Overlay for chain matrices replacing all input and output MatIdx indices of the original methods with PosIdx indices. The overlay is useless for boundary matrices as MatIdx == PosIdx for them. More...

Public Types
using	index = typename Master_matrix_type::index

using	id_index = typename Master_matrix_type::id_index

using	pos_index = typename Master_matrix_type::pos_index

using	dimension_type = typename Master_matrix_type::dimension_type

using	Field_operators = typename Master_matrix_type::Field_operators
	Field operators class. Necessary only if PersistenceMatrixOptions::is_z2 is false.

using	Field_element_type = typename Master_matrix_type::element_type

using	boundary_type = typename Master_matrix_type::boundary_type

using	Column_type = typename Master_matrix_type::Column_type

using	Row_type = typename Master_matrix_type::Row_type

using	bar_type = typename Master_matrix_type::Bar

using	barcode_type = typename Master_matrix_type::barcode_type

using	cycle_type = typename Master_matrix_type::cycle_type

using	cell_rep_type = typename Master_matrix_type::cell_rep_type

using	Cell_constructor = typename Master_matrix_type::Cell_constructor

using	Column_settings = typename Master_matrix_type::Column_settings

Public Member Functions
	Position_to_index_overlay (Column_settings *colSettings)
	Constructs an empty matrix. More...

template<class Boundary_type = boundary_type>
	Position_to_index_overlay (const std::vector< Boundary_type > &orderedBoundaries, Column_settings *colSettings)
	Constructs a new matrix from the given ranges of Matrix::cell_rep_type. Each range corresponds to a column (the order of the ranges are preserved). The content of the ranges is assumed to be sorted by increasing IDs. The IDs of the simplices are also assumed to be consecutifs, ordered by filtration value, starting with 0. More...

	Position_to_index_overlay (unsigned int numberOfColumns, Column_settings *colSettings)
	Constructs a new empty matrix and reserves space for the given number of columns. More...

template<typename BirthComparatorFunction , typename DeathComparatorFunction >
	Position_to_index_overlay (Column_settings *colSettings, const BirthComparatorFunction &birthComparator, const DeathComparatorFunction &deathComparator)
	Only available for chain matrices. Constructs an empty matrix and stores the given comparators. More...

template<typename BirthComparatorFunction , typename DeathComparatorFunction , class Boundary_type >
	Position_to_index_overlay (const std::vector< Boundary_type > &orderedBoundaries, Column_settings *colSettings, const BirthComparatorFunction &birthComparator, const DeathComparatorFunction &deathComparator)
	Only available for chain matrices. Constructs a new matrix from the given ranges of Matrix::cell_rep_type. Each range corresponds to a column (the order of the ranges are preserved). The content of the ranges is assumed to be sorted by increasing IDs. The IDs of the simplices are also assumed to be consecutifs, ordered by filtration value, starting with 0. More...

template<typename BirthComparatorFunction , typename DeathComparatorFunction >
	Position_to_index_overlay (unsigned int numberOfColumns, Column_settings *colSettings, const BirthComparatorFunction &birthComparator, const DeathComparatorFunction &deathComparator)
	Only available for chain matrices. Constructs a new empty matrix and reserves space for the given number of columns. More...

	Position_to_index_overlay (const Position_to_index_overlay &matrixToCopy, Column_settings *colSettings=nullptr)
	Copy constructor. If `colSettings` is not a null pointer, its value is kept instead of the one in the copied matrix. More...

	Position_to_index_overlay (Position_to_index_overlay &&other) noexcept
	Move constructor. More...

template<class Boundary_type = boundary_type>
void	insert_boundary (const Boundary_type &boundary, dimension_type dim=-1)
	Inserts at the end of the matrix a new ordered column corresponding to the given boundary. This means that it is assumed that this method is called on boundaries in the order of the filtration. It also assumes that the faces in the given boundary are identified by their relative position in the filtration, starting at 0. If it is not the case, use the other insert_boundary instead by indicating the face ID used in the boundaries when the face is inserted. More...

template<class Boundary_type = boundary_type>
void	insert_boundary (id_index faceIndex, const Boundary_type &boundary, dimension_type dim=-1)
	It does the same as the other version, but allows the boundary faces to be identified without restrictions except that all IDs have to be strictly increasing in the order of filtration. Note that you should avoid then to use the other insertion method to avoid overwriting IDs. More...

