/*    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_FUNCTION_AFFINE_PLANE_IN_RD_H_
#define FUNCTIONS_FUNCTION_AFFINE_PLANE_IN_RD_H_

#include <cstdlib>  // for std::size_t

#include <Eigen/Dense>

namespace Gudhi {

namespace coxeter_triangulation {

/**
 * \class Function_affine_plane_in_Rd
 * \brief A class for the function that defines an m-dimensional implicit affine plane
 * embedded in d-dimensional Euclidean space.
 */
struct Function_affine_plane_in_Rd {
  /**
   * \brief Value of the function at a specified point.
   * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
   */
  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
    Eigen::VectorXd result = normal_matrix_.transpose() * (p - off_);
    return result;
  }

  /** \brief Returns the domain dimension. Same as the ambient dimension of the sphere. */
  std::size_t amb_d() const { return d_; };

  /** \brief Returns the codomain dimension. Same as the codimension of the sphere. */
  std::size_t cod_d() const { return k_; };

  /** \brief Returns a point on the affine plane. */
  Eigen::VectorXd seed() const {
    Eigen::VectorXd result = off_;
    return result;
  }

  /**
   * \brief Constructor of the function that defines an m-dimensional implicit affine
   * plane in the d-dimensional Euclidean space.
   *
   * @param[in] normal_matrix A normal matrix of the affine plane. The number of rows should
   * correspond to the ambient dimension, the number of columns should correspond to
   * the size of the normal basis (codimension).
   * @param[in] offset The offset vector of the affine plane.
   * The dimension of the vector should be the ambient dimension of the manifold.
   */
  Function_affine_plane_in_Rd(const Eigen::MatrixXd& normal_matrix, const Eigen::VectorXd& offset)
      : normal_matrix_(normal_matrix), d_(normal_matrix.rows()), k_(normal_matrix.cols()), m_(d_ - k_), off_(offset) {
    normal_matrix_.colwise().normalize();
  }

  /**
   * \brief Constructor of the function that defines an m-dimensional implicit affine
   * plane in the d-dimensional Euclidean space that passes through origin.
   *
   * @param[in] normal_matrix A normal matrix of the affine plane. The number of rows should
   * correspond to the ambient dimension, the number of columns should correspond to
   * the size of the normal basis (codimension).
   */
  Function_affine_plane_in_Rd(const Eigen::MatrixXd& normal_matrix)
      : normal_matrix_(normal_matrix),
        d_(normal_matrix.rows()),
        k_(normal_matrix.cols()),
        m_(d_ - k_),
        off_(Eigen::VectorXd::Zero(d_)) {
    normal_matrix_.colwise().normalize();
  }

 private:
  Eigen::MatrixXd normal_matrix_;
  std::size_t d_, k_, m_;
  Eigen::VectorXd off_;
};

}  // namespace coxeter_triangulation

}  // namespace Gudhi

#endif