intrusive_set_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) 2022-24 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#ifndef PM_INTRUSIVE_SET_COLUMN_H
#define PM_INTRUSIVE_SET_COLUMN_H
 
#include <vector>
#include <stdexcept>
#include <type_traits>
#include <utility>  //std::swap, std::move & std::exchange
 
#include <boost/intrusive/set.hpp>
 
#include <gudhi/Debug_utils.h>
#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 Intrusive_set_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 =
      boost::intrusive::set<Entry,
                            boost::intrusive::constant_time_size<false>,
                            boost::intrusive::base_hook<typename Master_matrix::Base_hook_matrix_set_column> >;
  using Entry_constructor = typename Master_matrix::Entry_constructor;
 
 public:
  using iterator = typename Column_support::iterator;
  using const_iterator = typename Column_support::const_iterator;
  using reverse_iterator = typename Column_support::reverse_iterator;
  using const_reverse_iterator = typename Column_support::const_reverse_iterator;
 
  Intrusive_set_column(Column_settings* colSettings = nullptr);
  template <class Container = typename Master_matrix::Boundary>
  Intrusive_set_column(const Container& nonZeroRowIndices, Column_settings* colSettings);
  template <class Container = typename Master_matrix::Boundary, class Row_container>
  Intrusive_set_column(Index columnIndex,
                       const Container& nonZeroRowIndices,
                       Row_container* rowContainer,
                       Column_settings* colSettings);
  template <class Container = typename Master_matrix::Boundary>
  Intrusive_set_column(const Container& nonZeroChainRowIndices, Dimension dimension, Column_settings* colSettings);
  template <class Container = typename Master_matrix::Boundary, class Row_container>
  Intrusive_set_column(Index columnIndex,
                       const Container& nonZeroChainRowIndices,
                       Dimension dimension,
                       Row_container* rowContainer,
                       Column_settings* colSettings);
  Intrusive_set_column(const Intrusive_set_column& column, Column_settings* colSettings = nullptr);
  template <class Row_container>
  Intrusive_set_column(const Intrusive_set_column& column,
                       Index columnIndex,
                       Row_container* rowContainer,
                       Column_settings* colSettings = nullptr);
  Intrusive_set_column(Intrusive_set_column&& column) noexcept;
  ~Intrusive_set_column();
 
  std::vector<Field_element> get_content(int columnLength = -1) const;
  bool is_non_zero(ID_index rowIndex) const;
  bool is_empty() const;
  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;
 
  template <class Entry_range>
  Intrusive_set_column& operator+=(const Entry_range& column);
  Intrusive_set_column& operator+=(Intrusive_set_column& column);
 
  Intrusive_set_column& operator*=(unsigned int v);
 
  // this = v * this + column
  template <class Entry_range>
  Intrusive_set_column& multiply_target_and_add(const Field_element& val, const Entry_range& column);
  Intrusive_set_column& multiply_target_and_add(const Field_element& val, Intrusive_set_column& column);
  // this = this + column * v
  template <class Entry_range>
  Intrusive_set_column& multiply_source_and_add(const Entry_range& column, const Field_element& val);
  Intrusive_set_column& multiply_source_and_add(Intrusive_set_column& column, const Field_element& val);
 
  void push_back(const Entry& entry);
 
  friend bool operator==(const Intrusive_set_column& c1, const Intrusive_set_column& c2) {
    if (&c1 == &c2) return true;
 
    if constexpr (Master_matrix::Option_list::is_z2) {
      return c1.column_ == c2.column_;
    } else {
      auto it1 = c1.column_.begin();
      auto it2 = c2.column_.begin();
      if (c1.column_.size() != c2.column_.size()) return false;
      while (it1 != c1.column_.end() && it2 != c2.column_.end()) {
        if (it1->get_row_index() != it2->get_row_index() || it1->get_element() != it2->get_element()) return false;
        ++it1;
        ++it2;
      }
      return true;
    }
  }
 
