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diff --git a/test/test_unbalanced.py b/test/test_unbalanced.py
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+"""Tests for module Unbalanced OT with entropy regularization"""
+
+# Author: Hicham Janati <hicham.janati@inria.fr>
+#
+# License: MIT License
+
+import numpy as np
+import ot
+import pytest
+
+
+@pytest.mark.parametrize("method", ["sinkhorn"])
+def test_unbalanced_convergence(method):
+    # test generalized sinkhorn for unbalanced OT
+    n = 100
+    rng = np.random.RandomState(42)
+
+    x = rng.randn(n, 2)
+    a = ot.utils.unif(n)
+
+    # make dists unbalanced
+    b = ot.utils.unif(n) * 1.5
+
+    M = ot.dist(x, x)
+    epsilon = 1.
+    alpha = 1.
+    K = np.exp(- M / epsilon)
+
+    G, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon, alpha=alpha,
+                                               stopThr=1e-10, method=method,
+                                               log=True)
+    loss = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
+                                              method=method)
+    # check fixed point equations
+    fi = alpha / (alpha + epsilon)
+    v_final = (b / K.T.dot(log["u"])) ** fi
+    u_final = (a / K.dot(log["v"])) ** fi
+
+    np.testing.assert_allclose(
+        u_final, log["u"], atol=1e-05)
+    np.testing.assert_allclose(
+        v_final, log["v"], atol=1e-05)
+
+    # check if sinkhorn_unbalanced2 returns the correct loss
+    np.testing.assert_allclose((G * M).sum(), loss, atol=1e-5)
+
+
+@pytest.mark.parametrize("method", ["sinkhorn"])
+def test_unbalanced_multiple_inputs(method):
+    # test generalized sinkhorn for unbalanced OT
+    n = 100
+    rng = np.random.RandomState(42)
+
+    x = rng.randn(n, 2)
+    a = ot.utils.unif(n)
+
+    # make dists unbalanced
+    b = rng.rand(n, 2)
+
+    M = ot.dist(x, x)
+    epsilon = 1.
+    alpha = 1.
+    K = np.exp(- M / epsilon)
+
+    loss, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon,
+                                                  alpha=alpha,
+                                                  stopThr=1e-10, method=method,
+                                                  log=True)
+    # check fixed point equations
+    fi = alpha / (alpha + epsilon)
+    v_final = (b / K.T.dot(log["u"])) ** fi
+
+    u_final = (a[:, None] / K.dot(log["v"])) ** fi
+
+    np.testing.assert_allclose(
+        u_final, log["u"], atol=1e-05)
+    np.testing.assert_allclose(
+        v_final, log["v"], atol=1e-05)
+
+    assert len(loss) == b.shape[1]
+
+
+def test_unbalanced_barycenter():
+    # test generalized sinkhorn for unbalanced OT barycenter
+    n = 100
+    rng = np.random.RandomState(42)
+
+    x = rng.randn(n, 2)
+    A = rng.rand(n, 2)
+
+    # make dists unbalanced
+    A = A * np.array([1, 2])[None, :]
+    M = ot.dist(x, x)
+    epsilon = 1.
+    alpha = 1.
+    K = np.exp(- M / epsilon)
+
+    q, log = ot.unbalanced.barycenter_unbalanced(A, M, reg=epsilon, alpha=alpha,
+                                                 stopThr=1e-10,
+                                                 log=True)
+    # check fixed point equations
+    fi = alpha / (alpha + epsilon)
+    v_final = (q[:, None] / K.T.dot(log["u"])) ** fi
+    u_final = (A / K.dot(log["v"])) ** fi
+
+    np.testing.assert_allclose(
+        u_final, log["u"], atol=1e-05)
+    np.testing.assert_allclose(
+        v_final, log["v"], atol=1e-05)
+
+
+def test_implemented_methods():
+    IMPLEMENTED_METHODS = ['sinkhorn']
+    TO_BE_IMPLEMENTED_METHODS = ['sinkhorn_stabilized',
+                                 'sinkhorn_epsilon_scaling']
+    NOT_VALID_TOKENS = ['foo']
+    # test generalized sinkhorn for unbalanced OT barycenter
+    n = 3
+    rng = np.random.RandomState(42)
+
+    x = rng.randn(n, 2)
+    a = ot.utils.unif(n)
+
+    # make dists unbalanced
+    b = ot.utils.unif(n) * 1.5
+
+    M = ot.dist(x, x)
+    epsilon = 1.
+    alpha = 1.
+    for method in IMPLEMENTED_METHODS:
+        ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha,
+                                          method=method)
+        ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
+                                           method=method)
+    with pytest.warns(UserWarning, match='not implemented'):
+        for method in set(TO_BE_IMPLEMENTED_METHODS):
+            ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha,
+                                              method=method)
+            ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
+                                               method=method)
+    with pytest.raises(ValueError):
+        for method in set(NOT_VALID_TOKENS):
+            ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha,
+                                              method=method)
+            ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, alpha,
+                                               method=method)