text: /*    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 "weighted_alpha_complex"
  #include <boost/test/unit_test.hpp>
  #include <boost/mpl/list.hpp>
  
  #include <CGAL/Epick_d.h>
  #include <CGAL/Epeck_d.h>
  
  #include <cmath>  // float comparison
  #include <vector>
  #include <random>
  #include <array>
  #include <cmath> // for std::fabs
  
  #include <gudhi/Alpha_complex.h>
  #include <gudhi/Alpha_complex_3d.h>
  #include <gudhi/Simplex_tree.h>
  #include <gudhi/Unitary_tests_utils.h>
  
  using list_of_exact_kernel_variants = boost::mpl::list<CGAL::Epeck_d< CGAL::Dynamic_dimension_tag >,
                                                         CGAL::Epeck_d< CGAL::Dimension_tag<4> >
                                                         > ;
  
  BOOST_AUTO_TEST_CASE_TEMPLATE(Zero_weighted_alpha_complex, Kernel, list_of_exact_kernel_variants) {
    // Check that in exact mode for static dimension 4 the code for dD unweighted and for dD weighted with all weights
    // 0 give exactly the same simplex tree (simplices and filtration values).
  
    // Random points construction
    using Point_d = typename Kernel::Point_d;
    std::vector<Point_d> points;
    std::uniform_real_distribution<double> rd_pts(-10., 10.);
    std::random_device rand_dev;
    std::mt19937 rand_engine(rand_dev());
    for (int idx = 0; idx < 20; idx++) {
      std::vector<double> point {rd_pts(rand_engine), rd_pts(rand_engine), rd_pts(rand_engine), rd_pts(rand_engine)};
      points.emplace_back(point.begin(), point.end());
    }
    
    // Alpha complex from points
    Gudhi::alpha_complex::Alpha_complex<Kernel, false> alpha_complex_from_points(points);
    Gudhi::Simplex_tree<> simplex;
    Gudhi::Simplex_tree<>::Filtration_value infty = std::numeric_limits<Gudhi::Simplex_tree<>::Filtration_value>::infinity();
    BOOST_CHECK(alpha_complex_from_points.create_complex(simplex, infty, true));
    std::clog << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:"
              << std::endl;
    for (auto f_simplex : simplex.filtration_simplex_range()) {
      std::clog << "   ( ";
      for (auto vertex : simplex.simplex_vertex_range(f_simplex)) {
        std::clog << vertex << " ";
      }
      std::clog << ") -> " << "[" << simplex.filtration(f_simplex) << "] " << std::endl;
    }
  
    // Alpha complex from zero weighted points
    std::vector<typename Kernel::FT> weights(20, 0.);
    Gudhi::alpha_complex::Alpha_complex<Kernel, true> alpha_complex_from_zero_weighted_points(points, weights);
    Gudhi::Simplex_tree<> zw_simplex;
    BOOST_CHECK(alpha_complex_from_zero_weighted_points.create_complex(zw_simplex, infty, true));
  
    std::clog << "Iterator on zero weighted alpha complex simplices in the filtration order, with [filtration value]:"
              << std::endl;
    for (auto f_simplex : zw_simplex.filtration_simplex_range()) {
      std::clog << "   ( ";
      for (auto vertex : zw_simplex.simplex_vertex_range(f_simplex)) {
        std::clog << vertex << " ";
      }
      std::clog << ") -> " << "[" << zw_simplex.filtration(f_simplex) << "] " << std::endl;
    }
  
    BOOST_CHECK(zw_simplex == simplex);
  }
  
  template <typename Point_d>
  bool cgal_3d_point_sort (Point_d a,Point_d b) {
    if (a[0] != b[0])
      return a[0] < b[0];
    if (a[1] != b[1])
      return a[1] < b[1];
    return a[2] < b[2];
  }
  
