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Diffstat (limited to 'cython/doc')
43 files changed, 0 insertions, 2938 deletions
diff --git a/cython/doc/_templates/layout.html b/cython/doc/_templates/layout.html deleted file mode 100644 index bc0e9658..00000000 --- a/cython/doc/_templates/layout.html +++ /dev/null @@ -1,275 +0,0 @@ -{# - basic/layout.html - ~~~~~~~~~~~~~~~~~ - - Master layout template for Sphinx themes. - - :copyright: Copyright 2007-2016 by the Sphinx team, see AUTHORS. - :license: BSD, see LICENSE for details. -#} -{%- block doctype -%} -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" - "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> -{%- endblock %} -{%- set reldelim1 = reldelim1 is not defined and ' »' or reldelim1 %} -{%- set reldelim2 = reldelim2 is not defined and ' |' or reldelim2 %} -{%- set render_sidebar = (not embedded) and (not theme_nosidebar|tobool) and - (sidebars != []) %} -{%- set url_root = pathto('', 1) %} -{# XXX necessary? #} -{%- if url_root == '#' %}{% set url_root = '' %}{% endif %} -{%- if not embedded and docstitle %} - {%- set titlesuffix = " — "|safe + docstitle|e %} -{%- else %} - {%- set titlesuffix = "" %} -{%- endif %} - -{%- macro relbar() %} - <div class="related" role="navigation" aria-label="related navigation"> - <h3>{{ _('Navigation') }}</h3> - <ul> - {%- for rellink in rellinks %} - <li class="right" {% if loop.first %}style="margin-right: 10px"{% endif %}> - <a href="{{ pathto(rellink[0]) }}" title="{{ rellink[1]|striptags|e }}" - {{ accesskey(rellink[2]) }}>{{ rellink[3] }}</a> - {%- if not loop.first %}{{ reldelim2 }}{% endif %}</li> - {%- endfor %} - {%- block rootrellink %} - <li class="nav-item nav-item-0"><a href="{{ pathto(master_doc) }}">{{ shorttitle|e }}</a>{{ reldelim1 }}</li> - {%- endblock %} - {%- for parent in parents %} - <li class="nav-item nav-item-{{ loop.index }}"><a href="{{ parent.link|e }}" {% if loop.last %}{{ accesskey("U") }}{% endif %}>{{ parent.title }}</a>{{ reldelim1 }}</li> - {%- endfor %} - {%- block relbaritems %} {% endblock %} - </ul> - </div> -{%- endmacro %} - -{%- macro sidebar() %} - {%- if render_sidebar %} - <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> - <div class="sphinxsidebarwrapper"> - {%- block sidebarlogo %} - {%- if logo %} - <p class="logo"><a href="{{ pathto(master_doc) }}"> - <img class="logo" src="{{ pathto('_static/' + logo, 1) }}" alt="Logo"/> - </a></p> - {%- endif %} - {%- endblock %} - <h2><a href="index.html">GUDHI</a></h2> - <h2><a href="fileformats.html">File formats</a></h2> - <h2><a href="installation.html">GUDHI installation</a></h2> - <h2><a href="citation.html">Acknowledging the GUDHI library</a></h2> - <h2><a href="genindex.html">Index</a></h2> - <h2><a href="examples.html">Examples</a></h2> - {%- if sidebars != None %} - {#- new style sidebar: explicitly include/exclude templates #} - {%- for sidebartemplate in sidebars %} - {%- include sidebartemplate %} - {%- endfor %} - {%- else %} - {#- old style sidebars: using blocks -- should be deprecated #} - {%- block sidebartoc %} - {%- include "localtoc.html" %} - {%- endblock %} - {%- block sidebarrel %} - {%- include "relations.html" %} - {%- endblock %} - {%- block sidebarsourcelink %} - {%- include "sourcelink.html" %} - {%- endblock %} - {%- if customsidebar %} - {%- include customsidebar %} - {%- endif %} - {%- block sidebarsearch %} - {%- include "searchbox.html" %} - {%- endblock %} - {%- endif %} - </div> - </div> - {%- endif %} -{%- endmacro %} - -{%- macro script() %} - <script type="text/javascript"> - var DOCUMENTATION_OPTIONS = { - URL_ROOT: '{{ url_root }}', - VERSION: '{{ release|e }}', - COLLAPSE_INDEX: false, - FILE_SUFFIX: '{{ '' if no_search_suffix else file_suffix }}', - HAS_SOURCE: {{ has_source|lower }} - }; - </script> - {%- for scriptfile in script_files %} - <script type="text/javascript" src="{{ pathto(scriptfile, 1) }}"></script> - {%- endfor %} -{%- endmacro %} - -{%- macro css() %} -<!-- GUDHI website css for header BEGIN --> -<link rel="stylesheet" type="text/css" href="https://gudhi.inria.fr/assets/css/styles_feeling_responsive.css" /> -<!-- GUDHI website css for header END --> - <link rel="stylesheet" href="{{ pathto('_static/' + style, 1) }}" type="text/css" /> - <link rel="stylesheet" href="{{ pathto('_static/pygments.css', 1) }}" type="text/css" /> - {%- for cssfile in css_files %} - <link rel="stylesheet" href="{{ pathto(cssfile, 1) }}" type="text/css" /> - {%- endfor %} -{%- endmacro %} -<!-- GUDHI website html class for header BEGIN --> -<html xmlns="http://www.w3.org/1999/xhtml" class="no-js" lang="en"> -<!-- GUDHI website html class for header END --> - <head> - <meta http-equiv="Content-Type" content="text/html; charset={{ encoding }}" /> - {{ metatags }} - {%- block htmltitle %} - <title>{{ title|striptags|e }}{{ titlesuffix }}</title> - {%- endblock %} - {{ css() }} - {%- if not embedded %} - {{ script() }} - {%- if use_opensearch %} - <link rel="search" type="application/opensearchdescription+xml" - title="{% trans docstitle=docstitle|e %}Search within {{ docstitle }}{% endtrans %}" - href="{{ pathto('_static/opensearch.xml', 1) }}"/> - {%- endif %} - {%- if favicon %} - <link rel="shortcut icon" href="{{ pathto('_static/' + favicon, 1) }}"/> - {%- endif %} - {%- endif %} -{%- block linktags %} - {%- if hasdoc('about') %} - <link rel="author" title="{{ _('About these documents') }}" href="{{ pathto('about') }}" /> - {%- endif %} - {%- if hasdoc('genindex') %} - <link rel="index" title="{{ _('Index') }}" href="{{ pathto('genindex') }}" /> - {%- endif %} - {%- if hasdoc('search') %} - <link rel="search" title="{{ _('Search') }}" href="{{ pathto('search') }}" /> - {%- endif %} - {%- if hasdoc('copyright') %} - <link rel="copyright" title="{{ _('Copyright') }}" href="{{ pathto('copyright') }}" /> - {%- endif %} - <link rel="top" title="{{ docstitle|e }}" href="{{ pathto(master_doc) }}" /> - {%- if parents %} - <link rel="up" title="{{ parents[-1].title|striptags|e }}" href="{{ parents[-1].link|e }}" /> - {%- endif %} - {%- if next %} - <link rel="next" title="{{ next.title|striptags|e }}" href="{{ next.link|e }}" /> - {%- endif %} - {%- if prev %} - <link rel="prev" title="{{ prev.title|striptags|e }}" href="{{ prev.link|e }}" /> - {%- endif %} -{%- endblock %} -{%- block extrahead %} {% endblock %} - </head> - <body role="document"> - <!-- GUDHI website header BEGIN --> - <div id="navigation" class="sticky"> - <nav class="top-bar" role="navigation" data-topbar> - <ul class="title-area"> - <li class="name"> - <h1 class="show-for-small-only"><a href="" class="icon-tree"> GUDHI C++ library</a></h1> - </li> - <!-- Remove the class "menu-icon" to get rid of menu icon. Take out "Menu" to just have icon alone --> - <li class="toggle-topbar menu-icon"><a href="#"><span>Navigation</span></a></li> - </ul> - <section class="top-bar-section"> - <ul class="right"> - <li class="divider"></li> - <li><a href="/contact/">Contact</a></li> - </ul> - <ul class="left"> - <li><a href="/"> <img src="/assets/img/home.png" alt=" GUDHI"> GUDHI </a></li> - <li class="divider"></li> - <li class="has-dropdown"> - <a href="#">Project</a> - <ul class="dropdown"> - <li><a href="/people/">People</a></li> - <li><a href="/keepintouch/">Keep in touch</a></li> - <li><a href="/partners/">Partners and Funding</a></li> - <li><a href="/relatedprojects/">Related projects</a></li> - <li><a href="/theyaretalkingaboutus/">They are talking about us</a></li> - </ul> - </li> - <li class="divider"></li> - <li class="has-dropdown"> - <a href="#">Download</a> - <ul class="dropdown"> - <li><a href="/licensing/">Licensing</a></li> - <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5253/library-latest.zip" target="_blank">Get the latest sources</a></li> - <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5280/utils_osx-latest.zip" target="_blank">Utils for Mac OSx</a></li> - <li><a href="https://gforge.inria.fr/frs/download.php/latestzip/5279/utils_win64-latest.zip" target="_blank">Utils for Win x64</a></li> - </ul> - </li> - <li class="divider"></li> - <li class="has-dropdown"> - <a href="#">Documentation</a> - <ul class="dropdown"> - <li><a href="/doc/latest/">C++ documentation</a></li> - <li><a href="/doc/latest/installation.html">C++ installation manual</a></li> - <li><a href="/python/latest/">Python documentation</a></li> - <li><a href="/python/latest/installation.html">Python installation manual</a></li> - <li><a href="/utils/">Utilities</a></li> - <li><a href="/tutorials/">Tutorials</a></li> - <li><a href="/dockerfile/">Dockerfile</a></li> - </ul> - </li> - <li class="divider"></li> - <li><a href="/interfaces/">Interfaces</a></li> - <li class="divider"></li> - </ul> - </section> - </nav> - </div><!-- /#navigation --> - <!-- GUDHI website header BEGIN --> - - -{%- block header %}{% endblock %} - -{%- block relbar1 %}{% endblock %} - -{%- block content %} - {%- block sidebar1 %} {# possible location for sidebar #} {% endblock %} - - <div class="document"> - {%- block document %} - <div class="documentwrapper"> - {%- if render_sidebar %} - <div class="bodywrapper"> - {%- endif %} - <div class="body" role="main"> - {% block body %} {% endblock %} - </div> - {%- if render_sidebar %} - </div> - {%- endif %} - </div> - {%- endblock %} - - {%- block sidebar2 %}{{ sidebar() }}{% endblock %} - <div class="clearer"></div> - </div> -{%- endblock %} - -{%- block relbar2 %}{% endblock %} - -{%- block footer %} - <div class="footer" role="contentinfo"> - {%- if show_copyright %} - {%- if hasdoc('copyright') %} - {% trans path=pathto('copyright'), copyright=copyright|e %}© <a href="{{ path }}">Copyright</a> {{ copyright }}.{% endtrans %} - {%- else %} - {% trans copyright=copyright|e %} {{ copyright }}.{% endtrans %} - {%- endif %} - {%- endif %} - {%- if last_updated %} - {% trans last_updated=last_updated|e %}Last updated on {{ last_updated }}.{% endtrans %} - {%- endif %} - {%- if show_sphinx %} - {% trans sphinx_version=sphinx_version|e %}Created using <a href="http://sphinx-doc.org/">Sphinx</a> {{ sphinx_version }}.{% endtrans %} - {%- endif %} - </div> -{%- endblock %} - </body> -</html> - diff --git a/cython/doc/alpha_complex_ref.rst b/cython/doc/alpha_complex_ref.rst deleted file mode 100644 index 7da79543..00000000 --- a/cython/doc/alpha_complex_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -============================== -Alpha complex reference manual -============================== - -.. autoclass:: gudhi.AlphaComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.AlphaComplex.