How to use the geoopt.Sphere function in geoopt

)

    yield UnaryCase(
        manifold_shapes[geoopt.ProductManifold],
        product_manifold.pack_point(*x),
        product_manifold.pack_point(*ex),
        product_manifold.pack_point(*v),
        product_manifold.pack_point(*ev),
        product_manifold,
    )
    # + 1 case without stiefel
    torch.manual_seed(42)
    ex = [torch.randn(10), torch.randn(3) / 10, torch.randn(())]
    ev = [torch.randn(10), torch.randn(3) / 10, torch.randn(())]
    manifolds = [
        geoopt.Sphere(),
        geoopt.PoincareBall(),
        # geoopt.Stiefel(),
        geoopt.Euclidean(),
    ]
    x = [manifolds[i].projx(ex[i]) for i in range(len(manifolds))]
    v = [manifolds[i].proju(x[i], ev[i]) for i in range(len(manifolds))]

    product_manifold = geoopt.ProductManifold(
        *((manifolds[i], ex[i].shape) for i in range(len(ex)))
    )

    yield UnaryCase(
        manifold_shapes[geoopt.ProductManifold],
        product_manifold.pack_point(*x),
        product_manifold.pack_point(*ex),
        product_manifold.pack_point(*v),

def sphere_subspace_case():
    torch.manual_seed(42)
    shape = manifold_shapes[geoopt.manifolds.Sphere]
    subspace = torch.rand(shape[-1], 2, dtype=torch.float64)

    Q, _ = geoopt.linalg.batch_linalg.qr(subspace)
    P = Q @ Q.t()

    ex = torch.randn(*shape, dtype=torch.float64)
    ev = torch.randn(*shape, dtype=torch.float64)
    x = (ex @ P.t()) / torch.norm(ex @ P.t())
    v = (ev - (x @ ev) * x) @ P.t()

    manifold = geoopt.Sphere(intersection=subspace)
    x = geoopt.ManifoldTensor(x, manifold=manifold)
    case = UnaryCase(shape, x, ex, v, ev, manifold)
    yield case
    manifold = geoopt.SphereExact(intersection=subspace)
    x = geoopt.ManifoldTensor(x, manifold=manifold)
    case = UnaryCase(shape, x, ex, v, ev, manifold)
    yield case

def test_pickle2():
    t = torch.ones(10)
    p = geoopt.ManifoldParameter(t, manifold=geoopt.Sphere())
    with tempfile.TemporaryDirectory() as path:
        torch.save(p, os.path.join(path, "tens.t7"))
        p1 = torch.load(os.path.join(path, "tens.t7"))
    assert isinstance(p1, geoopt.ManifoldParameter)
    assert p.stride() == p1.stride()
    assert p.storage_offset() == p1.storage_offset()
    assert p.requires_grad == p1.requires_grad
    np.testing.assert_allclose(p.detach(), p1.detach())
    assert isinstance(p.manifold, type(p1.manifold))

def test_random_Sphere():
    manifold = geoopt.Sphere()
    point = manifold.random_uniform(3, 10, 10)
    manifold.assert_check_point_on_manifold(point)
    assert point.manifold is manifold

def test_fails_Sphere():
    with pytest.raises(ValueError):
        manifold = geoopt.Sphere()
        manifold.random_uniform(())
    with pytest.raises(ValueError):
        manifold = geoopt.Sphere()
        manifold.random_uniform(1)

def test_component_inner_product():
    pman = ProductManifold((Sphere(), 10), (Sphere(), (3, 2)), (Euclidean(), ()))
    point = [
        Sphere().random_uniform(5, 10),
        Sphere().random_uniform(5, 3, 2),
        Euclidean().random_normal(5),
    ]
    tensor = pman.pack_point(*point)
    tangent = torch.randn_like(tensor)
    tangent = pman.proju(tensor, tangent)

    inner = pman.component_inner(tensor, tangent)
    assert inner.shape == (5, pman.n_elements)