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...
#include <gudhi/Persistence_matrix/Position_to_index_overlay.h>
Public Types | |
using | Index = typename Master_matrix::Index |
using | ID_index = typename Master_matrix::ID_index |
using | Pos_index = typename Master_matrix::Pos_index |
using | Dimension = typename Master_matrix::Dimension |
using | Field_operators = typename Master_matrix::Field_operators |
Field operators class. Necessary only if PersistenceMatrixOptions::is_z2 is false. | |
using | Field_element = typename Master_matrix::Element |
using | Boundary = typename Master_matrix::Boundary |
using | Column = typename Master_matrix::Column |
using | Row = typename Master_matrix::Row |
using | Bar = typename Master_matrix::Bar |
using | Barcode = typename Master_matrix::Barcode |
using | Cycle = typename Master_matrix::Cycle |
using | Entry_representative = typename Master_matrix::Entry_representative |
using | Entry_constructor = typename Master_matrix::Entry_constructor |
using | Column_settings = typename Master_matrix::Column_settings |
Public Member Functions | |
Position_to_index_overlay (Column_settings *colSettings) | |
Constructs an empty matrix. More... | |
template<class Boundary_range = Boundary> | |
Position_to_index_overlay (const std::vector< Boundary_range > &orderedBoundaries, Column_settings *colSettings) | |
Constructs a new matrix from the given ranges of Matrix::Entry_representative. 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 consecutive, 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_range > | |
Position_to_index_overlay (const std::vector< Boundary_range > &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::Entry_representative. 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 consecutive, 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_range = Boundary> | |
void | insert_boundary (const Boundary_range &boundary, Dimension dim=Master_matrix::template get_null_value< Dimension >()) |
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 cells 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 cell ID used in the boundaries when the cell is inserted. More... | |
template<class Boundary_range = Boundary> | |
void | insert_boundary (ID_index cellIndex, const Boundary_range &boundary, Dimension dim=Master_matrix::template get_null_value< Dimension >()) |
It does the same as the other version, but allows the boundary cells 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 & | get_column (Pos_index position) |
Returns the column at the given PosIdx index. The type of the column depends on the chosen options, see PersistenceMatrixOptions::column_type. More... | |
const Column & | get_column (Pos_index position) const |
Returns the column at the given PosIdx index. The type of the column depends on the chosen options, see PersistenceMatrixOptions::column_type. More... | |
Row & | 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 chosen options, see PersistenceMatrixOptions::has_intrusive_rows. More... | |
const Row & | 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 chosen 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_cell (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 cell 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 cell 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 cell in the filtration from the matrix and updates the barcode if it is stored. More... | |
Dimension | get_max_dimension () const |
Returns the maximal dimension of a cell 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 | get_column_dimension (Pos_index position) const |
Returns the dimension of the given cell. 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 &coefficient, Pos_index targetPosition) |
Multiplies the target column with the coefficient and then adds the source column to it. That is: targetColumn = (targetColumn * coefficient) + sourceColumn . More... | |
void | multiply_source_and_add_to (const Field_element &coefficient, Pos_index sourcePosition, Pos_index targetPosition) |
Multiplies the source column with the coefficient before adding it to the target column. That is: targetColumn += (coefficient * sourceColumn) . The source column will not be modified. More... | |
bool | is_zero_entry (Pos_index position, ID_index rowIndex) const |
Indicates if the entry 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 cellIndex) 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 & | 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. Pre-computes 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 > & | get_representative_cycles () |
Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Returns all representative cycles of the current filtration. More... | |
const Cycle & | get_representative_cycle (const Bar &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 cells which are consecutive 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 cells at position position and position + 1 swapped. Of course, the two cells 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. | |
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.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Bar = typename Master_matrix::Bar |
Bar type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Barcode = typename Master_matrix::Barcode |
Barcode type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Boundary = typename Master_matrix::Boundary |
Type of an input column.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Column = typename Master_matrix::Column |
Column type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Column_settings = typename Master_matrix::Column_settings |
Structure giving access to the columns to necessary external classes.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Cycle = typename Master_matrix::Cycle |
Cycle type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Dimension = typename Master_matrix::Dimension |
Dimension value type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Entry_constructor = typename Master_matrix::Entry_constructor |
Factory of Entry classes.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Entry_representative = typename Master_matrix::Entry_representative |
Entry content representative.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Field_element = typename Master_matrix::Element |
Type of an field element.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::ID_index = typename Master_matrix::ID_index |
IDIdx index type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Index = typename Master_matrix::Index |
MatIdx index type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Pos_index = typename Master_matrix::Pos_index |
PosIdx index type.
using Gudhi::persistence_matrix::Position_to_index_overlay< Underlying_matrix, Master_matrix >::Row = typename Master_matrix::Row |
Row type, only necessary with row access option.
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Constructs an empty matrix.
colSettings | Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the chosen column type, such as custom allocators. |
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Constructs a new matrix from the given ranges of Matrix::Entry_representative. 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 consecutive, ordered by filtration value, starting with 0.
Boundary_range | Range type for Matrix::Entry_representative ranges. Assumed to have a begin(), end() and size() method. |
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 consecutive 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 chosen column type, such as custom allocators. |
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Constructs a new empty matrix and reserves space for the given number of columns.
