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/* Copyright 2013 IST Austria
Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus
This file is part of PHAT.
PHAT is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
PHAT 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 Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with PHAT. If not, see <http://www.gnu.org/licenses/>. */
#pragma once
#include <phat/persistence_pairs.h>
#include <phat/boundary_matrix.h>
#include <phat/helpers/dualize.h>
#include <phat/algorithms/twist_reduction.h>
namespace phat {
// Extracts persistence pairs in separate dimensions from a reduced
// boundary matrix representing ``double`` filtration. The pairs
// give persistent relative homology of the pair of filtrations.
// TODO: Use it with standard reduction algorithm (no template option).
template< typename ReductionAlgorithm, typename Representation >
void compute_relative_persistence_pairs(std::vector<persistence_pairs>& pairs, boundary_matrix<Representation>& boundary_matrix, const std::map<int, int>& L) {
ReductionAlgorithm reduce;
reduce(boundary_matrix);
std::map<int, bool> free;
std::map<int, int> invL;
for (std::map<int, int>::const_iterator it = L.begin(); it != L.end(); ++it) { invL[it->second] = it->first; }
for (std::vector<persistence_pairs>::iterator it = pairs.begin(); it != pairs.end(); ++it) { it->clear(); }
for (index idx = 0; idx < boundary_matrix.get_num_cols(); ++idx) {
int dimension = boundary_matrix.get_dim(idx);
if (L.find(idx) != L.end()) { ++dimension; }
free[idx] = true;
if (!boundary_matrix.is_empty(idx)) {
index birth = boundary_matrix.get_max_index(idx);
index death = idx;
pairs[dimension-1].append_pair(birth, death);
free[birth] = false;
free[death] = false;
} else {
// This is an L-simplex and a (dimension+1)-dimensional cycle
if (L.find(idx) != L.end()) {
assert(dimension < pairs.size());
pairs[dimension].append_pair(idx, -1);
}
}
}
for (std::map<int, bool>::iterator it = free.begin(); it != free.end(); ++it) {
if (it->second) {
int dimension = boundary_matrix.get_dim(it->first);
if (invL.find(it->first) == invL.end() && L.find(it->first) == L.end()) {
assert(dimension < pairs.size());
pairs[dimension].append_pair(it->first, -1);
}
}
}
}
// Extracts persistence pairs in separate dimensions; expects a d-dimensional vector of persistent_pairs
template< typename ReductionAlgorithm, typename Representation >
void compute_persistence_pairs(std::vector<persistence_pairs>& pairs, boundary_matrix<Representation>& boundary_matrix) {
ReductionAlgorithm reduce;
reduce(boundary_matrix);
std::map<int, bool> free;
for (std::vector<persistence_pairs>::iterator it = pairs.begin(); it != pairs.end(); ++it) { it->clear(); }
for (index idx = 0; idx < boundary_matrix.get_num_cols(); ++idx) {
int dimension = boundary_matrix.get_dim(idx);
free[idx] = true;
if (!boundary_matrix.is_empty(idx)) {
index birth = boundary_matrix.get_max_index(idx);
index death = idx;
pairs[dimension-1].append_pair(birth, death);
// Cannot be of the form (a, infinity)
free[birth] = false;
free[death] = false;
}
}
for (std::map<int, bool>::iterator it = free.begin(); it != free.end(); ++it) {
if (it->second) {
int dimension = boundary_matrix.get_dim(it->first);
pairs[dimension].append_pair(it->first, -1);
}
}
}
template< typename ReductionAlgorithm, typename Representation >
void compute_persistence_pairs( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
ReductionAlgorithm reduce;
reduce( boundary_matrix );
pairs.clear();
std::set<index> max_indices;
// finite pairs
for( index idx = 0; idx < boundary_matrix.get_num_cols(); idx++ ) {
if( !boundary_matrix.is_empty( idx ) ) {
index birth = boundary_matrix.get_max_index( idx );
max_indices.insert(birth);
index death = idx;
pairs.append_pair( birth, death );
}
}
// infinite pairs: column idx is 0, and row idx does not contain a lowest one
for( index idx = 0; idx < boundary_matrix.get_num_cols(); idx++ ) {
if(boundary_matrix.is_empty(idx) && max_indices.count(idx) == 0 ) {
pairs.append_pair( idx, k_infinity_index);
}
}
}
template< typename ReductionAlgorithm, typename Representation >
void compute_persistence_pairs_dualized( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
dualize( boundary_matrix );
compute_persistence_pairs< ReductionAlgorithm >( pairs, boundary_matrix );
dualize_persistence_pairs( pairs, boundary_matrix.get_num_cols() );
}
template< typename Representation >
void compute_persistence_pairs( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
phat::compute_persistence_pairs< twist_reduction >( pairs, boundary_matrix );
}
template< typename Representation >
void compute_persistence_pairs_dualized( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
compute_persistence_pairs_dualized< twist_reduction >( pairs, boundary_matrix );
}
}
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