How to use the orix.quaternion.symmetry.Symmetry function in orix
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pyxem / orix / orix / quaternion / symmetry.py View on Github 
n1 = axis.cross(nearest_diad).unit
n2 = -(r * n1)
n = Vector3d(np.concatenate((n.data, n1.data, n2.data)))
sr = SphericalRegion(n.unique())
return sr
# Triclinic
C1 = Symmetry((1, 0, 0, 0))
C1.name = "1"
Ci = Symmetry([(1, 0, 0, 0), (1, 0, 0, 0)])
Ci.improper = [0, 1]
Ci.name = "-1"
# Special generators
_mirror_xy = Symmetry([(1, 0, 0, 0), (0, 0.75 ** 0.5, -(0.75 ** 0.5), 0)])
_mirror_xy.improper = [0, 1]
_cubic = Symmetry([(1, 0, 0, 0), (0.5, 0.5, 0.5, 0.5)])
# 2-fold rotations
C2x = Symmetry([(1, 0, 0, 0), (0, 1, 0, 0)])
C2x.name = "211"
C2y = Symmetry([(1, 0, 0, 0), (0, 0, 1, 0)])
C2y.name = "121"
C2z = Symmetry([(1, 0, 0, 0), (0, 0, 0, 1)])
C2z.name = "112"
C2 = Symmetry(C2z)
C2.name = "2"
# Mirrors
Csx = Symmetry([(1, 0, 0, 0), (0, 1, 0, 0)])
Csx.improper = [0, 1][
(1, 0, 0, 0),
(0.5 ** 0.5, 0.5 ** 0.5, 0, 0),
(0, 1, 0, 0),
(-(0.5 ** 0.5), 0.5 ** 0.5, 0, 0),
]
)
C4y = Symmetry(
[
(1, 0, 0, 0),
(0.5 ** 0.5, 0, 0.5 ** 0.5, 0),
(0, 0, 1, 0),
(-(0.5 ** 0.5), 0, 0.5 ** 0.5, 0),
]
)
C4z = Symmetry(
[
(1, 0, 0, 0),
(0.5 ** 0.5, 0, 0, 0.5 ** 0.5),
(0, 0, 0, 1),
(-(0.5 ** 0.5), 0, 0, 0.5 ** 0.5),
]
)
C4 = Symmetry(C4z)
C4.name = "4"
# Tetragonal
S4 = Symmetry.from_generators(C2, Ci)
S4.name = "-4"
C4h = Symmetry.from_generators(C4, Cs)
C4h.name = "4/m"
D4 = Symmetry.from_generators(C4, C2x, C2y)n = Vector3d(np.concatenate((n.data, n1.data, n2.data)))
sr = SphericalRegion(n.unique())
return sr
# Triclinic
C1 = Symmetry((1, 0, 0, 0))
C1.name = "1"
Ci = Symmetry([(1, 0, 0, 0), (1, 0, 0, 0)])
Ci.improper = [0, 1]
Ci.name = "-1"
# Special generators
_mirror_xy = Symmetry([(1, 0, 0, 0), (0, 0.75 ** 0.5, -(0.75 ** 0.5), 0)])
_mirror_xy.improper = [0, 1]
_cubic = Symmetry([(1, 0, 0, 0), (0.5, 0.5, 0.5, 0.5)])
# 2-fold rotations
C2x = Symmetry([(1, 0, 0, 0), (0, 1, 0, 0)])
C2x.name = "211"
C2y = Symmetry([(1, 0, 0, 0), (0, 0, 1, 0)])
C2y.name = "121"
C2z = Symmetry([(1, 0, 0, 0), (0, 0, 0, 1)])
C2z.name = "112"
C2 = Symmetry(C2z)
C2.name = "2"
# Mirrors
Csx = Symmetry([(1, 0, 0, 0), (0, 1, 0, 0)])
Csx.improper = [0, 1]
Csx.name = "m11"
Csy = Symmetry([(1, 0, 0, 0), (0, 0, 1, 0)])>>> myS4.improper = [0, 1]
>>> mySymmetry = Symmetry.from_generators(myC2, myS4)
>>> mySymmetry
Symmetry (8,)
[[ 1. 0. 0. 0. ]
[ 0. 0.7071 -0.7071 0. ]
[ 0.7071 0. 0. 0.7071]
[ 0. 0. -1. 0. ]
[ 0. 1. 0. 0. ]
[-0.7071 0. 0. 0.7071]
[ 0. 0. 0. 1. ]
[ 0. -0.7071 -0.7071 0. ]]
"""
generator = cls((1, 0, 0, 0))
for g in generators:
generator = generator.outer(Symmetry(g)).unique()
