From ba76b65af98ad337e39b72fd4260baee17eb4f49 Mon Sep 17 00:00:00 2001 From: vrouvrea Date: Mon, 12 Sep 2016 12:47:01 +0000 Subject: 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 --- .../doc/Intro_persistent_cohomology.h | 62 ++++++++++++++++++---- 1 file changed, 53 insertions(+), 9 deletions(-) (limited to 'src/Persistent_cohomology/doc') 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. -
Topological Spaces:
+ \section persistencetopolocalspaces Topological Spaces Topological spaces are represented by simplicial complexes. Let \f$V = \{1, \cdots ,|V|\}\f$ be a set of vertices. A simplex \f$\sigma\f$ is a subset of vertices @@ -84,7 +84,7 @@ namespace persistent_cohomology { Filtration_value filtration (Simplex_handle) that returns the value of the filtration on the simplex represented by the handle. -
Homology:
+ \section persistencehomology Homology For a ring \f$\mathcal{R}\f$, the group of n-chains, 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. -
Indexing Scheme:
+ \section persistenceindexingscheme Indexing Scheme "Changing" a simplicial complex consists in applying a simplicial map. An indexing scheme 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 rips_persistence.cpp 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 rips_multifield_persistence.cpp computes the Rips complex of a point cloud and its persistence diagram -with a family of field coefficients. +\li +Persistent_cohomology/rips_persistence.cpp computes the Rips complex of a point cloud and its persistence diagram. -\li performance_rips_persistence.cpp 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 +Persistent_cohomology/rips_multifield_persistence.cpp computes the Rips complex of a point cloud and its +persistence diagram with a family of field coefficients. + +\li +Persistent_cohomology/performance_rips_persistence.cpp 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 +Persistent_cohomology/alpha_complex_3d_persistence.cpp 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 $> ./alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45 \endcode +\code Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 \endcode + +\li +Persistent_cohomology/alpha_complex_persistence.cpp computes the persistent homology with +\f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file. +\code $> ./alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off \endcode +\code Alpha complex is of dimension 3 - 9273 simplices - 300 vertices. +Simplex_tree dim: 3 +2 0 0 inf +2 1 0.0682162 1.0001 +2 1 0.0934117 1.00003 +2 2 0.56444 1.03938 \endcode + +\li +Persistent_cohomology/periodic_alpha_complex_3d_persistence.cpp computes the persistent homology with +\f$\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 +Persistent_cohomology/plain_homology.cpp computes the plain homology of a simple simplicial complex without +filtration values. + \copyright GNU General Public License v3. */ -- cgit v1.2.3