class TestEuclideanSpaceMethods(geomstats.tests.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.space = EuclideanSpace(self.dimension)
self.metric = self.space.metric
self.n_samples = 3
self.one_point_a = gs.array([0., 1.])
self.one_point_b = gs.array([2., 10.])
self.n_points_a = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
self.n_points_b = gs.array([[2., 10.], [8., -1.], [-3., 6.]])
def test_random_uniform_and_belongs(self):
point = self.space.random_uniform()
result = self.space.belongs(point)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_squared_norm_vectorization(self):
n_samples = self.n_samples
n_points = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
result = self.metric.squared_norm(n_points)
expected = gs.array([[5.], [20.], [26.]])
self.assertAllClose(gs.shape(result), (n_samples, 1))
self.assertAllClose(result, expected)
def test_norm_vectorization(self):
n_samples = self.n_samples
n_points = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
result = self.metric.norm(n_points)
expected = gs.array([[2.2360679775], [4.472135955], [5.09901951359]])
self.assertAllClose(gs.shape(result), (n_samples, 1))
self.assertAllClose(result, expected)
def test_exp_vectorization(self):
n_samples = self.n_samples
dim = self.dimension
one_tangent_vec = gs.array([0., 1.])
one_base_point = gs.array([2., 10.])
n_tangent_vecs = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
n_base_points = gs.array([[2., 10.], [8., -1.], [-3., 6.]])
result = self.metric.exp(one_tangent_vec, one_base_point)
expected = one_tangent_vec + one_base_point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
result = self.metric.exp(n_tangent_vecs, one_base_point)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.exp(one_tangent_vec, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.exp(n_tangent_vecs, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
def test_log_vectorization(self):
n_samples = self.n_samples
dim = self.dimension
one_point = gs.array([0., 1.])
one_base_point = gs.array([2., 10.])
n_points = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
n_base_points = gs.array([[2., 10.], [8., -1.], [-3., 6.]])
result = self.metric.log(one_point, one_base_point)
expected = one_point - one_base_point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
result = self.metric.log(n_points, one_base_point)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.log(one_point, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
result = self.metric.log(n_points, n_base_points)
self.assertAllClose(gs.shape(result), (n_samples, dim))
def test_squared_dist_vectorization(self):
n_samples = self.n_samples
one_point_a = gs.array([0., 1.])
one_point_b = gs.array([2., 10.])
n_points_a = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
n_points_b = gs.array([[2., 10.], [8., -1.], [-3., 6.]])
result = self.metric.squared_dist(one_point_a, one_point_b)
vec = one_point_a - one_point_b
expected = gs.dot(vec, gs.transpose(vec))
expected = helper.to_scalar(expected)
self.assertAllClose(result, expected)
result = self.metric.squared_dist(n_points_a, one_point_b)
self.assertAllClose(gs.shape(result), (n_samples, 1))
result = self.metric.squared_dist(one_point_a, n_points_b)
self.assertAllClose(gs.shape(result), (n_samples, 1))
result = self.metric.squared_dist(n_points_a, n_points_b)
expected = gs.array([[81.], [109.], [29.]])
self.assertAllClose(gs.shape(result), (n_samples, 1))
self.assertAllClose(result, expected)
def test_dist_vectorization(self):
n_samples = self.n_samples
one_point_a = gs.array([0., 1.])
one_point_b = gs.array([2., 10.])
n_points_a = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
n_points_b = gs.array([[2., 10.], [8., -1.], [-3., 6.]])
result = self.metric.dist(one_point_a, one_point_b)
vec = one_point_a - one_point_b
expected = gs.sqrt(gs.dot(vec, gs.transpose(vec)))
expected = helper.to_scalar(expected)
self.assertAllClose(result, expected)
result = self.metric.dist(n_points_a, one_point_b)
self.assertAllClose(gs.shape(result), (n_samples, 1))
result = self.metric.dist(one_point_a, n_points_b)
self.assertAllClose(gs.shape(result), (n_samples, 1))
result = self.metric.dist(n_points_a, n_points_b)
expected = gs.array([[9.], [gs.sqrt(109.)], [gs.sqrt(29.)]])
self.assertAllClose(gs.shape(result), (n_samples, 1))
self.assertAllClose(result, expected)
def test_belongs(self):
point = gs.array([0., 1.])
result = self.space.belongs(point)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_random_uniform(self):
result = self.space.random_uniform()
self.assertAllClose(gs.shape(result), (1, self.dimension))
def test_inner_product_matrix(self):
result = self.metric.inner_product_matrix()
expected = gs.eye(self.dimension)
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
def test_inner_product(self):
point_a = gs.array([0., 1.])
