added gaussian test

Author: Kilian Fatras

README.md

@@ -24,6 +24,7 @@ It provides the following solvers:
 * Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
 * Gromov-Wasserstein distances and barycenters ([13] and regularized [12])
 * Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
+* Non regularized free support Wasserstein barycenters [20].
 
 Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
 
@@ -163,7 +164,7 @@ The contributors to this library are:
 * [Stanislas Chambon](https://slasnista.github.io/)
 * [Antoine Rolet](https://arolet.github.io/)
 * Erwan Vautier (Gromov-Wasserstein)
-* [Kilian Fatras](https://kilianfatras.github.io/) (Stochastic optimization)
+* [Kilian Fatras](https://kilianfatras.github.io/)
 
 This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages):
 
@@ -222,6 +223,8 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 
 [17] Blondel, M., Seguy, V., & Rolet, A. (2018). [Smooth and Sparse Optimal Transport](https://arxiv.org/abs/1710.06276). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
 
-[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) [Stochastic Optimization for Large-scale Optimal Transport](arXiv preprint arxiv:1605.08527). Advances in Neural Information Processing Systems (2016).
+[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) [Stochastic Optimization for Large-scale Optimal Transport](https://arxiv.org/abs/1605.08527). Advances in Neural Information Processing Systems (2016).
 
 [19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A.& Blondel, M. [Large-scale Optimal Transport and Mapping Estimation](https://arxiv.org/pdf/1711.02283.pdf). International Conference on Learning Representation (2018)
+
+[20] Cuturi, M. and Doucet, A. (2014) [Fast Computation of Wasserstein Barycenters](http://proceedings.mlr.press/v32/cuturi14.html). International Conference in Machine Learning

test/test_stochastic.py

@@ -137,8 +137,8 @@ def test_stochastic_dual_sgd():
     # test sgd
     n = 10
     reg = 1
-    numItermax = 300000
-    batch_size = 8
+    numItermax = 15000
+    batch_size = 10
     rng = np.random.RandomState(0)
 
     x = rng.randn(n, 2)
@@ -151,9 +151,9 @@ def test_stochastic_dual_sgd():
 
     # check constratints
     np.testing.assert_allclose(
-        u, G.sum(1), atol=1e-02)  # cf convergence sgd
+        u, G.sum(1), atol=1e-04)  # cf convergence sgd
     np.testing.assert_allclose(
-        u, G.sum(0), atol=1e-02)  # cf convergence sgd
+        u, G.sum(0), atol=1e-04)  # cf convergence sgd
 
 
 #############################################################################
@@ -168,10 +168,11 @@ def test_dual_sgd_sinkhorn():
     # test all dual algorithms
     n = 10
     reg = 1
-    nb_iter = 300000
-    batch_size = 8
+    nb_iter = 150000
+    batch_size = 10
     rng = np.random.RandomState(0)
 
+# Test uniform
     x = rng.randn(n, 2)
     u = ot.utils.unif(n)
     zero = np.zeros(n)
@@ -184,8 +185,36 @@ def test_dual_sgd_sinkhorn():
 
     # check constratints
     np.testing.assert_allclose(
-        zero, (G_sgd - G_sinkhorn).sum(1), atol=1e-02)  # cf convergence sgd
+        zero, (G_sgd - G_sinkhorn).sum(1), atol=1e-04)  # cf convergence sgd
+    np.testing.assert_allclose(
+        zero, (G_sgd - G_sinkhorn).sum(0), atol=1e-04)  # cf convergence sgd
+    np.testing.assert_allclose(
+        G_sgd, G_sinkhorn, atol=1e-04)  # cf convergence sgd
+
+# Test gaussian
+    n = 30
+    n_source = n
+    n_target = n
+    reg = 1
+    numItermax = 150000
+    batch_size = 30
+
+    a = ot.datasets.get_1D_gauss(n_source, m=15, s=5)  # m= mean, s= std
+    b = ot.datasets.get_1D_gauss(n_target, m=15, s=5)
+    X_source = np.arange(n_source,dtype=np.float64)
+    Y_target = np.arange(n_target,dtype=np.float64)
+    M = ot.dist(X_source.reshape((n_source, 1)), Y_target.reshape((n_target, 1)))
+    M /= M.max()
+
+    G_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg, batch_size,
+                                              numItermax=nb_iter)
+
+    G_sinkhorn = ot.sinkhorn(a, b, M, reg)
+
+    # check constratints
+    np.testing.assert_allclose(
+        zero, (G_sgd - G_sinkhorn).sum(1), atol=1e-04)  # cf convergence sgd
     np.testing.assert_allclose(
-        zero, (G_sgd - G_sinkhorn).sum(0), atol=1e-02)  # cf convergence sgd
+        zero, (G_sgd - G_sinkhorn).sum(0), atol=1e-04)  # cf convergence sgd
     np.testing.assert_allclose(
-        G_sgd, G_sinkhorn, atol=1e-02)  # cf convergence sgd
+        G_sgd, G_sinkhorn, atol=1e-04)  # cf convergence sgd