__init__ diff --git a/cython/doc/alpha_complex_sum.inc b/cython/doc/alpha_complex_sum.inc deleted file mode 100644 index 1680a712..00000000 --- a/cython/doc/alpha_complex_sum.inc +++ /dev/null @@ -1,22 +0,0 @@ -================================================================= =================================== =================================== -:Author: Vincent Rouvreau :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: CGAL :math:`\geq` 4.7.0 Eigen3 -================================================================= =================================== =================================== - -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. 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` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ diff --git a/cython/doc/alpha_complex_user.rst b/cython/doc/alpha_complex_user.rst deleted file mode 100644 index d1e9c7cd..00000000 --- a/cython/doc/alpha_complex_user.rst +++ /dev/null @@ -1,210 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Alpha complex user manual -========================= -Definition ----------- - -.. include:: alpha_complex_sum.inc - -Alpha_complex is constructing a :doc:`Simplex_tree <simplex_tree_ref>` 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]]) - - simplex_tree = alpha_complex.create_simplex_tree(max_alpha_square=60.0) - result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \ - repr(simplex_tree.num_simplices()) + ' simplices - ' + \ - repr(simplex_tree.num_vertices()) + ' vertices.' - print(result_str) - fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): - print(fmt % tuple(filtered_value)) - -The output is: - -.. testoutput:: - - Alpha complex is of dimension 2 - 25 simplices - 7 vertices. - [0] -> 0.00 - [1] -> 0.00 - [2] -> 0.00 - [3] -> 0.00 - [4] -> 0.00 - [5] -> 0.00 - [6] -> 0.00 - [2, 3] -> 6.25 - [4, 5] -> 7.25 - [0, 2] -> 8.50 - [0, 1] -> 9.25 - [1, 3] -> 10.00 - [1, 2] -> 11.25 - [1, 2, 3] -> 12.50 - [0, 1, 2] -> 13.00 - [5, 6] -> 13.25 - [2, 4] -> 20.00 - [4, 6] -> 22.74 - [4, 5, 6] -> 22.74 - [3, 6] -> 30.25 - [2, 6] -> 36.50 - [2, 3, 6] -> 36.50 - [2, 4, 6] -> 37.24 - [0, 4] -> 59.71 - [0, 2, 4] -> 59.71 - - -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): - -.. figure:: - ../../doc/Alpha_complex/alpha_complex_doc.png - :figclass: align-center - :alt: Simplex tree structure construction example - - 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: - -.. figure:: - ../../doc/Alpha_complex/alpha_complex_doc_420.png - :figclass: align-center - :alt: Filtration value propagation example - - 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()` -in the `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=gudhi.__root_source_dir__ + \ - '/data/points/alphacomplexdoc.off') - simplex_tree = alpha_complex.create_simplex_tree(max_alpha_square=59.0) - result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \ - repr(simplex_tree.num_simplices()) + ' simplices - ' + \ - repr(simplex_tree.num_vertices()) + ' vertices.' - print(result_str) - fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): - print(fmt % tuple(filtered_value)) - -the program output is: - -.. testoutput:: - - Alpha complex is of dimension 2 - 23 simplices - 7 vertices. - [0] -> 0.00 - [1] -> 0.00 - [2] -> 0.00 - [3] -> 0.00 - [4] -> 0.00 - [5] -> 0.00 - [6] -> 0.00 - [2, 3] -> 6.25 - [4, 5] -> 7.25 - [0, 2] -> 8.50 - [0, 1] -> 9.25 - [1, 3] -> 10.00 - [1, 2] -> 11.25 - [1, 2, 3] -> 12.50 - [0, 1, 2] -> 13.00 - [5, 6] -> 13.25 - [2, 4] -> 20.00 - [4, 6] -> 22.74 - [4, 5, 6] -> 22.74 - [3, 6] -> 30.25 - [2, 6] -> 36.50 - [2, 3, 6] -> 36.50 - [2, 4, 6] -> 37.24 - -CGAL citations -============== - -.. bibliography:: ../../biblio/how_to_cite_cgal.bib - :filter: docnames - :style: unsrt diff --git a/cython/doc/bottleneck_distance_sum.inc b/cython/doc/bottleneck_distance_sum.inc deleted file mode 100644 index 030fad9e..00000000 --- a/cython/doc/bottleneck_distance_sum.inc +++ /dev/null @@ -1,15 +0,0 @@ -================================================================= =================================== =================================== -:Author: François Godi :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: CGAL :math:`\geq` 4.8.0 -================================================================= =================================== =================================== - -+-----------------------------------------------------------------+----------------------------------------------------------------------+ -| .. 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` | | -+-----------------------------------------------------------------+----------------------------------------------------------------------+ diff --git a/cython/doc/bottleneck_distance_user.rst b/cython/doc/bottleneck_distance_user.rst deleted file mode 100644 index 605db022..00000000 --- a/cython/doc/bottleneck_distance_user.rst +++ /dev/null @@ -1,40 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Bottleneck distance user manual -=============================== -Definition ----------- - -.. include:: bottleneck_distance_sum.inc - -Function --------- -.. autofunction:: gudhi.bottleneck_distance - - -Basic example -------------- - -This example computes the bottleneck distance from 2 persistence diagrams: - -.. testcode:: - - import gudhi - - diag1 = [[2.7, 3.7],[9.6, 14.],[34.2, 34.974], [3.,float('Inf')]] - diag2 = [[2.8, 4.45],[9.5, 14.1],[3.2,float('Inf')]] - - message = "Bottleneck distance approximation=" + '%.2f' % gudhi.bottleneck_distance(diag1, diag2, 0.1) - print(message) - - message = "Bottleneck distance value=" + '%.2f' % gudhi.bottleneck_distance(diag1, diag2) - print(message) - -The output is: - -.. testoutput:: - - Bottleneck distance approximation=0.81 - Bottleneck distance value=0.75 diff --git a/cython/doc/citation.rst b/cython/doc/citation.rst deleted file mode 100644 index 117eb9dd..00000000 --- a/cython/doc/citation.rst +++ /dev/null @@ -1,19 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Acknowledging the GUDHI library -############################### - -We kindly ask users to cite the GUDHI library as appropriately as possible in -their papers, and to mention the use of the GUDHI library on the web pages of -their projects using GUDHI and provide us with links to these web pages. Feel -free to contact us in case you have any question or remark on this topic. - -We provide GUDHI bibtex entries for the modules of the User and Reference -Manual, as well as for publications directly related to the GUDHI library. - -GUDHI bibtex -************ - -.. literalinclude:: ../../biblio/how_to_cite_gudhi.bib diff --git a/cython/doc/conf.py b/cython/doc/conf.py deleted file mode 100755 index 4a54d4fd..00000000 --- a/cython/doc/conf.py +++ /dev/null @@ -1,203 +0,0 @@ -# -*- coding: utf-8 -*- -# -# GUDHI documentation build configuration file, created by -# sphinx-quickstart on Thu Jun 30 09:55:51 2016. -# -# This file is execfile()d with the current directory set to its -# containing dir. -# -# Note that not all possible configuration values are present in this -# autogenerated file. -# -# All configuration values have a default; values that are commented out -# serve to show the default. - -import sys -import os - -# If extensions (or modules to document with autodoc) are in another directory, -# add these directories to sys.path here. If the directory is relative to the -# documentation root, use os.path.abspath to make it absolute, like shown here. -#sys.path.insert(0, os.path.abspath('.')) - -# Path to Gudhi.so from source path -sys.path.insert(0, os.path.abspath('.')) - -# -- General configuration ------------------------------------------------ - -# If your documentation needs a minimal Sphinx version, state it here. -#needs_sphinx = '1.0' - -# Add any Sphinx extension module names here, as strings. They can be -# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom -# ones. -extensions = [ - 'matplotlib.sphinxext.plot_directive', - 'sphinx.ext.autodoc', - 'sphinx.ext.doctest', - 'sphinx.ext.todo', - 'sphinx.ext.mathjax', - 'sphinx.ext.ifconfig', - 'sphinx.ext.viewcode', - 'sphinxcontrib.bibtex', -] - -todo_include_todos = True -# plot option : do not show hyperlinks (Source code, png, hires.png, pdf) -plot_html_show_source_link = False -plot_html_show_formats = False -# Add any paths that contain templates here, relative to this directory. -templates_path = ['_templates'] - -# The suffix of source filenames. -source_suffix = '.rst' - -# The encoding of source files. -#source_encoding = 'utf-8-sig' - -# The master toctree document. -master_doc = 'index' - -import gudhi - -# General information about the project. -project = gudhi.__name__ -copyright = gudhi.__copyright__ + ' - ' + gudhi.__license__ - -# The version info for the project you're documenting, acts as replacement for -# |version| and |release|, also used in various other places throughout the -# built documents. -# -# The short X.Y version. -version = gudhi.__version__ -# The full version, including alpha/beta/rc tags. -#release = '2.0.1-rc1' - -# The language for content autogenerated by Sphinx. Refer to documentation -# for a list of supported languages. -#language = None - -# There are two options for replacing |today|: either, you set today to some -# non-false value, then it is used: -#today = '' -# Else, today_fmt is used as the format for a strftime call. -#today_fmt = '%B %d, %Y' - -# List of patterns, relative to source directory, that match files and -# directories to ignore when looking for source files. -exclude_patterns = ['_build', '*.inc'] - -# The reST default role (used for this markup: `text`) to use for all -# documents. -#default_role = None - -# If true, '()' will be appended to :func: etc. cross-reference text. -#add_function_parentheses = True - -# If true, the current module name will be prepended to all description -# unit titles (such as .. function::). -#add_module_names = True - -# If true, sectionauthor and moduleauthor directives will be shown in the -# output. They are ignored by default. -#show_authors = False - -# The name of the Pygments (syntax highlighting) style to use. -pygments_style = 'sphinx' - -# A list of ignored prefixes for module index sorting. -#modindex_common_prefix = [] - -# If true, keep warnings as "system message" paragraphs in the built documents. -#keep_warnings = False - - -# -- Options for HTML output ---------------------------------------------- - -# The theme to use for HTML and HTML Help pages. See the documentation for -# a list of builtin themes. -html_theme = 'classic' - -# 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 -# documentation. -html_theme_options = { - "sidebarbgcolor": "#A1ADCD", - "sidebartextcolor": "black", - "sidebarlinkcolor": "#334D5C", - "body_max_width": "1200px", -} - -# Add any paths that contain custom themes here, relative to this directory. -#html_theme_path = [] - -# The name for this set of Sphinx documents. If None, it