chain_matrix.h

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/*    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):       Hannah Schreiber
 *
 *    Copyright (C) 2022-24 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#ifndef PM_CHAIN_MATRIX_H
#define PM_CHAIN_MATRIX_H
 
#include <iostream>   //print() only
#include <set>
#include <map>
#include <stdexcept>
#include <vector>
#include <utility>    //std::swap, std::move & std::exchange
#include <algorithm>  //std::sort
 
#include <gudhi/Persistence_matrix/overlay_ididx_to_matidx.h> //friend
 
namespace Gudhi {
namespace persistence_matrix {
 
template <class Master_matrix>
class Chain_matrix : public Master_matrix::Matrix_dimension_option,
                     public Master_matrix::Chain_pairing_option,
                     public Master_matrix::Chain_vine_swap_option,
                     public Master_matrix::Chain_representative_cycles_option,
                     public Master_matrix::Matrix_row_access_option 
{
 public:
  using Field_operators = typename Master_matrix::Field_operators;
  using Field_element_type = typename Master_matrix::element_type;    
  using Column_type = typename Master_matrix::Column_type;            
  using Row_type = typename Master_matrix::Row_type;                  
  using Cell = typename Master_matrix::Cell_type;                     
  using Cell_constructor = typename Master_matrix::Cell_constructor;  
  using Column_settings = typename Master_matrix::Column_settings;    
  using boundary_type = typename Master_matrix::boundary_type;        
  using cell_rep_type = typename Master_matrix::cell_rep_type;        
  using index = typename Master_matrix::index;                        
  using id_index = typename Master_matrix::id_index;                  
  using pos_index = typename Master_matrix::pos_index;                
  using dimension_type = typename Master_matrix::dimension_type;      
  Chain_matrix(Column_settings* colSettings);
  template <class Boundary_type = boundary_type>
  Chain_matrix(const std::vector<Boundary_type>& orderedBoundaries, 
               Column_settings* colSettings);
  Chain_matrix(unsigned int numberOfColumns, Column_settings* colSettings);
  template <typename BirthComparatorFunction, typename DeathComparatorFunction>
  Chain_matrix(Column_settings* colSettings, 
               const BirthComparatorFunction& birthComparator,
               const DeathComparatorFunction& deathComparator);
  template <typename BirthComparatorFunction, typename DeathComparatorFunction, class Boundary_type = boundary_type>
  Chain_matrix(const std::vector<Boundary_type>& orderedBoundaries, 
               Column_settings* colSettings, 
               const BirthComparatorFunction& birthComparator,
               const DeathComparatorFunction& deathComparator);
  template <typename BirthComparatorFunction, typename DeathComparatorFunction>
  Chain_matrix(unsigned int numberOfColumns, 
               Column_settings* colSettings,
               const BirthComparatorFunction& birthComparator, 
               const DeathComparatorFunction& deathComparator);
  Chain_matrix(const Chain_matrix& matrixToCopy, 
               Column_settings* colSettings = nullptr);
  Chain_matrix(Chain_matrix&& other) noexcept;
 
  template <class Boundary_type = boundary_type>
  std::vector<cell_rep_type> insert_boundary(const Boundary_type& boundary, dimension_type dim = -1);
  template <class Boundary_type = boundary_type>
  std::vector<cell_rep_type> insert_boundary(id_index faceID, const Boundary_type& boundary, dimension_type dim = -1);
  Column_type& get_column(index columnIndex);
  const Column_type& get_column(index columnIndex) const;
  void remove_maximal_face(id_index faceID);
  void remove_maximal_face(id_index faceID, const std::vector<id_index>& columnsToSwap);
  void remove_last();
 
  index get_number_of_columns() const;
 
  dimension_type get_column_dimension(index columnIndex) const;
 
  void add_to(index sourceColumnIndex, index targetColumnIndex);
  void multiply_target_and_add_to(index sourceColumnIndex, 
                                  const Field_element_type& coefficient,
                                  index targetColumnIndex);
  void multiply_source_and_add_to(const Field_element_type& coefficient, 
                                  index sourceColumnIndex,
                                  index targetColumnIndex);
 
  bool is_zero_cell(index columnIndex, id_index rowIndex) const;
  bool is_zero_column(index columnIndex);
 
  index get_column_with_pivot(id_index faceID) const;
  id_index get_pivot(index columnIndex);
 
  void reset(Column_settings* colSettings) {
    matrix_.clear();
    pivotToColumnIndex_.clear();
    nextIndex_ = 0;
    colSettings_ = colSettings;
  }
 
