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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: Mathieu Carriere
- *
- * Copyright (C) 2017 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 GIC_H_
-#define GIC_H_
-
-#ifdef GUDHI_USE_TBB
-#include <tbb/parallel_for.h>
-#include <tbb/mutex.h>
-#endif
-
-#include <gudhi/Debug_utils.h>
-#include <gudhi/graph_simplicial_complex.h>
-#include <gudhi/reader_utils.h>
-#include <gudhi/Simplex_tree.h>
-#include <gudhi/Rips_complex.h>
-#include <gudhi/Points_off_io.h>
-#include <gudhi/distance_functions.h>
-#include <gudhi/Persistent_cohomology.h>
-#include <gudhi/Bottleneck.h>
-
-#include <boost/config.hpp>
-#include <boost/graph/graph_traits.hpp>
-#include <boost/graph/adjacency_list.hpp>
-#include <boost/graph/connected_components.hpp>
-#include <boost/graph/dijkstra_shortest_paths.hpp>
-#include <boost/graph/subgraph.hpp>
-#include <boost/graph/graph_utility.hpp>
-
-#include <iostream>
-#include <vector>
-#include <map>
-#include <string>
-#include <limits> // for numeric_limits
-#include <utility> // for std::pair<>
-#include <algorithm> // for std::max
-#include <random>
-#include <cassert>
-#include <cmath>
-
-namespace Gudhi {
-
-namespace cover_complex {
-
-using Simplex_tree = Gudhi::Simplex_tree<>;
-using Filtration_value = Simplex_tree::Filtration_value;
-using Rips_complex = Gudhi::rips_complex::Rips_complex<Filtration_value>;
-using Persistence_diagram = std::vector<std::pair<double, double> >;
-using Graph = boost::subgraph<
- boost::adjacency_list<boost::setS, boost::vecS, boost::undirectedS, boost::no_property,
- boost::property<boost::edge_index_t, int, boost::property<boost::edge_weight_t, double> > > >;
-using Vertex_t = boost::graph_traits<Graph>::vertex_descriptor;
-using Index_map = boost::property_map<Graph, boost::vertex_index_t>::type;
-using Weight_map = boost::property_map<Graph, boost::edge_weight_t>::type;
-
-/**
- * \class Cover_complex
- * \brief Cover complex data structure.
- *
- * \ingroup cover_complex
- *
- * \details
- * The data structure is a simplicial complex, representing a
- * Graph Induced simplicial Complex (GIC) or a Nerve,
- * and whose simplices are computed with a cover C of a point
- * cloud P, which often comes from the preimages of intervals
- * covering the image of a function f defined on P.
- * These intervals are parameterized by their resolution
- * (either their length or their number)
- * and their gain (percentage of overlap).
- * To compute a GIC, one also needs a graph G built on top of P,
- * whose cliques with vertices belonging to different elements of C
- * correspond to the simplices of the GIC.
- *
- */
-template <typename Point>
-class Cover_complex {
- private:
- bool verbose = false; // whether to display information.
- std::string type; // Nerve or GIC
-
- std::vector<Point> point_cloud; // input point cloud.
- std::vector<std::vector<double> > distances; // all pairwise distances.
- int maximal_dim; // maximal dimension of output simplicial complex.
- int data_dimension; // dimension of input data.
- int n; // number of points.
-
- std::vector<double> func; // function used to compute the output simplicial complex.
- std::vector<double> func_color; // function used to compute the colors of the nodes of the output simplicial complex.
- bool functional_cover = false; // whether we use a cover with preimages of a function or not.
-
- Graph one_skeleton_OFF; // one-skeleton given by the input OFF file (if it exists).
- Graph one_skeleton; // one-skeleton used to compute the connected components.
- std::vector<Vertex_t> vertices; // vertices of one_skeleton.
-
- std::vector<std::vector<int> > simplices; // simplices of output simplicial complex.
- std::vector<int> voronoi_subsamples; // Voronoi germs (in case of Voronoi cover).
-
- Persistence_diagram PD;
- std::vector<double> distribution;
-
- std::vector<std::vector<int> >
- cover; // function associating to each data point the vector of cover elements to which it belongs.
- std::map<int, std::vector<int> >
- cover_back; // inverse of cover, in order to get the data points associated to a specific cover element.
- std::map<int, double> cover_std; // standard function (induced by func) used to compute the extended persistence
- // diagram of the output simplicial complex.
- std::map<int, int>
- cover_fct; // integer-valued function that allows to state if two elements of the cover are consecutive or not.
- std::map<int, std::pair<int, double> >
- cover_color; // size and coloring (induced by func_color) of the vertices of the output simplicial complex.
-
- int resolution_int = -1;
- double resolution_double = -1;
- double gain = -1;
- double rate_constant = 10; // Constant in the subsampling.
- double rate_power = 0.001; // Power in the subsampling.
- int mask = 0; // Ignore nodes containing less than mask points.
-
- std::map<int, int> name2id, name2idinv;
-
- std::string cover_name;
- std::string point_cloud_name;
- std::string color_name;
-
- // Remove all edges of a graph.
- void remove_edges(Graph& G) {
- boost::graph_traits<Graph>::edge_iterator ei, ei_end;
- for (boost::tie(ei, ei_end) = boost::edges(G); ei != ei_end; ++ei) boost::remove_edge(*ei, G);
- }
-
- // Thread local is not available on XCode version < V.8
- // If not available, random engine is a class member.
-#ifndef GUDHI_CAN_USE_CXX11_THREAD_LOCAL
- std::default_random_engine re;
-#endif // GUDHI_CAN_USE_CXX11_THREAD_LOCAL
-
- // Find random number in [0,1].
- double GetUniform() {
- // Thread local is not available on XCode version < V.8
- // If available, random engine is defined for each thread.
-#ifdef GUDHI_CAN_USE_CXX11_THREAD_LOCAL
- thread_local std::default_random_engine re;
-#endif // GUDHI_CAN_USE_CXX11_THREAD_LOCAL
- std::uniform_real_distribution<double> Dist(0, 1);
- return Dist(re);
- }
-
- // Subsample points.
- void SampleWithoutReplacement(int populationSize, int sampleSize, std::vector<int>& samples) {
- int t = 0;
- int m = 0;
- double u;
- while (m < sampleSize) {
- u = GetUniform();
- if ((populationSize - t) * u >= sampleSize - m) {
- t++;
- } else {
- samples[m] = t;
- t++;
- m++;
- }
- }
- }
-
- // *******************************************************************************************************************
- // Utils.