  BOOST_AUTO_TEST_CASE(Weighted_alpha_complex_3d_comparison) {
    // check that for random weighted 3d points in safe mode the 3D and dD codes give the same result with some tolerance
  
    // Random points construction
    using Kernel_dD = CGAL::Epeck_d< CGAL::Dimension_tag<3> >;
    using Bare_point_d = typename Kernel_dD::Point_d;
    using Weighted_point_d = typename Kernel_dD::Weighted_point_d;
    std::vector<Weighted_point_d> w_points_d;
  
    using Exact_weighted_alpha_complex_3d =
      Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, false>;
    using Bare_point_3 = typename Exact_weighted_alpha_complex_3d::Bare_point_3;
    using Weighted_point_3 = typename Exact_weighted_alpha_complex_3d::Weighted_point_3;
    std::vector<Weighted_point_3> w_points_3;
  
    std::uniform_real_distribution<double> rd_pts(-10., 10.);
    std::uniform_real_distribution<double> rd_wghts(-0.5, 0.5);
    std::random_device rand_dev;
    std::mt19937 rand_engine(rand_dev());
    for (int idx = 0; idx < 20; idx++) {
      std::vector<double> point {rd_pts(rand_engine), rd_pts(rand_engine), rd_pts(rand_engine)};
      double weight = rd_wghts(rand_engine);
      w_points_d.emplace_back(Bare_point_d(point.begin(), point.end()), weight);
      w_points_3.emplace_back(Bare_point_3(point[0], point[1], point[2]), weight);
    }
  
    // Structures necessary for comparison
    using Points = std::vector<std::array<double,3>>;
    using Points_and_filtrations = std::map<Points, double>;
    Points_and_filtrations pts_fltr_dD;
    Points_and_filtrations pts_fltr_3d;
  
    // Weighted alpha complex for dD version
    Gudhi::alpha_complex::Alpha_complex<Kernel_dD, true> alpha_complex_dD_from_weighted_points(w_points_d);
    Gudhi::Simplex_tree<> w_simplex_d;
    BOOST_CHECK(alpha_complex_dD_from_weighted_points.create_complex(w_simplex_d));
  
    std::clog << "Iterator on weighted alpha complex dD simplices in the filtration order, with [filtration value]:"
              << std::endl;
    for (auto f_simplex : w_simplex_d.filtration_simplex_range()) {
      Points points;
      for (auto vertex : w_simplex_d.simplex_vertex_range(f_simplex)) {
        CGAL::NT_converter<Kernel_dD::RT, double> cgal_converter;
        Bare_point_d pt = alpha_complex_dD_from_weighted_points.get_point(vertex).point();
        points.push_back({cgal_converter(pt[0]), cgal_converter(pt[1]), cgal_converter(pt[2])});
      }
      std::clog << "   ( ";
      std::sort (points.begin(), points.end());
      for (auto point : points) {
        std::clog << point[0] << " " << point[1] << " " << point[2] << " | ";
      }
      std::clog << ") -> " << "[" << w_simplex_d.filtration(f_simplex) << "] ";
      std::clog << std::endl;
      pts_fltr_dD[points] = w_simplex_d.filtration(f_simplex);
    }
  
    // Weighted alpha complex for 3D version
    Exact_weighted_alpha_complex_3d alpha_complex_3D_from_weighted_points(w_points_3);
    Gudhi::Simplex_tree<> w_simplex_3;
    BOOST_CHECK(alpha_complex_3D_from_weighted_points.create_complex(w_simplex_3));
  