  Chain_matrix& operator=(const Chain_matrix& other);
  friend void swap(Chain_matrix& matrix1, Chain_matrix& matrix2) {
    swap(static_cast<typename Master_matrix::Matrix_dimension_option&>(matrix1),
         static_cast<typename Master_matrix::Matrix_dimension_option&>(matrix2));
    swap(static_cast<typename Master_matrix::Chain_pairing_option&>(matrix1),
         static_cast<typename Master_matrix::Chain_pairing_option&>(matrix2));
    swap(static_cast<typename Master_matrix::Chain_vine_swap_option&>(matrix1),
         static_cast<typename Master_matrix::Chain_vine_swap_option&>(matrix2));
    swap(static_cast<typename Master_matrix::Chain_representative_cycles_option&>(matrix1),
         static_cast<typename Master_matrix::Chain_representative_cycles_option&>(matrix2));
    matrix1.matrix_.swap(matrix2.matrix_);
    matrix1.pivotToColumnIndex_.swap(matrix2.pivotToColumnIndex_);
    std::swap(matrix1.nextIndex_, matrix2.nextIndex_);
    std::swap(matrix1.colSettings_, matrix2.colSettings_);
 
    if constexpr (Master_matrix::Option_list::has_row_access) {
      swap(static_cast<typename Master_matrix::Matrix_row_access_option&>(matrix1),
           static_cast<typename Master_matrix::Matrix_row_access_option&>(matrix2));
    }
  }
 
  void print() const;  // for debug
 
  friend class Id_to_index_overlay<Chain_matrix<Master_matrix>, Master_matrix>;
 
 private:
  using dim_opt = typename Master_matrix::Matrix_dimension_option;
  using swap_opt = typename Master_matrix::Chain_vine_swap_option;
  using pair_opt = typename Master_matrix::Chain_pairing_option;
  using rep_opt = typename Master_matrix::Chain_representative_cycles_option;
  using ra_opt = typename Master_matrix::Matrix_row_access_option;
  using matrix_type = typename Master_matrix::column_container_type;
  using dictionnary_type = typename Master_matrix::template dictionnary_type<index>;
  using barcode_type = typename Master_matrix::barcode_type;
  using bar_dictionnary_type = typename Master_matrix::bar_dictionnary_type;
  using tmp_column_type = typename std::conditional<
      Master_matrix::Option_list::is_z2, 
      std::set<id_index>,
      std::map<id_index, Field_element_type>
    >::type;
 
  matrix_type matrix_;                  
  dictionnary_type pivotToColumnIndex_; 
  index nextIndex_;                     
  Column_settings* colSettings_;          
  template <class Boundary_type>
  std::vector<cell_rep_type> _reduce_boundary(id_index faceID, const Boundary_type& boundary, dimension_type dim);
  void _reduce_by_G(tmp_column_type& column, std::vector<cell_rep_type>& chainsInH, index currentPivot);
  void _reduce_by_F(tmp_column_type& column, std::vector<cell_rep_type>& chainsInF, index currentPivot);
  void _build_from_H(id_index faceID, tmp_column_type& column, std::vector<cell_rep_type>& chainsInH);
  void _update_largest_death_in_F(const std::vector<cell_rep_type>& chainsInF);
  void _insert_chain(const tmp_column_type& column, dimension_type dimension);
  void _insert_chain(const tmp_column_type& column, dimension_type dimension, index pair);
  void _add_to(const Column_type& column, tmp_column_type& set, unsigned int coef);
  template <typename F>
  void _add_to(Column_type& target, F&& addition);
  void _remove_last(index lastIndex);
  void _update_barcode(pos_index birth);
  void _add_bar(dimension_type dim);
  template <class Container_type>
  void _container_insert(const Container_type& column, index pos, dimension_type dim);
  void _container_insert(const Column_type& column, [[maybe_unused]] index pos = 0);
 
  constexpr barcode_type& _barcode();
  constexpr bar_dictionnary_type& _indexToBar();
  constexpr pos_index& _nextPosition();
};
 
template <class Master_matrix>
inline Chain_matrix<Master_matrix>::Chain_matrix(Column_settings* colSettings)
    : dim_opt(-1),
      pair_opt(),
      swap_opt(),
      rep_opt(),
      ra_opt(),
      nextIndex_(0),
      colSettings_(colSettings)
{}
 
template <class Master_matrix>
template <class Boundary_type>
inline Chain_matrix<Master_matrix>::Chain_matrix(const std::vector<Boundary_type>& orderedBoundaries,
                                                 Column_settings* colSettings)
    : dim_opt(-1),
      pair_opt(),
      swap_opt(),
      rep_opt(),
      ra_opt(orderedBoundaries.size()),
      nextIndex_(0),
      colSettings_(colSettings)
{
  matrix_.reserve(orderedBoundaries.size());
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    pivotToColumnIndex_.reserve(orderedBoundaries.size());
  } else {
    pivotToColumnIndex_.resize(orderedBoundaries.size(), -1);
  }
 
  for (const Boundary_type& b : orderedBoundaries) {
    insert_boundary(b);
  }
}
 
template <class Master_matrix>
inline Chain_matrix<Master_matrix>::Chain_matrix(unsigned int numberOfColumns, 
                                                 Column_settings* colSettings)
    : dim_opt(-1),
      pair_opt(),
      swap_opt(),
      rep_opt(),
      ra_opt(numberOfColumns),
      nextIndex_(0),
      colSettings_(colSettings)
{
  matrix_.reserve(numberOfColumns);
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    pivotToColumnIndex_.reserve(numberOfColumns);
  } else {
    pivotToColumnIndex_.resize(numberOfColumns, -1);
  }
}
 
