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diff --git a/src/Collapse/include/gudhi/Flag_complex_sparse_matrix.h b/src/Collapse/include/gudhi/Flag_complex_sparse_matrix.h new file mode 100644 index 00000000..7bbe86c4 --- /dev/null +++ b/src/Collapse/include/gudhi/Flag_complex_sparse_matrix.h @@ -0,0 +1,432 @@ +/* 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): Siddharth Pritam + * + * Copyright (C) 2018 INRIA Sophia Antipolis (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/>. + +*/ +#pragma once + +#include <gudhi/Rips_edge_list.h> +#include <boost/functional/hash.hpp> +// #include <boost/graph/adjacency_list.hpp> + +#include <iostream> +#include <utility> +#include <vector> +#include <queue> +#include <unordered_map> +#include <tuple> +#include <list> +#include <algorithm> +#include <chrono> + +#include <ctime> +#include <fstream> + +#include <Eigen/Sparse> + +typedef std::size_t Vertex; +using Edge = std::pair<Vertex, Vertex>; // This is an ordered pair, An edge is stored with convention of the first + // element being the smaller i.e {2,3} not {3,2}. However this is at the level + // of row indices on actual vertex lables +using EdgeFilt = std::pair<Edge, double>; +using edge_list = std::vector<Edge>; + +using MapVertexToIndex = std::unordered_map<Vertex, std::size_t>; +using Map = std::unordered_map<Vertex, Vertex>; + +using sparseRowMatrix = Eigen::SparseMatrix<double, Eigen::RowMajor>; +using rowInnerIterator = sparseRowMatrix::InnerIterator; + +using doubleVector = std::vector<double>; +using vertexVector = std::vector<Vertex>; +using boolVector = std::vector<bool>; + +using doubleQueue = std::queue<double>; + +using EdgeFiltQueue = std::queue<EdgeFilt>; +using EdgeFiltVector = std::vector<EdgeFilt>; + +typedef std::vector<std::tuple<double, Vertex, Vertex>> Filtered_sorted_edge_list; +typedef std::unordered_map<Edge, bool, boost::hash<Edge>> u_edge_map; +typedef std::unordered_map<Edge, std::size_t, boost::hash<Edge>> u_edge_to_idx_map; + +//! Class SparseMsMatrix +/*! + The class for storing the Vertices v/s MaxSimplices Sparse Matrix and performing collapses operations using the N^2() + Algorithm. +*/ +class Flag_complex_sparse_matrix { + private: + std::unordered_map<int, Vertex> rowToVertex; + + // Vertices strored as an unordered_set + std::unordered_set<Vertex> vertices; + + // Unordered set of removed edges. (to enforce removal from the matrix) + std::unordered_set<Edge, boost::hash<Edge>> u_set_removed_redges; + + // Unordered set of dominated edges. (to inforce removal from the matrix) + std::unordered_set<Edge, boost::hash<Edge>> u_set_dominated_redges; + + // Map from egde to its index + u_edge_to_idx_map edge_to_index_map; + // Boolean vector to indicate if the index is critical or not. + boolVector critical_edge_indicator; // critical indicator + + // Boolean vector to indicate if the index is critical or not. + boolVector dominated_edge_indicator; // domination indicator + + //! Stores the Map between vertices<B>rowToVertex and row indices <B>rowToVertex -> row-index</B>. + /*! + \code + MapVertexToIndex = std::unordered_map<Vertex,int> + \endcode + So, if the original simplex tree had vertices 0,1,4,5 <br> + <B>rowToVertex</B> would store : <br> + \verbatim + Values = | 0 | 1 | 4 | 5 | + Indices = 0 1 2 3 + \endverbatim + And <B>vertexToRow</B> would be a map like the following : <br> + \verbatim + 0 -> 0 + 1 -> 1 + 4 -> 2 + 5 -> 3 + \endverbatim + */ + MapVertexToIndex vertexToRow; + + //! Stores the Sparse matrix of double values representing the Original Simplicial Complex. + /*! + \code + sparseRowMatrix = Eigen::SparseMatrix<double, Eigen::RowMajor> ; + \endcode + ; + */ + + sparseRowMatrix* sparse_colpsd_adj_Matrix; // Stores the collapsed sparse matrix