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author | Vincent Rouvreau <10407034+VincentRouvreau@users.noreply.github.com> | 2020-07-02 12:25:08 -0700 |
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committer | GitHub <noreply@github.com> | 2020-07-02 12:25:08 -0700 |
commit | 444ec77fe16783c35ef86598011a662c5d6e8d92 (patch) | |
tree | 5020b95c18d0206fe8e693a40d1e4aaf132d6a51 /src | |
parent | 3c7a4d01ec758d68a219fae8981c9847cf8d7a0f (diff) | |
parent | e44b0a88e2241f81b51b9060f73ac86f53c9cfc1 (diff) |
Merge pull request #281 from VincentRouvreau/edge_collapse_integration_vincent
Edge collapse integration vincent
Diffstat (limited to 'src')
-rw-r--r-- | src/CMakeLists.txt | 1 | ||||
-rw-r--r-- | src/Collapse/doc/dominated_edge.png | bin | 0 -> 349766 bytes | |||
-rw-r--r-- | src/Collapse/doc/intro_edge_collapse.h | 101 | ||||
-rw-r--r-- | src/Collapse/example/CMakeLists.txt | 23 | ||||
-rw-r--r-- | src/Collapse/example/edge_collapse_basic_example.cpp | 36 | ||||
-rw-r--r-- | src/Collapse/example/edge_collapse_conserve_persistence.cpp | 159 | ||||
-rw-r--r-- | src/Collapse/example/edge_collapse_example_basic.txt | 5 | ||||
-rw-r--r-- | src/Collapse/include/gudhi/Flag_complex_edge_collapser.h | 378 | ||||
-rw-r--r-- | src/Collapse/test/CMakeLists.txt | 9 | ||||
-rw-r--r-- | src/Collapse/test/collapse_unit_test.cpp | 198 | ||||
-rw-r--r-- | src/Collapse/utilities/CMakeLists.txt | 33 | ||||
-rw-r--r-- | src/Collapse/utilities/collapse.md | 63 | ||||
-rw-r--r-- | src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp | 152 | ||||
-rw-r--r-- | src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp | 181 | ||||
-rw-r--r-- | src/common/doc/main_page.md | 30 | ||||
-rw-r--r-- | src/common/include/gudhi/graph_simplicial_complex.h | 5 |
16 files changed, 1374 insertions, 0 deletions
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt index 561aa049..9e4d78ac 100644 --- a/src/CMakeLists.txt +++ b/src/CMakeLists.txt @@ -26,6 +26,7 @@ add_gudhi_module(Bitmap_cubical_complex) add_gudhi_module(Bottleneck_distance) add_gudhi_module(Cech_complex) add_gudhi_module(Contraction) +add_gudhi_module(Collapse) add_gudhi_module(Hasse_complex) add_gudhi_module(Persistence_representations) add_gudhi_module(Persistent_cohomology) diff --git a/src/Collapse/doc/dominated_edge.png b/src/Collapse/doc/dominated_edge.png Binary files differnew file mode 100644 index 00000000..5900a55a --- /dev/null +++ b/src/Collapse/doc/dominated_edge.png diff --git a/src/Collapse/doc/intro_edge_collapse.h b/src/Collapse/doc/intro_edge_collapse.h new file mode 100644 index 00000000..81edd79f --- /dev/null +++ b/src/Collapse/doc/intro_edge_collapse.h @@ -0,0 +1,101 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Siddharth Pritam + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#ifndef DOC_EDGE_COLLAPSE_INTRO_EDGE_COLLAPSE_H_ +#define DOC_EDGE_COLLAPSE_INTRO_EDGE_COLLAPSE_H_ + +namespace Gudhi { + +namespace collapse { + +/** \defgroup edge_collapse Edge collapse + * + * \author Siddharth Pritam + * + * @{ + * + * This module implements edge collapse of a filtered flag complex, in particular it reduces a filtration of + * Vietoris-Rips complex from its graph to another smaller flag filtration with same persistence. + * Where a filtration is a sequence of simplicial (here Rips) complexes connected with inclusions. + * + * \section edge_collapse_definition Edge collapse definition + * + * An edge \f$e\f$ in a simplicial complex \f$K\f$ is called a <b>dominated edge</b> if the link of \f$e\f$ in + * \f$K\f$, \f$lk_K(e)\f$ is a simplicial cone, that is, there exists a vertex \f$v^{\prime} \notin e\f$ and a + * subcomplex \f$L\f$ in \f$K\f$, such that \f$lk_K(e) = v^{\prime}L\f$. We say that the vertex \f$v^{\prime}\f$ is + * {dominating} \f$e\f$ and \f$e\f$ is {dominated} by \f$v^{\prime}\f$. + * An <b> elementary egde collapse </b> is the removal of a dominated edge \f$e\f$ from \f$K\f$, + * which we denote with \f$K\f$ \f${\searrow\searrow}^1 \f$ \f$K\setminus e\f$. + * The symbol \f$\mathbf{K\setminus e}\f$ (deletion of \f$e\f$ from \f$K\f$) refers to the subcomplex of \f$K\f$ which + * has all simplices of \f$K\f$ except \f$e\f$ and the ones containing \f$e\f$. + * There is an <b>edge collapse</b> from a simplicial complex \f$K\f$ to its subcomplex \f$L\f$, + * if there exists a series of elementary edge collapses from \f$K\f$ to \f$L\f$, denoted as \f$K\f$ + * \f${\searrow\searrow}\f$ \f$L\f$. + * + * An edge collapse is a homotopy preserving operation, and it can be further expressed as sequence of the classical + * elementary simple collapse. + * A complex without any dominated edge is called a \f$1\f$- minimal complex and the core \f$K^1\f$ of simplicial + * complex is a minimal complex such that \f$K\f$ \f${\searrow\searrow}\f$ \f$K^1\f$. + * Computation of a core (not unique) involves computation of dominated edges and the dominated edges can be easily + * characterized as follows: + * + * -- For general simplicial complex: An edge \f$e \in K\f$ is dominated by another vertex \f$v^{\prime} \in K\f$, + * <i>if and only if</i> all the maximal simplices of \f$K\f$ that contain \f$e\f$ also contain \f$v^{\prime}\f$ + * + * -- For a flag complex: An edge \f$e \in K\f$ is dominated by another vertex \f$v^{\prime} \in K\f$, <i>if and only + * if</i> all the vertices in \f$K\f$ that has an edge with both vertices of \f$e\f$ also has an edge with + * \f$v^{\prime}\f$. + * + * The algorithm to compute the smaller induced filtration is described in Section 5 \cite edgecollapsesocg2020. + * Edge collapse can be successfully employed to reduce any given filtration of flag complexes to a smaller induced + * filtration which preserves the persistent homology of the original filtration and is a flag complex as well. + * + * The general idea is that we consider edges in the filtered graph and sort them according to their filtration value + * giving them a total order. + * Each edge gets a unique index denoted as \f$i\f$ in this order. To reduce the filtration, we move forward with + * increasing filtration value + * in the graph and check if the current edge \f$e_i\f$ is dominated in the current graph \f$G_i := \{e_1, .. e_i\} \f$ + * or not. + * If the edge \f$e_i\f$ is dominated we remove it from the filtration and move forward to the next edge \f$e_{i+1}\f$. + * If \f$e_i\f$ is non-dominated then we keep it in the reduced filtration and then go backward in the current graph + * \f$G_i\f$ to look for new non-dominated edges that was dominated before but might become non-dominated at this + * point. + * If an edge \f$e_j, j < i \f$ during the backward search is found to be non-dominated, we include \f$e_j\f$ in to the + * reduced filtration and we set its new filtration value to be \f$i\f$ that is the index of \f$e_i\f$. + * The precise mechanism for this reduction has been described in Section 5 \cite edgecollapsesocg2020. + * Here we implement this mechanism for a filtration of Rips complex. + * After perfoming the reduction the filtration reduces to a flag-filtration with the same persistence as the original + * filtration. + * + * \subsection edgecollapseexample Basic edge collapse + * + * This example calls `Gudhi::collapse::flag_complex_collapse_edges()` from a