1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/glpapi07.c Mon Dec 06 13:09:21 2010 +0100
1.3 @@ -0,0 +1,451 @@
1.4 +/* glpapi07.c (exact simplex solver) */
1.5 +
1.6 +/***********************************************************************
1.7 +* This code is part of GLPK (GNU Linear Programming Kit).
1.8 +*
1.9 +* Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
1.10 +* 2009, 2010 Andrew Makhorin, Department for Applied Informatics,
1.11 +* Moscow Aviation Institute, Moscow, Russia. All rights reserved.
1.12 +* E-mail: <mao@gnu.org>.
1.13 +*
1.14 +* GLPK is free software: you can redistribute it and/or modify it
1.15 +* under the terms of the GNU General Public License as published by
1.16 +* the Free Software Foundation, either version 3 of the License, or
1.17 +* (at your option) any later version.
1.18 +*
1.19 +* GLPK is distributed in the hope that it will be useful, but WITHOUT
1.20 +* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
1.21 +* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
1.22 +* License for more details.
1.23 +*
1.24 +* You should have received a copy of the GNU General Public License
1.25 +* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
1.26 +***********************************************************************/
1.27 +
1.28 +#include "glpapi.h"
1.29 +#include "glpssx.h"
1.30 +
1.31 +/***********************************************************************
1.32 +* NAME
1.33 +*
1.34 +* glp_exact - solve LP problem in exact arithmetic
1.35 +*
1.36 +* SYNOPSIS
1.37 +*
1.38 +* int glp_exact(glp_prob *lp, const glp_smcp *parm);
1.39 +*
1.40 +* DESCRIPTION
1.41 +*
1.42 +* The routine glp_exact is a tentative implementation of the primal
1.43 +* two-phase simplex method based on exact (rational) arithmetic. It is
1.44 +* similar to the routine glp_simplex, however, for all internal
1.45 +* computations it uses arithmetic of rational numbers, which is exact
1.46 +* in mathematical sense, i.e. free of round-off errors unlike floating
1.47 +* point arithmetic.
1.48 +*
1.49 +* Note that the routine glp_exact uses inly two control parameters
1.50 +* passed in the structure glp_smcp, namely, it_lim and tm_lim.
1.51 +*
1.52 +* RETURNS
1.53 +*
1.54 +* 0 The LP problem instance has been successfully solved. This code
1.55 +* does not necessarily mean that the solver has found optimal
1.56 +* solution. It only means that the solution process was successful.
1.57 +*
1.58 +* GLP_EBADB
1.59 +* Unable to start the search, because the initial basis specified
1.60 +* in the problem object is invalid--the number of basic (auxiliary
1.61 +* and structural) variables is not the same as the number of rows in
1.62 +* the problem object.
1.63 +*
1.64 +* GLP_ESING
1.65 +* Unable to start the search, because the basis matrix correspodning
1.66 +* to the initial basis is exactly singular.
1.67 +*
1.68 +* GLP_EBOUND
1.69 +* Unable to start the search, because some double-bounded variables
1.70 +* have incorrect bounds.
1.71 +*
1.72 +* GLP_EFAIL
1.73 +* The problem has no rows/columns.
1.74 +*
1.75 +* GLP_EITLIM
1.76 +* The search was prematurely terminated, because the simplex
1.77 +* iteration limit has been exceeded.