- // *******************************************************************************************************************
-
- public:
- /** \brief Specifies whether the type of the output simplicial complex.
- *
- * @param[in] t std::string (either "GIC" or "Nerve").
- *
- */
- void set_type(const std::string& t) { type = t; }
-
- public:
- /** \brief Specifies whether the program should display information or not.
- *
- * @param[in] verb boolean (true = display info, false = do not display info).
- *
- */
- void set_verbose(bool verb = false) { verbose = verb; }
-
- public:
- /** \brief Sets the constants used to subsample the data set. These constants are
- * explained in \cite Carriere17c.
- *
- * @param[in] constant double.
- * @param[in] power double.
- *
- */
- void set_subsampling(double constant, double power) {
- rate_constant = constant;
- rate_power = power;
- }
-
- public:
- /** \brief Sets the mask, which is a threshold integer such that nodes in the complex that contain a number of data
- * points which is less than or equal to
- * this threshold are not displayed.
- *
- * @param[in] nodemask integer.
- *
- */
- void set_mask(int nodemask) { mask = nodemask; }
-
- public:
- /** \brief Reads and stores the input point cloud.
- *
- * @param[in] off_file_name name of the input .OFF or .nOFF file.
- *
- */
- bool read_point_cloud(const std::string& off_file_name) {
- point_cloud_name = off_file_name;
- std::ifstream input(off_file_name);
- std::string line;
-
- char comment = '#';
- while (comment == '#') {
- std::getline(input, line);
- if (!line.empty() && !all_of(line.begin(), line.end(), (int (*)(int))isspace))
- comment = line[line.find_first_not_of(' ')];
- }
- if (strcmp((char*)line.c_str(), "nOFF") == 0) {
- comment = '#';
- while (comment == '#') {
- std::getline(input, line);
- if (!line.empty() && !all_of(line.begin(), line.end(), (int (*)(int))isspace))
- comment = line[line.find_first_not_of(' ')];
- }
- std::stringstream stream(line);
- stream >> data_dimension;
- } else {
- data_dimension = 3;
- }
-
- comment = '#';
- int numedges, numfaces, i, dim;
- while (comment == '#') {
- std::getline(input, line);
- if (!line.empty() && !all_of(line.begin(), line.end(), (int (*)(int))isspace))
- comment = line[line.find_first_not_of(' ')];
- }
- std::stringstream stream(line);
- stream >> n;
- stream >> numfaces;
- stream >> numedges;
-
- i = 0;
- while (i < n) {
- std::getline(input, line);
- if (!line.empty() && line[line.find_first_not_of(' ')] != '#' &&
- !all_of(line.begin(), line.end(), (int (*)(int))isspace)) {
- std::stringstream iss(line);
- std::vector<double> point;
- point.assign(std::istream_iterator<double>(iss), std::istream_iterator<double>());
- point_cloud.emplace_back(point.begin(), point.begin() + data_dimension);
- boost::add_vertex(one_skeleton_OFF);
- vertices.push_back(boost::add_vertex(one_skeleton));
- cover.emplace_back();
- i++;
- }
- }
-
- i = 0;
- while (i < numfaces) {
- std::getline(input, line);
- if (!line.empty() && line[line.find_first_not_of(' ')] != '#' &&
- !all_of(line.begin(), line.end(), (int (*)(int))isspace)) {
- std::vector<int> simplex;
- std::stringstream iss(line);
- simplex.assign(std::istream_iterator<int>(iss), std::istream_iterator<int>());
- dim = simplex[0];
- for (int j = 1; j <= dim; j++)
- for (int k = j + 1; k <= dim; k++)
- boost::add_edge(vertices[simplex[j]], vertices[simplex[k]], one_skeleton_OFF);
- i++;
- }
- }
-
- return input.is_open();
- }
-
- // *******************************************************************************************************************
- // Graphs.
- // *******************************************************************************************************************
-
- public: // Set graph from file.
- /** \brief Creates a graph G from a file containing the edges.
- *
- * @param[in] graph_file_name name of the input graph file.
- * The graph file contains one edge per line,
- * each edge being represented by the IDs of its two nodes.
- *
- */
- void set_graph_from_file(const std::string& graph_file_name) {
- remove_edges(one_skeleton);
- int neighb;
- std::ifstream input(graph_file_name);
- std::string line;
- int source;
- while (std::getline(input, line)) {
- std::stringstream stream(line);
- stream >> source;
- while (stream >> neighb) boost::add_edge(vertices[source], vertices[neighb], one_skeleton);
- }
- }
-
- public: // Set graph from OFF file.
- /** \brief Creates a graph G from the triangulation given by the input .OFF file.
- *
- */
- void set_graph_from_OFF() {
- remove_edges(one_skeleton);
- if (num_edges(one_skeleton_OFF))
- one_skeleton = one_skeleton_OFF;
- else
- std::cout << "No triangulation read in OFF file!" << std::endl;
- }
-
- public: // Set graph from Rips complex.
- /** \brief Creates a graph G from a Rips complex.
- *
- * @param[in] threshold threshold value for the Rips complex.
- * @param[in] distance distance used to compute the Rips complex.
- *
- */
- template <typename Distance>
- void set_graph_from_rips(double threshold, Distance distance) {
- remove_edges(one_skeleton);
- if (distances.size() == 0) compute_pairwise_distances(distance);
- for (int i = 0; i < n; i++) {
- for (int j = i + 1; j < n; j++) {
- if (distances[i][j] <= threshold) {
- boost::add_edge(vertices[i], vertices[j], one_skeleton);
- boost::put(boost::edge_weight, one_skeleton, boost::edge(vertices[i], vertices[j], one_skeleton).first,
- distances[i][j]);
- }
- }
- }
- }
-
- public:
- void set_graph_weights() {
- Index_map index = boost::get(boost::vertex_index, one_skeleton);
- Weight_map weight = boost::get(boost::edge_weight, one_skeleton);
- boost::graph_traits<Graph>::edge_iterator ei, ei_end;
- for (boost::tie(ei, ei_end) = boost::edges(one_skeleton); ei != ei_end; ++ei)
- boost::put(weight, *ei,
- distances[index[boost::source(*ei, one_skeleton)]][index[boost::target(*ei, one_skeleton)]]);
- }
-
- public: // Pairwise distances.