defaults to -# "<project> v<release> documentation". -#html_title = None - -# A shorter title for the navigation bar. Default is the same as html_title. -#html_short_title = None - -# The name of an image file (relative to this directory) to place at the top -# of the sidebar. -#html_logo = - -# The name of an image file (within the static path) to use as favicon of the -# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 -# pixels large. -#html_favicon = - -# Add any paths that contain custom static files (such as style sheets) here, -# relative to this directory. They are copied after the builtin static files, -# so a file named "default.css" will overwrite the builtin "default.css". -html_static_path = ['_static'] - -# Add any extra paths that contain custom files (such as robots.txt or -# .htaccess) here, relative to this directory. These files are copied -# directly to the root of the documentation. -#html_extra_path = [] - -# If not '', a 'Last updated on:' timestamp is inserted at every page bottom, -# using the given strftime format. -html_last_updated_fmt = '%b %d, %Y' - -# If true, SmartyPants will be used to convert quotes and dashes to -# typographically correct entities. -#html_use_smartypants = True - -# Custom sidebar templates, maps document names to template names. -#html_sidebars = {} - -# Additional templates that should be rendered to pages, maps page names to -# template names. -#html_additional_pages = {'installation': 'installation.html'} - -# If false, no module index is generated. -#html_domain_indices = True - -# If false, no index is generated. -#html_use_index = True - -# If true, the index is split into individual pages for each letter. -#html_split_index = False - -# If true, links to the reST sources are added to the pages. -#html_show_sourcelink = True - -# If true, "Created using Sphinx" is shown in the HTML footer. Default is True. -#html_show_sphinx = True - -# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. -#html_show_copyright = True - -# If true, an OpenSearch description file will be output, and all pages will -# contain a <link> tag referring to it. The value of this option must be the -# base URL from which the finished HTML is served. -#html_use_opensearch = '' - -# This is the file name suffix for HTML files (e.g. ".xhtml"). -#html_file_suffix = None - -# Output file base name for HTML help builder. -htmlhelp_basename = 'GUDHIdoc' - diff --git a/cython/doc/cubical_complex_ref.rst b/cython/doc/cubical_complex_ref.rst deleted file mode 100644 index 1fe9d5fb..00000000 --- a/cython/doc/cubical_complex_ref.rst +++ /dev/null @@ -1,13 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Cubical complex reference manual -################################ - -.. autoclass:: gudhi.CubicalComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.CubicalComplex.__init__ diff --git a/cython/doc/cubical_complex_sum.inc b/cython/doc/cubical_complex_sum.inc deleted file mode 100644 index 280ad0e0..00000000 --- a/cython/doc/cubical_complex_sum.inc +++ /dev/null @@ -1,15 +0,0 @@ -================================================================= =================================== =================================== -:Author: Pawel Dlotko :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -================================================================= =================================== =================================== - -+--------------------------------------------------------------------------+----------------------------------------------------------------------+ -| .. 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` | -+--------------------------------------------------------------------------+----------------------------------------------------------------------+ diff --git a/cython/doc/cubical_complex_user.rst b/cython/doc/cubical_complex_user.rst deleted file mode 100644 index 320bd79b..00000000 --- a/cython/doc/cubical_complex_user.rst +++ /dev/null @@ -1,162 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -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` | -+---------------------------------------------+----------------------------------------------------------------------+ - -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}`. - -.. figure:: - ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png - :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 -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. -The file format is described here: :doc:`Perseus <fileformats>`. - -.. testcode:: - - import gudhi - cubical_complex = gudhi.CubicalComplex(perseus_file=gudhi.__root_source_dir__ + \ - '/data/bitmap/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 (see :doc:`Perseus <fileformats>`) for the specific periodic case: - -.. testcode:: - - import gudhi - periodic_cc = gudhi.PeriodicCubicalComplex(perseus_file=gudhi.__root_source_dir__ + \ - '/data/bitmap/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. - -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_dimensions=[True, False]) - 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. - -Bibliography -============ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: docnames - :style: unsrt diff --git a/cython/doc/euclidean_strong_witness_complex_ref.rst b/cython/doc/euclidean_strong_witness_complex_ref.rst deleted file mode 100644 index 1a602cd5..00000000 --- a/cython/doc/euclidean_strong_witness_complex_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -================================================= -Euclidean strong witness complex reference manual -================================================= - -.. autoclass:: gudhi.EuclideanStrongWitnessComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.EuclideanStrongWitnessComplex.__init__ diff --git a/cython/doc/euclidean_witness_complex_ref.rst b/cython/doc/euclidean_witness_complex_ref.rst deleted file mode 100644 index 28daf965..00000000 --- a/cython/doc/euclidean_witness_complex_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -========================================== -Euclidean witness complex reference manual -========================================== - -.. autoclass:: gudhi.EuclideanWitnessComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.EuclideanWitnessComplex.__init__ diff --git a/cython/doc/examples.rst b/cython/doc/examples.rst deleted file mode 100644 index 1f02f8a2..00000000 --- a/cython/doc/examples.rst +++ /dev/null @@ -1,29 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Examples -######## - -.. only:: builder_html - - * :download:`rips_complex_from_points_example.py <../example/rips_complex_from_points_example.py>` - * :download:`alpha_complex_from_points_example.py <../example/alpha_complex_from_points_example.py>` - * :download:`simplex_tree_example.py <../example/simplex_tree_example.py>` - * :download:`alpha_rips_persistence_bottleneck_distance.py <../example/alpha_rips_persistence_bottleneck_distance.py>` - * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` - * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` - * :download:`periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py <../example/periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py>` - * :download:`bottleneck_basic_example.py <../example/bottleneck_basic_example.py>` - * :download:`gudhi_graphical_tools_example.py <../example/gudhi_graphical_tools_example.py>` - * :download:`witness_complex_from_nearest_landmark_table.py <../example/witness_complex_from_nearest_landmark_table.py>` - * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` - * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` - * :download:`rips_complex_diagram_persistence_from_off_file_example.py <../example/rips_complex_diagram_persistence_from_off_file_example.py>` - * :download:`rips_complex_diagram_persistence_from_distance_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_distance_matrix_file_example.py>` - * :download:`rips_persistence_diagram.py <../example/rips_persistence_diagram.py>` - * :download:`random_cubical_complex_persistence_example.py <../example/random_cubical_complex_persistence_example.py>` - * :download:`coordinate_graph_induced_complex.py <../example/coordinate_graph_induced_complex.py>` - * :download:`functional_graph_induced_complex.py <../example/functional_graph_induced_complex.py>` - * :download:`voronoi_graph_induced_complex.py <../example/voronoi_graph_induced_complex.py>` - * :download:`nerve_of_a_covering.py <../example/nerve_of_a_covering.py>` diff --git a/cython/doc/fileformats.rst b/cython/doc/fileformats.rst deleted file mode 100644 index ff20f26e..00000000 --- a/cython/doc/fileformats.rst +++ /dev/null @@ -1,90 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -File formats -############ - -Persistence Diagram -******************* - -Such a file, whose extension is usually ``.pers``, contains a list of -persistence intervals. - -Lines starting with ``#`` are ignored (comments). - -Other lines might contain 2, 3 or 4 values (the number of values on each line -must be the same for all lines):: - - [[field] dimension] birth death - -Here is a simple sample file:: - - # Persistence diagram example - 2 2.7 3.7 - 2 9.6 14. - # Some comments - 3 34.2 34.974 - 4 3. inf - -Other sample files can be found in the `data/persistence_diagram` folder. - -Such files can be generated with -:meth:`gudhi.SimplexTree.write_persistence_diagram`, read with -:meth:`gudhi.read_persistence_intervals_grouped_by_dimension`, or -:meth:`gudhi.read_persistence_intervals_in_dimension` and displayed with -:meth:`gudhi.plot_persistence_barcode` or -:meth:`gudhi.plot_persistence_diagram`. - -Iso-cuboid -********** - -Such a file describes an iso-oriented cuboid with diagonal opposite vertices -(min_x, min_y, min_z,...) and (max_x, max_y, max_z, ...). The format is:: - - min_x min_y [min_z ...] - max_x max_y [max_z ...] - -Here is a simple sample file in the 3D case:: - - -1. -1. -1. - 1. 1. 