[MRG] Sliced and 1D Wasserstein distances : backend versions (#256)

* add numpy and torch backends

* stat sets on functions

* proper import

* install recent torch on windows

* install recent torch on windows

* now testing all functions in backedn

* add jax backedn

* clenaup windowds

* proper convert for jax backedn

* pep8

* try again windows tests

* test jax conversion

* try proper widows tests

* emd fuction ses backedn

* better test partial OT

* proper tests to_numpy and teplate Backend

* pep8

* pep8 x2

* feaking sinkhorn works with torch

* sinkhorn2 compatible

* working ot.emd2

* important detach

* it should work

* jax autodiff emd

* pep8

* no tast same for jax

* new independat tests per backedn

* freaking pep8

* add tests for gradients

* deprecate ot.gpu

* worging dist function

* working dist

* dist done in backedn

* not in

* remove indexing

* change accuacy for jax

* first pull backend

* projection simplex

* projection simplex

* projection simplex

* projection simplex no ci

* projection simplex no ci

* projection simplex no ci

* pep8

* add backedn discusion to quickstart guide

* projection simplex no ci

* projection simplex no ci

* projection simplex no ci

* pep8 + better doc

* proper links

* corect doctest

* big debug documentation

* doctest again

* doctest again bis

* doctest again ter (last one or i kill myself)

* backend test + doc proj simplex

* correction test_utils

* correction test_utils

* correction cumsum

* correction flip

* correction flip v2

* more debug

* more debug

* more debug + pep8

* pep8

* argh

* proj_simplex

* backedn works for sort

* proj simplex

* jax sucks

* update doc

* Update test/test_utils.py

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update docs/source/quickstart.rst

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update docs/source/quickstart.rst

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update docs/source/quickstart.rst

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update docs/source/readme.rst

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update test/test_utils.py

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update ot/utils.py

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update docs/source/readme.rst

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* Update ot/lp/__init__.py

Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

* begin comment alex

* comment alex part 2

* optimize test gromov

* proj_simplex on vectors

* add awesome gradient decsnt example on the weights

* pep98 of course

* proof read example by alex

* pep8 again

* encoding oos in translation

* correct legend

* new backend functions for sliced

* small indent pb

* Optimized backendversion of sliced W

* error in sliced W

* after master merge

* error sliced

* error sliced

* pep8

* test_sliced pep8

* doctest + precision for sliced

* doctest

* type win test_backend gather

* type win test_backend gather

* Update sliced.py

change argument of padding pad_width

* Update backend.py

update redefinition

* Update backend.py

pep8

* Update backend.py

pep 8 again....

* pep8

* build docs

* emd2_1D example

* refectoring emd_1d and variants

* remove unused previous wasserstein_1d

* pep8

* upate example

* move stuff

* tesys should work + implemù random backend

* test random generayor functions

* correction

* better random generation

* update sliced

* update sliced

* proper tests sliced

* max sliced

* chae file nam

* add stuff

* example sliced flow and barycenter

* correct typo + update readme

* exemple sliced flow done

* pep8

* solver1d works

* pep8

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>
Co-authored-by: Alexandre Gramfort <alexandre.gramfort@m4x.org>

1 files changed, 87 insertions, 3 deletions

diff --git a/test/test_sliced.py b/test/test_sliced.py
index a07d975..0bd74ec 100644
--- a/test/test_sliced.py
+++ b/test/test_sliced.py
@@ -1,6 +1,7 @@
 """Tests for module sliced"""
 
 # Author: Adrien Corenflos <adrien.corenflos@aalto.fi>
+#         Nicolas Courty <ncourty@irisa.fr>
 #
 # License: MIT License
 
@@ -14,7 +15,7 @@ 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.)
+    np.testing.assert_almost_equal(np.sum(projections ** 2, 0), 1.)
 
 
 def test_sliced_same_dist():
@@ -48,12 +49,12 @@ def test_sliced_log():
     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)
+    res, log = ot.sliced_wasserstein_distance(x, y, u, u, 10, p=1, seed=rng, log=True)
     assert len(log) == 2
     projections = log["projections"]
     projected_emds = log["projected_emds"]
 
-    assert len(projections) == len(projected_emds) == 10
+    assert projections.shape[1] == len(projected_emds) == 10
     for emd in projected_emds:
         assert emd > 0
 
@@ -83,3 +84,86 @@ def test_1d_sliced_equals_emd():
     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)
+
+
+def test_max_sliced_same_dist():
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    u = ot.utils.unif(n)
+
+    res = ot.max_sliced_wasserstein_distance(x, x, u, u, 10, seed=rng)
+    np.testing.assert_almost_equal(res, 0.)
+
+
+def test_max_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, log = ot.max_sliced_wasserstein_distance(x, y, u, u, 10, seed=rng, log=True)
+    assert res > 0.
+
+
+def test_sliced_backend(nx):
+
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    y = rng.randn(2 * n, 2)
+
+    P = rng.randn(2, 20)
+    P = P / np.sqrt((P**2).sum(0, keepdims=True))
+
+    n_projections = 20
+
+    xb = nx.from_numpy(x)
+    yb = nx.from_numpy(y)
+    Pb = nx.from_numpy(P)
+
+    val0 = ot.sliced_wasserstein_distance(x, y, projections=P)
+
+    val = ot.sliced_wasserstein_distance(xb, yb, n_projections=n_projections, seed=0)
+    val2 = ot.sliced_wasserstein_distance(xb, yb, n_projections=n_projections, seed=0)
+
+    assert val > 0
+    assert val == val2
+
+    valb = nx.to_numpy(ot.sliced_wasserstein_distance(xb, yb, projections=Pb))
+
+    assert np.allclose(val0, valb)
+
+
+def test_max_sliced_backend(nx):
+
+    n = 100
+    rng = np.random.RandomState(0)
+
+    x = rng.randn(n, 2)
+    y = rng.randn(2 * n, 2)
+
+    P = rng.randn(2, 20)
+    P = P / np.sqrt((P**2).sum(0, keepdims=True))
+
+    n_projections = 20
+
+    xb = nx.from_numpy(x)
+    yb = nx.from_numpy(y)
+    Pb = nx.from_numpy(P)
+
+    val0 = ot.max_sliced_wasserstein_distance(x, y, projections=P)
+
+    val = ot.max_sliced_wasserstein_distance(xb, yb, n_projections=n_projections, seed=0)
+    val2 = ot.max_sliced_wasserstein_distance(xb, yb, n_projections=n_projections, seed=0)
+
+    assert val > 0
+    assert val == val2
+
+    valb = nx.to_numpy(ot.max_sliced_wasserstein_distance(xb, yb, projections=Pb))
+
+    assert np.allclose(val0, valb)