/usr/include/polymake/fan/hasse_diagram.h is in libpolymake-dev-common 3.2r2-3.
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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.
--------------------------------------------------------------------------------
*/
#ifndef POLYMAKE_FAN_HASSE_DIAGRAM_H
#define POLYMAKE_FAN_HASSE_DIAGRAM_H
#include "polymake/PowerSet.h"
#include "polymake/graph/Closure.h"
#include "polymake/graph/Lattice.h"
#include "polymake/graph/BasicLatticeTypes.h"
#include "polymake/graph/lattice_builder.h"
namespace polymake { namespace fan {
namespace lattice {
using namespace graph::lattice;
/*
* Given a closure operator, this can iterate over all closed sets lying above a given set.
*/
template <typename ClosureOperator>
class complex_closures_above_iterator {
public:
typedef typename ClosureOperator::ClosureData ClosureData;
typedef std::forward_iterator_tag iterator_category;
typedef ClosureData value_type;
typedef const value_type& reference;
typedef const value_type* pointer;
typedef ptrdiff_t difference_type;
complex_closures_above_iterator() {}
template <typename Iterator>
complex_closures_above_iterator(const ClosureOperator& cop, const ClosureData& H,
Iterator inter_it) : CO(&cop) {
bool empty_set_occured = false;
const Set<int>& dual_face = H.get_dual_face();
const int df_size = dual_face.size();
if(df_size) {
FacetList flist(CO->total_set_size());
for(; !inter_it.at_end(); ++inter_it) {
const Set<int> hc = dual_face * (*inter_it);
const int hc_size = hc.size();
if(hc_size == 0)
empty_set_occured = true;
else if(hc_size != df_size)
flist.replaceMax(hc);
}
for(auto mf = entire(flist); !mf.at_end(); ++mf) {
data.push_back(ClosureData(*CO, *mf));
}
if(flist.size() == 0 && empty_set_occured)
data.push_back(ClosureData(*CO,Set<int>()));
}
it = entire(data);
}
// The following are only for dual mode:
// Iterator for 1- and 2-dimensional cones: We don't need to intersect
complex_closures_above_iterator(const ClosureOperator& cop, const Set<int>& dual_face) : CO(&cop) {
for(auto subface = entire(Subsets_less_1< Set<int> >(dual_face)); !subface.at_end();
++subface) {
data.push_back(ClosureData(*CO, *subface));
}
it = entire(data);
}
// Iterator for maximal cones: Just list them
complex_closures_above_iterator(const ClosureOperator& cop) : CO(&cop) {
auto cone_it = ensure(rows(CO->get_maximal_cones()),
(pm::cons<pm::indexed,pm::end_sensitive>*)0).begin();
for(;!cone_it.at_end(); ++cone_it)
data.push_back(ClosureData(*cone_it, cone_it.index()));
it = entire(data);
}
//Iterator for facets of a maximal cone
complex_closures_above_iterator(const ClosureOperator& cop, const IncidenceMatrix<>& facets) : CO(&cop) {
for(auto fc = entire(rows(facets)); !fc.at_end(); ++fc)
data.push_back(ClosureData(*CO, *fc));
it = entire(data);
}
reference operator* () const { return it.operator*(); }
pointer operator->() const { return it.operator->(); }
complex_closures_above_iterator& operator++ () { ++it; return *this; }
const complex_closures_above_iterator operator++ (int) { complex_closures_above_iterator copy = *this; operator++(); return copy; }
bool at_end() const { return it.at_end(); }
protected:
const ClosureOperator* CO;
std::list<ClosureData> data;
typename Entire<std::list<ClosureData> >::const_iterator it;
};
//To preserve the artificial node in dual mode, the closure of the empty set needs to be redefined.
//In primal mode, the intersection of all cones might be a vertex, but the closure of the
//empty set is still the empty set, representing the empty fan.
