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diff --git a/test/test_smooth.py b/test/test_smooth.py
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+++ b/test/test_smooth.py
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+"""Tests for ot.smooth model """
+
+# Author: Remi Flamary <remi.flamary@unice.fr>
+#
+# License: MIT License
+
+import numpy as np
+import ot
+import pytest
+
+
+def test_smooth_ot_dual():
+
+    # get data
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    u = ot.utils.unif(n)
+
+    M = ot.dist(x, x)
+
+    with pytest.raises(NotImplementedError):
+        Gl2, log = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='none')
+
+    Gl2, log = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='l2', log=True, stopThr=1e-10)
+
+    # check constratints
+    np.testing.assert_allclose(
+        u, Gl2.sum(1), atol=1e-05)  # cf convergence sinkhorn
+    np.testing.assert_allclose(
+        u, Gl2.sum(0), atol=1e-05)  # cf convergence sinkhorn
+
+    # kl regyularisation
+    G = ot.smooth.smooth_ot_dual(u, u, M, 1, reg_type='kl', stopThr=1e-10)
+
+    # check constratints
+    np.testing.assert_allclose(
+        u, G.sum(1), atol=1e-05)  # cf convergence sinkhorn
+    np.testing.assert_allclose(
+        u, G.sum(0), atol=1e-05)  # cf convergence sinkhorn
+
+    G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10)
+    np.testing.assert_allclose(G, G2, atol=1e-05)
+
+
+def test_smooth_ot_semi_dual():
+
+    # get data
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    u = ot.utils.unif(n)
+
+    M = ot.dist(x, x)
+
+    with pytest.raises(NotImplementedError):
+        Gl2, log = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='none')
+
+    Gl2, log = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='l2', log=True, stopThr=1e-10)
+
+    # check constratints
+    np.testing.assert_allclose(
+        u, Gl2.sum(1), atol=1e-05)  # cf convergence sinkhorn
+    np.testing.assert_allclose(
+        u, Gl2.sum(0), atol=1e-05)  # cf convergence sinkhorn
+
+    # kl regyularisation
+    G = ot.smooth.smooth_ot_semi_dual(u, u, M, 1, reg_type='kl', stopThr=1e-10)
+
+    # check constratints
+    np.testing.assert_allclose(
+        u, G.sum(1), atol=1e-05)  # cf convergence sinkhorn
+    np.testing.assert_allclose(
+        u, G.sum(0), atol=1e-05)  # cf convergence sinkhorn
+
+    G2 = ot.sinkhorn(u, u, M, 1, stopThr=1e-10)
+    np.testing.assert_allclose(G, G2, atol=1e-05)