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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.
--------------------------------------------------------------------------------
*/
#pragma once
#include "polymake/graph/Lattice.h"
#include "polymake/graph/Decoration.h"
#include "polymake/Array.h"
#include "polymake/Set.h"
#include "polymake/Matrix.h"
#include "polymake/Rational.h"
#include "polymake/FacetList.h"
#include <string>
namespace polymake { namespace graph {
// Computes the barycentric subdivision
// @param HD A Lattice
// @param ignore_bottom_node If true, the bottom node is not included in the facet comptutation
// @param ignore_top_node If true, the top node is not included in the facet computation
// @return Array<Set<Int>> Facets of the barycentric subdivision.
// Indices are node indices in the Hasse diagram, in particular they need not start
// with 0.
template <typename Decoration, typename SeqType>
Array<Set<Int>> maximal_chains(const Lattice<Decoration, SeqType>& HD, bool ignore_bottom_node, bool ignore_top_node)
{
const Int total_rank = HD.rank();
const Int dim = total_rank-1-ignore_top_node;
const Int top_index = HD.top_node();
const Int bottom_index = HD.bottom_node();
// each old facet is divided into at least (dim+1)! cells, with equality iff the object is simplicial.
// each facet of the barycentric subdivision is a flag in the input face lattice HD,
// stored as the set of node indices of the constituent faces in HD
FacetList facets;
using out_edge = Graph<Directed>::out_edge_list::const_iterator;
using stack_type = std::vector<out_edge>; // vector is more efficient than list
stack_type flag;
flag.reserve(dim+1);
// If it has only the bottom node, return the empty list
if (HD.graph().nodes() == 1) {
Array<Set<Int>> trivial_result(ignore_top_node || ignore_bottom_node ? 0 : 1);
if (!(ignore_top_node || ignore_bottom_node)) {
trivial_result[0] = scalar2set(bottom_index);
}
return trivial_result;
}
// start with the "empty set" node - just for convenience
flag.push_back(HD.out_edges(bottom_index).begin());
do {
// complete the facet
while (true) {
Int n = flag.back().to_node();
if (n == top_index) break;
flag.push_back(HD.out_edges(n).begin()); // the index of the next face in the flag
}
// copy the facet
Set<Int> facet;
if (!ignore_bottom_node) facet += bottom_index;
for (auto s=entire(flag); !s.at_end(); ++s) {
if (!ignore_top_node || s->to_node() != top_index)
facet += s->to_node();
}
if (facet.size() > 0)
facets.insertMax(facet);
// depth-first search to the next facet
do {
if (!(++flag.back()).at_end()) break;
flag.pop_back();
} while (!flag.empty());
} while (!flag.empty());
return Array<Set<Int>>(facets);
}
// Computes the VERTEX_LABELS
// If ignore_top_node is true, the top node will get the empty face (i.e. the length of the list
// is always the number of nodes.
template <typename Decoration, typename SeqType>
Array<std::string> bs_labels(const Lattice<Decoration, SeqType>& HD, const Array<std::string>& old_labels, bool ignore_top_node)
{
Array<std::string> L(HD.nodes());
auto f = entire<indexed>(HD.decoration());
std::ostringstream label;
const bool convert_old_labels = !old_labels.empty();
const Int top_index = HD.top_node();
for (auto l=entire(L); !l.at_end(); ++l, ++f) {
if (ignore_top_node && f.index() == top_index) {
*l = label.str();
continue;
}
if (!convert_old_labels) {
wrap(label) << f->face;
} else {
wrap(label) << "{";
bool first = true;
for (auto fsit = entire(f->face); !fsit.at_end(); ++fsit) {
if (first) first = false;
else wrap(label) << " ";
wrap(label) << old_labels[*fsit];
}
wrap(label) << "}";
}
*l=label.str();
label.str("");
}
return L;
}
// Computes the GEOMETRIC_REALIZATION
// If ignore_top_node = true, the top node will get a zero vector (i.e. the length of the list
// is always the number of nodes
template <typename Scalar, typename Decoration, typename SeqType>
Matrix<Scalar> bs_geom_real(const Matrix<Scalar>& old_coord, const Lattice<Decoration, SeqType>& HD, bool ignore_top_node)
{
const Int ambient_dim = old_coord.cols();
const Int top_index = HD.top_node();
Matrix<Scalar> new_coord(HD.nodes(), ambient_dim);
auto f = entire<indexed>(HD.decoration());
for (auto r = entire(rows(new_coord)); !r.at_end(); ++r, ++f) {
if (ignore_top_node && f.index() == top_index) continue;
accumulate_in(entire(select(rows(old_coord), f->face)), operations::add(), *r);
if (f->face.size()) {
*r /= f->face.size();
} else {
(*r)[0] = one_value<Scalar>();
}
}
return new_coord;
}
} }
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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