summaryrefslogtreecommitdiff
path: root/src/cython/doc
diff options
context:
space:
mode:
authorvrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2016-08-12 15:03:09 +0000
committervrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2016-08-12 15:03:09 +0000
commit7de929fe3cc4dda0fd565bc7ce9bf92c521053ed (patch)
treee7f7674c7e45168bbf3cdbfd1f7b0568ff562be3 /src/cython/doc
parent359411b63f1d4698cca3413c0f00822f80243786 (diff)
move cython/doc/source in cython/src/doc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@1433 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: 9e9d17b611d04df874ab31a844c9549821bc16ee
Diffstat (limited to 'src/cython/doc')
-rw-r--r--src/cython/doc/source/alpha_complex_ref.rst10
-rw-r--r--src/cython/doc/source/alpha_complex_sum.rst21
-rw-r--r--src/cython/doc/source/alpha_complex_user.rst192
-rw-r--r--src/cython/doc/source/biblio.rst7
-rw-r--r--src/cython/doc/source/cgal_citation.rst8
-rw-r--r--src/cython/doc/source/cubical_complex_ref.rst9
-rw-r--r--src/cython/doc/source/cubical_complex_sum.rst12
-rw-r--r--src/cython/doc/source/cubical_complex_user.rst150
-rw-r--r--src/cython/doc/source/periodic_cubical_complex_ref.rst9
-rw-r--r--src/cython/doc/source/persistent_cohomology_sum.rst28
-rw-r--r--src/cython/doc/source/persistent_cohomology_user.rst104
-rw-r--r--src/cython/doc/source/simplex_tree_ref.rst10
-rw-r--r--src/cython/doc/source/simplex_tree_sum.rst13
-rw-r--r--src/cython/doc/source/simplex_tree_user.rst67
-rw-r--r--src/cython/doc/source/witness_complex_ref.rst10
-rw-r--r--src/cython/doc/source/witness_complex_sum.rst25
-rw-r--r--src/cython/doc/source/witness_complex_user.rst31
17 files changed, 0 insertions, 706 deletions
diff --git a/src/cython/doc/source/alpha_complex_ref.rst b/src/cython/doc/source/alpha_complex_ref.rst
deleted file mode 100644
index 6a122b09..00000000
--- a/src/cython/doc/source/alpha_complex_ref.rst
+++ /dev/null
@@ -1,10 +0,0 @@
-==============================
-Alpha complex reference manual
-==============================
-
-.. autoclass:: gudhi.AlphaComplex
- :members:
- :undoc-members:
- :show-inheritance:
-
- .. automethod:: gudhi.AlphaComplex.__init__
diff --git a/src/cython/doc/source/alpha_complex_sum.rst b/src/cython/doc/source/alpha_complex_sum.rst
deleted file mode 100644
index b608050e..00000000
--- a/src/cython/doc/source/alpha_complex_sum.rst
+++ /dev/null
@@ -1,21 +0,0 @@
-===================================== ===================================== =====================================
-:Author: Vincent Rouvreau :Introduced in: GUDHI PYTHON 1.4.0 :Copyright: GPL v3
-===================================== ===================================== =====================================
-
-+-------------------------------------------+----------------------------------------------------------------------+
-| .. 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` |
-+-------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/source/alpha_complex_user.rst b/src/cython/doc/source/alpha_complex_user.rst
deleted file mode 100644
index 07bfcabf..00000000
--- a/src/cython/doc/source/alpha_complex_user.rst
+++ /dev/null
@@ -1,192 +0,0 @@
-=========================
-Alpha complex user manual
-=========================
-Definition
-----------
-
-.. include:: alpha_complex_sum.rst
-
-Alpha_complex is constructing a :doc:`Simplex_tree <simplex_tree_sum>` using
-`Delaunay Triangulation <http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations>`_
-:cite:`cgal:hdj-t-15b` from `CGAL <http://www.cgal.org/>`_ (the Computational Geometry Algorithms Library
-:cite:`cgal:eb-15b`).
-
-Remarks
-^^^^^^^
-When Alpha_complex is constructed with an infinite value of :math:`\alpha`, the complex is a Delaunay complex.