template <class Master_matrix>
template <typename BirthComparatorFunction, typename DeathComparatorFunction>
inline Chain_matrix<Master_matrix>::Chain_matrix(Column_settings* colSettings,
                                                 const BirthComparatorFunction& birthComparator,
                                                 const DeathComparatorFunction& deathComparator)
    : dim_opt(-1),
      pair_opt(),
      swap_opt(birthComparator, deathComparator),
      rep_opt(),
      ra_opt(),
      nextIndex_(0),
      colSettings_(colSettings)
{}
 
template <class Master_matrix>
template <typename BirthComparatorFunction, typename DeathComparatorFunction, class Boundary_type>
inline Chain_matrix<Master_matrix>::Chain_matrix(const std::vector<Boundary_type>& orderedBoundaries,
                                                 Column_settings* colSettings,
                                                 const BirthComparatorFunction& birthComparator,
                                                 const DeathComparatorFunction& deathComparator)
    : dim_opt(-1),
      pair_opt(),
      swap_opt(birthComparator, deathComparator),
      rep_opt(),
      ra_opt(orderedBoundaries.size()),
      nextIndex_(0),
      colSettings_(colSettings)
{
  matrix_.reserve(orderedBoundaries.size());
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    pivotToColumnIndex_.reserve(orderedBoundaries.size());
  } else {
    pivotToColumnIndex_.resize(orderedBoundaries.size(), -1);
  }
  for (const Boundary_type& b : orderedBoundaries) {
    insert_boundary(b);
  }
}
 
template <class Master_matrix>
template <typename BirthComparatorFunction, typename DeathComparatorFunction>
inline Chain_matrix<Master_matrix>::Chain_matrix(unsigned int numberOfColumns, 
                                                 Column_settings* colSettings,
                                                 const BirthComparatorFunction& birthComparator,
                                                 const DeathComparatorFunction& deathComparator)
    : dim_opt(-1),
      pair_opt(),
      swap_opt(birthComparator, deathComparator),
      rep_opt(),
      ra_opt(numberOfColumns),
      nextIndex_(0),
      colSettings_(colSettings)
{
  matrix_.reserve(numberOfColumns);
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    pivotToColumnIndex_.reserve(numberOfColumns);
  } else {
    pivotToColumnIndex_.resize(numberOfColumns, -1);
  }
}
 
template <class Master_matrix>
inline Chain_matrix<Master_matrix>::Chain_matrix(const Chain_matrix& matrixToCopy, 
                                                 Column_settings* colSettings)
    : dim_opt(static_cast<const dim_opt&>(matrixToCopy)),
      pair_opt(static_cast<const pair_opt&>(matrixToCopy)),
      swap_opt(static_cast<const swap_opt&>(matrixToCopy)),
      rep_opt(static_cast<const rep_opt&>(matrixToCopy)),
      ra_opt(static_cast<const ra_opt&>(matrixToCopy)),
      pivotToColumnIndex_(matrixToCopy.pivotToColumnIndex_),
      nextIndex_(matrixToCopy.nextIndex_),
      colSettings_(colSettings == nullptr ? matrixToCopy.colSettings_ : colSettings)
{
  matrix_.reserve(matrixToCopy.matrix_.size());
  for (const auto& cont : matrixToCopy.matrix_){
    if constexpr (Master_matrix::Option_list::has_map_column_container){
      _container_insert(cont.second, cont.first);
    } else {
      _container_insert(cont);
    }
  }
}
 
template <class Master_matrix>
inline Chain_matrix<Master_matrix>::Chain_matrix(Chain_matrix&& other) noexcept
    : dim_opt(std::move(static_cast<dim_opt&>(other))),
      pair_opt(std::move(static_cast<pair_opt&>(other))),
      swap_opt(std::move(static_cast<swap_opt&>(other))),
      rep_opt(std::move(static_cast<rep_opt&>(other))),
      ra_opt(std::move(static_cast<ra_opt&>(other))),
      matrix_(std::move(other.matrix_)),
      pivotToColumnIndex_(std::move(other.pivotToColumnIndex_)),
      nextIndex_(std::exchange(other.nextIndex_, 0)),
      colSettings_(std::exchange(other.colSettings_, nullptr)) 
{}
 
template <class Master_matrix>
template <class Boundary_type>
inline std::vector<typename Master_matrix::cell_rep_type> Chain_matrix<Master_matrix>::insert_boundary(
    const Boundary_type& boundary, dimension_type dim) 
{
  return insert_boundary(nextIndex_, boundary, dim);
}
 
template <class Master_matrix>
template <class Boundary_type>
inline std::vector<typename Master_matrix::cell_rep_type> Chain_matrix<Master_matrix>::insert_boundary(
    id_index faceID, const Boundary_type& boundary, dimension_type dim) 
{
  if constexpr (!Master_matrix::Option_list::has_map_column_container) {
    if (pivotToColumnIndex_.size() <= faceID) {
      pivotToColumnIndex_.resize(faceID * 2 + 1, -1);
    }
  }
 
