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Diffstat (limited to 'src/Witness_complex/example/witness_complex_cubic_systems.cpp')
| -rw-r--r-- | src/Witness_complex/example/witness_complex_cubic_systems.cpp | 547 |
1 files changed, 547 insertions, 0 deletions
diff --git a/src/Witness_complex/example/witness_complex_cubic_systems.cpp b/src/Witness_complex/example/witness_complex_cubic_systems.cpp new file mode 100644 index 00000000..2f4ee1cb --- /dev/null +++ b/src/Witness_complex/example/witness_complex_cubic_systems.cpp @@ -0,0 +1,547 @@ +/* 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): Siargey Kachanovich + * + * Copyright (C) 2015 INRIA Sophia Antipolis-Méditerranée (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/>. + */ + +#include <iostream> +#include <fstream> +#include <ctime> +#include <utility> +#include <algorithm> +#include <set> +#include <iterator> + +#include <sys/types.h> +#include <sys/stat.h> +#include <unistd.h> + +//#include "gudhi/graph_simplicial_complex.h" +#include "gudhi/Witness_complex.h" +#include "gudhi/reader_utils.h" +#include "Torus_distance.h" + +#include <CGAL/Cartesian_d.h> +#include <CGAL/Search_traits.h> +#include <CGAL/Search_traits_adapter.h> +#include <CGAL/property_map.h> +#include <CGAL/Epick_d.h> +#include <CGAL/Orthogonal_k_neighbor_search.h> +#include <CGAL/Kd_tree.h> +#include <CGAL/Euclidean_distance.h> +#include <CGAL/Kernel_d/Sphere_d.h> + +#include <CGAL/Kernel_d/Vector_d.h> +#include <CGAL/point_generators_d.h> +#include <CGAL/constructions_d.h> +#include <CGAL/Fuzzy_sphere.h> +#include <CGAL/Random.h> +#include <CGAL/Delaunay_triangulation.h> + + +#include <boost/tuple/tuple.hpp> +#include <boost/iterator/zip_iterator.hpp> +#include <boost/iterator/counting_iterator.hpp> +#include <boost/range/iterator_range.hpp> + +using namespace Gudhi; +//using namespace boost::filesystem; + +typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K; +typedef K::Point_d Point_d; +//typedef CGAL::Cartesian_d<double> K; +//typedef CGAL::Point_d<K> Point_d; +typedef K::FT FT; +typedef CGAL::Search_traits< + FT, Point_d, + typename K::Cartesian_const_iterator_d, + typename K::Construct_cartesian_const_iterator_d> Traits_base; +typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance; + + +typedef std::vector< Vertex_handle > typeVectorVertex; + +//typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex; +//typedef std::pair< Simplex_tree<>::Simplex_handle, bool > typePairSimplexBool; + +typedef CGAL::Search_traits_adapter< + std::ptrdiff_t, Point_d*, Traits_base> STraits; +//typedef K TreeTraits; +//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter; +//typedef CGAL::Kd_tree<STraits> Kd_tree; +typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search; +typedef K_neighbor_search::Tree Tree; +typedef K_neighbor_search::Distance Distance; +typedef K_neighbor_search::iterator KNS_iterator; +typedef K_neighbor_search::iterator KNS_range; +typedef boost::container::flat_map<int, int> Point_etiquette_map; +typedef CGAL::Kd_tree<STraits> Tree2; + +typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere; + +typedef std::vector<Point_d> Point_Vector; + +//typedef K::Equal_d Equal_d; +//typedef CGAL::Random_points_in_cube_d<CGAL::Point_d<CGAL::Cartesian_d<FT> > > Random_cube_iterator; +typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator; +typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator; + +typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation; +typedef Delaunay_triangulation::Facet Facet; +typedef CGAL::Sphere_d<K> Sphere_d; + +bool toric=false; + + +/** + * \brief Customized version of read_points + * which takes into account a possible nbP first line + * + */ +inline void +read_points_cust ( std::string file_name , Point_Vector & points) +{ + std::ifstream in_file (file_name.c_str(),std::ios::in); + if(!in_file.is_open()) + { + std::cerr << "Unable to open file " << file_name << std::endl; + return; + } + std::string line; + double x; + while( getline ( in_file , line ) ) + { + std::vector< double > point; + std::istringstream