point_b = gs.array([2., 10.])
result = self.metric.inner_product(point_a, point_b)
expected = gs.array([[10.]])
self.assertAllClose(result, expected)
def test_inner_product_vectorization(self):
n_samples = 3
one_point_a = gs.array([0., 1.])
one_point_b = gs.array([2., 10.])
n_points_a = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
n_points_b = gs.array([[2., 10.], [8., -1.], [-3., 6.]])
result = self.metric.inner_product(one_point_a, one_point_b)
expected = gs.array([[10.]])
self.assertAllClose(gs.shape(result), (1, 1))
self.assertAllClose(result, expected)
result = self.metric.inner_product(n_points_a, one_point_b)
expected = gs.array([[14.], [-44.], [0.]])
self.assertAllClose(gs.shape(result), (n_samples, 1))
self.assertAllClose(result, expected)
result = self.metric.inner_product(one_point_a, n_points_b)
expected = gs.array([[10.], [-1.], [6.]])
self.assertAllClose(gs.shape(result), (n_samples, 1))
self.assertAllClose(result, expected)
result = self.metric.inner_product(n_points_a, n_points_b)
expected = gs.array([[14.], [-12.], [21.]])
self.assertAllClose(gs.shape(result), (n_samples, 1))
self.assertAllClose(result, expected)
def test_squared_norm(self):
point = gs.array([-2., 4.])
result = self.metric.squared_norm(point)
expected = gs.array([[20.]])
self.assertAllClose(result, expected)
def test_norm(self):
point = gs.array([-2., 4.])
result = self.metric.norm(point)
expected = gs.array([[4.472135955]])
self.assertAllClose(result, expected)
def test_exp(self):
base_point = gs.array([0., 1.])
vector = gs.array([2., 10.])
result = self.metric.exp(tangent_vec=vector, base_point=base_point)
expected = base_point + vector
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_log(self):
base_point = gs.array([0., 1.])
point = gs.array([2., 10.])
result = self.metric.log(point=point, base_point=base_point)
expected = point - base_point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_squared_dist(self):
point_a = gs.array([-1., 4.])
point_b = gs.array([1., 1.])
result = self.metric.squared_dist(point_a, point_b)
vec = point_b - point_a
expected = gs.dot(vec, vec)
expected = helper.to_scalar(expected)
self.assertAllClose(result, expected)
def test_dist(self):
point_a = gs.array([0., 1.])
point_b = gs.array([2., 10.])
result = self.metric.dist(point_a, point_b)
expected = gs.linalg.norm(point_b - point_a)
expected = helper.to_scalar(expected)
self.assertAllClose(result, expected)
def test_geodesic_and_belongs(self):
n_geodesic_points = 100
initial_point = gs.array([[2., -1.]])
initial_tangent_vec = gs.array([2., 0.])
geodesic = self.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec)
t = gs.linspace(start=0., stop=1., num=n_geodesic_points)
points = geodesic(t)
result = self.space.belongs(points)
expected = gs.array(n_geodesic_points * [[True]])
self.assertAllClose(expected, result)
def test_mean(self):
point = gs.array([[1., 4.]])
result = self.metric.mean(points=[point, point, point])
expected = point
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
points = gs.array([[1., 2.], [2., 3.], [3., 4.], [4., 5.]])
weights = gs.array([1., 2., 1., 2.])
result = self.metric.mean(points, weights)
expected = gs.array([16. / 6., 22. / 6.])
expected = helper.to_vector(expected)
self.assertAllClose(result, expected)
def test_variance(self):
points = gs.array([[1., 2.], [2., 3.], [3., 4.], [4., 5.]])
weights = gs.array([1., 2., 1., 2.])
base_point = gs.zeros(2)
result = self.metric.variance(points, weights, base_point)
# we expect the average of the points' sq norms.
expected = (1 * 5. + 2 * 13. + 1 * 25. + 2 * 41.) / 6.