  friend bool operator<(const Intrusive_set_column& c1, const Intrusive_set_column& c2) {
    if (&c1 == &c2) return false;
 
    if constexpr (Master_matrix::Option_list::is_z2) {
      return c1.column_ < c2.column_;
    } else {
      auto it1 = c1.column_.begin();
      auto it2 = c2.column_.begin();
      while (it1 != c1.column_.end() && it2 != c2.column_.end()) {
        if (it1->get_row_index() != it2->get_row_index()) return it1->get_row_index() < it2->get_row_index();
        if (it1->get_element() != it2->get_element()) return it1->get_element() < it2->get_element();
        ++it1;
        ++it2;
      }
      return it2 != c2.column_.end();
    }
  }
 
  // Disabled with row access.
  Intrusive_set_column& operator=(const Intrusive_set_column& other);
 
  friend void swap(Intrusive_set_column& col1, Intrusive_set_column& col2) {
    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;
 
  // Cloner object function for boost intrusive container
  struct New_cloner {
    New_cloner(Entry_constructor* entryPool) : entryPool_(entryPool) {};
 
    Entry* operator()(const Entry& clone_this) { return entryPool_->construct(clone_this); }
 
    Entry_constructor* entryPool_;
  };
 
  // The disposer object function for boost intrusive container
  struct Delete_disposer {
    Delete_disposer() {};
    Delete_disposer(Intrusive_set_column* col) : col_(col) {};
 
    void operator()(Entry* delete_this) {
      if constexpr (Master_matrix::Option_list::has_row_access) col_->unlink(delete_this);
      col_->entryPool_->destroy(delete_this);
    }
 
    Intrusive_set_column* col_;
  };
 
  Column_support column_;
  Field_operators* 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(iterator& it);
  Entry* _insert_entry(const Field_element& value, ID_index rowIndex, const iterator& position);
  void _insert_entry(ID_index rowIndex, const iterator& position);
  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 Intrusive_set_column<Master_matrix>::Intrusive_set_column(Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(),
      Chain_opt(),
      operators_(nullptr),
      entryPool_(colSettings == nullptr ? nullptr : &(colSettings->entryConstructor))
{
  if (operators_ == nullptr && entryPool_ == nullptr)
    return;  // to allow default constructor which gives a dummy column
  if constexpr (!Master_matrix::Option_list::is_z2) {
    operators_ = &(colSettings->operators);
  }
}
 
template <class Master_matrix>
template <class Container>
inline Intrusive_set_column<Master_matrix>::Intrusive_set_column(const Container& nonZeroRowIndices,
                                                                 Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(nonZeroRowIndices.size() == 0 ? 0 : nonZeroRowIndices.size() - 1),
      Chain_opt(),
      operators_(nullptr),
      entryPool_(&(colSettings->entryConstructor))
{
  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.");
 
  if constexpr (Master_matrix::Option_list::is_z2) {
    for (ID_index id : nonZeroRowIndices) {
      _insert_entry(id, column_.end());
    }
  } else {
    operators_ = &(colSettings->operators);
    for (const auto& p : nonZeroRowIndices) {
      _insert_entry(operators_->get_value(p.second), p.first, column_.end());
    }
  }
}
 
template <class Master_matrix>
template <class Container, class Row_container>
inline Intrusive_set_column<Master_matrix>::Intrusive_set_column(Index columnIndex,
                                                                 const Container& nonZeroRowIndices,
                                                                 Row_container* rowContainer,
                                                                 Column_settings* colSettings)
    : RA_opt(columnIndex, rowContainer),
      Dim_opt(nonZeroRowIndices.size() == 0 ? 0 : nonZeroRowIndices.size() - 1),
      Chain_opt([&] {
        if constexpr (Master_matrix::Option_list::is_z2) {
          return nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                     ? Master_matrix::template get_null_value<ID_index>()
                     : *std::prev(nonZeroRowIndices.end());
        } else {
          return nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                     ? Master_matrix::template get_null_value<ID_index>()
                     : std::prev(nonZeroRowIndices.end())->first;
        }
      }()),
      operators_(nullptr),
      entryPool_(&(colSettings->entryConstructor))
{
  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.");
 
