class TestSingleGrassmannManifold(ManifoldTestCase):
def setUp(self):
self.m = m = 5
self.n = n = 2
self.k = k = 1
self.manifold = Grassmann(m, n, k=k)
self.projection = lambda x, u: u - x @ x.T @ u
super().setUp()
def test_dist(self):
x = self.manifold.random_point()
y = self.manifold.random_point()
np_testing.assert_almost_equal(
self.manifold.dist(x, y),
self.manifold.norm(x, self.manifold.log(x, y)),
)
def test_euclidean_to_riemannian_hessian(self):
# Test this function at some randomly generated point.
x = self.manifold.random_point()
u = self.manifold.random_tangent_vector(x)
egrad = np.random.normal(size=(self.m, self.n))
ehess = np.random.normal(size=(self.m, self.n))
np_testing.assert_allclose(
testing.euclidean_to_riemannian_hessian(self.projection)(x, egrad,
ehess, u),
self.manifold.euclidean_to_riemannian_hessian(x, egrad, ehess, u),
)
def test_retraction(self):
# Test that the result is on the manifold and that for small
# tangent vectors it has little effect.
x = self.manifold.random_point()
u = self.manifold.random_tangent_vector(x)
xretru = self.manifold.retraction(x, u)
np_testing.assert_allclose(multitransp(xretru) @ xretru,
np.eye(self.n),
atol=1e-10)
u = u * 1e-6
xretru = self.manifold.retraction(x, u)
np_testing.assert_allclose(xretru, x + u)
def test_first_order_function_approximation(self):
self.run_gradient_approximation_test()
def test_second_order_function_approximation(self):
self.run_hessian_approximation_test()
# def test_norm(self):
def test_random_point(self):
# Just make sure that things generated are on the manifold and that
# if you generate two they are not equal.
X = self.manifold.random_point()
np_testing.assert_allclose(multitransp(X) @ X,
np.eye(self.n),
atol=1e-10)
Y = self.manifold.random_point()
assert np.linalg.norm(X - Y) > 1e-6
# def test_random_tangent_vector(self):
# def test_transport(self):
def test_exp_log_inverse(self):
s = self.manifold
x = s.random_point()
y = s.random_point()
u = s.log(x, y)
z = s.exp(x, u)
np_testing.assert_almost_equal(0, self.manifold.dist(y, z), decimal=5)
def test_log_exp_inverse(self):
s = self.manifold
x = s.random_point()
u = s.random_tangent_vector(x)
y = s.exp(x, u)
v = s.log(x, y)
# Check that the manifold difference between the tangent vectors u and
# v is 0
np_testing.assert_almost_equal(0, self.manifold.norm(x, u - v))
