[MRG] Projection Robust Wasserstein (#267)

* ot.dr: PRW code; text.text_dr: PRW test code.

* ot.dr: PRW code; test.test_dr: PRW test code.

* fix errors: pep8(3.8)

* fix errors: pep8(3.8)

* modified readme; prw code review

* fix pep error

* edit comment

* modified math comment

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

1 files changed, 37 insertions, 0 deletions

diff --git a/test/test_dr.py b/test/test_dr.py
index c5df287..fa75a18 100644
--- a/test/test_dr.py
+++ b/test/test_dr.py
@@ -1,6 +1,7 @@
 """Tests for module dr on Dimensionality Reduction """
 
 # Author: Remi Flamary <remi.flamary@unice.fr>
+#         Minhui Huang <mhhuang@ucdavis.edu>
 #
 # License: MIT License
 
@@ -57,3 +58,39 @@ def test_wda():
     projwda(xs)
 
     np.testing.assert_allclose(np.sum(Pwda**2, 0), np.ones(p))
+
+
+@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
+def test_prw():
+    d = 100  # Dimension
+    n = 100  # Number samples
+    k = 3  # Subspace dimension
+    dim = 3
+
+    def fragmented_hypercube(n, d, dim):
+        assert dim <= d
+        assert dim >= 1
+        assert dim == int(dim)
+
+        a = (1. / n) * np.ones(n)
+        b = (1. / n) * np.ones(n)
+
+        # First measure : uniform on the hypercube
+        X = np.random.uniform(-1, 1, size=(n, d))
+
+        # Second measure : fragmentation
+        tmp_y = np.random.uniform(-1, 1, size=(n, d))
+        Y = tmp_y + 2 * np.sign(tmp_y) * np.array(dim * [1] + (d - dim) * [0])
+        return a, b, X, Y
+
+    a, b, X, Y = fragmented_hypercube(n, d, dim)
+
+    tau = 0.002
+    reg = 0.2
+
+    pi, U = ot.dr.projection_robust_wasserstein(X, Y, a, b, tau, reg=reg, k=k, maxiter=1000, verbose=1)
+
+    U0 = np.random.randn(d, k)
+    U0, _ = np.linalg.qr(U0)
+
+    pi, U = ot.dr.projection_robust_wasserstein(X, Y, a, b, tau, U0=U0, reg=reg, k=k, maxiter=1000, verbose=1)