proximity graph represented as a list of + * `Filtered_edge`. + * Then it collapses edges and displays a new list of `Filtered_edge` (with less edges) + * that will preserve the persistence homology computation. + * + * \include Collapse/edge_collapse_basic_example.cpp + * + * When launching the example: + * + * \code $> ./Edge_collapse_example_basic + * \endcode + * + * the program output is: + * + * \include Collapse/edge_collapse_example_basic.txt + */ +/** @} */ // end defgroup strong_collapse + +} // namespace collapse + +} // namespace Gudhi + +#endif // DOC_EDGE_COLLAPSE_INTRO_EDGE_COLLAPSE_H_ diff --git a/src/Collapse/example/CMakeLists.txt b/src/Collapse/example/CMakeLists.txt new file mode 100644 index 00000000..ba0e75e3 --- /dev/null +++ b/src/Collapse/example/CMakeLists.txt @@ -0,0 +1,23 @@ +project(Edge_collapse_examples) + +# Point cloud +add_executable ( Edge_collapse_example_basic edge_collapse_basic_example.cpp ) + +if (TBB_FOUND) + target_link_libraries(Edge_collapse_example_basic ${TBB_LIBRARIES}) +endif() + +add_test(NAME Edge_collapse_example_basic COMMAND $<TARGET_FILE:Edge_collapse_example_basic>) + +# Point cloud +add_executable ( Edge_collapse_conserve_persistence edge_collapse_conserve_persistence.cpp ) + +if (TBB_FOUND) + target_link_libraries(Edge_collapse_conserve_persistence ${TBB_LIBRARIES}) +endif() + +add_test(NAME Edge_collapse_conserve_persistence_1 COMMAND $<TARGET_FILE:Edge_collapse_conserve_persistence> + "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" "0.2") + +add_test(NAME Edge_collapse_conserve_persistence_2 COMMAND $<TARGET_FILE:Edge_collapse_conserve_persistence> + "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" "1.8") diff --git a/src/Collapse/example/edge_collapse_basic_example.cpp b/src/Collapse/example/edge_collapse_basic_example.cpp new file mode 100644 index 00000000..1b3dc1b5 --- /dev/null +++ b/src/Collapse/example/edge_collapse_basic_example.cpp @@ -0,0 +1,36 @@ +#include <gudhi/Flag_complex_edge_collapser.h> + +#include <iostream> +#include <vector> +#include <tuple> + +int main() { + // Type definitions + using Filtration_value = float; + using Vertex_handle = short; + using Filtered_edge = std::tuple<Vertex_handle, Vertex_handle, Filtration_value>; + using Filtered_edge_list = std::vector<Filtered_edge>; + + // 1 2 + // o---o + // |\ /| + // | x | + // |/ \| + // o---o + // 0 3 + Filtered_edge_list graph = {{0, 1, 1.}, + {1, 2, 1.}, + {2, 3, 1.}, + {3, 0, 1.}, + {0, 2, 2.}, + {1, 3, 2.}}; + + auto remaining_edges = Gudhi::collapse::flag_complex_collapse_edges(graph); + + for (auto filtered_edge_from_collapse : remaining_edges) { + std::cout << "fn[" << std::get<0>(filtered_edge_from_collapse) << ", " << std::get<1>(filtered_edge_from_collapse) + << "] = " << std::get<2>(filtered_edge_from_collapse) << std::endl; + } + + return 0; +} diff --git a/src/Collapse/example/edge_collapse_conserve_persistence.cpp b/src/Collapse/example/edge_collapse_conserve_persistence.cpp new file mode 100644 index 00000000..b2c55e7a --- /dev/null +++ b/src/Collapse/example/edge_collapse_conserve_persistence.cpp @@ -0,0 +1,159 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Vincent Rouvreau + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#include <gudhi/Flag_complex_edge_collapser.h> +#include <gudhi/Simplex_tree.h> +#include <gudhi/Persistent_cohomology.h> +#include <gudhi/distance_functions.h> +#include <gudhi/Points_off_io.h> +#include <gudhi/graph_simplicial_complex.h> + +#include <boost/range/adaptor/transformed.hpp> + +#include<utility> // for std::pair +#include<vector> +#include<tuple> + +// Types definition + +using Simplex_tree = Gudhi::Simplex_tree<>; +using Filtration_value = Simplex_tree::Filtration_value; +using Vertex_handle = Simplex_tree::Vertex_handle; +using Point = std::vector<Filtration_value>; +using Vector_of_points = std::vector<Point>; + +using Proximity_graph = Gudhi::Proximity_graph<Simplex_tree>; + +using Field_Zp = Gudhi::persistent_cohomology::Field_Zp; +using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Field_Zp>; + +using Persistence_interval = std::tuple<int, Filtration_value, Filtration_value>; +/* + * Compare two intervals by dimension, then by length. + */ +struct cmp_intervals_by_length { + explicit cmp_intervals_by_length(Simplex_tree * sc) + : sc_(sc) { } + + template<typename Persistent_interval> + bool operator()(const Persistent_interval & p1, const Persistent_interval & p2) { + return (sc_->filtration(get < 1 > (p1)) - sc_->filtration(get < 0 > (p1)) + > sc_->filtration(get < 1 > (p2)) - sc_->filtration(get < 0 > (p2))); + } + Simplex_tree* sc_; +}; + +std::vector<Persistence_interval> get_persistence_intervals(Simplex_tree& st, int ambient_dim) { + std::vector<Persistence_interval> persistence_intervals; + st.expansion(ambient_dim); + + // Sort the simplices in the order of the filtration + st.initialize_filtration(); + // Compute the persistence diagram of the complex + Persistent_cohomology pcoh(st); + // initializes the coefficient field for homology - must be a prime number + int p = 11; + pcoh.init_coefficients(p); + + // Default min_interval_length = 0. + pcoh.compute_persistent_cohomology(); + // Custom sort and output persistence + cmp_intervals_by_length cmp(&st); + auto persistent_pairs = pcoh.get_persistent_pairs(); + std::sort(std::begin(persistent_pairs), std::end(persistent_pairs), cmp); + for (auto pair : persistent_pairs) { + persistence_intervals.emplace_back(st.dimension(get<0>(pair)), + st.filtration(get<0>(pair)), + st.filtration(get<1>(pair))); + } + return persistence_intervals; +} + +int main(int argc, char* argv[]) { + if (argc != 3) { + std::cerr << "This program requires an OFF file and minimal threshold value as parameter\n"; + std::cerr << "For instance: ./Edge_collapse_conserve_persistence ../../data/points/tore3D_300.off 1.\n"; + exit(-1); // ----- >> + } + + std::string off_file_points {argv[1]}; + double threshold {atof(argv[2])}; + + Gudhi::Points_off_reader<Point> off_reader(off_file_points); + if (!off_reader.is_valid()) { + std::cerr << "Unable to read file " << off_file_points << "\n"; + exit(-1); // ----- >> + } + + Vector_of_points point_vector = off_reader.get_point_cloud(); + if (point_vector.size() <= 0) { + std::cerr << "Empty point cloud." << std::endl; + exit(-1); // ----- >> + } + + Proximity_graph proximity_graph = Gudhi::compute_proximity_graph<Simplex_tree>(off_reader.get_point_cloud(), + threshold, + Gudhi::Euclidean_distance()); + + if (num_edges(proximity_graph) <= 0) { + std::cerr << "Total number of egdes are zero." << std::endl; + exit(-1); + } + + int ambient_dim = point_vector[0].size(); + + // ***** Simplex tree from a flag complex built after collapse ***** + auto remaining_edges = Gudhi::collapse::flag_complex_collapse_edges( + boost::adaptors::transform(edges(proximity_graph), [&](auto&&edge){ + return std::make_tuple(static_cast<Vertex_handle>(source(edge, proximity_graph)), + static_cast<Vertex_handle>(target(edge, proximity_graph)), + get(Gudhi::edge_filtration_t(), proximity_graph, edge)); + }) + ); + + Simplex_tree stree_from_collapse; + for (Vertex_handle vertex = 0; static_cast<std::size_t>(vertex) < point_vector.size(); vertex++) { + // insert the vertex with a 