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test_special_orthogonal3.py
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test_special_orthogonal3.py
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"""Unit tests for special orthogonal group SO(3)."""
import warnings
import tests.helper as helper
import geomstats.backend as gs
import geomstats.tests
from geomstats.geometry.invariant_metric import InvariantMetric
from geomstats.geometry.special_orthogonal import SpecialOrthogonal
EPSILON = 1e-5
ATOL = 1e-5
class TestSpecialOrthogonal3(geomstats.tests.TestCase):
def setUp(self):
warnings.simplefilter('ignore', category=ImportWarning)
warnings.simplefilter('ignore', category=UserWarning)
gs.random.seed(1234)
self.group = SpecialOrthogonal(n=3, point_type='vector')
# -- Rotation vectors with angles
# 0, close to 0, closely lower than pi, pi,
# between pi and 2pi, closely larger than 2pi, 2pi,
# and closely larger than 2pi
with_angle_0 = gs.zeros(3)
with_angle_close_0 = 1e-10 * gs.array([1., -1., 1.])
with_angle_close_pi_low = ((gs.pi - 1e-9) / gs.sqrt(2.)
* gs.array([0., 1., -1.]))
with_angle_pi = gs.pi / gs.sqrt(3.) * gs.array([1., 1., -1.])
with_angle_close_pi_high = ((gs.pi + 1e-9) / gs.sqrt(3.)
* gs.array([-1., 1., -1]))
with_angle_in_pi_2pi = ((gs.pi + 0.3) / gs.sqrt(5.)
* gs.array([-2., 1., 0.]))
with_angle_close_2pi_low = ((2. * gs.pi - 1e-9) / gs.sqrt(6.)
* gs.array([2., 1., -1]))
with_angle_2pi = 2. * gs.pi / gs.sqrt(3.) * gs.array([1., 1., -1.])
with_angle_close_2pi_high = ((2. * gs.pi + 1e-9) / gs.sqrt(2.)
* gs.array([1., 0., -1.]))
elements_all = {
3: {'with_angle_0': with_angle_0,
'with_angle_close_0': with_angle_close_0,
'with_angle_close_pi_low': with_angle_close_pi_low,
'with_angle_pi': with_angle_pi,
'with_angle_close_pi_high': with_angle_close_pi_high,
'with_angle_in_pi_2pi': with_angle_in_pi_2pi,
'with_angle_close_2pi_low': with_angle_close_2pi_low,
'with_angle_2pi': with_angle_2pi,
'with_angle_close_2pi_high': with_angle_close_2pi_high}
}
elements = elements_all
if geomstats.tests.tf_backend():
# Tf is extremely slow
elements = {
3: {
'with_angle_in_pi_2pi': with_angle_in_pi_2pi,
'with_angle_close_pi_low': with_angle_close_pi_low}}
# -- Metrics - only diagonals for now
canonical_metrics = {3: self.group.bi_invariant_metric}
diag_mats = {3: 9 * gs.eye(self.group.dim)}
left_diag_metrics = {
3: InvariantMetric(
group=self.group,
inner_product_mat_at_identity=diag_mats[3],
left_or_right='left')
}
right_diag_metrics = {
3: InvariantMetric(
group=self.group,
inner_product_mat_at_identity=diag_mats[3],
left_or_right='right')
}
mats = {2: 4 * gs.eye(1),
3: 87 * gs.eye(3)}
left_metrics = {
3: InvariantMetric(
group=self.group,
inner_product_mat_at_identity=mats[3],
left_or_right='left')
}
right_metrics = {
3: InvariantMetric(
group=self.group,
inner_product_mat_at_identity=mats[3],
left_or_right='right')
}
all_metrics = zip([3],
canonical_metrics.values(),
left_diag_metrics.values(),
right_diag_metrics.values(),
left_metrics.values(),
right_metrics.values())
metrics_all = {
n: {'canonical': canonical,
'left_diag': left_diag,
'right_diag': right_diag,
'left': left,
'right': right}
for n, canonical, left_diag, right_diag, left, right in all_metrics
}
metrics = metrics_all
if geomstats.tests.tf_backend():
metrics = {
3: {'right': InvariantMetric(
group=self.group,
inner_product_mat_at_identity=mats[3],
left_or_right='right')}
}
angles_close_to_pi_all = {
3: ['with_angle_close_pi_low',
'with_angle_pi',
'with_angle_close_pi_high']
}
