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Diffstat (limited to 'src/cython/doc/persistent_cohomology_sum.rst')
| -rw-r--r-- | src/cython/doc/persistent_cohomology_sum.rst | 50 |
1 files changed, 26 insertions, 24 deletions
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` | ++-----------------------------------------------------------------+-----------------------------------------------------------------------+ |