-
-Example from points
--------------------
-
-This example builds the Delaunay triangulation from the given points, and initializes the alpha complex with it:
-
-.. testcode::
-
- import gudhi
- alpha_complex = gudhi.AlphaComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]],
- max_alpha_square=60.0)
- result_str = 'Alpha complex is of dimension ' + repr(alpha_complex.dimension()) + ' - ' + \
- repr(alpha_complex.num_simplices()) + ' simplices - ' + \
- repr(alpha_complex.num_vertices()) + ' vertices.'
- print(result_str)
- for fitered_value in alpha_complex.get_filtered_tree():
- print(fitered_value)
-
-The output is:
-
-.. testoutput::
-
- Alpha complex is of dimension 2 - 25 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], 6.25)
- ([4, 5], 7.25)
- ([0, 2], 8.5)
- ([0, 1], 9.25)
- ([1, 3], 10.0)
- ([1, 2], 11.25)
- ([1, 2, 3], 12.5)
- ([0, 1, 2], 12.995867768595042)
- ([5, 6], 13.25)
- ([2, 4], 20.0)
- ([4, 6], 22.736686390532547)
- ([4, 5, 6], 22.736686390532547)
- ([3, 6], 30.25)
- ([2, 6], 36.5)
- ([2, 3, 6], 36.5)
- ([2, 4, 6], 37.24489795918368)
- ([0, 4], 59.710743801652896)
- ([0, 2, 4], 59.710743801652896)
-
-
-Algorithm
----------
-
-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::
- img/alpha_complex_doc.png
- :align: center
- :alt: Simplex tree structure construction example
-
-Filtration value computation algorithm
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
- **for** i : dimension :math:`\rightarrow` 0 **do**
- **for all** :math:`\sigma` of dimension i
- **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`)
- **end if**
- **end for**
- **end for**
- **end for**
-
- make_filtration_non_decreasing()
-
- prune_above_filtration()
-
-Dimension 2
-^^^^^^^^^^^
-
-From the example above, it means the algorithm looks into each triangle ([0,1,2], [0,2,4], [1,2,3], ...),
-computes the filtration value of the triangle, and then propagates the filtration value as described
-here:
-
-.. image::
- img/alpha_complex_doc_420.png
- :align: center
- :alt: Filtration value propagation example
-
-Dimension 1
-^^^^^^^^^^^
-
-Then, the algorithm looks into each edge ([0,1], [0,2], [1,2], ...),
-computes the filtration value of the edge (in this case, propagation will have no effect).
-
-Dimension 0
-^^^^^^^^^^^
-
-Finally, the algorithm looks into each vertex ([0], [1], [2], [3], [4], [5] and [6]) and
-sets the filtration value (0 in case of a vertex - propagation will have no effect).
-
-Non decreasing filtration values
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-As the squared radii computed by CGAL are an approximation, it might happen that these alpha squared values do not
-quite define a proper filtration (i.e. non-decreasing with respect to inclusion).
-We fix that up by calling `Simplex_tree::make_filtration_non_decreasing()` (cf.
-`C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_).
-
-Prune above given filtration value
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-The simplex tree is pruned from the given maximum alpha squared value (cf. `Simplex_tree::prune_above_filtration()`
-int he `C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_).
-In the following example, the value is given by the user as argument of the program.
-
-
-Example from OFF file
-^^^^^^^^^^^^^^^^^^^^^
-
-This example builds the Delaunay triangulation from the points given by an OFF file, and initializes the alpha complex
-with it.
-
-
-Then, it is asked to display information about the alpha complex:
-
-.. testcode::
-
- import gudhi
- alpha_complex = gudhi.AlphaComplex(off_file='source/alphacomplexdoc.off',
- max_alpha_square=59.0)
- result_str = 'Alpha complex is of dimension ' + repr(alpha_complex.dimension()) + ' - ' + \
- repr(alpha_complex.num_simplices()) + ' simplices - ' + \
- repr(alpha_complex.num_vertices()) + ' vertices.'