0. filtration value just like a Rips + stree_from_collapse.insert_simplex({vertex}, 0.); + } + for (auto remaining_edge : remaining_edges) { + stree_from_collapse.insert_simplex({std::get<0>(remaining_edge), std::get<1>(remaining_edge)}, + std::get<2>(remaining_edge)); + } + + std::vector<Persistence_interval> persistence_intervals_from_collapse = get_persistence_intervals(stree_from_collapse, ambient_dim); + + // ***** Simplex tree from the complete flag complex ***** + Simplex_tree stree_wo_collapse; + stree_wo_collapse.insert_graph(proximity_graph); + + std::vector<Persistence_interval> persistence_intervals_wo_collapse = get_persistence_intervals(stree_wo_collapse, ambient_dim); + + // ***** Comparison ***** + if (persistence_intervals_wo_collapse.size() != persistence_intervals_from_collapse.size()) { + std::cerr << "Number of persistence pairs with collapse is " << persistence_intervals_from_collapse.size() << std::endl; + std::cerr << "Number of persistence pairs without collapse is " << persistence_intervals_wo_collapse.size() << std::endl; + exit(-1); + } + + int return_value = 0; + auto ppwoc_ptr = persistence_intervals_wo_collapse.begin(); + for (auto ppfc: persistence_intervals_from_collapse) { + if (ppfc != *ppwoc_ptr) { + return_value++; + std::cerr << "Without collapse: " + << std::get<0>(*ppwoc_ptr) << " " << std::get<1>(*ppwoc_ptr) << " " << std::get<2>(*ppwoc_ptr) + << " - With collapse: " + << std::get<0>(ppfc) << " " << std::get<1>(ppfc) << " " << std::get<2>(ppfc) << std::endl; + } + ppwoc_ptr++; + } + return return_value; +} diff --git a/src/Collapse/example/edge_collapse_example_basic.txt b/src/Collapse/example/edge_collapse_example_basic.txt new file mode 100644 index 00000000..acecacaf --- /dev/null +++ b/src/Collapse/example/edge_collapse_example_basic.txt @@ -0,0 +1,5 @@ +fn[0, 1] = 1 +fn[1, 2] = 1 +fn[2, 3] = 1 +fn[3, 0] = 1 +fn[0, 2] = 2 diff --git a/src/Collapse/include/gudhi/Flag_complex_edge_collapser.h b/src/Collapse/include/gudhi/Flag_complex_edge_collapser.h new file mode 100644 index 00000000..b6b7f7c1 --- /dev/null +++ b/src/Collapse/include/gudhi/Flag_complex_edge_collapser.h @@ -0,0 +1,378 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Siddharth Pritam + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - 2020/03 Vincent Rouvreau: integration to the gudhi library + * - YYYY/MM Author: Description of the modification + */ + +#ifndef FLAG_COMPLEX_EDGE_COLLAPSER_H_ +#define FLAG_COMPLEX_EDGE_COLLAPSER_H_ + +#include <gudhi/Debug_utils.h> + +#include <boost/functional/hash.hpp> +#include <boost/iterator/iterator_facade.hpp> + +#include <Eigen/Sparse> + +#ifdef GUDHI_USE_TBB +#include <tbb/parallel_sort.h> +#endif + +#include <iostream> +#include <utility> // for std::pair +#include <vector> +#include <unordered_map> +#include <unordered_set> +#include <set> +#include <tuple> // for std::tie +#include <algorithm> // for std::includes +#include <iterator> // for std::inserter +#include <type_traits> // for std::decay + +namespace Gudhi { + +namespace collapse { + +/** \private + * + * \brief Flag complex sparse matrix data structure. + * + * \details + * This class stores a <a target="_blank" href="https://en.wikipedia.org/wiki/Clique_complex">Flag complex</a> + * in an <a target="_blank" href="https://eigen.tuxfamily.org/dox/group__TutorialSparse.html">Eigen sparse matrix</a>. + * + * \tparam Vertex type must be a signed integer type. It admits a total order <. + * \tparam Filtration type for the value of the filtration function. Must be comparable with <. + */ +template<typename Vertex, typename Filtration> +class Flag_complex_edge_collapser { + public: + /** \brief Re-define Vertex as Vertex_handle type to ease the interface with `Gudhi::Proximity_graph`. */ + using Vertex_handle = Vertex; + /** \brief Re-define Filtration as Filtration_value type to ease the interface with `Gudhi::Proximity_graph`. */ + using Filtration_value = Filtration; + + private: + // internal numbering of vertices and edges + using IVertex = std::size_t; + using Edge_index = std::size_t; + using IEdge = std::pair<IVertex, IVertex>; + + // The sparse matrix data type + // (Eigen::SparseMatrix<Edge_index, Eigen::RowMajor> has slow insertions) + using Sparse_vector = Eigen::SparseVector<Edge_index>; + using Sparse_row_matrix = std::vector<Sparse_vector>; + + // Range of neighbors of a vertex + template<bool closed> + struct Neighbours { + class iterator : public boost::iterator_facade<iterator, + IVertex, /* value_type */ + std::input_iterator_tag, // or boost::single_pass_traversal_tag + IVertex /* reference */ > + { + public: + iterator():ptr(nullptr){} + iterator(Neighbours const*p):ptr(p){find_valid();} + private: + friend class boost::iterator_core_access; + Neighbours const*ptr; + void increment(){ + ++ptr->it; + find_valid(); + } + void find_valid(){ + auto& it = ptr->it; + do { + if(!it) { ptr=nullptr; break; } + if(IVertex(it.index()) == ptr->u) { + if(closed) break; + else continue; + } + Edge_index e = it.value(); + if(e <= ptr->ec->current_backward || ptr->ec->critical_edge_indicator_[e]) break; + } while(++it, true); + } + bool equal(iterator const& other) const { return ptr == other.ptr; } + IVertex dereference() const { return ptr->it.index(); } + }; + typedef iterator const_iterator; + mutable typename Sparse_vector::InnerIterator it; + Flag_complex_edge_collapser const*ec; + IVertex u; + iterator begin() const { return this; } + iterator end() const { return {}; } + explicit Neighbours(Flag_complex_edge_collapser const*p,IVertex u):it(p->sparse_row_adjacency_matrix_[u]),ec(p),u(u){} + }; + + // A range of row indices + using IVertex_vector = std::vector<IVertex>; + + public: + /** \brief Filtered_edge is a type to store an edge with its filtration value. */ + using Filtered_edge = std::tuple<Vertex_handle, Vertex_handle, Filtration_value>; + + private: + // Map from row index to its vertex handle + std::vector<Vertex_handle> row_to_vertex_; + + // Index of the current edge in the backwards walk. Edges <= current_backward are part of the temporary graph, + // while edges > current_backward are removed unless critical_edge_indicator_. + Edge_index current_backward = -1; + + // Map from IEdge to its index + std::unordered_map<IEdge, Edge_index, boost::hash<IEdge>> iedge_to_index_map_; + + // Boolean vector to indicate if the edge is critical. + std::vector<bool> critical_edge_indicator_; + + // Map from vertex handle to its row index + std::unordered_map<Vertex_handle, IVertex> vertex_to_row_; + + // Stores the Sparse matrix of Filtration values representing the original graph. + // The matrix rows and columns are indexed by IVertex. + Sparse_row_matrix sparse_row_adjacency_matrix_; + + // The input, a vector of filtered edges. + std::vector<Filtered_edge> f_edge_vector_; + + // Edge is the actual edge (u,v), with Vertex_handle u and v, not IVertex. + bool edge_is_dominated(Vertex_handle u, Vertex_handle v) const + { + const IVertex rw_u = vertex_to_row_.at(u); + const IVertex rw_v = vertex_to_row_.at(v); +#ifdef DEBUG_TRACES + std::cout << "The edge {" << u << ", " << v << "} is going for domination check." << std::endl; +#endif // DEBUG_TRACES + auto common_neighbours = open_common_neighbours_row_index(rw_u, rw_v); +#ifdef