Change doc html theme.

Change tables


git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@2047 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: aaa29b8f610d506efc3762ad17c4fd768e74d399

20 files changed, 338 insertions, 169 deletions

diff --git a/src/cython/CMakeLists.txt b/src/cython/CMakeLists.txt
index 6c49c800..72be7b30 100644
--- a/src/cython/CMakeLists.txt
+++ b/src/cython/CMakeLists.txt
@@ -101,7 +101,7 @@ if(PYTHON_PATH AND CYTHON_PATH)
         WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
         COMMAND python "${CMAKE_CURRENT_BINARY_DIR}/cythonize_gudhi.py" "build_ext" "--inplace")
     
-    add_custom_target(cythonize_gudhi ALL DEPENDS "${CMAKE_CURRENT_BINARY_DIR}/gudhi.so"
+    add_custom_target(cython ALL DEPENDS "${CMAKE_CURRENT_BINARY_DIR}/gudhi.so"
                       COMMENT "Do not forget to add ${CMAKE_CURRENT_BINARY_DIR}/gudhi.so to your PYTHONPATH before using examples")
   
     # Unitary tests are available through py.test
@@ -135,11 +135,11 @@ if(PYTHON_PATH AND CYTHON_PATH)
       file(COPY "${CMAKE_SOURCE_DIR}/data/bitmap/3d_torus.txt" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/doc/")
       file(COPY "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/doc/")
       if (UNIX)
-        add_custom_target(html 
+        add_custom_target(sphinx
             WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/doc
             COMMAND make html && make doctest)
       else (UNIX)
-        add_custom_target(html 
+        add_custom_target(sphinx
             WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/doc
             COMMAND make.bat html)
       endif (UNIX)
diff --git a/src/cython/cython/rips_complex.pyx b/src/cython/cython/rips_complex.pyx
index 2e739ac3..7e04ca4b 100644
--- a/src/cython/cython/rips_complex.pyx
+++ b/src/cython/cython/rips_complex.pyx
@@ -40,22 +40,10 @@ cdef extern from "Rips_complex_interface.h" namespace "Gudhi":
 
 # RipsComplex python interface
 cdef class RipsComplex:
-    """RipsComplex is a simplicial complex constructed from the finite cells
-    of a Delaunay Triangulation.
-
-    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.
-
-    .. note::
-
-        When Rips_complex is constructed with an infinite value of alpha, the
-        complex is a Delaunay complex.
-
+    """The data structure is a one skeleton graph, or Rips graph, containing
+    edges when the edge length is less or equal to a given threshold. Edge
+    length is computed from a user given point cloud with a given distance
+    function, or a distance matrix.
     """
 
     cdef Rips_complex_interface * thisptr
diff --git a/src/cython/doc/alpha_complex_sum.rst b/src/cython/doc/alpha_complex_sum.rst
index af6c087f..0ccbcc21 100644
--- a/src/cython/doc/alpha_complex_sum.rst
+++ b/src/cython/doc/alpha_complex_sum.rst
@@ -1,23 +1,22 @@
-=====================================  =====================================  =====================================
-:Author: Vincent Rouvreau              :Introduced in: GUDHI 1.3.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
-:Requires: CGAL ≥ 4.7.0             Eigen3
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: Vincent Rouvreau                                          :Introduced in: GUDHI 1.3.0          :Copyright: GPL v3
+:Requires: CGAL :math:`\geq` 4.7.0                                 Eigen3
+=================================================================  ===================================  ===================================
 