  if constexpr (Master_matrix::Option_list::is_z2) {
    for (ID_index id : nonZeroRowIndices) {
      _insert_entry(id, column_.end());
    }
  } else {
    operators_ = &(colSettings->operators);
    for (const auto& p : nonZeroRowIndices) {
      _insert_entry(operators_->get_value(p.second), p.first, column_.end());
    }
  }
}
 
template <class Master_matrix>
template <class Container>
inline Intrusive_set_column<Master_matrix>::Intrusive_set_column(const Container& nonZeroRowIndices,
                                                                 Dimension dimension,
                                                                 Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(dimension),
      Chain_opt([&] {
        if constexpr (Master_matrix::Option_list::is_z2) {
          return nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                     ? Master_matrix::template get_null_value<ID_index>()
                     : *std::prev(nonZeroRowIndices.end());
        } else {
          return nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                     ? Master_matrix::template get_null_value<ID_index>()
                     : std::prev(nonZeroRowIndices.end())->first;
        }
      }()),
      operators_(nullptr),
      entryPool_(&(colSettings->entryConstructor))
{
  if constexpr (Master_matrix::Option_list::is_z2) {
    for (ID_index id : nonZeroRowIndices) {
      _insert_entry(id, column_.end());
    }
  } else {
    operators_ = &(colSettings->operators);
    for (const auto& p : nonZeroRowIndices) {
      _insert_entry(operators_->get_value(p.second), p.first, column_.end());
    }
  }
}
 
template <class Master_matrix>
template <class Container, class Row_container>
inline Intrusive_set_column<Master_matrix>::Intrusive_set_column(Index columnIndex,
                                                                 const Container& nonZeroRowIndices,
                                                                 Dimension dimension,
                                                                 Row_container* rowContainer,
                                                                 Column_settings* colSettings)
    : RA_opt(columnIndex, rowContainer),
      Dim_opt(dimension),
      Chain_opt([&] {
        if constexpr (Master_matrix::Option_list::is_z2) {
          return nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                     ? Master_matrix::template get_null_value<ID_index>()
                     : *std::prev(nonZeroRowIndices.end());
        } else {
          return nonZeroRowIndices.begin() == nonZeroRowIndices.end()
                     ? Master_matrix::template get_null_value<ID_index>()
                     : std::prev(nonZeroRowIndices.end())->first;
        }
      }()),
      operators_(nullptr),
      entryPool_(&(colSettings->entryConstructor))
{
  if constexpr (Master_matrix::Option_list::is_z2) {
    for (ID_index id : nonZeroRowIndices) {
      _insert_entry(id, column_.end());
    }
  } else {
    operators_ = &(colSettings->operators);
    for (const auto& p : nonZeroRowIndices) {
      _insert_entry(operators_->get_value(p.second), p.first, column_.end());
    }
  }
}
 
template <class Master_matrix>
inline Intrusive_set_column<Master_matrix>::Intrusive_set_column(const Intrusive_set_column& column,
                                                                 Column_settings* colSettings)
    : RA_opt(),
      Dim_opt(static_cast<const Dim_opt&>(column)),
      Chain_opt(static_cast<const Chain_opt&>(column)),
      operators_(colSettings == nullptr ? column.operators_ : nullptr),
      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.");
 
  if constexpr (!Master_matrix::Option_list::is_z2) {
    if (colSettings != nullptr) operators_ = &(colSettings->operators);
  }
 
  column_.clone_from(column.column_, New_cloner(entryPool_), Delete_disposer(this));
}
 
template <class Master_matrix>
template <class Row_container>
inline Intrusive_set_column<Master_matrix>::Intrusive_set_column(const Intrusive_set_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)),
      operators_(colSettings == nullptr ? column.operators_ : nullptr),
      entryPool_(colSettings == nullptr ? column.entryPool_ : &(colSettings->entryConstructor))
{
  if constexpr (!Master_matrix::Option_list::is_z2) {
    if (colSettings != nullptr) operators_ = &(colSettings->operators);
  }
 
