Persistence Matrix

Classes
class	Gudhi::persistence_matrix::FieldOperators
	Concept of the field operator classes needed for the class Matrix. More...
class	Gudhi::persistence_matrix::PersistenceMatrixColumn
	Concept of the column classes used by the Matrix class. The classes the columns inheritates from are either real or dummy classes, see Row_access_option, Column_dimension_option, Chain_column_option. If used with column compression, the column type has to have its std::hash method. More...
struct	Gudhi::persistence_matrix::PersistenceMatrixOptions
	Concept of the template parameter for the class Matrix. More...
struct	Gudhi::persistence_matrix::New_cell_constructor< Cell >
	Cell factory. Constructs and destroyes cell pointers with new and delete. More...
struct	Gudhi::persistence_matrix::Pool_cell_constructor< Cell >
	Cell factory. Uses Gudhi::Simple_object_pool, which is based on boost::object_pool, to construct and destroy cell pointer. More...
struct	Gudhi::persistence_matrix::Dummy_base_pairing
	Empty structure. Inheritated instead of Base_pairing, when the computation of the barcode was not enabled or if the pairing is already managed by the vine update classes. More...
struct	Gudhi::persistence_matrix::Dummy_base_swap
	Empty structure. Inheritated instead of Base_swap, when the column and row swaps are not enabled. More...
struct	Gudhi::persistence_matrix::Dummy_chain_pairing
	Empty structure. Inheritated instead of Chain_pairing, when the computation of the barcode was not enabled or if the pairing is already managed by the vine update classes. More...
struct	Gudhi::persistence_matrix::Dummy_chain_representative_cycles
	Empty structure. Inheritated instead of Chain_representative_cycles, when the computation of the representative cycles were not enabled. More...
struct	Gudhi::persistence_matrix::Dummy_chain_vine_swap
	Empty structure. Inheritated instead of Chain_vine_swap, when vine swappes are not enabled. More...
struct	Gudhi::persistence_matrix::Dummy_chain_vine_pairing
	Empty structure. Inheritated instead of Chain_barcode_swap, when the barcode is not stored. More...
class	Gudhi::persistence_matrix::Chain_barcode_swap< Master_matrix >
	Class managing the barcode for Chain_vine_swap. More...
struct	Gudhi::persistence_matrix::Dummy_cell_column_index_mixin
	Empty structure. Inheritated instead of Cell_column_index, when the row access is disabled. More...
struct	Gudhi::persistence_matrix::Dummy_cell_field_element_mixin
	Empty structure. Inheritated instead of Cell_field_element, when PersistenceMatrixOptions::is_z2 is true. More...
class	Gudhi::persistence_matrix::Cell_column_index< index >
	Class managing the column index access of a cell. More...
class	Gudhi::persistence_matrix::Cell_field_element< Field_element_type >
	Class managing the value access of a cell. More...
struct	std::hash< Gudhi::persistence_matrix::Cell< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Cell. More...
struct	Gudhi::persistence_matrix::Dummy_chain_properties
	Empty structure. Inheritated instead of Chain_column_extra_properties, when the columns are not meant for chain matrices. More...
struct	Gudhi::persistence_matrix::Dummy_dimension_holder
	Empty structure. Inheritated instead of Column_dimension_holder, when the columns are not storing a dimension. More...
struct	std::hash< Gudhi::persistence_matrix::Heap_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Heap_column. More...
struct	std::hash< Gudhi::persistence_matrix::Intrusive_list_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Intrusive_list_column. More...
struct	std::hash< Gudhi::persistence_matrix::Intrusive_set_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Intrusive_set_column. More...
struct	std::hash< Gudhi::persistence_matrix::List_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::List_column. More...