template <typename Decoration = BasicDecoration>
class ComplexClosure : public BasicClosureOperator<Decoration> {
public:
typedef typename BasicClosureOperator<Decoration>::ClosureData ParentClosureData;
class ClosureData : public ParentClosureData {
protected:
bool is_artificial;
bool is_maximal;
public:
ClosureData(const ComplexClosure<Decoration>& parent, const Set<int>& df) : ParentClosureData(parent,df), is_artificial(false), is_maximal(false) {}
template <typename TSet1, typename TSet2>
ClosureData(const GenericSet<TSet1,int>& f, const GenericSet<TSet2,int>& df) : ParentClosureData(f,df), is_artificial(false), is_maximal(false) {}
template <typename TSet>
ClosureData(const GenericSet<TSet,int> &df, const int index) :
ParentClosureData(scalar2set(index), df), is_artificial(false), is_maximal(true) {}
template <typename TSet>
ClosureData(const GenericSet<TSet,int> &df) : ParentClosureData( Set<int>(), df), is_artificial(true), is_maximal(false) {}
ClosureData(const ParentClosureData& p) : ParentClosureData(p) {}
const bool inline is_artificial_node() const { return is_artificial; }
const bool inline is_maximal_face() const { return is_maximal; }
};
ComplexClosure() { }
const ClosureData compute_closure_data(const Decoration &face) const {
return ClosureData( BasicClosureOperator<Decoration>::compute_closure_data(face));
}
};
template <typename Decoration = BasicDecoration>
class ComplexDualClosure : public ComplexClosure<Decoration> {
public:
typedef typename ComplexClosure<Decoration>::ClosureData ClosureData;
ComplexDualClosure() {}
ComplexDualClosure(const IncidenceMatrix<>& maximal_cones, const Array<IncidenceMatrix<> >& maximal_vifs, const FacetList& facet_data) :
maximal_cones(maximal_cones),
maximal_cones_as_list(maximal_cones.cols(), entire(rows(maximal_cones))),
non_redundant_facets(facet_data),
is_complete(non_redundant_facets.size() == 0),
maximal_vifs(maximal_vifs),
default_intersector(is_complete? maximal_cones_as_list: non_redundant_facets) {
BasicClosureOperator<Decoration>::total_size = maximal_cones.cols();
BasicClosureOperator<Decoration>::total_set =
sequence(0,BasicClosureOperator<Decoration>::total_size);
BasicClosureOperator<Decoration>::total_data =
ClosureData(BasicClosureOperator<Decoration>::total_set, Set<int>());
}
const ClosureData closure_of_empty_set() const {
return ClosureData(sequence(0, get_maximal_cones().cols()+1));
}
const ClosureData compute_closure_data(const Decoration& face) const {
if(face.face.contains(-1))
return closure_of_empty_set();
else return ComplexClosure<Decoration>::compute_closure_data(face);
}
complex_closures_above_iterator<ComplexDualClosure> get_closure_iterator(const ClosureData& face) const {
const int df_size = face.get_dual_face().size();
//Default iterator
if(__builtin_expect(!face.is_artificial_node() && (!face.is_maximal_face() || is_complete) && !(df_size <= 2),1))
return complex_closures_above_iterator<ComplexDualClosure>(*this,face,
entire(default_intersector));
//Artificial node
if(__builtin_expect(face.is_artificial_node(),0))
return complex_closures_above_iterator<ComplexDualClosure>(*this);
//Iterator for rays and twodimensional cones
if(__builtin_expect(df_size <= 2,0))
return complex_closures_above_iterator<ComplexDualClosure>(*this,face.get_dual_face());
//Iterator for facets of maximal cones
return complex_closures_above_iterator<ComplexDualClosure>(*this,
maximal_vifs[face.get_face().front()]);
}
const IncidenceMatrix<>& get_maximal_cones() const { return maximal_cones; }
const FacetList& get_non_redundant_facets() const { return non_redundant_facets; }
protected:
const IncidenceMatrix<> maximal_cones;
FacetList maximal_cones_as_list;
const FacetList& non_redundant_facets;
const bool is_complete;
const Array<IncidenceMatrix<> > maximal_vifs;
const FacetList& default_intersector;
};
template <typename Decoration = BasicDecoration>
class ComplexPrimalClosure : public ComplexClosure<Decoration> {
public:
typedef typename ComplexClosure<Decoration>::ClosureData ClosureData;
ComplexPrimalClosure() {}
ComplexPrimalClosure(const IncidenceMatrix<>& complete_incidence) {
BasicClosureOperator<Decoration>::facets = complete_incidence;
BasicClosureOperator<Decoration>::total_size = complete_incidence.rows();
BasicClosureOperator<Decoration>::total_set =
