void ipp_unload_sol(IPP *ipp, LPX *orig, int i_stat)
{ int i, j, k, len, *ind;
double temp, *row_mipx, *val;
xassert(ipp->orig_m == lpx_get_num_rows(orig));
xassert(ipp->orig_n == lpx_get_num_cols(orig));
xassert(ipp->orig_dir == lpx_get_obj_dir(orig));
/* all columns must be computed/recovered */
xassert(ipp->orig_n <= ipp->ncols);
for (j = 1; j <= ipp->ncols; j++) xassert(ipp->col_stat[j]);
/* compute values of auxiliary variables using known values of
structural variables (columns) */
row_mipx = xcalloc(1+ipp->orig_m, sizeof(double));
ind = xcalloc(1+ipp->orig_n, sizeof(int));
val = xcalloc(1+ipp->orig_n, sizeof(double));
for (i = 1; i <= ipp->orig_m; i++)
{ len = lpx_get_mat_row(orig, i, ind, val);
temp = 0.0;
for (k = 1; k <= len; k++)
temp += val[k] * ipp->col_mipx[ind[k]];
row_mipx[i] = temp;
}
xfree(ind);
xfree(val);
/* store solution components into the original problem object */
lpx_put_mip_soln(orig, i_stat, row_mipx, ipp->col_mipx);
xfree(row_mipx);
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_reduce_form(LPX *lp, int len, int ind[], double val[],
double _work[])
{ int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int i, j, k, t;
double *work = _work;
/* allocate working array */
if (_work == NULL) work = ucalloc(1+m+n, sizeof(double));
/* convert the original linear form to dense format */
for (k = 1; k <= m+n; k++)
work[k] = 0.0;
for (t = 1; t <= len; t++)
{ k = ind[t];
if (!(1 <= k && k <= m+n))
fault("lpx_reduce_form: ind[%d] = %d; ordinal number out of"
" range", t, k);
work[k] += val[t];
}
/* perform substitution */
for (i = 1; i <= m; i++)
{ /* substitute x[i] = a[i,1]*x[m+1] + ... + a[i,n]*x[m+n] */
if (work[i] == 0.0) continue;
len = lpx_get_mat_row(lp, i, ind, val);
for (t = 1; t <= len; t++)
{ j = ind[t];
work[m+j] += work[i] * val[t];
}
}
/* convert the resultant linear form to sparse format */
len = 0;
for (j = 1; j <= n; j++)
{ if (work[m+j] == 0.0) continue;
len++;
ind[len] = j;
val[len] = work[m+j];
}
/* free working array */
if (_work == NULL) ufree(work);
return len;
}
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 = ucalloc(1+lpp->orig_n, sizeof(double));
ndx = ucalloc(1+lpp->orig_n, sizeof(int));
val = ucalloc(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_col_coef(orig, j);
for (i = 1; i <= lpp->orig_m; i++)
{ /* obtain an objective coefficient at i-th row */
temp = lpx_get_row_coef(orig, i);
/* 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_c0(orig);
/* 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 */
insist(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 */
ufree(c);
ufree(ndx);
ufree(val);
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;
}
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;
}
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 lpx_check_int(LPX *lp, LPXKKT *kkt)
{ int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int *ind, i, len, t, j, k, type;
double *val, xR_i, g_i, xS_j, temp, lb, ub, x_k, h_k;
/*--------------------------------------------------------------*/
/* 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;
ind = xcalloc(1+n, sizeof(int));
val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ /* determine xR[i] */
xR_i = lpx_mip_row_val(lp, i);
/* g[i] := xR[i] */
g_i = xR_i;
/* g[i] := g[i] - (i-th row of A) * xS */
len = lpx_get_mat_row(lp, i, ind, val);
for (t = 1; t <= len; t++)
{ j = ind[t];
/* determine xS[j] */
xS_j = lpx_mip_col_val(lp, j);
/* g[i] := g[i] - a[i,j] * xS[j] */
g_i -= val[t] * xS_j;
}
/* 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(ind);
xfree(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)
{ i = k;
