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diff --git a/doc/common/main_page.h b/doc/common/main_page.h deleted file mode 100644 index db1e80ce..00000000 --- a/doc/common/main_page.h +++ /dev/null @@ -1,269 +0,0 @@ -/*! \mainpage The C++ library - * \tableofcontents - * \image html "Gudhi_banner.png" "" width=20cm - * - * \section Introduction Introduction - * The GUDHI library (Geometry Understanding in Higher Dimensions) is a generic open source - * <a class="el" target="_blank" href="http://gudhi.gforge.inria.fr/doc/latest/">C++ library</a> for - * Computational Topology and Topological Data Analysis - * (<a class="el" target="_blank" href="https://en.wikipedia.org/wiki/Topological_data_analysis">TDA</a>). - * 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 Simplification of simplicial complexes by edge contraction. - * \li Algorithms to compute persistent homology and bottleneck distance. - * - * 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 AlphaComplexDataStructure Alpha complex - \image html "alpha_complex_representation.png" "Alpha complex representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Vincent Rouvreau<br> - <b>Introduced in:</b> GUDHI 1.3.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Requires:</b> \ref cgal ≥ 4.7.0 and \ref eigen3 - </td> - <td width="75%"> - Alpha_complex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.<br> - The filtration value of each simplex is computed as the square of the circumradius of the simplex if the - circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration - values of the codimension 1 cofaces that make it not Gabriel otherwise. - All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into - the complex.<br> - <b>User manual:</b> \ref alpha_complex - <b>Reference manual:</b> Gudhi::alpha_complex::Alpha_complex - </td> - </tr> -</table> - \subsection CechComplexDataStructure Čech complex - \image html "cech_complex_representation.png" "Čech complex representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Vincent Rouvreau<br> - <b>Introduced in:</b> GUDHI 2.2.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - The Čech complex is a simplicial complex constructed from a proximity graph.<br> - The set of all simplices is filtered by the radius of their minimal enclosing ball.<br> - <b>User manual:</b> \ref cech_complex - <b>Reference manual:</b> Gudhi::cech_complex::Cech_complex - </td> - </tr> -</table> - \subsection CubicalComplexDataStructure Cubical complex - \image html "Cubical_complex_representation.png" "Cubical complex representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Pawel Dlotko<br> - <b>Introduced in:</b> GUDHI 1.3.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - The cubical complex is an example of a structured complex useful in computational mathematics (specially - rigorous numerics) and image analysis.<br> - <b>User manual:</b> \ref cubical_complex - <b>Reference manual:</b> Gudhi::cubical_complex::Bitmap_cubical_complex - </td> - </tr> -</table> - \subsection RipsComplexDataStructure Rips complex - \image html "rips_complex_representation.png" "Rips complex representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse<br> - <b>Introduced in:</b> GUDHI 2.0.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - Rips_complex is a simplicial complex constructed from a one skeleton graph.<br> - The filtration value of each edge is computed from a user-given distance function and is inserted until a - user-given threshold value.<br> - This complex can be built from a point cloud and a distance function, or from a distance matrix.<br> - <b>User manual:</b> \ref rips_complex - <b>Reference manual:</b> Gudhi::rips_complex::Rips_complex - </td> - </tr> -</table> - \subsection SimplexTreeDataStructure Simplex tree - \image html "Simplex_tree_representation.png" "Simplex tree representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Clément Maria<br> - <b>Introduced in:</b> GUDHI 1.0.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - The simplex tree is an efficient and flexible - data structure for representing general (filtered) simplicial complexes. The data structure - is described in \cite boissonnatmariasimplextreealgorithmica .<br> - <b>User manual:</b> \ref simplex_tree - <b>Reference manual:</b> Gudhi::Simplex_tree - </td> - </tr> -</table> - \subsection CoverComplexDataStructure Cover Complexes - \image html "gicvisu.jpg" "Graph Induced Complex of a point cloud." -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Mathieu Carrière<br> - <b>Introduced in:</b> GUDHI 2.1.