/*! \mainpage * \tableofcontents * \image html "Gudhi_banner.jpg" "" width=20cm * * \section Introduction Introduction * The Gudhi library (Geometric Understanding in Higher Dimensions) is a generic open source C++ library for * Computational Topology and Topological Data Analysis * (TDA). * 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: * * \li Data structures to represent, construct and manipulate simplicial complexes. * \li Algorithms to compute persistent homology and multi-field persistent homology. * \li 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. * \section DataStructures Data structures \subsection SimplexTreeDataStructure Simplex tree \image html "Simplex_tree_representation.png" "Simplex tree representation"
Introduced in: GUDHI 1.0.0 Copyright: GPL v3 |
Clément Maria The simplex tree is an efficient and flexible data structure for representing general (filtered) simplicial complexes. The data structure is described in \cite boissonnatmariasimplextreealgorithmica . User manual: \ref simplex_tree - Reference manual: Gudhi::Simplex_tree |
Introduced in: GUDHI 1.1.0 Copyright: GPL v3 |
David Salinas The Skeleton-Blocker data-structure proposes a light encoding for simplicial complexes by storing only an *implicit* representation of its simplices \cite socg_blockers_2011,\cite blockers2012. Intuitively, it just stores the 1-skeleton of a simplicial complex with a graph and the set of its "missing faces" that is very small in practice. This data-structure handles all simplicial complexes operations such as simplex enumeration or simplex removal but operations that are particularly efficient are operations that do not require simplex enumeration such as edge iteration, link computation or simplex contraction. User manual: \ref skbl - Reference manual: Gudhi::skbl::Skeleton_blocker_complex |
Introduced in: GUDHI 1.3.0 Copyright: GPL v3 |
Siargey Kachanovich Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$. The data structure is described in \cite boissonnatmariasimplextreealgorithmica . User manual: \ref witness_complex - Reference manual: Gudhi::witness_complex::SimplicialComplexForWitness |
Introduced in: GUDHI 1.0.0 Copyright: GPL v3 |
Clément Maria The theory of homology consists in attaching to a topological space a sequence of (homology) groups, capturing global topological features like connected components, holes, cavities, etc. Persistent homology studies the evolution -- birth, life and death -- of these features when the topological space is changing. Consequently, the theory is essentially composed of three elements: topological spaces, their homology groups and an evolution scheme. Computation of persistent cohomology using the algorithm of \cite DBLP:journals/dcg/SilvaMV11 and \cite DBLP:journals/corr/abs-1208-5018 and the Compressed Annotation Matrix implementation of \cite DBLP:conf/esa/BoissonnatDM13 . User manual: \ref persistent_cohomology |
Introduced in: GUDHI 1.1.0 Copyright: GPL v3 |
David Salinas The purpose of this package is to offer a user-friendly interface for edge contraction simplification of huge simplicial complexes. It uses the \ref skbl data-structure whose size remains small during simplification of most used geometrical complexes of topological data analysis such as the Rips or the Delaunay complexes. In practice, the size of this data-structure is even much lower than the total number of simplices. User manual: \ref contr |