type = lpx_get_row_type(lp, i);
lb = lpx_get_row_lb(lp, i);
ub = lpx_get_row_ub(lp, i);
x_k = lpx_mip_row_val(lp, i);
}
else
{ j = k - m;
type = lpx_get_col_type(lp, j);
lb = lpx_get_col_lb(lp, j);
ub = lpx_get_col_ub(lp, j);
x_k = lpx_mip_col_val(lp, j);
}
/* compute h[k] */
h_k = 0.0;
switch (type)
{ 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(type != type);
}
/* 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 = '?';
return;
}
void *lpx_create_cog(LPX *lp)
{ struct COG *cog = NULL;
int m, n, nb, i, j, p, q, len, *ind, *vert, *orig;
double L, U, lf_min, lf_max, *val;
xprintf("Creating the conflict graph...\n");
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* determine which binary variables should be included in the
conflict graph */
nb = 0;
vert = xcalloc(1+n, sizeof(int));
for (j = 1; j <= n; j++) vert[j] = 0;
orig = xcalloc(1+n, sizeof(int));
ind = xcalloc(1+n, sizeof(int));
val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ L = get_row_lb(lp, i);
U = get_row_ub(lp, i);
if (L == -DBL_MAX && U == +DBL_MAX) continue;
len = lpx_get_mat_row(lp, i, ind, val);
if (len > MAX_ROW_LEN) continue;
lf_min = eval_lf_min(lp, len, ind, val);
lf_max = eval_lf_max(lp, len, ind, val);
for (p = 1; p <= len; p++)
{ if (!is_binary(lp, ind[p])) continue;
for (q = p+1; q <= len; q++)
{ if (!is_binary(lp, ind[q])) continue;
if (probing(len, val, L, U, lf_min, lf_max, p, 0, q) ||
probing(len, val, L, U, lf_min, lf_max, p, 1, q))
{ /* there is a logical relation */
/* include the first variable in the graph */
j = ind[p];
if (vert[j] == 0) nb++, vert[j] = nb, orig[nb] = j;
/* incude the second variable in the graph */
j = ind[q];
if (vert[j] == 0) nb++, vert[j] = nb, orig[nb] = j;
}
}
}
}
/* if the graph is either empty or has too many vertices, do not
create it */
if (nb == 0 || nb > MAX_NB)
{ xprintf("The conflict graph is either empty or too big\n");
xfree(vert);
xfree(orig);
goto done;
}
/* create the conflict graph */
cog = xmalloc(sizeof(struct COG));
cog->n = n;
cog->nb = nb;
cog->ne = 0;
cog->vert = vert;
cog->orig = orig;
len = nb + nb; /* number of vertices */
len = (len * (len - 1)) / 2; /* number of entries in triangle */
len = (len + (CHAR_BIT - 1)) / CHAR_BIT; /* bytes needed */
cog->a = xmalloc(len);
memset(cog->a, 0, len);
for (j = 1; j <= nb; j++)
{ /* add edge between variable and its complement */
lpx_add_cog_edge(cog, +orig[j], -orig[j]);
}
for (i = 1; i <= m; i++)
{ L = get_row_lb(lp, i);
U = get_row_ub(lp, i);
if (L == -DBL_MAX && U == +DBL_MAX) continue;
len = lpx_get_mat_row(lp, i, ind, val);
if (len > MAX_ROW_LEN) continue;
lf_min = eval_lf_min(lp, len, ind, val);
lf_max = eval_lf_max(lp, len, ind, val);
for (p = 1; p <= len; p++)
{ if (!is_binary(lp, ind[p])) continue;
for (q = p+1; q <= len; q++)
{ if (!is_binary(lp, ind[q])) continue;
/* set x[p] to 0 and examine x[q] */
switch (probing(len, val, L, U, lf_min, lf_max, p, 0, q))
{ case 0:
/* no logical relation */
break;
case 1:
/* x[p] = 0 implies x[q] = 0 */
lpx_add_cog_edge(cog, -ind[p], +ind[q]);
break;
case 2:
/* x[p] = 0 implies x[q] = 1 */
lpx_add_cog_edge(cog, -ind[p], -ind[q]);
break;
default:
xassert(lp != lp);
}
/* set x[p] to 1 and examine x[q] */
switch (probing(len, val, L, U, lf_min, lf_max, p, 1, q))
{ case 0:
/* no logical relation */
break;
case 1:
/* x[p] = 1 implies x[q] = 0 */
lpx_add_cog_edge(cog, +ind[p], +ind[q]);
break;
case 2:
/* x[p] = 1 implies x[q] = 1 */
lpx_add_cog_edge(cog, +ind[p], -ind[q]);
break;
default:
xassert(lp != lp);
}
}
}
}
xprintf("The conflict graph has 2*%d vertices and %d edges\n",
cog->nb, cog->ne);
done: xfree(ind);
xfree(val);
return cog;
}