- /** \private \brief Computes all pairwise distances.
- */
- template <typename Distance>
- void compute_pairwise_distances(Distance ref_distance) {
- double d;
- std::vector<double> zeros(n);
- for (int i = 0; i < n; i++) distances.push_back(zeros);
- std::string distance = point_cloud_name + "_dist";
- std::ifstream input(distance, std::ios::out | std::ios::binary);
-
- if (input.good()) {
- if (verbose) std::cout << "Reading distances..." << std::endl;
- for (int i = 0; i < n; i++) {
- for (int j = i; j < n; j++) {
- input.read((char*)&d, 8);
- distances[i][j] = d;
- distances[j][i] = d;
- }
- }
- input.close();
- } else {
- if (verbose) std::cout << "Computing distances..." << std::endl;
- input.close();
- std::ofstream output(distance, std::ios::out | std::ios::binary);
- for (int i = 0; i < n; i++) {
- int state = (int)floor(100 * (i * 1.0 + 1) / n) % 10;
- if (state == 0 && verbose) std::cout << "\r" << state << "%" << std::flush;
- for (int j = i; j < n; j++) {
- double dis = ref_distance(point_cloud[i], point_cloud[j]);
- distances[i][j] = dis;
- distances[j][i] = dis;
- output.write((char*)&dis, 8);
- }
- }
- output.close();
- if (verbose) std::cout << std::endl;
- }
- }
-
- public: // Automatic tuning of Rips complex.
- /** \brief Creates a graph G from a Rips complex whose threshold value is automatically tuned with subsampling---see
- * \cite Carriere17c.
- *
- * @param[in] distance distance between data points.
- * @param[in] N number of subsampling iteration (the default reasonable value is 100, but there is no guarantee on
- * how to choose it).
- * @result delta threshold used for computing the Rips complex.
- *
- */
- template <typename Distance>
- double set_graph_from_automatic_rips(Distance distance, int N = 100) {
- int m = floor(n / std::exp((1 + rate_power) * std::log(std::log(n) / std::log(rate_constant))));
- m = std::min(m, n - 1);
- double delta = 0;
-
- if (verbose) std::cout << n << " points in R^" << data_dimension << std::endl;
- if (verbose) std::cout << "Subsampling " << m << " points" << std::endl;
-
- if (distances.size() == 0) compute_pairwise_distances(distance);
-
- // This cannot be parallelized if thread_local is not defined
- // thread_local is not defined for XCode < v.8
- #if defined(GUDHI_USE_TBB) && defined(GUDHI_CAN_USE_CXX11_THREAD_LOCAL)
- tbb::mutex deltamutex;
- tbb::parallel_for(0, N, [&](int i){
- std::vector<int> samples(m);
- SampleWithoutReplacement(n, m, samples);
- double hausdorff_dist = 0;
- for (int j = 0; j < n; j++) {
- double mj = distances[j][samples[0]];
- for (int k = 1; k < m; k++) mj = std::min(mj, distances[j][samples[k]]);
- hausdorff_dist = std::max(hausdorff_dist, mj);
- }
- deltamutex.lock();
- delta += hausdorff_dist / N;
- deltamutex.unlock();
- });
- #else
- for (int i = 0; i < N; i++) {
- std::vector<int> samples(m);
- SampleWithoutReplacement(n, m, samples);
- double hausdorff_dist = 0;
- for (int j = 0; j < n; j++) {
- double mj = distances[j][samples[0]];
- for (int k = 1; k < m; k++) mj = std::min(mj, distances[j][samples[k]]);
- hausdorff_dist = std::max(hausdorff_dist, mj);
- }
- delta += hausdorff_dist / N;
- }
- #endif
-
- if (verbose) std::cout << "delta = " << delta << std::endl;
- set_graph_from_rips(delta, distance);
- return delta;
- }
-
- // *******************************************************************************************************************
- // Functions.
- // *******************************************************************************************************************
-
- public: // Set function from file.
- /** \brief Creates the function f from a file containing the function values.
- *
- * @param[in] func_file_name name of the input function file.
- *
- */
- void set_function_from_file(const std::string& func_file_name) {
- int i = 0;
- std::ifstream input(func_file_name);
- std::string line;
- double f;
- while (std::getline(input, line)) {
- std::stringstream stream(line);
- stream >> f;
- func.push_back(f);
- i++;
- }
- functional_cover = true;
- cover_name = func_file_name;
- }
-
- public: // Set function from kth coordinate
- /** \brief Creates the function f from the k-th coordinate of the point cloud P.
- *
- * @param[in] k coordinate to use (start at 0).
- *
- */
- void set_function_from_coordinate(int k) {
- for (int i = 0; i < n; i++) func.push_back(point_cloud[i][k]);
- functional_cover = true;
- cover_name = "coordinate " + std::to_string(k);
- }
-
- public: // Set function from vector.
- /** \brief Creates the function f from a vector stored in memory.
- *
- * @param[in] function input vector of values.
- *
- */
- template <class InputRange>
- void set_function_from_range(InputRange const& function) {
- for (int i = 0; i < n; i++) func.push_back(function[i]);
- functional_cover = true;
- }
-
- // *******************************************************************************************************************
- // Covers.
- // *******************************************************************************************************************
-
- public: // Automatic tuning of resolution.
- /** \brief Computes the optimal length of intervals
- * (i.e. the smallest interval length avoiding discretization artifacts---see \cite Carriere17c) for a functional
- * cover.
- *
- * @result reso interval length used to compute the cover.
