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-:orphan:
-
-.. To get rid of WARNING: document isn't included in any toctree
-
-Bottleneck distance user manual
-===============================
-Definition
-----------
-
-.. include:: bottleneck_distance_sum.inc
-
-This implementation is based on ideas from "Geometry Helps in Bottleneck Matching and Related Problems"
-:cite:`DBLP:journals/algorithmica/EfratIK01`. Another relevant publication, although it was not used is
-"Geometry Helps to Compare Persistence Diagrams" :cite:`Kerber:2017:GHC:3047249.3064175`.
-
-Function
---------
-.. autofunction:: gudhi.bottleneck_distance
-
-Distance computation
---------------------
-
-The following example explains how the distance is computed:
-
-.. testcode::
-
- import gudhi
-
- message = "Bottleneck distance = " + '%.1f' % gudhi.bottleneck_distance([[0., 0.]], [[0., 13.]])
- print(message)
-
-.. testoutput::
-
- Bottleneck distance = 6.5
-
-.. figure::
- ../../doc/Bottleneck_distance/bottleneck_distance_example.png
- :figclass: align-center
-
- The point (0, 13) is at distance 6.5 from the diagonal and more
- specifically from the point (6.5, 6.5)
-
-
-Basic example
--------------
-
-This other 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