-+-------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                | Alpha_complex is a simplicial complex constructed from the finite    |
-|      img/alpha_complex_representation.png | cells of a Delaunay Triangulation.                                   |
-|                                           |                                                                      |
-|                                           | 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.                                                             |
-|                                           |                                                                      |
-|                                           | This package requires having CGAL version 4.7 or higher (4.8.1 is    |
-|                                           | advised for better perfomances).                                     |
-+-------------------------------------------+----------------------------------------------------------------------+
-| :doc:`alpha_complex_user`                 | :doc:`alpha_complex_ref`                                             |
-+-------------------------------------------+----------------------------------------------------------------------+
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| .. figure::                                                    | Alpha_complex is a simplicial complex constructed from the finite      |
+|      img/alpha_complex_representation.png                      | cells of a Delaunay Triangulation.                                     |
+|      :alt: Alpha complex representation                        |                                                                        |
+|      :figclass: align-center                                   | The filtration value of each simplex is computed as the square of the  |
+|                                                                | circumradius of the simplex if the circumsphere is empty (the simplex  |
+|      Alpha complex representation                              | 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.                                                               |
+|                                                                |                                                                        |
+|                                                                | This package requires having CGAL version 4.7 or higher (4.8.1 is      |
+|                                                                | advised for better perfomances).                                       |
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| :doc:`alpha_complex_user`                                      | :doc:`alpha_complex_ref`                                               |
++----------------------------------------------------------------+------------------------------------------------------------------------+
diff --git a/src/cython/doc/alpha_complex_user.rst b/src/cython/doc/alpha_complex_user.rst
index 1ca96b6e..f1c57248 100644
--- a/src/cython/doc/alpha_complex_user.rst
+++ b/src/cython/doc/alpha_complex_user.rst
@@ -74,11 +74,13 @@ Data structure
 In order to build the alpha complex, first, a Simplex tree is built from the cells of a Delaunay Triangulation.
 (The filtration value is set to NaN, which stands for unknown value):
 
-.. image::
+.. figure::
     img/alpha_complex_doc.png
-    :align: center
+    :figclass: align-center
     :alt: Simplex tree structure construction example
 
+    Simplex tree structure construction example
+
 Filtration value computation algorithm
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
@@ -87,9 +89,9 @@ Filtration value computation algorithm
       **if** filtration(:math:`\sigma`) is NaN **then**
         filtration(:math:`\sigma`) = :math:`\alpha^2(\sigma)`
       **end if**
-  
+
       *//propagate alpha filtration value*
-  
+
       **for all** :math:`\tau` face of :math:`\sigma`
         **if** filtration(:math:`\tau`) is not NaN **then**
           filtration(:math:`\tau`) = filtration(:math:`\sigma`)
@@ -109,11 +111,13 @@ From the example above, it means the algorithm looks into each triangle ([0,1,2]
 computes the filtration value of the triangle, and then propagates the filtration value as described
 here:
 
-.. image::
+.. figure::
     img/alpha_complex_doc_420.png
-    :align: center
+    :figclass: align-center
     :alt: Filtration value propagation example
 
+    Filtration value propagation example
+
 Dimension 1
 ^^^^^^^^^^^
 
diff --git a/src/cython/doc/biblio.rst b/src/cython/doc/biblio.rst
index b8e733ed..3995e9c0 100644
--- a/src/cython/doc/biblio.rst
+++ b/src/cython/doc/biblio.rst
@@ -1,6 +1,5 @@
-============
 Bibliography
-============
+************
 
 .. bibliography:: bibliography.bib
    :filter: docnames
diff --git a/src/cython/doc/bottleneck_distance_sum.rst b/src/cython/doc/bottleneck_distance_sum.rst
index 6cffa122..6fec9b7e 100644
--- a/src/cython/doc/bottleneck_distance_sum.rst
+++ b/src/cython/doc/bottleneck_distance_sum.rst
@@ -1,15 +1,15 @@
-=====================================  =====================================  =====================================
-:Author: Francois Godi                 :Introduced in: GUDHI 1.4.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
-:Requires: CGAL ≥ 4.8.0
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: François Godi                                             :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
+:Requires: CGAL :math:`\geq` 4.8.0
+=================================================================  ===================================  ===================================
 
-+-------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                | Bottleneck distance measures the similarity between two persistence  |
-|      img/perturb_pd.png                   | 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.                                                  |
-+-------------------------------------------+----------------------------------------------------------------------+
-| :doc:`bottleneck_distance_user`           | :doc:`bottleneck_distance_ref`                                       |
-+-------------------------------------------+----------------------------------------------------------------------+
++-----------------------------------------------------------------+----------------------------------------------------------------------+
+| .. figure::                                                     | Bottleneck distance measures the similarity between two persistence  |
+|      img/perturb_pd.png                                         | diagrams. It's the shortest distance b for which there exists a      |
+|      :figclass: align-center                                    | perfect matching between the points of the two diagrams (+ all the   |
+|                                                                 | diagonal points) such that any couple of matched points are at       |
+|      Bottleneck distance is the length of                       | distance at most b.                                                  |
+|      the longest edge                                           |                                                                      |
++-----------------------------------------------------------------+----------------------------------------------------------------------+
+| :doc:`bottleneck_distance_user`                                 | :doc:`bottleneck_distance_ref`                                       |
++-----------------------------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/bottleneck_distance_user.rst b/src/cython/doc/bottleneck_distance_user.rst
index 08c6e451..3bc170f4 100644
--- a/src/cython/doc/bottleneck_distance_user.rst
+++ b/src/cython/doc/bottleneck_distance_user.rst
@@ -8,7 +8,7 @@ Definition
 
