/* glpapi08.c (interior-point method routines) */

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

*  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 "glpipm.h"

#include "glpnpp.h"

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

*  NAME

*

*  glp_interior - solve LP problem with the interior-point method

*

*  SYNOPSIS

*

*  int glp_interior(glp_prob *P, const glp_iptcp *parm);

*

*  The routine glp_interior is a driver to the LP solver based on the

*  interior-point method.

*

*  The interior-point solver has a set of control parameters. Values of

*  the control parameters can be passed in a structure glp_iptcp, which

*  the parameter parm points to.

*

*  Currently this routine implements an easy variant of the primal-dual

*  interior-point method based on Mehrotra's technique.

*

*  This routine transforms the original LP problem to an equivalent LP

*  problem in the standard formulation (all constraints are equalities,

*  all variables are non-negative), calls the routine ipm_main to solve

*  the transformed problem, and then transforms an obtained solution to

*  the solution of the original problem.

*

*  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_EFAIL

*     The problem has no rows/columns.

*

*  GLP_ENOCVG

*     Very slow convergence or divergence.

*

*  GLP_EITLIM

*     Iteration limit exceeded.

*

*  GLP_EINSTAB

*     Numerical instability on solving Newtonian system. */

static void transform(NPP *npp)

{     /* transform LP to the standard formulation */

      NPPROW *row, *prev_row;

      NPPCOL *col, *prev_col;

      for (row = npp->r_tail; row != NULL; row = prev_row)

      {  prev_row = row->prev;

         if (row->lb == -DBL_MAX && row->ub == +DBL_MAX)

            npp_free_row(npp, row);

         else if (row->lb == -DBL_MAX)

            npp_leq_row(npp, row);

         else if (row->ub == +DBL_MAX)

            npp_geq_row(npp, row);

         else if (row->lb != row->ub)

         {  if (fabs(row->lb) < fabs(row->ub))

               npp_geq_row(npp, row);

            else

               npp_leq_row(npp, row);

         }

      }

      for (col = npp->c_tail; col != NULL; col = prev_col)

      {  prev_col = col->prev;

         if (col->lb == -DBL_MAX && col->ub == +DBL_MAX)

            npp_free_col(npp, col);

         else if (col->lb == -DBL_MAX)

            npp_ubnd_col(npp, col);

         else if (col->ub == +DBL_MAX)

         {  if (col->lb != 0.0)

               npp_lbnd_col(npp, col);

         }

         else if (col->lb != col->ub)

         {  if (fabs(col->lb) < fabs(col->ub))

            {  if (col->lb != 0.0)

                  npp_lbnd_col(npp, col);

            }

            else

               npp_ubnd_col(npp, col);

            npp_dbnd_col(npp, col);

         }

         else

            npp_fixed_col(npp, col);

      }

      for (row = npp->r_head; row != NULL; row = row->next)

         xassert(row->lb == row->ub);

      for (col = npp->c_head; col != NULL; col = col->next)

         xassert(col->lb == 0.0 && col->ub == +DBL_MAX);

      return;

}

int glp_interior(glp_prob *P, const glp_iptcp *parm)

{     glp_iptcp _parm;

      GLPROW *row;

      GLPCOL *col;

      NPP *npp = NULL;

      glp_prob *prob = NULL;

      int i, j, ret;

      /* check control parameters */

      if (parm == NULL)

         glp_init_iptcp(&_parm), parm = &_parm;

      if (!(parm->msg_lev == GLP_MSG_OFF ||

            parm->msg_lev == GLP_MSG_ERR ||

            parm->msg_lev == GLP_MSG_ON  ||

            parm->msg_lev == GLP_MSG_ALL))

         xerror("glp_interior: msg_lev = %d; invalid parameter\n",

            parm->msg_lev);

      if (!(parm->ord_alg == GLP_ORD_NONE ||

            parm->ord_alg == GLP_ORD_QMD ||

            parm->ord_alg == GLP_ORD_AMD ||

            parm->ord_alg == GLP_ORD_SYMAMD))

         xerror("glp_interior: ord_alg = %d; invalid parameter\n",

            parm->ord_alg);

