diff options
Diffstat (limited to 'src/cython/doc')
-rw-r--r-- | src/cython/doc/alpha_complex_sum.inc | 40 | ||||
-rw-r--r-- | src/cython/doc/bottleneck_distance_sum.inc | 27 | ||||
-rwxr-xr-x | src/cython/doc/conf.py | 2 | ||||
-rw-r--r-- | src/cython/doc/cubical_complex_sum.inc | 27 | ||||
-rw-r--r-- | src/cython/doc/fileformats.rst | 29 | ||||
-rw-r--r-- | src/cython/doc/index.rst | 79 | ||||
-rw-r--r-- | src/cython/doc/nerve_gic_complex_sum.inc | 16 | ||||
-rw-r--r-- | src/cython/doc/nerve_gic_complex_sum.rst | 15 | ||||
-rw-r--r-- | src/cython/doc/nerve_gic_complex_user.rst | 5 | ||||
-rw-r--r-- | src/cython/doc/persistence_graphical_tools_sum.inc | 24 | ||||
-rw-r--r-- | src/cython/doc/persistent_cohomology_sum.inc | 51 | ||||
-rw-r--r-- | src/cython/doc/rips_complex_sum.inc | 31 | ||||
-rw-r--r-- | src/cython/doc/rips_complex_user.rst | 4 | ||||
-rw-r--r-- | src/cython/doc/simplex_tree_sum.inc | 25 | ||||
-rw-r--r-- | src/cython/doc/tangential_complex_sum.inc | 27 | ||||
-rw-r--r-- | src/cython/doc/witness_complex_sum.inc | 34 |
16 files changed, 225 insertions, 211 deletions
diff --git a/src/cython/doc/alpha_complex_sum.inc b/src/cython/doc/alpha_complex_sum.inc index 1680a712..806988bb 100644 --- a/src/cython/doc/alpha_complex_sum.inc +++ b/src/cython/doc/alpha_complex_sum.inc @@ -1,22 +1,20 @@ -================================================================= =================================== =================================== -:Author: Vincent Rouvreau :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: CGAL :math:`\geq` 4.7.0 Eigen3 -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. figure:: | Alpha_complex is a simplicial complex constructed from the finite | -| ../../doc/Alpha_complex/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 performance). | -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| :doc:`alpha_complex_user` | :doc:`alpha_complex_ref` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------+ + | .. figure:: | Alpha complex is a simplicial complex constructed from the finite | :Author: Vincent Rouvreau | + | ../../doc/Alpha_complex/alpha_complex_representation.png | cells of a Delaunay Triangulation. | | + | :alt: Alpha complex representation | | :Introduced in: GUDHI 2.0.0 | + | :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 | :Copyright: GPL v3 | + | | is then said to be Gabriel), and as the minimum of the filtration | | + | | values of the codimension 1 cofaces that make it not Gabriel | :Requires: Eigen3 and CGAL :math:`\geq` 4.7.0 | + | | 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 performance). | | + +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------------------------+ + | * :doc:`alpha_complex_user` | * :doc:`alpha_complex_ref` | + +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+ diff --git a/src/cython/doc/bottleneck_distance_sum.inc b/src/cython/doc/bottleneck_distance_sum.inc index 030fad9e..41b9c5a3 100644 --- a/src/cython/doc/bottleneck_distance_sum.inc +++ b/src/cython/doc/bottleneck_distance_sum.inc @@ -1,15 +1,14 @@ -================================================================= =================================== =================================== -:Author: François Godi :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: CGAL :math:`\geq` 4.8.0 -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+-----------------------------------------------------------------+----------------------------------------------------------------------+ -| .. figure:: | Bottleneck distance measures the similarity between two persistence | -| ../../doc/Bottleneck_distance/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` | | -+-----------------------------------------------------------------+----------------------------------------------------------------------+ + +-----------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------+ + | .. figure:: | Bottleneck distance measures the similarity between two persistence | :Author: François Godi | + | ../../doc/Bottleneck_distance/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 | :Introduced in: GUDHI 2.0.0 | + | | diagonal points) such that any couple of matched points are at | | + | Bottleneck distance is the length of | distance at most b. | :Copyright: GPL v3 | + | the longest edge | | | + | | | :Requires: CGAL :math:`\geq` 4.8.0 | + +-----------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------+ + | * :doc:`bottleneck_distance_user` | | + +-----------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------+ diff --git a/src/cython/doc/conf.py b/src/cython/doc/conf.py index 4a54d4fd..ce08f679 100755 --- a/src/cython/doc/conf.py +++ b/src/cython/doc/conf.py @@ -125,7 +125,7 @@ html_theme_options = { "sidebarbgcolor": "#A1ADCD", "sidebartextcolor": "black", "sidebarlinkcolor": "#334D5C", - "body_max_width": "1200px", + "body_max_width": "100%", } # Add