DEBUG_TRACES + std::cout << "And its common neighbours are." << std::endl; + for (auto neighbour : common_neighbours) { + std::cout << row_to_vertex_[neighbour] << ", " ; + } + std::cout<< std::endl; +#endif // DEBUG_TRACES + if (common_neighbours.size() == 1) + return true; + else + for (auto rw_c : common_neighbours) { + auto neighbours_c = neighbours_row_index<true>(rw_c); + // If neighbours_c contains the common neighbours. + if (std::includes(neighbours_c.begin(), neighbours_c.end(), + common_neighbours.begin(), common_neighbours.end())) + return true; + } + return false; + } + + // Returns the edges connecting u and v (extremities of crit) to their common neighbors (not themselves) + std::set<Edge_index> three_clique_indices(Edge_index crit) { + std::set<Edge_index> edge_indices; + + Vertex_handle u = std::get<0>(f_edge_vector_[crit]); + Vertex_handle v = std::get<1>(f_edge_vector_[crit]); + +#ifdef DEBUG_TRACES + std::cout << "The current critical edge to re-check criticality with filt value is : f {" << u << "," << v + << "} = " << std::get<2>(f_edge_vector_[crit]) << std::endl; +#endif // DEBUG_TRACES + auto rw_u = vertex_to_row_[u]; + auto rw_v = vertex_to_row_[v]; + + IVertex_vector common_neighbours = open_common_neighbours_row_index(rw_u, rw_v); + + for (auto rw_c : common_neighbours) { + IEdge e_with_new_nbhr_v = std::minmax(rw_u, rw_c); + IEdge e_with_new_nbhr_u = std::minmax(rw_v, rw_c); + edge_indices.emplace(iedge_to_index_map_[e_with_new_nbhr_v]); + edge_indices.emplace(iedge_to_index_map_[e_with_new_nbhr_u]); + } + return edge_indices; + } + + // Detect and set all edges that are becoming critical + template<typename FilteredEdgeOutput> + void set_edge_critical(Edge_index indx, Filtration_value filt, FilteredEdgeOutput filtered_edge_output) { +#ifdef DEBUG_TRACES + std::cout << "The curent index with filtration value " << indx << ", " << filt << " is primary critical" << + std::endl; +#endif // DEBUG_TRACES + std::set<Edge_index> effected_indices = three_clique_indices(indx); + // Cannot use boost::adaptors::reverse in such dynamic cases apparently + for (auto it = effected_indices.rbegin(); it != effected_indices.rend(); ++it) { + current_backward = *it; + Vertex_handle u = std::get<0>(f_edge_vector_[current_backward]); + Vertex_handle v = std::get<1>(f_edge_vector_[current_backward]); + // If current_backward is not critical so it should be processed, otherwise it stays in the graph + if (!critical_edge_indicator_[current_backward]) { + if (!edge_is_dominated(u, v)) { +#ifdef DEBUG_TRACES + std::cout << "The curent index became critical " << current_backward << std::endl; +#endif // DEBUG_TRACES + critical_edge_indicator_[current_backward] = true; + filtered_edge_output(u, v, filt); + std::set<Edge_index> inner_effected_indcs = three_clique_indices(current_backward); + for (auto inr_idx : inner_effected_indcs) { + if(inr_idx < current_backward) // && !critical_edge_indicator_[inr_idx] + effected_indices.emplace(inr_idx); + } +#ifdef DEBUG_TRACES + std::cout << "The following edge is critical with filt value: {" << u << "," << v << "}; " + << filt << std::endl; +#endif // DEBUG_TRACES + } + } + } + // Clear the implicit "removed from graph" data structure + current_backward = -1; + } + + // Returns list of neighbors of a particular vertex. + template<bool closed> + auto neighbours_row_index(IVertex rw_u) const + { + return Neighbours<closed>(this, rw_u); + } + + // Returns the list of open neighbours of the edge :{u,v}. + IVertex_vector open_common_neighbours_row_index(IVertex rw_u, IVertex rw_v) const + { + auto non_zero_indices_u = neighbours_row_index<false>(rw_u); + auto non_zero_indices_v = neighbours_row_index<false>(rw_v); + IVertex_vector common; + std::set_intersection(non_zero_indices_u.begin(), non_zero_indices_u.end(), non_zero_indices_v.begin(), + non_zero_indices_v.end(), std::back_inserter(common)); + + return common; + } + + // Insert a vertex in the data structure + IVertex insert_vertex(Vertex_handle vertex) { + auto n = row_to_vertex_.size(); + auto result = vertex_to_row_.emplace(vertex, n); + // If it was not already inserted - Value won't be updated by emplace if it is already present + if (result.second) { + // Expand the matrix. The size of rows is irrelevant. + sparse_row_adjacency_matrix_.emplace_back((std::numeric_limits<Eigen::Index>::max)()); + // Initializing the diagonal element of the adjency matrix corresponding to rw_b. + sparse_row_adjacency_matrix_[n].insert(n) = -1; // not an edge + // Must be done after reading its size() + row_to_vertex_.push_back(vertex); + } + return result.first->second; + } + + // Insert an edge in the data structure + // @exception std::invalid_argument In debug mode, if u == v + IEdge insert_new_edge(Vertex_handle u, Vertex_handle v, Edge_index idx) + { + GUDHI_CHECK((u != v), std::invalid_argument("Flag_complex_edge_collapser::insert_new_edge with u == v")); + // The edge must not be added before, it should be a new edge. + IVertex rw_u = insert_vertex(u); + IVertex rw_v = insert_vertex(v); +#ifdef DEBUG_TRACES + std::cout << "Inserting the edge " << u <<", " << v << std::endl; +#endif // DEBUG_TRACES + sparse_row_adjacency_matrix_[rw_u].insert(rw_v) = idx; + sparse_row_adjacency_matrix_[rw_v].insert(rw_u) = idx; + return std::minmax(rw_u, rw_v); + } + + public: + /** \brief Flag_complex_edge_collapser constructor from a range of filtered edges. + * + * @param[in] edges Range of Filtered edges range.There is no need the range to be sorted, as it will be performed in + * `Flag_complex_edge_collapser::process_edges`. + * + * \tparam FilteredEdgeRange must be a range for which std::begin and std::end return iterators on a + * `Flag_complex_edge_collapser::Filtered_edge`. + */ + template<typename FilteredEdgeRange> + Flag_complex_edge_collapser(const FilteredEdgeRange& edges) + : f_edge_vector_(std::begin(edges), std::end(edges)) { } + + /** \brief Performs edge collapse in a increasing sequence of the filtration value. + * + * \tparam filtered_edge_output is a functor that is called on the output edges, in non-decreasing order of + * filtration, as filtered_edge_output(u, v, f) where u and v are Vertex_handle representing the extremities of the + * edge, and f is its new Filtration_value. + */ + template<typename FilteredEdgeOutput> + void process_edges(FilteredEdgeOutput filtered_edge_output) { + // Sort edges + auto sort_by_filtration = [](const Filtered_edge& edge_a, const Filtered_edge& edge_b) -> bool + { + return (std::get<2>(edge_a) < std::get<2>(edge_b)); + }; + +#ifdef GUDHI_USE_TBB + tbb::parallel_sort(f_edge_vector_.begin(), f_edge_vector_.end(), sort_by_filtration); +#else + std::sort(f_edge_vector_.begin(), f_edge_vector_.end(), sort_by_filtration); +#endif + + for (Edge_index endIdx = 0; endIdx < f_edge_vector_.size(); endIdx++) { + Filtered_edge fec = f_edge_vector_[endIdx]; + Vertex_handle u = std::get<0>(fec); + Vertex_handle v = std::get<1>(fec); + Filtration_value filt = std::get<2>(fec); + + // Inserts the edge in the sparse matrix to update the graph (G_i) + IEdge ie = insert_new_edge(u, v, endIdx); + + iedge_to_index_map_.emplace(ie, endIdx); + critical_edge_indicator_.push_back(false); + + if (!edge_is_dominated(u, v)) { + critical_edge_indicator_[endIdx] = true; + filtered_edge_output(u, v, filt); + if (endIdx > 1) + set_edge_critical(endIdx, filt, filtered_edge_output); + } + } + } + +}; + +/** \brief Implicitly constructs a flag complex from edges as an input, collapses edges while preserving the persistent + * homology and returns the remaining edges as a range. + * + * \param[in] edges Range of Filtered edges.There is no need the range to be sorted, as it will be performed. + * + * \tparam FilteredEdgeRange furnishes `std::begin` and `std::end` methods and returns an iterator on a + * FilteredEdge of type `std::tuple<Vertex_handle, Vertex_handle, Filtration_value>` where `Vertex_handle` is the type + * of a vertex index and `Filtration_value` is the type of an edge filtration value. + * + * \return Remaining edges after collapse as a range of + * `std::tuple<Vertex_handle, Vertex_handle, Filtration_value>`. + * + * \ingroup edge_collapse + * + */ +template<class FilteredEdgeRange> auto flag_complex_collapse_edges(const FilteredEdgeRange& edges) { + auto first_edge_itr = std::begin(edges); + using Vertex_handle = std::decay_t<decltype(std::get<0>(*first_edge_itr))>; + using Filtration_value = std::decay_t<decltype(std::get<2>(*first_edge_itr))>; + using Edge_collapser = Flag_complex_edge_collapser<Vertex_handle, Filtration_value>; + std::vector<typename Edge_collapser::Filtered_edge> remaining_edges; + if (first_edge_itr != std::end(edges)) { + Edge_collapser edge_collapser(edges); + edge_collapser.process_edges( + [&remaining_edges](Vertex_handle u, Vertex_handle v, Filtration_value filtration) { + // insert the edge + remaining_edges.emplace_back(u, v, filtration); + }); + } + return remaining_edges; +} + +} // namespace collapse + +} // namespace Gudhi + +#endif // FLAG_COMPLEX_EDGE_COLLAPSER_H_ diff --git a/src/Collapse/test/CMakeLists.txt b/src/Collapse/test/CMakeLists.txt new file mode 100644 index 00000000..c7eafb46 --- /dev/null +++ b/src/Collapse/test/CMakeLists.txt @@ -0,0 +1,9 @@ +project(Collapse_tests) + +include(GUDHI_boost_test) + +add_executable ( Collapse_test_unit collapse_unit_test.cpp ) +if (TBB_FOUND) + target_link_libraries(Collapse_test_unit ${TBB_LIBRARIES}) +endif() +gudhi_add_boost_test(Collapse_test_unit) diff --git a/src/Collapse/test/collapse_unit_test.cpp b/src/Collapse/test/collapse_unit_test.cpp new file mode 100644 index 00000000..b8876246 --- /dev/null +++ b/src/Collapse/test/collapse_unit_test.cpp @@ -0,0 +1,198 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Vincent Rouvreau + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + + +#define BOOST_TEST_DYN_LINK +#define BOOST_TEST_MODULE "collapse" +#include <boost/test/unit_test.hpp> +#include <boost/mpl/list.hpp> +#include <boost/range/adaptor/transformed.hpp> + +#include <gudhi/Flag_complex_edge_collapser.h> +#include <gudhi/distance_functions.h> +#include <gudhi/graph_simplicial_complex.h> + +#include <iostream> +#include <tuple> +#include <vector> +#include <array> +#include <cmath> + +struct Simplicial_complex { + using Vertex_handle = short; + using Filtration_value = float; +}; + +using Vertex_handle = Simplicial_complex::Vertex_handle; +using Filtration_value = Simplicial_complex::Filtration_value; +using Filtered_edge = std::tuple<Vertex_handle, Vertex_handle, Filtration_value>; +using Filtered_edge_list = std::vector<Filtered_edge>; + +template<typename Filtered_edge_range> +bool find_edge_in_list(const Filtered_edge& edge, const Filtered_edge_range& edge_list) { + for (auto edge_from_list : edge_list) { + if (edge_from_list == edge) + return true; + } + return false; +} + +template<typename Filtered_edge_range> +void trace_and_check_collapse(const Filtered_edge_range& filtered_edges, const Filtered_edge_list& removed_edges) { + std::cout << "BEFORE COLLAPSE - Total number of edges: " << filtered_edges.size() << std::endl; + BOOST_CHECK(filtered_edges.size() > 0); + for (auto filtered_edge : filtered_edges) { + std::cout << "f[" << std::get<0>(filtered_edge) << ", " << std::get<1>(filtered_edge) << "] = " + << std::get<2>(filtered_edge) << std::endl; + } + + std::cout << "COLLAPSE - keep edges: " << std::endl; + auto remaining_edges = Gudhi::collapse::flag_complex_collapse_edges(filtered_edges); + + std::cout << "AFTER COLLAPSE - Total number of edges: " << remaining_edges.size() << std::endl; + BOOST_CHECK(remaining_edges.size() <= filtered_edges.size()); + for (auto filtered_edge_from_collapse : remaining_edges) { + std::cout << "f[" << std::get<0>(filtered_edge_from_collapse) << ", " << std::get<1>(filtered_edge_from_collapse) + << "] = " << std::get<2>(filtered_edge_from_collapse) << std::endl; + // Check each edge from collapse is in the input + BOOST_CHECK(find_edge_in_list(filtered_edge_from_collapse, filtered_edges)); + } + + std::cout << "CHECK COLLAPSE - Total number of removed edges: " << removed_edges.size() << std::endl; + for (auto removed_filtered_edge : removed_edges) { + std::cout << "f[" << std::get<0>(removed_filtered_edge) << ", " << std::get<1>(removed_filtered_edge) << "] = " + << std::get<2>(removed_filtered_edge) << std::endl; + // Check each removed edge from collapse is in the input + BOOST_CHECK(!find_edge_in_list(removed_filtered_edge, remaining_edges)); + } + +} + +BOOST_AUTO_TEST_CASE(collapse) { + std::cout << "***** COLLAPSE *****" << std::endl; + // 1 2 + // o---o + // | | + // | | + // | | + // o---o + // 0 3 + Filtered_edge_list edges {{0, 1, 1.}, + {1, 2, 1.}, + {2, 3, 1.}, + {3, 0, 1.}}; + trace_and_check_collapse(edges, {}); + + // 1 2 + // o---o + // |\ /| + // | x | + // |/ \| + // o---o + // 0 3 + edges.emplace_back(0, 2, 2.); + edges.emplace_back(1, 3, 2.); + trace_and_check_collapse(edges, {{1, 3, 2.}}); + + // 1 2 4 + // o---o---o + // |\ /| | + // | x | | + // |/ \| | + // o---o---o + // 0 3 5 + edges.emplace_back(2, 4, 3.); + edges.emplace_back(4, 5, 3.); + edges.emplace_back(5, 3, 3.); + trace_and_check_collapse(edges, {{1, 3, 2.}}); + + // 1 2 4 + // o---o---o + // |\ /|\ /| + // | x | x | + // |/ \|/ \| + // o---o---o + // 0 3 5 + edges.emplace_back(2, 5, 4.); + edges.emplace_back(4, 3, 4.); + trace_and_check_collapse(edges, {{1, 3, 2.}, {4, 3, 4.}}); + + // 1 2 4 + // o---o---o + // |\ /|\ /| + // | x | x | + [0,4] and [1,5] + // |/ \|/ \| + // o---o---o + // 0 3 5 + edges.emplace_back(1, 5, 5.); + edges.emplace_back(0, 4, 5.); + trace_and_check_collapse(edges, {{1, 3, 2.}, {4, 3, 4.}, {0, 4, 5.}}); +} + +BOOST_AUTO_TEST_CASE(collapse_from_array) { + std::cout << "***** COLLAPSE FROM ARRAY *****" << std::endl; + // 1 2 + // o---o + // |\ /| + // | x | + // |/ \| + // o---o + // 0 3 + std::array<Filtered_edge, 6> f_edge_array = {{{0, 1, 1.}, + {1, 2, 1.}, + {2, 3, 1.}, + {3, 0, 1.}, + {0, 2, 2.}, + {1, 3, 2.}}}; + trace_and_check_collapse(f_edge_array, {{1, 3, 2.}}); +} + +BOOST_AUTO_TEST_CASE(collapse_from_proximity_graph) { + std::cout << "***** COLLAPSE FROM PROXIMITY GRAPH *****" << std::endl; + // 1 2 + // o---o + // |\ /| + // | x | + // |/ \| + // o---o + // 0 3 + std::vector<std::vector<Filtration_value>> point_cloud = {{0., 0.}, + {0., 1.}, + {1., 0.}, + {1., 1.