  if constexpr (Master_matrix::Option_list::has_vine_update && Master_matrix::Option_list::has_column_pairings) {
    if constexpr (Master_matrix::Option_list::has_map_column_container) {
      swap_opt::CP::pivotToPosition_.try_emplace(faceID, _nextPosition());
    } else {
      if (swap_opt::CP::pivotToPosition_.size() <= faceID)
        swap_opt::CP::pivotToPosition_.resize(pivotToColumnIndex_.size(), -1);
      swap_opt::CP::pivotToPosition_[faceID] = _nextPosition();
    }
  }
 
  if constexpr (Master_matrix::Option_list::has_matrix_maximal_dimension_access) {
    dim_opt::update_up(dim == static_cast<dimension_type>(-1) ? (boundary.size() == 0 ? 0 : boundary.size() - 1) : dim);
  }
 
  return _reduce_boundary(faceID, boundary, dim);
}
 
template <class Master_matrix>
inline typename Chain_matrix<Master_matrix>::Column_type& Chain_matrix<Master_matrix>::get_column(index columnIndex) 
{
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    return matrix_.at(columnIndex);
  } else {
    return matrix_[columnIndex];
  }
}
 
template <class Master_matrix>
inline const typename Chain_matrix<Master_matrix>::Column_type& Chain_matrix<Master_matrix>::get_column(
    index columnIndex) const 
{
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    return matrix_.at(columnIndex);
  } else {
    return matrix_[columnIndex];
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::remove_maximal_face(id_index faceID) 
{
  static_assert(Master_matrix::Option_list::has_removable_columns,
                "'remove_maximal_face' is not implemented for the chosen options.");
  static_assert(Master_matrix::Option_list::has_map_column_container && 
                    Master_matrix::Option_list::has_vine_update &&
                    Master_matrix::Option_list::has_column_pairings,
                "'remove_maximal_face' is not implemented for the chosen options.");
 
  // TODO: find simple test to verify that col at columnIndex is maximal even without row access.
 
  const auto& pivotToPosition = swap_opt::CP::pivotToPosition_;
  auto it = pivotToPosition.find(faceID);
  if (it == pivotToPosition.end()) return;  // face does not exists. TODO: put an assert instead?
  pos_index startPos = it->second;
  index startIndex = pivotToColumnIndex_.at(faceID);
 
  if (startPos != _nextPosition() - 1) {
    std::vector<index> colToSwap;
    colToSwap.reserve(matrix_.size());
 
    for (auto& p : pivotToPosition) {
      if (p.second > startPos) colToSwap.push_back(pivotToColumnIndex_.at(p.first));
    }
    std::sort(colToSwap.begin(), colToSwap.end(), [&](index c1, index c2) {
      return pivotToPosition.at(get_pivot(c1)) < pivotToPosition.at(get_pivot(c2));
    });
 
    for (index i : colToSwap) {
      startIndex = swap_opt::vine_swap(startIndex, i);
    }
  }
 
  _remove_last(startIndex);
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::remove_maximal_face(id_index faceID,
                                                             const std::vector<id_index>& columnsToSwap) 
{
  static_assert(Master_matrix::Option_list::has_removable_columns,
                "'remove_maximal_face' is not implemented for the chosen options.");
  static_assert(Master_matrix::Option_list::has_map_column_container && Master_matrix::Option_list::has_vine_update,
                "'remove_maximal_face' is not implemented for the chosen options.");
 
  // TODO: find simple test to verify that col at columnIndex is maximal even without row access.
 
  index startIndex = pivotToColumnIndex_.at(faceID);
 
  for (id_index i : columnsToSwap) {
    startIndex = swap_opt::vine_swap(startIndex, pivotToColumnIndex_.at(i));
  }
 
  _remove_last(startIndex);
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::remove_last() 
{
  static_assert(Master_matrix::Option_list::has_removable_columns,
                "'remove_last' is not implemented for the chosen options.");
  static_assert(Master_matrix::Option_list::has_map_column_container || !Master_matrix::Option_list::has_vine_update,
                "'remove_last' is not implemented for the chosen options.");
 
  if (nextIndex_ == 0 || matrix_.empty()) return;  // empty matrix
 
  if constexpr (Master_matrix::Option_list::has_vine_update) {
    // carefull: linear because of the search of the last index. It is better to keep track of the @ref IDIdx index
    // of the last column while performing swaps (or the @ref MatIdx with the return values of `vine_swap` + get_pivot)
    // and then call `remove_maximal_face` with it and an empty `columnsToSwap`.
 
