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/* Copyright (c) 1997-2021
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.
--------------------------------------------------------------------------------
*/
#ifndef __FAN__STACKY_FUNDAMENTAL_DOMAIN_H
#define __FAN__STACKY_FUNDAMENTAL_DOMAIN_H
#include "polymake/fan/stacky_fan.h"
namespace polymake { namespace fan {
template<typename InnerLabel>
void
fundamental_domain_in_first_bc(const Array<Set<Int>>& SD_facets,
const Array<Set<InnerLabel>>& SD_labels,
const Array<Array<Int>>& rays_perm_generators,
Array<Set<Int>>& reordered_facet_reps,
Array<Set<InnerLabel>>& reordered_label_reps)
{
#if MY_POLYMAKE_DEBUG
const Int debug_level(3); //get_debug_level());
#endif
BigObject SC("topaz::SimplicialComplex",
"FACETS", SD_facets);
const Graph<> dual_graph = SC.give("DUAL_GRAPH.ADJACENCY");
Array<Set<Int>> inner_label_orbits;
Array<Array<Int>> generators_on_inner_labels;
Array<Set<Int>> indexed_SD_facets;
Array<Set<Int>> indexed_SD_labels;
Array<Set<Int>> indexed_label_orbits;
Map<Set<Int>, Int> index_of_indexed_label_orbit;
Array<Array<Int>> generators_on_indexed_label_orbits;
index_label_orbits(SD_facets, SD_labels, rays_perm_generators,
inner_label_orbits, generators_on_inner_labels, indexed_SD_facets, indexed_SD_labels, indexed_label_orbits, index_of_indexed_label_orbit, generators_on_indexed_label_orbits);
const group::PermlibGroup indexed_label_g(generators_on_indexed_label_orbits);
Set<Int> seen_indices {0};
std::list<Int> queue {0};
std::vector<Int> accepted_indices;
Set<Set<Int>> facet_reps;
while (queue.size()) {
const Int current_index(queue.front()); queue.pop_front();
#if MY_POLYMAKE_DEBUG
if (debug_level>2)
cerr << "\nqueue now " << queue << ", current_index: " << current_index << ": " << indexed_SD_facets[current_index] << endl;
#endif
const Set<Int> rep = indexed_label_g.lex_min_representative(indexed_SD_facets[current_index]);
#if MY_POLYMAKE_DEBUG
if (debug_level>2)
cerr << "rep of " << indexed_SD_facets[current_index] << ": "
<< "(orbit " << indexed_label_g.orbit(indexed_SD_facets[current_index]) << "): "
<< rep << endl;
#endif
if (facet_reps.collect(rep))
continue;
accepted_indices.push_back(current_index);
for (auto nb_iter = entire(dual_graph.adjacent_nodes(current_index)); !nb_iter.at_end(); ++nb_iter)
if (!seen_indices.contains(*nb_iter)) {
queue.push_back(*nb_iter);
seen_indices += *nb_iter;
#if MY_POLYMAKE_DEBUG
if (debug_level>2)
cerr << "added neighbor " << *nb_iter << ": " << indexed_SD_facets[*nb_iter] << endl;
#endif
}
}
// facet_reps now contains one representative of each orbit of simplices in the barycentric subdivision, expressed in the original vertex indices
// we now reorder these indices and store the appropriate original vertex labels, without identifications
#if MY_POLYMAKE_DEBUG
if (debug_level)
cerr << "\nfundamental_domain_impl, before index reordering:\n"
<< "accepted_indices(" << accepted_indices.size() << "):\n" << accepted_indices << endl;
#endif
if (convert_to<Int>(accepted_indices.size()) == indexed_SD_facets.size()) {
#if MY_POLYMAKE_DEBUG
if (debug_level)
cerr << "\ninput is a fundamental domain." << endl;
#endif
reordered_facet_reps = SD_facets;
reordered_label_reps = SD_labels;
return;
}
Set<Int> used_inner_label_indices;
for (auto F_it = entire(select(indexed_SD_facets, accepted_indices)); !F_it.at_end(); ++F_it)
used_inner_label_indices += *F_it;
Array<Int> reordered_index_of_inner_label;
reordered_facet_reps.resize(accepted_indices.size());
reorder_indices(entire(select(indexed_SD_facets, accepted_indices)), indexed_label_orbits, inner_label_orbits, used_inner_label_indices, generators_on_indexed_label_orbits,
entire(reordered_facet_reps), reordered_label_reps, reordered_index_of_inner_label);
#if MY_POLYMAKE_DEBUG
if (debug_level) {
cerr << "\nfundamental_domain_impl, after index reordering:\n"
<< "reordered_facet_reps(" << reordered_facet_reps.size() << "):\n" << reordered_facet_reps << "\n"
<< "reordered_label_reps(" << reordered_label_reps.size() << "):\n";
for (Int i=0; i<reordered_label_reps.size(); ++i)
cerr << i << ": " << reordered_label_reps[i] << "\n";
cerr << endl;
}
#endif
}
}}
#endif // __FAN__STACKY_FUNDAMENTAL_DOMAIN_H
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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