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The concept FilteredComplex describes the requirements for a type to implement a filtered cell complex, from which one can compute persistent homology via a model of the concept PersistentHomology. More...
Public Types | |
| typedef unspecified | Simplex_handle |
| Handle to specify a simplex. | |
| typedef unspecified | Filtration_value |
| Type for the value of the filtration function. More... | |
| typedef unspecified | Indexing_tag |
| Specifies the nature of the indexing scheme. More... | |
| typedef unspecified | Boundary_simplex_iterator |
| Iterator on the simplices belonging to the boundary of a simplex. More... | |
| typedef unspecified | Boundary_simplex_range |
| Range giving access to the simplices in the boundary of a simplex. More... | |
| typedef unspecified | Filtration_simplex_iterator |
| Iterator over all simplices of the complex in the order of the indexing scheme. More... | |
| typedef unspecified | Filtration_simplex_range |
| Range over the simplices of the complex in the order of the filtration. More... | |
Public Member Functions | |
| Simplex_handle | null_simplex () |
| Returns a Simplex_handle that is different from all simplex handles of the simplices. | |
| size_t | num_simplices () |
| Returns the number of simplices in the complex. More... | |
| int | dimension (Simplex_handle sh) |
| Returns the dimension of a simplex. | |
| Filtration_value | filtration (Simplex_handle sh) |
| Returns the filtration value of a simplex. More... | |
| Simplex_handle | simplex (size_t idx) |
| Returns the simplex that has index idx in the filtration. More... | |
| Boundary_simplex_range | boundary_simplex_range (Simplex_handle sh) |
| Returns a range giving access to all simplices of the boundary of a simplex, i.e. the set of codimension 1 subsimplices of the Simplex. More... | |
| Filtration_simplex_range | filtration_simplex_range () |
| Returns a range over the simplices of the complex in the order of the filtration. More... | |
Map interface | |
Conceptually a | |
| typedef unspecified | Simplex_key |
| Data stored for each simplex. More... | |
| Simplex_key | null_key () |
Returns a constant dummy number that is either negative, or at least as large as num_simplices(). Suggested value: -1. | |
| Simplex_key | key (Simplex_handle sh) |
Returns the number stored for a simplex by assign_key. More... | |
| void | assign_key (Simplex_handle sh, Simplex_key n) |
Store a number for a simplex, which can later be retrieved with key(sh). More... | |
The concept FilteredComplex describes the requirements for a type to implement a filtered cell complex, from which one can compute persistent homology via a model of the concept PersistentHomology.
| typedef unspecified FilteredComplex::Boundary_simplex_iterator |
Iterator on the simplices belonging to the boundary of a simplex.
value_type must be 'Simplex_handle'.
| typedef unspecified FilteredComplex::Boundary_simplex_range |
Range giving access to the simplices in the boundary of a simplex.
.begin() and .end() return type Boundary_simplex_iterator.
| typedef unspecified FilteredComplex::Filtration_simplex_iterator |
Iterator over all simplices of the complex in the order of the indexing scheme.
'value_type' must be 'Simplex_handle'.
| typedef unspecified FilteredComplex::Filtration_simplex_range |
Range over the simplices of the complex in the order of the filtration.
.begin() and .end() return type Filtration_simplex_iterator.
| typedef unspecified FilteredComplex::Filtration_value |
Type for the value of the filtration function.
Must be comparable with <.
| typedef unspecified FilteredComplex::Indexing_tag |
Specifies the nature of the indexing scheme.
is model of IndexingTag.
| typedef unspecified FilteredComplex::Simplex_key |
Data stored for each simplex.
Must be an integer type.
| void FilteredComplex::assign_key | ( | Simplex_handle | sh, |
| Simplex_key | n | ||
| ) |
Store a number for a simplex, which can later be retrieved with key(sh).
This is never called on null_simplex().
| Boundary_simplex_range FilteredComplex::boundary_simplex_range | ( | Simplex_handle | sh | ) |
Returns a range giving access to all simplices of the boundary of a simplex, i.e. the set of codimension 1 subsimplices of the Simplex.
If the simplex is \([v_0, \cdots ,v_d]\), with canonical orientation induced by \( v_0 < \cdots < v_d \), the iterator enumerates the simplices of the boundary in the order: \([v_0,\cdots,\widehat{v_i},\cdots,v_d]\) for \(i\) from 0 to d
We note that the alternate sum of the simplices given by the iterator gives the chains corresponding to the boundary of the simplex.
| Filtration_value FilteredComplex::filtration | ( | Simplex_handle | sh | ) |
Returns the filtration value of a simplex.
If sh is null_simplex(), returns the maximal value of the filtration function on the complex.
| Filtration_simplex_range FilteredComplex::filtration_simplex_range | ( | ) |
Returns a range over the simplices of the complex in the order of the filtration.
.begin() and .end() return type Filtration_simplex_iterator.
| Simplex_key FilteredComplex::key | ( | Simplex_handle | sh | ) |
Returns the number stored for a simplex by assign_key.
This is never called on null_simplex().
| size_t FilteredComplex::num_simplices | ( | ) |
Returns the number of simplices in the complex.
Does not count the empty simplex.
| Simplex_handle FilteredComplex::simplex | ( | size_t | idx | ) |
Returns the simplex that has index idx in the filtration.
This is only called on valid indices.
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