Column_type &	get_column (pos_index position)
	Returns the column at the given PosIdx index. The type of the column depends on the choosen options, see PersistenceMatrixOptions::column_type. More...

const Column_type &	get_column (pos_index position) const
	Returns the column at the given PosIdx index. The type of the column depends on the choosen options, see PersistenceMatrixOptions::column_type. More...

Row_type &	get_row (id_index rowIndex)
	Only available if PersistenceMatrixOptions::has_row_access is true. Returns the row at the given row index. The type of the row depends on the choosen options, see PersistenceMatrixOptions::has_intrusive_rows. More...

const Row_type &	get_row (id_index rowIndex) const
	Only available if PersistenceMatrixOptions::has_row_access is true. Returns the row at the given row index. The type of the row depends on the choosen options, see PersistenceMatrixOptions::has_intrusive_rows. More...

void	erase_empty_row (id_index rowIndex)
	Only available if PersistenceMatrixOptions::has_row_access and PersistenceMatrixOptions::has_removable_rows are true. Assumes that the row is empty and removes it. More...

void	remove_maximal_face (pos_index position)
	Only available if PersistenceMatrixOptions::has_removable_columns, PersistenceMatrixOptions::has_vine_update and PersistenceMatrixOptions::has_map_column_container are true. Assumes that the face is maximal in the current complex and removes it such that the matrix remains consistent (i.e., the matrix is still a compatible bases of the chain complex in the sense of [41]). The maximality of the face is not verified. Also updates the barcode if it was computed. More...

void	remove_last ()
	Only available if PersistenceMatrixOptions::has_removable_columns is true and, if PersistenceMatrixOptions::has_map_column_container is true or PersistenceMatrixOptions::has_vine_update is false. Removes the last face in the filtration from the matrix and updates the barcode if it is stored. More...

dimension_type	get_max_dimension () const
	Returns the maximal dimension of a face stored in the matrix. Only available if PersistenceMatrixOptions::has_matrix_maximal_dimension_access is true. More...

index	get_number_of_columns () const
	Returns the current number of columns in the matrix. More...

dimension_type	get_column_dimension (pos_index position) const
	Returns the dimension of the given face. More...

void	add_to (pos_index sourcePosition, pos_index targetPosition)
	Adds column corresponding to `sourcePosition` onto the column corresponding to `targetPosition`. More...

void	multiply_target_and_add_to (pos_index sourcePosition, const Field_element_type &coefficient, pos_index targetPosition)
	Multiplies the target column with the coefficiant and then adds the source column to it. That is: `targetColumn = (targetColumn * coefficient) + sourceColumn`. More...

void	multiply_source_and_add_to (const Field_element_type &coefficient, pos_index sourcePosition, pos_index targetPosition)
	Multiplies the source column with the coefficiant before adding it to the target column. That is: `targetColumn += (coefficient * sourceColumn)`. The source column will not be modified. More...

bool	is_zero_cell (pos_index position, id_index rowIndex) const
	Indicates if the cell at given coordinates has value zero. More...

bool	is_zero_column (pos_index position)
	Indicates if the column at given index has value zero. More...

pos_index	get_column_with_pivot (id_index faceIndex) const
	Returns the PosIdx index of the column which has the given row index as pivot. Assumes that the pivot exists. More...

id_index	get_pivot (pos_index position)
	Returns the row index of the pivot of the given column. More...

void	reset (Column_settings *colSettings)
	Resets the matrix to an empty matrix. More...

Position_to_index_overlay &	operator= (const Position_to_index_overlay &other)
	Assign operator.

const barcode_type &	get_current_barcode () const
	Returns the current barcode of the matrix. Available only if PersistenceMatrixOptions::has_column_pairings is true. More...

void	update_representative_cycles ()
	Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Precomputes the representative cycles of the current state of the filtration represented by the matrix. It does not need to be called before `get_representative_cycles` is called for the first time, but needs to be called before calling `get_representative_cycles` again if the matrix was modified in between. Otherwise the old cycles will be returned.

const std::vector< cycle_type > &	get_representative_cycles ()
	Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Returns all representative cycles of the current filtration. More...

const cycle_type &	get_representative_cycle (const bar_type &bar)
	Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Returns the cycle representing the given bar. More...

