[WIP] Wasserstein distance on the circle and Spherical Sliced-Wasserstein (#434)

* 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

1 files changed, 46 insertions, 0 deletions

diff --git a/test/test_backend.py b/test/test_backend.py
index 3628f61..fd9a761 100644
--- a/test/test_backend.py
+++ b/test/test_backend.py
@@ -282,6 +282,20 @@ def test_empty_backend():
         nx.array_equal(M, M)
     with pytest.raises(NotImplementedError):
         nx.is_floating_point(M)
+    with pytest.raises(NotImplementedError):
+        nx.tile(M, (10, 1))
+    with pytest.raises(NotImplementedError):
+        nx.floor(M)
+    with pytest.raises(NotImplementedError):
+        nx.prod(M)
+    with pytest.raises(NotImplementedError):
+        nx.sort2(M)
+    with pytest.raises(NotImplementedError):
+        nx.qr(M)
+    with pytest.raises(NotImplementedError):
+        nx.atan2(v, v)
+    with pytest.raises(NotImplementedError):
+        nx.transpose(M)
 
 
 def test_func_backends(nx):
@@ -603,6 +617,38 @@ def test_func_backends(nx):
         lst_b.append(nx.to_numpy(A))
         lst_name.append("isfinite")
 
+        A = nx.tile(vb, (10, 1))
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("tile")
+
+        A = nx.floor(Mb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("floor")
+
+        A = nx.prod(Mb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("prod")
+
+        A, B = nx.sort2(Mb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("sort2 sort")
+        lst_b.append(nx.to_numpy(B))
+        lst_name.append("sort2 argsort")
+
+        A, B = nx.qr(Mb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("QR Q")
+        lst_b.append(nx.to_numpy(B))
+        lst_name.append("QR R")
+
+        A = nx.atan2(vb, vb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("atan2")
+
+        A = nx.transpose(Mb)
+        lst_b.append(nx.to_numpy(A))
+        lst_name.append("transpose")
+
         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(