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:orphan:
.. To get rid of WARNING: document isn't included in any toctree
Wasserstein distance user manual
================================
Definition
----------
.. include:: wasserstein_distance_sum.inc
This implementation is based on ideas from "Frechet means for distribution of persistence diagrams", Turner et al. 2014.
Function
--------
.. autofunction:: gudhi.barycenter.lagrangian_barycenter
Basic example
-------------
This example computes the Frechet mean (aka Wasserstein barycenter) between four persistence diagrams.
It is initialized on the 4th diagram, which is the empty diagram. It is encoded by np.array([]).
Note that persistence diagrams must be submitted as (n x 2) numpy arrays and must not contain inf values.
.. testcode::
import gudhi.barycenter
import numpy as np
dg1 = np.array([[0.2, 0.5]])
dg2 = np.array([[0.2, 0.7]])
dg3 = np.array([[0.3, 0.6], [0.7, 0.8], [0.2, 0.3]])
dg4 = np.array([])
bary = gudhi.barycenter.lagrangian_barycenter(pdiagset=[dg1, dg2, dg3, dg4],init=3))
message = "Wasserstein barycenter estimated:"
print(message)
print(bary)
The output is:
.. testoutput::
Wasserstein barycenter estimated:
[[0.27916667 0.55416667]
[0.7375 0.7625 ]
[0.2375 0.2625 ]]
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