def test_average(self, angle, lattice):
R_1 = Orientation(
Rotation.from_axis_angle([0, 0, 1, 10], degrees=True), lattice)
R_2 = Orientation(
Rotation.from_axis_angle([0, 0, 1, angle], degrees=True), lattice)
avg_angle = R_1.average(R_2).rotation.as_axis_angle(degrees=True,
pair=True)[1]
assert np.isclose(avg_angle, 10 + (angle - 10) / 2.)
def test_matrix(self, set_of_rotations):
for rot in set_of_rotations:
m = rot.as_axis_angle()
o = Rotation.from_axis_angle(rot.as_axis_angle()).as_axis_angle()
ok = np.allclose(m, o, atol=atol)
if np.isclose(m[3], np.pi, atol=atol):
ok = ok or np.allclose(
m * np.array([-1., -1., -1., 1.]), o, atol=atol)
assert ok and np.isclose(np.linalg.norm(o[:3]),1.0) \
and o[3]<=np.pi+1.e-9, f'{m},{o},{rot.as_quaternion()}'
def test_matrix(self, default):
for rot in default:
m = rot.as_axis_angle()
o = Rotation.from_axis_angle(rot.as_axis_angle()).as_axis_angle()
ok = np.allclose(m, o, atol=atol)
if np.isclose(m[3], np.pi, atol=atol):
ok = ok or np.allclose(
m * np.array([-1., -1., -1., 1.]), o, atol=atol)
print(m, o, rot.as_quaternion())
assert ok and np.isclose(np.linalg.norm(o[:3]),
1.0) and o[3] <= np.pi + 1.e-9
def test_axis_angle(self, set_of_rotations, degrees, normalize, P):
c = np.array([P * -1, P * -1, P * -1, 1.])
for rot in set_of_rotations:
m = rot.as_Eulers()
o = Rotation.from_axis_angle(
rot.as_axis_angle(degrees) * c, degrees, normalize,
P).as_Eulers()
u = np.array([np.pi * 2, np.pi, np.pi * 2])
ok = np.allclose(m, o, atol=atol)
ok |= np.allclose(np.where(np.isclose(m, u), m - u, m),
np.where(np.isclose(o, u), o - u, o),
atol=atol)
if np.isclose(m[1], 0.0, atol=atol) or np.isclose(
m[1], np.pi, atol=atol):
sum_phi = np.unwrap([m[0] + m[2], o[0] + o[2]])
ok |= np.isclose(sum_phi[0], sum_phi[1], atol=atol)
assert ok and (np.zeros(3)-1.e-9 <= o).all() \
and (o <= np.array([np.pi*2.,np.pi,np.pi*2.])+1.e-9).all(), f'{m},{o},{rot.as_quaternion()}'
def test_from_fiber_component(self, N, sigma):
p = []
for run in range(5):
alpha = np.random.random() * 2 * np.pi, np.arccos(
np.random.random())
beta = np.random.random() * 2 * np.pi, np.arccos(
np.random.random())
f_in_C = np.array([
np.sin(alpha[0]) * np.cos(alpha[1]),
np.sin(alpha[0]) * np.sin(alpha[1]),
np.cos(alpha[0])
])
f_in_S = np.array([
np.sin(beta[0]) * np.cos(beta[1]),
np.sin(beta[0]) * np.sin(beta[1]),
np.cos(beta[0])
])
ax = np.append(np.cross(f_in_C, f_in_S),
-np.arccos(np.dot(f_in_C, f_in_S)))
n = Rotation.from_axis_angle(
ax if ax[3] > 0.0 else ax * -1.0, normalize=True
) # rotation to align fiber axis in crystal and sample system
o = Rotation.from_fiber_component(alpha, beta, np.radians(sigma),
N, False)
angles = np.arccos(
np.clip(
np.dot(o @ np.broadcast_to(f_in_S, (N, 3)), n @ f_in_S),
-1, 1))
dist = np.array(angles) * (np.random.randint(0, 2, N) * 2 - 1)
p.append(stats.normaltest(dist)[1])
sigma_out = np.degrees(np.std(dist))
p = np.average(p)
assert (.9 < sigma / sigma_out <
1.1) and p > 1e-2, f'{sigma/sigma_out},{p}'
def test_rotate360(self,default,axis_angle):
modified = default.copy()
for i in range(np.rint(360/axis_angle[3]).astype(int)):
modified.rotate(Rotation.from_axis_angle(axis_angle,degrees=True))
assert grid_equal(default,modified)
def test_rotate360(self,default,axis_angle):
modified = copy.deepcopy(default)
for i in range(np.rint(360/axis_angle[3]).astype(int)):
modified.rotate(Rotation.from_axis_angle(axis_angle,degrees=True))
assert geom_equal(modified,default)