 Function
 --------
-.. automethod:: gudhi.bottleneck_distance
+.. autofunction:: gudhi.bottleneck_distance
 
 
 Basic example
diff --git a/src/cython/doc/conf.py b/src/cython/doc/conf.py
index 8b42ce37..680377b3 100755
--- a/src/cython/doc/conf.py
+++ b/src/cython/doc/conf.py
@@ -114,7 +114,7 @@ pygments_style = 'sphinx'
 
 # The theme to use for HTML and HTML Help pages.  See the documentation for
 # a list of builtin themes.
-html_theme = 'default'
+html_theme = 'bizstyle'
 
 # Theme options are theme-specific and customize the look and feel of a theme
 # further.  For a list of options available for each theme, see the
diff --git a/src/cython/doc/cubical_complex_sum.rst b/src/cython/doc/cubical_complex_sum.rst
index 98e23849..399c2357 100644
--- a/src/cython/doc/cubical_complex_sum.rst
+++ b/src/cython/doc/cubical_complex_sum.rst
@@ -1,12 +1,15 @@
-=====================================  =====================================  =====================================
-:Author: Pawel Dlotko                  :Introduced in: GUDHI 1.3.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: Pawel Dlotko                                              :Introduced in: GUDHI 1.3.0          :Copyright: GPL v3
+=================================================================  ===================================  ===================================
 
-+---------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                  | The cubical complex is an example of a structured complex useful in  |
-|      img/Cubical_complex_representation.png | computational mathematics (specially rigorous numerics) and image    |
-|                                             | analysis.                                                            |
-+---------------------------------------------+----------------------------------------------------------------------+
-| :doc:`cubical_complex_user`                 | * :doc:`cubical_complex_ref`                                         |
-|                                             | * :doc:`periodic_cubical_complex_ref`                                |
-+---------------------------------------------+----------------------------------------------------------------------+
++-----------------------------------------------------------------+----------------------------------------------------------------------+
+| .. figure::                                                     | The cubical complex is an example of a structured complex useful in  |
+|      img/Cubical_complex_representation.png                     | computational mathematics (specially rigorous numerics) and image    |
+|      :alt: Cubical complex representation                       | analysis.                                                            |
+|      :figclass: align-center                                    |                                                                      |
+|                                                                 |                                                                      |
+|      Cubical complex representation                             |                                                                      |
++-----------------------------------------------------------------+----------------------------------------------------------------------+
+| :doc:`cubical_complex_user`                                     | * :doc:`cubical_complex_ref`                                         |
+|                                                                 | * :doc:`periodic_cubical_complex_ref`                                |
++-----------------------------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/cubical_complex_user.rst b/src/cython/doc/cubical_complex_user.rst
index 16712de5..809aaddf 100644
--- a/src/cython/doc/cubical_complex_user.rst
+++ b/src/cython/doc/cubical_complex_user.rst
@@ -5,7 +5,7 @@ Definition
 ----------
 
 =====================================  =====================================  =====================================
-:Author: Pawel Dlotko                  :Introduced in: GUDHI PYTHON 1.4.0     :Copyright: GPL v3
+:Author: Pawel Dlotko                  :Introduced in: GUDHI PYTHON 1.3.0     :Copyright: GPL v3
 =====================================  =====================================  =====================================
 
 +---------------------------------------------+----------------------------------------------------------------------+
@@ -59,10 +59,12 @@ of filtration. This, together with dimension of :math:`\mathcal{K}` and the size
 directions, allows to determine, dimension, neighborhood, boundary and coboundary of every cube
 :math:`C \in \mathcal{K}`.
 
-.. image::
+.. figure::
     img/Cubical_complex_representation.png
-    :align: center
     :alt: Cubical complex.
+    :figclass: align-center
+
+    Cubical complex.
 