- *
- */
- double set_automatic_resolution() {
- if (!functional_cover) {
- std::cout << "Cover needs to come from the preimages of a function." << std::endl;
- return 0;
- }
- if (type != "Nerve" && type != "GIC") {
- std::cout << "Type of complex needs to be specified." << std::endl;
- return 0;
- }
-
- double reso = 0;
- Index_map index = boost::get(boost::vertex_index, one_skeleton);
-
- if (type == "GIC") {
- boost::graph_traits<Graph>::edge_iterator ei, ei_end;
- for (boost::tie(ei, ei_end) = boost::edges(one_skeleton); ei != ei_end; ++ei)
- reso = std::max(reso, std::abs(func[index[boost::source(*ei, one_skeleton)]] -
- func[index[boost::target(*ei, one_skeleton)]]));
- if (verbose) std::cout << "resolution = " << reso << std::endl;
- resolution_double = reso;
- }
-
- if (type == "Nerve") {
- boost::graph_traits<Graph>::edge_iterator ei, ei_end;
- for (boost::tie(ei, ei_end) = boost::edges(one_skeleton); ei != ei_end; ++ei)
- reso = std::max(reso, std::abs(func[index[boost::source(*ei, one_skeleton)]] -
- func[index[boost::target(*ei, one_skeleton)]]) /
- gain);
- if (verbose) std::cout << "resolution = " << reso << std::endl;
- resolution_double = reso;
- }
-
- return reso;
- }
-
- public:
- /** \brief Sets a length of intervals from a value stored in memory.
- *
- * @param[in] reso length of intervals.
- *
- */
- void set_resolution_with_interval_length(double reso) { resolution_double = reso; }
- /** \brief Sets a number of intervals from a value stored in memory.
- *
- * @param[in] reso number of intervals.
- *
- */
- void set_resolution_with_interval_number(int reso) { resolution_int = reso; }
- /** \brief Sets a gain from a value stored in memory (default value 0.3).
- *
- * @param[in] g gain.
- *
- */
- void set_gain(double g = 0.3) { gain = g; }
-
- public: // Set cover with preimages of function.
- /** \brief Creates a cover C from the preimages of the function f.
- *
- */
- void set_cover_from_function() {
- if (resolution_double == -1 && resolution_int == -1) {
- std::cout << "Number and/or length of intervals not specified" << std::endl;
- return;
- }
- if (gain == -1) {
- std::cout << "Gain not specified" << std::endl;
- return;
- }
-
- // Read function values and compute min and max
- double minf = std::numeric_limits<float>::max();
- double maxf = std::numeric_limits<float>::lowest();
- for (int i = 0; i < n; i++) {
- minf = std::min(minf, func[i]);
- maxf = std::max(maxf, func[i]);
- }
- if (verbose) std::cout << "Min function value = " << minf << " and Max function value = " << maxf << std::endl;
-
- // Compute cover of im(f)
- std::vector<std::pair<double, double> > intervals;
- int res;
-
- if (resolution_double == -1) { // Case we use an integer for the number of intervals.
- double incr = (maxf - minf) / resolution_int;
- double x = minf;
- double alpha = (incr * gain) / (2 - 2 * gain);
- double y = minf + incr + alpha;
- std::pair<double, double> interm(x, y);
- intervals.push_back(interm);
- for (int i = 1; i < resolution_int - 1; i++) {
- x = minf + i * incr - alpha;
- y = minf + (i + 1) * incr + alpha;
- std::pair<double, double> inter(x, y);
- intervals.push_back(inter);
- }
- x = minf + (resolution_int - 1) * incr - alpha;
- y = maxf;
- std::pair<double, double> interM(x, y);
- intervals.push_back(interM);
- res = intervals.size();
- if (verbose) {
- for (int i = 0; i < res; i++)
- std::cout << "Interval " << i << " = [" << intervals[i].first << ", " << intervals[i].second << "]"
- << std::endl;
- }
- } else {
- if (resolution_int == -1) { // Case we use a double for the length of the intervals.
- double x = minf;
- double y = x + resolution_double;
- while (y <= maxf && maxf - (y - gain * resolution_double) >= resolution_double) {
- std::pair<double, double> inter(x, y);
- intervals.push_back(inter);
- x = y - gain * resolution_double;
- y = x + resolution_double;
- }
- std::pair<double, double> interM(x, maxf);
- intervals.push_back(interM);
- res = intervals.size();
- if (verbose) {
- for (int i = 0; i < res; i++)
- std::cout << "Interval " << i << " = [" << intervals[i].first << ", " << intervals[i].second << "]"
- << std::endl;
- }
- } else { // Case we use an integer and a double for the length of the intervals.
- double x = minf;
- double y = x + resolution_double;
- int count = 0;
- while (count < resolution_int && y <= maxf && maxf - (y - gain * resolution_double) >= resolution_double) {
- std::pair<double, double> inter(x, y);
- intervals.push_back(inter);
- count++;
- x = y - gain * resolution_double;
- y = x + resolution_double;
- }
- res = intervals.size();
- if (verbose) {
- for (int i = 0; i < res; i++)
- std::cout << "Interval " << i << " = [" << intervals[i].first << ", " << intervals[i].second << "]"
- << std::endl;
- }
- }
- }
-
- // Sort points according to function values
- std::vector<int> points(n);
- for (int i = 0; i < n; i++) points[i] = i;
- std::sort(points.begin(), points.end(), [=](const int & p1, const int & p2){return (this->func[p1] < this->func[p2]);});
-
- int id = 0;
- int pos = 0;
- Index_map index = boost::get(boost::vertex_index, one_skeleton); // int maxc = -1;
- std::map<int, std::vector<int> > preimages;
- std::map<int, double> funcstd;
-
- if (verbose) std::cout << "Computing preimages..." << std::endl;
- for (int i = 0; i < res; i++) {
- // Find points in the preimage
- std::pair<double, double> inter1 = intervals[i];
- int tmp = pos;
- double u, v;
-
- if (i != res - 1) {
- if (i != 0) {
- std::pair<double, double> inter3 = intervals[i - 1];
- while (func[points[tmp]] < inter3.second && tmp != n) {
- preimages[i].push_back(points[tmp]);
- tmp++;
- }
- u = inter3.second;
- } else {
- u = inter1.first;
- }
-
- std::pair<double, double> inter2 = intervals[i + 1];
- while (func[points[tmp]] < inter2.first && tmp != n) {
- preimages[i].push_back(points[tmp]);
- tmp++;
- }
- v = inter2.first;
- pos = tmp;
- while (func[points[tmp]] < inter1.second && tmp != n) {
- preimages[i].push_back(points[tmp]);
- tmp++;
- }
-
- } else {
- std::pair<double, double> inter3 = intervals[i - 1];
- while (func[points[tmp]] < inter3.second && tmp != n) {
- preimages[i].push_back(points[tmp]);
- tmp++;
- }
- while (tmp != n) {
- preimages[i].push_back(points[tmp]);
- tmp++;
- }
- u = inter3.second;
- v = inter1.second;