    id_index pivot = 0;
    index colIndex = 0;
    for (auto& p : pivotToColumnIndex_) {
      if (p.first > pivot) {  // pivots have to be strictly increasing in order of filtration
        pivot = p.first;
        colIndex = p.second;
      }
    }
    _remove_last(colIndex);
  } else {
    _remove_last(nextIndex_ - 1);
  }
}
 
template <class Master_matrix>
inline typename Chain_matrix<Master_matrix>::index Chain_matrix<Master_matrix>::get_number_of_columns() const 
{
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    return matrix_.size();
  } else {
    return nextIndex_;  // matrix could have been resized much bigger while insert
  }
}
 
template <class Master_matrix>
inline typename Chain_matrix<Master_matrix>::dimension_type Chain_matrix<Master_matrix>::get_column_dimension(
    index columnIndex) const 
{
  return get_column(columnIndex).get_dimension();
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::add_to(index sourceColumnIndex, index targetColumnIndex) 
{
  auto& col = get_column(targetColumnIndex);
  _add_to(col, [&]() { col += get_column(sourceColumnIndex); });
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::multiply_target_and_add_to(index sourceColumnIndex,
                                                                    const Field_element_type& coefficient,
                                                                    index targetColumnIndex) 
{
  auto& col = get_column(targetColumnIndex);
  _add_to(col, [&]() { col.multiply_target_and_add(coefficient, get_column(sourceColumnIndex)); });
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::multiply_source_and_add_to(const Field_element_type& coefficient,
                                                                    index sourceColumnIndex, 
                                                                    index targetColumnIndex) 
{
  auto& col = get_column(targetColumnIndex);
  _add_to(col, [&]() { col.multiply_source_and_add(get_column(sourceColumnIndex), coefficient); });
}
 
template <class Master_matrix>
inline bool Chain_matrix<Master_matrix>::is_zero_cell(index columnIndex, id_index rowIndex) const 
{
  return !get_column(columnIndex).is_non_zero(rowIndex);
}
 
template <class Master_matrix>
inline bool Chain_matrix<Master_matrix>::is_zero_column(index columnIndex) 
{
  return get_column(columnIndex).is_empty();
}
 
template <class Master_matrix>
inline typename Chain_matrix<Master_matrix>::index Chain_matrix<Master_matrix>::get_column_with_pivot(
    id_index faceID) const 
{
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    return pivotToColumnIndex_.at(faceID);
  } else {
    return pivotToColumnIndex_[faceID];
  }
}
 
template <class Master_matrix>
inline typename Chain_matrix<Master_matrix>::id_index Chain_matrix<Master_matrix>::get_pivot(index columnIndex) 
{
  return get_column(columnIndex).get_pivot();
}
 
template <class Master_matrix>
inline Chain_matrix<Master_matrix>& Chain_matrix<Master_matrix>::operator=(const Chain_matrix& other) 
{
  dim_opt::operator=(other);
  swap_opt::operator=(other);
  pair_opt::operator=(other);
  rep_opt::operator=(other);
  matrix_.clear();
  pivotToColumnIndex_ = other.pivotToColumnIndex_;
  nextIndex_ = other.nextIndex_;
  colSettings_ = other.colSettings_;
 
  matrix_.reserve(other.matrix_.size());
  for (const auto& cont : other.matrix_){
    if constexpr (Master_matrix::Option_list::has_map_column_container){
      _container_insert(cont.second, cont.first);
    } else {
      _container_insert(cont);
    }
  }
 
  return *this;
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::print() const 
{
  std::cout << "Column Matrix:\n";
  if constexpr (!Master_matrix::Option_list::has_map_column_container) {
    for (id_index i = 0; i < pivotToColumnIndex_.size() && pivotToColumnIndex_[i] != static_cast<index>(-1); ++i) {
      index pos = pivotToColumnIndex_[i];
      const Column_type& col = matrix_[pos];
      for (const auto& cell : col) {
        std::cout << cell.get_row_index() << " ";
      }
      std::cout << "(" << i << ", " << pos << ")\n";
    }
    if constexpr (Master_matrix::Option_list::has_row_access) {
      std::cout << "\n";
      std::cout << "Row Matrix:\n";
      for (id_index i = 0; i < pivotToColumnIndex_.size() && pivotToColumnIndex_[i] != static_cast<index>(-1); ++i) {
        index pos = pivotToColumnIndex_[i];
        const Row_type& row = ra_opt::get_row(pos);
        for (const auto& cell : row) {
          std::cout << cell.get_column_index() << " ";
        }
        std::cout << "(" << i << ", " << pos << ")\n";
      }
    }
  } else {
    for (const auto& p : pivotToColumnIndex_) {
      const Column_type& col = matrix_.at(p.second);
      for (const auto& cell : col) {
        std::cout << cell.get_row_index() << " ";
      }
      std::cout << "(" << p.first << ", " << p.second << ")\n";
    }
    if constexpr (Master_matrix::Option_list::has_row_access) {
      std::cout << "\n";
      std::cout << "Row Matrix:\n";
      for (const auto& p : pivotToColumnIndex_) {
        const Row_type& row = ra_opt::get_row(p.first);
        for (const auto& cell : row) {
          std::cout << cell.get_column_index() << " ";
        }
        std::cout << "(" << p.first << ", " << p.second << ")\n";
      }
    }
  }
  std::cout << "\n";
}
 
