alpar@1: /* glpapi07.c (exact simplex solver) */
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  This code is part of GLPK (GNU Linear Programming Kit).
alpar@1: *
alpar@1: *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
alpar@1: *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,
alpar@1: *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.
alpar@1: *  E-mail: <mao@gnu.org>.
alpar@1: *
alpar@1: *  GLPK is free software: you can redistribute it and/or modify it
alpar@1: *  under the terms of the GNU General Public License as published by
alpar@1: *  the Free Software Foundation, either version 3 of the License, or
alpar@1: *  (at your option) any later version.
alpar@1: *
alpar@1: *  GLPK is distributed in the hope that it will be useful, but WITHOUT
alpar@1: *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
alpar@1: *  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
alpar@1: *  License for more details.
alpar@1: *
alpar@1: *  You should have received a copy of the GNU General Public License
alpar@1: *  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
alpar@1: ***********************************************************************/
alpar@1: 
alpar@1: #include "glpapi.h"
alpar@1: #include "glpssx.h"
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  glp_exact - solve LP problem in exact arithmetic
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  int glp_exact(glp_prob *lp, const glp_smcp *parm);
alpar@1: *
alpar@1: *  DESCRIPTION
alpar@1: *
alpar@1: *  The routine glp_exact is a tentative implementation of the primal
alpar@1: *  two-phase simplex method based on exact (rational) arithmetic. It is
alpar@1: *  similar to the routine glp_simplex, however, for all internal
alpar@1: *  computations it uses arithmetic of rational numbers, which is exact
alpar@1: *  in mathematical sense, i.e. free of round-off errors unlike floating
alpar@1: *  point arithmetic.
alpar@1: *
alpar@1: *  Note that the routine glp_exact uses inly two control parameters
alpar@1: *  passed in the structure glp_smcp, namely, it_lim and tm_lim.
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  0  The LP problem instance has been successfully solved. This code
alpar@1: *     does not necessarily mean that the solver has found optimal
alpar@1: *     solution. It only means that the solution process was successful.
alpar@1: *
alpar@1: *  GLP_EBADB
alpar@1: *     Unable to start the search, because the initial basis specified
alpar@1: *     in the problem object is invalid--the number of basic (auxiliary
alpar@1: *     and structural) variables is not the same as the number of rows in
alpar@1: *     the problem object.
alpar@1: *
alpar@1: *  GLP_ESING
alpar@1: *     Unable to start the search, because the basis matrix correspodning
alpar@1: *     to the initial basis is exactly singular.
alpar@1: *
alpar@1: *  GLP_EBOUND
alpar@1: *     Unable to start the search, because some double-bounded variables
alpar@1: *     have incorrect bounds.
alpar@1: *
alpar@1: *  GLP_EFAIL
alpar@1: *     The problem has no rows/columns.
alpar@1: *
alpar@1: *  GLP_EITLIM
alpar@1: *     The search was prematurely terminated, because the simplex
alpar@1: *     iteration limit has been exceeded.
alpar@1: *
alpar@1: *  GLP_ETMLIM
alpar@1: *     The search was prematurely terminated, because the time limit has
alpar@1: *     been exceeded. */
alpar@1: 
alpar@1: static void set_d_eps(mpq_t x, double val)
alpar@1: {     /* convert double val to rational x obtaining a more adequate
alpar@1:          fraction than provided by mpq_set_d due to allowing a small
alpar@1:          approximation error specified by a given relative tolerance;
alpar@1:          for example, mpq_set_d would give the following