- }
-
- funcstd[i] = 0.5 * (u + v);
- }
-
- #ifdef GUDHI_USE_TBB
- if (verbose) std::cout << "Computing connected components (parallelized)..." << std::endl;
- tbb::mutex covermutex, idmutex;
- tbb::parallel_for(0, res, [&](int i){
- // Compute connected components
- Graph G = one_skeleton.create_subgraph();
- int num = preimages[i].size();
- std::vector<int> component(num);
- for (int j = 0; j < num; j++) boost::add_vertex(index[vertices[preimages[i][j]]], G);
- boost::connected_components(G, &component[0]);
- int max = 0;
-
- // For each point in preimage
- for (int j = 0; j < num; j++) {
- // Update number of components in preimage
- if (component[j] > max) max = component[j];
-
- // Identify component with Cantor polynomial N^2 -> N
- int identifier = ((i + component[j])*(i + component[j]) + 3 * i + component[j]) / 2;
-
- // Update covers
- covermutex.lock();
- cover[preimages[i][j]].push_back(identifier);
- cover_back[identifier].push_back(preimages[i][j]);
- cover_fct[identifier] = i;
- cover_std[identifier] = funcstd[i];
- cover_color[identifier].second += func_color[preimages[i][j]];
- cover_color[identifier].first += 1;
- covermutex.unlock();
- }
-
- // Maximal dimension is total number of connected components
- idmutex.lock();
- id += max + 1;
- idmutex.unlock();
- });
- #else
- if (verbose) std::cout << "Computing connected components..." << std::endl;
- for (int i = 0; i < res; i++) {
- // Compute connected components
- Graph G = one_skeleton.create_subgraph();
- int num = preimages[i].size();
- std::vector<int> component(num);
- for (int j = 0; j < num; j++) boost::add_vertex(index[vertices[preimages[i][j]]], G);
- boost::connected_components(G, &component[0]);
- int max = 0;
-
- // For each point in preimage
- for (int j = 0; j < num; j++) {
- // Update number of components in preimage
- if (component[j] > max) max = component[j];
-
- // Identify component with Cantor polynomial N^2 -> N
- int identifier = (std::pow(i + component[j], 2) + 3 * i + component[j]) / 2;
-
- // Update covers
- cover[preimages[i][j]].push_back(identifier);
- cover_back[identifier].push_back(preimages[i][j]);
- cover_fct[identifier] = i;
- cover_std[identifier] = funcstd[i];
- cover_color[identifier].second += func_color[preimages[i][j]];
- cover_color[identifier].first += 1;
- }
-
- // Maximal dimension is total number of connected components
- id += max + 1;
- }
- #endif
-
- maximal_dim = id - 1;
- for (std::map<int, std::pair<int, double> >::iterator iit = cover_color.begin(); iit != cover_color.end(); iit++)
- iit->second.second /= iit->second.first;
- }
-
- public: // Set cover from file.
- /** \brief Creates the cover C from a file containing the cover elements of each point (the order has to be the same
- * as in the input file!).
- *
- * @param[in] cover_file_name name of the input cover file.
- *
- */
- void set_cover_from_file(const std::string& cover_file_name) {
- int i = 0;
- int cov;
- std::vector<int> cov_elts, cov_number;
- std::ifstream input(cover_file_name);
- std::string line;
- while (std::getline(input, line)) {
- cov_elts.clear();
- std::stringstream stream(line);
- while (stream >> cov) {
- cov_elts.push_back(cov);
- cov_number.push_back(cov);
- cover_fct[cov] = cov;
- cover_color[cov].second += func_color[i];
- cover_color[cov].first++;
- cover_back[cov].push_back(i);
- }
- cover[i] = cov_elts;
- i++;
- }
-
- std::sort(cov_number.begin(), cov_number.end());
- std::vector<int>::iterator it = std::unique(cov_number.begin(), cov_number.end());
- cov_number.resize(std::distance(cov_number.begin(), it));
-
- maximal_dim = cov_number.size() - 1;
- for (int i = 0; i <= maximal_dim; i++) cover_color[i].second /= cover_color[i].first;
- cover_name = cover_file_name;
- }
-
- public: // Set cover from Voronoi
- /** \brief Creates the cover C from the Voronoï cells of a subsampling of the point cloud.
- *
- * @param[in] distance distance between the points.
- * @param[in] m number of points in the subsample.
- *
- */
- template <typename Distance>
- void set_cover_from_Voronoi(Distance distance, int m = 100) {
- voronoi_subsamples.resize(m);
- SampleWithoutReplacement(n, m, voronoi_subsamples);
- if (distances.size() == 0) compute_pairwise_distances(distance);
- set_graph_weights();
- Weight_map weight = boost::get(boost::edge_weight, one_skeleton);
- Index_map index = boost::get(boost::vertex_index, one_skeleton);
- std::vector<double> mindist(n);
- for (int j = 0; j < n; j++) mindist[j] = std::numeric_limits<double>::max();
-
- // Compute the geodesic distances to subsamples with Dijkstra
- #ifdef GUDHI_USE_TBB
- if (verbose) std::cout << "Computing geodesic distances (parallelized)..." << std::endl;
- tbb::mutex coverMutex; tbb::mutex mindistMutex;
- tbb::parallel_for(0, m, [&](int i){
- int seed = voronoi_subsamples[i];
- std::vector<double> dmap(n);
- boost::dijkstra_shortest_paths(
- one_skeleton, vertices[seed],
- boost::weight_map(weight).distance_map(boost::make_iterator_property_map(dmap.begin(), index)));
-
- coverMutex.lock(); mindistMutex.lock();
- for (int j = 0; j < n; j++)
- if (mindist[j] > dmap[j]) {
- mindist[j] = dmap[j];
- if (cover[j].size() == 0)
- cover[j].push_back(i);
- else
- cover[j][0] = i;
- }
- coverMutex.unlock(); mindistMutex.unlock();
- });
- #else
- for (int i = 0; i < m; i++) {
- if (verbose) std::cout << "Computing geodesic distances to seed " << i << "..." << std::endl;
- int seed = voronoi_subsamples[i];
- std::vector<double> dmap(n);
- boost::dijkstra_shortest_paths(
- one_skeleton, vertices[seed],
- boost::weight_map(weight).distance_map(boost::make_iterator_property_map(dmap.begin(), index)));
-
- for (int j = 0; j < n; j++)
- if (mindist[j] > dmap[j]) {
- mindist[j] = dmap[j];
- if (cover[j].size() == 0)
- cover[j].push_back(i);
- else
- cover[j][0] = i;
- }
- }
- #endif
-
- for (int i = 0; i < n; i++) {
- cover_back[cover[i][0]].push_back(i);
- cover_color[cover[i][0]].second += func_color[i];
- cover_color[cover[i][0]].first++;
- }
- for (int i = 0; i < m; i++) cover_color[i].second /= cover_color[i].first;
- maximal_dim = m - 1;
- cover_name = "Voronoi";
- }
-
- public: // return subset of data corresponding to a node
- /** \brief Returns the data subset corresponding to a specific node of the created complex.