  for (const Entry& entry : column.column_) {
    if constexpr (Master_matrix::Option_list::is_z2) {
      _insert_entry(entry.get_row_index(), column_.end());
    } else {
      _insert_entry(entry.get_element(), entry.get_row_index(), column_.end());
    }
  }
}
 
template <class Master_matrix>
inline Intrusive_set_column<Master_matrix>::Intrusive_set_column(Intrusive_set_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 Intrusive_set_column<Master_matrix>::~Intrusive_set_column()
{
  column_.clear_and_dispose(Delete_disposer(this));
}
 
template <class Master_matrix>
inline std::vector<typename Intrusive_set_column<Master_matrix>::Field_element>
Intrusive_set_column<Master_matrix>::get_content(int columnLength) const
{
  if (columnLength < 0 && column_.size() > 0)
    columnLength = column_.rbegin()->get_row_index() + 1;
  else if (columnLength < 0)
    return std::vector<Field_element>();
 
  std::vector<Field_element> container(columnLength);
  for (auto it = column_.begin(); it != column_.end() && it->get_row_index() < static_cast<ID_index>(columnLength);
       ++it) {
    if constexpr (Master_matrix::Option_list::is_z2) {
      container[it->get_row_index()] = 1;
    } else {
      container[it->get_row_index()] = it->get_element();
    }
  }
  return container;
}
 
template <class Master_matrix>
inline bool Intrusive_set_column<Master_matrix>::is_non_zero(ID_index rowIndex) const
{
  return column_.find(Entry(rowIndex)) != column_.end();
}
 
template <class Master_matrix>
inline bool Intrusive_set_column<Master_matrix>::is_empty() const
{
  return column_.empty();
}
 
template <class Master_matrix>
inline std::size_t Intrusive_set_column<Master_matrix>::size() const
{
  return column_.size();
}
 
template <class Master_matrix>
template <class Row_index_map>
inline void Intrusive_set_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.");
 
  Column_support newSet;
 
  if constexpr (Master_matrix::Option_list::has_row_access) {
    for (auto it = column_.begin(); it != column_.end();) {
      Entry* newEntry = entryPool_->construct(
          columnIndex == Master_matrix::template get_null_value<Index>() ? RA_opt::columnIndex_ : columnIndex,
          valueMap.at(it->get_row_index()));
      if constexpr (!Master_matrix::Option_list::is_z2) {
        newEntry->set_element(it->get_element());
      }
      newSet.insert(newSet.end(), *newEntry);
      _delete_entry(it);                                          // increases it
      if constexpr (Master_matrix::Option_list::has_intrusive_rows) // intrusive list
        RA_opt::insert_entry(newEntry->get_row_index(), newEntry);
    }
 
    // when row is a set, all entries have to be deleted first, to avoid colliding when inserting
    if constexpr (!Master_matrix::Option_list::has_intrusive_rows) {  // set
      for (Entry& entry : newSet) {
        RA_opt::insert_entry(entry.get_row_index(), &entry);
      }
    }
  } else {
    for (auto it = column_.begin(); it != column_.end();) {
      Entry* newEntry = entryPool_->construct(valueMap.at(it->get_row_index()));
      if constexpr (!Master_matrix::Option_list::is_z2) {
        newEntry->set_element(it->get_element());
      }
      newSet.insert(newSet.end(), *newEntry);
      _delete_entry(it);  // increases it
    }
  }
 
  column_.swap(newSet);
}
 
template <class Master_matrix>
inline void Intrusive_set_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.");
 
