list_column.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 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */

 
#ifndef PM_LIST_COLUMN_H
#define PM_LIST_COLUMN_H
 
#include <vector>
#include <stdexcept>
#include <type_traits>
#include <list>
#include <utility>  //std::swap, std::move & std::exchange
 
#include <boost/range/iterator_range_core.hpp>
#include <boost/iterator/indirect_iterator.hpp>
 
#include <gudhi/Persistence_matrix/allocators/entry_constructors.h>
#include <gudhi/Persistence_matrix/columns/column_utilities.h>
 
namespace Gudhi {
namespace persistence_matrix {

template <class Master_matrix>
class List_column : public Master_matrix::Row_access_option,
                    public Master_matrix::Column_dimension_option,
                    public Master_matrix::Chain_column_option
{
 public:
  using Master = Master_matrix;
  using Index = typename Master_matrix::Index;
  using ID_index = typename Master_matrix::ID_index;
  using Dimension = typename Master_matrix::Dimension;
  using Field_element = typename Master_matrix::Element;
  using Entry = typename Master_matrix::Matrix_entry;
  using Column_settings = typename Master_matrix::Column_settings;
 
 private:
  using Field_operators = typename Master_matrix::Field_operators;
  using Column_support = std::list<Entry*>;
  using Entry_constructor = typename Master_matrix::Entry_constructor;
 
 public:
  using iterator = boost::indirect_iterator<typename Column_support::iterator>;
  using const_iterator = boost::indirect_iterator<typename Column_support::const_iterator>;
  using reverse_iterator = boost::indirect_iterator<typename Column_support::reverse_iterator>;
  using const_reverse_iterator = boost::indirect_iterator<typename Column_support::const_reverse_iterator>;
  using Content_range = boost::iterator_range<const_iterator>;
 
  List_column(Column_settings* colSettings = nullptr);
  template <class Container = typename Master_matrix::Boundary>
  List_column(const Container& nonZeroRowIndices, Column_settings* colSettings);
  template <class Container = typename Master_matrix::Boundary, class Row_container>
  List_column(Index columnIndex,
              const Container& nonZeroRowIndices,
              Row_container* rowContainer,
              Column_settings* colSettings);
  template <class Container = typename Master_matrix::Boundary,
            class = std::enable_if_t<!std::is_arithmetic_v<Container> > >
  List_column(const Container& nonZeroRowIndices, Dimension dimension, Column_settings* colSettings);
  template <class Container = typename Master_matrix::Boundary,
            class Row_container,
            class = std::enable_if_t<!std::is_arithmetic_v<Container> > >
  List_column(Index columnIndex,
              const Container& nonZeroRowIndices,
              Dimension dimension,
              Row_container* rowContainer,
              Column_settings* colSettings);
  List_column(ID_index idx, Dimension dimension, Column_settings* colSettings);
  List_column(ID_index idx, Field_element e, Dimension dimension, Column_settings* colSettings);
  template <class Row_container>
  List_column(Index columnIndex,
              ID_index idx,
              Dimension dimension,
              Row_container* rowContainer,
              Column_settings* colSettings);
  template <class Row_container>
  List_column(Index columnIndex,
              ID_index idx,
              Field_element e,
              Dimension dimension,
              Row_container* rowContainer,
              Column_settings* colSettings);
  List_column(const List_column& column, Column_settings* colSettings = nullptr);
  template <class Row_container>
  List_column(const List_column& column,
              Index columnIndex,
              Row_container* rowContainer,
              Column_settings* colSettings = nullptr);
  List_column(List_column&& column) noexcept;
  ~List_column();
 
  std::vector<Field_element> get_content(int columnLength = -1) const;
  bool is_non_zero(ID_index rowIndex) const;
  [[nodiscard]] bool is_empty() const;
  [[nodiscard]] std::size_t size() const;
 
  template <class Row_index_map>
  void reorder(const Row_index_map& valueMap,
               [[maybe_unused]] Index columnIndex = Master_matrix::template get_null_value<Index>());
  void clear();
  void clear(ID_index rowIndex);
 