alpar@1:          1/3 ~= 0.333333333333333314829616256247391... ->
alpar@1:              -> 6004799503160661/18014398509481984
alpar@1:          while this routine gives exactly 1/3 */
alpar@1:       int s, n, j;
alpar@1:       double f, p, q, eps = 1e-9;
alpar@1:       mpq_t temp;
alpar@1:       xassert(-DBL_MAX <= val && val <= +DBL_MAX);
alpar@1: #if 1 /* 30/VII-2008 */
alpar@1:       if (val == floor(val))
alpar@1:       {  /* if val is integral, do not approximate */
alpar@1:          mpq_set_d(x, val);
alpar@1:          goto done;
alpar@1:       }
alpar@1: #endif
alpar@1:       if (val > 0.0)
alpar@1:          s = +1;
alpar@1:       else if (val < 0.0)
alpar@1:          s = -1;
alpar@1:       else
alpar@1:       {  mpq_set_si(x, 0, 1);
alpar@1:          goto done;
alpar@1:       }
alpar@1:       f = frexp(fabs(val), &n);
alpar@1:       /* |val| = f * 2^n, where 0.5 <= f < 1.0 */
alpar@1:       fp2rat(f, 0.1 * eps, &p, &q);
alpar@1:       /* f ~= p / q, where p and q are integers */
alpar@1:       mpq_init(temp);
alpar@1:       mpq_set_d(x, p);
alpar@1:       mpq_set_d(temp, q);
alpar@1:       mpq_div(x, x, temp);
alpar@1:       mpq_set_si(temp, 1, 1);
alpar@1:       for (j = 1; j <= abs(n); j++)
alpar@1:          mpq_add(temp, temp, temp);
alpar@1:       if (n > 0)
alpar@1:          mpq_mul(x, x, temp);
alpar@1:       else if (n < 0)
alpar@1:          mpq_div(x, x, temp);
alpar@1:       mpq_clear(temp);
alpar@1:       if (s < 0) mpq_neg(x, x);
alpar@1:       /* check that the desired tolerance has been attained */
alpar@1:       xassert(fabs(val - mpq_get_d(x)) <= eps * (1.0 + fabs(val)));
alpar@1: done: return;
alpar@1: }
alpar@1: 
alpar@1: static void load_data(SSX *ssx, LPX *lp)
alpar@1: {     /* load LP problem data into simplex solver workspace */
alpar@1:       int m = ssx->m;
alpar@1:       int n = ssx->n;
alpar@1:       int nnz = ssx->A_ptr[n+1]-1;
alpar@1:       int j, k, type, loc, len, *ind;
alpar@1:       double lb, ub, coef, *val;
alpar@1:       xassert(lpx_get_num_rows(lp) == m);
alpar@1:       xassert(lpx_get_num_cols(lp) == n);
alpar@1:       xassert(lpx_get_num_nz(lp) == nnz);
alpar@1:       /* types and bounds of rows and columns */
alpar@1:       for (k = 1; k <= m+n; k++)
alpar@1:       {  if (k <= m)
alpar@1:          {  type = lpx_get_row_type(lp, k);
alpar@1:             lb = lpx_get_row_lb(lp, k);
alpar@1:             ub = lpx_get_row_ub(lp, k);
alpar@1:          }
alpar@1:          else
alpar@1:          {  type = lpx_get_col_type(lp, k-m);
alpar@1:             lb = lpx_get_col_lb(lp, k-m);
alpar@1:             ub = lpx_get_col_ub(lp, k-m);
alpar@1:          }
alpar@1:          switch (type)
alpar@1:          {  case LPX_FR: type = SSX_FR; break;
alpar@1:             case LPX_LO: type = SSX_LO; break;
alpar@1:             case LPX_UP: type = SSX_UP; break;
alpar@1:             case LPX_DB: type = SSX_DB; break;
alpar@1:             case LPX_FX: type = SSX_FX; break;
alpar@1:             default: xassert(type != type);
alpar@1:          }
alpar@1:          ssx->type[k] = type;
alpar@1:          set_d_eps(ssx->lb[k], lb);
alpar@1:          set_d_eps(ssx->ub[k], ub);
alpar@1:       }
alpar@1:       /* optimization direction */
alpar@1:       switch (lpx_get_obj_dir(lp))
alpar@1:       {  case LPX_MIN: ssx->dir = SSX_MIN; break;
alpar@1:          case LPX_MAX: ssx->dir = SSX_MAX; break;
alpar@1:          default: xassert(lp != lp);
alpar@1:       }
alpar@1:       /* objective coefficients */
alpar@1:       for (k = 0; k <= m+n; k++)
alpar@1:       {  if (k == 0)
alpar@1:             coef = lpx_get_obj_coef(lp, 0);
alpar@1:          else if (k <= m)
alpar@1:             coef = 0.0;
alpar@1:          else
alpar@1:             coef = lpx_get_obj_coef(lp, k-m);
