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Diffstat (limited to 'src/cython/doc/bottleneck_distance_user.rst')
| -rw-r--r-- | src/cython/doc/bottleneck_distance_user.rst | 37 |
1 files changed, 32 insertions, 5 deletions
diff --git a/src/cython/doc/bottleneck_distance_user.rst b/src/cython/doc/bottleneck_distance_user.rst index 605db022..9435c7f1 100644 --- a/src/cython/doc/bottleneck_distance_user.rst +++ b/src/cython/doc/bottleneck_distance_user.rst @@ -9,15 +9,42 @@ 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 example computes the bottleneck distance from 2 persistence diagrams: +This other example computes the bottleneck distance from 2 persistence diagrams: .. testcode:: @@ -26,15 +53,15 @@ This example computes the bottleneck distance from 2 persistence diagrams: 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) + message = "Bottleneck distance approximation = " + '%.2f' % gudhi.bottleneck_distance(diag1, diag2, 0.1) print(message) - message = "Bottleneck distance value=" + '%.2f' % gudhi.bottleneck_distance(diag1, diag2) + 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 + Bottleneck distance approximation = 0.81 + Bottleneck distance value = 0.75 |