def test_product_distance_extrinsic_representation(self):
"""Test the distance using the extrinsic representation."""
coords_type = 'extrinsic'
point_a_intrinsic = gs.array([[0.01, 0.0]])
point_b_intrinsic = gs.array([[0.0, 0.0]])
hyperbolic_space = Hyperbolic(dimension=2, coords_type=coords_type)
point_a = hyperbolic_space.from_coordinates(point_a_intrinsic,
"intrinsic")
point_b = hyperbolic_space.from_coordinates(point_b_intrinsic,
"intrinsic")
duplicate_point_a = gs.vstack([point_a, point_a])
duplicate_point_b = gs.vstack([point_b, point_b])
single_disk = PoincarePolydisk(n_disks=1, coords_type=coords_type)
two_disks = PoincarePolydisk(n_disks=2, coords_type=coords_type)
distance_single_disk = single_disk.metric.dist(point_a, point_b)
distance_two_disks = two_disks.metric.dist(duplicate_point_a,
duplicate_point_b)
result = distance_two_disks
expected = 3**0.5 * distance_single_disk
self.assertAllClose(result, expected)
def test_product_distance_extrinsic_representation(self, n_disks,
point_a_extrinsic,
point_b_extrinsic):
duplicate_point_a = gs.stack([point_a_extrinsic, point_a_extrinsic],
axis=0)
duplicate_point_b = gs.stack([point_b_extrinsic, point_b_extrinsic],
axis=0)
single_disk = PoincarePolydisk(n_disks=n_disks,
coords_type="extrinsic")
two_disks = PoincarePolydisk(n_disks=2 * n_disks,
coords_type="extrinsic")
distance_single_disk = single_disk.metric.dist(
point_a_extrinsic[None, :], point_b_extrinsic[None, :])
distance_two_disks = two_disks.metric.dist(duplicate_point_a,
duplicate_point_b)
result = distance_two_disks
expected = 3**0.5 * distance_single_disk
self.assertAllClose(result, expected)
def test_product_distance_extrinsic_representation(self):
point_type = 'extrinsic'
point_a_intrinsic = gs.array([0.01, 0.0])
point_b_intrinsic = gs.array([0.0, 0.0])
hyperbolic_space = HyperbolicSpace(dimension=2, point_type=point_type)
point_a = hyperbolic_space.intrinsic_to_extrinsic_coords(
point_a_intrinsic)
point_b = hyperbolic_space.intrinsic_to_extrinsic_coords(
point_b_intrinsic)
duplicate_point_a = gs.zeros((2,) + point_a.shape)
duplicate_point_a[0] = point_a
duplicate_point_a[1] = point_a
duplicate_point_b = gs.zeros((2,) + point_b.shape)
duplicate_point_b[0] = point_b
duplicate_point_b[1] = point_b
single_disk = PoincarePolydisk(n_disks=1, point_type=point_type)
two_disks = PoincarePolydisk(n_disks=2, point_type=point_type)
distance_single_disk = single_disk.metric.dist(point_a, point_b)
distance_two_disks = two_disks.metric.dist(
duplicate_point_a, duplicate_point_b)
result = distance_two_disks
expected = 3 ** 0.5 * distance_single_disk
self.assertAllClose(result, expected)
class PoincarePolydiskMetricTestData(TestData):
n_disks_list = random.sample(range(2, 4), 2)
metric_args_list = [(n_disks, ) for n_disks in n_disks_list]
shape_list = [(n_disks, 3) for n_disks in n_disks_list]
space_list = [PoincarePolydisk(n_disks) for n_disks in n_disks_list]
n_points_list = random.sample(range(1, 4), 2)
n_tangent_vecs_list = random.sample(range(1, 4), 2)
n_points_a_list = random.sample(range(1, 4), 2)
n_points_b_list = [1]
alpha_list = [1] * 2
n_rungs_list = [1] * 2
scheme_list = ["pole"] * 2
def signature_test_data(self):
smoke_data = [
dict(n_disks=2, expected=(4, 0)),
dict(n_disks=4, expected=(8, 0)),
]
return self.generate_tests(smoke_data)
def product_distance_extrinsic_representation_test_data(self):
point_a_intrinsic = gs.array([0.01, 0.0])
point_b_intrinsic = gs.array([0.0, 0.0])
hyperbolic_space = Hyperboloid(dim=2)
point_a_extrinsic = hyperbolic_space.from_coordinates(
point_a_intrinsic, "intrinsic")
point_b_extrinsic = hyperbolic_space.from_coordinates(
point_b_intrinsic, "intrinsic")
smoke_data = [
dict(
n_disks=1,
point_a_extrinsic=point_a_extrinsic,
point_b_extrinsic=point_b_extrinsic,
)
]
return self.generate_tests(smoke_data)
def test_dimension(self, n_disks, expected):
space = PoincarePolydisk(n_disks)
self.assertAllClose(space.dim, expected)
Plot a geodesic on the Poincare polydisk,
with Poincare Disk visualization.
"""
import os
import matplotlib.pyplot as plt
import numpy as np
import geomstats.backend as gs
import geomstats.visualization as visualization
from geomstats.geometry.poincare_polydisk import PoincarePolydisk
N_DISKS = 4
POINCARE_POLYDISK = PoincarePolydisk(n_disks=N_DISKS, point_type='extrinsic')
METRIC = POINCARE_POLYDISK.metric
def plot_geodesic_between_two_points(initial_point,
end_point,
n_steps=11,
ax=None):
"""Plot the geodesic between two points."""
geodesic = METRIC.geodesic(initial_point=initial_point,
end_point=end_point)
t = gs.linspace(0, 1, n_steps)
points = geodesic(t)
visualization.plot(points, ax=ax, space='poincare_polydisk')
def setUp(self):
gs.random.seed(1234)
self.n_disks = 5
self.space = PoincarePolydisk(n_disks=self.n_disks)
self.metric = self.space.metric
def setUp(self):
"""Define the elements to test."""
gs.random.seed(1234)
self.n_disks = 5
self.space = PoincarePolydisk(n_disks=self.n_disks)
self.metric = self.space.metric
"""Plot a geodesic on the Poincare polydisk.
Plot a geodesic on the Poincare polydisk,
with Poincare Disk visualization.
"""
import matplotlib.pyplot as plt
import geomstats.backend as gs
import geomstats.visualization as visualization
from geomstats.geometry.poincare_polydisk import PoincarePolydisk
N_DISKS = 4
POINCARE_POLYDISK = PoincarePolydisk(n_disks=N_DISKS, coords_type="extrinsic")
METRIC = POINCARE_POLYDISK.metric
def plot_geodesic_between_two_points(initial_point,
end_point,
n_steps=11,
ax=None):
"""Plot the geodesic between two points."""
geodesic = METRIC.geodesic(initial_point=initial_point,
end_point=end_point)
t = gs.linspace(0.0, 1.0, n_steps)
points = geodesic(t)
visualization.plot(points, ax=ax, space="poincare_polydisk")
def plot_geodesic_with_initial_tangent_vector(initial_point,