[MRG] Fix Bug binary_search_circle on GPU and Gradients (#457)

* W circle + SSW

* Tests + Example SSW_1

* Example Wasserstein Circle + Tests

* Wasserstein on the circle wrt Unif

* Example SSW unif

* pep8

* np.linalg.qr for numpy < 1.22 by batch + add python3.11 to tests

* np qr

* rm test python 3.11

* update names, tests, backend transpose

* Comment error batchs

* semidiscrete_wasserstein2_unif_circle example

* torch permute method instead of torch.permute for previous versions

* update comments and doc

* doc wasserstein circle model as [0,1[

* Added ot.utils.get_coordinate_circle to get coordinates on the circle in turn

* Bug cuda w_circle + gradient ssw

* Bug cuda w_circle + gradient ssw

* backend detach

* Add PR in Releases.md

---------

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

2 files changed, 30 insertions, 1 deletions

diff --git a/test/test_backend.py b/test/test_backend.py
index fd9a761..5351e52 100644
--- a/test/test_backend.py
+++ b/test/test_backend.py
@@ -296,6 +296,8 @@ def test_empty_backend():
         nx.atan2(v, v)
     with pytest.raises(NotImplementedError):
         nx.transpose(M)
+    with pytest.raises(NotImplementedError):
+        nx.detach(M)
 
 
 def test_func_backends(nx):
@@ -649,6 +651,16 @@ def test_func_backends(nx):
         lst_b.append(nx.to_numpy(A))
         lst_name.append("transpose")
 
+        A = nx.detach(Mb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("detach")
+
+        A, B = nx.detach(Mb, Mb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("detach A")
+        lst_b.append(nx.to_numpy(B))
+        lst_name.append("detach B")
+
         assert not nx.array_equal(Mb, vb), "array_equal (shape)"
         assert nx.array_equal(Mb, Mb), "array_equal (elements) - expected true"
         assert not nx.array_equal(
diff --git a/test/test_sliced.py b/test/test_sliced.py
index f54c799..7b7437a 100644
--- a/test/test_sliced.py
+++ b/test/test_sliced.py
@@ -10,7 +10,7 @@ import pytest
 
 import ot
 from ot.sliced import get_random_projections
-from ot.backend import tf
+from ot.backend import tf, torch
 
 
 def test_get_random_projections():
@@ -408,6 +408,23 @@ def test_sliced_sphere_backend_type_devices(nx):
         nx.assert_same_dtype_device(xb, valb)
 
 
+def test_sliced_sphere_gradient():
+    if torch:
+        import torch.nn.functional as F
+
+        X0 = torch.randn((500, 3))
+        X0 = F.normalize(X0, p=2, dim=-1)
+        X0.requires_grad_(True)
+
+        X1 = torch.randn((500, 3))
+        X1 = F.normalize(X1, p=2, dim=-1)
+
+        sw = ot.sliced_wasserstein_sphere(X1, X0, n_projections=500, p=2)
+        grad_x0 = torch.autograd.grad(sw, X0)[0]
+
+        assert not torch.any(torch.isnan(grad_x0))
+
+
 def test_sliced_sphere_unif_values_on_the_sphere():
     n = 100
     rng = np.random.RandomState(0)