bool	vine_swap_with_z_eq_1_case (pos_index position)
	Only available if PersistenceMatrixOptions::has_vine_update is true. Does the same than vine_swap, but assumes that the swap is non trivial and therefore skips a part of the case study. More...

bool	vine_swap (pos_index position)
	Only available if PersistenceMatrixOptions::has_vine_update is true. Does a vine swap between two faces which are consecutives in the filtration. Roughly, if \( F \) is the current filtration represented by the matrix, the method modifies the matrix such that the new state corresponds to a valid state for the filtration \( F' \) equal to \( F \) but with the two faces at position `position` and `position + 1` swapped. Of course, the two faces should not have a face/coface relation which each other ; \( F' \) has to be a valid filtration. See [21] for more information about vine and vineyards. More...

Friends
void	swap (Position_to_index_overlay &matrix1, Position_to_index_overlay &matrix2)
	Swap operator.

Detailed Description

template<class Matrix_type, class Master_matrix_type>
class Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >

Overlay for chain matrices replacing all input and output MatIdx indices of the original methods with PosIdx indices. The overlay is useless for boundary matrices as MatIdx == PosIdx for them.

Template Parameters

%Matrix_type	Matrix type taking the overlay.
Master_matrix_type	An instanciation of Matrix from which all types and options are deduced.

Member Typedef Documentation

◆ bar_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::bar_type = typename Master_matrix_type::Bar

Bar type.

◆ barcode_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::barcode_type = typename Master_matrix_type::barcode_type

Barcode type.

◆ boundary_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::boundary_type = typename Master_matrix_type::boundary_type

Type of an input column.

◆ Cell_constructor

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Cell_constructor = typename Master_matrix_type::Cell_constructor

Factory of Cell classes.

◆ cell_rep_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::cell_rep_type = typename Master_matrix_type::cell_rep_type

Cell content representative.

◆ Column_settings

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Column_settings = typename Master_matrix_type::Column_settings

Structure giving access to the columns to necessary external classes.

◆ Column_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Column_type = typename Master_matrix_type::Column_type

Column type.

◆ cycle_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::cycle_type = typename Master_matrix_type::cycle_type

Cycle type.

◆ dimension_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::dimension_type = typename Master_matrix_type::dimension_type

Dimension value type.

◆ Field_element_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Field_element_type = typename Master_matrix_type::element_type

Type of an field element.

◆ id_index

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::id_index = typename Master_matrix_type::id_index

IDIdx index type.

◆ index

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::index = typename Master_matrix_type::index

MatIdx index type.

◆ pos_index

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::pos_index = typename Master_matrix_type::pos_index

PosIdx index type.

◆ Row_type

template<class Matrix_type , class Master_matrix_type >

using Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Row_type = typename Master_matrix_type::Row_type

Row type, only necessary with row access option.

Constructor & Destructor Documentation

◆ Position_to_index_overlay() [1/8]

template<class Matrix_type , class Master_matrix_type >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay ( Column_settings * colSettings )

inline

Constructs an empty matrix.

Parameters

colSettings Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators.

◆ Position_to_index_overlay() [2/8]

template<class Matrix_type , class Master_matrix_type >

template<class Boundary_type >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay	(	const std::vector< Boundary_type > &	orderedBoundaries,
		Column_settings *	colSettings
	)

inline

Constructs a new matrix from the given ranges of Matrix::cell_rep_type. Each range corresponds to a column (the order of the ranges are preserved). The content of the ranges is assumed to be sorted by increasing IDs. The IDs of the simplices are also assumed to be consecutifs, ordered by filtration value, starting with 0.

Template Parameters

Boundary_type Range type for Matrix::cell_rep_type ranges. Assumed to have a begin(), end() and size() method.

Parameters

orderedBoundaries Range of boundaries: orderedBoundaries is interpreted as a boundary matrix of a filtered simplicial complex, whose boundaries are ordered by filtration order. Therefore, orderedBoundaries[i] should store the boundary of the \( i^{th} \) simplex in the filtration, as an ordered list of indices of its facets (again those indices correspond to their respective position in the matrix). That is why the indices of the simplices are assumed to be consecutifs and starting with 0 (an empty boundary is interpreted as a vertex boundary and not as a non existing simplex). All dimensions up to the maximal dimension of interest have to be present. If only a higher dimension is of interest and not everything should be stored, then use the insert_boundary method instead (after creating the matrix with the Position_to_index_overlay(unsigned int, Column_settings*) constructor preferably).

colSettings Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators.