size = 1
size_new = generator.size
while size_new != size and size_new < 48:
size = size_new
generator = generator.outer(generator).unique()
size_new = generator.size
return generator
# Tetragonal
S4 = Symmetry.from_generators(C2, Ci)
S4.name = "-4"
C4h = Symmetry.from_generators(C4, Cs)
C4h.name = "4/m"
D4 = Symmetry.from_generators(C4, C2x, C2y)
D4.name = "422"
C4v = Symmetry.from_generators(C4, Csx)
C4v.name = "4mm"
D2d = Symmetry.from_generators(D2, _mirror_xy)
D2d.name = "-42m"
D4h = Symmetry.from_generators(C4h, Csx, Csy)
D4h.name = "4/mmm"
# 3-fold rotations
C3x = Symmetry([(1, 0, 0, 0), (0.5, 0.75 ** 0.5, 0, 0), (-0.5, 0.75 ** 0.5, 0, 0)])
C3y = Symmetry([(1, 0, 0, 0), (0.5, 0, 0.75 ** 0.5, 0), (-0.5, 0, 0.75 ** 0.5, 0)])
C3z = Symmetry([(1, 0, 0, 0), (0.5, 0, 0, 0.75 ** 0.5), (-0.5, 0, 0, 0.75 ** 0.5)])
C3 = Symmetry(C3z)
C3.name = "3"
# Trigonal
S6 = Symmetry.from_generators(C3, Ci)
S6.name = "-3"
D3x = Symmetry.from_generators(C3, C2x)
D3x.name = "321"
D3y = Symmetry.from_generators(C3, C2y)
D3y.name = "312"
D3 = Symmetry(D3x)
D3.name = "32"
C3v = Symmetry.from_generators(C3, Csx)
C3v.name = "3m"# 2-fold rotations
C2x = Symmetry([(1, 0, 0, 0), (0, 1, 0, 0)])
C2x.name = "211"
C2y = Symmetry([(1, 0, 0, 0), (0, 0, 1, 0)])
C2y.name = "121"
C2z = Symmetry([(1, 0, 0, 0), (0, 0, 0, 1)])
C2z.name = "112"
C2 = Symmetry(C2z)
C2.name = "2"
# Mirrors
Csx = Symmetry([(1, 0, 0, 0), (0, 1, 0, 0)])
Csx.improper = [0, 1]
Csx.name = "m11"
Csy = Symmetry([(1, 0, 0, 0), (0, 0, 1, 0)])
Csy.improper = [0, 1]
Csy.name = "1m1"
Csz = Symmetry([(1, 0, 0, 0), (0, 0, 0, 1)])
Csz.improper = [0, 1]
Csz.name = "11m"
Cs = Symmetry(Csz)
Cs.name = "m"
# Monoclinic
C2h = Symmetry.from_generators(C2, Cs)
C2h.name = "2/m"
# Orthorhombic
D2 = Symmetry.from_generators(C2z, C2x, C2y)
D2.name = "222"
C2v = Symmetry.from_generators(C2x, Csz)# 3-fold rotations
C3x = Symmetry([(1, 0, 0, 0), (0.5, 0.75 ** 0.5, 0, 0), (-0.5, 0.75 ** 0.5, 0, 0)])
C3y = Symmetry([(1, 0, 0, 0), (0.5, 0, 0.75 ** 0.5, 0), (-0.5, 0, 0.75 ** 0.5, 0)])
C3z = Symmetry([(1, 0, 0, 0), (0.5, 0, 0, 0.75 ** 0.5), (-0.5, 0, 0, 0.75 ** 0.5)])
C3 = Symmetry(C3z)
C3.name = "3"
# Trigonal
S6 = Symmetry.from_generators(C3, Ci)
S6.name = "-3"
D3x = Symmetry.from_generators(C3, C2x)
D3x.name = "321"
D3y = Symmetry.from_generators(C3, C2y)
D3y.name = "312"
D3 = Symmetry(D3x)
D3.name = "32"
C3v = Symmetry.from_generators(C3, Csx)
C3v.name = "3m"
D3d = Symmetry.from_generators(S6, Csx)
D3d.name = "-3m"
# Hexagonal
C6 = Symmetry.from_generators(C3, C2)
C6.name = "6"
C3h = Symmetry.from_generators(C3, Cs)
C3h.name = "-6"
C6h = Symmetry.from_generators(C6, Cs)
C6h.name = "6/m"
D6 = Symmetry.from_generators(C6, C2x, C2y)
