doc/examples/index.rst
 author Camille Wormser Wed, 12 Aug 2009 07:16:35 -0700 branch dev changeset 162 eec482c29319 parent 142 ae2b1702c936 child 185 7241b887eabb permissions -rw-r--r--
Removing unused parameter names in order to avoid warnings -> no warning anymore in zigzag-persistence
```
.. _examples:

Examples
========

The most basic example and therefore a good place to start getting acquainted
with the library is the :ref:`triangle-example`. It adds simplices of a triangle
one by one, and then (in case of a :ref:`triangle-zigzag-example`), removes them
one by one.

.. toctree::

triangle
triangle-zigzag

The simplest example that instead of specifying the complex explicitly,
constructs it from the input point set is the :ref:`alpha-shape-example`. The
example reads points from a file, determines their dimension dynamically (based
on the number of coordinates in the first line of the file), and then constructs
an alpha shape and outputs its persistence diagram.

.. toctree::

alphashape

Another example that follows a similar strategy is the computation of the
Vietoris-Rips complex. Since only pairwise distances are required it works with
points in arbitrary dimension. (Of course, in dimensions 2 and 3 the complexes
are much larger than those for the :ref:`alpha-shape-example`).

.. toctree::
:maxdepth: 1

rips

One may use persistent cohomology algorithm to extract persistent cocycles,
turn them into harmonic cocycles, and use them to parametrize the input point
set; for details see [dSVJ09]_. The explanation of how to use Dionysus to
achieve this is available.

.. toctree::
:maxdepth: 1

cohomology

A simple example of computing persistence of a lower-star filtration is in
:sfile:`examples/lsfiltration.py`.
```