  ID_index get_pivot() const;
  Field_element get_pivot_value() const;
 
  iterator begin() noexcept;
  const_iterator begin() const noexcept;
  iterator end() noexcept;
  const_iterator end() const noexcept;
  reverse_iterator rbegin() noexcept;
  const_reverse_iterator rbegin() const noexcept;
  reverse_iterator rend() noexcept;
  const_reverse_iterator rend() const noexcept;
 
  Content_range get_non_zero_content_range() const;
 
  template <class Entry_range>
  List_column& operator+=(const Entry_range& column);
  List_column& operator+=(List_column& column);
 
  List_column& operator*=(const Field_element& v);
 
  // this = v * this + column
  template <class Entry_range>
  List_column& multiply_target_and_add(const Field_element& val, const Entry_range& column);
  List_column& multiply_target_and_add(const Field_element& val, List_column& column);
  // this = this + column * v
  template <class Entry_range>
  List_column& multiply_source_and_add(const Entry_range& column, const Field_element& val);
  List_column& multiply_source_and_add(List_column& column, const Field_element& val);
 
  void push_back(const Entry& entry);
 
  friend bool operator==(const List_column& c1, const List_column& c2)
  {
    if (&c1 == &c2) return true;
    if (c1.column_.size() != c2.column_.size()) return false;
 
    return std::equal(c1.column_.begin(),
                      c1.column_.end(),
                      c2.column_.begin(),
                      c2.column_.end(),
                      [](const Entry* e1, const Entry* e2) {
                        return e1->get_row_index() == e2->get_row_index() && e1->get_element() == e2->get_element();
                      });
  }
 
  friend bool operator<(const List_column& c1, const List_column& c2)
  {
    if (&c1 == &c2) return false;
 
    return std::lexicographical_compare(c1.column_.begin(),
                                        c1.column_.end(),
                                        c2.column_.begin(),
                                        c2.column_.end(),
                                        [](const Entry* e1, const Entry* e2) {
                                          if (e1->get_row_index() != e2->get_row_index())
                                            return e1->get_row_index() < e2->get_row_index();
                                          if (e1->get_element() != e2->get_element())
                                            return e1->get_element() < e2->get_element();
                                          return false;
                                        });
  }
 
  // Disabled with row access.
  List_column& operator=(const List_column& other);
  List_column& operator=(List_column&& other) noexcept;
 
  friend void swap(List_column& col1, List_column& col2) noexcept
  {
    swap(static_cast<typename Master_matrix::Row_access_option&>(col1),
         static_cast<typename Master_matrix::Row_access_option&>(col2));
    swap(static_cast<typename Master_matrix::Column_dimension_option&>(col1),
         static_cast<typename Master_matrix::Column_dimension_option&>(col2));
    swap(static_cast<typename Master_matrix::Chain_column_option&>(col1),
         static_cast<typename Master_matrix::Chain_column_option&>(col2));
    col1.column_.swap(col2.column_);
    std::swap(col1.operators_, col2.operators_);
    std::swap(col1.entryPool_, col2.entryPool_);
  }
 
 private:
  using RA_opt = typename Master_matrix::Row_access_option;
  using Dim_opt = typename Master_matrix::Column_dimension_option;
  using Chain_opt = typename Master_matrix::Chain_column_option;
 
  Column_support column_;
  Field_operators const* operators_;
  Entry_constructor* entryPool_;
 
  template <class Column, class Entry_iterator, typename F1, typename F2, typename F3, typename F4>
  friend void _generic_merge_entry_to_column(Column& targetColumn,
                                             Entry_iterator& itSource,
                                             typename Column::Column_support::iterator& itTarget,
                                             F1&& process_target,
                                             F2&& process_source,
                                             F3&& update_target1,
                                             F4&& update_target2,
                                             bool& pivotIsZeroed);
  template <class Column, class Entry_range, typename F1, typename F2, typename F3, typename F4, typename F5>
  friend bool _generic_add_to_column(const Entry_range& source,
                                     Column& targetColumn,
                                     F1&& process_target,
                                     F2&& process_source,
                                     F3&& update_target1,
                                     F4&& update_target2,
                                     F5&& finish_target);
  template <class Column, class Entry_range>
  friend bool _add_to_column(const Entry_range& source, Column& targetColumn);
  template <class Column, class Entry_range>
  friend bool _multiply_target_and_add_to_column(const typename Column::Field_element& val,
                                                 const Entry_range& source,
                                                 Column& targetColumn);
  template <class Column, class Entry_range>
  friend bool _multiply_source_and_add_to_column(const typename Column::Field_element& val,
                                                 const Entry_range& source,
                                                 Column& targetColumn);
 
