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

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    Cl&eacute;ment 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">