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# 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.
#-------------------------------------------------------------------------------
object Polytope {
# @category Optimization
# Linear program applied to the polytope
property LP : LinearProgram<Scalar> : multiple;
# @notest Rule defined "in stock" - currently without use
rule LP.ABSTRACT_OBJECTIVE : VertexPerm.LP.ABSTRACT_OBJECTIVE, VertexPerm.PERMUTATION {
$this->LP->ABSTRACT_OBJECTIVE=permuted($this->VertexPerm->LP->ABSTRACT_OBJECTIVE, $this->VertexPerm->PERMUTATION);
}
rule LP.DIRECTED_GRAPH.ADJACENCY, LP.MAXIMAL_VALUE, LP.MINIMAL_VALUE, LP.MAXIMAL_FACE, LP.MINIMAL_FACE \
: LP.LINEAR_OBJECTIVE, GRAPH.ADJACENCY, VERTICES, FAR_FACE {
$this->LP->DIRECTED_GRAPH->ADJACENCY=dgraph($this, $this->LP);
}
weight 2.50;
precondition : POINTED;
precondition : FEASIBLE;
rule LP.DIRECTED_GRAPH.ADJACENCY, LP.MAXIMAL_VALUE, LP.MINIMAL_VALUE, LP.MAXIMAL_FACE, LP.MINIMAL_FACE \
: LP.ABSTRACT_OBJECTIVE, GRAPH.ADJACENCY, VERTICES {
$this->LP->DIRECTED_GRAPH->ADJACENCY=dgraph($this, $this->LP);
}
weight 2.50;
precondition : POINTED;
precondition : FEASIBLE;
rule LP.MAXIMAL_FACE, LP.MAXIMAL_VALUE : LP.LINEAR_OBJECTIVE, VERTICES, GRAPH.ADJACENCY, FAR_FACE {
pseudo_simplex($this, $this->LP, 1);
}
precondition : POINTED;
precondition : FEASIBLE;
rule LP.MINIMAL_FACE, LP.MINIMAL_VALUE : LP.LINEAR_OBJECTIVE, VERTICES, GRAPH.ADJACENCY, FAR_FACE {
pseudo_simplex($this, $this->LP, 0);
}
precondition : POINTED;
precondition : FEASIBLE;
rule LP.MAXIMAL_VERTEX : VERTICES, FAR_FACE, LP.MAXIMAL_FACE {
my $f=$this->LP->MAXIMAL_FACE-$this->FAR_FACE;
if (@$f) {
$this->LP->MAXIMAL_VERTEX=$this->VERTICES->[$f->[0]];
}
}
weight 0.10;
rule LP.MINIMAL_VERTEX : VERTICES, FAR_FACE, LP.MINIMAL_FACE {
my $f=$this->LP->MINIMAL_FACE-$this->FAR_FACE;
if (@$f) {
$this->LP->MINIMAL_VERTEX=$this->VERTICES->[$f->[0]];
}
}
weight 0.10;
rule ONE_VERTEX : LP.MINIMAL_VERTEX | LP.MAXIMAL_VERTEX {
$this->ONE_VERTEX=$this->LP->give("MINIMAL_VERTEX | MAXIMAL_VERTEX");
}
precondition : POINTED;
weight 0.10;
rule ONE_VERTEX, FEASIBLE : FACETS | INEQUALITIES, CONE_AMBIENT_DIM {
my $lp=$this->add("LP", temporary, LINEAR_OBJECTIVE => new Vector<Scalar>($this->CONE_AMBIENT_DIM));
$this->ONE_VERTEX=$lp->MINIMAL_VERTEX;
$this->FEASIBLE=defined($lp->MINIMAL_VERTEX);
}
weight 3.20;
rule VALID_POINT = ONE_VERTEX;
}
object LinearProgram {
rule RANDOM_EDGE_EPL : DIRECTED_GRAPH.ADJACENCY {
$this->RANDOM_EDGE_EPL=random_edge_epl($this->DIRECTED_GRAPH->ADJACENCY);
}
}
# @category Optimization
# Read a linear programming problem given in LP-Format (as used by cplex & Co.)
# and convert it to a [[Polytope<Scalar>]] object.
#
# **WARNING** The property FEASIBLE is **NOT** computed upon creation.
# This is done to avoid possibly long computation times before the object becomes available to the caller.
# This is **NOT** in keeping with standard practice in polymake, but after, all, these are linear programs
# and not polytopes.
#
# @tparam Scalar coordinate type of the resulting polytope; default is [[Rational]].
# @param String file filename of a linear programming problem in LP-Format
# @param Vector testvec If present, after reading in each line of the LP it is checked whether testvec fulfills it
# @param String prefix If testvec is present, all variables in the LP file are assumed to have the form $prefix$i
# @option Int nocheck Do not automatically compute [[FEASIBLE]] for the polytope (recommended for very large LPs)
# @return Polytope<Scalar>
user_function lp2poly<Scalar=Rational>(String; Vector, String, {nocheck => 0}) {
require LPparser;
my ($filename, $testvec, $prefix, $options) = @_;
my $parser = defined($testvec)
? new LPparser($filename, $testvec, $prefix)
: new LPparser($filename);
my $P=new Polytope<Scalar>($parser->name);
$P->description = "Linear problem converted from file " . $parser->LPfile . "\n";
my $labels = new Array<String>($parser->X);
my $d = $labels->size();
# Specifying the dimension first is required for empty inequalities and coordinate labels
$P->CONE_AMBIENT_DIM = $d;
$P->COORDINATE_LABELS = $labels;
# FIXME #702: change the following kludge to
# $P->INEQUALITIES = new SparseMatrix<Scalar>($parser->Ineq)
my @AoH = $parser->Ineq;
my $Mineq = new SparseMatrix<Scalar>(scalar @AoH, $d);
my $i=0;
foreach my $ineq (@AoH) {
keys %{$ineq};
while (my ($k,$v) = each %{$ineq}) {
$Mineq->[$i]->[$k] = $v;
}
$i++;
}
$P->INEQUALITIES = $Mineq;
# FIXME #702: change the following kludge to
# $P->EQUATIONS = new SparseMatrix<Scalar>($parser->Eq)
@AoH = $parser->Eq;
my $MEq = new SparseMatrix<Scalar>(scalar @AoH, $d);
$i=0;
foreach my $eq (@AoH) {
keys %{$eq};
while (my ($k,$v) = each %{$eq}) {
$MEq->[$i]->[$k] = $v;
}
$i++;
}
$P->EQUATIONS = $MEq;
my $lp=new LinearProgram<Scalar>;
$lp->description="Objective sense was ".($parser->objsense eq "+" ? "MAXIMIZE" : "MINIMIZE")."\n";
# FIXME #702: change the following kludge to
# $P->LINEAR_OBJECTIVE = new SparseVector<Scalar>($parser->Obj)
my $ObjHash = $parser->Obj;
my $ObjVect = new SparseVector<Scalar>($d);
keys %{$ObjHash};
while (my ($k,$v) = each %{$ObjHash}) {
$ObjVect->[$k] = $v;
}
$lp->LINEAR_OBJECTIVE=$ObjVect;
if (@{$parser->Int}) {
$lp->attach("INTEGER_VARIABLES", new Array<Bool>($parser->Int));
}
$P->commit unless($options->{nocheck});
$P->add("LP",$lp);
$P;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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