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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    ]]
+
+