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 chosen column type, such as custom allocators. |
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Only available for chain matrices. Constructs an empty matrix and stores the given comparators.
BirthComparatorFunction | Type of the birth comparator: (Pos_index, Pos_index) -> bool |
DeathComparatorFunction | Type of the death comparator: (Pos_index, Pos_index) -> bool |
colSettings | Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the chosen 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. |
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Only available for chain matrices. Constructs a new matrix from the given ranges of Matrix::Entry_representative. 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 consecutive, ordered by filtration value, starting with 0.
BirthComparatorFunction | Type of the birth comparator: (Pos_index, Pos_index) -> bool |
DeathComparatorFunction | Type of the death comparator: (Pos_index, Pos_index) -> bool |
Boundary_range | Range type for Matrix::Entry_representative ranges. Assumed to have a begin(), end() and size() method. |
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 consecutive 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 chosen 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. |
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Only available for chain matrices. Constructs a new empty matrix and reserves space for the given number of columns.
BirthComparatorFunction | Type of the birth comparator: (Pos_index, Pos_index) -> bool |
DeathComparatorFunction | Type of the death comparator: (Pos_index, Pos_index) -> bool |
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 chosen 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. |
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Copy constructor. If colSettings
is not a null pointer, its value is kept instead of the one in the copied matrix.
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 chosen column type, such as custom allocators. If null pointer, the pointer stored in matrixToCopy is used instead. |
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Move constructor.
other | Matrix to move. |
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Adds column corresponding to sourcePosition
onto the column corresponding to targetPosition
.
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Only available if PersistenceMatrixOptions::has_row_access and PersistenceMatrixOptions::has_removable_rows are true. Assumes that the row is empty and removes it.
rowIndex | Row index of the empty row to remove. |
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Returns the column at the given PosIdx index. The type of the column depends on the chosen options, see PersistenceMatrixOptions::column_type.
position | PosIdx index of the column to return. |
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Returns the column at the given PosIdx index. The type of the column depends on the chosen options, see PersistenceMatrixOptions::column_type.
position | PosIdx index of the column to return. |
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Returns the dimension of the given cell.
position | PosIdx index of the cell. |
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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.
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Returns the maximal dimension of a cell stored in the matrix. Only available if PersistenceMatrixOptions::has_matrix_maximal_dimension_access is true.
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Returns the current number of columns in the matrix.
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Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Returns the cycle representing the given bar.
bar | A bar from the current barcode. |
bar
.
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Only available if PersistenceMatrixOptions::can_retrieve_representative_cycles is true. Returns all representative cycles of the current filtration.
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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 chosen options, see PersistenceMatrixOptions::has_intrusive_rows.
rowIndex | Row index of the row to return. |
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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 chosen options, see PersistenceMatrixOptions::has_intrusive_rows.
rowIndex | Row index of the row to return. |
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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 cells 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 cell ID used in the boundaries when the cell is inserted.
Different to the constructor, the boundaries do not have to come from a simplicial complex, but also from a more general entry 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.
Boundary_range | Range of Matrix::Entry_representative. Assumed to have a begin(), end() and size() method. |
boundary | Boundary generating the new column. The content should be ordered by ID. |
dim | Dimension of the cell 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. |
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It does the same as the other version, but allows the boundary cells 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 cell has to be inserted before one of its cofaces in a valid filtration (recall that it is assumed that the cells are inserted by order of filtration), it is sufficient to indicate the ID of the cell being inserted.
Boundary_range | Range of Matrix::Entry_representative. Assumed to have a begin(), end() and size() method. |
cellIndex | IDIdx index to use to identify the new cell. |
boundary | Boundary generating the new column. The indices of the boundary have to correspond to the cellID values of precedent calls of the method for the corresponding cells and should be ordered in increasing order. |
dim | Dimension of the cell 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. |
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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.
position | PosIdx index of the cell corresponding to the column. |
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Multiplies the source column with the coefficient before adding it to the target column. That is: targetColumn += (coefficient * sourceColumn)
. The source column will not be modified.
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Multiplies the target column with the coefficient and then adds the source column to it. That is: targetColumn = (targetColumn * coefficient) + sourceColumn
.
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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 cell in the filtration from the matrix and updates the barcode if it is stored.
See also remove_maximal_cell.
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Only available if PersistenceMatrixOptions::has_removable_columns, PersistenceMatrixOptions::has_vine_update and PersistenceMatrixOptions::has_map_column_container are true. Assumes that the cell 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 cell is not verified. Also updates the barcode if it was computed.
See also remove_last.
position | PosIdx index of the cell to remove. |
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Resets the matrix to an empty matrix.
colSettings | Pointer to an existing setting structure for the columns. The structure should contain all the necessary external classes specifically necessary for the chosen column type, such as custom allocators. |
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Only available if PersistenceMatrixOptions::has_vine_update is true. Does a vine swap between two cells which are consecutive 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 cells at position position
and position + 1
swapped. Of course, the two cells 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.
position | PosIdx index of the first cell to swap. The second one has to be at position + 1 . |
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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.
position | PosIdx index of the first cell to swap. The second one has to be at position + 1 . |