real_polyhedral_homotopy_continuation/reference/include/system/start/mhom.hpp

// This file is part of Bertini 2.
//
// mhom.hpp 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.
//
// mhom.hpp 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 mhom.hpp.  If not, see <http://www.gnu.org/licenses/>.
//
//  Copyright(C) 2015 - 2021 by Bertini2 Development Team
//
//  See <http://www.gnu.org/licenses/> for a copy of the license,
//  as well as COPYING.  Bertini2 is provided with permitted
//  additional terms in the b2/licenses/ directory.

// individual authors of this file include:
// Tim Hodges, Colorado State University
// silviana amethyst, university of wisconsin eau claire

/**
\file mhom.hpp

\brief Defines the MHomogeneous start system type.
*/

#pragma once

#include "system/start/utility.hpp"
#include "system/start_base.hpp"

namespace bertini {
namespace start_system {

/**
\brief The $m$-homogeneous start system for Numerical Algebraic Geometry


*/
class MHomogeneous : public StartSystem {
 public:
  MHomogeneous() = default;
  virtual ~MHomogeneous() = default;

  /**
   Constructor for making a multi-homogeneous start system from a polynomial
   system

   \throws std::runtime_error, if the input target system is not square, is not
   polynomial, has a path variable already.

   Constructor can take in a non-homogeneous system or homogeneous system.
  */
  MHomogeneous(System const& s);

  /**
  \brief Creates a degree matrix for constructing the multi-homogeneous start
  system.
  */
  void CreateDegreeMatrix(System const& s);

  /**
  \brief Creates all valid partitions for multi-homogeneous start system to
  create start points.
  */
  void GenerateValidPartitions(System const& s);

  /**
  \brief Helper function that is used to find valid partitions in the degree
  matrix.
  */
  int ChooseColumnInRow(System const& s, Vec<int>& variable_group_counter,
                        int row, int column);

  /**
  Get the number of start points for this m-homogeneous start system.  This is
  the Bezout bound for the target system.  Provided here for your convenience.
  */
  unsigned long long NumStartPoints() const override;

  unsigned long long NumStartPointsForPartition(Vec<int> partition) const;

  MHomogeneous& operator*=(Nd const& n);

  MHomogeneous& operator+=(System const& sys) = delete;

  /**
   \brief Degree matrix holding degrees for all functions in terms of all
   variable groups
   */
  Mat<int> degree_matrix_;  // stores degrees of all functions in all
                            // homogeneous variable groups.

  /**
   \brief Partitions used for creating start points in the multi-homogeneous
   start system.
   */
  std::deque<Vec<int>> valid_partitions_;

 private:
  /**
  Get the ith start point, in double precision.

  Called by the base StartSystem's StartPoint(index) method.
  */
  Vec<dbl> GenerateStartPoint(dbl, unsigned long long index) const override;

  /**
  Get the ith start point, in current default precision.

  Called by the base StartSystem's StartPoint(index) method.
  */
  Vec<mpfr_complex> GenerateStartPoint(mpfr_complex,
                                       unsigned long long index) const override;

  /**
   A local version of GenerateStartPoint that can be templated
  */
  template <typename T>
  void GenerateStartPointT(Vec<T>& start_point, unsigned long long index) const;

  std::vector<unsigned long long>
      degrees_;  ///< stores the degrees of the functions.
  std::vector<VariableGroup> var_groups_;
  Mat<std::shared_ptr<node::LinearProduct>>
      linprod_matrix_;  ///< All the linear products for each entry in the
                        ///< degree matrix.
  std::vector<std::vector<size_t>>
      variable_cols_;  ///< The columns associated with each variable.  The
                       ///< first index is the variable group, the second index
                       ///< is the particular variable in the group.

  mutable Vec<mpfr_complex> temp_v_mp_;

  friend class boost::serialization::access;

  template <typename Archive>
  void serialize(Archive& ar, const unsigned version) {
    ar& boost::serialization::base_object<StartSystem>(*this);
    ar & degrees_;
  }
};
}  // namespace start_system
}  // namespace bertini