  void _delete_entry(typename Column_support::iterator& it);
  Entry* _insert_entry(const typename Column_support::iterator& position,
                       ID_index rowIndex,
                       const Field_element& value);
  void _update_entry(const typename Column_support::iterator& position, ID_index rowIndex, const Field_element& value);
  template <class Entry_range>
  bool _add(const Entry_range& column);
  template <class Entry_range>
  bool _multiply_target_and_add(const Field_element& val, const Entry_range& column);
  template <class Entry_range>
  bool _multiply_source_and_add(const Entry_range& column, const Field_element& val);
};
 
template <class Master_matrix>
inline List_column<Master_matrix>::List_column(Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(),
      Chain_opt(),
      operators_(Master_matrix::get_operator_ptr(colSettings)),
      entryPool_(colSettings == nullptr ? nullptr : &(colSettings->entryConstructor))
{}
 
template <class Master_matrix>
template <class Container>
inline List_column<Master_matrix>::List_column(const Container& nonZeroRowIndices, Column_settings* colSettings)
    : List_column(nonZeroRowIndices, nonZeroRowIndices.size() == 0 ? 0 : nonZeroRowIndices.size() - 1, colSettings)
{
  static_assert(!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type,
                "Constructor not available for chain columns, please specify the dimension of the chain.");
}
 
template <class Master_matrix>
template <class Container, class Row_container>
inline List_column<Master_matrix>::List_column(Index columnIndex,
                                               const Container& nonZeroRowIndices,
                                               Row_container* rowContainer,
                                               Column_settings* colSettings)
    : List_column(columnIndex,
                  nonZeroRowIndices,
                  nonZeroRowIndices.size() == 0 ? 0 : nonZeroRowIndices.size() - 1,
                  rowContainer,
                  colSettings)
{
  static_assert(!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type,
                "Constructor not available for chain columns, please specify the dimension of the chain.");
}
 
template <class Master_matrix>
template <class Container, class>
inline List_column<Master_matrix>::List_column(const Container& nonZeroRowIndices,
                                               Dimension dimension,
                                               Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(dimension),
      Chain_opt(nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                    ? Master_matrix::template get_null_value<ID_index>()
                    : Master_matrix::get_row_index(*std::prev(nonZeroRowIndices.end()))),
      column_(nonZeroRowIndices.size()),
      operators_(Master_matrix::get_operator_ptr(colSettings)),
      entryPool_(&(colSettings->entryConstructor))
{
  auto it = column_.begin();
  for (const auto& id : nonZeroRowIndices) {
    _update_entry(it++,
                  Master_matrix::get_row_index(id),
                  Master_matrix::get_coefficient_value(Master_matrix::get_element(id), operators_));
  }
}
 
template <class Master_matrix>
template <class Container, class Row_container, class>
inline List_column<Master_matrix>::List_column(Index columnIndex,
                                               const Container& nonZeroRowIndices,
                                               Dimension dimension,
                                               Row_container* rowContainer,
                                               Column_settings* colSettings)
    : RA_opt(columnIndex, rowContainer),
      Dim_opt(dimension),
      Chain_opt(nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                    ? Master_matrix::template get_null_value<ID_index>()
                    : Master_matrix::get_row_index(*std::prev(nonZeroRowIndices.end()))),
      column_(nonZeroRowIndices.size()),
      operators_(Master_matrix::get_operator_ptr(colSettings)),
      entryPool_(&(colSettings->entryConstructor))
{
  auto it = column_.begin();
  for (const auto& id : nonZeroRowIndices) {
    _update_entry(it++,
                  Master_matrix::get_row_index(id),
                  Master_matrix::get_coefficient_value(Master_matrix::get_element(id), operators_));
  }
}
 