} }; + + Filtration_value threshold = std::numeric_limits<Filtration_value>::infinity(); + using Proximity_graph = Gudhi::Proximity_graph<Simplicial_complex>; + Proximity_graph proximity_graph = Gudhi::compute_proximity_graph<Simplicial_complex>(point_cloud, + threshold, + Gudhi::Euclidean_distance()); + + auto remaining_edges = Gudhi::collapse::flag_complex_collapse_edges( + boost::adaptors::transform(edges(proximity_graph), [&](auto&&edge){ + return std::make_tuple(static_cast<Vertex_handle>(source(edge, proximity_graph)), + static_cast<Vertex_handle>(target(edge, proximity_graph)), + get(Gudhi::edge_filtration_t(), proximity_graph, edge)); + }) + ); + + BOOST_CHECK(remaining_edges.size() == 5); + + std::size_t filtration_is_edge_length_nb = 0; + std::size_t filtration_is_diagonal_length_nb = 0; + float epsilon = std::numeric_limits<Filtration_value>::epsilon(); + for (auto filtered_edge : remaining_edges) { + if (std::get<2>(filtered_edge) == 1.) + filtration_is_edge_length_nb++; + if (std::fabs(std::get<2>(filtered_edge) - std::sqrt(2.)) <= epsilon) + filtration_is_diagonal_length_nb++; + } + BOOST_CHECK(filtration_is_edge_length_nb == 4); + BOOST_CHECK(filtration_is_diagonal_length_nb == 1); +} diff --git a/src/Collapse/utilities/CMakeLists.txt b/src/Collapse/utilities/CMakeLists.txt new file mode 100644 index 00000000..c742144b --- /dev/null +++ b/src/Collapse/utilities/CMakeLists.txt @@ -0,0 +1,33 @@ +project(Collapse_utilities) + +# From a point cloud +add_executable ( point_cloud_edge_collapse_rips_persistence point_cloud_edge_collapse_rips_persistence.cpp ) +target_link_libraries(point_cloud_edge_collapse_rips_persistence Boost::program_options) + +if (TBB_FOUND) + target_link_libraries(point_cloud_edge_collapse_rips_persistence ${TBB_LIBRARIES}) +endif() +add_test(NAME Edge_collapse_utilities_point_cloud_rips_persistence COMMAND $<TARGET_FILE:point_cloud_edge_collapse_rips_persistence> + "${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off" "-r" "0.25" "-m" "0.5" "-d" "3" "-p" "3" "-o" "off_results.pers") + +install(TARGETS point_cloud_edge_collapse_rips_persistence DESTINATION bin) + +# From a distance matrix +add_executable ( distance_matrix_edge_collapse_rips_persistence distance_matrix_edge_collapse_rips_persistence.cpp ) +target_link_libraries(distance_matrix_edge_collapse_rips_persistence Boost::program_options) + +if (TBB_FOUND) + target_link_libraries(distance_matrix_edge_collapse_rips_persistence ${TBB_LIBRARIES}) +endif() +add_test(NAME Edge_collapse_utilities_distance_matrix_rips_persistence COMMAND $<TARGET_FILE:distance_matrix_edge_collapse_rips_persistence> + "${CMAKE_SOURCE_DIR}/data/distance_matrix/tore3D_1307_distance_matrix.csv" "-r" "0.25" "-m" "0.5" "-d" "3" "-p" "3" "-o" "csv_results.pers") + +install(TARGETS distance_matrix_edge_collapse_rips_persistence DESTINATION bin) + +if (DIFF_PATH) + add_test(Edge_collapse_utilities_diff_persistence ${DIFF_PATH} + "off_results.pers" "csv_results.pers") + set_tests_properties(Edge_collapse_utilities_diff_persistence PROPERTIES DEPENDS + "Edge_collapse_utilities_point_cloud_rips_persistence;Edge_collapse_utilities_distance_matrix_rips_persistence") + +endif() diff --git a/src/Collapse/utilities/collapse.md b/src/Collapse/utilities/collapse.md new file mode 100644 index 00000000..1f41bb1f --- /dev/null +++ b/src/Collapse/utilities/collapse.md @@ -0,0 +1,63 @@ +--- +layout: page +title: "Collapse" +meta_title: "Edge collapse" +teaser: "" +permalink: /collapse/ +--- +{::comment} +Leave the lines above as it is required by the web site generator 'Jekyll' +{:/comment} + + +## point_cloud_edge_collapse_rips_persistence ## +This program computes the Rips graph defined on a set of input points, using Euclidean distance, and collapses edges. +This program finally computes persistent homology with coefficient field *Z/pZ* of the Rips complex built on top of these collapse edges. +The output diagram contains one bar per line, written with the convention: + +`p dim birth death` + +where `dim` is the dimension of the homological feature, `birth` and `death` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p` must be a prime number). + +**Usage** + +`point_cloud_edge_collapse_rips_persistence [options] <OFF input file>` + +**Allowed options** + +* `-h [ --help ]` Produce help message +* `-o [ --output-file ]` Name of file in which the persistence diagram is written. Default print in standard output. +* `-r [ --max-edge-length ]` (default = inf) Maximal length of an edge for the Rips complex construction. +* `-d [ --cpx-dimension ]` (default = 1) Maximal dimension of the Rips complex we want to compute. +* `-p [ --field-charac ]` (default = 11) Characteristic p of the coefficient field Z/pZ for computing homology. +* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals. +* `-i [ --edge-collapse-iterations ]` (default = 1) Number of iterations edge collapse is performed. + +Beware: this program may use a lot of RAM and take a lot of time if `max-edge-length` is set to a large value. + +**Example 1 with Z/2Z coefficients** + +`point_cloud_edge_collapse_rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2` + +**Example 2 with Z/3Z coefficients** + +`point_cloud_edge_collapse_rips_persistence ../../data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3` + + +## distance_matrix_edge_collapse_rips_persistence ## + +Same as `point_cloud_edge_collapse_rips_persistence` but taking a distance matrix as input. + +**Usage** + +`distance_matrix_edge_collapse_rips_persistence [options] <CSV input file>` + +where +`<CSV input file>` is the path to the file containing a distance matrix. Can be square or lower triangular matrix. Separator is ';'. +The code do not check if it is dealing with a distance matrix. It is the user responsibility to provide a valid input. +Please refer to data/distance_matrix/lower_triangular_distance_matrix.csv for an example of a file. + +**Example** + +`distance_matrix_edge_collapse_rips_persistence data/distance_matrix/full_square_distance_matrix.csv -r 15 -d 3 -p 3 -m 0` + diff --git a/src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp b/src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp new file mode 100644 index 00000000..11ee5871 --- /dev/null +++ b/src/Collapse/utilities/distance_matrix_edge_collapse_rips_persistence.cpp @@ -0,0 +1,152 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Siddharth Pritam, Vincent Rouvreau + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#include <gudhi/Flag_complex_edge_collapser.h> +#include <gudhi/Simplex_tree.h> +#include <gudhi/Persistent_cohomology.h> +#include <gudhi/reader_utils.h> +#include <gudhi/graph_simplicial_complex.h> + +#include <boost/program_options.hpp> +#include <boost/range/adaptor/transformed.hpp> + +using Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>; +using Filtration_value = Simplex_tree::Filtration_value; +using Vertex_handle = Simplex_tree::Vertex_handle; + +using Filtered_edge = std::tuple<Vertex_handle, Vertex_handle, Filtration_value>; +using Proximity_graph = Gudhi::Proximity_graph<Simplex_tree>; + +using Field_Zp = Gudhi::persistent_cohomology::Field_Zp; +using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Field_Zp>; +using Distance_matrix = std::vector<std::vector<Filtration_value>>; + +void program_options(int