/* glpapi07.c (exact simplex solver) */

/***********************************************************************

*  This code is part of GLPK (GNU Linear Programming Kit).

*

*  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

*  2009, 2010 Andrew Makhorin, Department for Applied Informatics,

*  Moscow Aviation Institute, Moscow, Russia. All rights reserved.

*  E-mail: <mao@gnu.org>.

*

*  GLPK is free software: you can redistribute it and/or modify it

*  under the terms of the GNU General Public License as published by

*  the Free Software Foundation, either version 3 of the License, or

*  (at your option) any later version.

*

*  GLPK is distributed in the hope that it will be useful, but WITHOUT

*  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY

*  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public

*  License for more details.

*

*  You should have received a copy of the GNU General Public License

*  along with GLPK. If not, see <http://www.gnu.org/licenses/>.

***********************************************************************/

#include "glpapi.h"

#include "glpssx.h"

/***********************************************************************

*  NAME

*

*  glp_exact - solve LP problem in exact arithmetic

*

*  SYNOPSIS

*

*  int glp_exact(glp_prob *lp, const glp_smcp *parm);

*

*  DESCRIPTION

*

*  The routine glp_exact is a tentative implementation of the primal

*  two-phase simplex method based on exact (rational) arithmetic. It is

*  similar to the routine glp_simplex, however, for all internal

*  computations it uses arithmetic of rational numbers, which is exact

*  in mathematical sense, i.e. free of round-off errors unlike floating

*  point arithmetic.

*

*  Note that the routine glp_exact uses inly two control parameters

*  passed in the structure glp_smcp, namely, it_lim and tm_lim.

*

*  RETURNS

*

*  0  The LP problem instance has been successfully solved. This code

*     does not necessarily mean that the solver has found optimal

*     solution. It only means that the solution process was successful.

*

*  GLP_EBADB

*     Unable to start the search, because the initial basis specified

*     in the problem object is invalid--the number of basic (auxiliary

*     and structural) variables is not the same as the number of rows in

*     the problem object.

*

*  GLP_ESING

*     Unable to start the search, because the basis matrix correspodning

*     to the initial basis is exactly singular.

*

*  GLP_EBOUND

*     Unable to start the search, because some double-bounded variables

*     have incorrect bounds.

*

*  GLP_EFAIL

*     The problem has no rows/columns.

*

*  GLP_EITLIM

*     The search was prematurely terminated, because the simplex

*     iteration limit has been exceeded.

*

*  GLP_ETMLIM

*     The search was prematurely terminated, because the time limit has

*     been exceeded. */

static void set_d_eps(mpq_t x, double val)

{     /* convert double val to rational x obtaining a more adequate

         fraction than provided by mpq_set_d due to allowing a small

         approximation error specified by a given relative tolerance;

         for example, mpq_set_d would give the following

         1/3 ~= 0.333333333333333314829616256247391... ->

             -> 6004799503160661/18014398509481984

         while this routine gives exactly 1/3 */

      int s, n, j;

      double f, p, q, eps = 1e-9;

      mpq_t temp;

      xassert(-DBL_MAX <= val && val <= +DBL_MAX);

#if 1 /* 30/VII-2008 */

      if (val == floor(val))

      {  /* if val is integral, do not approximate */

         mpq_set_d(x, val);

         goto done;

      }

#endif

      if (val > 0.0)

         s = +1;

      else if (val < 0.0)

         s = -1;

      else

      {  mpq_set_si(x, 0, 1);

         goto done;

      }

      f = frexp(fabs(val), &n);

      /* |val| = f * 2^n, where 0.5 <= f < 1.0 */

      fp2rat(f, 0.1 * eps, &p, &q);

      /* f ~= p / q, where p and q are integers */

      mpq_init(temp);

      mpq_set_d(x, p);

      mpq_set_d(temp, q);

      mpq_div(x, x, temp);

      mpq_set_si(temp, 1, 1);

      for (j = 1; j <= abs(n); j++)

         mpq_add(temp, temp, temp);

      if (n > 0)

         mpq_mul(x, x, temp);

      else if (n < 0)

         mpq_div(x, x, temp);

      mpq_clear(temp);

      if (s < 0) mpq_neg(x, x);

