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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): Clément Maria, Pawel Dlotko, Vincent Rouvreau
*
* Copyright (C) 2016 INRIA
*
* 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 RIPS_COMPLEX_H_
#define RIPS_COMPLEX_H_
#include <gudhi/Debug_utils.h>
#include <gudhi/graph_simplicial_complex.h>
#include <boost/graph/adjacency_list.hpp>
#include <iostream>
#include <vector>
#include <map>
#include <string>
#include <limits> // for numeric_limits
#include <utility> // for pair<>
namespace Gudhi {
namespace rips_complex {
/**
* \class Rips_complex
* \brief Rips complex data structure.
*
* \ingroup rips_complex
*
* \details
* The data structure is a one skeleton graph constructed from a point cloud, containing edges when the edge length is
* less or equal to a given threshold. Edge length is computed from a user given function.
*
* The complex is a template class requiring a Filtration_value type.
*
* \tparam Filtration_value must meet `SimplicialComplexForRips` concept.
*/
template<typename Filtration_value>
class Rips_complex {
private:
typedef typename boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS
, boost::property < vertex_filtration_t, Filtration_value >
, boost::property < edge_filtration_t, Filtration_value >> Graph_t;
typedef int Vertex_handle;
public:
/** \brief Rips_complex constructor from a list of points.
*
* @param[in] points Range of points.
* @param[in] threshold rips value.
* @param[in] distance distance function that returns a Filtration_value from 2 given points.
*
* The type InputPointRange must be a range for which std::begin and std::end return input iterators on a point.
*/
template<typename InputPointRange, typename Distance >
Rips_complex(const InputPointRange& points, Filtration_value threshold, Distance distance) {
compute_proximity_graph<InputPointRange, Distance >(points, threshold, distance);
}
/** \brief Rips_complex constructor from a distance matrix.
*
* @param[in] distance_matrix Range of distances.
* @param[in] threshold rips value.
*
* The type InputDistanceRange must be a range for which std::begin and std::end return input iterators on a point.
*/
template<typename InputDistanceRange>
Rips_complex(const InputDistanceRange& distance_matrix, Filtration_value threshold) {
compute_proximity_graph(boost::irange((size_t)0,distance_matrix.size()), threshold,
[&](size_t i, size_t j){return distance_matrix[j][i];});
}
/** \brief Initializes the simplicial complex from the 1-skeleton graph and expands it until a given maximal
* dimension.
*
* \tparam SimplicialComplexForRips must meet `SimplicialComplexForRips` concept.
*
* @param[in] complex SimplicialComplexForRips to be created.
* @param[in] dim_max graph expansion for rips until this given maximal dimension.
*
* @return true if creation succeeds, false otherwise.
*
*/
template <typename SimplicialComplexForRips>
bool create_complex(SimplicialComplexForRips& complex, int dim_max) {
if (complex.num_vertices() > 0) {
std::cerr << "Rips_complex create_complex - complex is not empty\n";
return false; // ----- >>
}
// insert the proximity graph in the simplicial complex
complex.insert_graph(rips_skeleton_graph_);
// expand the graph until dimension dim_max
complex.expansion(dim_max);
// --------------------------------------------------------------------------------------------
return true;
}
public:
/** \brief Output the proximity graph of the points.
*
* If points contains n elements, the proximity graph is the graph
* with n vertices, and an edge [u,v] iff the distance function between
* points u and v is smaller than threshold.
*
* The type PointCloud furnishes .begin() and .end() methods, that return
* iterators with value_type Point.
*/
template< typename InputPointRange, typename Distance >
void compute_proximity_graph(const InputPointRange& points, Filtration_value threshold,
Distance distance) {
std::vector< std::pair< Vertex_handle, Vertex_handle > > edges;
std::vector< Filtration_value > edges_fil;
std::map< Vertex_handle, Filtration_value > vertices;
// Compute the proximity graph of the points.
// If points contains n elements, the proximity graph is the graph with n vertices, and an edge [u,v] iff the
// distance function between points u and v is smaller than threshold.
// --------------------------------------------------------------------------------------------
// Creates the vector of edges and its filtration values (returned by distance function)
Vertex_handle idx_u, idx_v;
Filtration_value fil;
idx_u = 0;
for (auto it_u = std::begin(points); it_u != std::end(points); ++it_u) {
idx_v = idx_u + 1;
for (auto it_v = it_u + 1; it_v != std::end(points); ++it_v, ++idx_v) {
fil = distance(*it_u, *it_v);
if (fil <= threshold) {
edges.emplace_back(idx_u, idx_v);
edges_fil.push_back(fil);
}
}
++idx_u;
}
// --------------------------------------------------------------------------------------------
// Creates the proximity graph from edges and sets the property with the filtration value.
// Number of points is labeled from 0 to idx_u-1
rips_skeleton_graph_ = Graph_t(edges.begin(), edges.end(), edges_fil.begin(), idx_u);
auto vertex_prop = boost::get(vertex_filtration_t(), rips_skeleton_graph_);
using vertex_iterator = typename boost::graph_traits<Graph_t>::vertex_iterator;
vertex_iterator vi, vi_end;
for (std::tie(vi, vi_end) = boost::vertices(rips_skeleton_graph_);
vi != vi_end; ++vi) {
boost::put(vertex_prop, *vi, 0.);
}
}
private:
Graph_t rips_skeleton_graph_;
};
} // namespace rips_complex
} // namespace Gudhi
#endif // RIPS_COMPLEX_H_
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