template <class Master_matrix>
template <class Boundary_type>
inline std::vector<typename Master_matrix::cell_rep_type> Chain_matrix<Master_matrix>::_reduce_boundary(
    id_index faceID, const Boundary_type& boundary, dimension_type dim) 
{
  tmp_column_type column(boundary.begin(), boundary.end());
  if (dim == static_cast<dimension_type>(-1)) dim = boundary.begin() == boundary.end() ? 0 : boundary.size() - 1;
  std::vector<cell_rep_type> chainsInH;  // for corresponding indices in H (paired columns)
  std::vector<cell_rep_type> chainsInF;  // for corresponding indices in F (unpaired, essential columns)
 
  auto get_last = [&column]() {
    if constexpr (Master_matrix::Option_list::is_z2)
      return *(column.rbegin());
    else
      return column.rbegin()->first;
  };
 
  if (boundary.begin() == boundary.end()) {
    if constexpr (Master_matrix::Option_list::is_z2)
      column.insert(faceID);
    else
      column.emplace(faceID, 1);
    _insert_chain(column, dim);
    return chainsInF;
  }
 
  index currentIndex = get_column_with_pivot(get_last());
 
  while (get_column(currentIndex).is_paired()) {
    _reduce_by_G(column, chainsInH, currentIndex);
 
    if (column.empty()) {
      // produce the sum of all col_h in chains_in_H
      _build_from_H(faceID, column, chainsInH);
      // create a new cycle (in F) sigma - \sum col_h
      _insert_chain(column, dim);
      return chainsInF;
    }
 
    currentIndex = get_column_with_pivot(get_last());
  }
 
  while (!column.empty()) {
    currentIndex = get_column_with_pivot(get_last());
 
    if (!get_column(currentIndex).is_paired()) {
      // only fills currentEssentialCycleIndices if Z2 coefficients, so chainsInF remains empty
      _reduce_by_F(column, chainsInF, currentIndex);
    } else {
      _reduce_by_G(column, chainsInH, currentIndex);
    }
  }
 
  _update_largest_death_in_F(chainsInF);
 
  // Compute the new column zzsh + \sum col_h, for col_h in chains_in_H
  _build_from_H(faceID, column, chainsInH);
 
  // Create and insert (\sum col_h) + sigma (in H, paired with chain_fp) in matrix_
  if constexpr (Master_matrix::Option_list::is_z2)
    _insert_chain(column, dim, chainsInF[0]);
  else
    _insert_chain(column, dim, chainsInF[0].first);
 
  return chainsInF;
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_reduce_by_G(tmp_column_type& column, 
                                                      std::vector<cell_rep_type>& chainsInH,
                                                      index currentIndex) 
{
  Column_type& col = get_column(currentIndex);
  if constexpr (Master_matrix::Option_list::is_z2) {
    _add_to(col, column, 1u);                           // Reduce with the column col_g
    chainsInH.push_back(col.get_paired_chain_index());  // keep the col_h with which col_g is paired
  } else {
    Field_element_type coef = col.get_pivot_value();
    auto& operators = colSettings_->operators;
    coef = operators.get_inverse(coef);
    operators.multiply_inplace(coef, operators.get_characteristic() - column.rbegin()->second);
 
    _add_to(col, column, coef);                                       // Reduce with the column col_g
    chainsInH.emplace_back(col.get_paired_chain_index(), coef); // keep the col_h with which col_g is paired
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_reduce_by_F(tmp_column_type& column, 
                                                      std::vector<cell_rep_type>& chainsInF,
                                                      index currentIndex) 
{
  Column_type& col = get_column(currentIndex);
  if constexpr (Master_matrix::Option_list::is_z2) {
    _add_to(col, column, 1u);  // Reduce with the column col_g
    chainsInF.push_back(currentIndex);
  } else {
    Field_element_type coef = col.get_pivot_value();
    auto& operators = colSettings_->operators;
    coef = operators.get_inverse(coef);
    operators.multiply_inplace(coef, operators.get_characteristic() - column.rbegin()->second);
 
    _add_to(col, column, coef);  // Reduce with the column col_g
    chainsInF.emplace_back(currentIndex, operators.get_characteristic() - coef);
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_build_from_H(id_index faceID, 
                                                       tmp_column_type& column,
                                                       std::vector<cell_rep_type>& chainsInH) 
{
  if constexpr (Master_matrix::Option_list::is_z2) {
    column.insert(faceID);
    for (index idx_h : chainsInH) {
      _add_to(get_column(idx_h), column, 1u);
    }
  } else {
    column.emplace(faceID, 1);
    for (std::pair<index, Field_element_type>& idx_h : chainsInH) {
      _add_to(get_column(idx_h.first), column, idx_h.second);
    }
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_update_largest_death_in_F(const std::vector<cell_rep_type>& chainsInF) 
{
  if constexpr (Master_matrix::Option_list::is_z2) {
    index toUpdate = chainsInF[0];
    for (auto other_col_it = chainsInF.begin() + 1; other_col_it != chainsInF.end(); ++other_col_it) {
      add_to(*other_col_it, toUpdate);
    }
  } else {
    index toUpdate = chainsInF[0].first;
    get_column(toUpdate) *= chainsInF[0].second;
    for (auto other_col_it = chainsInF.begin() + 1; other_col_it != chainsInF.end(); ++other_col_it) {
      multiply_source_and_add_to(other_col_it->second, other_col_it->first, toUpdate);
    }
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_insert_chain(const tmp_column_type& column, dimension_type dimension) 
{
  _container_insert(column, nextIndex_, dimension);
  _add_bar(dimension);
 