- *
- * @param[in] c ID of the node.
- * @result cover_back(c) vector of IDs of data points.
- *
- */
- const std::vector<int>& subpopulation(int c) { return cover_back[name2idinv[c]]; }
-
- // *******************************************************************************************************************
- // Visualization.
- // *******************************************************************************************************************
-
- public: // Set color from file.
- /** \brief Computes the function used to color the nodes of the simplicial complex from a file containing the function
- * values.
- *
- * @param[in] color_file_name name of the input color file.
- *
- */
- void set_color_from_file(const std::string& color_file_name) {
- int i = 0;
- std::ifstream input(color_file_name);
- std::string line;
- double f;
- while (std::getline(input, line)) {
- std::stringstream stream(line);
- stream >> f;
- func_color.push_back(f);
- i++;
- }
- color_name = color_file_name;
- }
-
- public: // Set color from kth coordinate
- /** \brief Computes the function used to color the nodes of the simplicial complex from the k-th coordinate.
- *
- * @param[in] k coordinate to use (start at 0).
- *
- */
- void set_color_from_coordinate(int k = 0) {
- for (int i = 0; i < n; i++) func_color.push_back(point_cloud[i][k]);
- color_name = "coordinate ";
- color_name.append(std::to_string(k));
- }
-
- public: // Set color from vector.
- /** \brief Computes the function used to color the nodes of the simplicial complex from a vector stored in memory.
- *
- * @param[in] color input vector of values.
- *
- */
- void set_color_from_vector(std::vector<double> color) {
- for (unsigned int i = 0; i < color.size(); i++) func_color.push_back(color[i]);
- }
-
- public: // Create a .dot file that can be compiled with neato to produce a .pdf file.
- /** \brief Creates a .dot file called SC.dot for neato (part of the graphviz package) once the simplicial complex is
- * computed to get a visualization
- * of its 1-skeleton in a .pdf file.
- */
- void plot_DOT() {
- std::string mapp = point_cloud_name + "_sc.dot";
- std::ofstream graphic(mapp);
-
- double maxv = std::numeric_limits<double>::lowest();
- double minv = std::numeric_limits<double>::max();
- for (std::map<int, std::pair<int, double> >::iterator iit = cover_color.begin(); iit != cover_color.end(); iit++) {
- maxv = std::max(maxv, iit->second.second);
- minv = std::min(minv, iit->second.second);
- }
-
- int k = 0;
- std::vector<int> nodes;
- nodes.clear();
-
- graphic << "graph GIC {" << std::endl;
- int id = 0;
- for (std::map<int, std::pair<int, double> >::iterator iit = cover_color.begin(); iit != cover_color.end(); iit++) {
- if (iit->second.first > mask) {
- nodes.push_back(iit->first);
- name2id[iit->first] = id;
- name2idinv[id] = iit->first;
- id++;
- graphic << name2id[iit->first] << "[shape=circle fontcolor=black color=black label=\"" << name2id[iit->first]
- << ":" << iit->second.first << "\" style=filled fillcolor=\""
- << (1 - (maxv - iit->second.second) / (maxv - minv)) * 0.6 << ", 1, 1\"]" << std::endl;
- k++;
- }
- }
- int ke = 0;
- int num_simplices = simplices.size();
- for (int i = 0; i < num_simplices; i++)
- if (simplices[i].size() == 2) {
- if (cover_color[simplices[i][0]].first > mask && cover_color[simplices[i][1]].first > mask) {
- graphic << " " << name2id[simplices[i][0]] << " -- " << name2id[simplices[i][1]] << " [weight=15];"
- << std::endl;
- ke++;
- }
- }
- graphic << "}";
- graphic.close();
- std::cout << mapp << " file generated. It can be visualized with e.g. neato." << std::endl;
- }
-
- public: // Create a .txt file that can be compiled with KeplerMapper.
- /** \brief Creates a .txt file called SC.txt describing the 1-skeleton, which can then be plotted with e.g.
- * KeplerMapper.
- */
- void write_info() {
- int num_simplices = simplices.size();
- int num_edges = 0;
- std::string mapp = point_cloud_name + "_sc.txt";
- std::ofstream graphic(mapp);
-
- for (int i = 0; i < num_simplices; i++)
- if (simplices[i].size() == 2)
- if (cover_color[simplices[i][0]].first > mask && cover_color[simplices[i][1]].first > mask) num_edges++;
-
- graphic << point_cloud_name << std::endl;
- graphic << cover_name << std::endl;
- graphic << color_name << std::endl;
- graphic << resolution_double << " " << gain << std::endl;
- graphic << cover_color.size() << " " << num_edges << std::endl;
-
- int id = 0;
- for (std::map<int, std::pair<int, double> >::iterator iit = cover_color.begin(); iit != cover_color.end(); iit++) {
- graphic << id << " " << iit->second.second << " " << iit->second.first << std::endl;
- name2id[iit->first] = id;
- name2idinv[id] = iit->first;
- id++;
- }
-
- for (int i = 0; i < num_simplices; i++)
- if (simplices[i].size() == 2)
- if (cover_color[simplices[i][0]].first > mask && cover_color[simplices[i][1]].first > mask)
- graphic << name2id[simplices[i][0]] << " " << name2id[simplices[i][1]] << std::endl;
- graphic.close();
- std::cout << mapp
- << " generated. It can be visualized with e.g. python KeplerMapperVisuFromTxtFile.py and firefox."
- << std::endl;
- }
-
- public: // Create a .off file that can be visualized (e.g. with Geomview).
- /** \brief Creates a .off file called SC.off for 3D visualization, which contains the 2-skeleton of the GIC.