- print(result_str)
- for fitered_value in alpha_complex.get_filtered_tree():
- print(fitered_value)
-
-the program output is:
-
-.. testoutput::
-
- Alpha complex is of dimension 2 - 23 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], 6.25)
- ([4, 5], 7.25)
- ([0, 2], 8.5)
- ([0, 1], 9.25)
- ([1, 3], 10.0)
- ([1, 2], 11.25)
- ([1, 2, 3], 12.5)
- ([0, 1, 2], 12.995867768595042)
- ([5, 6], 13.25)
- ([2, 4], 20.0)
- ([4, 6], 22.736686390532547)
- ([4, 5, 6], 22.736686390532547)
- ([3, 6], 30.25)
- ([2, 6], 36.5)
- ([2, 3, 6], 36.5)
- ([2, 4, 6], 37.24489795918368)
diff --git a/src/cython/doc/source/biblio.rst b/src/cython/doc/source/biblio.rst
deleted file mode 100644
index b8e733ed..00000000
--- a/src/cython/doc/source/biblio.rst
+++ /dev/null
@@ -1,7 +0,0 @@
-============
-Bibliography
-============
-
-.. bibliography:: bibliography.bib
- :filter: docnames
- :style: unsrt
diff --git a/src/cython/doc/source/cgal_citation.rst b/src/cython/doc/source/cgal_citation.rst
deleted file mode 100644
index bbc4ef9e..00000000
--- a/src/cython/doc/source/cgal_citation.rst
+++ /dev/null
@@ -1,8 +0,0 @@
-==============
-CGAL citations
-==============
-
-..
- bibliography:: how_to_cite_cgal.bib
- :filter: docnames
- :style: unsrt
diff --git a/src/cython/doc/source/cubical_complex_ref.rst b/src/cython/doc/source/cubical_complex_ref.rst
deleted file mode 100644
index 84aa4223..00000000
--- a/src/cython/doc/source/cubical_complex_ref.rst
+++ /dev/null
@@ -1,9 +0,0 @@
-Cubical complex reference manual
-################################
-
-.. autoclass:: gudhi.CubicalComplex
- :members:
- :undoc-members:
- :show-inheritance:
-
- .. automethod:: gudhi.CubicalComplex.__init__
diff --git a/src/cython/doc/source/cubical_complex_sum.rst b/src/cython/doc/source/cubical_complex_sum.rst
deleted file mode 100644
index 4008a1fd..00000000
--- a/src/cython/doc/source/cubical_complex_sum.rst
+++ /dev/null
@@ -1,12 +0,0 @@
-===================================== ===================================== =====================================
-:Author: Pawel Dlotko :Introduced in: GUDHI PYTHON 1.4.0 :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` |
-+---------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/source/cubical_complex_user.rst b/src/cython/doc/source/cubical_complex_user.rst
deleted file mode 100644
index 38ff978c..00000000
--- a/src/cython/doc/source/cubical_complex_user.rst
+++ /dev/null
@@ -1,150 +0,0 @@
-===========================
-Cubical complex user manual
-===========================
-Definition
-----------
-
-===================================== ===================================== =====================================
-:Author: Pawel Dlotko :Introduced in: GUDHI PYTHON 1.4.0 :Copyright: GPL v3
-===================================== ===================================== =====================================
-
-+---------------------------------------------+----------------------------------------------------------------------+
-| :doc:`cubical_complex_user` | * :doc:`cubical_complex_ref` |
-| | * :doc:`periodic_cubical_complex_ref` |
-+---------------------------------------------+----------------------------------------------------------------------+
-
-The cubical complex is an example of a structured complex useful in computational mathematics (specially rigorous
-numerics) and image analysis.
-
-An *elementary interval* is an interval of a form :math:`[n,n+1]`, or :math:`[n,n]`, for :math:`n \in \mathcal{Z}`.
-The first one is called *non-degenerate*, while the second one is a *degenerate* interval. A
-*boundary of a elementary interval* is a chain :math:`\partial [n,n+1] = [n+1,n+1]-[n,n]` in case of
-non-degenerated elementary interval and :math:`\partial [n,n] = 0` in case of degenerate elementary interval. An
-*elementary cube* :math:`C` is a product of elementary intervals, :math:`C=I_1 \times \ldots \times I_n`.
-*Embedding dimension* of a cube is n, the number of elementary intervals (degenerate or not) in the product.
-A *dimension of a cube* :math:`C=I_1 \times ... \times I_n` is the number of non degenerate elementary
-intervals in the product. A *boundary of a cube* :math:`C=I_1 \times \ldots \times I_n` is a chain obtained
-in the following way:
-
-.. math::
-
- \partial C = (\partial I_1 \times \ldots \times I_n) + (I_1 \times \partial I_2 \times \ldots \times I_n) +
- \ldots + (I_1 \times I_2 \times \ldots \times \partial I_n).