1.78 +*
1.79 +* GLP_ETMLIM
1.80 +* The search was prematurely terminated, because the time limit has
1.81 +* been exceeded. */
1.82 +
1.83 +static void set_d_eps(mpq_t x, double val)
1.84 +{ /* convert double val to rational x obtaining a more adequate
1.85 + fraction than provided by mpq_set_d due to allowing a small
1.86 + approximation error specified by a given relative tolerance;
1.87 + for example, mpq_set_d would give the following
1.88 + 1/3 ~= 0.333333333333333314829616256247391... ->
1.89 + -> 6004799503160661/18014398509481984
1.90 + while this routine gives exactly 1/3 */
1.91 + int s, n, j;
1.92 + double f, p, q, eps = 1e-9;
1.93 + mpq_t temp;
1.94 + xassert(-DBL_MAX <= val && val <= +DBL_MAX);
1.95 +#if 1 /* 30/VII-2008 */
1.96 + if (val == floor(val))
1.97 + { /* if val is integral, do not approximate */
1.98 + mpq_set_d(x, val);
1.99 + goto done;
1.100 + }
1.101 +#endif
1.102 + if (val > 0.0)
1.103 + s = +1;
1.104 + else if (val < 0.0)
1.105 + s = -1;
1.106 + else
1.107 + { mpq_set_si(x, 0, 1);
1.108 + goto done;
1.109 + }
1.110 + f = frexp(fabs(val), &n);
1.111 + /* |val| = f * 2^n, where 0.5 <= f < 1.0 */
1.112 + fp2rat(f, 0.1 * eps, &p, &q);
1.113 + /* f ~= p / q, where p and q are integers */
1.114 + mpq_init(temp);
1.115 + mpq_set_d(x, p);
1.116 + mpq_set_d(temp, q);
1.117 + mpq_div(x, x, temp);
1.118 + mpq_set_si(temp, 1, 1);
1.119 + for (j = 1; j <= abs(n); j++)
1.120 + mpq_add(temp, temp, temp);
1.121 + if (n > 0)
1.122 + mpq_mul(x, x, temp);
1.123 + else if (n < 0)
1.124 + mpq_div(x, x, temp);
1.125 + mpq_clear(temp);
1.126 + if (s < 0) mpq_neg(x, x);
1.127 + /* check that the desired tolerance has been attained */
1.128 + xassert(fabs(val - mpq_get_d(x)) <= eps * (1.0 + fabs(val)));
1.129 +done: return;
1.130 +}
1.131 +
1.132 +static void load_data(SSX *ssx, LPX *lp)
1.133 +{ /* load LP problem data into simplex solver workspace */
1.134 + int m = ssx->m;
1.135 + int n = ssx->n;
1.136 + int nnz = ssx->A_ptr[n+1]-1;
1.137 + int j, k, type, loc, len, *ind;
1.138 + double lb, ub, coef, *val;
1.139 + xassert(lpx_get_num_rows(lp) == m);
1.140 + xassert(lpx_get_num_cols(lp) == n);
1.141 + xassert(lpx_get_num_nz(lp) == nnz);
1.142 + /* types and bounds of rows and columns */
1.143 + for (k = 1; k <= m+n; k++)
1.144 + { if (k <= m)
1.145 + { type = lpx_get_row_type(lp, k);
1.146 + lb = lpx_get_row_lb(lp, k);
1.147 + ub = lpx_get_row_ub(lp, k);
1.148 + }
1.149 + else
1.150 + { type = lpx_get_col_type(lp, k-m);
1.151 + lb = lpx_get_col_lb(lp, k-m);
1.152 + ub = lpx_get_col_ub(lp, k-m);
1.153 + }
1.154 + switch (type)
1.155 + { case LPX_FR: type = SSX_FR; break;
1.156 + case LPX_LO: type = SSX_LO; break;
1.157 + case LPX_UP: type = SSX_UP; break;
1.158 + case LPX_DB: type = SSX_DB; break;
1.159 + case LPX_FX: type = SSX_FX; break;
1.160 + default: xassert(type != type);
1.161 + }
1.162 + ssx->type[k] = type;
1.163 + set_d_eps(ssx->lb[k], lb);
1.164 + set_d_eps(ssx->ub[k], ub);
1.165 + }
1.166 + /* optimization direction */
