DBL_MAX)
fprintf(fp, "%13s ", "infinity");
else if (max_inc < 1.0e-12 && max_inc > 0)
fprintf(fp, "%13s ", "< eps");
else
fprintf(fp, "%13.6g ", max_inc);
if (max_dec == DBL_MAX)
fprintf(fp, "%13s ", "infinity");
else if (max_dec < 1.0e-12 && max_dec > 0)
fprintf(fp, "%13s ", "< eps");
else
fprintf(fp, "%13.6g ", max_dec);
fprintf(fp, "\n");
}
/* now check upper bound */
if (typx == LPX_UP || typx == LPX_DB ||
typx == LPX_FX)
{ int at_upper;
at_upper = 0;
if (tagx == LPX_BS || tagx == LPX_NL)
{ max_inc = DBL_MAX;
max_dec = ub - vx;
}
if (tagx == LPX_NS)
{ max_inc = 0.0;
max_dec = 0.0;
if (dir == LPX_MIN && dx < 0) at_upper = 1;
if (dir == LPX_MAX && dx > 0) at_upper = 1;
}
if (tagx == LPX_NU || at_upper == 1)
{ int len;
/* we have to see how it affects basic
variables */
len = lpx_eval_tab_col(lp, what==1?ij:ij+m,
index, val);
k = lpx_prim_ratio_test(lp, len, index, val, 1,
10e-7);
max_inc = DBL_MAX;
if (k != 0)
{ /*int stat;*/
int tagx2, typx2;
double vx2, dx2, lb2, ub2;
/*double delta;*/
double alpha;
int l;
for (l = 1; l <= len; l++)
if (index[l] == k) alpha = val[l];
if (k>m)
{ lpx_get_col_info(lp, k-m, &tagx2, &vx2,
&dx2);
lpx_get_col_bnds(lp, k-m, &typx2, &lb2,
&ub2);
}
else
{ lpx_get_row_info(lp, k, &tagx2, &vx2,
&dx2);
lpx_get_row_bnds(lp, k, &typx2, &lb2,
&ub2);
}
/* Check which direction;
remember this is upper bound */
if (alpha > 0)
max_inc = (ub2 - vx2)/ alpha;
else
max_inc = (lb2 - vx2)/ alpha;
}
/* now check lower bound */
k = lpx_prim_ratio_test(lp, len, index, val, -1,
10e-7);
max_dec = DBL_MAX;
if (k != 0)
{ /*int stat;*/
int tagx2, typx2;
double vx2, dx2, lb2, ub2;
/*double delta;*/
double alpha;
int l;
for (l = 1; l <= len; l++)
if (index[l] == k) alpha = val[l];
if (k>m)
{ lpx_get_col_info(lp, k-m, &tagx2, &vx2,
&dx2);
lpx_get_col_bnds(lp, k-m, &typx2, &lb2,
&ub2);
}
else
{ lpx_get_row_info(lp, k, &tagx2, &vx2,
&dx2);
lpx_get_row_bnds(lp, k, &typx2, &lb2,
&ub2);
}
/* Check which direction;
remember this is lower bound */
if (alpha > 0)
max_dec = (vx2 - lb2)/ alpha;
else
max_dec = (vx2 - ub2)/ alpha;
}
}
if (typx == LPX_DB || typx == LPX_FX)
{ if (max_dec > ub - lb)
max_dec = ub - lb;
}
/* bound */
fprintf(fp, " UPPER %13.6g ", ub);
if (max_inc == -0.0) max_inc = 0.0;
if (max_dec == -0.0) max_dec = 0.0;
if (max_inc == DBL_MAX)
fprintf(fp, "%13s ", "infinity");
else if (max_inc < 1.0e-12 && max_inc > 0)
fprintf(fp, "%13s ", "< eps");
else
fprintf(fp, "%13.6g ", max_inc);
if (max_dec == DBL_MAX)
fprintf(fp, "%13s ", "infinity");
else if (max_dec < 1.0e-12 && max_dec > 0)
fprintf(fp, "%13s ", "< eps");
else
fprintf(fp, "%13.6g ", max_dec);
fprintf(fp, "\n");
}
}
}
/* free the memory we used */
ufree(index);
ufree(val);
}
else fprintf(fp, "No range information since solution is not o"
"ptimal.\n");
}
fprintf(fp, "\n");
fprintf(fp, "End of output\n");
fflush(fp);
if (ferror(fp))
{ print("lpx_print_sens_bnds: can't write to `%s' - %s", fname,
strerror(errno));
goto fail;
}
ufclose(fp);
return 0;
fail: if (fp != NULL) ufclose(fp);
return 1;
}
void lpp_unload_sol(LPP *lpp, LPX *orig)
{ int i, j, k, m, n, typx, tagx, p_stat, d_stat;
double sum;
m = lpp->orig_m;
n = lpp->orig_n;
xassert(m == lpx_get_num_rows(orig));
xassert(n == lpx_get_num_cols(orig));
xassert(lpp->orig_dir == lpx_get_obj_dir(orig));
/* check row and column statuses */
xassert(m <= lpp->nrows);
xassert(n <= lpp->ncols);
for (k = 1; k <= m+n; k++)
{ tagx = (k <= m ? lpp->row_stat[k] : lpp->col_stat[k-m]);
if (tagx != LPX_BS)
{ if (k <= m)
lpx_get_row_bnds(orig, k, &typx, NULL, NULL);
else
lpx_get_col_bnds(orig, k-m, &typx, NULL, NULL);
switch (typx)
{ case LPX_FR:
xassert(tagx == LPX_NF);
break;
case LPX_LO:
xassert(tagx == LPX_NL);
break;
case LPX_UP:
xassert(tagx == LPX_NU);
break;
case LPX_DB:
xassert(tagx == LPX_NL || tagx == LPX_NU);
break;
case LPX_FX:
xassert(tagx == LPX_NS);
break;
default:
xassert(orig != orig);
}
}
}
/* if the original problem is maximization, change signs of dual
values */
if (lpp->orig_dir == LPX_MAX)
{ for (i = 1; i <= m; i++) lpp->row_dual[i] = -lpp->row_dual[i];