alpar@1:          set_d_eps(ssx->coef[k], coef);
alpar@1:       }
alpar@1:       /* constraint coefficients */
alpar@1:       ind = xcalloc(1+m, sizeof(int));
alpar@1:       val = xcalloc(1+m, sizeof(double));
alpar@1:       loc = 0;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  ssx->A_ptr[j] = loc+1;
alpar@1:          len = lpx_get_mat_col(lp, j, ind, val);
alpar@1:          for (k = 1; k <= len; k++)
alpar@1:          {  loc++;
alpar@1:             ssx->A_ind[loc] = ind[k];
alpar@1:             set_d_eps(ssx->A_val[loc], val[k]);
alpar@1:          }
alpar@1:       }
alpar@1:       xassert(loc == nnz);
alpar@1:       xfree(ind);
alpar@1:       xfree(val);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static int load_basis(SSX *ssx, LPX *lp)
alpar@1: {     /* load current LP basis into simplex solver workspace */
alpar@1:       int m = ssx->m;
alpar@1:       int n = ssx->n;
alpar@1:       int *type = ssx->type;
alpar@1:       int *stat = ssx->stat;
alpar@1:       int *Q_row = ssx->Q_row;
alpar@1:       int *Q_col = ssx->Q_col;
alpar@1:       int i, j, k;
alpar@1:       xassert(lpx_get_num_rows(lp) == m);
alpar@1:       xassert(lpx_get_num_cols(lp) == n);
alpar@1:       /* statuses of rows and columns */
alpar@1:       for (k = 1; k <= m+n; k++)
alpar@1:       {  if (k <= m)
alpar@1:             stat[k] = lpx_get_row_stat(lp, k);
alpar@1:          else
alpar@1:             stat[k] = lpx_get_col_stat(lp, k-m);
alpar@1:          switch (stat[k])
alpar@1:          {  case LPX_BS:
alpar@1:                stat[k] = SSX_BS;
alpar@1:                break;
alpar@1:             case LPX_NL:
alpar@1:                stat[k] = SSX_NL;
alpar@1:                xassert(type[k] == SSX_LO || type[k] == SSX_DB);
alpar@1:                break;
alpar@1:             case LPX_NU:
alpar@1:                stat[k] = SSX_NU;
alpar@1:                xassert(type[k] == SSX_UP || type[k] == SSX_DB);
alpar@1:                break;
alpar@1:             case LPX_NF:
alpar@1:                stat[k] = SSX_NF;
alpar@1:                xassert(type[k] == SSX_FR);
alpar@1:                break;
alpar@1:             case LPX_NS:
alpar@1:                stat[k] = SSX_NS;
alpar@1:                xassert(type[k] == SSX_FX);
alpar@1:                break;
alpar@1:             default:
alpar@1:                xassert(stat != stat);
alpar@1:          }
alpar@1:       }
alpar@1:       /* build permutation matix Q */
alpar@1:       i = j = 0;
alpar@1:       for (k = 1; k <= m+n; k++)
alpar@1:       {  if (stat[k] == SSX_BS)
alpar@1:          {  i++;
alpar@1:             if (i > m) return 1;
alpar@1:             Q_row[k] = i, Q_col[i] = k;
alpar@1:          }
alpar@1:          else
alpar@1:          {  j++;
alpar@1:             if (j > n) return 1;
alpar@1:             Q_row[k] = m+j, Q_col[m+j] = k;
alpar@1:          }
alpar@1:       }
alpar@1:       xassert(i == m && j == n);
alpar@1:       return 0;
alpar@1: }
alpar@1: 
alpar@1: int glp_exact(glp_prob *lp, const glp_smcp *parm)
alpar@1: {     glp_smcp _parm;
alpar@1:       SSX *ssx;
alpar@1:       int m = lpx_get_num_rows(lp);
alpar@1:       int n = lpx_get_num_cols(lp);
alpar@1:       int nnz = lpx_get_num_nz(lp);
alpar@1:       int i, j, k, type, pst, dst, ret, *stat;
alpar@1:       double lb, ub, *prim, *dual, sum;
alpar@1:       if (parm == NULL)
alpar@1:          parm = &_parm, glp_init_smcp((glp_smcp *)parm);
alpar@1:       /* check control parameters */
alpar@1:       if (parm->it_lim < 0)
alpar@1:          xerror("glp_exact: it_lim = %d; invalid parameter\n",
alpar@1:             parm->it_lim);
alpar@1:       if (parm->tm_lim < 0)
alpar@1:          xerror("glp_exact: tm_lim = %d; invalid parameter\n",
alpar@1:             parm->tm_lim);