 Note that the cubical complex in the figure above is, in a natural way, a product of one dimensional cubical
 complexes in :math:`\mathbb{R}`. The number of all cubes in each direction is equal :math:`2n+1`, where :math:`n` is
@@ -85,10 +87,12 @@ bitmap (2 in the example below). Next d lines are the numbers of top dimensional
 in the example below). Next, in lexicographical order, the filtration of top dimensional cubes is given (1 4 6 8
 20 4 7 6 5 in the example below).
 
-.. image::
+.. figure::
     img/exampleBitmap.png
-    :align: center
     :alt: Example of a input data.
+    :figclass: align-center
+
+    Example of a input data.
 
 The input file for the following complex is:
 
diff --git a/src/cython/doc/index.rst b/src/cython/doc/index.rst
index bd138fd5..236ef3a4 100644
--- a/src/cython/doc/index.rst
+++ b/src/cython/doc/index.rst
@@ -11,7 +11,6 @@ GUDHI's documentation
 
 Introduction
 ************
-:doc:`biblio`
 
 The Gudhi library (Geometry Understanding in Higher Dimensions) is a generic
 open source C++ library for Computational Topology and Topological Data
@@ -44,6 +43,11 @@ Cubical complex
 
 .. include:: cubical_complex_sum.rst
 
+Rips complex
+============
+
+.. include:: rips_complex_sum.rst
+
 Simplex tree
 ============
 
diff --git a/src/cython/doc/persistence_graphical_tools_sum.rst b/src/cython/doc/persistence_graphical_tools_sum.rst
index a4ee4398..d602daa7 100644
--- a/src/cython/doc/persistence_graphical_tools_sum.rst
+++ b/src/cython/doc/persistence_graphical_tools_sum.rst
@@ -1,13 +1,12 @@
-=====================================  =====================================  =====================================
-:Author: Vincent Rouvreau              :Introduced in: GUDHI 1.4.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
-:Requires: Matplotlib                  Numpy
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: Vincent Rouvreau                                          :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
+:Requires: Matplotlib                                              Numpy
+=================================================================  ===================================  ===================================
 
-+---------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                  | These graphical tools comes on top of persistence results and allows |
-|      img/graphical_tools_representation.png |  the user to build easily barcode and persistence diagram.           |
-|                                             |                                                                      |
-+---------------------------------------------+----------------------------------------------------------------------+
-|  :doc:`persistence_graphical_tools_user`    | :doc:`persistence_graphical_tools_ref`                               |
-+---------------------------------------------+----------------------------------------------------------------------+
++-----------------------------------------------------------------+-----------------------------------------------------------------------+
+| .. figure::                                                     | These graphical tools comes on top of persistence results and allows  |
+|      img/graphical_tools_representation.png                     | the user to build easily barcode and persistence diagram.             |
+|                                                                 |                                                                       |
++-----------------------------------------------------------------+-----------------------------------------------------------------------+
+|  :doc:`persistence_graphical_tools_user`                        | :doc:`persistence_graphical_tools_ref`                                |
++-----------------------------------------------------------------+-----------------------------------------------------------------------+
diff --git a/src/cython/doc/persistent_cohomology_sum.rst b/src/cython/doc/persistent_cohomology_sum.rst
index cf3029fc..5d059b00 100644
--- a/src/cython/doc/persistent_cohomology_sum.rst
+++ b/src/cython/doc/persistent_cohomology_sum.rst
@@ -1,25 +1,27 @@
-=====================================  =====================================  =====================================
-:Author: Clément Maria                 :Introduced in: GUDHI 1.0.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: Clément Maria                                             :Introduced in: GUDHI 1.0.0          :Copyright: GPL v3
+=================================================================  ===================================  ===================================
 