representaion. + sparseRowMatrix sparseRowAdjMatrix; // This is row-major version of the same sparse-matrix, to facilitate easy access + // to elements when traversing the matrix row-wise. + + //! Stores <I>true</I> for dominated rows and <I>false</I> for undominated rows. + /*! + Initialised to a vector of length equal to the value of the variable <B>rows</B> with all <I>false</I> values. + Subsequent removal of dominated vertices is reflected by concerned entries changing to <I>true</I> in this vector. + */ + boolVector vertDomnIndicator; //(domination indicator) + + boolVector contractionIndicator; //(contraction indicator) + + //! Stores the indices of the rows to-be checked for domination in the current iteration. + /*! + Initialised with all rows for the first iteration. + Subsequently once a dominated row is found, its non-dominated neighbhour indices are inserted. + */ + // doubleQueue rowIterator; + + doubleQueue rowIterator; + + // Queue of filtered edges, for edge-collapse, the indices of the edges are the row-indices. + EdgeFiltQueue filteredEgdeIter; + + // Vector of filtered edges, for edge-collapse, the indices of the edges are the row-indices. + EdgeFiltVector f_edge_vector; + + // List of non-dominated edges, the indices of the edges are the vertex lables!!. + Filtered_sorted_edge_list criticalCoreEdges; + // Stores the indices from the sorted filtered edge vector. + // std::set<std::size_t> recurCriticalCoreIndcs; + + //! Stores the number of vertices in the original Simplicial Complex. + /*! + This stores the count of vertices (which is also the number of rows in the Matrix). + */ + std::size_t rows; + + std::size_t numOneSimplices; + + bool edgeCollapsed; + + // Edge e is the actual edge (u,v). Not the row ids in the matrixs + bool check_edge_domination(Edge e) + { + auto u = std::get<0>(e); + auto v = std::get<1>(e); + + auto rw_u = vertexToRow[u]; + auto rw_v = vertexToRow[v]; + auto rw_e = std::make_pair(rw_u, rw_v); +#ifdef DEBUG_TRACES + std::cout << "The edge {" << u << ", " << v << "} is going for domination check." << std::endl; +#endif // DEBUG_TRACES + auto commonNeighbours = closed_common_neighbours_row_index(rw_e); +#ifdef DEBUG_TRACES + std::cout << "And its common neighbours are." << std::endl; + for (doubleVector::iterator it = commonNeighbours.begin(); it!=commonNeighbours.end(); it++) { + std::cout << rowToVertex[*it] << ", " ; + } + std::cout<< std::endl; +#endif // DEBUG_TRACES + if (commonNeighbours.size() > 2) { + if (commonNeighbours.size() == 3) + return true; + else + for (doubleVector::iterator it = commonNeighbours.begin(); it != commonNeighbours.end(); it++) { + auto rw_c = *it; // Typecasting + if (rw_c != rw_u and rw_c != rw_v) { + auto neighbours_c = closed_neighbours_row_index(rw_c); + // If neighbours_c contains the common neighbours. + if (std::includes(neighbours_c.begin(), neighbours_c.end(), commonNeighbours.begin(), + commonNeighbours.end())) + return true; + } + } + } + return false; + } + + // The edge should be sorted by the indices and indices are original + bool check_domination_indicator(Edge e) + { + return dominated_edge_indicator[edge_to_index_map[e]]; + } + + std::set<std::size_t> three_clique_indices(std::size_t crit) { + std::set<std::size_t> edge_indices; + + Edge e = std::get<0>(f_edge_vector[crit]); + Vertex u = std::get<0>(e); + Vertex v = std::get<1>(e); + +#ifdef DEBUG_TRACES + std::cout << "The current critical edge to re-check criticality with filt value is : f {" << u << "," << v + << "} = " << std::get<1>(f_edge_vector[crit]) << std::endl; +#endif // DEBUG_TRACES + auto rw_u = vertexToRow[u]; + auto rw_v = vertexToRow[v]; + auto rw_critical_edge = std::make_pair(rw_u, rw_v); + + doubleVector commonNeighbours = closed_common_neighbours_row_index(rw_critical_edge); + + if (commonNeighbours.size() > 2) { + for (doubleVector::iterator it = commonNeighbours.begin(); it != commonNeighbours.end(); it++) { + auto rw_c = *it; + if (rw_c != rw_u and rw_c != rw_v) { + auto e_with_new_nbhr_v = std::minmax(u, rowToVertex[rw_c]); + auto e_with_new_nbhr_u = std::minmax(v, rowToVertex[rw_c]); + edge_indices.emplace(edge_to_index_map[e_with_new_nbhr_v]); + edge_indices.emplace(edge_to_index_map[e_with_new_nbhr_u]); + } + } + } + return edge_indices; + } + + void set_edge_critical(std::size_t indx, double filt) { +#ifdef DEBUG_TRACES + std::cout << "The curent index with filtration value " << indx << ", " << filt << " is primary critical" << + std::endl; +#endif // DEBUG_TRACES + std::set<std::size_t> effectedIndcs = three_clique_indices(indx); + if (effectedIndcs.size() > 0) { + for (auto idx = indx - 1; idx > 0; idx--) { + Edge e = std::get<0>(f_edge_vector[idx]); + Vertex u = std::get<0>(e); + Vertex v = std::get<1>(e); + // If idx is not critical so it should be proceses, otherwise it stays in the graph // prev + // code : recurCriticalCoreIndcs.find(idx) == recurCriticalCoreIndcs.end() + if (not critical_edge_indicator.at(idx)) { + // If idx is affected + if (effectedIndcs.find(idx) != effectedIndcs.end()) { + if (not check_edge_domination(e)) { +#ifdef DEBUG_TRACES + std::cout << "The curent index became critical " << idx << std::endl; +#endif // DEBUG_TRACES + critical_edge_indicator.at(idx) = true; + criticalCoreEdges.push_back({filt, u, v}); + std::set<std::size_t> inner_effected_indcs = three_clique_indices(idx); + for (auto inr_idx = inner_effected_indcs.rbegin(); inr_idx != inner_effected_indcs.rend(); inr_idx++) { + if (*inr_idx < idx) effectedIndcs.emplace(*inr_idx); + } + inner_effected_indcs.clear(); +#ifdef DEBUG_TRACES + std::cout << "The following edge is critical with filt value: {" << std::get<0>(e) << "," << + std::get<1>(e) << "}; " << filt << std::endl; +#endif // DEBUG_TRACES + } else + u_set_dominated_redges.emplace(std::minmax(vertexToRow[u], vertexToRow[v])); + } else + // Idx is not affected hence dominated. + u_set_dominated_redges.emplace(std::minmax(vertexToRow[u], vertexToRow[v])); + } + } + } + effectedIndcs.clear(); + u_set_dominated_redges.clear(); + } + + // Returns list of non-zero columns of the particular indx. + doubleVector closed_neighbours_row_index(double indx) + { + doubleVector nonZeroIndices; + Vertex u = indx; + Vertex v; + // std::cout << "The neighbours of the vertex: " << rowToVertex[u] << " are. " << std::endl; + if (not vertDomnIndicator[indx]) { + // Iterate over the non-zero columns + for (rowInnerIterator it(sparseRowAdjMatrix, indx); it; ++it) { + v = it.index(); + // If the vertex v is not dominated and the edge {u,v} is still in the matrix + if (not vertDomnIndicator[v] and u_set_removed_redges.find(std::minmax(u, v)) == u_set_removed_redges.end() and + u_set_dominated_redges.find(std::minmax(u, v)) == u_set_dominated_redges.end()) { + // inner index, here it is equal to it.columns() + nonZeroIndices.push_back(it.index()); + // std::cout << rowToVertex[it.index()] << ", " ; + } + } + // std::cout << std::endl; + } + return nonZeroIndices; + } + + doubleVector closed_common_neighbours_row_index(Edge e) // Returns the list of closed neighbours of the edge :{u,v}. + { + doubleVector common; + doubleVector nonZeroIndices_u; + doubleVector nonZeroIndices_v; + double u = std::get<0>(e); + double v = std::get<1>(e); + + nonZeroIndices_u = closed_neighbours_row_index(u); + nonZeroIndices_v = closed_neighbours_row_index(v); + std::set_intersection(nonZeroIndices_u.begin(), nonZeroIndices_u.end(), nonZeroIndices_v.begin(), + nonZeroIndices_v.end(), std::inserter(common, common.begin())); + + return