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/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* Author(s): Siargey Kachanovich
*
* Copyright (C) 2015 INRIA (France)
*
* 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 3 of the License, or
* (at your option) any later version.
*
* 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.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef WITNESS_COMPLEX_H_
#define WITNESS_COMPLEX_H_
#include <gudhi/Active_witness/Active_witness.h>
#include <gudhi/Kd_tree_search.h>
#include <utility>
#include <vector>
#include <list>
#include <limits>
namespace gss = Gudhi::spatial_searching;
namespace Gudhi {
namespace witness_complex {
/**
* \private
* \class Witness_complex
* \brief Constructs (weak) witness complex for the given sets of witnesses and landmarks.
* \ingroup witness_complex
*
* \tparam Kernel_ requires a <a target="_blank"
* href="http://doc.cgal.org/latest/Kernel_d/classCGAL_1_1Epick__d.html">CGAL::Epick_d</a> class, which
* can be static if you know the ambiant dimension at compile-time, or dynamic if you don't.
* \tparam DimensionTag can be either <a target="_blank"
* href="http://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Dimension__tag.html">Dimension_tag<d></a>
* if you know the intrinsic dimension at compile-time,
* or <a target="_blank"
* href="http://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Dynamic__dimension__tag.html">CGAL::Dynamic_dimension_tag</a>
* if you don't.
*/
template< class Kernel_ >
class Witness_complex {
private:
typedef Kernel_ K;
typedef typename K::Point_d Point_d;
typedef typename K::FT FT;
typedef std::vector<Point_d> Point_range;
typedef gss::Kd_tree_search<Kernel_, Point_range> Kd_tree;
typedef typename Kd_tree::INS_range Nearest_landmark_range;
typedef typename std::vector<Nearest_landmark_range> Nearest_landmark_table;
typedef typename Nearest_landmark_range::iterator Nearest_landmark_row_iterator;
typedef std::vector< double > Point_t;
typedef std::vector< Point_t > Point_Vector;
typedef FT Filtration_value;
typedef std::size_t Witness_id;
typedef typename Nearest_landmark_range::Point_with_transformed_distance Id_distance_pair;
typedef typename Id_distance_pair::first_type Landmark_id;
typedef Active_witness<Id_distance_pair, Nearest_landmark_range> ActiveWitness;
typedef std::list< ActiveWitness > ActiveWitnessList;
typedef std::vector< Landmark_id > typeVectorVertex;
typedef std::pair< typeVectorVertex, Filtration_value> typeSimplex;
typedef Landmark_id Vertex_handle;
private:
Point_range witnesses_, landmarks_;
Kd_tree landmark_tree_;
public:
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/* @name Constructor
*/
//@{
/**
* \brief Initializes member variables before constructing simplicial complex.
* \details Records landmarks from the range [landmarks_first, landmarks_last) into a
* table internally, as well as witnesses from the range [witnesses_first, witnesses_last).
* All iterator parameters should satisfy <a target="_blank"
* href="http://en.cppreference.com/w/cpp/concept/InputIterator">InputIterator</a>
* C++ concept.
*/
template< typename InputIteratorLandmarks,
typename InputIteratorWitnesses >
Witness_complex(InputIteratorLandmarks landmarks_first,
InputIteratorLandmarks landmarks_last,
InputIteratorWitnesses witnesses_first,
InputIteratorWitnesses witnesses_last)
: witnesses_(witnesses_first, witnesses_last), landmarks_(landmarks_first, landmarks_last), landmark_tree_(landmarks_)
{
}
/** \brief Returns the point corresponding to the given vertex.
* @param[in] vertex Vertex handle of the point to retrieve.
*/
Point_d get_point( Vertex_handle vertex ) const
{
return landmarks_[vertex];
}
/** \brief Outputs the (weak) witness complex in a simplicial complex data structure.
* @param[out] complex Simplicial complex data structure compatible with 'find' and 'insert' operations.
* (Cf SimplicialComplexForWitness)
* @param[in] max_alpha_square Maximal squared relaxation parameter.
* @param[in] limit_dimension Represents the maximal dimension of the simplicial complex
* (default value = no limit).