alpar@1:       /* the problem must have at least one row and one column */
alpar@1:       if (!(m > 0 && n > 0))
alpar@1:       {  xprintf("glp_exact: problem has no rows/columns\n");
alpar@1:          return GLP_EFAIL;
alpar@1:       }
alpar@1: #if 1
alpar@1:       /* basic solution is currently undefined */
alpar@1:       lp->pbs_stat = lp->dbs_stat = GLP_UNDEF;
alpar@1:       lp->obj_val = 0.0;
alpar@1:       lp->some = 0;
alpar@1: #endif
alpar@1:       /* check that all double-bounded variables have correct bounds */
alpar@1:       for (k = 1; k <= m+n; k++)
alpar@1:       {  if (k <= m)
alpar@1:          {  type = lpx_get_row_type(lp, k);
alpar@1:             lb = lpx_get_row_lb(lp, k);
alpar@1:             ub = lpx_get_row_ub(lp, k);
alpar@1:          }
alpar@1:          else
alpar@1:          {  type = lpx_get_col_type(lp, k-m);
alpar@1:             lb = lpx_get_col_lb(lp, k-m);
alpar@1:             ub = lpx_get_col_ub(lp, k-m);
alpar@1:          }
alpar@1:          if (type == LPX_DB && lb >= ub)
alpar@1:          {  xprintf("glp_exact: %s %d has invalid bounds\n",
alpar@1:                k <= m ? "row" : "column", k <= m ? k : k-m);
alpar@1:             return GLP_EBOUND;
alpar@1:          }
alpar@1:       }
alpar@1:       /* create the simplex solver workspace */
alpar@1:       xprintf("glp_exact: %d rows, %d columns, %d non-zeros\n",
alpar@1:          m, n, nnz);
alpar@1: #ifdef HAVE_GMP
alpar@1:       xprintf("GNU MP bignum library is being used\n");
alpar@1: #else
alpar@1:       xprintf("GLPK bignum module is being used\n");
alpar@1:       xprintf("(Consider installing GNU MP to attain a much better perf"
alpar@1:          "ormance.)\n");
alpar@1: #endif
alpar@1:       ssx = ssx_create(m, n, nnz);
alpar@1:       /* load LP problem data into the workspace */
alpar@1:       load_data(ssx, lp);
alpar@1:       /* load current LP basis into the workspace */
alpar@1:       if (load_basis(ssx, lp))
alpar@1:       {  xprintf("glp_exact: initial LP basis is invalid\n");
alpar@1:          ret = GLP_EBADB;
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* inherit some control parameters from the LP object */
alpar@1: #if 0
alpar@1:       ssx->it_lim = lpx_get_int_parm(lp, LPX_K_ITLIM);
alpar@1:       ssx->it_cnt = lpx_get_int_parm(lp, LPX_K_ITCNT);
alpar@1:       ssx->tm_lim = lpx_get_real_parm(lp, LPX_K_TMLIM);
alpar@1: #else
alpar@1:       ssx->it_lim = parm->it_lim;
alpar@1:       ssx->it_cnt = lp->it_cnt;
alpar@1:       ssx->tm_lim = (double)parm->tm_lim / 1000.0;
alpar@1: #endif
alpar@1:       ssx->out_frq = 5.0;
alpar@1:       ssx->tm_beg = xtime();
alpar@1:       ssx->tm_lag = xlset(0);
alpar@1:       /* solve LP */
alpar@1:       ret = ssx_driver(ssx);
alpar@1:       /* copy back some statistics to the LP object */
alpar@1: #if 0
alpar@1:       lpx_set_int_parm(lp, LPX_K_ITLIM, ssx->it_lim);
alpar@1:       lpx_set_int_parm(lp, LPX_K_ITCNT, ssx->it_cnt);
alpar@1:       lpx_set_real_parm(lp, LPX_K_TMLIM, ssx->tm_lim);
alpar@1: #else
alpar@1:       lp->it_cnt = ssx->it_cnt;
alpar@1: #endif
alpar@1:       /* analyze the return code */
alpar@1:       switch (ret)
alpar@1:       {  case 0:
alpar@1:             /* optimal solution found */
alpar@1:             ret = 0;
alpar@1:             pst = LPX_P_FEAS, dst = LPX_D_FEAS;
alpar@1:             break;
alpar@1:          case 1:
alpar@1:             /* problem has no feasible solution */
alpar@1:             ret = 0;
alpar@1:             pst = LPX_P_NOFEAS, dst = LPX_D_INFEAS;
alpar@1:             break;
alpar@1:          case 2:
alpar@1:             /* problem has unbounded solution */
alpar@1:             ret = 0;
alpar@1:             pst = LPX_P_FEAS, dst = LPX_D_NOFEAS;
alpar@1: #if 1
alpar@1:             xassert(1 <= ssx->q && ssx->q <= n);