1. - - -Perseus -******* - -This file format is the format used by the -`Perseus software <http://www.sas.upenn.edu/~vnanda/perseus/>`_ by Vidit Nanda. -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). - -.. figure:: - ../../doc/Bitmap_cubical_complex/exampleBitmap.png - :alt: Example of a input data. - :figclass: align-center - - Example of a input data. - -The input file for the following complex is: - -.. literalinclude:: ../../data/bitmap/cubicalcomplexdoc.txt - -.. centered:: ../../data/bitmap/cubicalcomplexdoc.txt - -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:: ../../data/bitmap/periodiccubicalcomplexdoc.txt - -.. centered:: ../../data/bitmap/periodiccubicalcomplexdoc.txt - - -Indicate that we have imposed periodic boundary conditions in the direction x, -but not in the direction y. - -Other sample files can be found in the `data/bitmap` folder. diff --git a/cython/doc/img/graphical_tools_representation.png b/cython/doc/img/graphical_tools_representation.png Binary files differdeleted file mode 100644 index 9759f7ba..00000000 --- a/cython/doc/img/graphical_tools_representation.png +++ /dev/null diff --git a/cython/doc/index.rst b/cython/doc/index.rst deleted file mode 100644 index 15cbe267..00000000 --- a/cython/doc/index.rst +++ /dev/null @@ -1,93 +0,0 @@ -GUDHI Python module documentation -################################# - -.. figure:: - ../../doc/common/Gudhi_banner.png - :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: - -* Data structures to represent, construct and manipulate simplicial complexes. -* Simplification of simplicial complexes by edge contraction. -* Algorithms to compute persistent homology and bottleneck distance. - -We refer to :cite:`gudhilibrary_ICMS14` for a detailed description of the -design of the library. - -Data structures -*************** - -Alpha complex -============= - -.. include:: alpha_complex_sum.inc - -Cover complexes -=============== - -.. include:: nerve_gic_complex_sum.rst - -Cubical complex -=============== - -.. include:: cubical_complex_sum.inc - -Rips complex -============ - -.. include:: rips_complex_sum.inc - -Simplex tree -============ - -.. include:: simplex_tree_sum.inc - -Tangential complex -================== - -.. include:: tangential_complex_sum.inc - -Witness complex -=============== - -.. include:: witness_complex_sum.inc - - -Toolbox -******* - -Bottleneck distance -=================== - -.. include:: bottleneck_distance_sum.inc - -Persistence cohomology -====================== - -.. include:: persistent_cohomology_sum.inc - -Persistence graphical tools -=========================== - -.. include:: persistence_graphical_tools_sum.inc - -Bibliography -************ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: docnames - :style: unsrt diff --git a/cython/doc/installation.rst b/cython/doc/installation.rst deleted file mode 100644 index 43576ec9..00000000 --- a/cython/doc/installation.rst +++ /dev/null @@ -1,236 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Installation -############ - -Compiling -********* -The library uses c++11 and requires `Boost <https://www.boost.org/>`_ ≥ 1.48.0 -and `CMake <https://www.cmake.org/>`_ ≥ 3.1. -It is a multi-platform library and compiles on Linux, Mac OSX and Visual -Studio 2015. -It also requires cmake to generate makefiles, and cython to compile the -library. - -On `Windows <https://wiki.python.org/moin/WindowsCompilers>`_ , only Python -3.5 and 3.6 are available because of the required Visual Studio version. - -On other systems, if you have several Python/cython installed, the version 2.X -will be used by default, but you can force it by adding -:code:`-DPython_ADDITIONAL_VERSIONS=3` to the cmake command. - -GUDHI Cythonization -=================== - -To build the GUDHI cython module, run the following commands in a terminal: - -.. code-block:: bash - - cd /path-to-gudhi/ - mkdir build - cd build/ - cmake .. - make cython - -Test suites -=========== - -To test your build, `py.test <http://doc.pytest.org>`_ is optional. Run the -following command in a terminal: - -.. code-block:: bash - - cd /path-to-gudhi/build/cython - # For windows, you have to set PYTHONPATH environment variable - export PYTHONPATH='$PYTHONPATH:/path-to-gudhi/build/cython' - ctest -R py_test - -Debugging issues -================ - -If tests fail, please check your PYTHONPATH and try to :code:`import gudhi` -and check the errors. -The problem can come from a third-party library bad link or installation. - -If :code:`import gudhi` succeeds, please have a look to debug informations: - -.. code-block:: python - - import gudhi - print(gudhi.__debug_info__) - -You shall have something like: - -.. code-block:: none - - Python version 2.7.15 - Cython version 0.26.1 - Eigen3 version 3.1.1 - Installed modules are: off_reader;simplex_tree;rips_complex;cubical_complex;periodic_cubical_complex; - persistence_graphical_tools;reader_utils;witness_complex;strong_witness_complex;alpha_complex; - euclidean_witness_complex;euclidean_strong_witness_complex; - Missing modules are: bottleneck_distance;nerve_gic;subsampling;tangential_complex;persistence_graphical_tools; - CGAL version 4.7.1000 - GMP_LIBRARIES = /usr/lib/x86_64-linux-gnu/libgmp.so - GMPXX_LIBRARIES = /usr/lib/x86_64-linux-gnu/libgmpxx.so - TBB version 9107 found and used - -Here, you can see that bottleneck_distance, nerve_gic, subsampling and -tangential_complex are missing because of the CGAL version. -persistence_graphical_tools is not available as numpy and matplotlib are not -available. -Unitary tests cannot be run as pytest is missing. - -A complete configuration would be : - -.. code-block:: none - - Python version 3.6.5 - Cython version 0.28.2 - Pytest version 3.3.2 - Matplotlib version 2.2.2 - Numpy version 1.14.5 - Eigen3 version 3.3.4 - Installed modules are: off_reader;simplex_tree;rips_complex;cubical_complex;periodic_cubical_complex; - persistence_graphical_tools;reader_utils;witness_complex;strong_witness_complex;persistence_graphical_tools; - bottleneck_distance;nerve_gic;subsampling;tangential_complex;alpha_complex;euclidean_witness_complex; - euclidean_strong_witness_complex; - CGAL header only version 4.11.0 - GMP_LIBRARIES = /usr/lib/x86_64-linux-gnu/libgmp.so - GMPXX_LIBRARIES = /usr/lib/x86_64-linux-gnu/libgmpxx.so - TBB version 9107 found and used - -Documentation -============= - -To build the documentation, `sphinx-doc <http://http://www.sphinx-doc.org>`_ is -required. Please refer to *conf.py* file to see which -`sphinx-doc <http://http://www.sphinx-doc.org>`_ modules are required to -generate the documentation. Run the following commands in a terminal: - -.. code-block:: bash - - make sphinx - -Optional third-party library -**************************** - -CGAL -==== - -The :doc:`Alpha complex </alpha_complex_user>`, -:doc:`Tangential complex </tangential_complex_user>` and -:doc:`Witness complex </witness_complex_user>` data structures, and -:doc:`Bottleneck distance </bottleneck_distance_user>` requires CGAL, which is a -C++ library which provides easy access to efficient and reliable geometric -algorithms. - -Having CGAL, the Computational Geometry Algorithms Library, version 4.7.0 or -higher installed is recommended. The procedure to install this library -according to your operating system is detailed -`here <http://doc.cgal.org/latest/Manual/installation.html>`_. - -The following examples requires CGAL version ≥ 4.7.0: - -.. only:: builder_html - - * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` - * :download:`alpha_complex_from_points_example.py <../example/alpha_complex_from_points_example.py>` - -The following examples requires CGAL version ≥ 4.8.0: - -.. only:: builder_html - - * :download:`bottleneck_basic_example.py <../example/bottleneck_basic_example.py>` - * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` - -The following examples requires CGAL version ≥ 4.8.1: - -.. only:: builder_html - - * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` - * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` - -Eigen3 -====== - -The :doc:`Alpha complex </alpha_complex_user>`, -:doc:`Tangential complex </tangential_complex_user>` and -:doc:`Witness complex </witness_complex_user>` data structures and few -examples requires `Eigen3 <http://eigen.tuxfamily.org/>`_, a C++ template -library for linear algebra: matrices, vectors, numerical solvers, and related -algorithms. - -The following examples require the `Eigen3 <http://eigen.tuxfamily.org/>`_: - -.. only:: builder_html - - * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` - * :download:`alpha_complex_from_points_example.py <../example/alpha_complex_from_points_example.py>` - * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` - * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` - * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` - -Matplotlib -========== - -The :doc:`persistence graphical tools </persistence_graphical_tools_user>` -module requires `Matplotlib <http://matplotlib.org>`_, a Python 2D plotting -library which produces publication quality figures in a variety of hardcopy -formats and interactive environments across platforms. - -The following examples require the `Matplotlib <http://matplotlib.org>`_: - -.. only:: builder_html - - * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` - * :download:`gudhi_graphical_tools_example.py <../example/gudhi_graphical_tools_example.py>` - * :download:`periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py <../example/periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py>` - * :download:`rips_complex_diagram_persistence_from_off_file_example.py <../example/rips_complex_diagram_persistence_from_off_file_example.py>` - * :download:`rips_persistence_diagram.py <../example/rips_persistence_diagram.py>` - * :download:`rips_complex_diagram_persistence_from_distance_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_distance_matrix_file_example.py>` - * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` - * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` - * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` - -Numpy -===== - -The :doc:`persistence graphical tools </persistence_graphical_tools_user>` -module requires `NumPy <http://numpy.org>`_, a fundamental package for -scientific computing with Python. - -The following examples require the `NumPy <http://numpy.org>`_: - -.. only:: builder_html - - * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` - * :download:`gudhi_graphical_tools_example.py <../example/gudhi_graphical_tools_example.py>` - * :download:`periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py <../example/periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py>` - * :download:`rips_complex_diagram_persistence_from_off_file_example.py <../example/rips_complex_diagram_persistence_from_off_file_example.py>` - * :download:`rips_persistence_diagram.py <../example/rips_persistence_diagram.py>` - * :download:`rips_complex_diagram_persistence_from_distance_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_distance_matrix_file_example.py>` - * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` - * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` - * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` - -Threading Building Blocks -========================= - -`Intel® TBB <https://www.threadingbuildingblocks.org/>`_ lets you easily write -parallel C++ programs that take full advantage of multicore performance, that -are portable and composable, and that have future-proof scalability. - -Having Intel® TBB installed is recommended to parallelize and accelerate some -GUDHI computations. - -Bug reports and contributions -***************************** - -Please help us improving the quality of the GUDHI library. You may report bugs or suggestions to: - - Contact: gudhi-users@lists.gforge.inria.fr - -GUDHI is open to external contributions. If you want to join our development team, please contact us. diff --git a/cython/doc/nerve_gic_complex_ref.rst b/cython/doc/nerve_gic_complex_ref.rst deleted file mode 100644 index e24e01fc..00000000 --- a/cython/doc/nerve_gic_complex_ref.rst +++ /dev/null @@ -1,10 +0,0 @@ -================================ -Cover complexes reference manual -================================ - -.. autoclass:: gudhi.CoverComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.CoverComplex.