any paths that contain custom themes here, relative to this directory. diff --git a/src/cython/doc/cubical_complex_sum.inc b/src/cython/doc/cubical_complex_sum.inc index 280ad0e0..6dcf8e48 100644 --- a/src/cython/doc/cubical_complex_sum.inc +++ b/src/cython/doc/cubical_complex_sum.inc @@ -1,15 +1,14 @@ -================================================================= =================================== =================================== -:Author: Pawel Dlotko :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+--------------------------------------------------------------------------+----------------------------------------------------------------------+ -| .. figure:: | The cubical complex is an example of a structured complex useful in | -| ../../doc/Bitmap_cubical_complex/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` | -+--------------------------------------------------------------------------+----------------------------------------------------------------------+ + +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+ + | .. figure:: | The cubical complex is an example of a structured complex useful in | :Author: Pawel Dlotko | + | ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png | computational mathematics (specially rigorous numerics) and image | | + | :alt: Cubical complex representation | analysis. | :Introduced in: GUDHI 2.0.0 | + | :figclass: align-center | | | + | | | :Copyright: GPL v3 | + | | | | + +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+ + | * :doc:`cubical_complex_user` | * :doc:`cubical_complex_ref` | + | | * :doc:`periodic_cubical_complex_ref` | + +--------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+ diff --git a/src/cython/doc/fileformats.rst b/src/cython/doc/fileformats.rst index e205cc8b..345dfdba 100644 --- a/src/cython/doc/fileformats.rst +++ b/src/cython/doc/fileformats.rst @@ -5,6 +5,35 @@ File formats ############ +OFF file format +*************** + +OFF files must be conform to format described here: +http://www.geomview.org/docs/html/OFF.html + +OFF files are mainly used as point cloud inputs. Here is an example of 7 points +in a 3-dimensional space. As edges and faces are not used for point set, there +is no need to specify them (just set their numbers to 0): + +.. literalinclude:: ../../data/points/alphacomplexdoc.off + +.. centered:: ../../points/alphacomplexdoc.off + +For dimensions bigger than 3, the dimension can be set like here:: + + # Dimension is no more 3 + nOFF + # dimension 4 - 7 vertices - 0 face - 0 edge + 4 7 0 0 + # Point set: + 1.0 1.0 0.0 0.0 + 7.0 0.0 0.0 0.0 + 4.0 6.0 0.0 0.0 + 9.0 6.0 0.0 0.0 + 0.0 14.0 0.0 0.0 + 2.0 19.0 0.0 0.0 + 9.0 17.0 0.0 0.0 + Persistence Diagram ******************* diff --git a/src/cython/doc/index.rst b/src/cython/doc/index.rst index 15cbe267..e379bc23 100644 --- a/src/cython/doc/index.rst +++ b/src/cython/doc/index.rst @@ -6,80 +6,73 @@ GUDHI Python module documentation :alt: Gudhi banner :figclass: align-center -Introduction -************ - -The Python interface for the Gudhi library (Geometry Understanding in Higher -Dimensions) is a generic open source -`Python module <http://gudhi.gforge.inria.fr/python/latest/>`_, for -Computational Topology and Topological Data Analysis -(`TDA <https://en.wikipedia.org/wiki/Topological_data_analysis>`_). -The GUDHI library intends to help the development of new algorithmic solutions -in TDA and their transfer to applications. It provides robust, efficient, -flexible and easy to use implementations of state-of-the-art algorithms and -data structures. - -The current release of the GUDHI library includes: +Complexes +********* -* Data structures to represent, construct and manipulate simplicial complexes. -* Simplification of simplicial complexes by edge contraction. -* Algorithms to compute persistent homology and bottleneck distance. +Cubical complexes +================= -We refer to :cite:`gudhilibrary_ICMS14` for a detailed description of the -design of the library. +.. include:: cubical_complex_sum.inc -Data structures -*************** +Simplicial complexes +==================== Alpha complex -============= +------------- .. include:: alpha_complex_sum.inc -Cover complexes -=============== +Rips complex +------------- + +.. include:: rips_complex_sum.inc -.. include:: nerve_gic_complex_sum.rst +Witness complex +--------------- -Cubical complex +.. include:: witness_complex_sum.inc + +Cover complexes =============== -.. include:: cubical_complex_sum.inc +.. include:: nerve_gic_complex_sum.inc -Rips complex -============ +Data structures and basic operations +************************************ -.. include:: rips_complex_sum.inc +Data structures +=============== Simplex tree -============ +------------ .. include:: simplex_tree_sum.inc +Topological descriptors computation +*********************************** + +Persistence cohomology +====================== + +.. include:: persistent_cohomology_sum.inc + +Manifold reconstruction +*********************** + Tangential complex ================== .. include:: tangential_complex_sum.inc -Witness complex -=============== - -.. include:: witness_complex_sum.inc - -Toolbox -******* +Topological descriptors tools +***************************** Bottleneck distance =================== .. include:: bottleneck_distance_sum.inc -Persistence cohomology -====================== - -.. include:: persistent_cohomology_sum.inc - Persistence graphical tools =========================== diff --git a/src/cython/doc/nerve_gic_complex_sum.inc b/src/cython/doc/nerve_gic_complex_sum.inc new file mode 100644 index 00000000..0e606fe1 --- /dev/null +++ b/src/cython/doc/nerve_gic_complex_sum.inc @@ -0,0 +1,16 @@ +.. table:: + :widths: 30 50 20 + + +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+ + | .. figure:: | Nerves and Graph Induced Complexes are cover complexes, i.e. | :Author: Mathieu Carrière | + | ../../doc/Nerve_GIC/gicvisu.jpg | simplicial complexes that provably contain topological information | | + | :alt: Graph Induced Complex of a point cloud. | about the input data. They can be computed with a cover of the data, | :Introduced in: GUDHI 2.3.0 | + | :figclass: align-center | that comes i.e. from the preimage of a family of intervals covering | | + | | the image of a scalar-valued function defined on the data. | :Copyright: GPL v3 | + | | | | + | | | :Requires: CGAL :math:`\geq` 4.8.1 | + | | | | + | | | | + +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+ + | * :doc:`nerve_gic_complex_user` | * :doc:`nerve_gic_complex_ref` | + +----------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+ diff --git a/src/cython/doc/nerve_gic_complex_sum.rst b/src/cython/doc/nerve_gic_complex_sum.rst deleted file mode 100644 index 523c119f..00000000 --- a/src/cython/doc/nerve_gic_complex_sum.rst +++ /dev/null @@ -1,15 +0,0 @@ -================================================================= =================================== =================================== -:Author: Mathieu Carrière :Introduced in: GUDHI 2.3.0 :Copyright: GPL v3 -:Requires: CGAL :math:`\geq` 4.8.1 -================================================================= =================================== =================================== - -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. figure:: | Nerves and Graph Induced Complexes are cover complexes, i.e. | -| ../../doc/Nerve_GIC/gicvisu.jpg | simplicial complexes that provably contain topological information | -| :alt: Graph Induced Complex of a point cloud. | about the input data. They can be computed with a cover of the data, | -| :figclass: align-center | that comes i.e. from the preimage of a family of intervals covering | -| | the image of a scalar-valued function defined on the data. | -| Graph Induced Complex of a point cloud. | | -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| :doc:`nerve_gic_complex_user` | :doc:`nerve_gic_complex_ref` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ diff --git a/src/cython/doc/nerve_gic_complex_user.rst b/src/cython/doc/nerve_gic_complex_user.rst index 44f30e1a..9101f45d 100644 --- a/src/cython/doc/nerve_gic_complex_user.rst +++ b/src/cython/doc/nerve_gic_complex_user.rst @@ -7,14 +7,13 @@ Cover complexes user manual Definition ---------- -.. include:: nerve_gic_complex_sum.rst +.. include:: nerve_gic_complex_sum.inc Visualizations of the simplicial complexes can be done with either neato (from `graphviz <http://www.graphviz.org/>`_), `geomview <http://www.geomview.org/>`_, `KeplerMapper <https://github.com/MLWave/kepler-mapper>`_. -Input point clouds are assumed to be -`OFF files <http://www.geomview.org/docs/html/OFF.html>`_. +Input point clouds are assumed to be OFF files (cf. :doc:`fileformats`). Covers ------ diff --git a/src/cython/doc/persistence_graphical_tools_sum.inc b/src/cython/doc/persistence_graphical_tools_sum.inc index 5577cf99..b412de56 100644 --- a/src/cython/doc/persistence_graphical_tools_sum.inc +++ b/src/cython/doc/persistence_graphical_tools_sum.inc @@ -1,12 +1,14 @@ -================================================================= =================================== =================================== -:Author: Vincent Rouvreau :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: matplotlib numpy scipy -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ -| .. figure:: | These graphical tools comes on top of persistence results and allows | -| img/graphical_tools_representation.png | the user to build easily persistence barcode, diagram or density. | -| | | -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ -| :doc:`persistence_graphical_tools_user` | :doc:`persistence_graphical_tools_ref` | -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ + +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+ + | .. figure:: | These graphical tools comes on top of persistence results and allows | :Author: Vincent Rouvreau | + | img/graphical_tools_representation.png | the user to build easily persistence barcode, diagram or density. | | + | | | :Introduced in: GUDHI 2.0.0 | + | | | | + | | | :Copyright: GPL v3 | + | | | | + | | | :Requires: matplotlib, numpy and scipy | + +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+ + | * :doc:`persistence_graphical_tools_user` | * :doc:`persistence_graphical_tools_ref` | + +-----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------+ diff --git a/src/cython/doc/persistent_cohomology_sum.inc b/src/cython/doc/persistent_cohomology_sum.inc index a26df1dc..20ca073c 100644 --- a/src/cython/doc/persistent_cohomology_sum.inc +++ b/src/cython/doc/persistent_cohomology_sum.inc @@ -1,27 +1,26 @@ -================================================================= =================================== =================================== -:Author: Clément Maria :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ -| .. figure:: | The theory of homology consists in attaching to a topological space | -| ../../doc/Persistent_cohomology/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` | -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ + +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+ + | .. figure:: | The theory of homology consists in attaching to a topological space | :Author: Clément Maria | + | ../../doc/Persistent_cohomology/3DTorus_poch.png | a sequence of (homology) groups, capturing global topological | | + | :figclass: align-center | features like connected components, holes, cavities, etc. Persistent | :Introduced in: GUDHI 2.0.0 | + | | 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 | :Copyright: GPL v3 | + | 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_sum.inc b/src/cython/doc/rips_complex_sum.inc index ea26769a..e8e505e2 100644 --- a/src/cython/doc/rips_complex_sum.inc +++ b/src/cython/doc/rips_complex_sum.inc @@ -1,17 +1,16 @@ -===================================================================== =========================== =================================== -:Author: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -===================================================================== =========================== =================================== +.. table:: + :widths: 30 50 20 -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. figure:: | Rips complex is a simplicial complex constructed from a one skeleton | -| ../../doc/Rips_complex/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` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+ + | .. figure:: | Rips complex is a simplicial complex constructed from a one skeleton | :Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse | + | ../../doc/Rips_complex/rips_complex_representation.png | graph. | | + | :figclass: align-center | | :Introduced in: GUDHI 2.0.0 | + | | The filtration value of each edge is computed from a user-given | | + | | distance function and is inserted until a user-given threshold | :Copyright: GPL v3 | + | | 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 index e814b4c3..1d340dbe 100644 --- a/src/cython/doc/rips_complex_user.rst +++ b/src/cython/doc/rips_complex_user.rst @@ -50,8 +50,8 @@ by more than the length used to define "too close". A more general technique is to use a sparse approximation of the Rips introduced by Don Sheehy :cite:`sheehy13linear`. We are using the version described in :cite:`buchet16efficient` (except that we multiply all filtration -values by 2, to match the usual Rips complex), which proves a -:math:`\frac{1+\varepsilon}{1-\varepsilon}`-interleaving, although in practice the +values by 2, to match the usual Rips complex). :cite:`cavanna15geometric` proves +a :math:`\frac{1}{1-\varepsilon}`-interleaving, although in practice the error is usually smaller. A more intuitive presentation of the idea is available in :cite:`cavanna15geometric`, and in a video :cite:`cavanna15visualizing`. Passing an extra argument `sparse=0.3` at the diff --git a/src/cython/doc/simplex_tree_sum.inc b/src/cython/doc/simplex_tree_sum.inc index fb0e54c1..086c69d5 100644 --- a/src/cython/doc/simplex_tree_sum.inc +++ b/src/cython/doc/simplex_tree_sum.inc @@ -1,14 +1,13 @@ -================================================================= =================================== =================================== -:Author: Clément Maria :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. figure:: | The simplex tree is an efficient and flexible data structure for | -| ../../doc/Simplex_tree/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` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+ + | .. figure:: | The simplex tree