argc, char* argv[], std::string& csv_matrix_file, std::string& filediag, + Filtration_value& threshold, int& dim_max, int& p, int& edge_collapse_iter_nb, + Filtration_value& min_persistence); + +int main(int argc, char* argv[]) { + std::string csv_matrix_file; + std::string filediag; + Filtration_value threshold; + int dim_max = 2; + int p; + int edge_collapse_iter_nb; + Filtration_value min_persistence; + + program_options(argc, argv, csv_matrix_file, filediag, threshold, dim_max, p, edge_collapse_iter_nb, + min_persistence); + + Distance_matrix distances = Gudhi::read_lower_triangular_matrix_from_csv_file<Filtration_value>(csv_matrix_file); + std::cout << "Read the distance matrix succesfully, of size: " << distances.size() << std::endl; + + Proximity_graph proximity_graph = Gudhi::compute_proximity_graph<Simplex_tree>(boost::irange((size_t)0, + distances.size()), + threshold, + [&distances](size_t i, size_t j) { + return distances[j][i]; + }); + + auto edges_from_graph = boost::adaptors::transform(edges(proximity_graph), [&](auto&&edge){ + return std::make_tuple(source(edge, proximity_graph), + target(edge, proximity_graph), + get(Gudhi::edge_filtration_t(), proximity_graph, edge)); + }); + std::vector<Filtered_edge> edges_list(edges_from_graph.begin(), edges_from_graph.end()); + std::vector<Filtered_edge> remaining_edges; + for (int iter = 0; iter < edge_collapse_iter_nb; iter++) { + auto remaining_edges = Gudhi::collapse::flag_complex_collapse_edges(edges_list); + edges_list = std::move(remaining_edges); + remaining_edges.clear(); + } + + Simplex_tree stree; + for (Vertex_handle vertex = 0; static_cast<std::size_t>(vertex) < distances.size(); vertex++) { + // insert the vertex with a 0. filtration value just like a Rips + stree.insert_simplex({vertex}, 0.); + } + for (auto filtered_edge : edges_list) { + stree.insert_simplex({std::get<0>(filtered_edge), std::get<1>(filtered_edge)}, std::get<2>(filtered_edge)); + } + + stree.expansion(dim_max); + + std::cout << "The complex contains " << stree.num_simplices() << " simplices after collapse. \n"; + std::cout << " and has dimension " << stree.dimension() << " \n"; + + // Sort the simplices in the order of the filtration + stree.initialize_filtration(); + // Compute the persistence diagram of the complex + Persistent_cohomology pcoh(stree); + // initializes the coefficient field for homology + pcoh.init_coefficients(3); + + pcoh.compute_persistent_cohomology(min_persistence); + if (filediag.empty()) { + pcoh.output_diagram(); + } else { + std::ofstream out(filediag); + pcoh.output_diagram(out); + out.close(); + } + return 0; +} + +void program_options(int argc, char* argv[], std::string& csv_matrix_file, std::string& filediag, + Filtration_value& threshold, int& dim_max, int& p, int& edge_collapse_iter_nb, + Filtration_value& min_persistence) { + namespace po = boost::program_options; + po::options_description hidden("Hidden options"); + hidden.add_options()( + "input-file", po::value<std::string>(&csv_matrix_file), + "Name of file containing a distance matrix. Can be square or lower triangular matrix. Separator is ';'."); + + po::options_description visible("Allowed options", 100); + visible.add_options()("help,h", "produce help message")( + "output-file,o", po::value<std::string>(&filediag)->default_value(std::string()), + "Name of file in which the persistence diagram is written. Default print in std::cout")( + "max-edge-length,r", + po::value<Filtration_value>(&threshold)->default_value(std::numeric_limits<Filtration_value>::infinity()), + "Maximal length of an edge for the Rips complex construction.")( + "cpx-dimension,d", po::value<int>(&dim_max)->default_value(1), + "Maximal dimension of the Rips complex we want to compute.")( + "field-charac,p", po::value<int>(&p)->default_value(11), + "Characteristic p of the coefficient field Z/pZ for computing homology.")( + "edge-collapse-iterations,i", po::value<int>(&edge_collapse_iter_nb)->default_value(1), + "Number of iterations edge collapse is performed.")( + "min-persistence,m", po::value<Filtration_value>(&min_persistence), + "Minimal lifetime of homology feature to be recorded. Default is 0. Enter a negative value to see zero length " + "intervals"); + + po::positional_options_description pos; + pos.add("input-file", 1); + + po::options_description all; + all.add(visible).add(hidden); + + po::variables_map vm; + po::store(po::command_line_parser(argc, argv).options(all).positional(pos).run(), vm); + po::notify(vm); + + if (vm.count("help") || !vm.count("input-file")) { + std::cout << std::endl; + std::cout << "Compute the persistent homology with coefficient field Z/pZ \n"; + std::cout << "of a Rips complex after edge collapse defined on a set of distance matrix.\n \n"; + std::cout << "The output diagram contains one bar per line, written with the convention: \n"; + std::cout << " p dim b d \n"; + std::cout << "where dim is the dimension of the homological feature,\n"; + std::cout << "b and d are respectively the birth and death of the feature and \n"; + std::cout << "p is the characteristic of the field Z/pZ used for homology coefficients." << std::endl << std::endl; + + std::cout << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl; + std::cout << visible << std::endl; + exit(-1); + } +} diff --git a/src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp b/src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp new file mode 100644 index 00000000..0eea742c --- /dev/null +++ b/src/Collapse/utilities/point_cloud_edge_collapse_rips_persistence.cpp @@ -0,0 +1,181 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Siddharth Pritam, Vincent Rouvreau + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#include <gudhi/Flag_complex_edge_collapser.h> +#include <gudhi/Simplex_tree.h> +#include <gudhi/Persistent_cohomology.h> +#include <gudhi/distance_functions.h> +#include <gudhi/Points_off_io.h> +#include <gudhi/graph_simplicial_complex.h> + +#include <boost/program_options.hpp> +#include <boost/range/adaptor/transformed.hpp> + +#include<utility> // for std::pair +#include<vector> +#include<tuple> + +// Types definition + +using Simplex_tree = Gudhi::Simplex_tree<>; +using Filtration_value = Simplex_tree::Filtration_value; +using Vertex_handle = Simplex_tree::Vertex_handle; +using Point = std::vector<Filtration_value>; +using Vector_of_points = std::vector<Point>; + +using Filtered_edge = std::tuple<Vertex_handle, Vertex_handle, Filtration_value>; +using Proximity_graph = Gudhi::Proximity_graph<Simplex_tree>; + +using Field_Zp = Gudhi::persistent_cohomology::Field_Zp; +using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Field_Zp>; + +void program_options(int argc, char* argv[], std::string& off_file_points, std::string& filediag, + Filtration_value& threshold, int& dim_max, int& p, int& edge_collapse_iter_nb, + Filtration_value& min_persistence); + +int main(int argc, char* argv[]) { + std::string off_file_points; + std::string filediag; + double threshold; + int dim_max; + int p; + int edge_collapse_iter_nb; + double min_persistence; + + program_options(argc, argv, off_file_points, filediag, threshold, dim_max, p, edge_collapse_iter_nb, min_persistence); + + std::cout << "The current input values to run the program is: " << std::endl; + std::cout << "min_persistence, threshold, max_complex_dimension, off_file_points, filediag" + << std::endl; + std::cout << min_persistence << ", " << threshold << ", " << dim_max + << ", " << off_file_points << ", " << filediag << std::endl; + + Gudhi::Points_off_reader<Point> off_reader(off_file_points); + if (!off_reader.is_valid()) { + std::cerr << "Unable to read file " << off_file_points << "\n"; + exit(-1); // ----- >> + } + + Vector_of_points point_vector = off_reader.get_point_cloud(); + if (point_vector.size() <= 0) { + std::cerr << "Empty point cloud." << std::endl; + exit(-1); // ----- >> + } + + std::cout << "Successfully read " << point_vector.size() << " point_vector.