class TestVisualization(geomstats.tests.TestCase):
def setUp(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonal(n=3, point_type='vector')
self.SE3_GROUP = SpecialEuclidean(n=3, point_type='vector')
self.S1 = Hypersphere(dim=1)
self.S2 = Hypersphere(dim=2)
self.H2 = Hyperbolic(dim=2)
self.H2_half_plane = PoincareHalfSpace(dim=2)
plt.figure()
@staticmethod
def test_tutorial_matplotlib():
visualization.tutorial_matplotlib()
def test_plot_points_so3(self):
points = self.SO3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space='SO3_GROUP')
def test_plot_points_se3(self):
points = self.SE3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space='SE3_GROUP')
@geomstats.tests.np_and_pytorch_only
def test_plot_points_s1(self):
points = self.S1.random_uniform(self.n_samples)
visualization.plot(points, space='S1')
def test_plot_points_s2(self):
points = self.S2.random_uniform(self.n_samples)
visualization.plot(points, space='S2')
def test_plot_points_h2_poincare_disk(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_poincare_disk')
def test_plot_points_h2_poincare_half_plane_ext(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points,
space='H2_poincare_half_plane',
point_type='extrinsic')
def test_plot_points_h2_poincare_half_plane_none(self):
points = self.H2_half_plane.random_uniform(self.n_samples)
visualization.plot(points, space='H2_poincare_half_plane')
def test_plot_points_h2_poincare_half_plane_hs(self):
points = self.H2_half_plane.random_uniform(self.n_samples)
visualization.plot(points,
space='H2_poincare_half_plane',
point_type='half_space')
def test_plot_points_h2_klein_disk(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_klein_disk')
def setUp(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonal(n=3, point_type='vector')
self.SE3_GROUP = SpecialEuclidean(n=3, point_type='vector')
self.S1 = Hypersphere(dim=1)
self.S2 = Hypersphere(dim=2)
self.H2 = Hyperbolic(dim=2)
self.H2_half_plane = PoincareHalfSpace(dim=2)
plt.figure()
def setUp(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonal(n=3, point_type='vector')
self.SE3_GROUP = SpecialEuclidean(n=3, point_type='vector')
self.S1 = Hypersphere(dim=1)
self.S2 = Hypersphere(dim=2)
self.H2 = Hyperbolic(dim=2)
self.H2_half_plane = PoincareHalfSpace(dim=2)
self.M32 = Matrices(m=3, n=2)
self.S32 = PreShapeSpace(k_landmarks=3, m_ambient=2)
self.KS = visualization.KendallSphere()
self.M33 = Matrices(m=3, n=3)
self.S33 = PreShapeSpace(k_landmarks=3, m_ambient=3)
self.KD = visualization.KendallDisk()
plt.figure()
def __new__(cls, *args, default_coords_type='extrinsic', **kwargs):
"""Instantiate class that corresponds to the default_coords_type."""
errors.check_parameter_accepted_values(
default_coords_type, 'default_coords_type',
['extrinsic', 'ball', 'half-space'])
if default_coords_type == 'extrinsic':
return Hyperboloid(*args, **kwargs)
if default_coords_type == 'ball':
return PoincareBall(*args, **kwargs)
return PoincareHalfSpace(*args, **kwargs)
def __new__(cls, *args, default_coords_type="extrinsic", **kwargs):
"""Instantiate class that corresponds to the default_coords_type."""
