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# Copyright (c) 1997-2024
# Ewgenij Gawrilow, Michael Joswig, and the polymake team
# Technische Universität Berlin, Germany
# https://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 Cone {
# A Cone defined by [[RAYS]] only gets a trivial [[LINEALITY_SPACE]] assigned.
rule LINEALITY_SPACE : RAYS {
$this->LINEALITY_SPACE=new Matrix<Scalar>(0, $this->RAYS->cols);
}
weight 0.10;
# A Cone defined by [[FACETS]] only gets a trivial [[LINEAR_SPAN]] assigned.
rule LINEAR_SPAN : FACETS {
$this->LINEAR_SPAN=new Matrix<Scalar>(0, $this->FACETS->cols);
}
weight 0.10;
# Defining a cone or polytope with one of the linear span/lineality properties only is not allowed
# For the non-reduced properties [[INPUT_LINEALITY]] or [[EQUATIONS]] we require that [[INPUT_RAYS]] or [[INEQUALITIES]] are defined, resp.
#
# We specifically do not want the same kind of rules for the canonical versions [[LINEALITY_SPACE]] and [[AFFINE_HULL]]: There are
# too many different cases to check and we do not want an unnnessary slow-down.
#
# Here are reasons for the set-up chosen:
# * To define an initial rule that silently adds the vertex/facet property we would have to distinguish between cones and polytopes:
# the latter always need one entry in [[POINTS]]/[[VERTICES]] or [[INEQUALITIES]]/[[FACETS]] that represents the
# pointed part (i.e. the restriction to x0>=0 in the homogenization.
# * Another problem of silently adding this would be clients that define a new polytope and
# e.g. write [[VERTICES]]/[[LINEALITY_SPACE]] and [[AFFINE_HULL]], but not [[FACETS]].
# * An initial rule checking for [[AFFINE_HULL]] without [[FACETS]] would erroneously make [[FACETS]] empty.
rule initial : {
croak("\ninvalid input: to define a linear or affine space you have to specify INPUT_RAYS/POINTS explicitely\nThis should be an empty matrix for a Cone and a single point for a Polytope");
}
precondition : exists(INPUT_LINEALITY);
precondition : !exists(INPUT_RAYS);
rule initial : {
croak("\ninvalid input: to define a linear or affine space you have to specify INEQUALITIES explicitely\nThis should be an empty matrix; For a Polytope, it can also be a single inequality [1,0,0,...]");
}
precondition : exists(EQUATIONS);
precondition : !exists(INEQUALITIES);
# TODO: try to remove this and look for crashes; maybe there won't be anymore
# check for zero rows in input properties.
rule initial : {
foreach my $prop (qw(INPUT_RAYS INEQUALITIES INPUT_LINEALITY EQUATIONS)){
if(defined(my $m = $this->lookup($prop))){
foreach my $r (@{$m}){
if(is_zero( $r )){ croak("\ninvalid input: zero vector is not a valid entry for ",$prop); }
}
}
}
}
precondition : exists(INPUT_RAYS | INEQUALITIES | INPUT_LINEALITY | EQUATIONS);
rule CONE_AMBIENT_DIM : RAYS | FACETS | LINEAR_SPAN | LINEALITY_SPACE | INPUT_RAYS | INPUT_LINEALITY | INEQUALITIES | EQUATIONS {
my $d=0;
foreach (qw(RAYS FACETS LINEAR_SPAN LINEALITY_SPACE INPUT_RAYS INPUT_LINEALITY INEQUALITIES EQUATIONS)) {
my $m=$this->lookup($_);
last if defined($m) && ($d=$m->cols) > 0;
}
$this->CONE_AMBIENT_DIM=$d;
}
weight 0.1;
}
object Polytope {
rule FEASIBLE : INEQUALITIES | EQUATIONS {
$this->FEASIBLE = H_input_feasible($this);
}
weight 3.1;
# A Polytope defined by a non-empty set of [[VERTICES]] or [[POINTS]] is always [[FEASIBLE]].
rule FEASIBLE : VERTICES | POINTS {
$this->FEASIBLE = $this->give("VERTICES | POINTS")->rows > 0;
}
weight 0.1;
rule FEASIBLE : { $this->FEASIBLE=1 }
precondition : defined(ONE_VERTEX | VALID_POINT);
weight 0.1;
# A Polytope defined by a non-empty set of [[FACETS]] is [[FEASIBLE]].
rule FEASIBLE : FACETS {
$this->FEASIBLE = $this->FACETS->rows > 0;
}
weight 0.1;
}
object Cone {
# Sanity checks for all initial properties related to coordinates
# first those for cones and polytopes
# the non-input properties might also be empty
rule initial: CONE_AMBIENT_DIM {
my $dim=$this->CONE_AMBIENT_DIM;
my $M;
foreach (qw(RAYS LINEALITY_SPACE FACETS LINEAR_SPAN INPUT_RAYS INPUT_LINEALITY INEQUALITIES EQUATIONS)) {
if (defined ($M = $this->lookup($_))) {
if ($M->cols != $dim) {
if ($M->rows==0 && $M->cols==0) {
$this->take($_, new Matrix<Scalar>(0, $dim));
} else {
die "dimension mismatch between $_ and CONE_AMBIENT_DIM\n";
}
}
}
}
}
precondition : exists(RAYS | LINEALITY_SPACE | FACETS | LINEAR_SPAN | INPUT_RAYS | INPUT_LINEALITY | INEQUALITIES | EQUATIONS);
rule initial: CONE_AMBIENT_DIM {
my $dim=$this->CONE_AMBIENT_DIM;
my $A;
foreach (qw(COORDINATE_LABELS)) {
if (defined ($A = $this->lookup($_)) && $A->size != $dim) {
die "size mismatch between $_ and CONE_AMBIENT_DIM\n";
}
}
}
precondition : exists(COORDINATE_LABELS);
}
object Polytope {
# sanity checks which apply only to polytopes
rule initial: CONE_AMBIENT_DIM {
my $dim=$this->CONE_AMBIENT_DIM;
my $V;
foreach (qw(VALID_POINT ONE_VERTEX)) {
if (defined ($V = $this->lookup($_)) && $V->dim != $dim) {
die "dimension mismatch between $_ and CONE_AMBIENT_DIM\n";
}
}
}
precondition : exists(VALID_POINT | ONE_VERTEX);
# Unique representation of infeasible polytopes
rule FACETS, AFFINE_HULL, CONE_DIM : CONE_AMBIENT_DIM {
my $dim=$this->CONE_AMBIENT_DIM;
my $empty=new Matrix<Scalar>(0, $dim);
$this->FACETS = $empty;
$this->AFFINE_HULL = $empty;
$this->CONE_DIM = 0;
}
precondition : !FEASIBLE;
weight 0.10;
rule VERTICES, LINEALITY_SPACE, CONE_DIM : CONE_AMBIENT_DIM {
my $dim=$this->CONE_AMBIENT_DIM;
my $empty=new Matrix<Scalar>(0, $dim);
$this->VERTICES = $empty;
$this->LINEALITY_SPACE = $empty;
$this->CONE_DIM = 0;
}
precondition : !FEASIBLE;
weight 0.10;
}
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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