doc/python/static-persistence.rst
 author Dmitriy Morozov Mon, 11 May 2009 12:45:49 -0700 branch dev changeset 134 c270826fd4a8 child 181 1ee6edc17cb6 permissions -rw-r--r--
Added documentation; for now mostly for the Python bindings
```
:class:`StaticPersistence` class
================================

.. class:: StaticPersistence

.. method:: __init__(filtration)

Initializes :class:`StaticPersistence` with the given
:class:`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.

.. method:: pair_simplices()

Pairs simplices using the [ELZ02]_ algorithm.

.. method:: __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. For example, the
following snippet prints out all the unpaired simplices::

for i in persistence:
if i == i.pair: print complex[filtration[persistence(i)]]

.. method:: __iter__()

Iterator over the nodes (representing individual simplices). See
:class:`SPNode`.

.. method:: __len__()

Returns the number of nodes (i.e. the number of simplices).

.. class:: SPNode

The class represents nodes stored in :class:`StaticPersistence`. These nodes
are aware of their :meth:`sign` and :attr:`pair` (and :meth:`cycle` if
negative after :meth:`StaticPersistence.pair_simplices` has run).

.. method:: sign()

Returns the sign of the simplex: `True` for positive, `False` for
negative.

.. attribute:: pair

Simplex's pair. The pair is set to self if the siplex is unpaired.

.. method:: 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 :class:`SPNode`. For example, one can print the basis for
the (bounding) cycles::

for i in persistence:
for ii in i.cycle(): print complex[filtration[persistence(ii)]]

.. method:: __eq__(other)

Returns true if the two nodes are the same. Useful for determining if
the node is unpaired (iff ``i == i.pair``), e.g::

print len([i in persistence if i == i.pair])    # prints the number of unpaired simplices
```