      /* check that the desired tolerance has been attained */

      xassert(fabs(val - mpq_get_d(x)) <= eps * (1.0 + fabs(val)));

done: return;

}

static void load_data(SSX *ssx, LPX *lp)

{     /* load LP problem data into simplex solver workspace */

      int m = ssx->m;

      int n = ssx->n;

      int nnz = ssx->A_ptr[n+1]-1;

      int j, k, type, loc, len, *ind;

      double lb, ub, coef, *val;

      xassert(lpx_get_num_rows(lp) == m);

      xassert(lpx_get_num_cols(lp) == n);

      xassert(lpx_get_num_nz(lp) == nnz);

      /* types and bounds of rows and columns */

      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);

         }

         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);

         }

         switch (type)

         {  case LPX_FR: type = SSX_FR; break;

            case LPX_LO: type = SSX_LO; break;

            case LPX_UP: type = SSX_UP; break;

            case LPX_DB: type = SSX_DB; break;

            case LPX_FX: type = SSX_FX; break;

            default: xassert(type != type);

         }

         ssx->type[k] = type;

         set_d_eps(ssx->lb[k], lb);

         set_d_eps(ssx->ub[k], ub);

      }

      /* optimization direction */

      switch (lpx_get_obj_dir(lp))

      {  case LPX_MIN: ssx->dir = SSX_MIN; break;

         case LPX_MAX: ssx->dir = SSX_MAX; break;

         default: xassert(lp != lp);

      }

      /* objective coefficients */

      for (k = 0; k <= m+n; k++)

      {  if (k == 0)

            coef = lpx_get_obj_coef(lp, 0);

         else if (k <= m)

            coef = 0.0;

         else

            coef = lpx_get_obj_coef(lp, k-m);

         set_d_eps(ssx->coef[k], coef);

      }

      /* constraint coefficients */

      ind = xcalloc(1+m, sizeof(int));

      val = xcalloc(1+m, sizeof(double));

      loc = 0;

      for (j = 1; j <= n; j++)

      {  ssx->A_ptr[j] = loc+1;

         len = lpx_get_mat_col(lp, j, ind, val);

         for (k = 1; k <= len; k++)

         {  loc++;

            ssx->A_ind[loc] = ind[k];

            set_d_eps(ssx->A_val[loc], val[k]);

         }

      }

      xassert(loc == nnz);

      xfree(ind);

      xfree(val);

      return;

}

static int load_basis(SSX *ssx, LPX *lp)

{     /* load current LP basis into simplex solver workspace */

      int m = ssx->m;

      int n = ssx->n;

      int *type = ssx->type;

      int *stat = ssx->stat;

      int *Q_row = ssx->Q_row;

      int *Q_col = ssx->Q_col;

      int i, j, k;

      xassert(lpx_get_num_rows(lp) == m);

      xassert(lpx_get_num_cols(lp) == n);

      /* statuses of rows and columns */

      for (k = 1; k <= m+n; k++)

      {  if (k <= m)

            stat[k] = lpx_get_row_stat(lp, k);

         else

            stat[k] = lpx_get_col_stat(lp, k-m);

         switch (stat[k])

         {  case LPX_BS:

               stat[k] = SSX_BS;

               break;

            case LPX_NL:

               stat[k] = SSX_NL;

               xassert(type[k] == SSX_LO || type[k] == SSX_DB);

               break;

            case LPX_NU:

               stat[k] = SSX_NU;

               xassert(type[k] == SSX_UP || type[k] == SSX_DB);

               break;

            case LPX_NF:

               stat[k] = SSX_NF;

               xassert(type[k] == SSX_FR);

               break;

            case LPX_NS:

               stat[k] = SSX_NS;

               xassert(type[k] == SSX_FX);

               break;

            default:

               xassert(stat != stat);

