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doc/examples/index.rst

author | Dmitriy Morozov <dmitriy@mrzv.org> |

Thu, 15 Jul 2010 10:19:18 -0700 | |

branch | dev |

changeset 213 | 3568e0bfe2cd |

parent 212 | 291f6edf27b9 |

permissions | -rw-r--r-- |

Removed the warning about compiler versions (seems unnecessary after Andrew's fixes)

.. _examples: Examples ======== The most basic example and therefore a good place to start getting acquainted with the library is the :ref:`triangle-example`. It adds simplices of a triangle one by one, and then (in case of a :ref:`triangle-zigzag-example`), removes them one by one. .. toctree:: triangle triangle-zigzag The simplest example that instead of specifying the complex explicitly, constructs it from the input point set is the :ref:`alpha-shape-example`. The example reads points from a file, determines their dimension dynamically (based on the number of coordinates in the first line of the file), and then constructs an alpha shape and outputs its persistence diagram. .. toctree:: alphashape Another example that follows a similar strategy is the computation of the Vietoris-Rips complex. Since only pairwise distances are required it works with points in arbitrary dimension. (Of course, in dimensions 2 and 3 the complexes are much larger than those for the :ref:`alpha-shape-example`). .. toctree:: :maxdepth: 1 rips One may use persistent cohomology algorithm to extract persistent cocycles, turn them into harmonic cocycles, and use them to parametrize the input point set; for details see [dSVJ09]_. The explanation of how to use Dionysus to achieve this is available. .. toctree:: :maxdepth: 1 cohomology A simple example of computing persistence of a lower-star filtration is in :sfile:`examples/pl-functions/lsfiltration.py`. A C++-only, but useful example is computation of a vineyard of piecewise straight-line homotopy of piecewise-linear functions. .. toctree:: :maxdepth: 1 pl-vineyard