expected = helper.to_scalar(expected)
self.assertAllClose(result, expected)
class TestEuclideanSpaceMethods(unittest.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.space = EuclideanSpace(self.dimension)
self.metric = self.space.metric
self.n_samples = 10
def test_belongs(self):
point = self.space.random_uniform()
belongs = self.space.belongs(point)
gs.testing.assert_allclose(belongs.shape, (1, 1))
def test_random_uniform(self):
point = self.space.random_uniform()
gs.testing.assert_allclose(point.shape, (1, self.dimension))
def test_random_uniform_and_belongs(self):
point = self.space.random_uniform()
self.assertTrue(self.space.belongs(point))
def test_inner_product_matrix(self):
result = self.metric.inner_product_matrix()
expected = gs.eye(self.dimension)
expected = helper.to_matrix(expected)
gs.testing.assert_allclose(result, expected)
def test_inner_product(self):
point_a = gs.array([0, 1])
point_b = gs.array([2, 10])
result = self.metric.inner_product(point_a, point_b)
expected = gs.dot(point_a, point_b)
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
def test_inner_product_vectorization(self):
n_samples = self.n_samples
one_point_a = self.space.random_uniform(n_samples=1)
one_point_b = self.space.random_uniform(n_samples=1)
n_points_a = self.space.random_uniform(n_samples=n_samples)
n_points_b = self.space.random_uniform(n_samples=n_samples)
result = self.metric.inner_product(one_point_a, one_point_b)
expected = gs.dot(one_point_a, one_point_b.transpose())
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
result = self.metric.inner_product(n_points_a, one_point_b)
expected = gs.dot(n_points_a, one_point_b.transpose())
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
gs.testing.assert_allclose(result, expected)
result = self.metric.inner_product(one_point_a, n_points_b)
expected = gs.dot(one_point_a, n_points_b.transpose()).transpose()
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
gs.testing.assert_allclose(result, expected)
result = self.metric.inner_product(n_points_a, n_points_b)
expected = gs.zeros(n_samples)
for i in range(n_samples):
expected[i] = gs.dot(n_points_a[i], n_points_b[i])
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
gs.testing.assert_allclose(result, expected)
def test_squared_norm(self):
point = gs.array([-2, 4])
result = self.metric.squared_norm(point)
expected = gs.linalg.norm(point) ** 2
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
def test_squared_norm_vectorization(self):
n_samples = self.n_samples
n_points = self.space.random_uniform(n_samples=n_samples)
result = self.metric.squared_norm(n_points)
expected = gs.linalg.norm(n_points, axis=-1) ** 2
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
gs.testing.assert_allclose(result, expected)
def test_norm(self):
point = gs.array([-2, 4])
result = self.metric.norm(point)
expected = gs.linalg.norm(point)
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
def test_norm_vectorization(self):
n_samples = self.n_samples
n_points = self.space.random_uniform(n_samples=n_samples)
result = self.metric.norm(n_points)
expected = gs.linalg.norm(n_points, axis=1)
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
gs.testing.assert_allclose(result, expected)
def test_exp(self):
base_point = gs.array([0, 1])
vector = gs.array([2, 10])
result = self.metric.exp(tangent_vec=vector,
base_point=base_point)
expected = base_point + vector
expected = helper.to_vector(expected)
gs.testing.assert_allclose(result, expected)
def test_exp_vectorization(self):
n_samples = self.n_samples
dim = self.dimension
one_tangent_vec = self.space.random_uniform(n_samples=1)
one_base_point = self.space.random_uniform(n_samples=1)
n_tangent_vecs = self.space.random_uniform(n_samples=n_samples)
n_base_points = self.space.random_uniform(n_samples=n_samples)
result = self.metric.exp(one_tangent_vec, one_base_point)
expected = one_tangent_vec + one_base_point
expected = helper.to_vector(expected)
gs.testing.assert_allclose(result, expected)
result = self.metric.exp(n_tangent_vecs, one_base_point)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
result = self.metric.exp(one_tangent_vec, n_base_points)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
result = self.metric.exp(n_tangent_vecs, n_base_points)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
def test_log(self):
base_point = gs.array([0, 1])
point = gs.array([2, 10])
result = self.metric.log(point=point, base_point=base_point)
expected = point - base_point
expected = helper.to_vector(expected)
gs.testing.assert_allclose(result, expected)
def test_log_vectorization(self):
n_samples = self.n_samples
dim = self.dimension
one_point = self.space.random_uniform(n_samples=1)
one_base_point = self.space.random_uniform(n_samples=1)
n_points = self.space.random_uniform(n_samples=n_samples)
n_base_points = self.space.random_uniform(n_samples=n_samples)
result = self.metric.log(one_point, one_base_point)
expected = one_point - one_base_point
expected = helper.to_vector(expected)
