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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/Array.h"
#include "polymake/Set.h"
#include "polymake/graph/maximal_chains.h"
#include "polymake/topaz/hasse_diagram.h"
namespace polymake { namespace topaz {
using graph::lattice::BasicDecoration;
using graph::lattice::Nonsequential;
namespace {
inline
Int
adjusted_index(const Int i,
const Int bottom_node_index,
const bool ignore_bottom_node,
const Int top_node_index,
const bool ignore_top_node)
{
const Int adj =
i
- (ignore_bottom_node && i > bottom_node_index)
- (ignore_top_node && i > top_node_index);
assert(adj>=0);
return adj;
}
inline
Int
reverse_adjusted_index(const Int i,
const Int bottom_node_index,
const bool ignore_bottom_node,
const Int top_node_index,
const bool ignore_top_node)
{
return
i
+ (ignore_bottom_node && i >= bottom_node_index)
+ (ignore_top_node && i >= top_node_index);
}
// Renumbers node indices as if bottom node (and potentially top node)
// are removed
template <typename Decoration, typename SeqType>
void
bs_renumber_nodes(Array<Set<Int>>& facets,
const graph::Lattice<Decoration, SeqType>& HD,
const bool ignore_top_node)
{
const Int b_index = HD.bottom_node();
const Int t_index = HD.top_node();
for (auto f_it = entire(facets); !f_it.at_end(); ++f_it) {
Set<Int> nset;
for (auto n : (*f_it)) {
if (n<0)
cerr << "bs_renumber_nodes: weird *f_it: " << *f_it << endl;
nset += adjusted_index(n, b_index, true, t_index, ignore_top_node);
}
*f_it = nset;
}
}
} // end anonymous namespace
struct FacetsAndLabels {
Array<Set<Int>> facets;
Array<Set<Set<Int>>> labels;
};
/*
Template type of input Hasse diagram:
- for Polytope : SeqType = Sequential,
- for SimplicialComplex: SeqType = Nonsequential
Output: two arrays
- The first array contains the facets of the second barycentric subdivision
as a simplicial complex. The node indices refer to the nodes of the
Hasse diagram of the first barycentric subdivision, which is not returned
- The second array contains the label for each vertex in the first array.
This is a tuple of faces of the original complex such that the vertex
in question is the barycenter of those face barycenters.
*/
template<typename SeqType>
FacetsAndLabels
first_barycentric_subdivision(const Lattice<BasicDecoration, SeqType>& HD0,
const bool ignore_top_node = false)
{
// the Hasse diagram can come ordered top-to-bottom or bottom-to-top, or be unordered in the case of Nonsequential, and always has a top and a bottom node
// depending on this, we have to do some index gymnastics
const Int
HD0_top_index (HD0.top_node()),
HD0_bottom_index(HD0.bottom_node());
const bool
HD0_top_invalid(ignore_top_node || scalar2set(-1) == HD0.decoration()[HD0_top_index].face),
HD0_bottom_empty(0 == HD0.decoration()[HD0_bottom_index].face.size());
#if POLYMAKE_DEBUG
if (get_debug_level() > 1)
cerr << "ignore_top_node: " << ignore_top_node << "\n"
<< "HD0_top_index: " << HD0_top_index << "\n"
<< "HD0_bottom_index: " << HD0_bottom_index << "\n"
<< "HD0_top_invalid: " << HD0_top_invalid << "\n"
<< "HD0_bottom_empty: " << HD0_bottom_empty << endl;
#endif
FacetsAndLabels facets_and_labels;
// make the first barycentric subdivision
// Array<Set<Int>> HD1_facets = maximal_chains(HD0, HD0_bottom_empty, HD0_top_invalid);
facets_and_labels.facets = maximal_chains(HD0, HD0_bottom_empty, HD0_top_invalid);
topaz::bs_renumber_nodes(facets_and_labels.facets, HD0, HD0_top_invalid);
// make the vertex labels
facets_and_labels.labels = Array<Set<Set<Int>>> (HD0.nodes() - HD0_top_invalid - HD0_bottom_empty);
for (auto hd1_it = entire<indexed>(HD0.decoration()); !hd1_it.at_end(); ++hd1_it) {
if ((HD0_top_index == hd1_it.index() && HD0_top_invalid) ||
(HD0_bottom_index == hd1_it.index() && HD0_bottom_empty))
continue;
facets_and_labels.labels[topaz::adjusted_index(hd1_it.index(), HD0_bottom_index, true, HD0_top_index, HD0_top_invalid)] += hd1_it->face;
}
return facets_and_labels;
}
/*
Same input and output as for first_barycentric_subdivision.
There are some slight differences in the code that make refactoring not
really worthwhile.
*/
template<typename SeqType>
std::pair<Array<Set<Int>>, Array<Set<Set<Int>>>>
second_barycentric_subdivision(const Lattice<BasicDecoration, SeqType>& HD0,
const bool ignore_top_node = false)
{
// the Hasse diagram can come ordered top-to-bottom or bottom-to-top, or be unordered in the case of Nonsequential, and always has a top and a bottom node
// depending on this, we have to do some index gymnastics
const Int
HD0_top_index (HD0.top_node()),
HD0_bottom_index(HD0.bottom_node());
const bool
HD0_top_invalid(ignore_top_node || scalar2set(-1) == HD0.decoration()[HD0_top_index].face),
HD0_bottom_empty(0 == HD0.decoration()[HD0_bottom_index].face.size());
// make the first barycentric subdivision
Array<Set<Int>> HD1_facets = maximal_chains(HD0, HD0_bottom_empty, HD0_top_invalid);
bs_renumber_nodes(HD1_facets, HD0, HD0_top_invalid);
const Lattice<BasicDecoration, Nonsequential> HD1 = hasse_diagram_from_facets(HD1_facets);
// extract metadata from first barycentric subdivision
const Int
HD1_bottom_index(HD1.bottom_node()),
HD1_top_index(HD1.top_node());
const bool
HD1_bottom_empty(0 == HD1.decoration()[HD1_bottom_index].face.size()),
HD1_top_invalid(scalar2set(-1) == HD1.decoration()[HD1_top_index].face);
// make the facets of the second barycentric subdivision
Array<Set<Int>> HD2_facets = maximal_chains(HD1, HD1_bottom_empty, HD1_top_invalid);
bs_renumber_nodes(HD2_facets, HD1, HD1_top_invalid);
// make the vertex labels
Array<Set<Set<Int>>> HD2_labels_as_set(HD1.nodes() - HD1_top_invalid - HD1_bottom_empty);
auto HD2_labels_as_set_it = entire(HD2_labels_as_set);
for (auto hd1_it = entire<indexed>(HD1.decoration()); !hd1_it.at_end(); ++hd1_it) {
if ((HD1_top_index == hd1_it.index() && HD1_top_invalid) ||
(HD1_bottom_index == hd1_it.index() && HD1_bottom_empty))
continue;
for (const auto node_index: hd1_it->face)
*HD2_labels_as_set_it += HD0.decoration()[reverse_adjusted_index(node_index, HD0_bottom_index, true, HD0_top_index, HD0_top_invalid)].face;
++HD2_labels_as_set_it;
}
return std::make_pair(HD2_facets, HD2_labels_as_set);
}
} }
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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