-
-A *cubical complex* :math:`\mathcal{K}` is a collection of cubes closed under operation of taking boundary
-(i.e. boundary of every cube from the collection is in the collection). A cube :math:`C` in cubical complex
-:math:`\mathcal{K}` is *maximal* if it is not in a boundary of any other cube in :math:`\mathcal{K}`. A
-*support* of a cube :math:`C` is the set in :math:`\mathbb{R}^n` occupied by :math:`C` (:math:`n` is the embedding
-dimension of :math:`C`).
-
-Cubes may be equipped with a filtration values in which case we have filtered cubical complex. All the cubical
-complexes considered in this implementation are filtered cubical complexes (although, the range of a filtration may
-be a set of two elements).
-
-For further details and theory of cubical complexes, please consult :cite:`kaczynski2004computational` as well as the
-following paper :cite:`peikert2012topological`.
-
-Data structure.
----------------
-
-The implementation of Cubical complex provides a representation of complexes that occupy a rectangular region in
-:math:`\mathbb{R}^n`. This extra assumption allows for a memory efficient way of storing cubical complexes in a form
-of so called bitmaps. Let
-:math:`R = [b_1,e_1] \times \ldots \times [b_n,e_n]`, for :math:`b_1,...b_n,e_1,...,e_n \in \mathbb{Z}`,
-:math:`b_i \leq d_i` be the considered rectangular region and let :math:`\mathcal{K}` be a filtered
-cubical complex having the rectangle :math:`R` as its support. Note that the structure of the coordinate system gives
-a way a lexicographical ordering of cells of :math:`\mathcal{K}`. This ordering is a base of the presented
-bitmap-based implementation. In this implementation, the whole cubical complex is stored as a vector of the values
-of filtration. This, together with dimension of :math:`\mathcal{K}` and the sizes of :math:`\mathcal{K}` in all
-directions, allows to determine, dimension, neighborhood, boundary and coboundary of every cube
-:math:`C \in \mathcal{K}`.
-
-.. image::
- img/Cubical_complex_representation.png
- :align: center
- :alt: 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
-the number of maximal cubes in the considered direction. Let us consider a cube at the position :math:`k` in the
-bitmap.
-Knowing the sizes of the bitmap, by a series of modulo operation, we can determine which elementary intervals are
-present in the product that gives the cube :math:`C`. In a similar way, we can compute boundary and the coboundary of
-each cube. Further details can be found in the literature.
-
-Input Format.
--------------
-
-In the current implantation, filtration is given at the maximal cubes, and it is then extended by the lower star
-filtration to all cubes. There are a number of constructors that can be used to construct cubical complex by users
-who want to use the code directly. They can be found in the :doc:`cubical_complex_ref`.
-Currently one input from a text file is used. It uses a format used already in
-`Perseus software <http://www.sas.upenn.edu/~vnanda/perseus/>`_ by Vidit Nanda.
-Below we are providing a description of the format. The first line contains a number d begin the dimension of the
-bitmap (2 in the example below). Next d lines are the numbers of top dimensional cubes in each dimensions (3 and 3
-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::
- img/exampleBitmap.png
- :align: center
- :alt: Example of a input data.
-
-The input file for the following complex is:
-
-.. literalinclude:: cubicalcomplexdoc.txt
-
-.. centered:: cubicalcomplexdoc.txt
-
-.. testcode::
-
- import gudhi
- cubical_complex = gudhi.CubicalComplex(perseus_file='source/cubicalcomplexdoc.txt')
- result_str = 'Cubical complex is of dimension ' + repr(cubical_complex.dimension()) + ' - ' + \
- repr(cubical_complex.num_simplices()) + ' simplices.'
- print(result_str)
-
-the program output is:
-
-.. testoutput::
-
- Cubical complex is of dimension 2 - 49 simplices.
-
-Periodic boundary conditions.
------------------------------
-
-Often one would like to impose periodic boundary conditions to the cubical complex (cf.
-:doc:`periodic_cubical_complex_ref`).
-Let :math:`I_1\times ... \times I_n` be a box that is decomposed with a cubical complex :math:`\mathcal{K}`.