-+---------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                  | The theory of homology consists in attaching to a topological space  |
-|      img/3DTorus_poch.png                   | 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`.                                |
-|                                             |                                                                      |
-+---------------------------------------------+----------------------------------------------------------------------+
-|  :doc:`persistent_cohomology_user`          | Please refer to each data structure that contains persistence        |
-|                                             | feature for reference:                                               |
-|                                             |                                                                      |
-|                                             | * :doc:`simplex_tree_ref`                                            |
-+---------------------------------------------+----------------------------------------------------------------------+
++-----------------------------------------------------------------+-----------------------------------------------------------------------+
+| .. figure::                                                     | The theory of homology consists in attaching to a topological space   |
+|      img/3DTorus_poch.png                                       | a sequence of (homology) groups, capturing global topological         |
+|      :figclass: align-center                                    | features like connected components, holes, cavities, etc. Persistent  |
+|                                                                 | homology studies the evolution -- birth, life and death -- of these   |
+|      Rips Persistent Cohomology on a 3D                         | features when the topological space is changing. Consequently, the    |
+|      Torus                                                      | 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`.                                 |
+|                                                                 |                                                                       |
++-----------------------------------------------------------------+-----------------------------------------------------------------------+
+|  :doc:`persistent_cohomology_user`                              | Please refer to each data structure that contains persistence         |
+|                                                                 | feature for reference:                                                |
+|                                                                 |                                                                       |
+|                                                                 | * :doc:`simplex_tree_ref`                                             |
+|                                                                 | * :doc:`cubical_complex_ref`                                          |
+|                                                                 | * :doc:`periodic_cubical_complex_ref`                                 |
++-----------------------------------------------------------------+-----------------------------------------------------------------------+
diff --git a/src/cython/doc/rips_complex_ref.rst b/src/cython/doc/rips_complex_ref.rst
new file mode 100644
index 00000000..b17dc4e0
--- /dev/null
+++ b/src/cython/doc/rips_complex_ref.rst
@@ -0,0 +1,10 @@
+=============================
+Rips complex reference manual
+=============================
+
+.. autoclass:: gudhi.RipsComplex
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+   .. automethod:: gudhi.RipsComplex.__init__
diff --git a/src/cython/doc/rips_complex_sum.rst b/src/cython/doc/rips_complex_sum.rst
new file mode 100644
index 00000000..ad57e54e
--- /dev/null
+++ b/src/cython/doc/rips_complex_sum.rst
@@ -0,0 +1,17 @@
+=================================================================  ===================================  ===================================
+:Author: Clément Maria, Pawel Dlotko, Vincent Rouvreau             :Introduced in: GUDHI 1.0.0          :Copyright: GPL v3
+=================================================================  ===================================  ===================================
+
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| .. figure::                                                    | Rips_complex is a simplicial complex constructed from a one skeleton   |
+|      img/rips_complex_representation.png                       | graph.                                                                 |
+|      :figclass: align-center                                   |                                                                        |
+|                                                                | The filtration value of each edge is computed from a user-given        |
+|      Rips complex representation                               | distance function and is inserted until a user-given threshold         |
+|                                                                | value.                                                                 |
+|                                                                |                                                                        |
+|                                                                | This complex can be built from a point cloud and a distance function,  |
+|                                                                | or from a distance matrix.                                             |
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| :doc:`rips_complex_user`                                       | :doc:`rips_complex_ref`                                                |
++----------------------------------------------------------------+------------------------------------------------------------------------+
diff --git a/src/cython/doc/rips_complex_user.rst b/src/cython/doc/rips_complex_user.rst
new file mode 100644
index 00000000..be9481de
--- /dev/null
+++ b/src/cython/doc/rips_complex_user.rst
@@ -0,0 +1,133 @@
+=========================
+Rips complex user manual
+=========================
+Definition
+----------
+
+=======================================================  =====================================  =====================================
+:Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau  :Introduced in: GUDHI 2.0.0            :Copyright: GPL v3
+=======================================================  =====================================  =====================================
+
++-------------------------------------------+----------------------------------------------------------------------+
+| :doc:`rips_complex_user`                  | :doc:`rips_complex_ref`                                              |
++-------------------------------------------+----------------------------------------------------------------------+
+
+`Rips complex <https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex>`_ is a one skeleton graph that allows to
+construct a simplicial complex from it. The input can be a point cloud with a given distance function, or a distance
+matrix.
+
+The filtration value of each edge is computed from a user-given distance function, or directly from the distance
+matrix.
+
+All edges that have a filtration value strictly greater than a given threshold value are not inserted into the complex.
+
+When creating a simplicial complex from this one skeleton graph, Rips inserts the one skeleton graph into the data
+structure, and then expands the simplicial complex when required.
+
+Vertex name correspond to the index of the point in the given range (aka. the point cloud).
+
+.. figure::
+    img/rips_complex_representation.png
+    :align: center
+
+    Rips-complex one skeleton graph representation
+
+On this example, as edges (4,5), (4,6) and (5,6) are in the complex, simplex (4,5,6) is added with the filtration value
+set with :math:`max(filtration(4,5), filtration(4,6), filtration(5,6))`. And so on for simplex (0,1,2,3).
+
+If the Rips_complex interfaces are not detailed enough for your need, please refer to rips_persistence_step_by_step.cpp
+example, where the graph construction over the Simplex_tree is more detailed.
+
+Point cloud and distance function
+---------------------------------
+
+Example from a point cloud and a distance function
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This example builds the one skeleton graph from the given points, threshold value, and distance function. Then it
+creates a :doc:`Simplex_tree <simplex_tree_ref>` with it.
+
+Then, it is asked to display information about the simplicial complex.
+
+.. testcode::
+
+    import gudhi
+    rips_complex = gudhi.RipsComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]],
+        max_edge_length=12.0)
+
+    simplex_tree = rips_complex.create_simplex_tree(max_dimension=1)
+    result_str = 'Rips complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
+        repr(simplex_tree.num_simplices()) + ' simplices - ' + \
+        repr(simplex_tree.num_vertices()) + ' vertices.'
+    print(result_str)
+    for filtered_value in simplex_tree.get_filtered_tree():
+        print(filtered_value)
+
+The output is:
+
+.. testoutput::
+
+    Rips complex is of dimension 1 - 18 simplices - 7 vertices.
+    ([0], 0.0)
+    ([1], 0.0)
+    ([2], 0.0)
+    ([3], 0.0)
+    ([4], 0.0)
+    ([5], 0.0)
+    ([6], 0.0)
+    ([2, 3], 5.0)
+    ([4, 5], 5.385164807134504)
+    ([0, 2], 5.830951894845301)
+    ([0, 1], 6.082762530298219)
+    ([1, 3], 6.324555320336759)
+    ([1, 2], 6.708203932499369)
+    ([5, 6], 7.280109889280518)
+    ([2, 4], 8.94427190999916)
+    ([0, 3], 9.433981132056603)
+    ([4, 6], 9.486832980505138)
+    ([3, 6], 11.0)
+
+Example from OFF file
+^^^^^^^^^^^^^^^^^^^^^
+
+This example builds the :doc:`Rips_complex <rips_complex_ref>` from the given points in an OFF file, threshold value,
+and distance function. Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it.
+
+Then, it is asked to display information about the Rips complex.
+
+
+.. testcode::
+
+    import gudhi
+    rips_complex = gudhi.RipsComplex(off_file='alphacomplexdoc.off', max_edge_length=12.0)
+    simplex_tree = rips_complex.create_simplex_tree(max_dimension=1)
+    result_str = 'Rips complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
+        repr(simplex_tree.num_simplices()) + ' simplices - ' + \
+        repr(simplex_tree.num_vertices()) + ' vertices.'
+    print(result_str)
+    for filtered_value in simplex_tree.get_filtered_tree():
+        print(filtered_value)
+
+the program output is:
+
+.. testoutput::
+
+    Rips complex is of dimension 1 - 18 simplices - 7 vertices.
+    ([0], 0.0)
+    ([1], 0.0)
+    ([2], 0.0)
+    ([3], 0.0)
+    ([4], 0.0)
+    ([5], 0.0)
+    ([6], 0.0)
+    ([2, 3], 5.0)
+    ([4, 5], 5.385164807134504)
+    ([0, 2], 5.830951894845301)
+    ([0, 1], 6.082762530298219)
+    ([1, 3], 6.324555320336759)
+    ([1, 2], 6.708203932499369)
+    ([5, 6], 7.280109889280518)
+    ([2, 4], 8.94427190999916)
+    ([0, 3], 9.433981132056603)
+    ([4, 6], 9.486832980505138)
+    ([3, 6], 11.0)
diff --git a/src/cython/doc/simplex_tree_sum.rst b/src/cython/doc/simplex_tree_sum.rst
index 0f34888a..b79cf4fd 100644
--- a/src/cython/doc/simplex_tree_sum.rst
+++ b/src/cython/doc/simplex_tree_sum.rst
@@ -1,13 +1,14 @@
-=====================================  =====================================  =====================================
-:Author: Clément Maria                 :Introduced in: GUDHI 1.0.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: Clément Maria                                             :Introduced in: GUDHI 1.0.0          :Copyright: GPL v3
+=================================================================  ===================================  ===================================
 
