doc/python/cohomology-persistence.rst
 author Dmitriy Morozov Fri, 21 Aug 2009 14:26:56 -0700 branch dev changeset 166 1f3d54b2315b parent 146 4e27f1f7c169 child 172 a6605dc232f2 permissions -rw-r--r--
Exposed store argument to CohomologyPersistence.add() in Python

:class:CohomologyPersistence class
====================================

The :ref:rips-pairwise-cohomology illustrates the use of :class:CohomologyPersistence.

.. class:: CohomologyPersistence

.. method:: __init__(prime)

Initializes :class:CohomologyPersistence with the given prime; from
this point on all the computation will be performed with coefficients
coming from :math:\mathbb{Z}/prime \mathbb{Z}.

.. method:: add(boundary, birth, [store = True])

Adds a simplex with the given boundary to the complex, i.e.
:math:K_{i+1} = K_i \cup \sigma and boundary = :math:\partial \sigma.
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
:class:CohomologyPersistence. This is useful to not waste space on the
classes of the dimension equal to the maximum-dimensional simplices of
the complex since such classes will never die.

:returns: a pair (i, d). The first element is the index i.
It is the internal representation of the newly added simplex,
and should be used later for removal or 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
:meth:~CohomologyPersistence.add when the class that just
died was born.

.. method:: __iter__()

Iterator over the live cocycles stored in
:class:CohomologyPersistence. The returned elements are of the type
:class:Cocycle below.

.. class:: Cocycle

.. attribute:: birth

The birth value associated with the cocycle. It is passed to
:class:CohomologyPersistence in method
:meth:~CohomologyPersistence.add.

.. method:: __iter__()

Iterator over the individual nodes (simplices) of the cocycle, each of type
:class:CHSNode.

.. class:: CHSNode

.. attribute:: si

The index of the simplex, of type :class:CHSimplexIndex.

.. attribute:: coefficient

Coefficient in :math:\mathbb{Z}/prime \mathbb{Z} associated with the
simplex.

.. class:: CHSimplexIndex

.. attribute:: order

The count associated with the simplex when it is inserted into
:class:CohomologyPersistence.