GUDHI documentation
###################

.. image:: img/Gudhi_banner.png
   :align: center

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

The Gudhi library (Geometry Understanding in Higher Dimensions) is a generic
open source `C++ library <http://gudhi.gforge.inria.fr/doc/latest/>`_, with a
`Python interface <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.
* Algorithms to compute persistent homology and multi-field persistent homology.
* Simplication of simplicial complexes by edge contraction.

All data-structures are generic and several of their aspects can be
parameterized via template classes. We refer to :cite:`gudhilibrary_ICMS14`
for a detailed description of the design of the library.

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

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

.. include:: alpha_complex_sum.rst

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

.. include:: cubical_complex_sum.rst

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

.. include:: rips_complex_sum.rst

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

.. include:: simplex_tree_sum.rst

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

.. include:: tangential_complex_sum.rst

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

.. include:: witness_complex_sum.rst


Toolbox
*******

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

.. include:: bottleneck_distance_sum.rst

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

.. include:: persistent_cohomology_sum.rst

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

.. include:: persistence_graphical_tools_sum.rst

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

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