-+-------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                | The simplex tree is an efficient and flexible data structure for     |
-|      img/Simplex_tree_representation.png  | representing general (filtered) simplicial complexes.                |
-|                                           |                                                                      |
-|                                           | The data structure is described in                                   |
-|                                           | :cite:`boissonnatmariasimplextreealgorithmica`                       |
-+-------------------------------------------+----------------------------------------------------------------------+
-| :doc:`simplex_tree_user`                  | :doc:`simplex_tree_ref`                                              |
-+-------------------------------------------+----------------------------------------------------------------------+
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| .. figure::                                                    | The simplex tree is an efficient and flexible data structure for       |
+|      img/Simplex_tree_representation.png                       | representing general (filtered) simplicial complexes.                  |
+|      :alt: Simplex tree representation                         |                                                                        |
+|      :figclass: align-center                                   | The data structure is described in                                     |
+|                                                                | :cite:`boissonnatmariasimplextreealgorithmica`                         |
+|      Simplex tree representation                               |                                                                        |
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| :doc:`simplex_tree_user`                                       | :doc:`simplex_tree_ref`                                                |
++----------------------------------------------------------------+------------------------------------------------------------------------+
diff --git a/src/cython/doc/tangential_complex_sum.rst b/src/cython/doc/tangential_complex_sum.rst
index 4e358a7b..2b05bc10 100644
--- a/src/cython/doc/tangential_complex_sum.rst
+++ b/src/cython/doc/tangential_complex_sum.rst
@@ -1,16 +1,15 @@
-=====================================  =====================================  =====================================
-:Author: Clément Jamin                 :Introduced in: GUDHI 1.4.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
-:Requires: CGAL &ge; 4.8.0             Eigen3
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: Clément Jamin                                             :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
+:Requires: CGAL :math:`\geq` 4.8.0                                 Eigen3
+=================================================================  ===================================  ===================================
 