struct	std::hash< Gudhi::persistence_matrix::Naive_vector_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Naive_vector_column. More...
struct	Gudhi::persistence_matrix::Dummy_row_access
	Empty structure. Inheritated instead of Row_access, if the row access is not enabled. More...
struct	std::hash< Gudhi::persistence_matrix::Set_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Set_column. More...
struct	std::hash< Gudhi::persistence_matrix::Unordered_set_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Unordered_set_column. More...
struct	std::hash< Gudhi::persistence_matrix::Vector_column< Master_matrix > >
	Hash method for Gudhi::persistence_matrix::Vector_column. More...
struct	Gudhi::persistence_matrix::Dummy_matrix_dimension_holder
	Empty structure. Inheritated instead of Matrix_max_dimension_holder or Matrix_all_dimension_holder, when the maximal dimension of a matrix is not stored. More...
class	Gudhi::persistence_matrix::Matrix_max_dimension_holder< dimension_type >
	Class managing the maximal dimension of a face represented in the inheritating matrix, when the option of face removal is not enabled. More...
class	Gudhi::persistence_matrix::Matrix_all_dimension_holder< dimension_type >
	Class managing the maximal dimension of a face represented in the inheritating matrix, when the option of face removal is enabled. More...
struct	Gudhi::persistence_matrix::Dummy_matrix_row_access
	Empty structure. Inheritated instead of Matrix_row_access, when the the row access is not enabled. More...
struct	Gudhi::persistence_matrix::Dummy_ru_pairing
	Empty structure. Inheritated instead of RU_pairing, when the computation of the barcode was not enabled or if the pairing is already managed by the vine update classes. More...
struct	Gudhi::persistence_matrix::Dummy_ru_representative_cycles
	Empty structure. Inheritated instead of RU_representative_cycles, when the computation of the representative cycles were not enabled. More...
struct	Gudhi::persistence_matrix::Dummy_ru_vine_swap
	Empty structure. Inheritated instead of RU_vine_swap, when vine swappes are not enabled. More...
struct	Gudhi::persistence_matrix::Dummy_ru_vine_pairing
	Empty structure. Inheritated instead of RU_pairing, when the barcode is not stored. More...
class	Gudhi::persistence_matrix::Matrix< PersistenceMatrixOptions >
	Data structure for matrices, and in particular thought for matrices representing filtered complexes in order to compute persistence and/or representative cycles. More...
class	Gudhi::persistence_matrix::Base_matrix< Master_matrix >
	A basic matrix structure allowing to easily manipulate and access entire columns and rows, but not individual cells. More...
class	Gudhi::persistence_matrix::Base_matrix_with_column_compression< Master_matrix >
	A base matrix (also see Base_matrix), but with column compression. That is, all identical columns in the matrix are compressed together as the same column. For matrices with a lot of redundant columns, this will save a lot of space. Also, any addition made onto a column will be performed at the same time on all other identical columns, which is an advantage for the cohomology algorithm for example. More...
class	Gudhi::persistence_matrix::Base_pairing< Master_matrix >
	Class managing the barcode for Boundary_matrix if the option was enabled. More...
class	Gudhi::persistence_matrix::Base_swap< Master_matrix, Base_matrix >
	Class managing the column and row swaps in Base_matrix and Boundary_matrix. More...
class	Gudhi::persistence_matrix::Boundary_matrix< Master_matrix >
	Matrix structure to store the ordered boundary matrix \( R \) of a filtered complex in order to compute its persistent homology. Provides an access to its columns and rows as well as the possibility to remove the last faces of the filtration while maintaining a valid barcode. More...
class	Gudhi::persistence_matrix::Chain_matrix< Master_matrix >
