/usr/share/pyshared/ase/quaternions.py is in python-ase 3.6.0.2515-1.1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 | import numpy as np
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([[5, 3, 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')
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 __mult__(self, other):
sw, sx, sy, sz = self.q[0], self.q[1], self.q[2], self.q[3]
ow, ox, oy, oz = other.q[0], other.q[1], other.q[2], other.q[3]
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 rotate_byq(self, 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)
])
def from_matrix(self, matrix):
"""Build quaternion from rotation matrix."""
m = np.array(matrix)
assert m.shape == (3, 3)
qw = np.sqrt(1 + m[0, 0] + m[1, 1] + m[2, 2]) / 2.
qx = (m[2, 1] - m[1, 2]) / (4 * qw)
qy = (m[0, 2] - m[2, 0]) / (4 *qw)
qz = (m[1, 0] - m[0, 1]) / (4 *qw)
self.q = np.array([qw, qx, qy, qz])
return self
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