- * This function assumes that the cover has been computed with Voronoi. If data points are in 1D or 2D,
- * the remaining coordinates of the points embedded in 3D are set to 0.
- */
- void plot_OFF() {
- assert(cover_name == "Voronoi");
-
- int m = voronoi_subsamples.size();
- int numedges = 0;
- int numfaces = 0;
- std::vector<std::vector<int> > edges, faces;
- int numsimplices = simplices.size();
-
- std::string mapp = point_cloud_name + "_sc.off";
- std::ofstream graphic(mapp);
-
- graphic << "OFF" << std::endl;
- for (int i = 0; i < numsimplices; i++) {
- if (simplices[i].size() == 2) {
- numedges++;
- edges.push_back(simplices[i]);
- }
- if (simplices[i].size() == 3) {
- numfaces++;
- faces.push_back(simplices[i]);
- }
- }
- graphic << m << " " << numedges + numfaces << std::endl;
- for (int i = 0; i < m; i++) {
- if (data_dimension <= 3) {
- for (int j = 0; j < data_dimension; j++) graphic << point_cloud[voronoi_subsamples[i]][j] << " ";
- for (int j = data_dimension; j < 3; j++) graphic << 0 << " ";
- graphic << std::endl;
- } else {
- for (int j = 0; j < 3; j++) graphic << point_cloud[voronoi_subsamples[i]][j] << " ";
- }
- }
- for (int i = 0; i < numedges; i++) graphic << 2 << " " << edges[i][0] << " " << edges[i][1] << std::endl;
- for (int i = 0; i < numfaces; i++)
- graphic << 3 << " " << faces[i][0] << " " << faces[i][1] << " " << faces[i][2] << std::endl;
- graphic.close();
- std::cout << mapp << " generated. It can be visualized with e.g. geomview." << std::endl;
- }
-
- // *******************************************************************************************************************
- // Extended Persistence Diagrams.
- // *******************************************************************************************************************
-
- public:
- /** \brief Computes the extended persistence diagram of the complex.
- *
- */
- void compute_PD() {
- Simplex_tree st;
-
- // Compute max and min
- double maxf = std::numeric_limits<double>::lowest();
- double minf = std::numeric_limits<double>::max();
- for (std::map<int, double>::iterator it = cover_std.begin(); it != cover_std.end(); it++) {
- maxf = std::max(maxf, it->second);
- minf = std::min(minf, it->second);
- }
-
- // Build filtration
- for (auto const& simplex : simplices) {
- std::vector<int> splx = simplex; splx.push_back(-2);
- st.insert_simplex_and_subfaces(splx, -3);
- }
-
- for (std::map<int, double>::iterator it = cover_std.begin(); it != cover_std.end(); it++) {
- int vertex = it->first; float val = it->second;
- int vert[] = {vertex}; int edge[] = {vertex, -2};
- st.assign_filtration(st.find(vert), -2 + (val - minf)/(maxf - minf));
- st.assign_filtration(st.find(edge), 2 - (val - minf)/(maxf - minf));
- }
- st.make_filtration_non_decreasing();
-
- // Compute PD
- Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Gudhi::persistent_cohomology::Field_Zp> pcoh(st); pcoh.init_coefficients(2);
- pcoh.compute_persistent_cohomology();
-
- // Output PD
- int max_dim = st.dimension();
- for (int i = 0; i < max_dim; i++) {
- std::vector<std::pair<double, double> > bars = pcoh.intervals_in_dimension(i);
- int num_bars = bars.size(); if(i == 0) num_bars -= 1;
- if(verbose) std::cout << num_bars << " interval(s) in dimension " << i << ":" << std::endl;
- for (int j = 0; j < num_bars; j++) {
- double birth = bars[j].first;
- double death = bars[j].second;
- if (i == 0 && std::isinf(death)) continue;
- if (birth < 0)
- birth = minf + (birth + 2) * (maxf - minf);
- else
- birth = minf + (2 - birth) * (maxf - minf);
- if (death < 0)
- death = minf + (death + 2) * (maxf - minf);
- else
- death = minf + (2 - death) * (maxf - minf);
- PD.push_back(std::pair<double, double>(birth, death));
- if (verbose) std::cout << " [" << birth << ", " << death << "]" << std::endl;
- }
- }
- }
-
- public:
- /** \brief Computes bootstrapped distances distribution.
- *
- * @param[in] N number of bootstrap iterations.
- *
- */
- void compute_distribution(unsigned int N = 100) {
- unsigned int sz = distribution.size();
- if (sz >= N) {
- std::cout << "Already done!" << std::endl;
- } else {
- for (unsigned int i = 0; i < N - sz; i++) {
- if (verbose) std::cout << "Computing " << i << "th bootstrap, bottleneck distance = ";
-
- Cover_complex Cboot; Cboot.n = this->n; Cboot.data_dimension = this->data_dimension; Cboot.type = this->type; Cboot.functional_cover = true;
-
- std::vector<int> boot(this->n);
- for (int j = 0; j < this->n; j++) {
- double u = GetUniform();
- int id = std::floor(u * (this->n)); boot[j] = id;
- Cboot.point_cloud.push_back(this->point_cloud[id]); Cboot.cover.emplace_back(); Cboot.func.push_back(this->func[id]);
- boost::add_vertex(Cboot.one_skeleton_OFF); Cboot.vertices.push_back(boost::add_vertex(Cboot.one_skeleton));
- }
- Cboot.set_color_from_vector(Cboot.func);
-
- for (int j = 0; j < n; j++) {
- std::vector<double> dist(n);
- for (int k = 0; k < n; k++) dist[k] = distances[boot[j]][boot[k]];
- Cboot.distances.push_back(dist);
- }
-
- Cboot.set_graph_from_automatic_rips(Gudhi::Euclidean_distance());
- Cboot.set_gain();
- Cboot.set_automatic_resolution();
- Cboot.set_cover_from_function();
- Cboot.find_simplices();
- Cboot.compute_PD();
- double db = Gudhi::persistence_diagram::bottleneck_distance(this->PD, Cboot.PD);
- if (verbose) std::cout << db << std::endl;
- distribution.push_back(db);
- }
-
- std::sort(distribution.begin(), distribution.end());
- }
- }
-
- public:
- /** \brief Computes the bottleneck distance threshold corresponding to a specific confidence level.