-+-------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                | A Tangential Delaunay complex is a simplicial complex designed to    |
-|      img/tc_examples.png                  | reconstruct a :math:`k`-dimensional manifold embedded in :math:`d`-  |
-|                                           | dimensional Euclidean space. The input is a point sample coming from |
-|                                           | an unknown manifold. The running time depends only linearly on the   |
-|                                           | extrinsic dimension :math:`d` and exponentially on the intrinsic     |
-|                                           | dimension :math:`k`.                                                 |
-+-------------------------------------------+----------------------------------------------------------------------+
-| :doc:`tangential_complex_user`            | :doc:`tangential_complex_ref`                                        |
-+-------------------------------------------+----------------------------------------------------------------------+
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| .. figure::                                                    | A Tangential Delaunay complex is a simplicial complex designed to      |
+|      img/tc_examples.png                                       | reconstruct a :math:`k`-dimensional manifold embedded in :math:`d`-    |
+|      :figclass: align-center                                   | dimensional Euclidean space. The input is a point sample coming from   |
+|                                                                | an unknown manifold. The running time depends only linearly on the     |
+|      **Tangential complex representation**                     | extrinsic dimension :math:`d` and exponentially on the intrinsic       |
+|                                                                | dimension :math:`k`.                                                   |
++----------------------------------------------------------------+------------------------------------------------------------------------+
+| :doc:`tangential_complex_user`                                 | :doc:`tangential_complex_ref`                                          |
++----------------------------------------------------------------+------------------------------------------------------------------------+
diff --git a/src/cython/doc/tangential_complex_user.rst b/src/cython/doc/tangential_complex_user.rst
index 7b6c9e79..2679528c 100644
--- a/src/cython/doc/tangential_complex_user.rst
+++ b/src/cython/doc/tangential_complex_user.rst
@@ -26,6 +26,7 @@ example, with :math:`k = 1` and :math:`d = 2`. The input data is 4 points
 .. figure:: img/tc_example_01.png
     :alt: The input
     :figclass: align-center
+
     The input
 
 For each point :math:`p`, estimate its tangent subspace :math:`T_p` (e.g.
@@ -34,8 +35,10 @@ using PCA).
 .. figure:: img/tc_example_02.png
     :alt: The estimated normals
     :figclass: align-center
+
     The estimated normals
 
+
 Let us add the Voronoi diagram of the points in orange. For each point
 :math:`p`, construct its star in the Delaunay triangulation of :math:`P`
 restricted to :math:`T_p`.
@@ -43,6 +46,7 @@ restricted to :math:`T_p`.
 .. figure:: img/tc_example_03.png
     :alt: The Voronoi diagram
     :figclass: align-center
+
     The Voronoi diagram
 