1.167 + switch (lpx_get_obj_dir(lp))
1.168 + { case LPX_MIN: ssx->dir = SSX_MIN; break;
1.169 + case LPX_MAX: ssx->dir = SSX_MAX; break;
1.170 + default: xassert(lp != lp);
1.171 + }
1.172 + /* objective coefficients */
1.173 + for (k = 0; k <= m+n; k++)
1.174 + { if (k == 0)
1.175 + coef = lpx_get_obj_coef(lp, 0);
1.176 + else if (k <= m)
1.177 + coef = 0.0;
1.178 + else
1.179 + coef = lpx_get_obj_coef(lp, k-m);
1.180 + set_d_eps(ssx->coef[k], coef);
1.181 + }
1.182 + /* constraint coefficients */
1.183 + ind = xcalloc(1+m, sizeof(int));
1.184 + val = xcalloc(1+m, sizeof(double));
1.185 + loc = 0;
1.186 + for (j = 1; j <= n; j++)
1.187 + { ssx->A_ptr[j] = loc+1;
1.188 + len = lpx_get_mat_col(lp, j, ind, val);
1.189 + for (k = 1; k <= len; k++)
1.190 + { loc++;
1.191 + ssx->A_ind[loc] = ind[k];
1.192 + set_d_eps(ssx->A_val[loc], val[k]);
1.193 + }
1.194 + }
1.195 + xassert(loc == nnz);
1.196 + xfree(ind);
1.197 + xfree(val);
1.198 + return;
1.199 +}
1.200 +
1.201 +static int load_basis(SSX *ssx, LPX *lp)
1.202 +{ /* load current LP basis into simplex solver workspace */
1.203 + int m = ssx->m;
1.204 + int n = ssx->n;
1.205 + int *type = ssx->type;
1.206 + int *stat = ssx->stat;
1.207 + int *Q_row = ssx->Q_row;
1.208 + int *Q_col = ssx->Q_col;
1.209 + int i, j, k;
1.210 + xassert(lpx_get_num_rows(lp) == m);
1.211 + xassert(lpx_get_num_cols(lp) == n);
1.212 + /* statuses of rows and columns */
1.213 + for (k = 1; k <= m+n; k++)
1.214 + { if (k <= m)
1.215 + stat[k] = lpx_get_row_stat(lp, k);
1.216 + else
1.217 + stat[k] = lpx_get_col_stat(lp, k-m);
1.218 + switch (stat[k])
1.219 + { case LPX_BS:
1.220 + stat[k] = SSX_BS;
1.221 + break;
1.222 + case LPX_NL:
1.223 + stat[k] = SSX_NL;
1.224 + xassert(type[k] == SSX_LO || type[k] == SSX_DB);
1.225 + break;
1.226 + case LPX_NU:
1.227 + stat[k] = SSX_NU;
1.228 + xassert(type[k] == SSX_UP || type[k] == SSX_DB);
1.229 + break;
1.230 + case LPX_NF:
1.231 + stat[k] = SSX_NF;
1.232 + xassert(type[k] == SSX_FR);
1.233 + break;
1.234 + case LPX_NS:
1.235 + stat[k] = SSX_NS;
1.236 + xassert(type[k] == SSX_FX);
1.237 + break;
1.238 + default:
1.239 + xassert(stat != stat);
1.240 + }
1.241 + }
1.242 + /* build permutation matix Q */
1.243 + i = j = 0;
1.244 + for (k = 1; k <= m+n; k++)
1.245 + { if (stat[k] == SSX_BS)
1.246 + { i++;
1.247 + if (i > m) return 1;
1.248 + Q_row[k] = i, Q_col[i] = k;
1.249 + }
1.250 + else
1.251 + { j++;
1.252 + if (j > n) return 1;
1.253 + Q_row[k] = m+j, Q_col[m+j] = k;
1.254 + }
1.255 + }
1.256 + xassert(i == m && j == n);
1.257 + return 0;
1.258 +}
1.259 +
1.260 +int glp_exact(glp_prob *lp, const glp_smcp *parm)
1.261 +{ glp_smcp _parm;
1.262 + SSX *ssx;
1.263 + int m = lpx_get_num_rows(lp);
1.264 + int n = lpx_get_num_cols(lp);
1.265 + int nnz = lpx_get_num_nz(lp);
1.266 + int i, j, k, type, pst, dst, ret, *stat;
1.267 + double lb, ub, *prim, *dual, sum;
1.268 + if (parm == NULL)
1.269 + parm = &_parm, glp_init_smcp((glp_smcp *)parm);
1.270 + /* check control parameters */