angles_close_to_pi = angles_close_to_pi_all
if geomstats.tests.tf_backend():
angles_close_to_pi = {
3: ['with_angle_close_pi_low']
}
# -- Set attributes
self.elements = elements
self.elements_all = elements_all
self.metrics = metrics
self.metrics_all = metrics_all
self.angles_close_to_pi = angles_close_to_pi
self.angles_close_to_pi_all = angles_close_to_pi_all
self.n_samples = 4
def test_projection(self):
# Test 3D and nD cases
rot_mat = gs.eye(3)
delta = 1e-12 * gs.ones((3, 3))
rot_mat_plus_delta = rot_mat + delta
result = self.group.projection(rot_mat_plus_delta)
expected = rot_mat
self.assertAllClose(result, expected)
def test_projection_vectorization(self):
n_samples = self.n_samples
mats = gs.ones((n_samples, 3, 3))
result = self.group.projection(mats)
self.assertAllClose(gs.shape(result), (n_samples, 3, 3))
def test_skew_matrix_from_vector(self):
# Specific to 3D case
rot_vec = gs.array([0.9, -0.5, 1.1])
skew_matrix = self.group.skew_matrix_from_vector(rot_vec)
result = gs.dot(skew_matrix, rot_vec)
expected = gs.zeros(3)
self.assertAllClose(result, expected)
def test_skew_matrix_and_vector(self):
rot_vec = gs.array([0.8, 0.2, -0.1])
skew_mat = self.group.skew_matrix_from_vector(rot_vec)
result = self.group.vector_from_skew_matrix(skew_mat)
expected = rot_vec
self.assertAllClose(result, expected)
def test_skew_matrix_from_vector_vectorization(self):
n_samples = self.n_samples
rot_vecs = self.group.random_uniform(n_samples=n_samples)
result = self.group.skew_matrix_from_vector(rot_vecs)
self.assertAllClose(gs.shape(result), (n_samples, 3, 3))
def test_random_uniform_shape(self):
result = self.group.random_uniform()
self.assertAllClose(gs.shape(result), (self.group.dim,))
def test_random_and_belongs(self):
point = self.group.random_uniform()
result = self.group.belongs(point)
expected = True
self.assertAllClose(result, expected)
def test_random_and_belongs_vectorization(self):
n_samples = self.n_samples
points = self.group.random_uniform(n_samples=n_samples)
result = self.group.belongs(points)
expected = gs.array([True] * n_samples)
self.assertAllClose(result, expected)
def test_regularize(self):
point = self.elements_all[3]['with_angle_0']
self.assertAllClose(gs.linalg.norm(point), 0.)
result = self.group.regularize(point)
expected = point
self.assertAllClose(result, expected)
less_than_pi = ['with_angle_close_0',
'with_angle_close_pi_low']
for angle_type in less_than_pi:
point = self.elements_all[3][angle_type]
result = self.group.regularize(point)
expected = point
self.assertAllClose(result, expected)
# Note: by default, the rotation vector is inverted by
# the function regularize when the angle of the rotation is pi.
angle_type = 'with_angle_pi'
point = self.elements_all[3][angle_type]
result = self.group.regularize(point)
expected = point
self.assertAllClose(result, expected)
angle_type = 'with_angle_close_pi_high'
point = self.elements_all[3][angle_type]
result = self.group.regularize(point)
expected = point / gs.linalg.norm(point) * gs.pi
self.assertAllClose(result, expected)
in_pi_2pi = ['with_angle_in_pi_2pi',
'with_angle_close_2pi_low']
for angle_type in in_pi_2pi:
point = self.elements_all[3][angle_type]
point_initial = point
angle = gs.linalg.norm(point)
new_angle = gs.pi - (angle - gs.pi)
point_initial = point
result = self.group.regularize(point)
expected = - (new_angle / angle) * point_initial
self.assertAllClose(result, expected)
angle_type = 'with_angle_2pi'
point = self.elements_all[3][angle_type]
result = self.group.regularize(point)
expected = gs.array([0., 0., 0.])