-Imposing periodic boundary conditions in the direction i, means that the left and the right side of a complex
-:math:`\mathcal{K}` are considered the same. In particular, if for a bitmap :math:`\mathcal{K}` periodic boundary
-conditions are imposed in all directions, then complex :math:`\mathcal{K}` became n-dimensional torus. One can use
-various constructors from the file Bitmap_cubical_complex_periodic_boundary_conditions_base.h to construct cubical
-complex with periodic boundary conditions. One can also use Perseus style input files. To indicate periodic boundary
-conditions in a given direction, then number of top dimensional cells in this direction have to be multiplied by -1.
-For instance:
-
-.. literalinclude:: periodiccubicalcomplexdoc.txt
-
-.. centered:: periodiccubicalcomplexdoc.txt
-
-Indicate that we have imposed periodic boundary conditions in the direction x, but not in the direction y.
-
-.. testcode::
-
- import gudhi
- periodic_cc = gudhi.PeriodicCubicalComplex(perseus_file='source/periodiccubicalcomplexdoc.txt')
- result_str = 'Periodic cubical complex is of dimension ' + repr(periodic_cc.dimension()) + ' - ' + \
- repr(periodic_cc.num_simplices()) + ' simplices.'
- print(result_str)
-
-the program output is:
-
-.. testoutput::
-
- Periodic cubical complex is of dimension 2 - 42 simplices.
-
-Examples.
----------
-
-End user programs are available in cython/example/ folder.
diff --git a/src/cython/doc/source/periodic_cubical_complex_ref.rst b/src/cython/doc/source/periodic_cubical_complex_ref.rst
deleted file mode 100644
index c6190a1b..00000000
--- a/src/cython/doc/source/periodic_cubical_complex_ref.rst
+++ /dev/null
@@ -1,9 +0,0 @@
-Periodic cubical complex reference manual
-#########################################
-
-.. autoclass:: gudhi.PeriodicCubicalComplex
- :members:
- :undoc-members:
- :show-inheritance:
-
- .. automethod:: gudhi.PeriodicCubicalComplex.__init__
diff --git a/src/cython/doc/source/persistent_cohomology_sum.rst b/src/cython/doc/source/persistent_cohomology_sum.rst
deleted file mode 100644
index 081399a5..00000000
--- a/src/cython/doc/source/persistent_cohomology_sum.rst
+++ /dev/null
@@ -1,28 +0,0 @@
-===================================== ===================================== =====================================
-:Author: Clément Maria :Introduced in: GUDHI PYTHON 1.4.0 :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:`alpha_complex_ref` |
-| | * :doc:`cubical_complex_ref` |
-| | * :doc:`simplex_tree_ref` |
-| | * :doc:`witness_complex_ref` |
-+---------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/source/persistent_cohomology_user.rst b/src/cython/doc/source/persistent_cohomology_user.rst
deleted file mode 100644
index 33b19ce2..00000000
--- a/src/cython/doc/source/persistent_cohomology_user.rst
+++ /dev/null
@@ -1,104 +0,0 @@
-=================================
-Persistent cohomology user manual
-=================================
-Definition
-----------
-===================================== ===================================== =====================================
-:Author: Clément Maria :Introduced in: GUDHI PYTHON 1.4.0 :Copyright: GPL v3
-===================================== ===================================== =====================================
-
-+---------------------------------------------+----------------------------------------------------------------------+
-| :doc:`persistent_cohomology_user` | Please refer to each data structure that contains persistence |
-| | feature for reference: |
-| | |
-| | * :doc:`alpha_complex_ref` |
-| | * :doc:`cubical_complex_ref` |
-| | * :doc:`simplex_tree_ref` |
-| | * :doc:`witness_complex_ref` |
-+---------------------------------------------+----------------------------------------------------------------------+
-
-
-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`.
-
-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
-* an evolution scheme.
-
-Topological Spaces
-------------------
-
-Topological spaces are represented by simplicial complexes.
-Let :math:`V = \{1, \cdots ,|V|\}` be a set of *vertices*.
-A *simplex* :math:`\sigma` is a subset of vertices :math:`\sigma \subseteq V`.
-A *simplicial complex* :math:`\mathbf{K}` on :math:`V` is a collection of simplices :math:`\{\sigma\}`,
-:math:`\sigma \subseteq V`, such that :math:`\tau \subseteq \sigma \in \mathbf{K} \Rightarrow \tau \in \mathbf{K}`.
-The dimension :math:`n=|\sigma|-1` of :math:`\sigma` is its number of elements minus 1.