  ++nextIndex_;
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_insert_chain(const tmp_column_type& column, 
                                                       dimension_type dimension,
                                                       index pair) 
{
  // true when no vine updates and if nextIndex_ is updated in remove_last for special case of no vines
  // because then @ref PosIdx == @ref MatIdx
  pos_index pairPos = pair;
 
  _container_insert(column, nextIndex_, dimension);
 
  get_column(nextIndex_).assign_paired_chain(pair);
  auto& pairCol = get_column(pair);
  pairCol.assign_paired_chain(nextIndex_);
 
  if constexpr (Master_matrix::Option_list::has_column_pairings && Master_matrix::Option_list::has_vine_update) {
    pairPos = swap_opt::CP::pivotToPosition_[pairCol.get_pivot()];
  }
 
  _update_barcode(pairPos);
 
  ++nextIndex_;
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_add_to(const Column_type& column, 
                                                 tmp_column_type& set,
                                                 [[maybe_unused]] unsigned int coef) 
{
  if constexpr (Master_matrix::Option_list::is_z2) {
    std::pair<typename std::set<index>::iterator, bool> res_insert;
    for (const Cell& cell : column) {
      res_insert = set.insert(cell.get_row_index());
      if (!res_insert.second) {
        set.erase(res_insert.first);
      }
    }
  } else {
    auto& operators = colSettings_->operators;
    for (const Cell& cell : column) {
      auto res = set.emplace(cell.get_row_index(), cell.get_element());
      if (res.second){
        operators.multiply_inplace(res.first->second, coef);
      } else {
        operators.multiply_and_add_inplace_back(cell.get_element(), coef, res.first->second);
        if (res.first->second == Field_operators::get_additive_identity()) {
          set.erase(res.first);
        }
      }
    }
  }
}
 
template <class Master_matrix>
template <typename F>
inline void Chain_matrix<Master_matrix>::_add_to(Column_type& target, F&& addition) 
{
  auto pivot = target.get_pivot();
  addition();
 
  if (pivot != target.get_pivot()) {
    if constexpr (Master_matrix::Option_list::has_map_column_container) {
      std::swap(pivotToColumnIndex_.at(pivot), pivotToColumnIndex_.at(target.get_pivot()));
    } else {
      std::swap(pivotToColumnIndex_[pivot], pivotToColumnIndex_[target.get_pivot()]);
    }
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_remove_last(index lastIndex) 
{
  static_assert(Master_matrix::Option_list::has_removable_columns,
                "'_remove_last' is not implemented for the chosen options.");
  static_assert(Master_matrix::Option_list::has_map_column_container || !Master_matrix::Option_list::has_vine_update,
                "'_remove_last' is not implemented for the chosen options.");
 
  id_index pivot;
 
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    auto itToErase = matrix_.find(lastIndex);
    Column_type& colToErase = itToErase->second;
    pivot = colToErase.get_pivot();
 
    if constexpr (Master_matrix::Option_list::has_matrix_maximal_dimension_access) {
      dim_opt::update_down(colToErase.get_dimension());
    }
 
    if (colToErase.is_paired()) matrix_.at(colToErase.get_paired_chain_index()).unassign_paired_chain();
    pivotToColumnIndex_.erase(pivot);
    matrix_.erase(itToErase);
  } else {
    GUDHI_CHECK(lastIndex == nextIndex_ - 1 && nextIndex_ == matrix_.size(),
                std::logic_error("Chain_matrix::_remove_last - Indexation problem."));
 
    Column_type& colToErase = matrix_[lastIndex];
    pivot = colToErase.get_pivot();
 
    if constexpr (Master_matrix::Option_list::has_matrix_maximal_dimension_access) {
      dim_opt::update_down(colToErase.get_dimension());
    }
 
    if (colToErase.is_paired()) matrix_.at(colToErase.get_paired_chain_index()).unassign_paired_chain();
    pivotToColumnIndex_[pivot] = -1;
    matrix_.pop_back();
    // TODO: resize matrix_ when a lot is removed? Could be not the best strategy if user inserts a lot back afterwards.
  }
 
  if constexpr (!Master_matrix::Option_list::has_vine_update) {
    --nextIndex_;  // should not be updated when there are vine updates, as possibly lastIndex != nextIndex - 1
  }
 
  if constexpr (Master_matrix::Option_list::has_column_pairings) {
    auto it = _indexToBar().find(--_nextPosition());
    typename barcode_type::iterator bar = it->second;
 
    if (bar->death == static_cast<pos_index>(-1))
      _barcode().erase(bar);
    else
      bar->death = -1;
 