iss( line ); + while(iss >> x) { point.push_back(x); } + Point_d p(point.begin(), point.end()); + if (point.size() != 1) + points.push_back(p); + } + in_file.close(); +} + +void generate_points_random_box(Point_Vector& W, int nbP, int dim) +{ + /* + Random_cube_iterator rp(dim, 1); + for (int i = 0; i < nbP; i++) + { + std::vector<double> point; + for (auto it = rp->cartesian_begin(); it != rp->cartesian_end(); ++it) + point.push_back(*it); + W.push_back(Point_d(point)); + rp++; + } + */ + Random_cube_iterator rp(dim, 1.0); + for (int i = 0; i < nbP; i++) + { + W.push_back(*rp++); + } +} + + +void write_wl( std::string file_name, std::vector< std::vector <int> > & WL) +{ + std::ofstream ofs (file_name, std::ofstream::out); + for (auto w : WL) + { + for (auto l: w) + ofs << l << " "; + ofs << "\n"; + } + ofs.close(); +} + + +void write_points( std::string file_name, std::vector< Point_d > & points) +{ + std::ofstream ofs (file_name, std::ofstream::out); + for (auto w : points) + { + for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it) + ofs << *it << " "; + ofs << "\n"; + } + ofs.close(); +} + +void write_edges(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks) +{ + std::ofstream ofs (file_name, std::ofstream::out); + for (auto u: witness_complex.complex_vertex_range()) + for (auto v: witness_complex.complex_vertex_range()) + { + typeVectorVertex edge = {u,v}; + if (u < v && witness_complex.find(edge) != witness_complex.null_simplex()) + { + for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it) + ofs << *it << " "; + ofs << "\n"; + for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it) + ofs << *it << " "; + ofs << "\n\n\n"; + } + } + ofs.close(); +} + + +/** Function that chooses landmarks from W and place it in the kd-tree L. + * Note: nbL hould be removed if the code moves to Witness_complex + */ +void landmark_choice(Point_Vector &W, int nbP, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind) +{ + std::cout << "Enter landmark choice to kd tree\n"; + int chosen_landmark; + Point_d* p; + CGAL::Random rand; + for (int i = 0; i < nbL; i++) + { + // while (!res.second) + // { + do chosen_landmark = rand.get_int(0,nbP); + while (std::count(landmarks_ind.begin(),landmarks_ind.end(),chosen_landmark)!=0); + //rand++; + //std::cout << "Chose " << chosen_landmark << std::endl; + p = &W[chosen_landmark]; + //L_i.emplace(chosen_landmark,i); + // } + landmarks.push_back(*p); + landmarks_ind.push_back(chosen_landmark); + //std::cout << "Added landmark " << chosen_landmark << std::endl; + } + } + +void aux_fill_grid(Point_Vector& W, int& width, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<bool> & curr_pattern) +{ + int D = W[0].size(); + int nb_points = 1; + for (int i = 0; i < D; ++i) + nb_points *= width; + for (int i = 0; i < nb_points; ++i) + { + std::vector<double> point; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + if (curr_pattern[l]) + point.push_back(-1.0+(2.0/width)*(cell_i%width)+(1.0/width)); + else + point.push_back(-1.0+(2.0/width)*(cell_i%width)); + cell_i /= width; + } + landmarks.push_back(Point_d(point)); + landmarks_ind.push_back(0);//landmarks_ind.push_back(W.size()); + //std::cout << "Added point " << W.size() << std::endl;; + //W.push_back(Point_d(point)); + } +} + +void aux_put_halves(Point_Vector& W, int& width, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<bool>& curr_pattern, std::vector<bool>::iterator curr_pattern_it, std::vector<bool>::iterator bool_it, std::vector<bool>::iterator bool_end) +{ + if (curr_pattern_it != curr_pattern.end()) + { + if (bool_it != bool_end) + { + *curr_pattern_it = false; + aux_put_halves(W, width, landmarks, landmarks_ind, curr_pattern, curr_pattern_it+1, bool_it, bool_end); + *curr_pattern_it = true; + aux_put_halves(W, width, landmarks, landmarks_ind, curr_pattern, curr_pattern_it+1, bool_it+1, bool_end); + } + } + else + if (*bool_it) + { + std::cout << "Filling the pattern "; + for (bool b: curr_pattern) + if (b) std::cout << '1'; + else std::cout << '0'; + std::cout << "\n"; + aux_fill_grid(W, width, landmarks, landmarks_ind, curr_pattern); + } +} + +void landmark_choice_cs(Point_Vector& W, int width, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<bool>& face_centers) +{ + std::cout << "Enter landmark choice to kd tree\n"; + //int chosen_landmark; + CGAL::Random rand; + //To speed things up check the last true in the code and put it as the finishing condition + unsigned last_true = face_centers.size()-1; + while (!face_centers[last_true] && last_true != 0) + last_true--; + //Recursive procedure to understand where we put +1/2 in centers' coordinates + std::vector<bool> curr_pattern(W[0].size(), false); + aux_put_halves(W, width, landmarks, landmarks_ind, curr_pattern, curr_pattern.begin(), face_centers.begin(), face_centers.begin()+(last_true+1)); + std::cout << "The number of landmarks is: " << landmarks.size() << std::endl; + + } + +int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector<int>& landmarks_ind) +{ + //******************** Preface: origin point + int D = W[0].size(); + std::vector<FT> orig_vector; + for (int i=0; i<D; i++) + orig_vector.push_back(0); + Point_d origin(orig_vector); + + //******************** Constructing a WL matrix + int nbP = W.size(); + int nbL = landmarks.size(); + Euclidean_distance ed; + FT lambda = ed.transformed_distance(landmarks[0],landmarks[1]); + std::vector<Point_d> landmarks_ext; + int nb_cells = 1; + for (int i = 0; i < D; ++i) + nb_cells *= 3; + for (int i = 0; i < nb_cells; ++i) + for (int k = 0; k < nbL; ++k) + { + std::vector<double> point; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + point.push_back(landmarks[k][l] + 2.0*((cell_i%3)-1.0)); + cell_i /= 3; + } + landmarks_ext.push_back(point); + } + write_points("landmarks/initial_landmarks",landmarks_ext); + STraits traits(&(landmarks_ext[0])); + std::vector< std::vector <int> > WL(nbP); + + //********************** Neighbor search in a Kd tree + Tree L(boost::counting_iterator<std::ptrdiff_t>(0), + boost::counting_iterator<std::ptrdiff_t>(nb_cells*nbL), + typename Tree::Splitter(), + traits); + std::cout << "Enter (D+1) nearest landmarks\n"; + for (int i = 0; i < nbP; i++) + { + Point_d& w = W[i]; + ////Search D+1 nearest neighbours from the tree of landmarks L + K_neighbor_search search(L, w, D+1, FT(0), true, + CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>(&(landmarks_ext[0])) ); + for(K_neighbor_search::iterator it = search.begin(); it != search.end(); ++it) + { + if (std::find(WL[i].begin(), WL[i].end(), (it->first)%nbL) == WL[i].end()) + WL[i].push_back((it->first)%nbL); + } + if (i == landmarks_ind[WL[i][0]]) + { + FT dist = ed.transformed_distance(W[i], landmarks[WL[i][1]]); + if (dist < lambda) + lambda = dist; + } + } + std::string out_file = "wl_result"; + write_wl(out_file,WL); + + //******************** Constructng a witness complex + std::cout << "Entered witness complex construction\n"; + Witness_complex<> witnessComplex; + witnessComplex.setNbL(nbL); + witnessComplex.witness_complex(WL); + + //******************** Making a set of bad link landmarks + std::cout << "Entered bad links\n"; + std::set< int > perturbL; + int count_badlinks = 0; + //std::cout << "Bad links around "; + std::vector< int > count_bad(D); + std::vector< int > count_good(D); + for (auto u: witnessComplex.complex_vertex_range()) + { + if (!witnessComplex.has_good_link(u, count_bad, count_good, D)) + { + count_badlinks++; + Point_d& l = landmarks[u]; + Fuzzy_sphere fs(l, sqrt(lambda)*3, 0, traits); + std::vector<int> curr_perturb; + L.search(std::insert_iterator<std::vector<int>>(curr_perturb,curr_perturb.begin()),fs); + for (int i: curr_perturb) + perturbL.insert(i%nbL); + } + } + for (unsigned int i = 0; i != count_good.size(); i++) + if (count_good[i] != 0) + std::cout << "count_good[" << i << "] = " << count_good[i] << std::endl; + for (unsigned int i = 0; i != count_bad.size(); i++) + if (count_bad[i] != 0) + std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl; + std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl; + + //*********************** Perturb bad link landmarks + for (auto u: perturbL) + { + Random_point_iterator rp(D,sqrt(lambda)/8); + std::vector<FT> point; + for (int i = 0; i < D; i++) + { + while (K().squared_distance_d_object()(*rp,origin) < lambda/256) + rp++; + FT coord = landmarks[u][i] + (*rp)[i]; + if (coord > 1) + point.push_back(coord-1); + else if (coord < -1) + point.push_back(coord+1); + else + point.push_back(coord); + } + landmarks[u] = Point_d(point); + } + std::cout << "lambda=" << lambda << std::endl; + char buffer[100]; + int i = sprintf(buffer,"stree_result.txt"); + + if (i >= 0) + { + std::string out_file = (std::string)buffer; + std::ofstream ofs (out_file, std::ofstream::out); + witnessComplex.st_to_file(ofs); + ofs.close(); + } + write_edges("landmarks/edges", witnessComplex, landmarks); + return count_badlinks; +} + +void exaustive_search(Point_Vector& W, int width) +{ + int D = W[0].size()+1; + int nb_points = pow(2,D); + std::vector<bool> face_centers(D, false); + int bl = 0; //Bad links + std::vector<std::vector<bool>> good_patterns; + for (int i = 0; i < nb_points; ++i) + { + int cell_i = i; + for (int l = 0; l < D; ++l) + { + if (cell_i%2 == 0) + face_centers[l] = false; + else + face_centers[l] = true; + cell_i /= 2; + } + std::cout << "**Current pattern "; + for (bool b: face_centers) + if (b) std::cout << '1'; + else std::cout << '0'; + std::cout << "\n"; + Point_Vector landmarks; + std::vector<int> landmarks_ind; + Point_Vector W_copy(W); + landmark_choice_cs(W_copy, width, landmarks, landmarks_ind, face_centers); + if (landmarks.size() != 0) + { + bl = landmark_perturbation(W_copy, landmarks, landmarks_ind); + if ((1.0*bl)/landmarks.size() < 0.5) + good_patterns.push_back(face_centers); + } + } + std::cout << "The following patterns worked: "; + for (std::vector<bool> pattern : good_patterns) + { + std::cout << "["; + for (bool b: pattern) + if (b) std::cout << '1'; + else std::cout << '0'; + std::cout << "] "; + } + std::cout << "\n"; +} + +int main (int argc, char * const argv[]) +{ + unsigned nbP = atoi(argv[1]); + unsigned width = atoi(argv[2]); + unsigned dim = atoi(argv[3]); + std::string code = (std::string) argv[4]; + bool e_option = false; + int c; + if (argc != 5) + { + std::cerr << "Usage: " << argv[0] + << "witness_complex_cubic_systems nbP width dim code || witness_complex_systems -e nbP width dim\n" + << "where nbP stands for the number of witnesses, width for the width of the grid, dim for dimension " + << "and code is a sequence of (dim+1) symbols 0 and 1 representing if we take the centers of k-dimensional faces of the cubic system depending if it is 0 or 1." + << "-e stands for the 'exaustive' option"; + return 0; + } + while ((c = getopt (argc, argv, "e::")) != -1) + switch(c) + { + case 'e' : + e_option = true; + nbP = atoi(argv[2]); + width = atoi(argv[3]); + dim = atoi(argv[4]); + break; + default : + nbP = atoi(argv[1]); + width = atoi(argv[2]); + dim = atoi(argv[3]); + code = (std::string) argv[4]; + } + Point_Vector point_vector; + generate_points_random_box(point_vector, nbP, dim); + + // Exaustive search + if (e_option) + { + std::cout << "Start exaustive search!\n"; + exaustive_search(point_vector, width); + return 0; + } + // Search with a specific cubic system + std::vector<bool> face_centers; + if (code.size() != dim+1) + { + std::cerr << "The code should contain (dim+1) symbols"; + return 1; + } + for (char c: code) + if (c == '0') + face_centers.push_back(false); + else + face_centers.push_back(true); + std::cout << "Let the carnage begin!\n"; + Point_Vector L; + std::vector<int> chosen_landmarks; + + landmark_choice_cs(point_vector, width, L, chosen_landmarks, face_centers); + + int nbL = width; //!!!!!!!!!!!!! + int bl = nbL, curr_min = bl; + write_points("landmarks/initial_pointset",point_vector); + //write_points("landmarks/initial_landmarks",L); + //for (int i = 0; i < 1; i++) + for (int i = 0; bl > 0; i++) + { + std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n"; + bl=landmark_perturbation(point_vector, L, chosen_landmarks); + if (bl < curr_min) + curr_min=bl; + write_points("landmarks/landmarks0",L); + } + +} |