    std::clog << "Iterator on weighted alpha complex 3D simplices in the filtration order, with [filtration value]:"
              << std::endl;
    for (auto f_simplex : w_simplex_3.filtration_simplex_range()) {
      Points points;
      for (auto vertex : w_simplex_3.simplex_vertex_range(f_simplex)) {
        Bare_point_3 pt = alpha_complex_3D_from_weighted_points.get_point(vertex).point();
        CGAL::NT_converter<Exact_weighted_alpha_complex_3d::Kernel::RT, double> cgal_converter;
        points.push_back({cgal_converter(pt[0]), cgal_converter(pt[1]), cgal_converter(pt[2])});
      }
      std::clog << "   ( ";
      std::sort (points.begin(), points.end());
      for (auto point : points) {
        std::clog << point[0] << " " << point[1] << " " << point[2] << " | ";
      }
      std::clog << ") -> " << "[" << w_simplex_3.filtration(f_simplex) << "] " << std::endl;
      pts_fltr_3d[points] = w_simplex_d.filtration(f_simplex);
    }
  
    // Compares structures
    auto d3_itr = pts_fltr_3d.begin();
    auto dD_itr = pts_fltr_dD.begin();
    for (; d3_itr != pts_fltr_3d.end() && dD_itr != pts_fltr_dD.end(); ++d3_itr) {
      if (d3_itr->first != dD_itr->first) {
        for(auto point : d3_itr->first)
          std::clog << point[0] << " " << point[1] << " " << point[2] << " | ";
        std::clog << " versus ";
        for(auto point : dD_itr->first)
          std::clog << point[0] << " " << point[1] << " " << point[2] << " | ";
        std::clog << std::endl;
        BOOST_CHECK(false);
      }
      // In safe mode, relative error is less than 1e-5 (can be changed with set_relative_precision_of_to_double)
      if (std::fabs(d3_itr->second - dD_itr->second) > 1e-5 * (std::fabs(d3_itr->second) + std::fabs(dD_itr->second))) {
        std::clog << d3_itr->second << " versus " << dD_itr->second << " diff "
                  << std::fabs(d3_itr->second - dD_itr->second) << std::endl;
        BOOST_CHECK(false);
      }
      ++dD_itr;
    }
  }
  
  using list_of_1d_kernel_variants = boost::mpl::list<CGAL::Epeck_d< CGAL::Dynamic_dimension_tag >,
                                                      CGAL::Epeck_d< CGAL::Dimension_tag<1>>,
                                                      CGAL::Epick_d< CGAL::Dynamic_dimension_tag >,
                                                      CGAL::Epick_d< CGAL::Dimension_tag<1>>
                                                      >;
  
  BOOST_AUTO_TEST_CASE_TEMPLATE(Weighted_alpha_complex_non_visible_points, Kernel, list_of_1d_kernel_variants) {
    // check that for 2 closed weighted 1-d points, one with a high weight to hide the second one with a small weight,
    // that the point with a small weight has the same high filtration value than the edge formed by the 2 points
    using Point_d = typename Kernel::Point_d;
    std::vector<Point_d> points;
    std::vector<double> p1 {0.};
    points.emplace_back(p1.begin(), p1.end());
    // closed enough points
    std::vector<double> p2 {0.1};
    points.emplace_back(p2.begin(), p2.end());
    std::vector<typename Kernel::FT> weights {100., 0.01};
  
    Gudhi::alpha_complex::Alpha_complex<Kernel, true> alpha_complex(points, weights);
    Gudhi::Simplex_tree<> stree;
    BOOST_CHECK(alpha_complex.create_complex(stree));
  
    std::clog << "Iterator on weighted alpha complex simplices in the filtration order, with [filtration value]:"
              << std::endl;
    for (auto f_simplex : stree.filtration_simplex_range()) {
      std::clog << "   ( ";
      for (auto vertex : stree.simplex_vertex_range(f_simplex)) {
        std::clog << vertex << " ";
      }
      std::clog << ") -> " << "[" << stree.filtration(f_simplex) << "] " << std::endl;
    }
  
    BOOST_CHECK(stree.filtration(stree.find({0})) == -100.);
    BOOST_CHECK(stree.filtration(stree.find({1})) == stree.filtration(stree.find({0, 1})));
    BOOST_CHECK(stree.filtration(stree.find({1})) > 100000);
  }