    _indexToBar().erase(it);
    if constexpr (Master_matrix::Option_list::has_vine_update) swap_opt::CP::pivotToPosition_.erase(pivot);
  }
 
  if constexpr (Master_matrix::Option_list::has_row_access) {
    GUDHI_CHECK(
        ra_opt::get_row(pivot).size() == 0,
        std::invalid_argument(
            "Chain_matrix::_remove_last - Column asked to be removed does not corresponds to a maximal simplex."));
    if constexpr (Master_matrix::Option_list::has_removable_rows) {
      ra_opt::erase_empty_row(pivot);
    }
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_update_barcode(pos_index birth) 
{
  if constexpr (Master_matrix::Option_list::has_column_pairings) {
    if constexpr (Master_matrix::Option_list::has_removable_columns) {
      auto& barIt = _indexToBar().at(birth);
      barIt->death = _nextPosition();
      _indexToBar().try_emplace(_nextPosition(), barIt);  // list so iterators are stable
    } else {
      _barcode()[_indexToBar()[birth]].death = _nextPosition();
      _indexToBar().push_back(_indexToBar()[birth]);
    }
    ++_nextPosition();
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_add_bar(dimension_type dim) 
{
  if constexpr (Master_matrix::Option_list::has_column_pairings) {
    _barcode().emplace_back(dim, _nextPosition(), -1);
    if constexpr (Master_matrix::Option_list::has_removable_columns) {
      _indexToBar().try_emplace(_nextPosition(), --_barcode().end());
    } else {
      _indexToBar().push_back(_barcode().size() - 1);
    }
    ++_nextPosition();
  }
}
 
template <class Master_matrix>
template <class Container_type>
inline void Chain_matrix<Master_matrix>::_container_insert(const Container_type& column,
                                                              index pos,
                                                              dimension_type dim)
{
  id_index pivot;
  if constexpr (Master_matrix::Option_list::is_z2) {
    pivot = *(column.rbegin());
  } else {
    pivot = column.rbegin()->first;
  }
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    pivotToColumnIndex_.try_emplace(pivot, pos);
    if constexpr (Master_matrix::Option_list::has_row_access) {
      matrix_.try_emplace(pos, Column_type(pos, column, dim, ra_opt::rows_, colSettings_));
    } else {
      matrix_.try_emplace(pos, Column_type(column, dim, colSettings_));
    }
  } else {
    if constexpr (Master_matrix::Option_list::has_row_access) {
      matrix_.emplace_back(pos, column, dim, ra_opt::rows_, colSettings_);
    } else {
      matrix_.emplace_back(column, dim, colSettings_);
    }
    pivotToColumnIndex_[pivot] = pos;
  }
}
 
template <class Master_matrix>
inline void Chain_matrix<Master_matrix>::_container_insert(const Column_type& column, [[maybe_unused]] index pos)
{
  if constexpr (Master_matrix::Option_list::has_map_column_container) {
    if constexpr (Master_matrix::Option_list::has_row_access) {
      matrix_.try_emplace(pos, Column_type(column, column.get_column_index(), ra_opt::rows_, colSettings_));
    } else {
      matrix_.try_emplace(pos, Column_type(column, colSettings_));
    }
  } else {
    if constexpr (Master_matrix::Option_list::has_row_access) {
      matrix_.emplace_back(column, column.get_column_index(), ra_opt::rows_, colSettings_);
    } else {
      matrix_.emplace_back(column, colSettings_);
    }
  }
}
 
template <class Master_matrix>
inline constexpr typename Chain_matrix<Master_matrix>::barcode_type& Chain_matrix<Master_matrix>::_barcode() 
{
  if constexpr (Master_matrix::Option_list::has_vine_update)
    return swap_opt::template Chain_pairing<Master_matrix>::barcode_;
  else
    return pair_opt::barcode_;
}
 
template <class Master_matrix>
inline constexpr typename Chain_matrix<Master_matrix>::bar_dictionnary_type&
Chain_matrix<Master_matrix>::_indexToBar() 
{
  if constexpr (Master_matrix::Option_list::has_vine_update)
    return swap_opt::template Chain_pairing<Master_matrix>::indexToBar_;
  else
    return pair_opt::indexToBar_;
}
 
template <class Master_matrix>
inline constexpr typename Chain_matrix<Master_matrix>::pos_index& Chain_matrix<Master_matrix>::_nextPosition() 
{
  if constexpr (Master_matrix::Option_list::has_vine_update)
    return swap_opt::template Chain_pairing<Master_matrix>::nextPosition_;
  else
    return pair_opt::nextPosition_;
}
 
}  // namespace persistence_matrix
}  // namespace Gudhi
 
#endif  // PM_CHAIN_MATRIX_H