:orphan:

.. To get rid of WARNING: document isn't included in any toctree

Bottleneck distance user manual
===============================
Definition
----------

.. include:: bottleneck_distance_sum.inc

Function
--------
.. autofunction:: gudhi.bottleneck_distance

Distance computation
--------------------

Bottleneck distance does not use Euclidean distance, like explained in the following example:

.. 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 6.5 distance from the diagonal and more
    specifically from the point (6.5, 6.5)


Basic example
-------------

This another 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