1.271 + if (parm->it_lim < 0)
1.272 + xerror("glp_exact: it_lim = %d; invalid parameter\n",
1.273 + parm->it_lim);
1.274 + if (parm->tm_lim < 0)
1.275 + xerror("glp_exact: tm_lim = %d; invalid parameter\n",
1.276 + parm->tm_lim);
1.277 + /* the problem must have at least one row and one column */
1.278 + if (!(m > 0 && n > 0))
1.279 + { xprintf("glp_exact: problem has no rows/columns\n");
1.280 + return GLP_EFAIL;
1.281 + }
1.282 +#if 1
1.283 + /* basic solution is currently undefined */
1.284 + lp->pbs_stat = lp->dbs_stat = GLP_UNDEF;
1.285 + lp->obj_val = 0.0;
1.286 + lp->some = 0;
1.287 +#endif
1.288 + /* check that all double-bounded variables have correct bounds */
1.289 + for (k = 1; k <= m+n; k++)
1.290 + { if (k <= m)
1.291 + { type = lpx_get_row_type(lp, k);
1.292 + lb = lpx_get_row_lb(lp, k);
1.293 + ub = lpx_get_row_ub(lp, k);
1.294 + }
1.295 + else
1.296 + { type = lpx_get_col_type(lp, k-m);
1.297 + lb = lpx_get_col_lb(lp, k-m);
1.298 + ub = lpx_get_col_ub(lp, k-m);
1.299 + }
1.300 + if (type == LPX_DB && lb >= ub)
1.301 + { xprintf("glp_exact: %s %d has invalid bounds\n",
1.302 + k <= m ? "row" : "column", k <= m ? k : k-m);
1.303 + return GLP_EBOUND;
1.304 + }
1.305 + }
1.306 + /* create the simplex solver workspace */
1.307 + xprintf("glp_exact: %d rows, %d columns, %d non-zeros\n",
1.308 + m, n, nnz);
1.309 +#ifdef HAVE_GMP
1.310 + xprintf("GNU MP bignum library is being used\n");
1.311 +#else
1.312 + xprintf("GLPK bignum module is being used\n");
1.313 + xprintf("(Consider installing GNU MP to attain a much better perf"
1.314 + "ormance.)\n");
1.315 +#endif
1.316 + ssx = ssx_create(m, n, nnz);
1.317 + /* load LP problem data into the workspace */
1.318 + load_data(ssx, lp);
1.319 + /* load current LP basis into the workspace */
1.320 + if (load_basis(ssx, lp))
1.321 + { xprintf("glp_exact: initial LP basis is invalid\n");
1.322 + ret = GLP_EBADB;
1.323 + goto done;
1.324 + }
1.325 + /* inherit some control parameters from the LP object */
1.326 +#if 0
1.327 + ssx->it_lim = lpx_get_int_parm(lp, LPX_K_ITLIM);
1.328 + ssx->it_cnt = lpx_get_int_parm(lp, LPX_K_ITCNT);
1.329 + ssx->tm_lim = lpx_get_real_parm(lp, LPX_K_TMLIM);
1.330 +#else
1.331 + ssx->it_lim = parm->it_lim;
1.332 + ssx->it_cnt = lp->it_cnt;
1.333 + ssx->tm_lim = (double)parm->tm_lim / 1000.0;
1.334 +#endif
1.335 + ssx->out_frq = 5.0;
1.336 + ssx->tm_beg = xtime();
1.337 + ssx->tm_lag = xlset(0);
1.338 + /* solve LP */
1.339 + ret = ssx_driver(ssx);
1.340 + /* copy back some statistics to the LP object */
1.341 +#if 0
1.342 + lpx_set_int_parm(lp, LPX_K_ITLIM, ssx->it_lim);
1.343 + lpx_set_int_parm(lp, LPX_K_ITCNT, ssx->it_cnt);
1.344 + lpx_set_real_parm(lp, LPX_K_TMLIM, ssx->tm_lim);
1.345 +#else
1.346 + lp->it_cnt = ssx->it_cnt;
1.347 +#endif
1.348 + /* analyze the return code */
1.349 + switch (ret)
1.350 + { case 0:
1.351 + /* optimal solution found */
1.352 + ret = 0;
1.353 + pst = LPX_P_FEAS, dst = LPX_D_FEAS;
1.354 + break;
1.355 + case 1:
1.356 + /* problem has no feasible solution */
1.357 + ret = 0;
1.358 + pst = LPX_P_NOFEAS, dst = LPX_D_INFEAS;
1.359 + break;
1.360 + case 2:
1.361 + /* problem has unbounded solution */
1.362 + ret = 0;
1.363 + pst = LPX_P_FEAS, dst = LPX_D_NOFEAS;
1.364 +#if 1
1.365 + xassert(1 <= ssx->q && ssx->q <= n);
1.366 + lp->some = ssx->Q_col[m + ssx->q];
1.367 + xassert(1 <= lp->some && lp->some <= m+n);
1.368 +#endif
1.369 + break;
1.370 + case 3:
1.371 + /* iteration limit exceeded (phase I) */
1.372 + ret = GLP_EITLIM;
1.373 + pst = LPX_P_INFEAS, dst = LPX_D_INFEAS;
1.374 + break;
1.375 + case 4:
1.376 + /* iteration limit exceeded (phase II) */
1.377 + ret = GLP_EITLIM;
1.378 + pst = LPX_P_FEAS, dst = LPX_D_INFEAS;
1.379 + break;
1.380 + case 5:
1.381 + /* time limit exceeded (phase I) */
1.382 + ret = GLP_ETMLIM;
1.383 + pst = LPX_P_INFEAS, dst = LPX_D_INFEAS;
1.384 + break;
1.385 + case 6:
1.386 + /* time limit exceeded (phase II) */
1.387 + ret = GLP_ETMLIM;
1.388 + pst = LPX_P_FEAS, dst = LPX_D_INFEAS;
1.389 + break;
1.390 + case 7:
1.391 + /* initial basis matrix is singular */
1.392 + ret = GLP_ESING;
1.393 + goto done;
1.394 + default:
1.395 + xassert(ret != ret);
1.396 + }
1.397 + /* obtain final basic solution components */
1.398 + stat = xcalloc(1+m+n, sizeof(int));
1.399 + prim = xcalloc(1+m+n, sizeof(double));
1.400 + dual = xcalloc(1+m+n, sizeof(double));
1.401 + for (k = 1; k <= m+n; k++)
1.402 + { if (ssx->stat[k] == SSX_BS)
1.403 + { i = ssx->Q_row[k]; /* x[k] = xB[i] */
1.404 + xassert(1 <= i && i <= m);
1.405 + stat[k] = LPX_BS;
1.406 + prim[k] = mpq_get_d(ssx->bbar[i]);
1.407 + dual[k] = 0.0;
1.408 + }
1.409 + else
1.410 + { j = ssx->Q_row[k] - m; /* x[k] = xN[j] */
1.411 + xassert(1 <= j && j <= n);
1.412 + switch (ssx->stat[k])
1.413 + { case SSX_NF:
1.414 + stat[k] = LPX_NF;
1.415 + prim[k] = 0.0;
1.416 + break;
1.417 + case SSX_NL:
1.418 + stat[k] = LPX_NL;
1.419 + prim[k] = mpq_get_d(ssx->lb[k]);
1.420 + break;
1.421 + case SSX_NU:
1.422 + stat[k] = LPX_NU;
1.423 + prim[k] = mpq_get_d(ssx->ub[k]);
1.424 + break;
1.425 + case SSX_NS:
1.426 + stat[k] = LPX_NS;
1.427 + prim[k] = mpq_get_d(ssx->lb[k]);
1.428 + break;
1.429 + default:
1.430 + xassert(ssx != ssx);
1.431 + }
1.432 + dual[k] = mpq_get_d(ssx->cbar[j]);
1.433 + }
1.434 + }
1.435 + /* and store them into the LP object */
1.436 + pst = pst - LPX_P_UNDEF + GLP_UNDEF;
1.437 + dst = dst - LPX_D_UNDEF + GLP_UNDEF;
1.438 + for (k = 1; k <= m+n; k++)
1.439 + stat[k] = stat[k] - LPX_BS + GLP_BS;
1.440 + sum = lpx_get_obj_coef(lp, 0);
1.441 + for (j = 1; j <= n; j++)
1.442 + sum += lpx_get_obj_coef(lp, j) * prim[m+j];
1.443 + lpx_put_solution(lp, 1, &pst, &dst, &sum,
1.444 + &stat[0], &prim[0], &dual[0], &stat[m], &prim[m], &dual[m]);
1.445 + xfree(stat);
1.446 + xfree(prim);
1.447 + xfree(dual);
1.448 +done: /* delete the simplex solver workspace */
1.449 + ssx_delete(ssx);
1.450 + /* return to the application program */
1.451 + return ret;
1.452 +}
1.453 +
1.454 +/* eof */