-A *filtration* of a simplicial complex is a function :math:`f:\mathbf{K} \rightarrow \mathbb{R}` satisfying
-:math:`f(\tau)\leq f(\sigma)` whenever :math:`\tau \subseteq \sigma`.
-
-Homology
---------
-
-For a ring :math:`\mathcal{R}`, the group of *n-chains*, denoted :math:`\mathbf{C}_n(\mathbf{K},\mathcal{R})`, of
-:math:`\mathbf{K}` is the group of formal sums of n-simplices with :math:`\mathcal{R}` coefficients. The
-*boundary operator* is a linear operator
-:math:`\partial_n: \mathbf{C}_n(\mathbf{K},\mathcal{R}) \rightarrow \mathbf{C}_{n-1}(\mathbf{K},\mathcal{R})`
-such that :math:`\partial_n \sigma = \partial_n [v_0, \cdots , v_n] = \sum_{i=0}^n (-1)^{i}[v_0,\cdots ,\widehat{v_i}, \cdots,v_n]`,
-where :math:`\widehat{v_i}` means :math:`v_i` is omitted from the list. The chain groups form a sequence:
-
-.. math::
-
- \cdots \ \ \mathbf{C}_n(\mathbf{K},\mathcal{R}) \xrightarrow{\ \partial_n\ }
- \mathbf{C}_{n-1}(\mathbf{K},\mathcal{R}) \xrightarrow{\partial_{n-1}} \cdots \xrightarrow{\ \partial_2 \ }
- \mathbf{C}_1(\mathbf{K},\mathcal{R}) \xrightarrow{\ \partial_1 \ } \mathbf{C}_0(\mathbf{K},\mathcal{R})
-
-of finitely many groups :math:`\mathbf{C}_n(\mathbf{K},\mathcal{R})` and homomorphisms :math:`\partial_n`, indexed by
-the dimension :math:`n \geq 0`. The boundary operators satisfy the property :math:`\partial_n \circ \partial_{n+1}=0`
-for every :math:`n > 0` and we define the homology groups:
-
-.. math::
-
- \mathbf{H}_n(\mathbf{K},\mathcal{R}) = \ker \partial_n / \mathrm{im} \ \partial_{n+1}
-
-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
----------------
-
-"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 consecutive nodes in the graph are connected by an arrow (either forward
-or backward).
-The nodes represent simplicial complexes and the directed edges simplicial maps.
-
-From the computational point of view, there are two types of indexing schemes of interest in persistent homology:
-
-* linear ones
- :math:`\bullet \longrightarrow \bullet \longrightarrow \cdots \longrightarrow \bullet \longrightarrow \bullet`
- in persistent homology :cite:`DBLP:journals/dcg/ZomorodianC05`,
-* zigzag ones
- :math:`\bullet \longrightarrow \bullet \longleftarrow \cdots \longrightarrow \bullet \longleftarrow \bullet`
- in zigzag persistent homology :cite:`DBLP:journals/focm/CarlssonS10`.
-
-These indexing schemes have a natural left-to-right traversal order, and we describe them with ranges and iterators.
-In the current release of the Gudhi library, only the linear case is implemented.
-
-In the following, we consider the case where the indexing scheme is induced by a filtration.
-
-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.
-
-Examples
---------
-
-We provide several example files: run these examples with -h for details on their use.
-
-.. todo::
- examples for persistence
diff --git a/src/cython/doc/source/simplex_tree_ref.rst b/src/cython/doc/source/simplex_tree_ref.rst
deleted file mode 100644
index 6d196843..00000000
--- a/src/cython/doc/source/simplex_tree_ref.rst
+++ /dev/null
@@ -1,10 +0,0 @@
-=============================
-Simplex tree reference manual
-=============================
-
-.. autoclass:: gudhi.SimplexTree
- :members:
- :undoc-members:
- :show-inheritance:
-
- .. automethod:: gudhi.SimplexTree.__init__
diff --git a/src/cython/doc/source/simplex_tree_sum.rst b/src/cython/doc/source/simplex_tree_sum.rst
deleted file mode 100644
index ffdb2cf4..00000000
--- a/src/cython/doc/source/simplex_tree_sum.rst
+++ /dev/null
@@ -1,13 +0,0 @@
-===================================== ===================================== =====================================
-:Author: Clément Maria :Introduced in: GUDHI PYTHON 1.4.0 :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` |
-+-------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/source/simplex_tree_user.rst b/src/cython/doc/source/simplex_tree_user.rst
deleted file mode 100644
index 3a00f1ac..00000000
--- a/src/cython/doc/source/simplex_tree_user.rst
+++ /dev/null
@@ -1,67 +0,0 @@
-========================
-Simplex tree user manual
-========================
-Definition
-----------
-
-.. include:: simplex_tree_sum.rst
-
-A simplicial complex :math:`\mathbf{K}` on a set of vertices :math:`V = \{1, \cdots ,|V|\}` is a collection of
-simplices :math:`\{\sigma\}`, :math:`\sigma \subseteq V` such that
-:math:`\tau \subseteq \sigma \in \mathbf{K} \rightarrow \tau \in \mathbf{K}`. The dimension :math:`n=|\sigma|-1` of
-:math:`\sigma` is its number of elements minus `1`.