errors.check_parameter_accepted_values(
default_coords_type,
"default_coords_type",
["extrinsic", "ball", "half-space"],
)
if default_coords_type == "extrinsic":
return Hyperboloid(*args, **kwargs)
if default_coords_type == "ball":
return PoincareBall(*args, **kwargs)
return PoincareHalfSpace(*args, **kwargs)
class TestVisualization(geomstats.tests.TestCase):
def setUp(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonal(n=3, point_type='vector')
self.SE3_GROUP = SpecialEuclidean(n=3, point_type='vector')
self.S1 = Hypersphere(dim=1)
self.S2 = Hypersphere(dim=2)
self.H2 = Hyperbolic(dim=2)
self.H2_half_plane = PoincareHalfSpace(dim=2)
self.M32 = Matrices(m=3, n=2)
self.S32 = PreShapeSpace(k_landmarks=3, m_ambient=2)
self.KS = visualization.KendallSphere()
self.M33 = Matrices(m=3, n=3)
self.S33 = PreShapeSpace(k_landmarks=3, m_ambient=3)
self.KD = visualization.KendallDisk()
plt.figure()
@staticmethod
def test_tutorial_matplotlib():
visualization.tutorial_matplotlib()
def test_plot_points_so3(self):
points = self.SO3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space='SO3_GROUP')
def test_plot_points_se3(self):
points = self.SE3_GROUP.random_point(self.n_samples)
visualization.plot(points, space='SE3_GROUP')
def test_draw_pre_shape_2d(self):
self.KS.draw()
def test_draw_points_pre_shape_2d(self):
points = self.S32.random_point(self.n_samples)
visualization.plot(points, space='S32')
points = self.M32.random_point(self.n_samples)
visualization.plot(points, space='M32')
self.KS.clear_points()
def test_draw_curve_pre_shape_2d(self):
self.KS.draw()
base_point = self.S32.random_point()
vec = self.S32.random_point()
tangent_vec = self.S32.to_tangent(vec, base_point)
times = gs.linspace(0., 1., 1000)
speeds = gs.array([-t * tangent_vec for t in times])
points = self.S32.ambient_metric.exp(speeds, base_point)
self.KS.add_points(points)
self.KS.draw_curve()
self.KS.clear_points()
def test_draw_vector_pre_shape_2d(self):
self.KS.draw()
base_point = self.S32.random_point()
vec = self.S32.random_point()
tangent_vec = self.S32.to_tangent(vec, base_point)
self.KS.draw_vector(tangent_vec, base_point)
def test_convert_to_spherical_coordinates_pre_shape_2d(self):
points = self.S32.random_point(self.n_samples)
coords = self.KS.convert_to_spherical_coordinates(points)
x = coords[:, 0]
y = coords[:, 1]
z = coords[:, 2]
result = x**2 + y**2 + z**2
expected = .25 * gs.ones(self.n_samples)
self.assertAllClose(result, expected)
def test_rotation_pre_shape_2d(self):
theta = gs.random.rand(1)[0]
phi = gs.random.rand(1)[0]
rot = self.KS.rotation(theta, phi)
result = _SpecialOrthogonalMatrices(3).belongs(rot)
expected = True
self.assertAllClose(result, expected)
def test_draw_pre_shape_3d(self):
self.KD.draw()
def test_draw_points_pre_shape_3d(self):
points = self.S33.random_point(self.n_samples)
visualization.plot(points, space='S33')
points = self.M33.random_point(self.n_samples)
visualization.plot(points, space='M33')
self.KD.clear_points()
def test_draw_curve_pre_shape_3d(self):
self.KD.draw()
base_point = self.S33.random_point()
vec = self.S33.random_point()
tangent_vec = self.S33.to_tangent(vec, base_point)
tangent_vec = .5 * tangent_vec / self.S33.ambient_metric.norm(
tangent_vec)
times = gs.linspace(0., 1., 1000)
speeds = gs.array([-t * tangent_vec for t in times])
points = self.S33.ambient_metric.exp(speeds, base_point)
self.KD.add_points(points)
self.KD.draw_curve()
self.KD.clear_points()
def test_draw_vector_pre_shape_3d(self):
self.KS.draw()
base_point = self.S32.random_point()
vec = self.S32.random_point()
tangent_vec = self.S32.to_tangent(vec, base_point)
self.KS.draw_vector(tangent_vec, base_point)
def test_convert_to_planar_coordinates_pre_shape_3d(self):
points = self.S33.random_point(self.n_samples)
coords = self.KD.convert_to_planar_coordinates(points)
x = coords[:, 0]
y = coords[:, 1]
radius = x**2 + y**2
