StaticPersistence
class¶StaticPersistence
¶__init__
(filtration)¶Initializes StaticPersistence
with the given
Filtration
. This operation effectively computes the boundary
matrix of the complex captured by the filtration with rows and columns
sorted with respect to the filtration ordering.
pair_simplices
(store_negative = False)¶Pairs simplices using the [ELZ02] algorithm. store_negative indicates whether to store the negative simplices in the cycles.
__call__
(i)¶Given an SPNode in the internal representation, the method returns its integer offset from the beginning of the filtration. This is useful to lookup the actual name of the simplex in the complex.
make_simplex_map
(filtration)¶Creates an auxilliary PersistenceSimplexMap
used to lookup the actual
simplices from the persistence indices. For example, the following
snippet prints out all the unpaired simplices:
smap = persistence.make_simplex_map(filtration)
for i in persistence:
if i.unpaired(): print smap[i]
__len__
()¶Returns the number of nodes (i.e. the number of simplices).
SPNode
¶The class represents nodes stored in StaticPersistence
. These nodes
are aware of their sign()
and pair
(and cycle()
if
negative after StaticPersistence.pair_simplices()
has run).
sign
()¶Returns the sign of the simplex: True for positive, False for negative.
pair
()¶Simplex’s pair. The pair is set to self if the siplex is unpaired.
cycle
¶If the simplex is negative, its cycle (that it kills) is non-empty, and
can be accessed using this method. The cycle itself is an iterable
container of SPNode
. For example, one can print the basis for
the (bounding) cycles:
smap = persistence.make_simplex_map(filtration)
for i in persistence:
for ii in i.cycle: print smap[ii]
unpaired
()¶Indicates whether the simplex is unpaired.
DynamicPersistenceChains
class¶DynamicPersistenceChains
¶This class works exactly like StaticPersistence
, providing all the
same methods. The only difference is that when iterating over it, the
elements are of type DPCNode
, described below.
DPCNode
¶This class works just like SPNode
, except it has an additional
attribute chain
.
chain
¶It allows one to retrieve the “chain” associated with the simplex.
(In terms of the decomposition, it gives access to the
columns of the matrix .) In case of the positive simplex, this
is a cycle created by the addition of this simplex. This access is
particularly useful for the unpaired positive simplices, allowing one to
recover the cycles they create. In case of the negative simplex, this chain’s
boundary is exactly what’s stored in the cycle
attribute.
For example, to print out all the essential cycles of the complex, one can run the following loop:
smap = persistence.make_simplex_map(filtration)
for i in persistence:
if i.unpaired()
for ii in i.chain: print smap[ii]