sequence(0,BasicClosureOperator<Decoration>::total_size);
BasicClosureOperator<Decoration>::total_data =
ClosureData(BasicClosureOperator<Decoration>::total_set, Set<int>());
}
const ClosureData closure_of_empty_set() const {
return ClosureData(Set<int>(), sequence(0,BasicClosureOperator<Decoration>::facets.rows() + 1));
}
const ClosureData compute_closure_data(const Decoration& face) const {
if(face.face.size() == 0)
return closure_of_empty_set();
else return ComplexClosure<Decoration>::compute_closure_data(face);
}
complex_closures_above_iterator<ComplexPrimalClosure> get_closure_iterator(const ClosureData& face) const {
return complex_closures_above_iterator<ComplexPrimalClosure>(*this,face, entire(cols(BasicClosureOperator<Decoration>::facets)));
}
};
//Complex decorator
class BasicComplexDecorator : public BasicDecorator<ComplexClosure<>::ClosureData> {
protected:
const int artificial_rank;
Map< Set<int>, int> max_combinatorial_dims;
const bool full_set_is_artificial;
const int n_vertices;
const bool is_pure;
public:
typedef ComplexClosure<>::ClosureData FaceData;
typedef BasicDecorator<FaceData> ParentType;
using ParentType::total_size;
using ParentType::initial_rank;
using ParentType::built_dually;
using ParentType::artificial_set;
//Primal version
BasicComplexDecorator(int comb_dim, const Set<int> artificial, bool full_set_is_artificial,
int n_vertices) :
ParentType(0, artificial), artificial_rank(comb_dim +2),
full_set_is_artificial(full_set_is_artificial),n_vertices(n_vertices), is_pure(false) {}
//Dual version
BasicComplexDecorator(IncidenceMatrix<> maximal_cones,
int comb_dim,
const Array<int>& max_comb_dims,
const Set<int> artificial, bool is_pure)
: ParentType(maximal_cones.cols(), comb_dim+2, artificial), artificial_rank(0),
full_set_is_artificial(false), n_vertices(0), is_pure(is_pure) {
if(!is_pure) {
auto md = entire(max_comb_dims);
for(auto mc = entire(rows(maximal_cones)); !mc.at_end(); ++mc, ++md) {
max_combinatorial_dims[*mc] = *md;
}
}
}
const BasicDecoration compute_initial_decoration(const FaceData &face) const {
BasicDecoration data;
data.rank = initial_rank;
data.face = built_dually? artificial_set : face.get_face();
return data;
}
const BasicDecoration compute_decoration(const FaceData& face,
const BasicDecoration& predecessor_data) const {
BasicDecoration data;
data.face = built_dually? face.get_dual_face() : face.get_face();
if(full_set_is_artificial && data.face.size() == n_vertices) {
data.face = artificial_set;
data.rank = artificial_rank;
return data;
}
if(predecessor_data.rank == initial_rank && built_dually && !is_pure) data.rank = max_combinatorial_dims[data.face] + 1;
else data.rank = predecessor_data.rank + (built_dually? -1 : 1);
return data;
}
const BasicDecoration compute_artificial_decoration(const NodeMap<Directed, BasicDecoration> &decor,
const std::list<int>& max_nodes) const {
if(built_dually)
return BasicDecoration( Set<int>(),0);
else
return ParentType::compute_artificial_decoration(decor,max_nodes);
}
};
struct TopologicalType {
bool is_pure; // All maximal cells have the same dimension
bool is_complete; // Essentially means coatomic: Every cell is an intersection of maximal cells..
TopologicalType() : is_pure(false), is_complete(false) {}
TopologicalType(bool p_arg, bool c_arg) : is_pure(p_arg), is_complete(c_arg) {}
};
}//END namespace lattice
perl::Object lower_hasse_diagram(perl::Object fan, int boundary_rank, bool is_pure, bool is_complete);
/*
* @brief Computes the Hasse diagram of a fan, polyhedral complex or simplicial complex
* @param IncidenceMatrix maximal_cones The maximal cells
* @param Array<InicidenceMatrix> maximal_vifs The facets of each maximal cell. Can be empty, if tt.is_complete is true
* @param int top_combinatorial_dim The combinatorial dim of the (artificial) top face. Needed if built dually.
* @param Array<int> maximal_dims The ranks of the maximal cells. Can be empty if tt.pure = true
* @param RankRestriction rr. Whether the hasse diagram should only partially be computed (upwards or downwards) up to a certain dimension.
* @param TopologicalType tt. Indicates whether the complex is pure and/or complete (the latter meaning, that the intersections of the maximal cells generate the full Hasse diagram).
* @param Set<int> far_vertices. If not trivial, only the faces not intersecting this set are computed.
