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doc/examples/rips.rst

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

Mon, 11 May 2009 12:45:49 -0700 | |

branch | dev |

changeset 134 | c270826fd4a8 |

child 181 | 1ee6edc17cb6 |

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

Added documentation; for now mostly for the Python bindings

.. _rips-example: Rips complex example ==================== .. todo:: Explain `Vietoris-Rips complex`_. There is an elementary example in :sfile:`examples/rips/rips.py` that computes a Rips complex of a few points with integer coordinates on a line. It illustrates the use of Rips complexes and in particular of defining your own notion of a :ref:`Distance <Distances>` based on which the Rips complex is constructed. A more useful example is given in :sfile:`examples/rips/rips-pairwise.py` (and its C++ counterpart in :sfile:`examples/rips/rips-pairwise.cpp`). The example takes on the command line the filename of a file with points in Euclidean space (one point per line), and a cut off parameters for the skeleton and the :math:`\epsilon` parameter for the Rips complex construction. It then constructs the Rips complex up to these cutoff parameters, computes its persistence, and outputs the persistence diagram (one point per line). .. literalinclude:: ../../examples/rips/rips-pairwise.py The bit that sets up the Rips complex is:: distances = PairwiseDistances(points) rips = Rips(distances) simplices = [] rips.generate(skeleton, max, simplices.append) The computation of persistence and output of the persistence diagram are the same as in the :ref:`alpha-shape-example`. The example also incorporates the :ref:`speed-up-suggestions` given in the :ref:`tutorial`. C++ sketch ---------- .. highlight:: cpp .. warning:: This section is not finished. The example given in :sfile:`examples/rips/rips.cpp` illustrates how one can use the library to compute persistence of a `Vietoris-Rips complex`_ for a given set of distances. At the top of the file a `struct Distances` is defined. The particular distances in the example are trivial (they are points with integer coordinates on a real line), however, the `struct` illustrates the basic requirements of any such class to be passed to the `Rips<Distances>` class. .. _`Vietoris-Rips complex`: http://en.wikipedia.org/wiki/Vietoris-Rips_complex The Rips complex itself is generated in the line:: rips.generate(2, 50, make_push_back_functor(complex)); which tells it to generate a 2-skeleton of the Rips complex up to distance value of 50, and insert the simplices into the previously defined vector `complex`. Subsequent sort is unnecessary since Bron-Kerbosch algorithm that generates the complex will actually generate the simplices in lexicographic order; it's there for illustration purposes only (the simplices must be sorted lexicographically). The following "paragraph" sets up the filtration with respect to simplex sizes (specified by `Generator::Comparison(distances)`), and computes its persistence:: // Generate filtration with respect to distance and compute its persistence Fltr f(complex.begin(), complex.end(), Generator::Comparison(distances)); Persistence p(f); p.pair_simplices();