◆ Position_to_index_overlay() [3/8]

template<class Matrix_type , class Master_matrix_type >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay	(	unsigned int	numberOfColumns,
		Column_settings *	colSettings
	)

inline

Constructs a new empty matrix and reserves space for the given number of columns.

Parameters

numberOfColumns	Number of columns to reserve space for.
colSettings	Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators.

◆ Position_to_index_overlay() [4/8]

template<class Matrix_type , class Master_matrix_type >

template<typename BirthComparatorFunction , typename DeathComparatorFunction >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay	(	Column_settings *	colSettings,
		const BirthComparatorFunction &	birthComparator,
		const DeathComparatorFunction &	deathComparator
	)

inline

Only available for chain matrices. Constructs an empty matrix and stores the given comparators.

Warning: If PersistenceMatrixOptions::has_vine_update is false, the comparators are not used. And if PersistenceMatrixOptions::has_vine_update is true, but PersistenceMatrixOptions::has_column_pairings is also true, the comparators are ignored and the current barcode is used to compare birth and deaths. Therefore it is useless to provide them in those cases.

Template Parameters

BirthComparatorFunction	Type of the birth comparator: (pos_index, pos_index) -> bool
DeathComparatorFunction	Type of the death comparator: (pos_index, pos_index) -> bool

Parameters

colSettings	Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators.
birthComparator	Method taking two PosIdx indices as input and returning true if and only if the birth associated to the first position is strictly less than birth associated to the second one with respect to some self defined order. It is used while swapping two unpaired or two negative columns.
deathComparator	Method taking two PosIdx indices as input and returning true if and only if the death associated to the first position is strictly less than death associated to the second one with respect to some self defined order. It is used while swapping two positive but paired columns.

◆ Position_to_index_overlay() [5/8]

template<class Matrix_type , class Master_matrix_type >

template<typename BirthComparatorFunction , typename DeathComparatorFunction , class Boundary_type >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay	(	const std::vector< Boundary_type > &	orderedBoundaries,
		Column_settings *	colSettings,
		const BirthComparatorFunction &	birthComparator,
		const DeathComparatorFunction &	deathComparator
	)

inline

Only available for chain matrices. Constructs a new matrix from the given ranges of Matrix::cell_rep_type. Each range corresponds to a column (the order of the ranges are preserved). The content of the ranges is assumed to be sorted by increasing IDs. The IDs of the simplices are also assumed to be consecutifs, ordered by filtration value, starting with 0.

Warning: If PersistenceMatrixOptions::has_vine_update is false, the comparators are not used. And if PersistenceMatrixOptions::has_vine_update is true, but PersistenceMatrixOptions::has_column_pairings is also true, the comparators are ignored and the current barcode is used to compare birth and deaths. Therefore it is useless to provide them in those cases.

Template Parameters

BirthComparatorFunction	Type of the birth comparator: (pos_index, pos_index) -> bool
DeathComparatorFunction	Type of the death comparator: (pos_index, pos_index) -> bool
Boundary_type	Range type for Matrix::cell_rep_type ranges. Assumed to have a begin(), end() and size() method.

Parameters

orderedBoundaries	Range of boundaries: `orderedBoundaries` is interpreted as a boundary matrix of a filtered simplicial complex, whose boundaries are ordered by filtration order. Therefore, `orderedBoundaries[i]` should store the boundary of the \( i^{th} \) simplex in the filtration, as an ordered list of indices of its facets (again those indices correspond to their respective position in the matrix). That is why the indices of the simplices are assumed to be consecutifs and starting with 0 (an empty boundary is interpreted as a vertex boundary and not as a non existing simplex). All dimensions up to the maximal dimension of interest have to be present. If only a higher dimension is of interest and not everything should be stored, then use the insert_boundary method instead (after creating the matrix with the Position_to_index_overlay(unsigned int, Column_settings*, const BirthComparatorFunction&, const DeathComparatorFunction&) constructor preferably).
colSettings	Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators.
birthComparator	Method taking two PosIdx indices as input and returning true if and only if the birth associated to the first position is strictly less than birth associated to the second one with respect to some self defined order. It is used while swapping two unpaired or two negative columns.
deathComparator	Method taking two PosIdx indices as input and returning true if and only if the death associated to the first position is strictly less than death associated to the second one with respect to some self defined order. It is used while swapping two positive but paired columns.