__init__ diff --git a/cython/doc/nerve_gic_complex_sum.rst b/cython/doc/nerve_gic_complex_sum.rst deleted file mode 100644 index 72782c7a..00000000 --- a/cython/doc/nerve_gic_complex_sum.rst +++ /dev/null @@ -1,15 +0,0 @@ -================================================================= =================================== =================================== -:Author: Mathieu Carrière :Introduced in: GUDHI 2.1.0 :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/cython/doc/nerve_gic_complex_user.rst b/cython/doc/nerve_gic_complex_user.rst deleted file mode 100644 index d774827e..00000000 --- a/cython/doc/nerve_gic_complex_user.rst +++ /dev/null @@ -1,312 +0,0 @@ -Cover complexes user manual -=========================== -Definition ----------- - -.. include:: nerve_gic_complex_sum.rst - -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>`_. - -Covers ------- - -Nerves and Graph Induced Complexes require a cover C of the input point cloud P, -that is a set of subsets of P whose union is P itself. -Very often, this cover is obtained from the preimage of a family of intervals covering -the image of some scalar-valued function f defined on P. This family is parameterized -by its resolution, which can be either the number or the length of the intervals, -and its gain, which is the overlap percentage between consecutive intervals (ordered by their first values). - -Nerves ------- - -Nerve definition -^^^^^^^^^^^^^^^^ - -Assume you are given a cover C of your point cloud P. Then, the Nerve of this cover -is the simplicial complex that has one k-simplex per k-fold intersection of cover elements. -See also `Wikipedia <https://en.wikipedia.org/wiki/Nerve_of_a_covering>`_. - -.. figure:: - ../../doc/Nerve_GIC/nerve.png - :figclass: align-center - :alt: Nerve of a double torus - - Nerve of a double torus - -Example -^^^^^^^ - -This example builds the Nerve of a point cloud sampled on a 3D human shape (human.off). -The cover C comes from the preimages of intervals (10 intervals with gain 0.3) -covering the height function (coordinate 2), -which are then refined into their connected components using the triangulation of the .OFF file. - -.. testcode:: - - import gudhi - nerve_complex = gudhi.CoverComplex() - nerve_complex.set_verbose(True) - - if (nerve_complex.read_point_cloud(gudhi.__root_source_dir__ + \ - '/data/points/human.off')): - nerve_complex.set_type('Nerve') - nerve_complex.set_color_from_coordinate(2) - nerve_complex.set_function_from_coordinate(2) - nerve_complex.set_graph_from_OFF() - nerve_complex.set_resolution_with_interval_number(10) - nerve_complex.set_gain(0.3) - nerve_complex.set_cover_from_function() - nerve_complex.find_simplices() - nerve_complex.write_info() - simplex_tree = nerve_complex.create_simplex_tree() - nerve_complex.compute_PD() - result_str = 'Nerve 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_filtration(): - print(filtered_value[0]) - -the program output is: - -.. code-block:: none - - Min function value = -0.979672 and Max function value = 0.816414 - Interval 0 = [-0.979672, -0.761576] - Interval 1 = [-0.838551, -0.581967] - Interval 2 = [-0.658942, -0.402359] - Interval 3 = [-0.479334, -0.22275] - Interval 4 = [-0.299725, -0.0431414] - Interval 5 = [-0.120117, 0.136467] - Interval 6 = [0.059492, 0.316076] - Interval 7 = [0.239101, 0.495684] - Interval 8 = [0.418709, 0.675293] - Interval 9 = [0.598318, 0.816414] - Computing preimages... - Computing connected components... - 5 interval(s) in dimension 0: - [-0.909111, 0.0081753] - [-0.171433, 0.367393] - [-0.171433, 0.367393] - [-0.909111, 0.745853] - 0 interval(s) in dimension 1: - -.. testoutput:: - - Nerve is of dimension 1 - 41 simplices - 21 vertices. - [0] - [1] - [4] - [1, 4] - [2] - [0, 2] - [8] - [2, 8] - [5] - [4, 5] - [9] - [8, 9] - [13] - [5, 13] - [14] - [9, 14] - [19] - [13, 19] - [25] - [32] - [20] - [20, 32] - [33] - [25, 33] - [26] - [14, 26] - [19, 26] - [42] - [26, 42] - [34] - [33, 34] - [27] - [20, 27] - [35] - [27, 35] - [34, 35] - [35, 42] - [44] - [35, 44] - [54] - [44, 54] - - -The program also writes a file ../../data/points/human.off_sc.txt. The first -three lines in this file are the location of the input point cloud and the -function used to compute the cover. -The fourth line contains the number of vertices nv and edges ne of the Nerve. -The next nv lines represent the vertices. Each line contains the vertex ID, -the number of data points it contains, and their average color function value. -Finally, the next ne lines represent the edges, characterized by the ID of -their vertices. - -Using KeplerMapper, one can obtain the following visualization: - -.. figure:: - ../../doc/Nerve_GIC/nervevisu.jpg - :figclass: align-center - :alt: Visualization with KeplerMapper - - Visualization with KeplerMapper - -Graph Induced Complexes (GIC) ------------------------------ - -GIC definition -^^^^^^^^^^^^^^ - -Again, assume you are given a cover C of your point cloud P. Moreover, assume -you are also given a graph G built on top of P. Then, for any clique in G -whose nodes all belong to different elements of C, the GIC includes a -corresponding simplex, whose dimension is the number of nodes in the clique -minus one. -See :cite:`Dey13` for more details. - -.. figure:: - ../../doc/Nerve_GIC/GIC.jpg - :figclass: align-center - :alt: GIC of a point cloud - - GIC of a point cloud - -Example with cover from Voronoï -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -This example builds the GIC of a point cloud sampled on a 3D human shape -(human.off). -We randomly subsampled 100 points in the point cloud, which act as seeds of -a geodesic Voronoï diagram. Each cell of the diagram is then an element of C. -The graph G (used to compute both the geodesics for Voronoï and the GIC) -comes from the triangulation of the human shape. Note that the resulting -simplicial complex is in dimension 3 in this example. - -.. testcode:: - - import gudhi - nerve_complex = gudhi.CoverComplex() - - if (nerve_complex.read_point_cloud(gudhi.__root_source_dir__ + \ - '/data/points/human.off')): - nerve_complex.set_type('GIC') - nerve_complex.set_color_from_coordinate() - nerve_complex.set_graph_from_OFF() - nerve_complex.set_cover_from_Voronoi(700) - nerve_complex.find_simplices() - nerve_complex.plot_off() - -the program outputs SC.off. Using e.g. - -.. code-block:: none - - geomview ../../data/points/human.off_sc.off - -one can obtain the following visualization: - -.. figure:: - ../../doc/Nerve_GIC/gicvoronoivisu.jpg - :figclass: align-center - :alt: Visualization with Geomview - - Visualization with Geomview - -Functional GIC -^^^^^^^^^^^^^^ - -If one restricts to the cliques in G whose nodes all belong to preimages of -consecutive intervals (assuming the cover of the height function is minimal, -i.e. no more than two intervals can intersect at a time), the GIC is of -dimension one, i.e. a graph. -We call this graph the functional GIC. See :cite:`Carriere16` for more details. - -Example -^^^^^^^ - -Functional GIC comes with automatic selection of the Rips threshold, -the resolution and the gain of the function cover. See :cite:`Carriere17c` for -more details. In this example, we compute the functional GIC of a Klein bottle -embedded in R^5, where the graph G comes from a Rips complex with automatic -threshold, and the cover C comes from the preimages of intervals covering the -first coordinate, with automatic resolution and gain. Note that automatic -threshold, resolution and gain can be computed as well for the Nerve. - -.. testcode:: - - import gudhi - nerve_complex = gudhi.CoverComplex() - - if (nerve_complex.read_point_cloud(gudhi.__root_source_dir__ + \ - '/data/points/KleinBottle5D.off')): - nerve_complex.set_type('GIC') - nerve_complex.set_color_from_coordinate(0) - nerve_complex.set_function_from_coordinate(0) - nerve_complex.set_graph_from_automatic_rips() - nerve_complex.set_automatic_resolution() - nerve_complex.set_gain() - nerve_complex.set_cover_from_function() - nerve_complex.find_simplices() - nerve_complex.plot_dot() - -the program outputs SC.dot. Using e.g. - -.. code-block:: none - - neato ../../data/points/KleinBottle5D.off_sc.dot -Tpdf -o ../../data/points/KleinBottle5D.off_sc.pdf - -one can obtain the following visualization: - -.. figure:: - ../../doc/Nerve_GIC/coordGICvisu2.jpg - :figclass: align-center - :alt: Visualization with neato - - Visualization with neato - -where nodes are colored by the filter function values and, for each node, the -first number is its ID and the second is the number of data points that its -contain. - -We also provide an example on a set of 72 pictures taken around the same object -(lucky_cat.off). -The function is now the first eigenfunction given by PCA, whose values are -written in a file (lucky_cat_PCA1). Threshold, resolution and gain are -automatically selected as before. - -.. testcode:: - - import gudhi - nerve_complex = gudhi.CoverComplex() - - if (nerve_complex.read_point_cloud(gudhi.__root_source_dir__ + \ - '/data/points/COIL_database/lucky_cat.off')): - nerve_complex.set_type('GIC') - pca_file = gudhi.__root_source_dir__ + \ - '/data/points/COIL_database/lucky_cat_PCA1' - nerve_complex.set_color_from_file(pca_file) - nerve_complex.set_function_from_file(pca_file) - nerve_complex.set_graph_from_automatic_rips() - nerve_complex.set_automatic_resolution() - nerve_complex.set_gain() - nerve_complex.set_cover_from_function() - nerve_complex.find_simplices() - nerve_complex.plot_dot() - -the program outputs again SC.dot which gives the following visualization after using neato: - -.. figure:: - ../../doc/Nerve_GIC/funcGICvisu.jpg - :figclass: align-center - :alt: Visualization with neato - - Visualization with neato diff --git a/cython/doc/periodic_cubical_complex_ref.rst b/cython/doc/periodic_cubical_complex_ref.rst deleted file mode 100644 index 4b831647..00000000 --- a/cython/doc/periodic_cubical_complex_ref.rst +++ /dev/null @@ -1,13 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Periodic cubical complex reference manual -######################################### - -.. autoclass:: gudhi.PeriodicCubicalComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.PeriodicCubicalComplex.