template <class Master_matrix>
inline List_column<Master_matrix>::List_column(ID_index idx, Dimension dimension, Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(dimension),
      Chain_opt(idx),
      column_(1),
      operators_(nullptr),
      entryPool_(&(colSettings->entryConstructor))
{
  static_assert(Master_matrix::Option_list::is_z2,
                "Constructor not available for Zp != Z2. Please specify the coefficient.");
  _update_entry(column_.begin(), idx, 1);
}
 
template <class Master_matrix>
inline List_column<Master_matrix>::List_column(ID_index idx,
                                               Field_element e,
                                               Dimension dimension,
                                               Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(dimension),
      Chain_opt(idx),
      column_(1),
      operators_(&(colSettings->operators)),
      entryPool_(&(colSettings->entryConstructor))
{
  static_assert(!Master_matrix::Option_list::is_z2,
                "Constructor not available for Zp == Z2. Please do not specify any coefficient.");
  _update_entry(column_.begin(), idx, operators_->get_value(e));
}
 
template <class Master_matrix>
template <class Row_container>
inline List_column<Master_matrix>::List_column(Index columnIndex,
                                               ID_index idx,
                                               Dimension dimension,
                                               Row_container* rowContainer,
                                               Column_settings* colSettings)
    : RA_opt(columnIndex, rowContainer),
      Dim_opt(dimension),
      Chain_opt(idx),
      column_(1),
      operators_(nullptr),
      entryPool_(&(colSettings->entryConstructor))
{
  static_assert(Master_matrix::Option_list::is_z2,
                "Constructor not available for Zp != Z2. Please specify the coefficient.");
  _update_entry(column_.begin(), idx, 1);
}
 
template <class Master_matrix>
template <class Row_container>
inline List_column<Master_matrix>::List_column(Index columnIndex,
                                               ID_index idx,
                                               Field_element e,
                                               Dimension dimension,
                                               Row_container* rowContainer,
                                               Column_settings* colSettings)
    : RA_opt(columnIndex, rowContainer),
      Dim_opt(dimension),
      Chain_opt(idx),
      column_(1),
      operators_(&(colSettings->operators)),
      entryPool_(&(colSettings->entryConstructor))
{
  static_assert(!Master_matrix::Option_list::is_z2,
                "Constructor not available for Zp == Z2. Please do not specify any coefficient.");
  _update_entry(column_.begin(), idx, operators_->get_value(e));
}
 
template <class Master_matrix>
inline List_column<Master_matrix>::List_column(const List_column& column, Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(static_cast<const Dim_opt&>(column)),
      Chain_opt(static_cast<const Chain_opt&>(column)),
      column_(column.column_.size()),
      operators_(colSettings == nullptr ? column.operators_ : Master_matrix::get_operator_ptr(colSettings)),
      entryPool_(colSettings == nullptr ? column.entryPool_ : &(colSettings->entryConstructor))
{
  static_assert(!Master_matrix::Option_list::has_row_access,
                "Simple copy constructor not available when row access option enabled. Please specify the new column "
                "index and the row container.");
 
  auto it = column_.begin();
  for (const Entry* entry : column.column_) {
    _update_entry(it++, entry->get_row_index(), entry->get_element());
  }
}
 
template <class Master_matrix>
template <class Row_container>
inline List_column<Master_matrix>::List_column(const List_column& column,
                                               Index columnIndex,
                                               Row_container* rowContainer,
                                               Column_settings* colSettings)
    : RA_opt(columnIndex, rowContainer),
      Dim_opt(static_cast<const Dim_opt&>(column)),
      Chain_opt(static_cast<const Chain_opt&>(column)),
      column_(column.column_.size()),
      operators_(colSettings == nullptr ? column.operators_ : Master_matrix::get_operator_ptr(colSettings)),
      entryPool_(colSettings == nullptr ? column.entryPool_ : &(colSettings->entryConstructor))
{
  auto it = column_.begin();
  for (const Entry* entry : column.column_) {
    _update_entry(it++, entry->get_row_index(), entry->get_element());
  }
}
 
