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| author | Marc Glisse <marc.glisse@inria.fr> | 2019-07-10 15:51:10 +0200 |
|---|---|---|
| committer | Marc Glisse <marc.glisse@inria.fr> | 2019-08-09 14:17:28 +0200 |
| commit | f057131902f352f8ccc30a0bacdfc69c5d21384b (patch) | |
| tree | 2f2342b9a0305b1de886e77bffd0e5dd4b88f440 | |
| parent | c3e26b923680c1ed82369382dbe46cadb2385c53 (diff) | |
More max_alpha_square hiding/warning. Warn about alternate definition of Rips.
| -rw-r--r-- | src/cython/doc/alpha_complex_user.rst | 7 | ||||
| -rw-r--r-- | src/cython/doc/rips_complex_user.rst | 4 |
2 files changed, 7 insertions, 4 deletions
diff --git a/src/cython/doc/alpha_complex_user.rst b/src/cython/doc/alpha_complex_user.rst index d1e9c7cd..f9662a6d 100644 --- a/src/cython/doc/alpha_complex_user.rst +++ b/src/cython/doc/alpha_complex_user.rst @@ -28,7 +28,7 @@ This example builds the Delaunay triangulation from the given points, and initia 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) + simplex_tree = alpha_complex.create_simplex_tree() result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \ repr(simplex_tree.num_simplices()) + ' simplices - ' + \ repr(simplex_tree.num_vertices()) + ' vertices.' @@ -146,8 +146,9 @@ 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. +in the `C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_). Note that this does not provide any kind +of speed-up, since we always first build the full filtered complex, so it is recommended not to use `max_alpha_square`. +In the following example, a threshold of 59 is used. Example from OFF file diff --git a/src/cython/doc/rips_complex_user.rst b/src/cython/doc/rips_complex_user.rst index 1d340dbe..3f6b960d 100644 --- a/src/cython/doc/rips_complex_user.rst +++ b/src/cython/doc/rips_complex_user.rst @@ -19,7 +19,9 @@ The `Rips complex <https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex>` 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 filtration can be restricted to values α smaller than some threshold, to reduce its size. Beware that some +people define the Rips complex using a bound of 2α instead of α, particularly when comparing it to an ambient +Čech complex. They end up with the same combinatorial object, but filtration values which are half of ours. The input discrete metric space can be provided as a point cloud plus a distance function, or as a distance matrix. |