gs.testing.assert_allclose(result, expected)
result = self.metric.log(n_points, one_base_point)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
result = self.metric.log(one_point, n_base_points)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
result = self.metric.log(n_points, n_base_points)
gs.testing.assert_allclose(result.shape, (n_samples, dim))
def test_squared_dist(self):
point_a = gs.array([-1, 4])
point_b = gs.array([1, 1])
result = self.metric.squared_dist(point_a, point_b)
vec = point_b - point_a
expected = gs.dot(vec, vec)
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
def test_squared_dist_vectorization(self):
n_samples = self.n_samples
one_point_a = self.space.random_uniform(n_samples=1)
one_point_b = self.space.random_uniform(n_samples=1)
n_points_a = self.space.random_uniform(n_samples=n_samples)
n_points_b = self.space.random_uniform(n_samples=n_samples)
result = self.metric.squared_dist(one_point_a, one_point_b)
vec = one_point_a - one_point_b
expected = gs.dot(vec, vec.transpose())
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
result = self.metric.squared_dist(n_points_a, one_point_b)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
result = self.metric.squared_dist(one_point_a, n_points_b)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
result = self.metric.squared_dist(n_points_a, n_points_b)
expected = gs.zeros(n_samples)
for i in range(n_samples):
vec = n_points_a[i] - n_points_b[i]
expected[i] = gs.dot(vec, vec.transpose())
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
gs.testing.assert_allclose(result, expected)
def test_dist(self):
point_a = gs.array([0, 1])
point_b = gs.array([2, 10])
result = self.metric.dist(point_a, point_b)
expected = gs.linalg.norm(point_b - point_a)
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
def test_dist_vectorization(self):
n_samples = self.n_samples
one_point_a = self.space.random_uniform(n_samples=1)
one_point_b = self.space.random_uniform(n_samples=1)
n_points_a = self.space.random_uniform(n_samples=n_samples)
n_points_b = self.space.random_uniform(n_samples=n_samples)
result = self.metric.dist(one_point_a, one_point_b)
vec = one_point_a - one_point_b
expected = gs.sqrt(gs.dot(vec, vec.transpose()))
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
result = self.metric.dist(n_points_a, one_point_b)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
result = self.metric.dist(one_point_a, n_points_b)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
result = self.metric.dist(n_points_a, n_points_b)
expected = gs.zeros(n_samples)
for i in range(n_samples):
vec = n_points_a[i] - n_points_b[i]
expected[i] = gs.sqrt(gs.dot(vec, vec.transpose()))
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result.shape, (n_samples, 1))
gs.testing.assert_allclose(result, expected)
def test_geodesic_and_belongs(self):
initial_point = self.space.random_uniform()
initial_tangent_vec = gs.array([2., 0.])
geodesic = self.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec)
t = gs.linspace(start=0, stop=1, num=100)
points = geodesic(t)
self.assertTrue(gs.all(self.space.belongs(points)))
def test_mean(self):
point = gs.array([1, 4])
result = self.metric.mean(points=[point, point, point])
expected = point
expected = helper.to_vector(expected)
gs.testing.assert_allclose(result, expected)
points = gs.array([[1, 2],
[2, 3],
[3, 4],
[4, 5]])
weights = gs.array([1, 2, 1, 2])
result = self.metric.mean(points, weights)
expected = gs.array([16., 22.]) / 6.
expected = helper.to_vector(expected)
gs.testing.assert_allclose(result, expected)
def test_variance(self):
points = gs.array([[1, 2],
[2, 3],
[3, 4],
[4, 5]])
weights = gs.array([1, 2, 1, 2])
base_point = gs.zeros(2)
result = self.metric.variance(points, weights, base_point)
# we expect the average of the points' sq norms.
expected = (1 * 5. + 2 * 13. + 1 * 25. + 2 * 41.) / 6.
expected = helper.to_scalar(expected)
gs.testing.assert_allclose(result, expected)
class TestEuclideanSpaceMethodsTensorFlow(tf.test.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.space = EuclideanSpace(self.dimension)
self.metric = self.space.metric
self.n_samples = 3
@classmethod
def setUpClass(cls):
os.environ['GEOMSTATS_BACKEND'] = 'tensorflow'
importlib.reload(gs)
@classmethod
def tearDownClass(cls):
os.environ['GEOMSTATS_BACKEND'] = 'numpy'
importlib.reload(gs)
def test_belongs(self):
point = self.space.random_uniform()
belongs = self.space.belongs(point)
expected = tf.convert_to_tensor([[True]])
with self.test_session():
self.assertAllClose(gs.eval(belongs), gs.eval(expected))
def test_random_uniform(self):
point = self.space.random_uniform()
point_numpy = np.random.uniform(size=(1, self.dimension))
with self.test_session():
self.assertShapeEqual(point_numpy, point)
def test_inner_product_matrix(self):
result = self.metric.inner_product_matrix()
expected = gs.eye(self.dimension)
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_inner_product(self):
point_a = tf.convert_to_tensor([0., 1.])
