GUDHI Python module documentation
#################################

.. figure::
     ../../doc/common/Gudhi_banner.png
     :alt: Gudhi banner
     :figclass: align-center

Introduction
************

The Python interface for the Gudhi library (Geometry Understanding in Higher
Dimensions) is a generic open source
`Python module <http://gudhi.gforge.inria.fr/python/latest/>`_, for
Computational Topology and Topological Data Analysis
(`TDA <https://en.wikipedia.org/wiki/Topological_data_analysis>`_).
The GUDHI library intends to help the development of new algorithmic solutions
in TDA and their transfer to applications. It provides robust, efficient,
flexible and easy to use implementations of state-of-the-art algorithms and
data structures.

The current release of the GUDHI library includes:

* Data structures to represent, construct and manipulate simplicial complexes.
* Simplification of simplicial complexes by edge contraction.
* Algorithms to compute persistent homology and bottleneck distance.

We refer to :cite:`gudhilibrary_ICMS14` for a detailed description of the
design of the library.

Data structures
***************

Alpha complex
=============

.. include:: alpha_complex_sum.inc

Cubical complex
===============

.. include:: cubical_complex_sum.inc

Rips complex
============

.. include:: rips_complex_sum.inc

Simplex tree
============

.. include:: simplex_tree_sum.inc

Tangential complex
==================

.. include:: tangential_complex_sum.inc

Witness complex
===============

.. include:: witness_complex_sum.inc


Toolbox
*******

Bottleneck distance
===================

.. include:: bottleneck_distance_sum.inc

Persistence cohomology
======================

.. include:: persistent_cohomology_sum.inc

Persistence graphical tools
===========================

.. include:: persistence_graphical_tools_sum.inc

Bibliography
************

.. bibliography:: ../../biblio/bibliography.bib
   :filter: docnames
   :style: unsrt