◆ Position_to_index_overlay() [6/8]

template<class Matrix_type , class Master_matrix_type >

template<typename BirthComparatorFunction , typename DeathComparatorFunction >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay	(	unsigned int	numberOfColumns,
		Column_settings *	colSettings,
		const BirthComparatorFunction &	birthComparator,
		const DeathComparatorFunction &	deathComparator
	)

inline

Only available for chain matrices. Constructs a new empty matrix and reserves space for the given number of columns.

Warning: If PersistenceMatrixOptions::has_vine_update is false, the comparators are not used. And if PersistenceMatrixOptions::has_vine_update is true, but PersistenceMatrixOptions::has_column_pairings is also true, the comparators are ignored and the current barcode is used to compare birth and deaths. Therefore it is useless to provide them in those cases.

Template Parameters

BirthComparatorFunction	Type of the birth comparator: (pos_index, pos_index) -> bool
DeathComparatorFunction	Type of the death comparator: (pos_index, pos_index) -> bool

Parameters

numberOfColumns	Number of columns to reserve space for.
colSettings	Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators.
birthComparator	Method taking two PosIdx indices as input and returning true if and only if the birth associated to the first position is strictly less than birth associated to the second one with respect to some self defined order. It is used while swapping two unpaired or two negative columns.
deathComparator	Method taking two PosIdx indices as input and returning true if and only if the death associated to the first position is strictly less than death associated to the second one with respect to some self defined order. It is used while swapping two positive but paired columns.

◆ Position_to_index_overlay() [7/8]

template<class Matrix_type , class Master_matrix_type >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay	(	const Position_to_index_overlay< Matrix_type, Master_matrix_type > &	matrixToCopy,
		Column_settings *	colSettings = `nullptr`
	)

inline

Copy constructor. If colSettings is not a null pointer, its value is kept instead of the one in the copied matrix.

Parameters

matrixToCopy	Matrix to copy.
colSettings	Either a pointer to an existing setting structure for the columns or a null pointer. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators. If null pointer, the pointer stored in `matrixToCopy` is used instead.

◆ Position_to_index_overlay() [8/8]

template<class Matrix_type , class Master_matrix_type >

Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::Position_to_index_overlay ( Position_to_index_overlay< Matrix_type, Master_matrix_type > && other )

inlinenoexcept

Move constructor.

Parameters

other Matrix to move.

Member Function Documentation

◆ add_to()

template<class Matrix_type , class Master_matrix_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::add_to	(	pos_index	sourcePosition,
		pos_index	targetPosition
	)

inline

Adds column corresponding to sourcePosition onto the column corresponding to targetPosition.

Warning: They will be no verification to ensure that the addition makes sense for the validity of the matrix. For example, a right-to-left addition could corrupt the computation of the barcode if done blindly. So should be used with care.

Parameters

sourcePosition	PosIdx index of the source column.
targetPosition	PosIdx index of the target column.

◆ erase_empty_row()

template<class Matrix_type , class Master_matrix_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::erase_empty_row ( id_index rowIndex )

inline

Only available if PersistenceMatrixOptions::has_row_access and PersistenceMatrixOptions::has_removable_rows are true. Assumes that the row is empty and removes it.

Warning: The removed rows are always assumed to be empty. If it is not the case, the deleted row cells are not removed from their columns. And in the case of intrusive rows, this will generate a segmentation fault when the column cells are destroyed later. The row access is just meant as a "read only" access to the rows and the erase_empty_row method just as a way to specify that a row is empty and can therefore be removed from dictionnaries. This allows to avoid testing the emptiness of a row at each column cell removal, what can be quite frequent.

Parameters

rowIndex Row index of the empty row to remove.

◆ get_column() [1/2]

template<class Matrix_type , class Master_matrix_type >

Position_to_index_overlay< Matrix_type, Master_matrix_type >::Column_type & Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_column ( pos_index position )

inline

Returns the column at the given PosIdx index. The type of the column depends on the choosen options, see PersistenceMatrixOptions::column_type.

Parameters

position PosIdx index of the column to return.

Returns: Reference to the column.

◆ get_column() [2/2]

template<class Matrix_type , class Master_matrix_type >

const Position_to_index_overlay< Matrix_type, Master_matrix_type >::Column_type & Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_column ( pos_index position ) const

inline

Returns the column at the given PosIdx index. The type of the column depends on the choosen options, see PersistenceMatrixOptions::column_type.