result = [r <= 1. for r in radius]
self.assertTrue(gs.all(result))
@geomstats.tests.np_and_pytorch_only
def test_plot_points_s1(self):
points = self.S1.random_uniform(self.n_samples)
visualization.plot(points, space='S1')
def test_plot_points_s2(self):
points = self.S2.random_uniform(self.n_samples)
visualization.plot(points, space='S2')
def test_plot_points_h2_poincare_disk(self):
points = self.H2.random_point(self.n_samples)
visualization.plot(points, space='H2_poincare_disk')
def test_plot_points_h2_poincare_half_plane_ext(self):
points = self.H2.random_point(self.n_samples)
visualization.plot(points,
space='H2_poincare_half_plane',
point_type='extrinsic')
def test_plot_points_h2_poincare_half_plane_none(self):
points = self.H2_half_plane.random_point(self.n_samples)
visualization.plot(points, space='H2_poincare_half_plane')
def test_plot_points_h2_poincare_half_plane_hs(self):
points = self.H2_half_plane.random_point(self.n_samples)
visualization.plot(points,
space='H2_poincare_half_plane',
point_type='half_space')
def test_plot_points_h2_klein_disk(self):
points = self.H2.random_point(self.n_samples)
visualization.plot(points, space='H2_klein_disk')
@staticmethod
def test_plot_points_se2():
points = SpecialEuclidean(n=2, point_type='vector').random_point(4)
visu = visualization.SpecialEuclidean2(points, point_type='vector')
ax = visu.set_ax()
visu.draw(ax)
from geomstats.geometry.hypersphere import Hypersphere
from geomstats.geometry.matrices import Matrices
from geomstats.geometry.poincare_half_space import PoincareHalfSpace
from geomstats.geometry.pre_shape import KendallShapeMetric, PreShapeSpace
from geomstats.geometry.special_euclidean import SpecialEuclidean
from geomstats.geometry.special_orthogonal import SpecialOrthogonal
from mpl_toolkits.mplot3d import Axes3D # NOQA
SE3_GROUP = SpecialEuclidean(n=3, point_type='vector')
SE2_GROUP = SpecialEuclidean(n=2, point_type='matrix')
SE2_VECT = SpecialEuclidean(n=2, point_type='vector')
SO3_GROUP = SpecialOrthogonal(n=3, point_type='vector')
S1 = Hypersphere(dim=1)
S2 = Hypersphere(dim=2)
H2 = Hyperboloid(dim=2)
POINCARE_HALF_PLANE = PoincareHalfSpace(dim=2)
M32 = Matrices(m=3, n=2)
S32 = PreShapeSpace(k_landmarks=3, m_ambient=2)
METRIC_S32 = KendallShapeMetric(k_landmarks=3, m_ambient=2)
M33 = Matrices(m=3, n=3)
S33 = PreShapeSpace(k_landmarks=3, m_ambient=3)
METRIC_S33 = KendallShapeMetric(k_landmarks=3, m_ambient=3)
AX_SCALE = 1.2
IMPLEMENTED = [
'SO3_GROUP', 'SE3_GROUP', 'SE2_GROUP', 'S1', 'S2', 'H2_poincare_disk',
'H2_poincare_half_plane', 'H2_klein_disk', 'poincare_polydisk', 'S32',
'M32', 'S33', 'M33'
]
class TestVisualization(geomstats.tests.TestCase):
def setup_method(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonal(n=3, point_type="vector")
self.SE3_GROUP = SpecialEuclidean(n=3, point_type="vector")
self.S1 = Hypersphere(dim=1)
self.S2 = Hypersphere(dim=2)
self.H2 = Hyperbolic(dim=2)
self.H2_half_plane = PoincareHalfSpace(dim=2)
self.M32 = Matrices(m=3, n=2)
self.S32 = PreShapeSpace(k_landmarks=3, m_ambient=2)
self.KS = visualization.KendallSphere()
self.M33 = Matrices(m=3, n=3)
self.S33 = PreShapeSpace(k_landmarks=3, m_ambient=3)
self.KD = visualization.KendallDisk()
self.spd = SPDMatrices(n=2)
plt.figure()
@staticmethod
def test_tutorial_matplotlib():
visualization.tutorial_matplotlib()
def test_plot_points_so3(self):
points = self.SO3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space="SO3_GROUP")
def test_plot_points_se3(self):
points = self.SE3_GROUP.random_point(self.n_samples)
visualization.plot(points, space="SE3_GROUP")
def test_draw_pre_shape_2d(self):
self.KS.draw()
def test_draw_points_pre_shape_2d(self):
points = self.S32.random_point(self.n_samples)
visualization.plot(points, space="S32")
points = self.M32.random_point(self.n_samples)
visualization.plot(points, space="M32")
self.KS.clear_points()
def test_draw_curve_pre_shape_2d(self):