         }

      }

      /* build permutation matix Q */

      i = j = 0;

      for (k = 1; k <= m+n; k++)

      {  if (stat[k] == SSX_BS)

         {  i++;

            if (i > m) return 1;

            Q_row[k] = i, Q_col[i] = k;

         }

         else

         {  j++;

            if (j > n) return 1;

            Q_row[k] = m+j, Q_col[m+j] = k;

         }

      }

      xassert(i == m && j == n);

      return 0;

}

int glp_exact(glp_prob *lp, const glp_smcp *parm)

{     glp_smcp _parm;

      SSX *ssx;

      int m = lpx_get_num_rows(lp);

      int n = lpx_get_num_cols(lp);

      int nnz = lpx_get_num_nz(lp);

      int i, j, k, type, pst, dst, ret, *stat;

      double lb, ub, *prim, *dual, sum;

      if (parm == NULL)

         parm = &_parm, glp_init_smcp((glp_smcp *)parm);

      /* check control parameters */

      if (parm->it_lim < 0)

         xerror("glp_exact: it_lim = %d; invalid parameter\n",

            parm->it_lim);

      if (parm->tm_lim < 0)

         xerror("glp_exact: tm_lim = %d; invalid parameter\n",

            parm->tm_lim);

      /* the problem must have at least one row and one column */

      if (!(m > 0 && n > 0))

      {  xprintf("glp_exact: problem has no rows/columns\n");

         return GLP_EFAIL;

      }

#if 1

      /* basic solution is currently undefined */

      lp->pbs_stat = lp->dbs_stat = GLP_UNDEF;

      lp->obj_val = 0.0;

      lp->some = 0;

#endif

      /* check that all double-bounded variables have correct bounds */

      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);

         }

         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);

         }

         if (type == LPX_DB && lb >= ub)

         {  xprintf("glp_exact: %s %d has invalid bounds\n",

               k <= m ? "row" : "column", k <= m ? k : k-m);

            return GLP_EBOUND;

         }

      }

      /* create the simplex solver workspace */

      xprintf("glp_exact: %d rows, %d columns, %d non-zeros\n",

         m, n, nnz);

#ifdef HAVE_GMP

      xprintf("GNU MP bignum library is being used\n");

#else

      xprintf("GLPK bignum module is being used\n");

      xprintf("(Consider installing GNU MP to attain a much better perf"

         "ormance.)\n");

#endif

      ssx = ssx_create(m, n, nnz);

      /* load LP problem data into the workspace */

      load_data(ssx, lp);

      /* load current LP basis into the workspace */

      if (load_basis(ssx, lp))

      {  xprintf("glp_exact: initial LP basis is invalid\n");

         ret = GLP_EBADB;

         goto done;

      }

      /* inherit some control parameters from the LP object */

#if 0

      ssx->it_lim = lpx_get_int_parm(lp, LPX_K_ITLIM);

      ssx->it_cnt = lpx_get_int_parm(lp, LPX_K_ITCNT);

      ssx->tm_lim = lpx_get_real_parm(lp, LPX_K_TMLIM);

#else

      ssx->it_lim = parm->it_lim;

      ssx->it_cnt = lp->it_cnt;

      ssx->tm_lim = (double)parm->tm_lim / 1000.0;

#endif

      ssx->out_frq = 5.0;

      ssx->tm_beg = xtime();

      ssx->tm_lag = xlset(0);

      /* solve LP */

      ret = ssx_driver(ssx);

      /* copy back some statistics to the LP object */

#if 0

      lpx_set_int_parm(lp, LPX_K_ITLIM, ssx->it_lim);

      lpx_set_int_parm(lp, LPX_K_ITCNT, ssx->it_cnt);

      lpx_set_real_parm(lp, LPX_K_TMLIM, ssx->tm_lim);

#else

      lp->it_cnt = ssx->it_cnt;