__init__ diff --git a/cython/doc/persistence_graphical_tools_ref.rst b/cython/doc/persistence_graphical_tools_ref.rst deleted file mode 100644 index a2c6bcef..00000000 --- a/cython/doc/persistence_graphical_tools_ref.rst +++ /dev/null @@ -1,11 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -============================================ -Persistence graphical tools reference manual -============================================ - -.. autofunction:: gudhi.__min_birth_max_death -.. autofunction:: gudhi.plot_persistence_barcode -.. autofunction:: gudhi.plot_persistence_diagram diff --git a/cython/doc/persistence_graphical_tools_sum.inc b/cython/doc/persistence_graphical_tools_sum.inc deleted file mode 100644 index d602daa7..00000000 --- a/cython/doc/persistence_graphical_tools_sum.inc +++ /dev/null @@ -1,12 +0,0 @@ -================================================================= =================================== =================================== -:Author: Vincent Rouvreau :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: Matplotlib Numpy -================================================================= =================================== =================================== - -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ -| .. 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/cython/doc/persistence_graphical_tools_user.rst b/cython/doc/persistence_graphical_tools_user.rst deleted file mode 100644 index 292915eb..00000000 --- a/cython/doc/persistence_graphical_tools_user.rst +++ /dev/null @@ -1,62 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Persistence graphical tools user manual -======================================= -Definition ----------- -.. include:: persistence_graphical_tools_sum.inc - - -Show persistence as a barcode ------------------------------ - -This function can display the persistence result as a barcode: - -.. plot:: - :include-source: - - import gudhi - - perseus_file = gudhi.__root_source_dir__ + '/data/bitmap/3d_torus.txt' - periodic_cc = gudhi.PeriodicCubicalComplex(perseus_file=perseus_file) - diag = periodic_cc.persistence() - print("diag = ", diag) - plt = gudhi.plot_persistence_barcode(diag) - plt.show() - -Show persistence as a diagram ------------------------------ - -This function can display the persistence result as a diagram: - -.. plot:: - :include-source: - - import gudhi - - # rips_on_tore3D_1307.pers obtained from write_persistence_diagram method - persistence_file=gudhi.__root_source_dir__ + \ - '/data/persistence_diagram/rips_on_tore3D_1307.pers' - plt = gudhi.plot_persistence_diagram(persistence_file=persistence_file, - legend=True) - plt.show() - -If you want more information on a specific dimension, for instance: - -.. plot:: - :include-source: - - import gudhi - - persistence_file=gudhi.__root_source_dir__ + \ - '/data/persistence_diagram/rips_on_tore3D_1307.pers' - diag = \ - gudhi.read_persistence_intervals_grouped_by_dimension(persistence_file=\ - persistence_file) - dim = 1 - # Display all points with some transparency - plt = gudhi.plot_persistence_diagram([(dim,interval) for interval in diag[dim]], - max_plots=0, alpha=0.1) - plt.show() diff --git a/cython/doc/persistent_cohomology_sum.inc b/cython/doc/persistent_cohomology_sum.inc deleted file mode 100644 index a26df1dc..00000000 --- a/cython/doc/persistent_cohomology_sum.inc +++ /dev/null @@ -1,27 +0,0 @@ -================================================================= =================================== =================================== -:Author: Clément Maria :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -================================================================= =================================== =================================== - -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ -| .. 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` | -+-----------------------------------------------------------------+-----------------------------------------------------------------------+ diff --git a/cython/doc/persistent_cohomology_user.rst b/cython/doc/persistent_cohomology_user.rst deleted file mode 100644 index ce7fc685..00000000 --- a/cython/doc/persistent_cohomology_user.rst +++ /dev/null @@ -1,118 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Persistent cohomology user manual -================================= -Definition ----------- -===================================== ===================================== ===================================== -:Author: Clément Maria :Introduced in: GUDHI PYTHON 2.0.0 :Copyright: GPL v3 -===================================== ===================================== ===================================== - -+---------------------------------------------+----------------------------------------------------------------------+ -| :doc:`persistent_cohomology_user` | Please refer to each data structure that contains persistence | -| | feature for reference: | -| | | -| | * :doc:`simplex_tree_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. - -.. only:: builder_html - - * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` - * :download:`periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py <../example/periodic_cubical_complex_barcode_persistence_from_perseus_file_example.py>` - * :download:`rips_complex_diagram_persistence_from_off_file_example.py <../example/rips_complex_diagram_persistence_from_off_file_example.py>` - * :download:`rips_persistence_diagram.py <../example/rips_persistence_diagram.py>` - * :download:`rips_complex_diagram_persistence_from_distance_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_distance_matrix_file_example.py>` - * :download:`random_cubical_complex_persistence_example.py <../example/random_cubical_complex_persistence_example.py>` - * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` - -Bibliography -============ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: docnames - :style: unsrt diff --git a/cython/doc/python3-sphinx-build.py b/cython/doc/python3-sphinx-build.py deleted file mode 100755 index 84d158cf..00000000 --- a/cython/doc/python3-sphinx-build.py +++ /dev/null @@ -1,11 +0,0 @@ -#!/usr/bin/env python3 - -""" -Emulate sphinx-build for python3 -""" - -from sys import exit, argv -from sphinx import main - -if __name__ == '__main__': - exit(main(argv)) diff --git a/cython/doc/reader_utils_ref.rst b/cython/doc/reader_utils_ref.rst deleted file mode 100644 index f3ecebad..00000000 --- a/cython/doc/reader_utils_ref.rst +++ /dev/null @@ -1,15 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -============================= -Reader utils reference manual -============================= - -.. autofunction:: gudhi.read_off - -.. autofunction:: gudhi.read_lower_triangular_matrix_from_csv_file - -.. autofunction:: gudhi.read_persistence_intervals_grouped_by_dimension - -.. autofunction:: gudhi.read_persistence_intervals_in_dimension diff --git a/cython/doc/rips_complex_ref.rst b/cython/doc/rips_complex_ref.rst deleted file mode 100644 index 22b5616c..00000000 --- a/cython/doc/rips_complex_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -============================= -Rips complex reference manual -============================= - -.. autoclass:: gudhi.RipsComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.RipsComplex.__init__ diff --git a/cython/doc/rips_complex_sum.inc b/cython/doc/rips_complex_sum.inc deleted file mode 100644 index 5616bfa9..00000000 --- a/cython/doc/rips_complex_sum.inc +++ /dev/null @@ -1,17 +0,0 @@ -================================================================= =================================== =================================== -:Author: Clément Maria, Pawel Dlotko, Vincent Rouvreau :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -================================================================= =================================== =================================== - -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. 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` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ diff --git a/cython/doc/rips_complex_user.rst b/cython/doc/rips_complex_user.rst deleted file mode 100644 index a8c06cf9..00000000 --- a/cython/doc/rips_complex_user.rst +++ /dev/null @@ -1,316 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -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:: - ../../doc/Rips_complex/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 ------------ - -Example from a point cloud -^^^^^^^^^^^^^^^^^^^^^^^^^^ - -This example builds the one skeleton graph from the given points, and max_edge_length value. -Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it. - -Finally, 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) - fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): - print(fmt % tuple(filtered_value)) - -When launching (Rips maximal distance between 2 points is 12.0, is expanded -until dimension 1 - one skeleton graph in other words), the output is: - -.. testoutput:: - - Rips complex is of dimension 1 - 18 simplices - 7 vertices. - [0] -> 0.00 - [1] -> 0.00 - [2] -> 0.00 - [3] -> 0.00 - [4] -> 0.00 - [5] -> 0.00 - [6] -> 0.00 - [2, 3] -> 5.00 - [4, 5] -> 5.39 - [0, 2] -> 5.83 - [0, 1] -> 6.08 - [1, 3] -> 6.32 - [1, 2] -> 6.71 - [5, 6] -> 7.28 - [2, 4] -> 8.94 - [0, 3] -> 9.43 - [4, 6] -> 9.49 - [3, 6] -> 11.00 - -Example from OFF file -^^^^^^^^^^^^^^^^^^^^^ - -This example builds the :doc:`Rips_complex <rips_complex_ref>` from the given -points in an OFF file, and max_edge_length value. -Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it. - -Finally, it is asked to display information about the Rips complex. - - -.. testcode:: - - import gudhi - point_cloud = gudhi.read_off(off_file=gudhi.