self.KS.draw()
base_point = self.S32.random_point()
vec = self.S32.random_point()
tangent_vec = self.S32.to_tangent(vec, base_point)
times = gs.linspace(0.0, 1.0, 1000)
speeds = gs.array([-t * tangent_vec for t in times])
points = self.S32.ambient_metric.exp(speeds, base_point)
self.KS.add_points(points)
self.KS.draw_curve()
self.KS.clear_points()
def test_draw_vector_pre_shape_2d(self):
self.KS.draw()
base_point = self.S32.random_point()
vec = self.S32.random_point()
tangent_vec = self.S32.to_tangent(vec, base_point)
self.KS.draw_vector(tangent_vec, base_point)
def test_convert_to_spherical_coordinates_pre_shape_2d(self):
points = self.S32.random_point(self.n_samples)
coords = self.KS.convert_to_spherical_coordinates(points)
x = coords[:, 0]
y = coords[:, 1]
z = coords[:, 2]
result = x**2 + y**2 + z**2
expected = 0.25 * gs.ones(self.n_samples)
self.assertAllClose(result, expected)
def test_rotation_pre_shape_2d(self):
theta = gs.random.rand(1)[0]
phi = gs.random.rand(1)[0]
rot = self.KS.rotation(theta, phi)
result = _SpecialOrthogonalMatrices(3).belongs(rot)
expected = True
self.assertAllClose(result, expected)
def test_draw_pre_shape_3d(self):
self.KD.draw()
def test_draw_points_pre_shape_3d(self):
points = self.S33.random_point(self.n_samples)
visualization.plot(points, space="S33")
points = self.M33.random_point(self.n_samples)
visualization.plot(points, space="M33")
self.KD.clear_points()
def test_draw_curve_pre_shape_3d(self):
self.KD.draw()
base_point = self.S33.random_point()
vec = self.S33.random_point()
tangent_vec = self.S33.to_tangent(vec, base_point)
tangent_vec = 0.5 * tangent_vec / self.S33.ambient_metric.norm(
tangent_vec)
times = gs.linspace(0.0, 1.0, 1000)
speeds = gs.array([-t * tangent_vec for t in times])
points = self.S33.ambient_metric.exp(speeds, base_point)
self.KD.add_points(points)
self.KD.draw_curve()
self.KD.clear_points()
def test_draw_vector_pre_shape_3d(self):
self.KS.draw()
base_point = self.S32.random_point()
vec = self.S32.random_point()
tangent_vec = self.S32.to_tangent(vec, base_point)
self.KS.draw_vector(tangent_vec, base_point)
def test_convert_to_planar_coordinates_pre_shape_3d(self):
points = self.S33.random_point(self.n_samples)
coords = self.KD.convert_to_planar_coordinates(points)
x = coords[:, 0]
y = coords[:, 1]
radius = x**2 + y**2
result = [r <= 1.0 for r in radius]
self.assertTrue(gs.all(result))
@geomstats.tests.np_autograd_and_torch_only
def test_plot_points_s1(self):
points = self.S1.random_uniform(self.n_samples)
visualization.plot(points, space="S1")
def test_plot_points_s2(self):
points = self.S2.random_uniform(self.n_samples)
visualization.plot(points, space="S2")
def test_plot_points_h2_poincare_disk(self):
points = self.H2.random_point(self.n_samples)
visualization.plot(points, space="H2_poincare_disk")
def test_plot_points_h2_poincare_half_plane_ext(self):
points = self.H2.random_point(self.n_samples)
visualization.plot(points,
space="H2_poincare_half_plane",
point_type="extrinsic")
def test_plot_points_h2_poincare_half_plane_none(self):
points = self.H2_half_plane.random_point(self.n_samples)
visualization.plot(points, space="H2_poincare_half_plane")
def test_plot_points_h2_poincare_half_plane_hs(self):
points = self.H2_half_plane.random_point(self.n_samples)
visualization.plot(points,
space="H2_poincare_half_plane",
point_type="half_space")
def test_plot_points_h2_klein_disk(self):
points = self.H2.random_point(self.n_samples)
visualization.plot(points, space="H2_klein_disk")
@staticmethod
def test_plot_points_se2():
points = SpecialEuclidean(n=2, point_type="vector").random_point(4)
visu = visualization.SpecialEuclidean2(points, point_type="vector")
ax = visu.set_ax()
visu.draw_points(ax)
def test_plot_points_spd2(self):
one_point = self.spd.random_point()
visualization.plot(one_point, space="SPD2")
points = self.spd.random_point(4)
visualization.plot(points, space="SPD2")