template <class Master_matrix>
inline List_column<Master_matrix>::List_column(List_column&& column) noexcept
    : RA_opt(std::move(static_cast<RA_opt&>(column))),
      Dim_opt(std::move(static_cast<Dim_opt&>(column))),
      Chain_opt(std::move(static_cast<Chain_opt&>(column))),
      column_(std::move(column.column_)),
      operators_(std::exchange(column.operators_, nullptr)),
      entryPool_(std::exchange(column.entryPool_, nullptr))
{}
 
template <class Master_matrix>
inline List_column<Master_matrix>::~List_column()
{
  for (auto* entry : column_) {
    if constexpr (Master_matrix::Option_list::has_row_access) RA_opt::unlink(entry);
    entryPool_->destroy(entry);
  }
}
 
template <class Master_matrix>
inline std::vector<typename List_column<Master_matrix>::Field_element> List_column<Master_matrix>::get_content(
    int columnLength) const
{
  if (columnLength < 0 && column_.size() > 0)
    columnLength = column_.back()->get_row_index() + 1;
  else if (columnLength < 0)
    return std::vector<Field_element>();
 
  std::vector<Field_element> container(columnLength, 0);
  for (auto it = column_.begin(); it != column_.end() && (*it)->get_row_index() < static_cast<ID_index>(columnLength);
       ++it) {
    container[(*it)->get_row_index()] = Master_matrix::get_element(**it);
  }
  return container;
}
 
template <class Master_matrix>
inline bool List_column<Master_matrix>::is_non_zero(ID_index rowIndex) const
{
  // could be changed to dichotomic search as column is ordered by row index,
  // but I am not sure if it is really worth it as there is no random access
  // and the columns should not be that long anyway.
  for (const Entry* entry : column_)
    if (entry->get_row_index() == rowIndex) return true;
 
  return false;
}
 
template <class Master_matrix>
inline bool List_column<Master_matrix>::is_empty() const
{
  return column_.empty();
}
 
template <class Master_matrix>
inline std::size_t List_column<Master_matrix>::size() const
{
  return column_.size();
}
 
template <class Master_matrix>
template <class Row_index_map>
inline void List_column<Master_matrix>::reorder(const Row_index_map& valueMap, [[maybe_unused]] Index columnIndex)
{
  static_assert(!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type,
                "Method not available for chain columns.");
 
  for (auto it = column_.begin(); it != column_.end(); ++it) {
    Entry* entry = *it;
    if constexpr (Master_matrix::Option_list::has_row_access) {
      RA_opt::unlink(entry);
      if (columnIndex != Master_matrix::template get_null_value<Index>()) entry->set_column_index(columnIndex);
    }
    entry->set_row_index(valueMap.at(entry->get_row_index()));
    if constexpr (Master_matrix::Option_list::has_intrusive_rows && Master_matrix::Option_list::has_row_access)
      RA_opt::insert_entry(entry->get_row_index(), entry);
  }
 
  // all entries have to be deleted first, to avoid problem with insertion when row is a set
  if constexpr (!Master_matrix::Option_list::has_intrusive_rows && Master_matrix::Option_list::has_row_access) {
    for (auto it = column_.begin(); it != column_.end(); ++it) {
      Entry* entry = *it;
      RA_opt::insert_entry(entry->get_row_index(), entry);
    }
  }
 
  column_.sort([](const Entry* c1, const Entry* c2) { return *c1 < *c2; });
}
 
template <class Master_matrix>
inline void List_column<Master_matrix>::clear()
{
  static_assert(!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type,
                "Method not available for chain columns as a base element should not be empty.");
 
  for (auto* entry : column_) {
    if constexpr (Master_matrix::Option_list::has_row_access) RA_opt::unlink(entry);
    entryPool_->destroy(entry);
  }
 
  column_.clear();
}
 
template <class Master_matrix>
inline void List_column<Master_matrix>::clear(ID_index rowIndex)
{
  static_assert(!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type,
                "Method not available for chain columns.");
 
  auto it = column_.begin();
  while (it != column_.end() && (*it)->get_row_index() != rowIndex) it++;
  if (it != column_.end()) _delete_entry(it);
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::ID_index List_column<Master_matrix>::get_pivot() const
{
  static_assert(Master_matrix::isNonBasic,
                "Method not available for base columns.");  // could technically be, but is the notion useful then?
 
