/usr/lib/python3/dist-packages/ase/quaternions.py is in python3-ase 3.15.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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from ase.atoms import Atoms
class Quaternions(Atoms):
def __init__(self, *args, **kwargs):
quaternions = None
if 'quaternions' in kwargs:
quaternions = np.array(kwargs['quaternions'])
del kwargs['quaternions']
Atoms.__init__(self, *args, **kwargs)
if quaternions is not None:
self.set_array('quaternions', quaternions, shape=(4,))
# set default shapes
self.set_shapes(np.array([[3, 2, 1]] * len(self)))
def set_shapes(self, shapes):
self.set_array('shapes', shapes, shape=(3,))
def set_quaternions(self, quaternions):
self.set_array('quaternions', quaternions, quaternion=(4,))
def get_shapes(self):
return self.get_array('shapes')
def get_quaternions(self):
return self.get_array('quaternions').copy()
class Quaternion:
def __init__(self, qin=[1, 0, 0, 0]):
assert(len(qin) == 4)
self.q = np.array(qin)
def __str__(self):
return self.q.__str__()
def __mul__(self, other):
sw, sx, sy, sz = self.q
ow, ox, oy, oz = other.q
return Quaternion([sw * ow - sx * ox - sy * oy - sz * oz,
sw * ox + sx * ow + sy * oz - sz * oy,
sw * oy + sy * ow + sz * ox - sx * oz,
sw * oz + sz * ow + sx * oy - sy * ox])
def conjugate(self):
return Quaternion(-self.q * np.array([-1., 1., 1., 1.]))
def rotate(self, vector):
"""Apply the rotation matrix to a vector."""
qw, qx, qy, qz = self.q[0], self.q[1], self.q[2], self.q[3]
x, y, z = vector[0], vector[1], vector[2]
ww = qw * qw
xx = qx * qx
yy = qy * qy
zz = qz * qz
wx = qw * qx
wy = qw * qy
wz = qw * qz
xy = qx * qy
xz = qx * qz
yz = qy * qz
return np.array(
[(ww + xx - yy - zz) * x + 2 * ((xy - wz) * y + (xz + wy) * z),
(ww - xx + yy - zz) * y + 2 * ((xy + wz) * x + (yz - wx) * z),
(ww - xx - yy + zz) * z + 2 * ((xz - wy) * x + (yz + wx) * y)])
def rotation_matrix(self):
qw, qx, qy, qz = self.q[0], self.q[1], self.q[2], self.q[3]
ww = qw * qw
xx = qx * qx
yy = qy * qy
zz = qz * qz
wx = qw * qx
wy = qw * qy
wz = qw * qz
xy = qx * qy
xz = qx * qz
yz = qy * qz
return np.array([[ww + xx - yy - zz, 2 * (xy + wz), 2 * (xz - wy)],
[2 * (xy - wz), ww - xx + yy - zz, 2 * (yz + wx)],
[2 * (xz + wy), 2 * (yz - wx), ww - xx - yy + zz]])
def axis_angle(self):
"""Returns axis and angle (in radians) for the rotation described
by this Quaternion"""
sinth_2 = np.linalg.norm(self.q[1:])
theta = np.arctan2(sinth_2, self.q[0])*2
n = self.q[1:]/sinth_2
return n, theta
def euler_angles(self, mode='zyz'):
"""Return three Euler angles describing the rotation, in radians.
Mode can be zyz or zxz. Default is zyz."""
if mode == 'zyz':
# These are (a+c)/2 and (a-c)/2 respectively
apc = np.arctan2(self.q[3], self.q[0])
amc = np.arctan2(-self.q[1], self.q[2])
a, c = (apc+amc), (apc-amc)
cos_amc = np.cos(amc)
if cos_amc != 0:
sinb2 = self.q[2]/cos_amc
else:
sinb2 = -self.q[1]/np.sin(amc)
cos_apc = np.cos(apc)
if cos_apc != 0:
cosb2 = self.q[0]/cos_apc
else:
cosb2 = self.q[3]/np.sin(apc)
b = np.arctan2(sinb2, cosb2)*2
elif mode == 'zxz':
# These are (a+c)/2 and (a-c)/2 respectively
apc = np.arctan2(self.q[3], self.q[0])
amc = np.arctan2(self.q[2], self.q[1])
a, c = (apc+amc), (apc-amc)
cos_amc = np.cos(amc)
if cos_amc != 0:
sinb2 = self.q[1]/cos_amc
else:
sinb2 = self.q[2]/np.sin(amc)
cos_apc = np.cos(apc)
if cos_apc != 0:
cosb2 = self.q[0]/cos_apc
else:
cosb2 = self.q[3]/np.sin(apc)
b = np.arctan2(sinb2, cosb2)*2
else:
raise ValueError('Invalid Euler angles mode {0}'.format(mode))
return np.array([a, b, c])
def arc_distance(self, other):
"""Gives a metric of the distance between two quaternions,
expressed as 1-|q1.q2|"""
return 1.0 - np.abs(np.dot(self.q, other.q))
@staticmethod
def rotate_byq(q, vector):
"""Apply the rotation matrix to a vector."""
