def sphere_case():
torch.manual_seed(42)
shape = manifold_shapes[geoopt.manifolds.Sphere]
ex = torch.randn(*shape, dtype=torch.float64)
ev = torch.randn(*shape, dtype=torch.float64)
x = ex / torch.norm(ex)
v = ev - (x @ ev) * x
manifold = geoopt.Sphere()
x = geoopt.ManifoldTensor(x, manifold=manifold)
case = UnaryCase(shape, x, ex, v, ev, manifold)
yield case
manifold = geoopt.SphereExact()
x = geoopt.ManifoldTensor(x, manifold=manifold)
case = UnaryCase(shape, x, ex, v, ev, manifold)
yield case
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, "reduced")
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 sphere_compliment_case():
torch.manual_seed(42)
shape = manifold_shapes[geoopt.manifolds.Sphere]
complement = torch.rand(shape[-1], 1, dtype=torch.float64)
Q, _ = geoopt.linalg.batch_linalg.qr(complement, "reduced")
P = -Q @ Q.transpose(-1, -2)
P[..., torch.arange(P.shape[-2]), torch.arange(P.shape[-2])] += 1
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(complement=complement)
x = geoopt.ManifoldTensor(x, manifold=manifold)
case = UnaryCase(shape, x, ex, v, ev, manifold)
yield case
manifold = geoopt.SphereExact(complement=complement)
x = geoopt.ManifoldTensor(x, manifold=manifold)
case = UnaryCase(shape, x, ex, v, ev, manifold)
yield case