Parameters

position PosIdx index of the column to return.

Returns: Const reference to the column.

◆ get_column_dimension()

template<class Matrix_type , class Master_matrix_type >

Position_to_index_overlay< Matrix_type, Master_matrix_type >::dimension_type Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_column_dimension ( pos_index position ) const

inline

Returns the dimension of the given face.

Parameters

position PosIdx index of the face.

Returns: Dimension of the face.

◆ get_column_with_pivot()

template<class Matrix_type , class Master_matrix_type >

Position_to_index_overlay< Matrix_type, Master_matrix_type >::pos_index Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_column_with_pivot ( id_index faceIndex ) const

inline

Returns the PosIdx index of the column which has the given row index as pivot. Assumes that the pivot exists.

Parameters

faceIndex Row index of the pivot.

Returns: PosIdx index of the column with the given pivot.

◆ get_current_barcode()

template<class Matrix_type , class Master_matrix_type >

const Position_to_index_overlay< Matrix_type, Master_matrix_type >::barcode_type & Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_current_barcode

inline

Returns the current barcode of the matrix. Available only if PersistenceMatrixOptions::has_column_pairings is true.

Recall that we assume that the boundaries were inserted in the order of filtration for the barcode to be valid.

Returns: A reference to the barcode. The barcode is a vector of Matrix::Bar. A bar stores three informations: the PosIdx birth index, the PosIdx death index and the dimension of the bar.

◆ get_max_dimension()

template<class Matrix_type , class Master_matrix_type >

Position_to_index_overlay< Matrix_type, Master_matrix_type >::dimension_type Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_max_dimension

inline

Returns the maximal dimension of a face stored in the matrix. Only available if PersistenceMatrixOptions::has_matrix_maximal_dimension_access is true.

Returns: The maximal dimension.

◆ get_number_of_columns()

template<class Matrix_type , class Master_matrix_type >

Position_to_index_overlay< Matrix_type, Master_matrix_type >::index Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_number_of_columns

inline

Returns the current number of columns in the matrix.

Returns: The number of columns.

◆ get_pivot()

template<class Matrix_type , class Master_matrix_type >

Position_to_index_overlay< Matrix_type, Master_matrix_type >::id_index Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_pivot ( pos_index position )

inline

Returns the row index of the pivot of the given column.

Parameters

position PosIdx index of the face corresponding to the column.

Returns: The row index of the pivot.

◆ get_representative_cycle()

template<class Matrix_type , class Master_matrix_type >

const Position_to_index_overlay< Matrix_type, Master_matrix_type >::cycle_type & Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_representative_cycle ( const bar_type & bar )

inline

Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Returns the cycle representing the given bar.

Parameters

bar	A bar from the current barcode.

Returns: A const reference to the cycle representing bar.

◆ get_representative_cycles()

template<class Matrix_type , class Master_matrix_type >

const std::vector< typename Position_to_index_overlay< Matrix_type, Master_matrix_type >::cycle_type > & Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_representative_cycles

inline

Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Returns all representative cycles of the current filtration.

Returns: A const reference to the vector of representative cycles.

◆ get_row() [1/2]

template<class Matrix_type , class Master_matrix_type >

Position_to_index_overlay< Matrix_type, Master_matrix_type >::Row_type & Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_row ( id_index rowIndex )

inline

Only available if PersistenceMatrixOptions::has_row_access is true. Returns the row at the given row index. The type of the row depends on the choosen options, see PersistenceMatrixOptions::has_intrusive_rows.

Parameters

rowIndex Row index of the row to return.

Returns: Reference to the row.

◆ get_row() [2/2]

template<class Matrix_type , class Master_matrix_type >

const Position_to_index_overlay< Matrix_type, Master_matrix_type >::Row_type & Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::get_row ( id_index rowIndex ) const

inline

Only available if PersistenceMatrixOptions::has_row_access is true. Returns the row at the given row index. The type of the row depends on the choosen options, see PersistenceMatrixOptions::has_intrusive_rows.

Parameters

rowIndex Row index of the row to return.

Returns: Const reference to the row.