self.assertAllClose(result, expected)
angle_type = 'with_angle_close_2pi_high'
point = self.elements_all[3][angle_type]
angle = gs.linalg.norm(point)
new_angle = angle - 2 * gs.pi
result = self.group.regularize(point)
expected = new_angle * point / angle
self.assertAllClose(result, expected)
def test_regularize_vectorization(self):
n_samples = self.n_samples
rot_vecs = self.group.random_uniform(n_samples=n_samples)
result = self.group.regularize(rot_vecs)
self.assertAllClose(gs.shape(result), (n_samples, self.group.dim))
def test_matrix_from_rotation_vector(self):
rot_vec_0 = self.group.identity
result = self.group.matrix_from_rotation_vector(rot_vec_0)
expected = gs.eye(3)
self.assertAllClose(result, expected)
rot_vec_1 = gs.array([gs.pi / 3., 0., 0.])
result = self.group.matrix_from_rotation_vector(rot_vec_1)
expected = gs.array([
[1., 0., 0.],
[0., 0.5, -gs.sqrt(3.) / 2],
[0., gs.sqrt(3.) / 2, 0.5]])
self.assertAllClose(result, expected)
rot_vec_3 = 1e-11 * gs.array([12., 1., -81.])
angle = gs.linalg.norm(rot_vec_3)
skew_rot_vec_3 = 1e-11 * gs.array([[0., 81., 1.],
[-81., 0., -12.],
[-1., 12., 0.]])
coef_1 = gs.sin(angle) / angle
coef_2 = (1. - gs.cos(angle)) / (angle ** 2)
expected = (
gs.eye(3)
+ coef_1 * skew_rot_vec_3
+ coef_2 * gs.matmul(skew_rot_vec_3, skew_rot_vec_3))
result = self.group.matrix_from_rotation_vector(rot_vec_3)
self.assertAllClose(result, expected)
rot_vec_6 = gs.array([.1, 1.3, -.5])
angle = gs.linalg.norm(rot_vec_6)
skew_rot_vec_6 = gs.array([[0., .5, 1.3],
[-.5, 0., -.1],
[-1.3, .1, 0.]])
coef_1 = gs.sin(angle) / angle
coef_2 = (1 - gs.cos(angle)) / (angle ** 2)
result = self.group.matrix_from_rotation_vector(rot_vec_6)
expected = (
gs.eye(3)
+ coef_1 * skew_rot_vec_6
+ coef_2 * gs.matmul(skew_rot_vec_6, skew_rot_vec_6))
self.assertAllClose(result, expected)
def test_matrix_from_rotation_vector_vectorization(self):
n_samples = self.n_samples
rot_vecs = self.group.random_uniform(n_samples=n_samples)
rot_mats = self.group.matrix_from_rotation_vector(rot_vecs)
self.assertAllClose(
gs.shape(rot_mats), (n_samples, self.group.n, self.group.n))
def test_rotation_vector_from_matrix(self):
angle = .12
rot_mat = gs.array([[1., 0., 0.],
[0., gs.cos(angle), -gs.sin(angle)],
[0, gs.sin(angle), gs.cos(angle)]])
result = self.group.rotation_vector_from_matrix(rot_mat)
expected = .12 * gs.array([1., 0., 0.])
self.assertAllClose(result, expected)
def test_rotation_vector_and_rotation_matrix(self):
"""
This tests that the composition of
rotation_vector_from_matrix
and
matrix_from_rotation_vector
is the identity.