	Matrix structure storing a compatible base of a filtered chain complex. See [41]. The base is constructed from the boundaries of the faces in the complex. Allows the persistent homology to be computed, as well as representative cycles. Supports vineyards (see [21]) and the removal of maximal faces while maintaining a valid barcode. Provides an access to its columns and rows. More...
class	Gudhi::persistence_matrix::Chain_pairing< Master_matrix >
	Class managing the barcode for Chain_matrix if the option was enabled. More...
class	Gudhi::persistence_matrix::Chain_representative_cycles< Master_matrix >
	Class managing the representative cycles for Chain_matrix if the option was enabled. More...
class	Gudhi::persistence_matrix::Chain_vine_swap< Master_matrix >
	Class managing the vine swaps for Chain_matrix. More...
class	Gudhi::persistence_matrix::Cell< Master_matrix >
	Matrix cell class. Stores by default only the row index it belongs to, but can also store its column index when the row access is enabled, as well as its value when they are different from only 0 and 1. Zero-valued cells are never explicited in the matrix. More...
class	Gudhi::persistence_matrix::Chain_column_extra_properties< Master_matrix >
	Class managing the pivot and partitioning of columns in Chain_matrix. More...
class	Gudhi::persistence_matrix::Column_dimension_holder< Master_matrix >
	Class managing the dimension access of a column. More...
class	Gudhi::persistence_matrix::Heap_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. Not compatible with row access. More...
class	Gudhi::persistence_matrix::Intrusive_list_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. More...
class	Gudhi::persistence_matrix::Intrusive_set_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. More...
class	Gudhi::persistence_matrix::List_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. More...
class	Gudhi::persistence_matrix::Naive_vector_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. More...
class	Gudhi::persistence_matrix::Row_access< Master_matrix >
	Class managing the row access for the columns. More...
class	Gudhi::persistence_matrix::Set_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. More...
class	Gudhi::persistence_matrix::Unordered_set_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. More...
class	Gudhi::persistence_matrix::Vector_column< Master_matrix >
	Column class following the PersistenceMatrixColumn concept. More...
class	Gudhi::persistence_matrix::Matrix_row_access< Row_type, Row_container_type, has_removable_rows, id_index >
	Class managing the row access for the inheritating matrix. More...
class	Gudhi::persistence_matrix::Id_to_index_overlay< Matrix_type, Master_matrix_type >
	Overlay for non-basic matrices replacing all input and output MatIdx indices of the original methods with IDIdx indices. More...
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. More...
class	Gudhi::persistence_matrix::RU_matrix< Master_matrix >
	Matrix structure to store the ordered boundary matrix \( R \cdot U \) of a filtered complex in order to compute its persistent homology, as well as representative cycles. Supports vineyards (see [21]) and the removal of maximal faces while maintaining a valid barcode. Provides an access to its columns and rows. More...
class	Gudhi::persistence_matrix::RU_pairing< Master_matrix >
	Class managing the barcode for RU_matrix if the option was enabled. More...
class	Gudhi::persistence_matrix::RU_representative_cycles< Master_matrix >
	Class managing the representative cycles for RU_matrix if the option was enabled. More...
class	Gudhi::persistence_matrix::RU_vine_swap< Master_matrix >
	Class managing the vine swaps for RU_matrix. More...
struct	Gudhi::persistence_matrix::Default_options< col_type, is_z2_only, FieldOperators >
	Default option structure for Matrix class. See the PersistenceMatrixOptions concept for a more detailed description of the fields. Produces a base matrix with no enabled option. More...