for (j = 1; j <= n; j++) lpp->col_dual[j] = -lpp->col_dual[j];
}
/* store solution components into the original problem object (it
is assumed that the recovered solution is optimal) */
p_stat = d_stat = GLP_FEAS;
for (i = 1; i <= m; i++)
lpp->row_stat[i] = lpp->row_stat[i] - LPX_BS + GLP_BS;
for (j = 1; j <= n; j++)
lpp->col_stat[j] = lpp->col_stat[j] - LPX_BS + GLP_BS;
sum = lpx_get_obj_coef(orig, 0);
for (j = 1; j <= n; j++)
sum += lpx_get_obj_coef(orig, j) * lpp->col_prim[j];
glp_put_solution(orig, 1, &p_stat, &d_stat, &sum,
lpp->row_stat, lpp->row_prim, lpp->row_dual,
lpp->col_stat, lpp->col_prim, lpp->col_dual);
for (i = 1; i <= m; i++)
lpp->row_stat[i] = lpp->row_stat[i] - GLP_BS + LPX_BS;
for (j = 1; j <= n; j++)
lpp->col_stat[j] = lpp->col_stat[j] - GLP_BS + LPX_BS;
return;
}
void lpp_load_orig(LPP *lpp, LPX *orig)
{ LPPROW *row;
LPPCOL *col, **map;
int i, j, t, len, typx, *ndx;
double lb, ub, temp, *c, *val;
/* save some information about the original problem */
lpp->orig_m = lpx_get_num_rows(orig);
lpp->orig_n = lpx_get_num_cols(orig);
lpp->orig_nnz = lpx_get_num_nz(orig);
lpp->orig_dir = lpx_get_obj_dir(orig);
/* allocate working arrays */
c = xcalloc(1+lpp->orig_n, sizeof(double));
ndx = xcalloc(1+lpp->orig_n, sizeof(int));
val = xcalloc(1+lpp->orig_n, sizeof(double));
/* auxiliary variables (i.e. rows) in the original problem may
have non-zero objective coefficients; so, we substitute these
auxiliary variables into the objective function in order that
it depends only on structural variables (i.e. columns); the
resultant vector of objective coefficients is accumulated in
the working array c */
for (j = 1; j <= lpp->orig_n; j++)
c[j] = lpx_get_obj_coef(orig, j);
for (i = 1; i <= lpp->orig_m; i++)
{ /* obtain an objective coefficient at i-th row */
#if 0
temp = lpx_get_row_coef(orig, i);
#else
temp = 0.0;
#endif
/* substitute i-th row into the objective function */
if (temp != 0.0)
{ len = lpx_get_mat_row(orig, i, ndx, val);
for (t = 1; t <= len; t++) c[ndx[t]] += val[t] * temp;
}
}
/* copy rows of the original problem into the workspace; each
row created in the workspace is assigned a reference number,
which is its ordinal number in the original problem */
for (i = 1; i <= lpp->orig_m; i++)
{ lpx_get_row_bnds(orig, i, &typx, &lb, &ub);
if (typx == LPX_FR || typx == LPX_UP) lb = -DBL_MAX;
if (typx == LPX_FR || typx == LPX_LO) ub = +DBL_MAX;
if (typx == LPX_FX) ub = lb;
lpp_add_row(lpp, lb, ub);
}
/* copy columns of the original problem into the workspace; each
column created in the workspace is assigned a reference number,
which its ordinal number in the original problem */
for (j = 1; j <= lpp->orig_n; j++)
{ lpx_get_col_bnds(orig, j, &typx, &lb, &ub);
if (typx == LPX_FR || typx == LPX_UP) lb = -DBL_MAX;
if (typx == LPX_FR || typx == LPX_LO) ub = +DBL_MAX;
if (typx == LPX_FX) ub = lb;
lpp_add_col(lpp, lb, ub, c[j]);
}
/* copy the constant term of the original objective function */
lpp->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 (lpp->orig_dir == LPX_MAX)
{ for (col = lpp->col_ptr; col != NULL; col = col->next)
col->c = - col->c;
lpp->c0 = - lpp->c0;
}
/* build an auxiliary array to map column ordinal numbers to the
corresponding pointers */
xassert(sizeof(LPPCOL *) <= sizeof(double));
map = (LPPCOL **)c;
for (col = lpp->col_ptr; col != NULL; col = col->next)
map[col->j] = col;
/* copy the original constraint matrix into the workspace */
for (row = lpp->row_ptr; row != NULL; row = row->next)
#if 1
{ len = lpx_get_mat_row(orig, row->i, ndx, val);
for (t = 1; t <= len; t++)
lpp_add_aij(lpp, row, map[ndx[t]], val[t]);
}
#else /* 27/XI-2003 (the problem persists) */
{ double big, eps;
len = lpx_get_mat_row(orig, row->i, ndx, val);
big = 0.0;
for (t = 1; t <= len; t++)
if (big < fabs(val[t])) big = fabs(val[t]);
eps = 1e-10 * big;
for (t = 1; t <= len; t++)
{ if (fabs(val[t]) < eps) continue;
lpp_add_aij(lpp, row, map[ndx[t]], val[t]);
}
}
#endif
/* free working arrays */
xfree(c);
xfree(ndx);
xfree(val);
return;
}