  if constexpr (Master_matrix::Option_list::is_of_boundary_type) {
    if (column_.empty()) return Master_matrix::template get_null_value<ID_index>();
    return column_.back()->get_row_index();
  } else {
    return Chain_opt::_get_pivot();
  }
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::Field_element List_column<Master_matrix>::get_pivot_value() const
{
  static_assert(Master_matrix::isNonBasic,
                "Method not available for base columns.");  // could technically be, but is the notion useful then?
 
  if constexpr (Master_matrix::Option_list::is_z2) {
    return 1;
  } else {
    if constexpr (Master_matrix::Option_list::is_of_boundary_type) {
      if (column_.empty()) return 0;
      return column_.back()->get_element();
    } else {
      if (Chain_opt::_get_pivot() == Master_matrix::template get_null_value<ID_index>()) return Field_element();
      for (const Entry* entry : column_) {
        if (entry->get_row_index() == Chain_opt::_get_pivot()) return entry->get_element();
      }
      return Field_element();  // should never happen if chain column is used properly
    }
  }
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::iterator List_column<Master_matrix>::begin() noexcept
{
  return column_.begin();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::const_iterator List_column<Master_matrix>::begin() const noexcept
{
  return column_.begin();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::iterator List_column<Master_matrix>::end() noexcept
{
  return column_.end();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::const_iterator List_column<Master_matrix>::end() const noexcept
{
  return column_.end();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::reverse_iterator List_column<Master_matrix>::rbegin() noexcept
{
  return column_.rbegin();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::const_reverse_iterator List_column<Master_matrix>::rbegin() const noexcept
{
  return column_.rbegin();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::reverse_iterator List_column<Master_matrix>::rend() noexcept
{
  return column_.rend();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::const_reverse_iterator List_column<Master_matrix>::rend() const noexcept
{
  return column_.rend();
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::Content_range List_column<Master_matrix>::get_non_zero_content_range() const
{
  return Content_range(column_.begin(), column_.end());
}
 
template <class Master_matrix>
template <class Entry_range>
inline List_column<Master_matrix>& List_column<Master_matrix>::operator+=(const Entry_range& column)
{
  static_assert((!Master_matrix::isNonBasic || std::is_same_v<Entry_range, List_column>),
                "For boundary columns, the range has to be a column of same type to help ensure the validity of the "
                "base element.");  // could be removed, if we give the responsibility to the user.
  static_assert((!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type),
                "For chain columns, the given column cannot be constant.");
 
  _add(column);
 
  return *this;
}
 
template <class Master_matrix>
inline List_column<Master_matrix>& List_column<Master_matrix>::operator+=(List_column& column)
{
  if constexpr (Master_matrix::isNonBasic && !Master_matrix::Option_list::is_of_boundary_type) {
    // assumes that the addition never zeros out this column.
    if (_add(column)) {
      Chain_opt::_swap_pivots(column);
      Dim_opt::_swap_dimension(column);
    }
  } else {
    _add(column);
  }
 
  return *this;
}
 
template <class Master_matrix>
inline List_column<Master_matrix>& List_column<Master_matrix>::operator*=(const Field_element& v)
{
  Field_element val = Master_matrix::get_coefficient_value(v, operators_);
 
  if (val == Field_operators::get_additive_identity()) {
    if constexpr (Master_matrix::isNonBasic && !Master_matrix::Option_list::is_of_boundary_type) {
      throw std::invalid_argument("A chain column should not be multiplied by 0.");
    } else {
      clear();
    }
    return *this;
  }
 
  if (val == Field_operators::get_multiplicative_identity()) return *this;
 