is an efficient and flexible data structure for | :Author: Clément Maria | + | ../../doc/Simplex_tree/Simplex_tree_representation.png | representing general (filtered) simplicial complexes. | | + | :alt: Simplex tree representation | | :Introduced in: GUDHI 2.0.0 | + | :figclass: align-center | The data structure is described in | | + | | :cite:`boissonnatmariasimplextreealgorithmica` | :Copyright: GPL v3 | + | | | | + +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+ + | * :doc:`simplex_tree_user` | * :doc:`simplex_tree_ref` | + +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------+ diff --git a/src/cython/doc/tangential_complex_sum.inc b/src/cython/doc/tangential_complex_sum.inc index 72b4d7ba..0f03ffb3 100644 --- a/src/cython/doc/tangential_complex_sum.inc +++ b/src/cython/doc/tangential_complex_sum.inc @@ -1,15 +1,14 @@ -================================================================= =================================== =================================== -:Author: Clément Jamin :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: CGAL :math:`\geq` 4.8.0 Eigen3 -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. figure:: | A Tangential Delaunay complex is a simplicial complex designed to | -| ../../doc/Tangential_complex/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` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+ + | .. figure:: | A Tangential Delaunay complex is a simplicial complex designed to | :Author: Clément Jamin | + | ../../doc/Tangential_complex/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 | :Introduced in: GUDHI 2.0.0 | + | | an unknown manifold. The running time depends only linearly on the | | + | | extrinsic dimension :math:`d` and exponentially on the intrinsic | :Copyright: GPL v3 | + | | dimension :math:`k`. | | + | | | :Requires: CGAL :math:`\geq` 4.8.0 | + +----------------------------------------------------------------+------------------------------------------------------------------------+------------------------------------+ + | * :doc:`tangential_complex_user` | * :doc:`tangential_complex_ref` | + +----------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+ diff --git a/src/cython/doc/witness_complex_sum.inc b/src/cython/doc/witness_complex_sum.inc index a8a126a0..49577745 100644 --- a/src/cython/doc/witness_complex_sum.inc +++ b/src/cython/doc/witness_complex_sum.inc @@ -1,19 +1,17 @@ -================================================================= =================================== =================================== -:Author: Siargey Kachanovich :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Euclidean version requires: CGAL :math:`\geq` 4.6.0 Eigen3 -================================================================= =================================== =================================== +.. table:: + :widths: 30 50 20 -+-------------------------------------------------------------------+----------------------------------------------------------------------+ -| .. figure:: | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on | -| ../../doc/Witness_complex/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`. | -| :alt: Witness complex representation | | -| :figclass: align-center | The data structure is described in | -| | :cite:`boissonnatmariasimplextreealgorithmica`. | -| | | -| Witness complex representation | | -+-------------------------------------------------------------------+----------------------------------------------------------------------+ -| :doc:`witness_complex_user` | * :doc:`witness_complex_ref` | -| | * :doc:`strong_witness_complex_ref` | -| | * :doc:`euclidean_witness_complex_ref` | -| | * :doc:`euclidean_strong_witness_complex_ref` | -+-------------------------------------------------------------------+----------------------------------------------------------------------+ + +-------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------------------------------------+ + | .. figure:: | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on | :Author: Siargey Kachanovich | + | ../../doc/Witness_complex/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`. | | + | :alt: Witness complex representation | | :Introduced in: GUDHI 2.0.0 | + | :figclass: align-center | The data structure is described in | | + | | :cite:`boissonnatmariasimplextreealgorithmica`. | :Copyright: GPL v3 | + | | | | + | | | :Requires: Eigen3 and CGAL :math:`\geq` 4.6.0 for Euclidean versions only | + +-------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------------------------------------------------------+ + | * :doc:`witness_complex_user` | * :doc:`witness_complex_ref` | + | | * :doc:`strong_witness_complex_ref` | + | | * :doc:`euclidean_witness_complex_ref` | + | | * :doc:`euclidean_strong_witness_complex_ref` | + +-------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------+ |