def test_compute_coordinates_spd2(self):
point = gs.eye(2)
ellipsis = visualization.Ellipses(n_sampling_points=4)
x, y = ellipsis.compute_coordinates(point)
self.assertAllClose(x, gs.array([1, 0, -1, 0, 1]))
self.assertAllClose(y, gs.array([0, 1, 0, -1, 0]))
@staticmethod
def teardown_method():
plt.close()
class TestPoincareHalfSpace(geomstats.tests.TestCase):
def setup_method(self):
self.manifold = PoincareHalfSpace(2)
self.metric = self.manifold.metric
self.hyperboloid_manifold = Hyperboloid(2)
self.hyperboloid_metric = self.hyperboloid_manifold.metric
def test_belongs(self):
point = gs.array([1.5, 2.3])
result = self.manifold.belongs(point)
self.assertTrue(result)
points = gs.array([[1.5, 2.0], [2.5, -0.3]])
result = self.manifold.belongs(points)
expected = gs.array([True, False])
self.assertAllClose(result, expected)
def test_inner_product_vectorization(self):
tangent_vec = gs.array([[1.0, 2.0], [3.0, 4.0]])
base_point = gs.array([[0.0, 1.0], [0.0, 5.0]])
result = self.metric.inner_product(tangent_vec, tangent_vec, base_point)
expected = gs.array([5.0, 1.0])
self.assertAllClose(result, expected)
def test_half_space_to_ball_coordinates(self):
point_half_space = gs.array([0.0, 1.0])
result = self.manifold.half_space_to_ball_coordinates(point_half_space)
expected = gs.zeros(2)
self.assertAllClose(result, expected)
def test_half_space_to_ball_coordinates_vectorization(self):
point_half_space = gs.array([[0.0, 1.0], [0.0, 2.0]])
point_ball = self.manifold.half_space_to_ball_coordinates(point_half_space)
expected = gs.array([[0.0, 0.0], [0.0, 1.0 / 3.0]])
self.assertAllClose(point_ball, expected)
def test_ball_to_half_space_coordinates(self):
point_ball = gs.array([-0.3, 0.7])
point_half_space = self.manifold.ball_to_half_space_coordinates(point_ball)
point_ext = self.hyperboloid_manifold.from_coordinates(point_ball, "ball")
point_half_space_expected = self.hyperboloid_manifold.to_coordinates(
point_ext, "half-space"
)
self.assertAllClose(point_half_space, point_half_space_expected)
def test_coordinates(self):
point_half_space = gs.array([1.5, 2.3])
point_ball = self.manifold.half_space_to_ball_coordinates(point_half_space)
result = self.manifold.ball_to_half_space_coordinates(point_ball)
self.assertAllClose(result, point_half_space)
def test_exp_and_coordinates_tangent(self):
base_point = gs.array([1.5, 2.3])
tangent_vec = gs.array([0.0, 1.0])
end_point = self.metric.exp(tangent_vec, base_point)
self.assertAllClose(base_point[0], end_point[0])
def test_ball_half_plane_are_inverse(self):
base_point = gs.array([1.5, 2.3])
base_point_ball = self.manifold.half_space_to_ball_coordinates(base_point)
result = self.manifold.ball_to_half_space_coordinates(base_point_ball)
self.assertAllClose(result, base_point)
def test_ball_half_plane_tangent_are_inverse(self):
base_point = gs.array([1.5, 2.3])
tangent_vec = gs.array([0.5, 1.0])
tangent_vec_ball = self.manifold.half_space_to_ball_tangent(
tangent_vec, base_point
)
base_point_ball = self.manifold.half_space_to_ball_coordinates(base_point)
result = self.manifold.ball_to_half_space_tangent(
tangent_vec_ball, base_point_ball
)
self.assertAllClose(result, tangent_vec)
@geomstats.tests.np_and_autograd_only
def test_exp(self):
point = gs.array([1.0, 1.0])
tangent_vec = gs.array([2.0, 1.0])
end_point = self.metric.exp(tangent_vec, point)
circle_center = point[0] + point[1] * tangent_vec[1] / tangent_vec[0]
circle_radius = gs.sqrt((circle_center - point[0]) ** 2 + point[1] ** 2)
moebius_d = 1
moebius_c = 1 / (2 * circle_radius)
moebius_b = circle_center - circle_radius
moebius_a = (circle_center + circle_radius) * moebius_c
point_complex = point[0] + 1j * point[1]
tangent_vec_complex = tangent_vec[0] + 1j * tangent_vec[1]
point_moebius = (
1j
* (moebius_d * point_complex - moebius_b)
/ (moebius_c * point_complex - moebius_a)
)
tangent_vec_moebius = (
-1j
* tangent_vec_complex