-
-A filtration of a simplicial complex is a function :math:`f:\mathbf{K} \rightarrow \mathbb{R}` satisfying
-:math:`f(\tau)\leq f(\sigma)` whenever :math:`\tau \subseteq \sigma`. 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.
-
-
-Implementation
---------------
-
-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`.
-
-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.
-
-Example
--------
-
-.. testcode::
-
- import gudhi
- st = gudhi.SimplexTree()
- if st.insert([0, 1]):
- print("[0, 1] inserted")
- if st.insert([0, 1, 2], filtration=4.0):
- print("[0, 1, 2] inserted")
- if st.find([0, 1]):
- print("[0, 1] found")
- print("num_vertices=", st.num_vertices())
- print("num_simplices=", st.num_simplices())
- print("skeleton_tree(2) =")
- for sk_value in st.get_skeleton_tree(2):
- print(sk_value)
-
-
-The output is:
-
-.. testoutput::
-
- [0, 1] inserted
- [0, 1, 2] inserted
- [0, 1] found
- ('num_vertices=', 3)
- ('num_simplices=', 7)
- skeleton_tree(2) =
- ([0, 1, 2], 4.0)
- ([0, 1], 0.0)
- ([0, 2], 4.0)
- ([0], 0.0)
- ([1, 2], 4.0)
- ([1], 0.0)
- ([2], 4.0)
diff --git a/src/cython/doc/source/witness_complex_ref.rst b/src/cython/doc/source/witness_complex_ref.rst
deleted file mode 100644
index c78760cb..00000000
--- a/src/cython/doc/source/witness_complex_ref.rst
+++ /dev/null
@@ -1,10 +0,0 @@
-================================
-Witness complex reference manual
-================================
-
-.. autoclass:: gudhi.WitnessComplex
- :members:
- :undoc-members:
- :show-inheritance:
-
- .. automethod:: gudhi.WitnessComplex.__init__
diff --git a/src/cython/doc/source/witness_complex_sum.rst b/src/cython/doc/source/witness_complex_sum.rst
deleted file mode 100644
index 0d65d420..00000000
--- a/src/cython/doc/source/witness_complex_sum.rst
+++ /dev/null
@@ -1,25 +0,0 @@
-===================================== ===================================== =====================================
-:Author: Siargey Kachanovich :Introduced in: GUDHI PYTHON 1.4.0 :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` |
-+---------------------------------------------+----------------------------------------------------------------------+
diff --git a/src/cython/doc/source/witness_complex_user.rst b/src/cython/doc/source/witness_complex_user.rst
deleted file mode 100644
index 604c7357..00000000
--- a/src/cython/doc/source/witness_complex_user.rst
+++ /dev/null
@@ -1,31 +0,0 @@
-===========================
-Witness complex user manual
-===========================
-Definition
-----------
-
-.. include:: witness_complex_sum.rst
-
-Implementation
---------------
-
-The principal class of this module is Gudhi::Witness_complex.
-
-In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a
-witness and consists of landmarks sorted by distance to this witness.
-
-.. todo::
- This table can be constructed by two additional classes Landmark_choice_by_furthest_point and
- Landmark_choice_by_random_point also included in the module.
-
-.. figure::
- img/bench_Cy8.png
- :align: center
-
- Running time as function on number of landmarks.
-
-.. figure::
- img/bench_sphere.png
- :align: center
-
- Running time as function on number of witnesses for |L|=300.