alpar@1:             lp->some = ssx->Q_col[m + ssx->q];
alpar@1:             xassert(1 <= lp->some && lp->some <= m+n);
alpar@1: #endif
alpar@1:             break;
alpar@1:          case 3:
alpar@1:             /* iteration limit exceeded (phase I) */
alpar@1:             ret = GLP_EITLIM;
alpar@1:             pst = LPX_P_INFEAS, dst = LPX_D_INFEAS;
alpar@1:             break;
alpar@1:          case 4:
alpar@1:             /* iteration limit exceeded (phase II) */
alpar@1:             ret = GLP_EITLIM;
alpar@1:             pst = LPX_P_FEAS, dst = LPX_D_INFEAS;
alpar@1:             break;
alpar@1:          case 5:
alpar@1:             /* time limit exceeded (phase I) */
alpar@1:             ret = GLP_ETMLIM;
alpar@1:             pst = LPX_P_INFEAS, dst = LPX_D_INFEAS;
alpar@1:             break;
alpar@1:          case 6:
alpar@1:             /* time limit exceeded (phase II) */
alpar@1:             ret = GLP_ETMLIM;
alpar@1:             pst = LPX_P_FEAS, dst = LPX_D_INFEAS;
alpar@1:             break;
alpar@1:          case 7:
alpar@1:             /* initial basis matrix is singular */
alpar@1:             ret = GLP_ESING;
alpar@1:             goto done;
alpar@1:          default:
alpar@1:             xassert(ret != ret);
alpar@1:       }
alpar@1:       /* obtain final basic solution components */
alpar@1:       stat = xcalloc(1+m+n, sizeof(int));
alpar@1:       prim = xcalloc(1+m+n, sizeof(double));
alpar@1:       dual = xcalloc(1+m+n, sizeof(double));
alpar@1:       for (k = 1; k <= m+n; k++)
alpar@1:       {  if (ssx->stat[k] == SSX_BS)
alpar@1:          {  i = ssx->Q_row[k]; /* x[k] = xB[i] */
alpar@1:             xassert(1 <= i && i <= m);
alpar@1:             stat[k] = LPX_BS;
alpar@1:             prim[k] = mpq_get_d(ssx->bbar[i]);
alpar@1:             dual[k] = 0.0;
alpar@1:          }
alpar@1:          else
alpar@1:          {  j = ssx->Q_row[k] - m; /* x[k] = xN[j] */
alpar@1:             xassert(1 <= j && j <= n);
alpar@1:             switch (ssx->stat[k])
alpar@1:             {  case SSX_NF:
alpar@1:                   stat[k] = LPX_NF;
alpar@1:                   prim[k] = 0.0;
alpar@1:                   break;
alpar@1:                case SSX_NL:
alpar@1:                   stat[k] = LPX_NL;
alpar@1:                   prim[k] = mpq_get_d(ssx->lb[k]);
alpar@1:                   break;
alpar@1:                case SSX_NU:
alpar@1:                   stat[k] = LPX_NU;
alpar@1:                   prim[k] = mpq_get_d(ssx->ub[k]);
alpar@1:                   break;
alpar@1:                case SSX_NS:
alpar@1:                   stat[k] = LPX_NS;
alpar@1:                   prim[k] = mpq_get_d(ssx->lb[k]);
alpar@1:                   break;
alpar@1:                default:
alpar@1:                   xassert(ssx != ssx);
alpar@1:             }
alpar@1:             dual[k] = mpq_get_d(ssx->cbar[j]);
alpar@1:          }
alpar@1:       }
alpar@1:       /* and store them into the LP object */
alpar@1:       pst = pst - LPX_P_UNDEF + GLP_UNDEF;
alpar@1:       dst = dst - LPX_D_UNDEF + GLP_UNDEF;
alpar@1:       for (k = 1; k <= m+n; k++)
alpar@1:          stat[k] = stat[k] - LPX_BS + GLP_BS;
alpar@1:       sum = lpx_get_obj_coef(lp, 0);
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:          sum += lpx_get_obj_coef(lp, j) * prim[m+j];
alpar@1:       lpx_put_solution(lp, 1, &pst, &dst, &sum,
alpar@1:          &stat[0], &prim[0], &dual[0], &stat[m], &prim[m], &dual[m]);
alpar@1:       xfree(stat);
alpar@1:       xfree(prim);
alpar@1:       xfree(dual);
alpar@1: done: /* delete the simplex solver workspace */
alpar@1:       ssx_delete(ssx);
alpar@1:       /* return to the application program */
alpar@1:       return ret;
alpar@1: }
alpar@1: 
alpar@1: /* eof */