D6.name = "622"
C6v = Symmetry.from_generators(C6, Csx)C4h = Symmetry.from_generators(C4, Cs)
C4h.name = "4/m"
D4 = Symmetry.from_generators(C4, C2x, C2y)
D4.name = "422"
C4v = Symmetry.from_generators(C4, Csx)
C4v.name = "4mm"
D2d = Symmetry.from_generators(D2, _mirror_xy)
D2d.name = "-42m"
D4h = Symmetry.from_generators(C4h, Csx, Csy)
D4h.name = "4/mmm"
# 3-fold rotations
C3x = Symmetry([(1, 0, 0, 0), (0.5, 0.75 ** 0.5, 0, 0), (-0.5, 0.75 ** 0.5, 0, 0)])
C3y = Symmetry([(1, 0, 0, 0), (0.5, 0, 0.75 ** 0.5, 0), (-0.5, 0, 0.75 ** 0.5, 0)])
C3z = Symmetry([(1, 0, 0, 0), (0.5, 0, 0, 0.75 ** 0.5), (-0.5, 0, 0, 0.75 ** 0.5)])
C3 = Symmetry(C3z)
C3.name = "3"
# Trigonal
S6 = Symmetry.from_generators(C3, Ci)
S6.name = "-3"
D3x = Symmetry.from_generators(C3, C2x)
D3x.name = "321"
D3y = Symmetry.from_generators(C3, C2y)
D3y.name = "312"
D3 = Symmetry(D3x)
D3.name = "32"
C3v = Symmetry.from_generators(C3, Csx)
C3v.name = "3m"
D3d = Symmetry.from_generators(S6, Csx)
D3d.name = "-3m"if isinstance(next(iter(phases.values())), Phase):
d = phases
except StopIteration:
pass
elif isinstance(phases, Phase):
if ids is None:
ids = 0
d = {ids: phases}
else:
# Ensure possible single strings or single objects have
# iterables of length 1
if isinstance(names, str):
names = list((names,))
if (
isinstance(symmetries, str)
or isinstance(symmetries, Symmetry)
or isinstance(symmetries, int)
):
symmetries = list((symmetries,))
if isinstance(colors, str) or isinstance(colors, tuple):
colors = list((colors,))
if isinstance(ids, int):
ids = [ids]
if isinstance(structures, Structure):
structures = [structures]
# Get the maximum number of entries in the input lists (also
# handling the case where some lists are None)
max_entries = max(
[
len(i) if i is not None else 0
for i in [names, symmetries, ids, structures]orix
orix is an open-source Python library for handling crystal orientation mapping data
Package Health Score
81 / 100Popular orix functions
- orix.base.Object3d
- orix.crystal_map.CrystalMap
- orix.crystal_map.Phase
- orix.crystal_map.phase_list.Phase
- orix.crystal_map.PhaseList
- orix.quaternion.orientation.Orientation
- orix.quaternion.Quaternion
- orix.quaternion.rotation.Rotation
- orix.quaternion.rotation.Rotation.from_euler
- orix.quaternion.rotation.Rotation.from_neo_euler
- orix.quaternion.rotation.Rotation.stack
- orix.quaternion.symmetry.Symmetry
- orix.quaternion.symmetry.Symmetry.from_generators
- orix.scalar.Scalar
- orix.vector.__init__.Vector3d
- orix.vector.neo_euler.AxAngle
- orix.vector.neo_euler.AxAngle.from_axes_angles
- orix.vector.Vector3d
- orix.vector.Vector3d.from_polar
- orix.vector.Vector3d.zvector