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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
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#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, or Rips graph, containing edges when the edge length is less or equal
* to a given threshold. Edge length is computed from a user given point cloud with a given distance function, or a
* distance matrix.
*
* \tparam Filtration_value is the type used to store the filtration values of the simplicial complex.
*/
template<typename Filtration_value>
class Rips_complex {
public:
/**
* \brief Type of the one skeleton graph stored inside the Rips complex structure.
*/
typedef typename boost::adjacency_list < boost::vecS, boost::vecS, boost::directedS
, boost::property < vertex_filtration_t, Filtration_value >
, boost::property < edge_filtration_t, Filtration_value >> OneSkeletonGraph;
private:
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.
*
* \tparam ForwardPointRange must be a range for which `std::begin` and `std::end` return input iterators on a
* point.
*
* \tparam Distance furnishes `operator()(const Point& p1, const Point& p2)`, where
* `Point` is a point from the `ForwardPointRange`, and that returns a `Filtration_value`.
*/
template<typename ForwardPointRange, typename Distance >
Rips_complex(const ForwardPointRange& points, Filtration_value threshold, Distance distance) {
compute_proximity_graph(points, threshold, distance);
}
/** \brief Rips_complex constructor from a distance matrix.
*
* @param[in] distance_matrix Range of distances.
* @param[in] threshold Rips value.
*
* \tparam DistanceMatrix must have a `size()` method and on which `distance_matrix[i][j]` returns
* the distance between points \f$i\f$ and \f$j\f$ as long as \f$ 0 \leqslant j < i \leqslant
* distance\_matrix.size().\f$
*/
template<typename DistanceMatrix>
Rips_complex(const DistanceMatrix& 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 Rips 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.
* @exception std::invalid_argument In debug mode, if `complex.num_vertices()` does not return 0.
*
*/
template <typename SimplicialComplexForRips>
void create_complex(SimplicialComplexForRips& complex, int dim_max) {
GUDHI_CHECK(complex.num_vertices() == 0,
std::invalid_argument("Rips_complex::create_complex - simplicial complex is not empty"));
// 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);
}
private:
/** \brief Computes 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.
*
* \tparam ForwardPointRange furnishes `.begin()` and `.end()`
* methods.
*
* \tparam Distance furnishes `operator()(const Point& p1, const Point& p2)`, where
* `Point` is a point from the `ForwardPointRange`, and that returns a `Filtration_value`.
*/
template< typename ForwardPointRange, typename Distance >
void compute_proximity_graph(const ForwardPointRange& points, Filtration_value threshold,
Distance distance) {
std::vector< std::pair< Vertex_handle, Vertex_handle > > edges;
std::vector< Filtration_value > edges_fil;
// 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 = 0;
for (auto it_u = std::begin(points); it_u != std::end(points); ++it_u, ++idx_u) {
Vertex_handle idx_v = idx_u + 1;
for (auto it_v = it_u + 1; it_v != std::end(points); ++it_v, ++idx_v) {
Filtration_value fil = distance(*it_u, *it_v);
if (fil <= threshold) {
edges.emplace_back(idx_u, idx_v);
edges_fil.push_back(fil);
}
}
}
// --------------------------------------------------------------------------------------------
// 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
// --------------------------------------------------------------------------------------------
// Do not use : rips_skeleton_graph_ = OneSkeletonGraph(...) -> deep copy of the graph (boost graph is not
// move-enabled)
rips_skeleton_graph_.~OneSkeletonGraph();
new(&rips_skeleton_graph_)OneSkeletonGraph(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<OneSkeletonGraph>::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:
OneSkeletonGraph rips_skeleton_graph_;
};
} // namespace rips_complex
} // namespace Gudhi
#endif // RIPS_COMPLEX_H_
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