[MRG] Sliced wasserstein (#203)

* example for log treatment in bregman.py

* Improve doc

* Revert "example for log treatment in bregman.py"

This reverts commit 9f51c14e

* Add comments by Flamary

* Delete repetitive description

* Added raw string to avoid pbs with backslashes

* Implements sliced wasserstein

* Changed formatting of string for py3.5 support

* Docstest, expected 0.0 and not 0.

* Adressed comments by @rflamary

* No 3d plot here

* add sliced to the docs

* Incorporate comments by @rflamary

* add link to pdf

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

1 files changed, 85 insertions, 0 deletions

diff --git a/test/test_sliced.py b/test/test_sliced.py
new file mode 100644
index 0000000..a07d975
--- /dev/null
+++ b/test/test_sliced.py
@@ -0,0 +1,85 @@
+"""Tests for module sliced"""
+
+# Author: Adrien Corenflos <adrien.corenflos@aalto.fi>
+#
+# License: MIT License
+
+import numpy as np
+import pytest
+
+import ot
+from ot.sliced import get_random_projections
+
+
+def test_get_random_projections():
+    rng = np.random.RandomState(0)
+    projections = get_random_projections(1000, 50, rng)
+    np.testing.assert_almost_equal(np.sum(projections ** 2, 1), 1.)
+
+
+def test_sliced_same_dist():
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    u = ot.utils.unif(n)
+
+    res = ot.sliced_wasserstein_distance(x, x, u, u, 10, seed=rng)
+    np.testing.assert_almost_equal(res, 0.)
+
+
+def test_sliced_bad_shapes():
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    y = rng.randn(n, 4)
+    u = ot.utils.unif(n)
+
+    with pytest.raises(ValueError):
+        _ = ot.sliced_wasserstein_distance(x, y, u, u, 10, seed=rng)
+
+
+def test_sliced_log():
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 4)
+    y = rng.randn(n, 4)
+    u = ot.utils.unif(n)
+
+    res, log = ot.sliced_wasserstein_distance(x, y, u, u, 10, seed=rng, log=True)
+    assert len(log) == 2
+    projections = log["projections"]
+    projected_emds = log["projected_emds"]
+
+    assert len(projections) == len(projected_emds) == 10
+    for emd in projected_emds:
+        assert emd > 0
+
+
+def test_sliced_different_dists():
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    u = ot.utils.unif(n)
+    y = rng.randn(n, 2)
+
+    res = ot.sliced_wasserstein_distance(x, y, u, u, 10, seed=rng)
+    assert res > 0.
+
+
+def test_1d_sliced_equals_emd():
+    n = 100
+    m = 120
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 1)
+    a = rng.uniform(0, 1, n)
+    a /= a.sum()
+    y = rng.randn(m, 1)
+    u = ot.utils.unif(m)
+    res = ot.sliced_wasserstein_distance(x, y, a, u, 10, seed=42)
+    expected = ot.emd2_1d(x.squeeze(), y.squeeze(), a, u)
+    np.testing.assert_almost_equal(res ** 2, expected)