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diff --git a/src/python/test/test_wasserstein_distance.py b/src/python/test/test_wasserstein_distance.py
new file mode 100755
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+++ b/src/python/test/test_wasserstein_distance.py
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+import gudhi
+import numpy as np
+
+""" This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+    Author(s):       Theo Lacombe
+
+    Copyright (C) 2019 Inria
+
+    Modification(s):
+      - YYYY/MM Author: Description of the modification
+"""
+
+__author__ = "Theo Lacombe"
+__copyright__ = "Copyright (C) 2019 Inria"
+__license__ = "MIT"
+
+
+def test_basic_wasserstein():
+    diag1 = np.array([[2.7, 3.7], [9.6, 14.0], [34.2, 34.974]])
+    diag2 = np.array([[2.8, 4.45], [9.5, 14.1]])
+    diag3 = np.array([[0, 2], [4, 6]])
+    diag4 = np.array([[0, 3], [4, 8]])
+    emptydiag = np.array([[]])
+
+    assert gudhi.wasserstein_distance(emptydiag, emptydiag, q=2., p=1.) == 0.
+    assert gudhi.wasserstein_distance(emptydiag, emptydiag, q=np.inf, p=1.) == 0.
+    assert gudhi.wasserstein_distance(emptydiag, emptydiag, q=np.inf, p=2.) == 0.
+    assert gudhi.wasserstein_distance(emptydiag, emptydiag, q=2., p=2.) == 0.
+
+    assert gudhi.wasserstein_distance(diag3, emptydiag, q=np.inf, p=1.) == 2.
+    assert gudhi.wasserstein_distance(diag3, emptydiag, q=1., p=1.) == 4.
+
+    assert gudhi.wasserstein_distance(diag4, emptydiag, q=1., p=2.) == 5.  # thank you Pythagorician triplets
+    assert gudhi.wasserstein_distance(diag4, emptydiag, q=np.inf, p=2.) == 2.5
+    assert gudhi.wasserstein_distance(diag4, emptydiag, q=2., p=2.) == 3.5355339059327378
+
+    assert gudhi.wasserstein_distance(diag1, diag2, q=2., p=1.) == 1.4453593023967701
+    assert gudhi.wasserstein_distance(diag1, diag2, q=2.35, p=1.74) == 0.9772734057168739
+
+    assert gudhi.wasserstein_distance(diag1, emptydiag, q=2.35, p=1.7863) == 3.141592214572228
+
+    assert gudhi.wasserstein_distance(diag3, diag4, q=1., p=1.) == 3.
+    assert gudhi.wasserstein_distance(diag3, diag4, q=np.inf, p=1.) == 3.  # no diag matching here
+    assert gudhi.wasserstein_distance(diag3, diag4, q=np.inf, p=2.) == np.sqrt(5)
+    assert gudhi.wasserstein_distance(diag3, diag4, q=1., p=2.) == np.sqrt(5)
+    assert gudhi.wasserstein_distance(diag3, diag4, q=4.5, p=2.) == np.sqrt(5)
+
+    
+