"""
for angle_type in self.elements[3]:
point = self.elements[3][angle_type]
if angle_type in self.angles_close_to_pi[3]:
continue
rot_mat = self.group.matrix_from_rotation_vector(point)
result = self.group.rotation_vector_from_matrix(rot_mat)
expected = self.group.regularize(point)
self.assertAllClose(result, expected)
def test_matrix_from_tait_bryan_angles_extrinsic_xyz(self):
tait_bryan_angles = gs.array([0., 0., 0.])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_xyz(
tait_bryan_angles)
expected = gs.eye(3)
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
tait_bryan_angles = gs.array([angle, 0., 0.])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_xyz(
tait_bryan_angles)
expected = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., angle, 0.])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_xyz(
tait_bryan_angles)
expected = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., 0., angle])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_xyz(
tait_bryan_angles)
expected = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
self.assertAllClose(result, expected)
def test_matrix_from_tait_bryan_angles_extrinsic_zyx(self):
tait_bryan_angles = gs.array([0., 0., 0.])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_zyx(
tait_bryan_angles)
expected = gs.eye(3)
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
tait_bryan_angles = gs.array([angle, 0., 0.])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_zyx(
tait_bryan_angles)
expected = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., angle, 0.])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_zyx(
tait_bryan_angles)
expected = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., 0., angle])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_zyx(
tait_bryan_angles)
expected = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
self.assertAllClose(result, expected)
angle_bis = gs.pi / 7.
cos_angle_bis = gs.cos(angle_bis)
sin_angle_bis = gs.sin(angle_bis)
tait_bryan_angles = gs.array([angle, angle_bis, 0.])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_zyx(
tait_bryan_angles)
expected = gs.array([[cos_angle_bis, 0., sin_angle_bis],
[sin_angle * sin_angle_bis,
cos_angle,
- sin_angle * cos_angle_bis],
[- cos_angle * sin_angle_bis,
sin_angle,
cos_angle * cos_angle_bis]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([angle, 0., angle_bis])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_zyx(
tait_bryan_angles)
expected = gs.array([[cos_angle_bis, - sin_angle_bis, 0.],
[cos_angle * sin_angle_bis,
cos_angle * cos_angle_bis,
- sin_angle],
[sin_angle * sin_angle_bis,
sin_angle * cos_angle_bis,
cos_angle]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., angle, angle_bis])
result = self.group.matrix_from_tait_bryan_angles_extrinsic_zyx(
tait_bryan_angles)
expected = gs.array([[cos_angle * cos_angle_bis,
- cos_angle * sin_angle_bis,
sin_angle],
[sin_angle_bis, cos_angle_bis, 0.],
[- sin_angle * cos_angle_bis,
sin_angle * sin_angle_bis,
cos_angle]])
self.assertAllClose(result, expected)
def test_matrix_from_tait_bryan_angles_intrinsic_xyz(self):
"""
This tests that the rotation matrix computed from the
Tait-Bryan angles [0, 0, 0] is the identiy as expected.
"""
order = 'xyz'
extrinsic_or_intrinsic = 'intrinsic'
tait_bryan_angles = gs.array([0., 0., 0.])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.eye(3)
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
tait_bryan_angles = gs.array([angle, 0., 0.])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., angle, 0.])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., 0., angle])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
self.assertAllClose(result, expected)
def test_matrix_from_tait_bryan_angles_intrinsic_zyx(self):
"""
This tests that the matrix computed from the
Tait-Bryan angles[0, 0, 0] is [1, 0., 0., 0.] as expected.
"""
order = 'zyx'
extrinsic_or_intrinsic = 'intrinsic'
tait_bryan_angles = gs.array([0., 0., 0.])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.eye(3)
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
tait_bryan_angles = gs.array([angle, 0., 0.])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., angle, 0.])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
self.assertAllClose(result, expected)
tait_bryan_angles = gs.array([0., 0., angle])
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
self.assertAllClose(result, expected)
def test_tait_bryan_angles_from_matrix_extrinsic_xyz(self):
extrinsic_or_intrinsic = 'extrinsic'
order = 'xyz'
matrix = gs.eye(3)
result = self.group.tait_bryan_angles_from_matrix(
matrix, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., 0.])
