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-:orphan:
-
-.. To get rid of WARNING: document isn't included in any toctree
-
-Barycenter user manual
-================================
-Definition
-----------
-
-.. include:: barycenter_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.
-As the algorithm is not convex, its output depends on the initialization and
-is only a local minimum of the objective function.
-Initialization can be either given as an integer (in which case the i-th
-diagram of the list is used as initial estimate) or as a diagram.
-If None, it will randomly select one of the diagram of the list
-as initial estimate.
-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([])
- pdiagset = [dg1, dg2, dg3, dg4]
- bary = gudhi.barycenter.lagrangian_barycenter(pdiagset=pdiagset,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 ]]
-
-