Initializes CohomologyPersistence with the given prime; from this point on all the computation will be performed with coefficients in .
Adds a simplex with the given boundary to the complex, i.e. and boundary = . If a new class is born as a result of the addition, birth is stored with it for future reference.
If store is False and a class is born, it will not be stored in CohomologyPersistence. This avoids wasting space on the classes of the dimension equal to the maximum-dimensional simplices of the complex since such classes will never die.
The image parameter allows one to work with a case of a space where the filtration of induces a filtration of . In this case, one may want to compute image persistence (i.e. the persistence of the sequences of the images given by the inclusion of in ). image indicates whether the simplex added belongs to or not.
If given, coefficients is a list parallel to boundary that provides coefficients for the corresponding boundary elements. If empty, it is assumed to be .
|Returns:||a triple (i, d, ccl). The first element is the index i. It is the internal representation of the newly added simplex, and should be used later when constructing the boundaries of its cofaces. In other words, boundary must consist of these indices. The second element d is the death element. It is None if a birth occurred, otherwise it contains the value passed as birth to add() when the class that just died was born. The third element ccl returns the dying cocycle (iterable over instances of CHSNode), in case of a death. It’s empty if a birth occurs.|
Coefficient in associated with the simplex.
Given a node in the internal representation, the method returns its integer offset from the beginning of the filtration.
Creates an auxilliary map from the nodes to the simplices:
smap = persistence.make_simplex_map(filtration) for i in persistence: if i.unpaired(): print smap[i]
Returns the number of nodes (i.e. the number of simplices).
The following methods behave the same way as they do in SPNode.
The only crucial distinction in the behavior comes with the attribute cocycle.
This class is another wrapper around CohomologyPersistence that can compute image persistence induced by inclusion of a subcomplex. Its interface is the same as StaticCohomologyPersistence above, except for the constructor:
subcomplex is a function called with every simplex. It should return True if the simplex belong to the subcomplex; False otherwise.