#endif

      /* analyze the return code */

      switch (ret)

      {  case 0:

            /* optimal solution found */

            ret = 0;

            pst = LPX_P_FEAS, dst = LPX_D_FEAS;

            break;

         case 1:

            /* problem has no feasible solution */

            ret = 0;

            pst = LPX_P_NOFEAS, dst = LPX_D_INFEAS;

            break;

         case 2:

            /* problem has unbounded solution */

            ret = 0;

            pst = LPX_P_FEAS, dst = LPX_D_NOFEAS;

#if 1

            xassert(1 <= ssx->q && ssx->q <= n);

            lp->some = ssx->Q_col[m + ssx->q];

            xassert(1 <= lp->some && lp->some <= m+n);

#endif

            break;

         case 3:

            /* iteration limit exceeded (phase I) */

            ret = GLP_EITLIM;

            pst = LPX_P_INFEAS, dst = LPX_D_INFEAS;

            break;

         case 4:

            /* iteration limit exceeded (phase II) */

            ret = GLP_EITLIM;

            pst = LPX_P_FEAS, dst = LPX_D_INFEAS;

            break;

         case 5:

            /* time limit exceeded (phase I) */

            ret = GLP_ETMLIM;

            pst = LPX_P_INFEAS, dst = LPX_D_INFEAS;

            break;

         case 6:

            /* time limit exceeded (phase II) */

            ret = GLP_ETMLIM;

            pst = LPX_P_FEAS, dst = LPX_D_INFEAS;

            break;

         case 7:

            /* initial basis matrix is singular */

            ret = GLP_ESING;

            goto done;

         default:

            xassert(ret != ret);

      }

      /* obtain final basic solution components */

      stat = xcalloc(1+m+n, sizeof(int));

      prim = xcalloc(1+m+n, sizeof(double));

      dual = xcalloc(1+m+n, sizeof(double));

      for (k = 1; k <= m+n; k++)

      {  if (ssx->stat[k] == SSX_BS)

         {  i = ssx->Q_row[k]; /* x[k] = xB[i] */

            xassert(1 <= i && i <= m);

            stat[k] = LPX_BS;

            prim[k] = mpq_get_d(ssx->bbar[i]);

            dual[k] = 0.0;

         }

         else

         {  j = ssx->Q_row[k] - m; /* x[k] = xN[j] */

            xassert(1 <= j && j <= n);

            switch (ssx->stat[k])

            {  case SSX_NF:

                  stat[k] = LPX_NF;

                  prim[k] = 0.0;

                  break;

               case SSX_NL:

                  stat[k] = LPX_NL;

                  prim[k] = mpq_get_d(ssx->lb[k]);

                  break;

               case SSX_NU:

                  stat[k] = LPX_NU;

                  prim[k] = mpq_get_d(ssx->ub[k]);

                  break;

               case SSX_NS:

                  stat[k] = LPX_NS;

                  prim[k] = mpq_get_d(ssx->lb[k]);

                  break;

               default:

                  xassert(ssx != ssx);

            }

            dual[k] = mpq_get_d(ssx->cbar[j]);

         }

      }

      /* and store them into the LP object */

      pst = pst - LPX_P_UNDEF + GLP_UNDEF;

      dst = dst - LPX_D_UNDEF + GLP_UNDEF;

      for (k = 1; k <= m+n; k++)

         stat[k] = stat[k] - LPX_BS + GLP_BS;

      sum = lpx_get_obj_coef(lp, 0);

      for (j = 1; j <= n; j++)

         sum += lpx_get_obj_coef(lp, j) * prim[m+j];

      lpx_put_solution(lp, 1, &pst, &dst, &sum,

         &stat[0], &prim[0], &dual[0], &stat[m], &prim[m], &dual[m]);

      xfree(stat);

      xfree(prim);

      xfree(dual);

done: /* delete the simplex solver workspace */

      ssx_delete(ssx);

      /* return to the application program */

      return ret;

}

/* eof */