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
rot_mat = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., angle])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., angle, 0.])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([angle, 0., 0.])
self.assertAllClose(result, expected)
def test_tait_bryan_angles_from_matrix_extrinsic_zyx(self):
extrinsic_or_intrinsic = 'extrinsic'
order = 'zyx'
rot_mat = gs.eye(3)
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., 0.])
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
rot_mat = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([angle, 0., 0.])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., angle, 0.])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., angle])
self.assertAllClose(result, expected)
angle_bis = gs.pi / 7.
cos_angle_bis = gs.cos(angle_bis)
sin_angle_bis = gs.sin(angle_bis)
matrix = gs.array([[cos_angle_bis, 0., sin_angle_bis],
[sin_angle * sin_angle_bis,
cos_angle,
- sin_angle * cos_angle_bis],
[- cos_angle * sin_angle_bis,
sin_angle,
cos_angle * cos_angle_bis]])
result = self.group.tait_bryan_angles_from_matrix(
matrix,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([angle, angle_bis, 0.])
matrix = gs.array([[cos_angle_bis, - sin_angle_bis, 0.],
[cos_angle * sin_angle_bis,
cos_angle * cos_angle_bis,
- sin_angle],
[sin_angle * sin_angle_bis,
sin_angle * cos_angle_bis,
cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
matrix,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([angle, 0., angle_bis])
matrix = gs.array([[cos_angle * cos_angle_bis,
- cos_angle * sin_angle_bis,
sin_angle],
[sin_angle_bis, cos_angle_bis, 0.],
[- sin_angle * cos_angle_bis,
sin_angle * sin_angle_bis,
cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
matrix,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = gs.array([0., angle, angle_bis])
self.assertAllClose(result, expected)
def test_tait_bryan_angles_from_matrix_intrinsic_xyz(self):
extrinsic_or_intrinsic = 'intrinsic'
order = 'xyz'
matrix = gs.eye(3)
result = self.group.tait_bryan_angles_from_matrix(
matrix, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., 0.])
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
rot_mat = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., angle])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., angle, 0.])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([angle, 0., 0.])
self.assertAllClose(result, expected)
def test_tait_bryan_angles_from_matrix_intrinsic_zyx(self):
extrinsic_or_intrinsic = 'intrinsic'
order = 'zyx'
rot_mat = gs.eye(3)
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., 0.])
self.assertAllClose(result, expected)
angle = gs.pi / 6.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
rot_mat = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([angle, 0., 0.])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., angle, 0.])
self.assertAllClose(result, expected)
rot_mat = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
result = self.group.tait_bryan_angles_from_matrix(
rot_mat, extrinsic_or_intrinsic, order)
expected = gs.array([0., 0., angle])
self.assertAllClose(result, expected)
def test_matrix_and_tait_bryan_angles_extrinsic_xyz(self):
"""
This tests that the composition of
rotation_vector_from_tait_bryan_angles
and
tait_bryan_angles_from_rotation_vector
is the identity.
"""
order = 'xyz'
extrinsic_or_intrinsic = 'extrinsic'
point = gs.pi / (6. * gs.sqrt(3.)) * gs.array([1., 1., 1.])
matrix = self.group.matrix_from_rotation_vector(point)
tait_bryan_angles = self.group.tait_bryan_angles_from_matrix(
matrix,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = matrix
self.assertTrue(gs.allclose(result, expected),
' for {} Tait-Bryan angles with order {}\n'
' result = \n{};'
' expected = \n{}.'.format(
extrinsic_or_intrinsic,
order,
result,
expected))
def test_matrix_and_tait_bryan_angles_extrinsic_zyx(self):
"""
This tests that the composition of
rotation_vector_from_tait_bryan_angles
and
tait_bryan_angles_from_rotation_vector
is the identity.