*/
template <typename IMatrix>
graph::Lattice<graph::lattice::BasicDecoration> hasse_diagram_general(
const GenericIncidenceMatrix<IMatrix>& maximal_cones,
const Array<IncidenceMatrix<> >& maximal_vifs,
const int top_combinatorial_dim,
const Array<int>& maximal_dims,
lattice::RankRestriction rr,
lattice::TopologicalType tt,
const Set<int>& far_vertices) {
using namespace graph::lattice_builder;
using namespace fan::lattice;
//Detect trivial rank restriction
if(rr.rank_restricted)
if( (rr.rank_restriction_type == lattice::RankCutType::GreaterEqual && rr.boundary_rank <= 0) ||
(rr.rank_restriction_type == lattice::RankCutType::LesserEqual && rr.boundary_rank >= top_combinatorial_dim + 2))
rr.rank_restricted = false;
const int n_vertices = maximal_cones.cols();
FacetList non_redundant_facets(n_vertices);
if(!tt.is_complete)
for(auto mvf : maximal_vifs)
for(auto fct = entire(rows(mvf)); !fct.at_end(); ++fct)
non_redundant_facets.replaceMax(*fct);
const bool is_dual =
!(rr.rank_restricted && rr.rank_restriction_type == lattice::RankCutType::LesserEqual)
&& far_vertices.size() == 0;
RestrictedIncidenceMatrix<> building_matrix;
if(!is_dual) {
building_matrix /= maximal_cones;
for(auto nrf = entire(non_redundant_facets); !nrf.at_end(); ++nrf)
building_matrix /= *nrf;
}
const ComplexPrimalClosure<> primal_cop(IncidenceMatrix<>(std::move(building_matrix)));
const ComplexDualClosure<> dual_cop(maximal_cones, maximal_vifs, non_redundant_facets);
const Set<int> artificial_set = scalar2set(-1);
const lattice::BasicComplexDecorator dec = is_dual?
lattice::BasicComplexDecorator(maximal_cones, top_combinatorial_dim, maximal_dims, scalar2set(-1), tt.is_pure) :
lattice::BasicComplexDecorator(top_combinatorial_dim, artificial_set, maximal_cones.rows() > 1 && far_vertices.size() == 0, n_vertices);
//Plain version
if(!rr.rank_restricted && far_vertices.size() == 0) {
//For a complete complex in dual mode, we need an artificial final (i.e. bottom) node, if the
//intersection of all cones is a vertex.
//Note that in primal mode, if there are at least two maximal cones,
//the artificial top node is created automatically as a closure.
bool need_artificial_node = is_dual?
tt.is_complete && !accumulate(rows(maximal_cones), operations::mul()).empty() :
maximal_cones.rows() == 1;
return is_dual?
compute_lattice_from_closure<lattice::BasicDecoration>(dual_cop,
lattice::TrivialCut<lattice::BasicDecoration>(),
dec, need_artificial_node, Dual()) :
compute_lattice_from_closure<lattice::BasicDecoration>(primal_cop,
lattice::TrivialCut<lattice::BasicDecoration>(),
dec, need_artificial_node, Primal());
}
//Bounded version
if(far_vertices.size() > 0) {
typedef lattice::SetAvoidingCut<lattice::BasicDecoration> setcut;
typedef lattice::RankCut<lattice::BasicDecoration, lattice::RankCutType::LesserEqual> rankcut;
setcut bounded_cut(far_vertices);
rankcut rank_cut(rr.boundary_rank);
lattice::CutAnd<setcut, rankcut> combined_cut(bounded_cut, rank_cut);
if(rr.rank_restricted)
return compute_lattice_from_closure<lattice::BasicDecoration>(primal_cop,
combined_cut, dec, true, Primal());
else
return compute_lattice_from_closure<lattice::BasicDecoration>(primal_cop,
bounded_cut, dec, true, Primal());
}
//Rank-restricted version
typedef lattice::NotFullSetCut<lattice::BasicDecoration> NFSCut;
typedef lattice::RankCut<lattice::BasicDecoration, lattice::RankCutType::LesserEqual> LCut;
typedef lattice::RankCut<lattice::BasicDecoration, lattice::RankCutType::GreaterEqual> GCut;
NFSCut nfSetCut(n_vertices);
LCut lesser_cut(rr.boundary_rank);
GCut greater_cut(rr.boundary_rank);
return rr.rank_restriction_type == lattice::RankCutType::GreaterEqual?
compute_lattice_from_closure<lattice::BasicDecoration>(dual_cop,
lattice::CutAnd<NFSCut, GCut>(nfSetCut,greater_cut), dec, true, Dual()) :
compute_lattice_from_closure<lattice::BasicDecoration>(primal_cop,
lattice::CutAnd<NFSCut, LCut>(nfSetCut,lesser_cut), dec, true, Primal());
}
}}
#endif
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