Merge pull request #95 from tlacombe/wdist-theo

wasserstein distance added on fork

1 files changed, 40 insertions, 0 deletions

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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 "Large Scale Computation of Means and Cluster for Persistence Diagrams via Optimal Transport".
+
+Function
+--------
+.. autofunction:: gudhi.wasserstein_distance
+
+
+Basic example
+-------------
+
+This example computes the 1-Wasserstein distance from 2 persistence diagrams with euclidean ground metric.
+Note that persistence diagrams must be submitted as (n x 2) numpy arrays and must not contain inf values.
+
+.. testcode::
+
+    import gudhi
+    import numpy as np
+
+    diag1 = np.array([[2.7, 3.7],[9.6, 14.],[34.2, 34.974]])
+    diag2 = np.array([[2.8, 4.45],[9.5, 14.1]])
+
+    message = "Wasserstein distance value = " + '%.2f' % gudhi.wasserstein_distance(diag1, diag2, q=2., p=1.)
+    print(message)
+
+The output is:
+
+.. testoutput::
+
+    Wasserstein distance value = 1.45