  column_.clear_and_dispose(Delete_disposer(this));
}
 
template <class Master_matrix>
inline void Intrusive_set_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_.find(Entry(rowIndex));
  if (it != column_.end()) {
    _delete_entry(it);
  }
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::ID_index Intrusive_set_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_.rbegin()->get_row_index();
  } else {
    return Chain_opt::get_pivot();
  }
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::Field_element
Intrusive_set_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_.rbegin()->get_element();
    } else {
      if (Chain_opt::get_pivot() == Master_matrix::template get_null_value<ID_index>()) return 0;
      auto it = column_.find(Entry(Chain_opt::get_pivot()));
      GUDHI_CHECK(it != column_.end(),
                  "Intrusive_set_column::get_pivot_value - Pivot not found only if the column was misused.");
      return it->get_element();
    }
  }
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::iterator Intrusive_set_column<Master_matrix>::begin() noexcept
{
  return column_.begin();
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::const_iterator Intrusive_set_column<Master_matrix>::begin()
    const noexcept
{
  return column_.begin();
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::iterator Intrusive_set_column<Master_matrix>::end() noexcept
{
  return column_.end();
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::const_iterator Intrusive_set_column<Master_matrix>::end()
    const noexcept
{
  return column_.end();
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::reverse_iterator
Intrusive_set_column<Master_matrix>::rbegin() noexcept
{
  return column_.rbegin();
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::const_reverse_iterator
Intrusive_set_column<Master_matrix>::rbegin() const noexcept
{
  return column_.rbegin();
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::reverse_iterator
Intrusive_set_column<Master_matrix>::rend() noexcept
{
  return column_.rend();
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::const_reverse_iterator Intrusive_set_column<Master_matrix>::rend()
    const noexcept
{
  return column_.rend();
}
 
template <class Master_matrix>
template <class Entry_range>
inline Intrusive_set_column<Master_matrix>& Intrusive_set_column<Master_matrix>::operator+=(const Entry_range& column)
{
  static_assert((!Master_matrix::isNonBasic || std::is_same_v<Entry_range, Intrusive_set_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 Intrusive_set_column<Master_matrix>& Intrusive_set_column<Master_matrix>::operator+=(
    Intrusive_set_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 Intrusive_set_column<Master_matrix>& Intrusive_set_column<Master_matrix>::operator*=(unsigned int v)
{
  if constexpr (Master_matrix::Option_list::is_z2) {
    if (v % 2 == 0) {
      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();
      }
    }
  } else {
    Field_element val = operators_->get_value(v);
 
    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;
 
    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 Intrusive_set_column<Master_matrix>& Intrusive_set_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, Intrusive_set_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.");
 
  if constexpr (Master_matrix::Option_list::is_z2) {
    if (val) {
      _add(column);
    } else {
      clear();
      _add(column);
    }
  } else {
    _multiply_target_and_add(val, column);
  }
 
  return *this;
}
 
template <class Master_matrix>
inline Intrusive_set_column<Master_matrix>& Intrusive_set_column<Master_matrix>::multiply_target_and_add(
    const Field_element& val,
    Intrusive_set_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 constexpr (Master_matrix::Option_list::is_z2) {
      if (val) {
        if (_add(column)) {
          Chain_opt::swap_pivots(column);
          Dim_opt::swap_dimension(column);
        }
      } else {
        throw std::invalid_argument("A chain column should not be multiplied by 0.");
      }
    } else {
      if (_multiply_target_and_add(val, column)) {
        Chain_opt::swap_pivots(column);
        Dim_opt::swap_dimension(column);
      }
    }
  } else {
    if constexpr (Master_matrix::Option_list::is_z2) {
      if (val) {
        _add(column);
      } else {
        clear();
        _add(column);
      }
    } else {
      _multiply_target_and_add(val, column);
    }
  }
 
  return *this;
}
 
template <class Master_matrix>
template <class Entry_range>
inline Intrusive_set_column<Master_matrix>& Intrusive_set_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, Intrusive_set_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.");
 
  if constexpr (Master_matrix::Option_list::is_z2) {
    if (val) {
      _add(column);
    }
  } else {
    _multiply_source_and_add(column, val);
  }
 