  // multiply_inplace needs a non-const reference to element, so even if Z2 never reaches here, it won't compile
  // without the constexpr, as we are not storing a dummy value just for this purpose.
  if constexpr (!Master_matrix::Option_list::is_z2) {
    for (Entry* entry : column_) {
      operators_->multiply_inplace(entry->get_element(), val);
      if constexpr (Master_matrix::Option_list::has_row_access) RA_opt::update_entry(*entry);
    }
  }
 
  return *this;
}
 
template <class Master_matrix>
template <class Entry_range>
inline List_column<Master_matrix>& List_column<Master_matrix>::multiply_target_and_add(const Field_element& val,
                                                                                       const Entry_range& column)
{
  static_assert((!Master_matrix::isNonBasic || std::is_same_v<Entry_range, List_column>),
                "For boundary columns, the range has to be a column of same type to help ensure the validity of the "
                "base element.");  // could be removed, if we give the responsibility to the user.
  static_assert((!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type),
                "For chain columns, the given column cannot be constant.");
 
  _multiply_target_and_add(Master_matrix::get_coefficient_value(val, operators_), column);
 
  return *this;
}
 
template <class Master_matrix>
inline List_column<Master_matrix>& List_column<Master_matrix>::multiply_target_and_add(const Field_element& val,
                                                                                       List_column& column)
{
  if constexpr (Master_matrix::isNonBasic && !Master_matrix::Option_list::is_of_boundary_type) {
    // assumes that the addition never zeros out this column.
    if (_multiply_target_and_add(Master_matrix::get_coefficient_value(val, operators_), column)) {
      Chain_opt::_swap_pivots(column);
      Dim_opt::_swap_dimension(column);
    }
  } else {
    _multiply_target_and_add(Master_matrix::get_coefficient_value(val, operators_), column);
  }
 
  return *this;
}
 
template <class Master_matrix>
template <class Entry_range>
inline List_column<Master_matrix>& List_column<Master_matrix>::multiply_source_and_add(const Entry_range& column,
                                                                                       const Field_element& val)
{
  static_assert((!Master_matrix::isNonBasic || std::is_same_v<Entry_range, List_column>),
                "For boundary columns, the range has to be a column of same type to help ensure the validity of the "
                "base element.");  // could be removed, if we give the responsibility to the user.
  static_assert((!Master_matrix::isNonBasic || Master_matrix::Option_list::is_of_boundary_type),
                "For chain columns, the given column cannot be constant.");
 
  _multiply_source_and_add(column, Master_matrix::get_coefficient_value(val, operators_));
 
  return *this;
}
 
template <class Master_matrix>
inline List_column<Master_matrix>& List_column<Master_matrix>::multiply_source_and_add(List_column& column,
                                                                                       const Field_element& val)
{
  if constexpr (Master_matrix::isNonBasic && !Master_matrix::Option_list::is_of_boundary_type) {
    // assumes that the addition never zeros out this column.
    if (_multiply_source_and_add(column, Master_matrix::get_coefficient_value(val, operators_))) {
      Chain_opt::_swap_pivots(column);
      Dim_opt::_swap_dimension(column);
    }
  } else {
    _multiply_source_and_add(column, Master_matrix::get_coefficient_value(val, operators_));
  }
 
  return *this;
}
 
template <class Master_matrix>
inline void List_column<Master_matrix>::push_back(const Entry& entry)
{
  static_assert(Master_matrix::Option_list::is_of_boundary_type, "`push_back` is not available for Chain matrices.");
 
  GUDHI_CHECK(entry.get_row_index() > get_pivot(),
              std::invalid_argument("The new row index has to be higher than the current pivot."));
 
  _insert_entry(column_.end(), entry.get_row_index(), entry.get_element());
}
 
template <class Master_matrix>
inline List_column<Master_matrix>& List_column<Master_matrix>::operator=(const List_column& other)
{
  static_assert(!Master_matrix::Option_list::has_row_access, "= assignment not enabled with row access option.");
 
  // to avoid destroying the column when building from it-self in the for loop below...
  if (this == &other) return *this;
 