"""
order = 'zyx'
extrinsic_or_intrinsic = 'extrinsic'
angle = gs.pi / 7.
cos_angle = gs.cos(angle)
sin_angle = gs.sin(angle)
rot_mat = gs.array([[1., 0., 0.],
[0., cos_angle, - sin_angle],
[0., sin_angle, cos_angle]])
tait_bryan_angles = self.group.tait_bryan_angles_from_matrix(
rot_mat,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = rot_mat
self.assertTrue(gs.allclose(result, expected),
' result = {};'
' expected = {}.'.format(
result,
expected))
rot_mat = gs.array([[cos_angle, 0., sin_angle],
[0., 1., 0.],
[- sin_angle, 0., cos_angle]])
tait_bryan_angles = self.group.tait_bryan_angles_from_matrix(
rot_mat,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = rot_mat
self.assertTrue(gs.allclose(result, expected),
' result = \n{};'
' expected = \n{}.'.format(
result,
expected))
rot_mat = gs.array([[cos_angle, - sin_angle, 0.],
[sin_angle, cos_angle, 0.],
[0., 0., 1.]])
tait_bryan_angles = self.group.tait_bryan_angles_from_matrix(
rot_mat,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = rot_mat
self.assertTrue(gs.allclose(result, expected),
' result = \n{};'
' expected = \n{}.'.format(
result,
expected))
angle_bis = gs.pi / 8.
cos_angle_bis = gs.cos(angle_bis)
sin_angle_bis = gs.sin(angle_bis)
rot_mat = gs.array([[cos_angle_bis, 0., sin_angle_bis],
[sin_angle * sin_angle_bis,
cos_angle,
- sin_angle * cos_angle_bis],
[- cos_angle * sin_angle_bis,
sin_angle,
cos_angle * cos_angle_bis]])
# This matrix corresponds to tait-bryan angles (angle, angle_bis, 0.)
tait_bryan_angles = self.group.tait_bryan_angles_from_matrix(
rot_mat,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = rot_mat
self.assertTrue(gs.allclose(result, expected),
' result = \n{};'
' expected = \n{}.'.format(
result,
expected))
point = gs.pi / (6. * gs.sqrt(3.)) * gs.array([0., 2., 1.])
rot_mat = self.group.matrix_from_rotation_vector(point)
tait_bryan_angles = self.group.tait_bryan_angles_from_matrix(
rot_mat,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = rot_mat
self.assertTrue(gs.allclose(result, expected),
' result = \n{};'
' expected = \n{}.'.format(
result,
expected))
def test_tait_bryan_angles_and_matrix_extrinsic_xyz(self):
"""
This tests that the composition of
rotation_vector_from_tait_bryan_angles
and
tait_bryan_angles_from_rotation_vector
is the identity.
"""
order = 'xyz'
extrinsic_or_intrinsic = 'extrinsic'
tait_bryan_angles = gs.array([0., 0., 0.])
matrix = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.tait_bryan_angles_from_matrix(
matrix,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = tait_bryan_angles
self.assertTrue(gs.allclose(result, expected),
' for tait-bryan angles = {}'
' result = \n{};'
' expected = \n{}.'.format(
tait_bryan_angles,
result,
expected))
angle = gs.pi / 6.
tait_bryan_angles = gs.array([angle, 0., 0.])
matrix = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
result = self.group.tait_bryan_angles_from_matrix(
matrix,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,
order=order)
expected = tait_bryan_angles
self.assertTrue(gs.allclose(result, expected),
' for tait-bryan angles = {}'
' result = \n{};'
' expected = \n{}.'.format(
tait_bryan_angles,
result,
expected))
tait_bryan_angles = gs.array([0., angle, 0.])
matrix = self.group.matrix_from_tait_bryan_angles(
tait_bryan_angles,
extrinsic_or_intrinsic=extrinsic_or_intrinsic,