  return *this;
}
 
template <class Master_matrix>
inline Intrusive_set_column<Master_matrix>& Intrusive_set_column<Master_matrix>::multiply_source_and_add(
    Intrusive_set_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 constexpr (Master_matrix::Option_list::is_z2) {
      if (val) {
        if (_add(column)) {
          Chain_opt::swap_pivots(column);
          Dim_opt::swap_dimension(column);
        }
      }
    } else {
      if (_multiply_source_and_add(column, val)) {
        Chain_opt::swap_pivots(column);
        Dim_opt::swap_dimension(column);
      }
    }
  } else {
    if constexpr (Master_matrix::Option_list::is_z2) {
      if (val) {
        _add(column);
      }
    } else {
      _multiply_source_and_add(column, val);
    }
  }
 
  return *this;
}
 
template <class Master_matrix>
inline void Intrusive_set_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(), "The new row index has to be higher than the current pivot.");
 
  if constexpr (Master_matrix::Option_list::is_z2) {
    _insert_entry(entry.get_row_index(), column_.end());
  } else {
    _insert_entry(entry.get_element(), entry.get_row_index(), column_.end());
  }
}
 
template <class Master_matrix>
inline Intrusive_set_column<Master_matrix>& Intrusive_set_column<Master_matrix>::operator=(
    const Intrusive_set_column& other)
{
  static_assert(!Master_matrix::Option_list::has_row_access, "= assignment not enabled with row access option.");
 
  Dim_opt::operator=(other);
  Chain_opt::operator=(other);
 
  // order is important
  column_.clear_and_dispose(Delete_disposer(this));
  operators_ = other.operators_;
  entryPool_ = other.entryPool_;
  column_.clone_from(other.column_, New_cloner(entryPool_), Delete_disposer(this));
 
  return *this;
}
 
template <class Master_matrix>
inline void Intrusive_set_column<Master_matrix>::_delete_entry(iterator& it)
{
  it = column_.erase_and_dispose(it, Delete_disposer(this));
}
 
template <class Master_matrix>
inline typename Intrusive_set_column<Master_matrix>::Entry* Intrusive_set_column<Master_matrix>::_insert_entry(
    const Field_element& value,
    ID_index rowIndex,
    const iterator& position)
{
  if constexpr (Master_matrix::Option_list::has_row_access) {
    Entry* newEntry = entryPool_->construct(RA_opt::columnIndex_, rowIndex);
    newEntry->set_element(value);
    column_.insert(position, *newEntry);
    RA_opt::insert_entry(rowIndex, newEntry);
    return newEntry;
  } else {
    Entry* newEntry = entryPool_->construct(rowIndex);
    newEntry->set_element(value);
    column_.insert(position, *newEntry);
    return newEntry;
  }
}
 
template <class Master_matrix>
inline void Intrusive_set_column<Master_matrix>::_insert_entry(ID_index rowIndex, const iterator& position)
{
  if constexpr (Master_matrix::Option_list::has_row_access) {
    Entry* newEntry = entryPool_->construct(RA_opt::columnIndex_, rowIndex);
    column_.insert(position, *newEntry);
    RA_opt::insert_entry(rowIndex, newEntry);
  } else {
    Entry* newEntry = entryPool_->construct(rowIndex);
    column_.insert(position, *newEntry);
  }
}
 
template <class Master_matrix>
template <class Entry_range>
inline bool Intrusive_set_column<Master_matrix>::_add(const Entry_range& column)
{
  return _add_to_column(column, *this);
}
 
template <class Master_matrix>
template <class Entry_range>
inline bool Intrusive_set_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 Intrusive_set_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::Intrusive_set_column<Master_matrix> > {
  std::size_t operator()(const Gudhi::persistence_matrix::Intrusive_set_column<Master_matrix>& column) const {
    return Gudhi::persistence_matrix::hash_column(column);
  }
};
 
#endif  // PM_INTRUSIVE_SET_COLUMN_H