class TestGrassmannianMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.n = 3
self.k = 2
self.space = Grassmannian(self.n, self.k)
self.metric = GrassmannianCanonicalMetric(self.n, self.k)
@geomstats.tests.np_only
def test_exp_np(self):
result = self.metric.exp(pi_2 * r_y, gs.array([p_xy, p_yz]))
expected = gs.array([p_yz, p_xy])
self.assertAllClose(result, expected)
result = self.metric.exp(pi_2 * gs.array([r_y, r_z]),
gs.array([p_xy, p_yz]))
expected = gs.array([p_yz, p_xz])
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_log(self):
result = self.metric.log(self.metric.exp(pi_4 * r_y, p_xy), p_xy)
expected = pi_4 * r_y
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_log_vectorized(self):
tangent_vecs = pi_4 * gs.array([r_y, r_z])
base_points = gs.array([p_xy, p_xz])
points = self.metric.exp(tangent_vecs, base_points)
result = self.metric.log(points, base_points)
expected = tangent_vecs
self.assertAllClose(result, expected)
class TestGrassmannian(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.n = 3
self.k = 2
self.space = Grassmannian(self.n, self.k)
self.metric = GrassmannianCanonicalMetric(self.n, self.k)
def test_exp_np(self):
vec = Matrices.bracket(pi_2 * r_y, gs.array([p_xy, p_yz]))
result = self.metric.exp(vec, gs.array([p_xy, p_yz]))
expected = gs.array([p_yz, p_xy])
self.assertAllClose(result, expected)
vec = Matrices.bracket(pi_2 * gs.array([r_y, r_z]),
gs.array([p_xy, p_yz]))
result = self.metric.exp(vec, gs.array([p_xy, p_yz]))
expected = gs.array([p_yz, p_xz])
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_log(self):
expected = Matrices.bracket(pi_4 * r_y, p_xy)
result = self.metric.log(self.metric.exp(expected, p_xy), p_xy)
self.assertTrue(self.space.is_tangent(result, p_xy))
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_log_vectorized(self):
tangent_vecs = pi_4 * gs.array([r_y, r_z])
base_points = gs.array([p_xy, p_xz])
points = self.metric.exp(tangent_vecs, base_points)
result = self.metric.log(points, base_points)
expected = tangent_vecs
self.assertAllClose(result, expected)
def test_belongs(self):
point = p_xy
result = self.space.belongs(point)
self.assertTrue(result)
point = gs.array([p_yz, p_xz])
result = self.space.belongs(point)
self.assertTrue(gs.all(result))
not_a_point = gs.random.rand(3, 2)
self.assertRaises(ValueError, self.space.belongs, not_a_point)
not_a_point = gs.random.rand(3, 3)
result = self.space.belongs(not_a_point)
self.assertTrue(~result)
point = gs.array([p_xy, not_a_point])
result = self.space.belongs(point)
expected = gs.array([True, False])
self.assertAllClose(result, expected)
def test_random_and_belongs(self):
point = self.space.random_uniform()
result = self.space.belongs(point)
self.assertTrue(result)
expected = (self.n, ) * 2
result_shape = point.shape
self.assertAllClose(result_shape, expected)
n_samples = 5
points = self.space.random_uniform(n_samples)
result = gs.all(self.space.belongs(points))
self.assertTrue(result)
expected = (n_samples, ) + (self.n, ) * 2
result_shape = points.shape
self.assertAllClose(result_shape, expected)
def test_is_to_tangent(self):
base_point = self.space.random_uniform()
vector = gs.random.rand(self.n, self.n)
tangent_vec = self.space.to_tangent(vector, base_point)
result = self.space.is_tangent(tangent_vec, base_point)
self.assertTrue(result)
reprojected = self.space.to_tangent(tangent_vec, base_point)
self.assertAllClose(tangent_vec, reprojected)