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test_euclidean.py
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test_euclidean.py
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"""Unit tests for the Euclidean space."""
import geomstats.backend as gs
import geomstats.tests
from geomstats.geometry.euclidean import Euclidean
class TestEuclidean(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.space = Euclidean(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 = 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,))
self.assertAllClose(result, expected)
def test_norm_vectorization_single_sample(self):
one_point = gs.array([[0., 1.]])
result = self.metric.norm(one_point)
expected = gs.array([1.])
self.assertAllClose(gs.shape(result), (1,))
self.assertAllClose(result, expected)
one_point = gs.array([0., 1.])
result = self.metric.norm(one_point)
expected = 1.
self.assertAllClose(gs.shape(result), ())
self.assertAllClose(result, expected)
def test_norm_vectorization_n_samples(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,))
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
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
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))
self.assertAllClose(result, expected)
result = self.metric.squared_dist(n_points_a, one_point_b)
self.assertAllClose(gs.shape(result), (n_samples,))
result = self.metric.squared_dist(one_point_a, n_points_b)
self.assertAllClose(gs.shape(result), (n_samples,))
result = self.metric.squared_dist(n_points_a, n_points_b)
expected = gs.array([81., 109., 29.])
self.assertAllClose(gs.shape(result), (n_samples,))
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)))
self.assertAllClose(result, expected)
result = self.metric.dist(n_points_a, one_point_b)
self.assertAllClose(gs.shape(result), (n_samples,))
result = self.metric.dist(one_point_a, n_points_b)
self.assertAllClose(gs.shape(result), (n_samples,))
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,))
self.assertAllClose(result, expected)
def test_belongs(self):
point = gs.array([0., 1.])
result = self.space.belongs(point)
expected = True
self.assertAllClose(result, expected)
def test_random_uniform(self):
result = self.space.random_uniform()
self.assertAllClose(gs.shape(result), (self.dimension,))
def test_inner_product_matrix(self):
result = self.metric.inner_product_matrix()
expected = gs.eye(self.dimension)
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 = 10.
self.assertAllClose(result, expected)
def test_inner_product_vectorization_single_sample(self):
one_point_a = gs.array([[0., 1.]])
one_point_b = gs.array([[2., 10.]])
result = self.metric.inner_product(one_point_a, one_point_b)
expected = gs.array([10.])
self.assertAllClose(gs.shape(result), (1,))
self.assertAllClose(result, expected)
one_point_a = gs.array([[0., 1.]])
one_point_b = gs.array([2., 10.])
result = self.metric.inner_product(one_point_a, one_point_b)
expected = gs.array([10.])
self.assertAllClose(gs.shape(result), (1,))
self.assertAllClose(result, expected)
one_point_a = gs.array([0., 1.])
one_point_b = gs.array([[2., 10.]])
result = self.metric.inner_product(one_point_a, one_point_b)
expected = gs.array([10.])
self.assertAllClose(gs.shape(result), (1,))
self.assertAllClose(result, expected)
one_point_a = gs.array([0., 1.])
one_point_b = gs.array([2., 10.])
result = self.metric.inner_product(one_point_a, one_point_b)
expected = 10.
self.assertAllClose(gs.shape(result), ())
self.assertAllClose(result, expected)
def test_inner_product_vectorization_n_samples(self):
n_samples = 3
n_points_a = gs.array([
[2., 1.],
[-2., -4.],
[-5., 1.]])
n_points_b = gs.array([
[2., 10.],
[8., -1.],
[-3., 6.]])
one_point_a = gs.array([0., 1.])
one_point_b = gs.array([2., 10.])
result = self.metric.inner_product(n_points_a, one_point_b)
expected = gs.array([14., -44., 0.])
self.assertAllClose(gs.shape(result), (n_samples,))
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,))
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,))
self.assertAllClose(result, expected)
one_point_a = gs.array([[0., 1.]])
one_point_b = gs.array([[2., 10]])
result = self.metric.inner_product(n_points_a, one_point_b)
expected = gs.array([14., -44., 0.])
self.assertAllClose(gs.shape(result), (n_samples,))
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,))
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,))
self.assertAllClose(result, expected)
one_point_a = gs.array([[0., 1.]])
one_point_b = gs.array([2., 10.])
result = self.metric.inner_product(n_points_a, one_point_b)
expected = gs.array([14., -44., 0.])
self.assertAllClose(gs.shape(result), (n_samples,))
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,))
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,))
self.assertAllClose(result, expected)
one_point_a = gs.array([0., 1.])
one_point_b = gs.array([[2., 10.]])
result = self.metric.inner_product(n_points_a, one_point_b)
expected = gs.array([14., -44., 0.])
self.assertAllClose(gs.shape(result), (n_samples,))
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,))
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,))
self.assertAllClose(result, expected)
def test_squared_norm(self):
point = gs.array([-2., 4.])
result = self.metric.squared_norm(point)
expected = 20.
self.assertAllClose(result, expected)
def test_norm(self):
point = gs.array([-2., 4.])
result = self.metric.norm(point)
expected = 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
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
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)
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)
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)