qw, qx, qy, qz = q[0], q[1], q[2], q[3]
x, y, z = vector[0], vector[1], vector[2]
ww = qw * qw
xx = qx * qx
yy = qy * qy
zz = qz * qz
wx = qw * qx
wy = qw * qy
wz = qw * qz
xy = qx * qy
xz = qx * qz
yz = qy * qz
return np.array(
[(ww + xx - yy - zz) * x + 2 * ((xy - wz) * y + (xz + wy) * z),
(ww - xx + yy - zz) * y + 2 * ((xy + wz) * x + (yz - wx) * z),
(ww - xx - yy + zz) * z + 2 * ((xz - wy) * x + (yz + wx) * y)])
@staticmethod
def from_matrix(matrix):
"""Build quaternion from rotation matrix."""
m = np.array(matrix)
assert m.shape == (3, 3)
# Now we need to find out the whole quaternion
# This method takes into account the possibility of qw being nearly
# zero, so it picks the stablest solution
if m[2, 2] < 0:
if (m[0, 0] > m[1, 1]):
# Use x-form
qx = np.sqrt(1 + m[0, 0] - m[1, 1] - m[2, 2]) / 2.0
fac = 1.0 / (4 * qx)
qw = (m[2, 1] - m[1, 2]) * fac
qy = (m[0, 1] + m[1, 0]) * fac
qz = (m[0, 2] + m[2, 0]) * fac
else:
# Use y-form
qy = np.sqrt(1 - m[0, 0] + m[1, 1] - m[2, 2]) / 2.0
fac = 1.0 / (4 * qy)
qw = (m[0, 2] - m[2, 0]) * fac
qx = (m[0, 1] + m[1, 0]) * fac
qz = (m[1, 2] + m[2, 1]) * fac
else:
if (m[0, 0] < -m[1, 1]):
# Use z-form
qz = np.sqrt(1 - m[0, 0] - m[1, 1] + m[2, 2]) / 2.0
fac = 1.0 / (4 * qz)
qw = (m[1, 0] - m[0, 1]) * fac
qx = (m[2, 0] + m[0, 2]) * fac
qy = (m[1, 2] + m[2, 1]) * fac
else:
# Use w-form
qw = np.sqrt(1 + m[0, 0] + m[1, 1] + m[2, 2]) / 2.0
fac = 1.0 / (4 * qw)
qx = (m[2, 1] - m[1, 2]) * fac
qy = (m[0, 2] - m[2, 0]) * fac
qz = (m[1, 0] - m[0, 1]) * fac
return Quaternion(np.array([qw, qx, qy, qz]))
@staticmethod
def from_axis_angle(n, theta):
"""Build quaternion from axis (n, vector of 3 components) and angle
(theta, in radianses)."""
n = np.array(n, float)/np.linalg.norm(n)
return Quaternion(np.concatenate([[np.cos(theta/2.0)],
np.sin(theta/2.0)*n]))
@staticmethod
def from_euler_angles(a, b, c, mode='zyz'):
"""Build quaternion from Euler angles, given in radians. Default
mode is ZYZ, but it can be set to ZXZ as well."""
q_a = Quaternion.from_axis_angle([0, 0, 1], a)
q_c = Quaternion.from_axis_angle([0, 0, 1], c)
if mode == 'zyz':
q_b = Quaternion.from_axis_angle([0, 1, 0], b)
elif mode == 'zxz':
q_b = Quaternion.from_axis_angle([1, 0, 0], b)
else:
raise ValueError('Invalid Euler angles mode {0}'.format(mode))
return q_c*q_b*q_a
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