def setUp(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonalGroup(n=3)
self.SE3_GROUP = SpecialEuclideanGroup(n=3)
self.S1 = Hypersphere(dimension=1)
self.S2 = Hypersphere(dimension=2)
self.H2 = HyperbolicSpace(dimension=2)
plt.figure()
def setUp(self):
warnings.simplefilter('ignore', category=ImportWarning)
gs.random.seed(1234)
n = 3
group = SpecialEuclideanGroup(n=n)
# Diagonal left and right invariant metrics
diag_mat_at_identity = gs.eye(group.dimension)
left_diag_metric = InvariantMetric(
group=group,
inner_product_mat_at_identity=diag_mat_at_identity,
left_or_right='left')
right_diag_metric = InvariantMetric(
group=group,
inner_product_mat_at_identity=diag_mat_at_identity,
left_or_right='right')
# General left and right invariant metrics
# TODO(nina): Replace the matrix below by a general SPD matrix.
sym_mat_at_identity = gs.eye(group.dimension)
left_metric = InvariantMetric(
group=group,
inner_product_mat_at_identity=sym_mat_at_identity,
left_or_right='left')
right_metric = InvariantMetric(
group=group,
inner_product_mat_at_identity=sym_mat_at_identity,
left_or_right='right')
metrics = {
'left_diag': left_diag_metric,
'right_diag_metric': right_diag_metric,
'left': left_metric,
'right': right_metric
}
# General case for the point
point_1 = gs.array([[-0.2, 0.9, 0.5, 5., 5., 5.]])
point_2 = gs.array([[0., 2., -0.1, 30., 400., 2.]])
# Edge case for the point, angle < epsilon,
point_small = gs.array([[-1e-7, 0., -7 * 1e-8, 6., 5., 9.]])
self.group = group
self.metrics = metrics
self.left_diag_metric = left_diag_metric
self.right_diag_metric = right_diag_metric
self.left_metric = left_metric
self.right_metric = right_metric
self.point_1 = point_1
self.point_2 = point_2
self.point_small = point_small
class TestVisualizationMethods(geomstats.tests.TestCase):
def setUp(self):
self.n_samples = 10
self.SO3_GROUP = SpecialOrthogonalGroup(n=3)
self.SE3_GROUP = SpecialEuclideanGroup(n=3)
self.S1 = Hypersphere(dimension=1)
self.S2 = Hypersphere(dimension=2)
self.H2 = HyperbolicSpace(dimension=2)
plt.figure()
@geomstats.tests.np_only
def test_plot_points_so3(self):
points = self.SO3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space='SO3_GROUP')
@geomstats.tests.np_only
def test_plot_points_se3(self):
points = self.SE3_GROUP.random_uniform(self.n_samples)
visualization.plot(points, space='SE3_GROUP')
@geomstats.tests.np_only
def test_plot_points_s1(self):
points = self.S1.random_uniform(self.n_samples)
visualization.plot(points, space='S1')
@geomstats.tests.np_only
def test_plot_points_s2(self):
points = self.S2.random_uniform(self.n_samples)
visualization.plot(points, space='S2')
@geomstats.tests.np_only
def test_plot_points_h2_poincare_disk(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_poincare_disk')
@geomstats.tests.np_only
def test_plot_points_h2_poincare_half_plane(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_poincare_half_plane')
@geomstats.tests.np_only
def test_plot_points_h2_klein_disk(self):
points = self.H2.random_uniform(self.n_samples)
visualization.plot(points, space='H2_klein_disk')
"""
Plot a geodesic of SE(3) equipped
with its left-invariant canonical METRIC.
"""
import os
import matplotlib.pyplot as plt
import numpy as np
import geomstats.visualization as visualization
from geomstats.geometry.special_euclidean_group import SpecialEuclideanGroup
SE3_GROUP = SpecialEuclideanGroup(n=3)
METRIC = SE3_GROUP.left_canonical_metric
def main():
initial_point = SE3_GROUP.identity
initial_tangent_vec = [1.8, 0.2, 0.3, 3., 3., 1.]
geodesic = METRIC.geodesic(initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec)
n_steps = 40
t = np.linspace(-3, 3, n_steps)
points = geodesic(t)
visualization.plot(points, space='SE3_GROUP')
plt.show()
"""
Predict on SE3: losses.
"""
import os
import tensorflow as tf
import geomstats.backend as gs
import geomstats.geometry.lie_group as lie_group
from geomstats.geometry.special_euclidean_group import SpecialEuclideanGroup
from geomstats.geometry.special_orthogonal_group import SpecialOrthogonalGroup
SE3 = SpecialEuclideanGroup(n=3)
SO3 = SpecialOrthogonalGroup(n=3)
def loss(y_pred,
y_true,
metric=SE3.left_canonical_metric,
representation='vector'):
"""
Loss function given by a riemannian metric on a Lie group,
by default the left-invariant canonical metric.
"""
if gs.ndim(y_pred) == 1:
y_pred = gs.expand_dims(y_pred, axis=0)
if gs.ndim(y_true) == 1:
y_true = gs.expand_dims(y_true, axis=0)
if representation == 'quaternion':