diff options
author | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-09-12 12:47:01 +0000 |
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committer | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-09-12 12:47:01 +0000 |
commit | ba76b65af98ad337e39b72fd4260baee17eb4f49 (patch) | |
tree | 20eac403b7e6b8a0bb998b98c021235cdafa20dd /src | |
parent | 4308b8bc38b55053ddad94f0b9cf20095d53b81c (diff) |
Modify filtered complexes sections and examples.
Modify persistence sections and examples
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/trunk@1487 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: 6b0bdc7199f7229ac152175c4cbc6ebd79c9bc67
Diffstat (limited to 'src')
-rw-r--r-- | src/Persistent_cohomology/doc/Intro_persistent_cohomology.h | 62 | ||||
-rw-r--r-- | src/Simplex_tree/example/README | 4 | ||||
-rw-r--r-- | src/Simplex_tree/include/gudhi/Simplex_tree.h | 32 | ||||
-rw-r--r-- | src/common/doc/main_page.h | 10 |
4 files changed, 61 insertions, 47 deletions
diff --git a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h index c8081cac..0cba6361 100644 --- a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h +++ b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h @@ -46,7 +46,7 @@ namespace persistent_cohomology { composed of three elements: topological spaces, their homology groups and an evolution scheme. - <DT>Topological Spaces:</DT> + \section persistencetopolocalspaces Topological Spaces Topological spaces are represented by simplicial complexes. Let \f$V = \{1, \cdots ,|V|\}\f$ be a set of <EM>vertices</EM>. A <EM>simplex</EM> \f$\sigma\f$ is a subset of vertices @@ -84,7 +84,7 @@ namespace persistent_cohomology { <CODE>Filtration_value filtration (Simplex_handle)</CODE> that returns the value of the filtration on the simplex represented by the handle. - <DT>Homology:</DT> + \section persistencehomology Homology For a ring \f$\mathcal{R}\f$, the group of <EM>n-chains</EM>, denoted \f$\mathbf{C}_n(\mathbf{K},\mathcal{R})\f$, of \f$\mathbf{K}\f$ is the group of formal sums of @@ -111,7 +111,7 @@ namespace persistent_cohomology { We refer to \cite Munkres-elementsalgtop1984 for an introduction to homology theory and to \cite DBLP:books/daglib/0025666 for an introduction to persistent homology. - <DT>Indexing Scheme:</DT> + \section persistenceindexingscheme Indexing Scheme "Changing" a simplicial complex consists in applying a simplicial map. An <EM>indexing scheme</EM> is a directed graph together with a traversal order, such that two @@ -140,18 +140,62 @@ namespace persistent_cohomology { its subsimplices of same filtration value) provides an indexing scheme. \section Examples - We provide several example files: run these examples with -h for details on their use, and read the README file. -\li <CODE>rips_persistence.cpp</CODE> computes the Rips complex of a point cloud and its persistence diagram. +We provide several example files: run these examples with -h for details on their use, and read the README file. -\li <CODE>rips_multifield_persistence.cpp</CODE> computes the Rips complex of a point cloud and its persistence diagram -with a family of field coefficients. +\li <a href="_persistent_cohomology_2rips_persistence_8cpp-example.html"> +Persistent_cohomology/rips_persistence.cpp</a> computes the Rips complex of a point cloud and its persistence diagram. -\li <CODE>performance_rips_persistence.cpp</CODE> provides timings for the construction of the Rips complex on a set of -points sampling a Klein bottle in \f$\mathbb{R}^5\f$ with a simplex tree, its conversion to a +\li <a href="_persistent_cohomology_2rips_multifield_persistence_8cpp-example.html"> +Persistent_cohomology/rips_multifield_persistence.cpp</a> computes the Rips complex of a point cloud and its +persistence diagram with a family of field coefficients. + +\li <a href="_persistent_cohomology_2performance_rips_persistence_8cpp-example.html"> +Persistent_cohomology/performance_rips_persistence.cpp</a> provides timings for the construction of the Rips complex +on a set of points sampling a Klein bottle in \f$\mathbb{R}^5\f$ with a simplex tree, its conversion to a Hasse diagram and the computation of persistent homology and multi-field persistent homology for the different representations. +\li <a href="_persistent_cohomology_2alpha_complex_3d_persistence_8cpp-example.html"> +Persistent_cohomology/alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. +\code $> ./alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45 \endcode +\code Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 \endcode + +\li <a href="_persistent_cohomology_2alpha_complex_persistence_8cpp-example.html"> +Persistent_cohomology/alpha_complex_persistence.cpp</a> computes the persistent homology with +\f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. +\code $> ./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off \endcode +\code Alpha complex is of dimension 3 - 9273 simplices - 300 vertices. +Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 \endcode + +\li <a href="_persistent_cohomology_2periodic_alpha_complex_3d_persistence_8cpp-example.html"> +Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with +\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the periodic alpha complex on points sampling from an OFF file. +\code $> ./periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off 3 1.0 \endcode +\code Periodic Delaunay computed. +Simplex_tree dim: 3 +3 0 0 inf +3 1 0.0025 inf +3 1 0.0025 inf +3 1 0.0025 inf +3 2 0.005 inf +3 2 0.005 inf +3 2 0.005 inf +3 3 0.0075 inf \endcode + +\li <a href="_persistent_cohomology_2plain_homology_8cpp-example.html"> +Persistent_cohomology/plain_homology.cpp</a> computes the plain homology of a simple simplicial complex without +filtration values. + \copyright GNU General Public License v3. */ diff --git a/src/Simplex_tree/example/README b/src/Simplex_tree/example/README index 03c759cb..e37af790 100644 --- a/src/Simplex_tree/example/README +++ b/src/Simplex_tree/example/README @@ -52,7 +52,7 @@ EXAMPLE OF SIMPLE INSERTION *** Simplex tree construction with Z/2Z coefficients on weighted graph Klein bottle file: -./simplex_tree_from_file ../../../data/points/Klein_bottle_complex.txt 2 +./simplex_tree_from_cliques_of_graph ../../../data/points/Klein_bottle_complex.txt 2 Insert the 1-skeleton in the simplex tree in 0 s. Expand the simplex tree in 0 s. Information of the Simplex Tree: @@ -60,7 +60,7 @@ Information of the Simplex Tree: with Z/3Z coefficients: -./simplex_tree_from_file ../../../data/points/Klein_bottle_complex.txt 3 +./simplex_tree_from_cliques_of_graph ../../../data/points/Klein_bottle_complex.txt 3 Insert the 1-skeleton in the simplex tree in 0 s. Expand the simplex tree in 0 s. diff --git a/src/Simplex_tree/include/gudhi/Simplex_tree.h b/src/Simplex_tree/include/gudhi/Simplex_tree.h index fa9c0800..63e3f0e5 100644 --- a/src/Simplex_tree/include/gudhi/Simplex_tree.h +++ b/src/Simplex_tree/include/gudhi/Simplex_tree.h @@ -51,38 +51,6 @@ #include <cstdint> // for std::uint32_t namespace Gudhi { -/** \defgroup simplex_tree Filtered Complexes - * \author Clément Maria - * - * A simplicial complex \f$\mathbf{K}\f$ - * on a set of vertices \f$V = \{1, \cdots ,|V|\}\f$ is a collection of simplices - * \f$\{\sigma\}\f$, - * \f$\sigma \subseteq V\f$ such that \f$\tau \subseteq \sigma \in \mathbf{K} \rightarrow \tau \in - * \mathbf{K}\f$. The - * dimension \f$n=|\sigma|-1\f$ of \f$\sigma\f$ is its number of elements minus \f$1\f$. - * - * A filtration of a simplicial complex is - * a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying \f$f(\tau)\leq f(\sigma)\f$ whenever - * \f$\tau \subseteq \sigma\f$. Ordering the simplices by increasing filtration values - * (breaking ties so as a simplex appears after its subsimplices of same filtration value) - * provides an indexing scheme. - * - - <DT>Implementations:</DT> - There are two implementation of complexes. The first on is the Simplex_tree data structure. - The simplex tree is an efficient and flexible - data structure for representing general (filtered) simplicial complexes. The data structure - is described in \cite boissonnatmariasimplextreealgorithmica - \image html "Simplex_tree_representation.png" "Simplex tree representation" - - The second one is the Hasse_complex. The Hasse complex is a data structure representing - explicitly all co-dimension 1 incidence relations in a complex. It is consequently faster - when accessing the boundary of a simplex, but is less compact and harder to construct from - scratch. - - * \copyright GNU General Public License v3. - * @{ - */ struct Simplex_tree_options_full_featured; diff --git a/src/common/doc/main_page.h b/src/common/doc/main_page.h index 9146bed1..0983051d 100644 --- a/src/common/doc/main_page.h +++ b/src/common/doc/main_page.h @@ -13,8 +13,8 @@ * 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. + * \li Simplification of simplicial complexes by edge contraction. + * \li Algorithms to compute persistent homology persistent homology. * * 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. @@ -266,8 +266,10 @@ make \endverbatim * Simplex_tree/simplex_tree_from_alpha_shapes_3.cpp</a> * \li <a href="_simplex_tree_2simplex_tree_from_cliques_of_graph_8cpp-example.html"> * Simplex_tree/simplex_tree_from_cliques_of_graph.cpp</a> - * \li <a href="_persistent_cohomology_2alpha_shapes_persistence_8cpp-example.html"> - * Persistent_cohomology/alpha_shapes_persistence.cpp</a> + * \li <a href="_persistent_cohomology_2alpha_complex_3d_persistence_8cpp-example.html"> + * Persistent_cohomology/alpha_complex_3d_persistence.cpp</a> + * \li <a href="_persistent_cohomology_2alpha_complex_persistence_8cpp-example.html"> + * Persistent_cohomology/alpha_complex_persistence.cpp</a> * \li <a href="_persistent_cohomology_2rips_persistence_via_boundary_matrix_8cpp-example.html"> * Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp</a> * \li <a href="_persistent_cohomology_2performance_rips_persistence_8cpp-example.html"> |