      /* interior-point solution is currently undefined */

      P->ipt_stat = GLP_UNDEF;

      P->ipt_obj = 0.0;

      /* check bounds of double-bounded variables */

      for (i = 1; i <= P->m; i++)

      {  row = P->row[i];

         if (row->type == GLP_DB && row->lb >= row->ub)

         {  if (parm->msg_lev >= GLP_MSG_ERR)

               xprintf("glp_interior: row %d: lb = %g, ub = %g; incorre"

                  "ct bounds\n", i, row->lb, row->ub);

            ret = GLP_EBOUND;

            goto done;

         }

      }

      for (j = 1; j <= P->n; j++)

      {  col = P->col[j];

         if (col->type == GLP_DB && col->lb >= col->ub)

         {  if (parm->msg_lev >= GLP_MSG_ERR)

               xprintf("glp_interior: column %d: lb = %g, ub = %g; inco"

                  "rrect bounds\n", j, col->lb, col->ub);

            ret = GLP_EBOUND;

            goto done;

         }

      }

      /* transform LP to the standard formulation */

      if (parm->msg_lev >= GLP_MSG_ALL)

         xprintf("Original LP has %d row(s), %d column(s), and %d non-z"

            "ero(s)\n", P->m, P->n, P->nnz);

      npp = npp_create_wksp();

      npp_load_prob(npp, P, GLP_OFF, GLP_IPT, GLP_ON);

      transform(npp);

      prob = glp_create_prob();

      npp_build_prob(npp, prob);

      if (parm->msg_lev >= GLP_MSG_ALL)

         xprintf("Working LP has %d row(s), %d column(s), and %d non-ze"

            "ro(s)\n", prob->m, prob->n, prob->nnz);

#if 1

      /* currently empty problem cannot be solved */

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

      {  if (parm->msg_lev >= GLP_MSG_ERR)

            xprintf("glp_interior: unable to solve empty problem\n");

         ret = GLP_EFAIL;

         goto done;

      }

#endif

      /* scale the resultant LP */

      {  ENV *env = get_env_ptr();

         int term_out = env->term_out;

         env->term_out = GLP_OFF;

         glp_scale_prob(prob, GLP_SF_EQ);

         env->term_out = term_out;

      }

      /* warn about dense columns */

      if (parm->msg_lev >= GLP_MSG_ON && prob->m >= 200)

      {  int len, cnt = 0;

         for (j = 1; j <= prob->n; j++)

         {  len = glp_get_mat_col(prob, j, NULL, NULL);

            if ((double)len >= 0.20 * (double)prob->m) cnt++;

         }

         if (cnt == 1)

            xprintf("WARNING: PROBLEM HAS ONE DENSE COLUMN\n");

         else if (cnt > 0)

            xprintf("WARNING: PROBLEM HAS %d DENSE COLUMNS\n", cnt);

      }

      /* solve the transformed LP */

      ret = ipm_solve(prob, parm);

      /* postprocess solution from the transformed LP */

      npp_postprocess(npp, prob);

      /* and store solution to the original LP */

      npp_unload_sol(npp, P);

done: /* free working program objects */

      if (npp != NULL) npp_delete_wksp(npp);

      if (prob != NULL) glp_delete_prob(prob);

      /* return to the application program */

      return ret;

}

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

*  NAME

*

*  glp_init_iptcp - initialize interior-point solver control parameters

*

*  SYNOPSIS

*

*  void glp_init_iptcp(glp_iptcp *parm);

*

*  DESCRIPTION

*

*  The routine glp_init_iptcp initializes control parameters, which are

*  used by the interior-point solver, with default values.