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Requires:</b> \ref cgal ≥ 4.8.1 - </td> - <td width="75%"> - Nerves and Graph Induced Complexes are cover complexes, i.e. simplicial complexes that provably contain - topological information about the input data. They can be computed with a cover of the - data, that comes i.e. from the preimage of a family of intervals covering the image - of a scalar-valued function defined on the data. <br> - <b>User manual:</b> \ref cover_complex - <b>Reference manual:</b> Gudhi::cover_complex::Cover_complex - </td> - </tr> -</table> - \subsection SkeletonBlockerDataStructure Skeleton blocker - \image html "ds_representation.png" "Skeleton blocker representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> David Salinas<br> - <b>Introduced in:</b> GUDHI 1.1.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - 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.<br> - <b>User manual:</b> \ref skbl - <b>Reference manual:</b> Gudhi::skeleton_blocker::Skeleton_blocker_complex - </td> - </tr> -</table> - \subsection TangentialComplexDataStructure Tangential complex - \image html "tc_examples.png" "Tangential complex representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Clément Jamin<br> - <b>Introduced in:</b> GUDHI 2.0.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Requires:</b> \ref cgal ≥ 4.8.1 and \ref eigen3 - </td> - <td width="75%"> - A Tangential Delaunay complex is a <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a> - designed to reconstruct a \f$ k \f$-dimensional manifold embedded in \f$ d \f$-dimensional Euclidean space. - The input is a point sample coming from an unknown manifold. - The running time depends only linearly on the extrinsic dimension \f$ d \f$ - and exponentially on the intrinsic dimension \f$ k \f$.<br> - <b>User manual:</b> \ref tangential_complex - <b>Reference manual:</b> Gudhi::tangential_complex::Tangential_complex - </td> - </tr> -</table> - \subsection WitnessComplexDataStructure Witness complex - \image html "Witness_complex_representation.png" "Witness complex representation" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Siargey Kachanovich<br> - <b>Introduced in:</b> GUDHI 1.3.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Euclidean version requires:</b> \ref cgal ≥ 4.6.0 and \ref eigen3 - </td> - <td width="75%"> - Witness complex \f$ 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 .<br> - <b>User manual:</b> \ref witness_complex - <b>Reference manual:</b> Gudhi::witness_complex::SimplicialComplexForWitness - </td> - </tr> -</table> - - \section Toolbox Toolbox - - \subsection BottleneckDistanceToolbox Bottleneck distance - \image html "perturb_pd.png" "Bottleneck distance is the length of the longest edge" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> François Godi<br> - <b>Introduced in:</b> GUDHI 2.0.0<br> - <b>Copyright:</b> GPL v3<br> - <b>Requires:</b> \ref cgal ≥ 4.8.1 - </td> - <td width="75%"> - Bottleneck distance measures the similarity between two persistence diagrams. - It's the shortest distance b for which there exists a perfect matching between - the points of the two diagrams (+ all the diagonal points) such that - any couple of matched points are at distance at most b. - <br> - <b>User manual:</b> \ref bottleneck_distance - </td> - </tr> -</table> - \subsection ContractionToolbox Contraction - \image html "sphere_contraction_representation.png" "Sphere contraction example" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> David Salinas<br> - <b>Introduced in:</b> GUDHI 1.1.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - 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.<br> - <b>User manual:</b> \ref contr - </td> - </tr> -</table> - \subsection PersistentCohomologyToolbox Persistent Cohomology - \image html "3DTorus_poch.png" "Rips Persistent Cohomology on a 3D Torus" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Clément Maria<br> - <b>Introduced in:</b> GUDHI 1.0.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - 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 .<br> - <b>User manual:</b> \ref persistent_cohomology - <b>Reference manual:</b> Gudhi::persistent_cohomology::Persistent_cohomology - </td> - </tr> -</table> - \subsection PersistenceRepresentationsToolbox Persistence representations - \image html "average_landscape.png" "Persistence representations" -<table border="0"> - <tr> - <td width="25%"> - <b>Author:</b> Pawel Dlotko<br> - <b>Introduced in:</b> GUDHI 2.1.0<br> - <b>Copyright:</b> GPL v3<br> - </td> - <td width="75%"> - It contains implementation of various representations of persistence diagrams; diagrams themselves, persistence - landscapes (rigorous and grid version), persistence heath maps, vectors and others. It implements basic - functionalities which are neccessary to use persistence in statistics and machine learning.<br> - <b>User manual:</b> \ref Persistence_representations - </td> - </tr> -</table> - -*/ |