\n"; + std::cout << "Ambient dimension is " << point_vector[0].size() << ".\n"; + + Proximity_graph proximity_graph = Gudhi::compute_proximity_graph<Simplex_tree>(point_vector, + threshold, + Gudhi::Euclidean_distance()); + + if (num_edges(proximity_graph) <= 0) { + std::cerr << "Total number of egdes are zero." << std::endl; + exit(-1); + } + + auto edges_from_graph = boost::adaptors::transform(edges(proximity_graph), [&](auto&&edge){ + return std::make_tuple(source(edge, proximity_graph), + target(edge, proximity_graph), + get(Gudhi::edge_filtration_t(), proximity_graph, edge)); + }); + std::vector<Filtered_edge> edges_list(edges_from_graph.begin(), edges_from_graph.end()); + + std::vector<Filtered_edge> remaining_edges; + for (int iter = 0; iter < edge_collapse_iter_nb; iter++) { + auto remaining_edges = Gudhi::collapse::flag_complex_collapse_edges(edges_list); + edges_list = std::move(remaining_edges); + remaining_edges.clear(); + } + + Simplex_tree stree; + for (Vertex_handle vertex = 0; static_cast<std::size_t>(vertex) < point_vector.size(); vertex++) { + // insert the vertex with a 0. filtration value just like a Rips + stree.insert_simplex({vertex}, 0.); + } + + for (auto filtered_edge : edges_list) { + stree.insert_simplex({std::get<0>(filtered_edge), std::get<1>(filtered_edge)}, std::get<2>(filtered_edge)); + } + + stree.expansion(dim_max); + + std::cout << "The complex contains " << stree.num_simplices() << " simplices after collapse. \n"; + std::cout << " and has dimension " << stree.dimension() << " \n"; + + // Sort the simplices in the order of the filtration + stree.initialize_filtration(); + // Compute the persistence diagram of the complex + Persistent_cohomology pcoh(stree); + // initializes the coefficient field for homology + pcoh.init_coefficients(p); + + pcoh.compute_persistent_cohomology(min_persistence); + if (filediag.empty()) { + pcoh.output_diagram(); + } else { + std::ofstream out(filediag); + pcoh.output_diagram(out); + out.close(); + } + + return 0; +} + +void program_options(int argc, char* argv[], std::string& off_file_points, std::string& filediag, + Filtration_value& threshold, int& dim_max, int& p, int& edge_collapse_iter_nb, + Filtration_value& min_persistence) { + namespace po = boost::program_options; + po::options_description hidden("Hidden options"); + hidden.add_options()("input-file", po::value<std::string>(&off_file_points), + "Name of an OFF file containing a point set.\n"); + + po::options_description visible("Allowed options", 100); + visible.add_options()("help,h", "produce help message")( + "output-file,o", po::value<std::string>(&filediag)->default_value(std::string()), + "Name of file in which the persistence diagram is written. Default print in std::cout")( + "max-edge-length,r", + po::value<Filtration_value>(&threshold)->default_value(std::numeric_limits<Filtration_value>::infinity()), + "Maximal length of an edge for the Rips complex construction.")( + "cpx-dimension,d", po::value<int>(&dim_max)->default_value(1), + "Maximal dimension of the Rips complex we want to compute.")( + "field-charac,p", po::value<int>(&p)->default_value(11), + "Characteristic p of the coefficient field Z/pZ for computing homology.")( + "edge-collapse-iterations,i", po::value<int>(&edge_collapse_iter_nb)->default_value(1), + "Number of iterations edge collapse is performed.")( + "min-persistence,m", po::value<Filtration_value>(&min_persistence), + "Minimal lifetime of homology feature to be recorded. Default is 0. Enter a negative value to see zero length " + "intervals"); + + po::positional_options_description pos; + pos.add("input-file", 1); + + po::options_description all; + all.add(visible).add(hidden); + + po::variables_map vm; + po::store(po::command_line_parser(argc, argv).options(all).positional(pos).run(), vm); + po::notify(vm); + + if (vm.count("help") || !vm.count("input-file")) { + std::cout << std::endl; + std::cout << "Compute the persistent homology with coefficient field Z/pZ \n"; + std::cout << "of a Rips complex, after edge collapse, defined on a set of input points.\n \n"; + std::cout << "The output diagram contains one bar per line, written with the convention: \n"; + std::cout << " p dim b d \n"; + std::cout << "where dim is the dimension of the homological feature,\n"; + std::cout << "b and d are respectively the birth and death of the feature and \n"; + std::cout << "p is the characteristic of the field Z/pZ used for homology coefficients." << std::endl << std::endl; + + std::cout << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl; + std::cout << visible << std::endl; + exit(-1); + } +} diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md index a33d98cd..e19af537 100644 --- a/src/common/doc/main_page.md +++ b/src/common/doc/main_page.md @@ -217,6 +217,36 @@ </tr> </table> +### Edge collapse + +<table> + <tr> + <td width="35%" rowspan=2> + \image html "dominated_edge.png" + </td> + <td width="50%"> + Edge collapse is able to reduce any flag filtration to a smaller flag filtration with the same persistence, using + only the 1-skeletons of a simplicial complex. + The reduction is exact and the persistence homology of the reduced sequence is identical to the persistence + homology of the input sequence. The resulting method is simple and extremely efficient. + + Computation of edge collapse and persistent homology of a filtered flag complex via edge collapse as described in + \cite edgecollapsesocg2020. + </td> + <td width="15%"> + <b>Author:</b> Siddharth Pritam<br> + <b>Introduced in:</b> GUDHI 3.3.0<br> + <b>Copyright:</b> MIT<br> + <b>Requires:</b> \ref eigen + </td> + </tr> + <tr> + <td colspan=2 height="25"> + <b>User manual:</b> \ref edge_collapse + </td> + </tr> +</table> + ### Witness complex <table> diff --git a/src/common/include/gudhi/graph_simplicial_complex.h b/src/common/include/gudhi/graph_simplicial_complex.h index b8508697..da9dee7d 100644 --- a/src/common/include/gudhi/graph_simplicial_complex.h +++ b/src/common/include/gudhi/graph_simplicial_complex.h @@ -19,6 +19,9 @@ #include <tuple> // for std::tie namespace Gudhi { +/** @file + * @brief Graph simplicial complex methods + */ /* Edge tag for Boost PropertyGraph. */ struct edge_filtration_t { @@ -46,6 +49,8 @@ using Proximity_graph = typename boost::adjacency_list < boost::vecS, boost::vec * 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 SimplicialComplexForProximityGraph furnishes `Filtration_value` and `Vertex_handle` type definitions. + * * \tparam ForwardPointRange furnishes `.begin()` and `.end()` methods. * * \tparam Distance furnishes `operator()(const Point& p1, const Point& p2)`, where |