PL_approximation.h

/*    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):       Siargey Kachanovich
 *
 *    Copyright (C) 2019 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#ifndef FUNCTIONS_PL_APPROXIMATION_H_
#define FUNCTIONS_PL_APPROXIMATION_H_
 
#include <cstdlib>  // for std::size_t
 
#include <Eigen/Dense>
 
namespace Gudhi {
 
namespace coxeter_triangulation {
 
template <class Function_, class Triangulation_>
struct PL_approximation {
  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
    std::size_t cod_d = this->cod_d();
    std::size_t amb_d = this->amb_d();
    auto s = tr_.locate_point(p);
    Eigen::MatrixXd matrix(cod_d, s.dimension() + 1);
    Eigen::MatrixXd vertex_matrix(amb_d + 1, s.dimension() + 1);
    for (std::size_t i = 0; i < s.dimension() + 1; ++i) vertex_matrix(0, i) = 1;
    std::size_t j = 0;
    for (auto v : s.vertex_range()) {
      Eigen::VectorXd pt_v = tr_.cartesian_coordinates(v);
      Eigen::VectorXd fun_v = fun_(pt_v);
      for (std::size_t i = 1; i < amb_d + 1; ++i) vertex_matrix(i, j) = pt_v(i - 1);
      for (std::size_t i = 0; i < cod_d; ++i) matrix(i, j) = fun_v(i);
      j++;
    }
    assert(j == s.dimension() + 1);
    Eigen::VectorXd z(amb_d + 1);
    z(0) = 1;
    for (std::size_t i = 1; i < amb_d + 1; ++i) z(i) = p(i - 1);
    Eigen::VectorXd lambda = vertex_matrix.colPivHouseholderQr().solve(z);
    Eigen::VectorXd result = matrix * lambda;
    return result;
  }
 
  std::size_t amb_d() const { return fun_.amb_d(); }
 
  std::size_t cod_d() const { return fun_.cod_d(); }
 
  Eigen::VectorXd seed() const {
    // TODO: not finished. Should use an oracle.
    return Eigen::VectorXd(amb_d());
  }
 
  PL_approximation(const Function_& function, const Triangulation_& triangulation)
      : fun_(function), tr_(triangulation) {}
 
 private:
  Function_ fun_;
  Triangulation_ tr_;
};
 
template <class Function_, class Triangulation_>
PL_approximation<Function_, Triangulation_> make_pl_approximation(const Function_& function,
                                                                  const Triangulation_& triangulation) {
  return PL_approximation<Function_, Triangulation_>(function, triangulation);
}
 
}  // namespace coxeter_triangulation
 
}  // namespace Gudhi
 
#endif