Typedefs
using	Gudhi::persistence_matrix::Row_access_option = Row_access
	If PersistenceMatrixOptions::has_row_access is true, then Row_access. Otherwise Dummy_row_access. Can eventually be removed if the structure of the column does not allow row access (as for Heap_column), but then it needs to be notified in the documentation of Column_types and as static_assert in Matrix::_assert_options.
using	Gudhi::persistence_matrix::Column_dimension_option = Column_dimension_holder
	If PersistenceMatrixOptions::has_column_pairings or PersistenceMatrixOptions::has_vine_update or PersistenceMatrixOptions::can_retrieve_representative_cycles is true, then Column_dimension_holder. Otherwise Dummy_dimension_holder.
using	Gudhi::persistence_matrix::Chain_column_option = Chain_column_extra_properties
	If PersistenceMatrixOptions::is_of_boundary_type is false, and, PersistenceMatrixOptions::has_column_pairings or PersistenceMatrixOptions::has_vine_update or PersistenceMatrixOptions::can_retrieve_representative_cycles is true, then Chain_column_extra_properties. Otherwise Dummy_chain_properties.

Enumerations
enum	Gudhi::persistence_matrix::Column_types {   Gudhi::persistence_matrix::LIST , Gudhi::persistence_matrix::SET , Gudhi::persistence_matrix::HEAP , Gudhi::persistence_matrix::VECTOR ,   Gudhi::persistence_matrix::NAIVE_VECTOR , Gudhi::persistence_matrix::UNORDERED_SET , Gudhi::persistence_matrix::INTRUSIVE_LIST , Gudhi::persistence_matrix::INTRUSIVE_SET }
	List of column types. More...
enum	Gudhi::persistence_matrix::Column_indexation_types { Gudhi::persistence_matrix::CONTAINER , Gudhi::persistence_matrix::POSITION , Gudhi::persistence_matrix::IDENTIFIER }
	List if indexation schemes. See description of indexation schemes for more details about the meaning of the indexation types. More...

Functions
constexpr bool	Gudhi::persistence_matrix::_no_G_death_comparator ([[maybe_unused]] unsigned int columnIndex1, [[maybe_unused]] unsigned int columnIndex2)
	Default death comparator. Simply assumes that two positive paired columns are never swapped. Which is true for the use case in zigzag persistence for example. More...

Detailed Description

Author

Hannah Schreiber

The module provides a data structure for matrices, in particular thought for matrices representing filtered complexes and used as backend for persistence algorithms, such at persistent homology, Persistent Cohomology, or zigzag [41].

The structure is entirely accessed via the class Matrix and it provides several functionnalities which can be enabled or disabled through a template argument following the PersistenceMatrixOptions concept. The main functionnalities are:

• column and row access,
• column addition and scalar multiplication,
• removal of maximal faces while maintaining a valid reduced boundary matrix or compatible chain complex base and a valid barcode with respect to the new filtration,
• computation of persistent homology (but note that if the barcode is your only necessity, using the Persistent Cohomology module is often more performant),
• computation of representative cycles for the cycle classes,
• swapping of two consecutive faces in a filtration (cf. vineyards [21]) while maintaining a valid reduced boundary matrix or compatible chain complex base and a valid barcode with respect to the new filtration,

Note

Matrix API is in a beta version and may change in incompatible ways in the near future.

Examples

Here is a list of examples using the module:

• Persistence_matrix/representative_cycles_from_matrix.cpp - A simple example on how to use the matrix to compute representative cycles.

• Persistence_matrix/simplex_tree_to_matrix.cpp - A simplex example on how to build a the different matrices from a simplex tree.

Enumeration Type Documentation

Column_indexation_types

enum Gudhi::persistence_matrix::Column_indexation_types

List if indexation schemes. See description of indexation schemes for more details about the meaning of the indexation types.

Enumerator
CONTAINER	Default use of MatIdx indices.
POSITION	All input and output MatIdx indices are replaced with PosIdx indices.
IDENTIFIER	All input and output MatIdx indices are replaced with IDIdx indices.

Column_types

enum Gudhi::persistence_matrix::Column_types

List of column types.

Enumerator
LIST	List_column: Underlying container is a std::list<Cell*>.
SET	Set_column: Underlying container is a std::set<Cell*>.
HEAP	Heap_column: Underlying container is a std::vector<Cell*> ordered as a heap. Is not compatible with row access and column compression.
VECTOR	Vector_column: Underlying container is a std::vector<Cell*> with a lazy removal method.
NAIVE_VECTOR	Naive_vector_column: Underlying container is a std::vector<Cell*>.
UNORDERED_SET	Unordered_set_column: Underlying container is a std::unordered_set<Cell*>.
INTRUSIVE_LIST	Intrusive_list_column: Underlying container is a boost::intrusive::list<Cell>.
INTRUSIVE_SET	Intrusive_set_column: Underlying container is a boost::intrusive::set<Cell>.

Examples

representative_cycles_from_matrix.cpp, and simplex_tree_to_matrix.cpp.

Function Documentation

_no_G_death_comparator()

constexpr bool Gudhi::persistence_matrix::_no_G_death_comparator ( [[maybe_unused] ] unsigned int  columnIndex1, [[maybe_unused] ] unsigned int  columnIndex2  )

constexpr

Default death comparator. Simply assumes that two positive paired columns are never swapped. Which is true for the use case in zigzag persistence for example.

Parameters

columnIndex1	First column index.
columnIndex2	Second column index.

Returns

false