#  Copyright (c) 1997-2018
#  Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
#  http://www.polymake.org
#
#  This program 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 2, or (at your option) any
#  later version: http://www.gnu.org/licenses/gpl.txt.
#
#  This program 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.
#-----------------------------------------------------------------------------

# @file integer_hull_unb
#
# Script to generate the integer hull arising from a given LP file
# that specifies a (possibly) unbounded polyhedron.
#
# More precisely, the following is done:
# - a linear system is read from an LP file
# - we compute the H-description of the corresponding polyhedron
# - the integer points (lattice points) in Minkowski sum of the finite
#   part of the H-description plus the parallelotope given by the generators
#   of the recession cone are generated
# - the facets of the convex hull of these integer points are computed
#
# The script is intended for people that want to see the facets for
# problems for which they know an LP-relaxation. Usually, the
# LP-relaxation can be generated by hand or a modelling language like
# ZIMPL. This script (and polymake) does the rest.
#
# Note that the script assumes that all variables are integer. To
# handle mixed-integer problems one needs to do a projection step
# first. This would be interesting to implement.
#
#
# @synopsis integer_hull_unb <lp file>
#
# @reading  <lp-file>
# @writing  FACETS AFFINE_HULL
#
# @author Marc Pfetsch
# @date   03/2012

use application 'polytope';

die "usage: polymake --script integer_hull_unb <lp file>\n" unless @ARGV;

# read file
my $f = lp2poly("$ARGV[0]");

printf("Read file <%s>.\n", $ARGV[0]);

# get bool array that indicates whether the variables are integer
my @a = $f->LP->get_attachment("INTEGER_VARIABLES");

# test whether all variables are integer
for (my $j = 0; $j <= $#a; ++$j)
{
   if ( $a[$j] eq "false" )
   {
      print $a[$j]."\n";
      warn_print("Not all variables are integer.\n");
      exit;
   }
}
printf("All variables are integral.\n");

# convert to rational polytope
my $pin = new Polytope<Rational>($f);

# ---------------------------------------------------
# treat unbounded part

# get rays, i.e., vertices that define unbounded part
my $rays = $pin->VERTICES->minor($pin->FAR_FACE, All);
print "\nRays of input:\n";
print $rays;
print "\n";

# loop through rays
my $zero = unit_vector<Rational>($pin->DIM + 1, 0);
my $B = new Polytope<Rational>(POINTS=>$zero);
foreach my $r (@$rays)
{
   my $M = new Matrix<Rational>(primitive($r));
   # convert ray to a point
   $M->[0]->[0] = 1;
   $M = $M / $zero;
   my $ptemp = new Polytope<Rational>(POINTS=>$M);
   $B = minkowski_sum($B, $ptemp);
}
print "\n[0,1] * rays:\n";
print $B->VERTICES;
print "\n";

# get bounded part
my $boundedvert = $pin->VERTICES->minor($pin->BOUNDED_VERTICES, All);
my $boundedpart = new Polytope<Rational>(POINTS=>$boundedvert);

# create new polytope
my $p = minkowski_sum($boundedpart, $B);

# compute integer points (uncomment to prefer client integer_points_bbox)
# prefer_now "bbox";

my $lp = $p->LATTICE_POINTS;

# get number of lattice points
print "Number of integer (lattice) points: ";
print $lp->rows;
print "\n";

printf("Creating new polytope based on lattice points.\n");

# put lattice points together with rays
my $newpoints = new Matrix<Rational>($lp) / $rays;

# create new polytope that has the lattice points as points
my $q=new Polytope(POINTS=>$newpoints, COORDINATE_LABELS=>$pin->COORDINATE_LABELS);

# output facets of integer hull
print "Number of facets: ";
print $q->N_FACETS;
print "\n";
# print_constraints($i);

return $q;