 The Tangential Delaunay complex is the union of those stars.
@@ -62,6 +66,7 @@ Let us take the same example.
 .. figure:: img/tc_example_07_before.png
     :alt: Before
     :figclass: align-center
+
     Before
 
 Let us slightly move the tangent subspace :math:`T_q`
@@ -69,6 +74,7 @@ Let us slightly move the tangent subspace :math:`T_q`
 .. figure:: img/tc_example_07_after.png
     :alt: After
     :figclass: align-center
+
     After
 
 Now, the star of :math:`Q` contains :math:`QP`, but the star of :math:`P` does
@@ -77,6 +83,7 @@ not contain :math:`QP`. We have an inconsistency.
 .. figure:: img/tc_example_08.png
     :alt: After
     :figclass: align-center
+
     After
 
 One way to solve inconsistencies is to randomly perturb the positions of the
diff --git a/src/cython/doc/witness_complex_sum.rst b/src/cython/doc/witness_complex_sum.rst
index 005a5a41..22ef36ea 100644
--- a/src/cython/doc/witness_complex_sum.rst
+++ b/src/cython/doc/witness_complex_sum.rst
@@ -1,25 +1,25 @@
-=====================================  =====================================  =====================================
-:Author: Siargey Kachanovich           :Introduced in: GUDHI 1.3.0            :Copyright: GPL v3
-=====================================  =====================================  =====================================
+=================================================================  ===================================  ===================================
+:Author: Siargey Kachanovich                                       :Introduced in: GUDHI 1.3.0          :Copyright: GPL v3
+=================================================================  ===================================  ===================================
 
-+---------------------------------------------+----------------------------------------------------------------------+
-| .. image::                                  | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on  |
-|      img/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`:Wit(W,L)` is a simplicial |
-|                                             | complex defined on two sets of points in :math:`\mathbb{R}^D`:       |
-|                                             |                                                                      |
-|                                             | * :math:`W` set of **witnesses** and                                 |
-|                                             | * :math:`L \subseteq W` set of **landmarks**.                        |
-|                                             |                                                                      |
-|                                             | The simplices are based on landmarks and a simplex belongs to the    |
-|                                             | witness complex if and only if it is witnessed, that is:             |
-|                                             |                                                                      |
-|                                             | :math:`\sigma \subset L` is witnessed if there exists a point        |
-|                                             | :math:`w \in W` such that w is closer to the vertices of             |
-|                                             | :math:`\sigma` than other points in :math:`L` and all of its faces   |
-|                                             | are witnessed as well.                                               |
-|                                             |                                                                      |
-|                                             | The data structure is described in                                   |
-|                                             | :cite:`boissonnatmariasimplextreealgorithmica`.                      |
-+---------------------------------------------+----------------------------------------------------------------------+
-| :doc:`witness_complex_user`                 | :doc:`witness_complex_ref`                                           |
-+---------------------------------------------+----------------------------------------------------------------------+
++-----------------------------------------------------------------+----------------------------------------------------------------------+
+| .. image::                                                      | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on  |
+|      img/Witness_complex_representation.png                     | two sets of points in :math:`\mathbb{R}^D`:Wit(W,L)` is a simplicial |
+|                                                                 | complex defined on two sets of points in :math:`\mathbb{R}^D`:       |
+|                                                                 |                                                                      |
+|                                                                 | * :math:`W` set of **witnesses** and                                 |
+|                                                                 | * :math:`L \subseteq W` set of **landmarks**.                        |
+|                                                                 |                                                                      |
+|                                                                 | The simplices are based on landmarks and a simplex belongs to the    |
+|                                                                 | witness complex if and only if it is witnessed, that is:             |
+|                                                                 |                                                                      |
+|                                                                 | :math:`\sigma \subset L` is witnessed if there exists a point        |
+|                                                                 | :math:`w \in W` such that w is closer to the vertices of             |
+|                                                                 | :math:`\sigma` than other points in :math:`L` and all of its faces   |
+|                                                                 | are witnessed as well.                                               |
+|                                                                 |                                                                      |
+|                                                                 | The data structure is described in                                   |
+|                                                                 | :cite:`boissonnatmariasimplextreealgorithmica`.                      |
++-----------------------------------------------------------------+----------------------------------------------------------------------+
+| :doc:`witness_complex_user`                                     | :doc:`witness_complex_ref`                                           |
++-----------------------------------------------------------------+----------------------------------------------------------------------+