  Dim_opt::operator=(other);
  Chain_opt::operator=(other);
 
  auto tmpPool = entryPool_;
  entryPool_ = other.entryPool_;
 
  while (column_.size() > other.column_.size()) {
    if (column_.back() != nullptr) {
      tmpPool->destroy(column_.back());
    }
    column_.pop_back();
  }
 
  column_.resize(other.column_.size(), nullptr);
  auto it = column_.begin();
  for (const Entry* entry : other.column_) {
    if (*it != nullptr) {
      tmpPool->destroy(*it);
    }
    _update_entry(it++, entry->get_row_index(), entry->get_element());
  }
 
  operators_ = other.operators_;
 
  return *this;
}
 
template <class Master_matrix>
inline List_column<Master_matrix>& List_column<Master_matrix>::operator=(List_column&& other) noexcept
{
  static_assert(!Master_matrix::Option_list::has_row_access, "= assignment not enabled with row access option.");
 
  // to avoid destroying the column before building from it-self...
  if (&column_ == &(other.column_)) return *this;
 
  Dim_opt::operator=(std::move(other));
  Chain_opt::operator=(std::move(other));
 
  for (auto* entry : column_) {
    if (entry != nullptr) entryPool_->destroy(entry);
  }
 
  column_ = std::move(other.column_);
  operators_ = std::exchange(other.operators_, nullptr);
  entryPool_ = std::exchange(other.entryPool_, nullptr);
 
  return *this;
}
 
template <class Master_matrix>
inline void List_column<Master_matrix>::_delete_entry(typename Column_support::iterator& it)
{
  if constexpr (Master_matrix::Option_list::has_row_access) RA_opt::unlink(*it);
  entryPool_->destroy(*it);
  it = column_.erase(it);
}
 
template <class Master_matrix>
inline typename List_column<Master_matrix>::Entry* List_column<Master_matrix>::_insert_entry(
    const typename Column_support::iterator& position,
    ID_index rowIndex,
    const Field_element& value)
{
  Entry* newEntry;
  if constexpr (Master_matrix::Option_list::has_row_access) {
    newEntry = entryPool_->construct(RA_opt::get_column_index(), rowIndex);
  } else {
    newEntry = entryPool_->construct(rowIndex);
  }
  newEntry->set_element(value);
  column_.insert(position, newEntry);
  if constexpr (Master_matrix::Option_list::has_row_access) RA_opt::insert_entry(rowIndex, newEntry);
  return newEntry;
}
 
template <class Master_matrix>
inline void List_column<Master_matrix>::_update_entry(const typename Column_support::iterator& position,
                                                      ID_index rowIndex,
                                                      const Field_element& value)
{
  if constexpr (Master_matrix::Option_list::has_row_access) {
    *position = entryPool_->construct(RA_opt::get_column_index(), rowIndex);
  } else {
    *position = entryPool_->construct(rowIndex);
  }
  (*position)->set_element(value);
  if constexpr (Master_matrix::Option_list::has_row_access) RA_opt::insert_entry(rowIndex, *position);
}
 
template <class Master_matrix>
template <class Entry_range>
inline bool List_column<Master_matrix>::_add(const Entry_range& column)
{
  if (column.begin() == column.end()) return false;
  if (column_.empty()) {  // chain should never enter here.
    column_.resize(column.size());
    auto it = column_.begin();
    for (const Entry& entry : column) {
      _update_entry(it++, entry.get_row_index(), entry.get_element());
    }
    return true;
  }
 
  return _add_to_column(column, *this);
}
 
template <class Master_matrix>
template <class Entry_range>
inline bool List_column<Master_matrix>::_multiply_target_and_add(const Field_element& val, const Entry_range& column)
{
  return _multiply_target_and_add_to_column(val, column, *this);
}
 
template <class Master_matrix>
template <class Entry_range>
inline bool List_column<Master_matrix>::_multiply_source_and_add(const Entry_range& column, const Field_element& val)
{
  return _multiply_source_and_add_to_column(val, column, *this);
}
 
}  // namespace persistence_matrix
}  // namespace Gudhi

template <class Master_matrix>
struct std::hash<Gudhi::persistence_matrix::List_column<Master_matrix> > {
  std::size_t operator()(const Gudhi::persistence_matrix::List_column<Master_matrix>& column) const
  {
    return Gudhi::persistence_matrix::hash_column(column);
  }
};
 
#endif  // PM_LIST_COLUMN_H