common; + } + + public: + //! Main Constructor + /*! + Argument is an instance of Filtered_sorted_edge_list. <br> + This is THE function that initialises all data members to appropriate values. <br> + <B>rowToVertex</B>, <B>vertexToRow</B>, <B>rows</B>, <B>cols</B>, <B>sparseRowAdjMatrix</B> are initialised here. + <B>vertDomnIndicator</B> ,<B>rowIterator<B> are initialised by init() function which is + called at the begining of this. <br> + */ + Flag_complex_sparse_matrix(const size_t& num_vertices, const Filtered_sorted_edge_list& edge_t) + : rows(0), + numOneSimplices(0), + edgeCollapsed(false) { + // Initializing sparseRowAdjMatrix, This is a row-major sparse matrix. + sparseRowAdjMatrix = sparseRowMatrix(num_vertices, num_vertices); + + for (size_t bgn_idx = 0; bgn_idx < edge_t.size(); bgn_idx++) { + f_edge_vector.push_back( + {{std::get<1>(edge_t.at(bgn_idx)), std::get<2>(edge_t.at(bgn_idx))}, std::get<0>(edge_t.at(bgn_idx))}); + } + } + + // Performs edge collapse in a decreasing sequence of the filtration value. + Filtered_sorted_edge_list filtered_edge_collapse() { + std::size_t endIdx = 0; + + u_set_removed_redges.clear(); + u_set_dominated_redges.clear(); + critical_edge_indicator.clear(); + + while (endIdx < f_edge_vector.size()) { + EdgeFilt fec = f_edge_vector[endIdx]; + Edge e = std::get<0>(fec); + Vertex u = std::get<0>(e); + Vertex v = std::get<1>(e); + double filt = std::get<1>(fec); + + // Inserts the edge in the sparse matrix to update the graph (G_i) + insert_new_edges(u, v, filt); + + edge_to_index_map.emplace(std::minmax(u, v), endIdx); + critical_edge_indicator.push_back(false); + dominated_edge_indicator.push_back(false); + + if (not check_edge_domination(e)) { + critical_edge_indicator.at(endIdx) = true; + dominated_edge_indicator.at(endIdx) = false; + criticalCoreEdges.push_back({filt, u, v}); + if (endIdx > 1) + set_edge_critical(endIdx, filt); + } else + dominated_edge_indicator.at(endIdx) = true; + endIdx++; + } + +#ifdef DEBUG_TRACES + std::cout << "The total number of critical edges is: " << criticalCoreEdges.size() << std::endl; + std::cout << "The total number of non-critical edges is: " << f_edge_vector.size() - criticalCoreEdges.size() << std::endl; +#endif // DEBUG_TRACES + edgeCollapsed = true; + return criticalCoreEdges; + } + + void insert_vertex(const Vertex& vertex, double filt_val) { + auto rw = vertexToRow.find(vertex); + if (rw == vertexToRow.end()) { + // Initializing the diagonal element of the adjency matrix corresponding to rw_b. + sparseRowAdjMatrix.insert(rows, rows) = filt_val; + vertDomnIndicator.push_back(false); + contractionIndicator.push_back(false); + rowIterator.push(rows); + vertexToRow.insert(std::make_pair(vertex, rows)); + rowToVertex.insert(std::make_pair(rows, vertex)); + vertices.emplace(vertex); + rows++; + } + } + + void insert_new_edges(const Vertex& u, const Vertex& v, double filt_val) + { + // The edge must not be added before, it should be a new edge. + insert_vertex(u, filt_val); + if (u != v) { + insert_vertex(v, filt_val); +#ifdef DEBUG_TRACES + std::cout << "Insertion of the edge begins " << u <<", " << v << std::endl; +#endif // DEBUG_TRACES + + auto rw_u = vertexToRow.find(u); + auto rw_v = vertexToRow.find(v); +#ifdef DEBUG_TRACES + std::cout << "Inserting the edge " << u <<", " << v << std::endl; +#endif // DEBUG_TRACES + sparseRowAdjMatrix.insert(rw_u->second, rw_v->second) = filt_val; + sparseRowAdjMatrix.insert(rw_v->second, rw_u->second) = filt_val; + numOneSimplices++; + } +#ifdef DEBUG_TRACES + else { + std::cout << "Already a member simplex, skipping..." << std::endl; + } +#endif // DEBUG_TRACES + } + + std::size_t num_vertices() const { return vertices.size(); } + +};
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