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Diffstat (limited to 'src/python/doc/cubical_complex_user.rst')
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1 files changed, 16 insertions, 25 deletions
diff --git a/src/python/doc/cubical_complex_user.rst b/src/python/doc/cubical_complex_user.rst index b13b500e..42a23875 100644 --- a/src/python/doc/cubical_complex_user.rst +++ b/src/python/doc/cubical_complex_user.rst @@ -7,14 +7,7 @@ Cubical complex user manual Definition ---------- -===================================== ===================================== ===================================== -:Author: Pawel Dlotko :Introduced in: GUDHI PYTHON 2.0.0 :Copyright: GPL v3 -===================================== ===================================== ===================================== - -+---------------------------------------------+----------------------------------------------------------------------+ -| :doc:`cubical_complex_user` | * :doc:`cubical_complex_ref` | -| | * :doc:`periodic_cubical_complex_ref` | -+---------------------------------------------+----------------------------------------------------------------------+ +.. include:: cubical_complex_sum.inc The cubical complex is an example of a structured complex useful in computational mathematics (specially rigorous numerics) and image analysis. @@ -47,8 +40,8 @@ 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. ---------------- +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 @@ -77,8 +70,8 @@ Knowing the sizes of the bitmap, by a series of modulo operation, we can determi 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. -------------- +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 @@ -91,7 +84,7 @@ Currently one input from a text file is used. It uses a format inspired from the we allow any filtration values. As a consequence one cannot use ``-1``'s to indicate missing cubes. If you have missing cubes in your complex, please set their filtration to :math:`+\infty` (aka. ``inf`` in the file). -The file format is described in details in :ref:`Perseus file format` file format section. +The file format is described in details in `Perseus file format <fileformats.html#perseus>`_ section. .. testcode:: @@ -108,8 +101,8 @@ the program output is: Cubical complex is of dimension 2 - 49 simplices. -Periodic boundary conditions. ------------------------------ +Periodic boundary conditions +---------------------------- Often one would like to impose periodic boundary conditions to the cubical complex (cf. :doc:`periodic_cubical_complex_ref`). @@ -120,7 +113,7 @@ conditions are imposed in all directions, then complex :math:`\mathcal{K}` becam 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 (see :doc:`Perseus <fileformats>`) for the specific periodic case: +One can also use Perseus style input files (see `Perseus file format <fileformats.html#perseus>`_) for the specific periodic case: .. testcode:: @@ -142,8 +135,7 @@ Or it can be defined as follows: .. testcode:: from gudhi import PeriodicCubicalComplex as pcc - periodic_cc = pcc(dimensions=[3,3], - top_dimensional_cells= [0, 0, 0, 0, 1, 0, 0, 0, 0], + periodic_cc = pcc(top_dimensional_cells = [[0, 0, 0], [0, 1, 0], [0, 0, 0]], periodic_dimensions=[True, False]) result_str = 'Periodic cubical complex is of dimension ' + repr(periodic_cc.dimension()) + ' - ' + \ repr(periodic_cc.num_simplices()) + ' simplices.' @@ -155,14 +147,13 @@ the program output is: Periodic cubical complex is of dimension 2 - 42 simplices. -Examples. ---------- +Examples +-------- End user programs are available in python/example/ folder. -Bibliography -============ +Tutorial +-------- -.. bibliography:: ../../biblio/bibliography.bib - :filter: docnames - :style: unsrt +This `notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-cubical-complexes.ipynb>`_ +explains how to represent sublevels sets of functions using cubical complexes. |