__root_source_dir__ + '/data/points/alphacomplexdoc.off') - rips_complex = gudhi.RipsComplex(points=point_cloud, 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) - fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): - print(fmt % tuple(filtered_value)) - -the program output is: - -.. testoutput:: - - Rips complex is of dimension 1 - 18 simplices - 7 vertices. - [0] -> 0.00 - [1] -> 0.00 - [2] -> 0.00 - [3] -> 0.00 - [4] -> 0.00 - [5] -> 0.00 - [6] -> 0.00 - [2, 3] -> 5.00 - [4, 5] -> 5.39 - [0, 2] -> 5.83 - [0, 1] -> 6.08 - [1, 3] -> 6.32 - [1, 2] -> 6.71 - [5, 6] -> 7.28 - [2, 4] -> 8.94 - [0, 3] -> 9.43 - [4, 6] -> 9.49 - [3, 6] -> 11.00 - -Distance matrix ---------------- - -Example from a distance matrix -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -This example builds the one skeleton graph from the given distance matrix, and max_edge_length value. -Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it. - -Finally, it is asked to display information about the simplicial complex. - -.. testcode:: - - import gudhi - rips_complex = gudhi.RipsComplex(distance_matrix=[[], - [6.0827625303], - [5.8309518948, 6.7082039325], - [9.4339811321, 6.3245553203, 5], - [13.0384048104, 15.6524758425, 8.94427191, 12.0415945788], - [18.0277563773, 19.6468827044, 13.152946438, 14.7648230602, 5.3851648071], - [17.88854382, 17.1172427686, 12.0830459736, 11, 9.4868329805, 7.2801098893]], - 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) - fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): - print(fmt % tuple(filtered_value)) - -When launching (Rips maximal distance between 2 points is 12.0, is expanded -until dimension 1 - one skeleton graph in other words), the output is: - -.. testoutput:: - - Rips complex is of dimension 1 - 18 simplices - 7 vertices. - [0] -> 0.00 - [1] -> 0.00 - [2] -> 0.00 - [3] -> 0.00 - [4] -> 0.00 - [5] -> 0.00 - [6] -> 0.00 - [2, 3] -> 5.00 - [4, 5] -> 5.39 - [0, 2] -> 5.83 - [0, 1] -> 6.08 - [1, 3] -> 6.32 - [1, 2] -> 6.71 - [5, 6] -> 7.28 - [2, 4] -> 8.94 - [0, 3] -> 9.43 - [4, 6] -> 9.49 - [3, 6] -> 11.00 - -Example from csv file -^^^^^^^^^^^^^^^^^^^^^ - -This example builds the :doc:`Rips_complex <rips_complex_ref>` from the given -distance matrix in a csv file, and max_edge_length value. -Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it. - -Finally, it is asked to display information about the Rips complex. - - -.. testcode:: - - import gudhi - distance_matrix = gudhi.read_lower_triangular_matrix_from_csv_file(csv_file=gudhi.__root_source_dir__ + \ - '/data/distance_matrix/full_square_distance_matrix.csv') - rips_complex = gudhi.RipsComplex(distance_matrix=distance_matrix, 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) - fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): - print(fmt % tuple(filtered_value)) - -the program output is: - -.. testoutput:: - - Rips complex is of dimension 1 - 18 simplices - 7 vertices. - [0] -> 0.00 - [1] -> 0.00 - [2] -> 0.00 - [3] -> 0.00 - [4] -> 0.00 - [5] -> 0.00 - [6] -> 0.00 - [2, 3] -> 5.00 - [4, 5] -> 5.39 - [0, 2] -> 5.83 - [0, 1] -> 6.08 - [1, 3] -> 6.32 - [1, 2] -> 6.71 - [5, 6] -> 7.28 - [2, 4] -> 8.94 - [0, 3] -> 9.43 - [4, 6] -> 9.49 - [3, 6] -> 11.00 - -Correlation matrix ------------------- - -Example from a correlation matrix -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Analogously to the case of distance matrix, Rips complexes can be also constructed based on correlation matrix. -Given a correlation matrix M, comportment-wise 1-M is a distance matrix. -This example builds the one skeleton graph from the given corelation matrix and threshold value. -Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it. - -Finally, it is asked to display information about the simplicial complex. - -.. testcode:: - - import gudhi - import numpy as np - - # User defined correlation matrix is: - # |1 0.06 0.23 0.01 0.89| - # |0.06 1 0.74 0.01 0.61| - # |0.23 0.74 1 0.72 0.03| - # |0.01 0.01 0.72 1 0.7 | - # |0.89 0.61 0.03 0.7 1 | - correlation_matrix=np.array([[1., 0.06, 0.23, 0.01, 0.89], - [0.06, 1., 0.74, 0.01, 0.61], - [0.23, 0.74, 1., 0.72, 0.03], - [0.01, 0.01, 0.72, 1., 0.7], - [0.89, 0.61, 0.03, 0.7, 1.]], float) - - distance_matrix = np.ones((correlation_matrix.shape),float) - correlation_matrix - rips_complex = gudhi.RipsComplex(distance_matrix=distance_matrix, max_edge_length=1.0) - - 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) - fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): - print(fmt % tuple(filtered_value)) - -When launching (Rips maximal distance between 2 points is 12.0, is expanded -until dimension 1 - one skeleton graph in other words), the output is: - -.. testoutput:: - - Rips complex is of dimension 1 - 15 simplices - 5 vertices. - [0] -> 0.00 - [1] -> 0.00 - [2] -> 0.00 - [3] -> 0.00 - [4] -> 0.00 - [0, 4] -> 0.11 - [1, 2] -> 0.26 - [2, 3] -> 0.28 - [3, 4] -> 0.30 - [1, 4] -> 0.39 - [0, 2] -> 0.77 - [0, 1] -> 0.94 - [2, 4] -> 0.97 - [0, 3] -> 0.99 - [1, 3] -> 0.99 - -.. note:: - As persistence diagrams points will be under the diagonal, - bottleneck distance and persistence graphical tool will not work properly, - this is a known issue. diff --git a/cython/doc/simplex_tree_ref.rst b/cython/doc/simplex_tree_ref.rst deleted file mode 100644 index 9eb8c199..00000000 --- a/cython/doc/simplex_tree_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -============================= -Simplex tree reference manual -============================= - -.. autoclass:: gudhi.SimplexTree - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.SimplexTree.__init__ diff --git a/cython/doc/simplex_tree_sum.inc b/cython/doc/simplex_tree_sum.inc deleted file mode 100644 index fb0e54c1..00000000 --- a/cython/doc/simplex_tree_sum.inc +++ /dev/null @@ -1,14 +0,0 @@ -================================================================= =================================== =================================== -:Author: Clément Maria :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -================================================================= =================================== =================================== - -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. 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` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ diff --git a/cython/doc/simplex_tree_user.rst b/cython/doc/simplex_tree_user.rst deleted file mode 100644 index aebeb29f..00000000 --- a/cython/doc/simplex_tree_user.rst +++ /dev/null @@ -1,72 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Simplex tree user manual -======================== -Definition ----------- - -.. include:: simplex_tree_sum.inc - -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") - result_str = 'num_vertices=' + repr(st.num_vertices()) - print(result_str) - result_str = 'num_simplices=' + repr(st.num_simplices()) - print(result_str) - print("skeleton(2) =") - for sk_value in st.get_skeleton(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(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/cython/doc/strong_witness_complex_ref.rst b/cython/doc/strong_witness_complex_ref.rst deleted file mode 100644 index d624d711..00000000 --- a/cython/doc/strong_witness_complex_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -======================================= -Strong witness complex reference manual -======================================= - -.. autoclass:: gudhi.StrongWitnessComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.StrongWitnessComplex.__init__ diff --git a/cython/doc/tangential_complex_ref.rst b/cython/doc/tangential_complex_ref.rst deleted file mode 100644 index cdfda082..00000000 --- a/cython/doc/tangential_complex_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -=================================== -Tangential complex reference manual -=================================== - -.. autoclass:: gudhi.TangentialComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.TangentialComplex.__init__ diff --git a/cython/doc/tangential_complex_sum.inc b/cython/doc/tangential_complex_sum.inc deleted file mode 100644 index 72b4d7ba..00000000 --- a/cython/doc/tangential_complex_sum.inc +++ /dev/null @@ -1,15 +0,0 @@ -================================================================= =================================== =================================== -:Author: Clément Jamin :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Requires: CGAL :math:`\geq` 4.8.0 Eigen3 -================================================================= =================================== =================================== - -+----------------------------------------------------------------+------------------------------------------------------------------------+ -| .. 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` | -+----------------------------------------------------------------+------------------------------------------------------------------------+ diff --git a/cython/doc/tangential_complex_user.rst b/cython/doc/tangential_complex_user.rst deleted file mode 100644 index 5ce69e86..00000000 --- a/cython/doc/tangential_complex_user.rst +++ /dev/null @@ -1,201 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Tangential complex user manual -============================== -.. include:: tangential_complex_sum.inc - -Definition ----------- - -A Tangential Delaunay complex is a simplicial complex designed to reconstruct a -:math:`k`-dimensional smooth manifold embedded in :math:`d`-dimensional -Euclidean space. The input is a point sample coming from an unknown manifold, -which means that the points lie close to a structure of "small" intrinsic -dimension. The running time depends only linearly on the extrinsic dimension -:math:`d` and exponentially on the intrinsic dimension :math:`k`. - -An extensive description of the Tangential complex can be found in -:cite:`tangentialcomplex2014`. - -What is a Tangential Complex? -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Let us start with the description of the Tangential complex of a simple -example, with :math:`k = 1` and :math:`d = 2`. The input data is 4 points -:math:`P` located on a curve embedded in 2D. - -.. figure:: ../../doc/Tangential_complex/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. -using PCA). - -.. figure:: ../../doc/Tangential_complex/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`. - -.. figure:: ../../doc/Tangential_complex/tc_example_03.png - :alt: The Voronoi diagram - :figclass: align-center - - The Voronoi diagram - -The Tangential Delaunay complex is the union of those stars. - -In practice, neither the ambient Voronoi diagram nor the ambient Delaunay -triangulation is computed. Instead, local :math:`k`-dimensional regular -triangulations are computed with a limited number of points as we only need the -star of each point. More details can be found in :cite:`tangentialcomplex2014`. - -Inconsistencies -^^^^^^^^^^^^^^^ -Inconsistencies between the stars can occur. An inconsistency occurs when a -simplex is not in the star of all its vertices. - -Let us take the same example. - -.. figure:: ../../doc/Tangential_complex/tc_example_07_before.png - :alt: Before - :figclass: align-center - - Before - -Let us slightly move the tangent subspace :math:`T_q` - -.. figure:: ../../doc/Tangential_complex/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 -not contain :math:`QP`. We have an inconsistency. - -.. figure:: ../../doc/Tangential_complex/tc_example_08.png - :alt: After - :figclass: align-center - - After - -One