*

*  Default values of the control parameters are stored in the glp_iptcp

*  structure, which the parameter parm points to. */

void glp_init_iptcp(glp_iptcp *parm)

{     parm->msg_lev = GLP_MSG_ALL;

      parm->ord_alg = GLP_ORD_AMD;

      return;

}

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

*  NAME

*

*  glp_ipt_status - retrieve status of interior-point solution

*

*  SYNOPSIS

*

*  int glp_ipt_status(glp_prob *lp);

*

*  RETURNS

*

*  The routine glp_ipt_status reports the status of solution found by

*  the interior-point solver as follows:

*

*  GLP_UNDEF  - interior-point solution is undefined;

*  GLP_OPT    - interior-point solution is optimal;

*  GLP_INFEAS - interior-point solution is infeasible;

*  GLP_NOFEAS - no feasible solution exists. */

int glp_ipt_status(glp_prob *lp)

{     int ipt_stat = lp->ipt_stat;

      return ipt_stat;

}

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

*  NAME

*

*  glp_ipt_obj_val - retrieve objective value (interior point)

*

*  SYNOPSIS

*

*  double glp_ipt_obj_val(glp_prob *lp);

*

*  RETURNS

*

*  The routine glp_ipt_obj_val returns value of the objective function

*  for interior-point solution. */

double glp_ipt_obj_val(glp_prob *lp)

{     /*struct LPXCPS *cps = lp->cps;*/

      double z;

      z = lp->ipt_obj;

      /*if (cps->round && fabs(z) < 1e-9) z = 0.0;*/

      return z;

}

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

*  NAME

*

*  glp_ipt_row_prim - retrieve row primal value (interior point)

*

*  SYNOPSIS

*

*  double glp_ipt_row_prim(glp_prob *lp, int i);

*

*  RETURNS

*

*  The routine glp_ipt_row_prim returns primal value of the auxiliary

*  variable associated with i-th row. */

double glp_ipt_row_prim(glp_prob *lp, int i)

{     /*struct LPXCPS *cps = lp->cps;*/

      double pval;

      if (!(1 <= i && i <= lp->m))

         xerror("glp_ipt_row_prim: i = %d; row number out of range\n",

            i);

      pval = lp->row[i]->pval;

      /*if (cps->round && fabs(pval) < 1e-9) pval = 0.0;*/

      return pval;

}

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

*  NAME

*

*  glp_ipt_row_dual - retrieve row dual value (interior point)

*

*  SYNOPSIS

*

*  double glp_ipt_row_dual(glp_prob *lp, int i);

*

*  RETURNS

*

*  The routine glp_ipt_row_dual returns dual value (i.e. reduced cost)

*  of the auxiliary variable associated with i-th row. */

double glp_ipt_row_dual(glp_prob *lp, int i)

{     /*struct LPXCPS *cps = lp->cps;*/

      double dval;

      if (!(1 <= i && i <= lp->m))

         xerror("glp_ipt_row_dual: i = %d; row number out of range\n",

            i);

      dval = lp->row[i]->dval;

      /*if (cps->round && fabs(dval) < 1e-9) dval = 0.0;*/

      return dval;

}

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

*  NAME

*

*  glp_ipt_col_prim - retrieve column primal value (interior point)

*

*  SYNOPSIS

*

*  double glp_ipt_col_prim(glp_prob *lp, int j);

*

*  RETURNS

*

*  The routine glp_ipt_col_prim returns primal value of the structural

*  variable associated with j-th column. */

double glp_ipt_col_prim(glp_prob *lp, int j)

{     /*struct LPXCPS *cps = lp->cps;*/

      double pval;

      if (!(1 <= j && j <= lp->n))

         xerror("glp_ipt_col_prim: j = %d; column number out of range\n"

            , j);

      pval = lp->col[j]->pval;

      /*if (cps->round && fabs(pval) < 1e-9) pval = 0.0;*/

      return pval;

}

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

*  NAME

*

*  glp_ipt_col_dual - retrieve column dual value (interior point)

*

*  SYNOPSIS

*

*  #include "glplpx.h"

*  double glp_ipt_col_dual(glp_prob *lp, int j);

*

*  RETURNS

*

*  The routine glp_ipt_col_dual returns dual value (i.e. reduced cost)

*  of the structural variable associated with j-th column. */

double glp_ipt_col_dual(glp_prob *lp, int j)

{     /*struct LPXCPS *cps = lp->cps;*/

      double dval;

      if (!(1 <= j && j <= lp->n))

         xerror("glp_ipt_col_dual: j = %d; column number out of range\n"

            , j);

      dval = lp->col[j]->dval;

      /*if (cps->round && fabs(dval) < 1e-9) dval = 0.0;*/

      return dval;

}

/* eof */