* (1j * moebius_c * point_moebius + moebius_d) ** 2
)
end_point_moebius = point_moebius * gs.exp(tangent_vec_moebius / point_moebius)
end_point_complex = (moebius_a * 1j * end_point_moebius + moebius_b) / (
moebius_c * 1j * end_point_moebius + moebius_d
)
end_point_expected = gs.hstack(
[np.real(end_point_complex), np.imag(end_point_complex)]
)
self.assertAllClose(end_point, end_point_expected)
@geomstats.tests.np_and_autograd_only
def test_exp_vectorization(self):
point = gs.array([[1.0, 1.0], [1.0, 1.0]])
tangent_vec = gs.array([[2.0, 1.0], [2.0, 1.0]])
result = self.metric.exp(tangent_vec, point)
point = point[0]
tangent_vec = tangent_vec[0]
circle_center = point[0] + point[1] * tangent_vec[1] / tangent_vec[0]
circle_radius = gs.sqrt((circle_center - point[0]) ** 2 + point[1] ** 2)
moebius_d = 1
moebius_c = 1 / (2 * circle_radius)
moebius_b = circle_center - circle_radius
moebius_a = (circle_center + circle_radius) * moebius_c
point_complex = point[0] + 1j * point[1]
tangent_vec_complex = tangent_vec[0] + 1j * tangent_vec[1]
point_moebius = (
1j
* (moebius_d * point_complex - moebius_b)
/ (moebius_c * point_complex - moebius_a)
)
tangent_vec_moebius = (
-1j
* tangent_vec_complex
* (1j * moebius_c * point_moebius + moebius_d) ** 2
)
end_point_moebius = point_moebius * gs.exp(tangent_vec_moebius / point_moebius)
end_point_complex = (moebius_a * 1j * end_point_moebius + moebius_b) / (
moebius_c * 1j * end_point_moebius + moebius_d
)
end_point_expected = gs.hstack(
[np.real(end_point_complex), np.imag(end_point_complex)]
)
expected = gs.stack([end_point_expected, end_point_expected])
self.assertAllClose(result, expected)
def test_exp_and_log_are_inverse(self):
points = gs.array([[1.0, 1.0], [1.0, 1.0]])
tangent_vecs = gs.array([[2.0, 1.0], [2.0, 1.0]])
end_points = self.metric.exp(tangent_vecs, points)
result = self.metric.log(end_points, points)
expected = tangent_vecs
self.assertAllClose(result, expected)
def test_projection(self):
point = gs.array([[1.0, -1.0], [0.0, 1.0]])
projected = self.manifold.projection(point)
result = self.manifold.belongs(projected)
self.assertTrue(gs.all(result))
projected = self.manifold.projection(point[0])
result = self.manifold.belongs(projected)
self.assertTrue(result)
def setup_method(self):
self.manifold = PoincareHalfSpace(2)
self.metric = self.manifold.metric
self.hyperboloid_manifold = Hyperboloid(2)
self.hyperboloid_metric = self.hyperboloid_manifold.metric
class PoincareHalfSpaceMetricTestData(_RiemannianMetricTestData):
dim_list = random.sample(range(2, 5), 2)
metric_args_list = [(dim, ) for dim in dim_list]
shape_list = [(dim, ) for dim in dim_list]
space_list = [PoincareHalfSpace(dim) for dim in dim_list]
n_points_list = random.sample(range(1, 5), 2)
n_tangent_vecs_list = random.sample(range(1, 5), 2)
n_points_a_list = random.sample(range(1, 5), 2)
n_points_b_list = [1]
alpha_list = [1] * 2
n_rungs_list = [1] * 2
scheme_list = ["pole"] * 2
def inner_product_test_data(self):
smoke_data = [
dict(
dim=2,
tangent_vec_a=[[1.0, 2.0], [3.0, 4.0]],
tangent_vec_b=[[1.0, 2.0], [3.0, 4.0]],
base_point=[[0.0, 1.0], [0.0, 5.0]],
expected=[5.0, 1.0],
)
]
return self.generate_tests(smoke_data)
def exp_and_coordinates_tangent_test_data(self):
smoke_data = [
dict(
dim=2,
tangent_vec=gs.array([0.0, 1.0]),
base_point=gs.array([1.5, 2.3]),
)
]
return self.generate_tests(smoke_data)
def exp_test_data(self):
def _exp(tangent_vec, base_point):
circle_center = (base_point[0] +
base_point[1] * tangent_vec[1] / tangent_vec[0])
circle_radius = gs.sqrt((circle_center - base_point[0])**2 +
base_point[1]**2)
moebius_d = 1
moebius_c = 1 / (2 * circle_radius)
moebius_b = circle_center - circle_radius
moebius_a = (circle_center + circle_radius) * moebius_c
point_complex = base_point[0] + 1j * base_point[1]
tangent_vec_complex = tangent_vec[0] + 1j * tangent_vec[1]
point_moebius = (1j * (moebius_d * point_complex - moebius_b) /
