def test_quaternion(self, set_of_rotations, P, accept_homomorph):
c = np.array([1, P * -1, P * -1, P * -1
]) * (-1 if accept_homomorph else 1)
for rot in set_of_rotations:
m = rot.as_cubochoric()
o = Rotation.from_quaternion(rot.as_quaternion() * c,
accept_homomorph, P).as_cubochoric()
ok = np.allclose(m, o, atol=atol)
if np.count_nonzero(np.isclose(np.abs(o), np.pi**(2. / 3.) * .5)):
ok |= np.allclose(m * -1., o, atol=atol)
assert ok and o.max() < np.pi**(
2. / 3.) * 0.5 + 1.e-9, f'{m},{o},{rot.as_quaternion()}'
def test_quaternion(self, default, P, accept_homomorph):
c = np.array([1, P * -1, P * -1, P * -1
]) * (-1 if accept_homomorph else 1)
for rot in default:
m = rot.as_cubochoric()
o = Rotation.from_quaternion(rot.as_quaternion() * c,
accept_homomorph, P).as_cubochoric()
ok = np.allclose(m, o, atol=atol)
if np.count_nonzero(np.isclose(np.abs(o), np.pi**(2. / 3.) * .5)):
ok = ok or np.allclose(m * -1., o, atol=atol)
print(m, o, rot.as_quaternion())
assert ok and o.max() < np.pi**(2. / 3.) * 0.5 + 1.e-9
def set_of_rotations(set_of_quaternions):
return [Rotation.from_quaternion(s) for s in set_of_quaternions]
def default():
"""A set of n random rotations."""
specials = np.array([
[1.0, 0.0, 0.0, 0.0],
#----------------------
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0],
[0.0, -1.0, 0.0, 0.0],
[0.0, 0.0, -1.0, 0.0],
[0.0, 0.0, 0.0, -1.0],
#----------------------
[1.0, 1.0, 0.0, 0.0],
[1.0, 0.0, 1.0, 0.0],
[1.0, 0.0, 0.0, 1.0],
[0.0, 1.0, 1.0, 0.0],
[0.0, 1.0, 0.0, 1.0],
[0.0, 0.0, 1.0, 1.0],
#----------------------
[1.0, -1.0, 0.0, 0.0],
[1.0, 0.0, -1.0, 0.0],
[1.0, 0.0, 0.0, -1.0],
[0.0, 1.0, -1.0, 0.0],
[0.0, 1.0, 0.0, -1.0],
[0.0, 0.0, 1.0, -1.0],
#----------------------
[0.0, 1.0, -1.0, 0.0],
[0.0, 1.0, 0.0, -1.0],
[0.0, 0.0, 1.0, -1.0],
#----------------------
[0.0, -1.0, -1.0, 0.0],
[0.0, -1.0, 0.0, -1.0],
[0.0, 0.0, -1.0, -1.0],
#----------------------
[1.0, 1.0, 1.0, 0.0],
[1.0, 1.0, 0.0, 1.0],
[1.0, 0.0, 1.0, 1.0],
[1.0, -1.0, 1.0, 0.0],
[1.0, -1.0, 0.0, 1.0],
[1.0, 0.0, -1.0, 1.0],
[1.0, 1.0, -1.0, 0.0],
[1.0, 1.0, 0.0, -1.0],
[1.0, 0.0, 1.0, -1.0],
[1.0, -1.0, -1.0, 0.0],
[1.0, -1.0, 0.0, -1.0],
[1.0, 0.0, -1.0, -1.0],
#----------------------
[0.0, 1.0, 1.0, 1.0],
[0.0, 1.0, -1.0, 1.0],
[0.0, 1.0, 1.0, -1.0],
[0.0, -1.0, 1.0, 1.0],
[0.0, -1.0, -1.0, 1.0],
[0.0, -1.0, 1.0, -1.0],
[0.0, -1.0, -1.0, -1.0],
#----------------------
[1.0, 1.0, 1.0, 1.0],
[1.0, -1.0, 1.0, 1.0],
[1.0, 1.0, -1.0, 1.0],
[1.0, 1.0, 1.0, -1.0],
[1.0, -1.0, -1.0, 1.0],
[1.0, -1.0, 1.0, -1.0],
[1.0, 1.0, -1.0, -1.0],
[1.0, -1.0, -1.0, -1.0],
])
specials /= np.linalg.norm(specials, axis=1).reshape(-1, 1)
specials_scatter = specials + np.broadcast_to(
np.random.rand(4) * scatter, specials.shape)
specials_scatter /= np.linalg.norm(specials_scatter, axis=1).reshape(-1, 1)
specials_scatter[specials_scatter[:, 0] < 0] *= -1
return [Rotation.from_quaternion(s) for s in specials] + \
[Rotation.from_quaternion(s) for s in specials_scatter] + \
[Rotation.from_random() for _ in range(n-len(specials)-len(specials_scatter))]