◆ insert_boundary() [1/2]

template<class Matrix_type , class Master_matrix_type >

template<class Boundary_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::insert_boundary	(	const Boundary_type &	boundary,
		dimension_type	dim = `-1`
	)

inline

Inserts at the end of the matrix a new ordered column corresponding to the given boundary. This means that it is assumed that this method is called on boundaries in the order of the filtration. It also assumes that the faces in the given boundary are identified by their relative position in the filtration, starting at 0. If it is not the case, use the other insert_boundary instead by indicating the face ID used in the boundaries when the face is inserted.

Different to the constructor, the boundaries do not have to come from a simplicial complex, but also from a more general cell complex. This includes cubical complexes or Morse complexes for example.

When inserted, the given boundary is reduced and from the reduction process, the column is deduced in the form of: IDIdx + linear combination of older column IDIdxs. If the barcode is stored, it will be updated.

Template Parameters

Boundary_type Range of Matrix::cell_rep_type. Assumed to have a begin(), end() and size() method.

Parameters

boundary	Boundary generating the new column. The content should be ordered by ID.
dim	Dimension of the face whose boundary is given. If the complex is simplicial, this parameter can be omitted as it can be deduced from the size of the boundary.

◆ insert_boundary() [2/2]

template<class Matrix_type , class Master_matrix_type >

template<class Boundary_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::insert_boundary	(	id_index	faceIndex,
		const Boundary_type &	boundary,
		dimension_type	dim = `-1`
	)

inline

It does the same as the other version, but allows the boundary faces to be identified without restrictions except that all IDs have to be strictly increasing in the order of filtration. Note that you should avoid then to use the other insertion method to avoid overwriting IDs.

As a face has to be inserted before one of its cofaces in a valid filtration (recall that it is assumed that the faces are inserted by order of filtration), it is sufficient to indicate the ID of the face being inserted.

Template Parameters

Boundary_type Range of Matrix::cell_rep_type. Assumed to have a begin(), end() and size() method.

Parameters

faceID	IDIdx index to use to indentify the new face.
boundary	Boundary generating the new column. The indices of the boundary have to correspond to the `faceID` values of precedent calls of the method for the corresponding faces and should be ordered in increasing order.
dim	Dimension of the face whose boundary is given. If the complex is simplicial, this parameter can be omitted as it can be deduced from the size of the boundary.

◆ is_zero_cell()

template<class Matrix_type , class Master_matrix_type >

bool Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::is_zero_cell	(	pos_index	position,
		id_index	rowIndex
	)		const

inline

Indicates if the cell at given coordinates has value zero.

Parameters

position	PosIdx index of the face corresponding to the column of the cell.
rowIndex	Row index of the row of the cell.

Returns: true If the cell has value zero.; false Otherwise.

◆ is_zero_column()

template<class Matrix_type , class Master_matrix_type >

bool Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::is_zero_column ( pos_index position )

inline

Indicates if the column at given index has value zero.

Note that this method should always return false, as a valid chain matrix never has empty columns.

Parameters

position PosIdx index of the face corresponding to the column.

Returns: true If the column has value zero.; false Otherwise.

◆ multiply_source_and_add_to()

template<class Matrix_type , class Master_matrix_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::multiply_source_and_add_to	(	const Field_element_type &	coefficient,
		pos_index	sourcePosition,
		pos_index	targetPosition
	)

inline

Multiplies the source column with the coefficiant before adding it to the target column. That is: targetColumn += (coefficient * sourceColumn). The source column will not be modified.

Warning: They will be no verification to ensure that the addition makes sense for the validity of the matrix. For example, a right-to-left addition could corrupt the computation of the barcode if done blindly. So should be used with care.

Parameters

coefficient	Value to multiply.
sourcePosition	PosIdx index of the source column.
targetPosition	PosIdx index of the target column.

◆ multiply_target_and_add_to()

template<class Matrix_type , class Master_matrix_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::multiply_target_and_add_to	(	pos_index	sourcePosition,
		const Field_element_type &	coefficient,
		pos_index	targetPosition
	)

inline

Multiplies the target column with the coefficiant and then adds the source column to it. That is: targetColumn = (targetColumn * coefficient) + sourceColumn.

Warning: They will be no verification to ensure that the addition makes sense for the validity of the matrix. For example, a right-to-left addition could corrupt the computation of the barcode if done blindly. So should be used with care.

Parameters

sourcePosition	PosIdx index of the source column.
coefficient	Value to multiply.
targetPosition	PosIdx index of the target column.