way to solve inconsistencies is to randomly perturb the positions of the -points involved in an inconsistency. In the current implementation, this -perturbation is done in the tangent subspace of each point. The maximum -perturbation radius is given as a parameter to the constructor. - -In most cases, we recommend to provide a point set where the minimum distance -between any two points is not too small. This can be achieved using the -functions provided by the Subsampling module. Then, a good value to start with -for the maximum perturbation radius would be around half the minimum distance -between any two points. The Example with perturbation below shows an example of -such a process. - -In most cases, this process is able to dramatically reduce the number of -inconsistencies, but is not guaranteed to succeed. - -Output -^^^^^^ -The result of the computation is exported as a Simplex_tree. It is the union of -the stars of all the input points. A vertex in the Simplex Tree is the index of -the point in the range provided by the user. The point corresponding to a -vertex can also be obtained through the Tangential_complex::get_point function. -Note that even if the positions of the points are perturbed, their original -positions are kept (e.g. Tangential_complex::get_point returns the original -position of the point). - -The result can be obtained after the computation of the Tangential complex -itself and/or after the perturbation process. - - -Simple example --------------- - -This example builds the Tangential complex of point set read in an OFF file. - -.. testcode:: - - import gudhi - tc = gudhi.TangentialComplex(intrisic_dim = 1, - off_file=gudhi.__root_source_dir__ + '/data/points/alphacomplexdoc.off') - result_str = 'Tangential contains ' + repr(tc.num_simplices()) + \ - ' simplices - ' + repr(tc.num_vertices()) + ' vertices.' - print(result_str) - - st = tc.create_simplex_tree() - result_str = 'Simplex tree is of dimension ' + repr(st.dimension()) + \ - ' - ' + repr(st.num_simplices()) + ' simplices - ' + \ - repr(st.num_vertices()) + ' vertices.' - print(result_str) - for filtered_value in st.get_filtration(): - print(filtered_value[0]) - -The output is: - -.. testoutput:: - - Tangential contains 12 simplices - 7 vertices. - Simplex tree is of dimension 1 - 15 simplices - 7 vertices. - [0] - [1] - [0, 1] - [2] - [0, 2] - [1, 2] - [3] - [1, 3] - [4] - [2, 4] - [5] - [4, 5] - [6] - [3, 6] - [5, 6] - - -Example with perturbation -------------------------- - -This example builds the Tangential complex of a point set, then tries to solve -inconsistencies by perturbing the positions of points involved in inconsistent -simplices. - -.. testcode:: - - import gudhi - tc = gudhi.TangentialComplex(intrisic_dim = 1, - points=[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]) - result_str = 'Tangential contains ' + repr(tc.num_vertices()) + ' vertices.' - print(result_str) - - if tc.num_inconsistent_simplices() > 0: - print('Tangential contains inconsistencies.') - - tc.fix_inconsistencies_using_perturbation(10, 60) - if tc.num_inconsistent_simplices() == 0: - print('Inconsistencies has been fixed.') - -The output is: - -.. testoutput:: - - Tangential contains 4 vertices. - Inconsistencies has been fixed. - - -Bibliography -============ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: docnames - :style: unsrt diff --git a/cython/doc/todos.rst b/cython/doc/todos.rst deleted file mode 100644 index ca274ced..00000000 --- a/cython/doc/todos.rst +++ /dev/null @@ -1,9 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -========== -To be done -========== - -.. todolist:: diff --git a/cython/doc/witness_complex_ref.rst b/cython/doc/witness_complex_ref.rst deleted file mode 100644 index 9987d3fd..00000000 --- a/cython/doc/witness_complex_ref.rst +++ /dev/null @@ -1,14 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -================================ -Witness complex reference manual -================================ - -.. autoclass:: gudhi.WitnessComplex - :members: - :undoc-members: - :show-inheritance: - - .. automethod:: gudhi.WitnessComplex.__init__ diff --git a/cython/doc/witness_complex_sum.inc b/cython/doc/witness_complex_sum.inc deleted file mode 100644 index a8a126a0..00000000 --- a/cython/doc/witness_complex_sum.inc +++ /dev/null @@ -1,19 +0,0 @@ -================================================================= =================================== =================================== -:Author: Siargey Kachanovich :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 -:Euclidean version requires: CGAL :math:`\geq` 4.6.0 Eigen3 -================================================================= =================================== =================================== - -+-------------------------------------------------------------------+----------------------------------------------------------------------+ -| .. 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` | -+-------------------------------------------------------------------+----------------------------------------------------------------------+ diff --git a/cython/doc/witness_complex_user.rst b/cython/doc/witness_complex_user.rst deleted file mode 100644 index 40e94134..00000000 --- a/cython/doc/witness_complex_user.rst +++ /dev/null @@ -1,135 +0,0 @@ -:orphan: - -.. To get rid of WARNING: document isn't included in any toctree - -Witness complex user manual -=========================== - -.. include:: witness_complex_sum.inc - -Definitions ------------ - -Witness complex is a simplicial complex defined on two sets of points in :math:`\mathbb{R}^D`: - -- :math:`W` set of **witnesses** and -- :math:`L` set of **landmarks**. - -Even though often the set of landmarks :math:`L` is a subset of the set of witnesses :math:`W`, it is not a requirement -for the current implementation. - -Landmarks are the vertices of the simplicial complex and witnesses help to decide on which simplices are inserted via a -predicate "is witnessed". - -De Silva and Carlsson in their paper :cite:`de2004topological` differentiate **weak witnessing** and -**strong witnessing**: - -- *weak*: :math:`\sigma \subset L` is witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L \setminus \sigma},\ d(w,l) \leq d(w,l')` -- *strong*: :math:`\sigma \subset L` is witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L},\ d(w,l) \leq d(w,l')` - -where :math:`d(.,.)` is a distance function. - -Both definitions can be relaxed by a real value :math:`\alpha`: - -- *weak*: :math:`\sigma \subset L` is :math:`\alpha`-witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L \setminus \sigma},\ d(w,l)^2 \leq d(w,l')^2 + \alpha^2` -- *strong*: :math:`\sigma \subset L` is :math:`\alpha`-witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L},\ d(w,l)^2 \leq d(w,l')^2 + \alpha^2` - -which leads to definitions of **weak relaxed witness complex** (or just relaxed witness complex for short) and -**strong relaxed witness complex** respectively. - -.. figure:: ../../doc/Witness_complex/swit.svg - :alt: Strongly witnessed simplex - :figclass: align-center - - Strongly witnessed simplex - - -In particular case of 0-relaxation, weak complex corresponds to **witness complex** introduced in -:cite:`de2004topological`, whereas 0-relaxed strong witness complex consists of just vertices and is not very -interesting. Hence for small relaxation weak version is preferable. -However, to capture the homotopy type (for example using Gudhi::persistent_cohomology::Persistent_cohomology) it is -often necessary to work with higher filtration values. In this case strong relaxed witness complex is faster to compute -and offers similar results. - -Implementation --------------- - -The two complexes described above are implemented in the corresponding classes - -- :doc:`witness_complex_ref` -- :doc:`strong_witness_complex_ref` -- :doc:`euclidean_witness_complex_ref` -- :doc:`euclidean_strong_witness_complex_ref` - -The construction of the Euclidean versions of complexes follow the same scheme: - -1. Construct a search tree on landmarks. -2. Construct lists of nearest landmarks for each witness. -3. Construct the witness complex for nearest landmark lists. - -In the non-Euclidean classes, the lists of nearest landmarks are supposed to be given as input. - -The constructors take on the steps 1 and 2, while the function 'create_complex' executes the step 3. - -Constructing weak relaxed witness complex from an off file ----------------------------------------------------------- - -Let's start with a simple example, which reads an off point file and computes a weak witness complex. - -.. code-block:: python - - import gudhi - import argparse - - parser = argparse.ArgumentParser(description='EuclideanWitnessComplex creation from ' - 'points read in a OFF file.', - epilog='Example: ' - 'example/witness_complex_diagram_persistence_from_off_file_example.py ' - '-f ../data/points/tore3D_300.off -a 1.0 -n 20 -d 2' - '- Constructs a alpha complex with the ' - 'points from the given OFF file.') - parser.add_argument("-f", "--file", type=str, required=True) - parser.add_argument("-a", "--max_alpha_square", type=float, required=True) - parser.add_argument("-n", "--number_of_landmarks", type=int, required=True) - parser.add_argument("-d", "--limit_dimension", type=int, required=True) - - args = parser.parse_args() - - with open(args.file, 'r') as f: - first_line = f.readline() - if (first_line == 'OFF\n') or (first_line == 'nOFF\n'): - print("#####################################################################") - print("EuclideanWitnessComplex creation from points read in a OFF file") - - witnesses = gudhi.read_off(off_file=args.file) - landmarks = gudhi.pick_n_random_points(points=witnesses, nb_points=args.number_of_landmarks) - - message = "EuclideanWitnessComplex with max_edge_length=" + repr(args.max_alpha_square) + \ - " - Number of landmarks=" + repr(args.number_of_landmarks) - print(message) - - witness_complex = gudhi.EuclideanWitnessComplex(witnesses=witnesses, landmarks=landmarks) - simplex_tree = witness_complex.create_simplex_tree(max_alpha_square=args.max_alpha_square, - limit_dimension=args.limit_dimension) - - message = "Number of simplices=" + repr(simplex_tree.num_simplices()) - print(message) - else: - print(args.file, "is not a valid OFF file") - - f.close() - - -Example2: Computing persistence using strong relaxed witness complex --------------------------------------------------------------------- - -Here is an example of constructing a strong witness complex filtration and computing persistence on it: - -* :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` - -Bibliography -============ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: docnames - :style: unsrt |