- *
- * @param[in] alpha Confidence level.
- *
- */
- double compute_distance_from_confidence_level(double alpha) {
- unsigned int N = distribution.size();
- double d = distribution[std::floor(alpha * N)];
- if (verbose) std::cout << "Distance corresponding to confidence " << alpha << " is " << d << std::endl;
- return d;
- }
-
- public:
- /** \brief Computes the confidence level of a specific bottleneck distance threshold.
- *
- * @param[in] d Bottleneck distance.
- *
- */
- double compute_confidence_level_from_distance(double d) {
- unsigned int N = distribution.size();
- double level = 1;
- for (unsigned int i = 0; i < N; i++)
- if (distribution[i] > d){ level = i * 1.0 / N; break; }
- if (verbose) std::cout << "Confidence level of distance " << d << " is " << level << std::endl;
- return level;
- }
-
- public:
- /** \brief Computes the p-value, i.e. the opposite of the confidence level of the largest bottleneck
- * distance preserving the points in the persistence diagram of the output simplicial complex.
- *
- */
- double compute_p_value() {
- double distancemin = std::numeric_limits<double>::max(); int N = PD.size();
- for (int i = 0; i < N; i++) distancemin = std::min(distancemin, 0.5 * std::abs(PD[i].second - PD[i].first));
- double p_value = 1 - compute_confidence_level_from_distance(distancemin);
- if (verbose) std::cout << "p value = " << p_value << std::endl;
- return p_value;
- }
-
- // *******************************************************************************************************************
- // Computation of simplices.
- // *******************************************************************************************************************
-
- public:
- /** \brief Creates the simplicial complex.
- *
- * @param[in] complex SimplicialComplex to be created.
- *
- */
- template <typename SimplicialComplex>
- void create_complex(SimplicialComplex& complex) {
- unsigned int dimension = 0;
- for (auto const& simplex : simplices) {
- int numvert = simplex.size();
- double filt = std::numeric_limits<double>::lowest();
- for (int i = 0; i < numvert; i++) filt = std::max(cover_color[simplex[i]].second, filt);
- complex.insert_simplex_and_subfaces(simplex, filt);
- if (dimension < simplex.size() - 1) dimension = simplex.size() - 1;
- }
- }
-
- public:
- /** \brief Computes the simplices of the simplicial complex.
- */
- void find_simplices() {
- if (type != "Nerve" && type != "GIC") {
- std::cout << "Type of complex needs to be specified." << std::endl;
- return;
- }
-
- if (type == "Nerve") {
- for(int i = 0; i < n; i++) simplices.push_back(cover[i]);
- std::sort(simplices.begin(), simplices.end());
- std::vector<std::vector<int> >::iterator it = std::unique(simplices.begin(), simplices.end());
- simplices.resize(std::distance(simplices.begin(), it));
- }
-
- if (type == "GIC") {
- Index_map index = boost::get(boost::vertex_index, one_skeleton);
-
- if (functional_cover) {
- // Computes the simplices in the GIC by looking at all the edges of the graph and adding the
- // corresponding edges in the GIC if the images of the endpoints belong to consecutive intervals.
-
- if (gain >= 0.5)
- throw std::invalid_argument(
- "the output of this function is correct ONLY if the cover is minimal, i.e. the gain is less than 0.5.");
-
- // Loop on all edges.
- boost::graph_traits<Graph>::edge_iterator ei, ei_end;
- for (boost::tie(ei, ei_end) = boost::edges(one_skeleton); ei != ei_end; ++ei) {
- int nums = cover[index[boost::source(*ei, one_skeleton)]].size();
- for (int i = 0; i < nums; i++) {
- int vs = cover[index[boost::source(*ei, one_skeleton)]][i];
- int numt = cover[index[boost::target(*ei, one_skeleton)]].size();
- for (int j = 0; j < numt; j++) {
- int vt = cover[index[boost::target(*ei, one_skeleton)]][j];
- if (cover_fct[vs] == cover_fct[vt] + 1 || cover_fct[vt] == cover_fct[vs] + 1) {
- std::vector<int> edge(2);
- edge[0] = std::min(vs, vt);
- edge[1] = std::max(vs, vt);
- simplices.push_back(edge);
- goto afterLoop;
- }
- }
- }
- afterLoop:;
- }
- std::sort(simplices.begin(), simplices.end());
- std::vector<std::vector<int> >::iterator it = std::unique(simplices.begin(), simplices.end());
- simplices.resize(std::distance(simplices.begin(), it));
-
- } else {
- // Find edges to keep
- Simplex_tree st;
- boost::graph_traits<Graph>::edge_iterator ei, ei_end;
- for (boost::tie(ei, ei_end) = boost::edges(one_skeleton); ei != ei_end; ++ei)
- if (!(cover[index[boost::target(*ei, one_skeleton)]].size() == 1 &&
- cover[index[boost::target(*ei, one_skeleton)]] == cover[index[boost::source(*ei, one_skeleton)]])) {
- std::vector<int> edge(2);
- edge[0] = index[boost::source(*ei, one_skeleton)];
- edge[1] = index[boost::target(*ei, one_skeleton)];
- st.insert_simplex_and_subfaces(edge);
- }
-
- // st.insert_graph(one_skeleton);
-
- // Build the Simplex Tree corresponding to the graph
- st.expansion(maximal_dim);
-
- // Find simplices of GIC
- simplices.clear();
- for (auto simplex : st.complex_simplex_range()) {
- if (!st.has_children(simplex)) {
- std::vector<int> simplx;
- for (auto vertex : st.simplex_vertex_range(simplex)) {
- unsigned int sz = cover[vertex].size();
- for (unsigned int i = 0; i < sz; i++) {
- simplx.push_back(cover[vertex][i]);
- }
- }
- std::sort(simplx.begin(), simplx.end());
- std::vector<int>::iterator it = std::unique(simplx.begin(), simplx.end());
- simplx.resize(std::distance(simplx.begin(), it));
- simplices.push_back(simplx);
- }
- }
- std::sort(simplices.begin(), simplices.end());
- std::vector<std::vector<int> >::iterator it = std::unique(simplices.begin(), simplices.end());
- simplices.resize(std::distance(simplices.begin(), it));
- }
- }
- }
-};
-
-} // namespace cover_complex
-
-} // namespace Gudhi
-
-#endif // GIC_H_
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