(moebius_c * point_complex - moebius_a))
tangent_vec_moebius = (
-1j * tangent_vec_complex *
(1j * moebius_c * point_moebius + moebius_d)**2)
end_point_moebius = point_moebius * gs.exp(
tangent_vec_moebius / point_moebius)
end_point_complex = (
moebius_a * 1j * end_point_moebius +
moebius_b) / (moebius_c * 1j * end_point_moebius + moebius_d)
end_point_expected = gs.hstack(
[np.real(end_point_complex),
np.imag(end_point_complex)])
return end_point_expected
inputs_to_exp = [(gs.array([2.0, 1.0]), gs.array([1.0, 1.0]))]
smoke_data = []
if not geomstats.tests.tf_backend():
for tangent_vec, base_point in inputs_to_exp:
smoke_data.append(
dict(
dim=2,
tangent_vec=tangent_vec,
base_point=base_point,
expected=_exp(tangent_vec, base_point),
))
return self.generate_tests(smoke_data)
def exp_shape_test_data(self):
return self._exp_shape_test_data(self.metric_args_list,
self.space_list, self.shape_list)
def log_shape_test_data(self):
return self._log_shape_test_data(
self.metric_args_list,
self.space_list,
)
def squared_dist_is_symmetric_test_data(self):
return self._squared_dist_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
atol=gs.atol * 1000,
)
def exp_belongs_test_data(self):
return self._exp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
belongs_atol=gs.atol * 10000,
)
def log_is_tangent_test_data(self):
return self._log_is_tangent_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
is_tangent_atol=gs.atol * 10900,
)
def geodesic_ivp_belongs_test_data(self):
return self._geodesic_ivp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_points_list,
belongs_atol=gs.atol * 1000,
)
def geodesic_bvp_belongs_test_data(self):
return self._geodesic_bvp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
belongs_atol=gs.atol * 1000,
)
def exp_after_log_test_data(self):
return self._exp_after_log_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
def log_after_exp_test_data(self):
return self._log_after_exp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
def exp_ladder_parallel_transport_test_data(self):
return self._exp_ladder_parallel_transport_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
self.n_rungs_list,
self.alpha_list,
self.scheme_list,
)
def exp_geodesic_ivp_test_data(self):
return self._exp_geodesic_ivp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
self.n_points_list,
rtol=gs.rtol * 100000,
atol=gs.atol * 100000,
)
def parallel_transport_ivp_is_isometry_test_data(self):
return self._parallel_transport_ivp_is_isometry_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
is_tangent_atol=gs.atol * 1000,
atol=gs.atol * 1000,
)
def parallel_transport_bvp_is_isometry_test_data(self):
return self._parallel_transport_bvp_is_isometry_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_list,
is_tangent_atol=gs.atol * 1000,
atol=gs.atol * 1000,
)
def dist_is_symmetric_test_data(self):
return self._dist_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_is_positive_test_data(self):
return self._dist_is_positive_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def squared_dist_is_positive_test_data(self):
return self._squared_dist_is_positive_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_is_norm_of_log_test_data(self):
return self._dist_is_norm_of_log_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_point_to_itself_is_zero_test_data(self):
return self._dist_point_to_itself_is_zero_test_data(
self.metric_args_list, self.space_list, self.n_points_list)
def triangle_inequality_of_dist_test_data(self):
return self._triangle_inequality_of_dist_test_data(
self.metric_args_list, self.space_list, self.n_points_list)
def inner_product_is_symmetric_test_data(self):
return self._inner_product_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
)
def retraction_lifting_test_data(self):
return self._log_after_exp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