point_b = tf.convert_to_tensor([2., 10.])
result = self.metric.inner_product(point_a, point_b)
expected = gs.dot(point_a, point_b)
expected = helper.to_scalar(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_inner_product_vectorization(self):
n_samples = 3
one_point_a = tf.convert_to_tensor([0., 1.])
one_point_b = tf.convert_to_tensor([2., 10.])
n_points_a = tf.convert_to_tensor([[2., 1.], [-2., -4.], [-5., 1.]])
n_points_b = tf.convert_to_tensor([[2., 10.], [8., -1.], [-3., 6.]])
result = self.metric.inner_product(one_point_a, one_point_b)
expected = gs.dot(one_point_a, gs.transpose(one_point_b))
expected = helper.to_scalar(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
result = self.metric.inner_product(n_points_a, one_point_b)
point_numpy = np.random.uniform(size=(n_samples, 1))
# TODO(nina): Fix this test with assertShapeEqual
with self.test_session():
self.assertAllClose(point_numpy.shape, gs.eval(gs.shape(result)))
result = self.metric.inner_product(one_point_a, n_points_b)
point_numpy = np.random.uniform(size=(n_samples, 1))
# TODO(nina): Fix this test with assertShapeEqual
with self.test_session():
self.assertAllClose(point_numpy.shape, gs.eval(gs.shape(result)))
result = self.metric.inner_product(n_points_a, n_points_b)
point_numpy = np.random.uniform(size=(n_samples, 1))
# TODO(nina): Fix this test with assertShapeEqual
with self.test_session():
self.assertAllClose(point_numpy.shape, gs.eval(gs.shape(result)))
def test_squared_norm(self):
point = tf.convert_to_tensor([-2., 4.])
result = self.metric.squared_norm(point)
expected = gs.linalg.norm(point)**2
expected = helper.to_scalar(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_norm(self):
point = tf.convert_to_tensor([-2., 4.])
result = self.metric.norm(point)
expected = gs.linalg.norm(point)
expected = helper.to_scalar(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_exp(self):
base_point = tf.convert_to_tensor([0., 1.])
vector = tf.convert_to_tensor([2., 10.])
result = self.metric.exp(tangent_vec=vector, base_point=base_point)
expected = base_point + vector
expected = helper.to_vector(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_log(self):
base_point = tf.convert_to_tensor([0., 1.])
point = tf.convert_to_tensor([2., 10.])
result = self.metric.log(point=point, base_point=base_point)
expected = point - base_point
expected = helper.to_vector(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_squared_dist(self):
point_a = tf.convert_to_tensor([-1., 4.])
point_b = tf.convert_to_tensor([1., 1.])
result = self.metric.squared_dist(point_a, point_b)
vec = point_b - point_a
expected = gs.dot(vec, vec)
expected = helper.to_scalar(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_dist(self):
point_a = tf.convert_to_tensor([0., 1.])
point_b = tf.convert_to_tensor([2., 10.])
result = self.metric.dist(point_a, point_b)
expected = gs.linalg.norm(point_b - point_a)
expected = helper.to_scalar(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_geodesic_and_belongs(self):
n_geodesic_points = 100
initial_point = self.space.random_uniform()
initial_tangent_vec = tf.convert_to_tensor([2., 0.])
geodesic = self.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec)
t = gs.linspace(start=0., stop=1., num=n_geodesic_points)
points = geodesic(t)
bool_belongs = self.space.belongs(points)
expected = tf.convert_to_tensor(n_geodesic_points * [[True]])
with self.test_session():
self.assertAllClose(gs.eval(expected), gs.eval(bool_belongs))
def test_mean(self):
# TODO(nina): Fix the fact that it doesn't work for [1., 4.]
point = tf.convert_to_tensor([[1., 4.]])
result = self.metric.mean(points=[point, point, point])
expected = point
expected = helper.to_vector(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
points = tf.convert_to_tensor([[1., 2.], [2., 3.], [3., 4.], [4., 5.]])
weights = gs.array([1., 2., 1., 2.])
result = self.metric.mean(points, weights)
expected = tf.convert_to_tensor([16. / 6., 22. / 6.])
expected = helper.to_vector(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_variance(self):
points = tf.convert_to_tensor([[1., 2.], [2., 3.], [3., 4.], [4., 5.]])
weights = tf.convert_to_tensor([1., 2., 1., 2.])
base_point = gs.zeros(2)
result = self.metric.variance(points, weights, base_point)
# we expect the average of the points' sq norms.
expected = (1 * 5. + 2 * 13. + 1 * 25. + 2 * 41.) / 6.
expected = helper.to_scalar(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))