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Diffstat (limited to 'src')
-rw-r--r-- | src/cython/doc/rips_complex_user.rst | 12 |
1 files changed, 9 insertions, 3 deletions
diff --git a/src/cython/doc/rips_complex_user.rst b/src/cython/doc/rips_complex_user.rst index cddf4f16..933643e2 100644 --- a/src/cython/doc/rips_complex_user.rst +++ b/src/cython/doc/rips_complex_user.rst @@ -15,7 +15,7 @@ Definition | :doc:`rips_complex_user` | :doc:`rips_complex_ref` | +-------------------------------------------+----------------------------------------------------------------------+ -The `Rips complex <https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex>`_ is a simplicial complex that generalizes proximity (ε-ball) graphs to higher dimensions. The vertices correspond to the input points, and a simplex is present if and only if its diameter is smaller than some parameter α. Considering all parameters α defines a filtered simplicial complex, where the filtration value of a simplex is its diameter. The filtration can be restricted to values α smaller than some threshold, to reduce its size. +The `Rips complex <https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex>`_ is a simplicial complex that generalizes proximity (:math:`\varepsilon`-ball) graphs to higher dimensions. The vertices correspond to the input points, and a simplex is present if and only if its diameter is smaller than some parameter α. Considering all parameters α defines a filtered simplicial complex, where the filtration value of a simplex is its diameter. The filtration can be restricted to values α smaller than some threshold, to reduce its size. The input discrete metric space can be provided as a point cloud plus a distance function, or as a distance matrix. @@ -50,7 +50,7 @@ error is usually smaller. A more intuitive presentation of the idea is available in :cite:`cavanna15geometric`, and in a video :cite:`cavanna15visualizing`. Passing an extra argument `sparse=0.3` at the construction of a `RipsComplex` object asks it to build a sparse Rips with -parameter `ε=0.3`, while the default `sparse=None` builds the +parameter :math:`\varepsilon=0.3`, while the default `sparse=None` builds the regular Rips complex. @@ -105,7 +105,13 @@ until dimension 1 - one skeleton graph in other words), the output is: [4, 6] -> 9.49 [3, 6] -> 11.00 -Notice that if we use `rips_complex = gudhi.RipsComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]], max_edge_length=12.0, sparse=2)`, asking for very sparse version (theory only gives some guarantee on the meaning of the output if `sparse<1`), 2 to 5 edges disappear, depending on the random vertex used to start the sparsification. +Notice that if we use + +.. code-block:: python + + rips_complex = gudhi.RipsComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]], max_edge_length=12.0, sparse=2) + +asking for a very sparse version (theory only gives some guarantee on the meaning of the output if `sparse<1`), 2 to 5 edges disappear, depending on the random vertex used to start the sparsification. Example from OFF file ^^^^^^^^^^^^^^^^^^^^^ |