*/
template < typename SimplicialComplexForWitness >
bool create_complex(SimplicialComplexForWitness& complex,
FT max_alpha_square,
Landmark_id limit_dimension = std::numeric_limits<Landmark_id>::max())
{
std::size_t nbL = landmarks_.size();
if (complex.num_vertices() > 0) {
std::cerr << "Witness complex cannot create complex - complex is not empty.\n";
return false;
}
if (max_alpha_square < 0) {
std::cerr << "Witness complex cannot create complex - squared relaxation parameter must be non-negative.\n";
return false;
}
if (limit_dimension < 0) {
std::cerr << "Witness complex cannot create complex - limit dimension must be non-negative.\n";
return false;
}
typeVectorVertex vv;
ActiveWitnessList active_witnesses;
for (unsigned i = 0; i != nbL; ++i) {
// initial fill of 0-dimensional simplices
// by doing it we don't assume that landmarks are necessarily witnesses themselves anymore
vv = {i};
complex.insert_simplex(vv, Filtration_value(0.0));
}
Landmark_id k = 1; /* current dimension in iterative construction */
for (auto w: witnesses_)
active_witnesses.push_back(ActiveWitness(landmark_tree_.query_incremental_nearest_neighbors(w)));
ActiveWitness aw_copy(active_witnesses.front());
while (!active_witnesses.empty() && k <= limit_dimension ) {
typename ActiveWitnessList::iterator aw_it = active_witnesses.begin();
std::vector<Landmark_id> simplex;
simplex.reserve(k+1);
while (aw_it != active_witnesses.end()) {
bool ok = add_all_faces_of_dimension(k,
max_alpha_square,
std::numeric_limits<double>::infinity(),
aw_it->begin(),
simplex,
complex,
aw_it->end());
assert(simplex.empty());
if (!ok)
active_witnesses.erase(aw_it++); //First increase the iterator and then erase the previous element
else
aw_it++;
}
k++;
}
complex.set_dimension(k-1);
return true;
}
//@}
private:
/* \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness
* Iterator is needed to know until how far we can take landmarks to form simplexes
* simplex is the prefix of the simplexes to insert
* The output value indicates if the witness rests active or not
*/
template < typename SimplicialComplexForWitness >
bool add_all_faces_of_dimension(int dim,
double alpha2,
double norelax_dist2,
typename ActiveWitness::iterator curr_l,
std::vector<Landmark_id>& simplex,
SimplicialComplexForWitness& sc,
typename ActiveWitness::iterator end)
{
if (curr_l == end)
return false;
bool will_be_active = false;
typename ActiveWitness::iterator l_it = curr_l;
if (dim > 0)
for (; l_it->second - alpha2 <= norelax_dist2 && l_it != end; ++l_it) {
simplex.push_back(l_it->first);
if (sc.find(simplex) != sc.null_simplex()) {
typename ActiveWitness::iterator next_it = l_it;
will_be_active = add_all_faces_of_dimension(dim-1,
alpha2,
norelax_dist2,
++next_it,
simplex,
sc,
end) || will_be_active;
}
assert(!simplex.empty());
simplex.pop_back();
// If norelax_dist is infinity, change to first omitted distance
if (l_it->second <= norelax_dist2)
norelax_dist2 = l_it->second;
typename ActiveWitness::iterator next_it = l_it;
will_be_active = add_all_faces_of_dimension(dim,
alpha2,
norelax_dist2,
++next_it,
simplex,
sc,
end) || will_be_active;
}
else if (dim == 0)
for (; l_it->second - alpha2 <= norelax_dist2 && l_it != end; ++l_it) {
simplex.push_back(l_it->first);
double filtration_value = 0;
// if norelax_dist is infinite, relaxation is 0.
if (l_it->second > norelax_dist2)
filtration_value = l_it->second - norelax_dist2;
if (all_faces_in(simplex, &filtration_value, sc)) {
will_be_active = true;
sc.insert_simplex(simplex, filtration_value);
}
assert(!simplex.empty());
simplex.pop_back();
// If norelax_dist is infinity, change to first omitted distance
if (l_it->second < norelax_dist2)
norelax_dist2 = l_it->second;
}
return will_be_active;
}
/* \brief Check if the facets of the k-dimensional simplex witnessed
* by witness witness_id are already in the complex.
* inserted_vertex is the handle of the (k+1)-th vertex witnessed by witness_id
*/
template < typename SimplicialComplexForWitness >
bool all_faces_in(typeVectorVertex& simplex,
double* filtration_value,
SimplicialComplexForWitness& sc)
{
typedef typename SimplicialComplexForWitness::Simplex_handle Simplex_handle;
typeVectorVertex facet;
for (typename typeVectorVertex::iterator not_it = simplex.begin(); not_it != simplex.end(); ++not_it)
{
facet.clear();
for (typename typeVectorVertex::iterator it = simplex.begin(); it != simplex.end(); ++it)
if (it != not_it)
facet.push_back(*it);
Simplex_handle facet_sh = sc.find(facet);
if (facet_sh == sc.null_simplex())
return false;
else if (sc.filtration(facet_sh) > *filtration_value)
*filtration_value = sc.filtration(facet_sh);
}
return true;
}
};
} // namespace witness_complex
} // namespace Gudhi
#endif // WITNESS_COMPLEX_H_
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