◆ remove_last()

template<class Matrix_type , class Master_matrix_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::remove_last

inline

Only available if PersistenceMatrixOptions::has_removable_columns is true and, if PersistenceMatrixOptions::has_map_column_container is true or PersistenceMatrixOptions::has_vine_update is false. Removes the last face in the filtration from the matrix and updates the barcode if it is stored.

◆ remove_maximal_face()

template<class Matrix_type , class Master_matrix_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::remove_maximal_face ( pos_index position )

inline

Only available if PersistenceMatrixOptions::has_removable_columns, PersistenceMatrixOptions::has_vine_update and PersistenceMatrixOptions::has_map_column_container are true. Assumes that the face is maximal in the current complex and removes it such that the matrix remains consistent (i.e., the matrix is still a compatible bases of the chain complex in the sense of [41]). The maximality of the face is not verified. Also updates the barcode if it was computed.

◆ reset()

template<class Matrix_type , class Master_matrix_type >

void Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::reset ( Column_settings * colSettings )

inline

Resets the matrix to an empty matrix.

Parameters

colSettings Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the choosen column type, such as custom allocators.

◆ vine_swap()

template<class Matrix_type , class Master_matrix_type >

bool Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::vine_swap ( pos_index position )

inline

Only available if PersistenceMatrixOptions::has_vine_update is true. Does a vine swap between two faces which are consecutives in the filtration. Roughly, if \( F \) is the current filtration represented by the matrix, the method modifies the matrix such that the new state corresponds to a valid state for the filtration \( F' \) equal to \( F \) but with the two faces at position position and position + 1 swapped. Of course, the two faces should not have a face/coface relation which each other ; \( F' \) has to be a valid filtration. See [21] for more information about vine and vineyards.

Parameters

position PosIdx index of the first face to swap. The second one has to be at position + 1.

Returns: true If the barcode changed from the swap.; false Otherwise.

◆ vine_swap_with_z_eq_1_case()

template<class Matrix_type , class Master_matrix_type >

bool Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >::vine_swap_with_z_eq_1_case ( pos_index position )

inline

Only available if PersistenceMatrixOptions::has_vine_update is true. Does the same than vine_swap, but assumes that the swap is non trivial and therefore skips a part of the case study.

Parameters

position PosIdx index of the first face to swap. The second one has to be at position + 1.

Returns: true If the barcode changed from the swap.; false Otherwise.

The documentation for this class was generated from the following file:

include/gudhi/Persistence_matrix/overlay_posidx_to_matidx.h

Public Types

Public Member Functions

Friends

Detailed Description

template<class Matrix_type, class Master_matrix_type> class Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >

Member Typedef Documentation

◆ bar_type

◆ barcode_type

◆ boundary_type

◆ Cell_constructor

◆ cell_rep_type

◆ Column_settings

◆ Column_type

◆ cycle_type

◆ dimension_type

◆ Field_element_type

◆ id_index

◆ index

◆ pos_index

◆ Row_type

Constructor & Destructor Documentation

◆ Position_to_index_overlay() [1/8]

◆ Position_to_index_overlay() [2/8]

◆ Position_to_index_overlay() [3/8]

◆ Position_to_index_overlay() [4/8]

◆ Position_to_index_overlay() [5/8]

◆ Position_to_index_overlay() [6/8]

◆ Position_to_index_overlay() [7/8]

◆ Position_to_index_overlay() [8/8]

Member Function Documentation

◆ add_to()

◆ erase_empty_row()

◆ get_column() [1/2]

◆ get_column() [2/2]

◆ get_column_dimension()

◆ get_column_with_pivot()

◆ get_current_barcode()

◆ get_max_dimension()

◆ get_number_of_columns()

◆ get_pivot()

◆ get_representative_cycle()

◆ get_representative_cycles()

◆ get_row() [1/2]

◆ get_row() [2/2]

◆ insert_boundary() [1/2]

◆ insert_boundary() [2/2]

◆ is_zero_cell()

◆ is_zero_column()

◆ multiply_source_and_add_to()

◆ multiply_target_and_add_to()

◆ remove_last()

◆ remove_maximal_face()

◆ reset()

◆ vine_swap()

◆ vine_swap_with_z_eq_1_case()

template<class Matrix_type, class Master_matrix_type>
class Gudhi::persistence_matrix::Position_to_index_overlay< Matrix_type, Master_matrix_type >