# Source code for gyroid.space_group

```# -*- coding: utf-8 -*-
"""
gyroid.space_group
==================

"""

import numpy as np
from numpy.linalg import inv

from .symmetry import Symmetry

__all__ = ["symmetry_generator1",
"symmetry_generator2",
"symmetry_generator3"
]

[docs]def symmetry_generator1(ITA_number,b,h):
''' Output 1D space point group symmetry generators.

There are **2** 1D space groups.
Currently, all 1D space groups are supported::

[1, 2]

:param ITA_number: 1 for P1, 2 for P-1
:type ITA_number: integer
:param b: basis type
:type b: string
:param h: the shape of a unit cell
:type h: :class:`Shape`
:returns: the minimun number of symmetries which can be further expanded to the full set of point group symmetries
:rtype: a list of :class:`Symmetry` objects

'''

I = np.eye(1)
t0 = np.zeros(1)
sI = Symmetry(1,b,h,I,t0)
if ITA_number == 1:
return [sI]
elif ITA_number == 2:
return [sI,
Symmetry(1,b,h,-1.0*I,t0)
]
else:
raise ValueError('ITA number is not 1D.')

[docs]def symmetry_generator2(ITA_number,b,h):
''' Output 2D space point group symmetry generators.

There are **17** 2D space groups.
Currently, Only following 2D space groups are supported::

[1,2,3,4,5,6,17]

:param ITA_number: a sequential number as given in the International Tables for Crystallography, Vol. A, allowed range `[1,17]`
:type ITA_number: integer
:param b: basis type
:type b: string
:param h: the shape of a unit cell
:type h: :class:`Shape`
:returns: the minimun number of symmetries which can be further expande to the full set of point group symmetries
:rtype: a list of :class:`Symmetry` objects

'''

I = np.eye(2)
t0 = np.zeros(2)
sI = Symmetry(2,b,h,I,t0)
# q = 1/4, r = 3/4, s= 1/2, o = 1/8
# Rotation
R200 = np.array([[-1., 0.],
[ 0.,-1.]])

R20y = np.array([[-1.,0.],
[ 0.,1.]])

R300 = np.array([[0.,-1.],
[1.,-1.]])

Rmxx = np.array([[ 0.,-1.],
[-1., 0.]])

Rmx0 = np.array([[1., 0.],
[0.,-1.]])
# Translation
t0s = np.array([.0,.5])
ts0 = np.array([.5,.0])
tss = np.array([.5,.5])

if ITA_number == 1:
# P1, Oblique
return [sI]

if ITA_number == 2:
# P2, Oblique
return [sI,
Symmetry(2,b,h,R200,t0)
]

if ITA_number == 3:
# Pm, Rectangular
return [sI,
Symmetry(2,b,h,R20y,t0)
]

if ITA_number == 4:
# Pg, Rectangular
return [sI,
Symmetry(2,b,h,R20y,t0s)
]

if ITA_number == 5:
# cm, Rectangular
return [sI,
Symmetry(2,b,h,R20y,t0),
Symmetry(2,b,h,I,tss)
]

if ITA_number == 6:
# P2mm, Rectangular
return [sI,
Symmetry(2,b,h,R20y,t0),
Symmetry(2,b,h,R200,t0)
]

if ITA_number == 17:
# "P6mm 2D", Hexagonal
return [sI,
Symmetry(2,b,h,R300,t0),
Symmetry(2,b,h,R200,t0),
Symmetry(2,b,h,Rmxx,t0)
]

raise ValueError('ITA number not supported.')

[docs]def symmetry_generator3(ITA_number,b,h):
''' Output 3D space point group symmetry generators.

There are **230** 3D space groups. The symmetry generators can
be found at http://cryst.ehu.es/cryst/get_gen.html.
Currently, the supported 3D space groups are::

[183, 229, 230]

:param ITA_number: a sequential number as given in the International Tables for Crystallography, Vol. A, allowed range `[1,17]`
:type ITA_number: integer
:param b: basis type
:type b: string
:param h: the shape of a unit cell
:type h: :class:`Shape`
:returns: the minimun number of symmetries which can be further expande to the full set of point group symmetries
:rtype: a list of :class:`Symmetry`

'''

I = np.eye(3)
t0 = np.zeros(3)
sI = Symmetry(3,b,h,I,t0)
# q = 1/4, r = 3/4, s= 1/2, o = 1/8
# Rotation
R300z = np.array([[0.,-1.,0.],
[1.,-1.,0.],
[0., 0.,1.]])

R200z = np.array([[-1., 0.,0.],
[ 0.,-1.,0.],
[ 0., 0.,1.]])

R20y0 = np.array([[-1.,0., 0.],
[ 0.,1., 0.],
[ 0.,0.,-1.]])

Rmxxz = np.array([[ 0.,-1.,0.],
[-1., 0.,0.],
[ 0., 0.,1.]])

R2q0z = np.array([[-1., 0.,0.],
[ 0.,-1.,0.],
[ 0., 0.,1.]])

R20yq = np.array([[-1.,0., 0.],
[ 0.,1., 0.],
[ 0.,0.,-1.]])

R3xxx = np.array([[0.,0.,1.],
[1.,0.,0.],
[0.,1.,0.]])

R2xxo = np.array([[0.,1., 0.],
[1.,0., 0.],
[0.,0.,-1.]])

R2xx0 = np.array([[0.,1., 0.],
[1.,0., 0.],
[0.,0.,-1.]])

R1000 = np.array([[-1., 0., 0.],
[ 0.,-1., 0.],
[ 0., 0.,-1.]])
# Translation
Ts0s = np.array([.5,.0,.5])
T0ss = np.array([.0,.5,.5])
Trqq = np.array([.75,.25,.25])
Tsss = np.array([.5,.5,.5])

if ITA_number == 183:
# "P6mm 3D", Hexagonal
return [sI,
Symmetry(3,b,h,R300z,t0),
Symmetry(3,b,h,R200z,t0),
Symmetry(3,b,h,Rmxxz,t0)
]
if ITA_number == 229:
# "Im-3m 3D", Cubic
return [sI,
Symmetry(3,b,h,R200z,t0),
Symmetry(3,b,h,R20y0,t0),
Symmetry(3,b,h,R3xxx,t0),
Symmetry(3,b,h,R2xx0,t0),
Symmetry(3,b,h,R1000,t0),
Symmetry(3,b,h,I,Tsss)
]

if ITA_number == 230:
# "Ia-3d 3D", Cubic
return [sI,
Symmetry(3,b,h,R2q0z,Ts0s),
Symmetry(3,b,h,R20yq,T0ss),
Symmetry(3,b,h,R3xxx,t0),
Symmetry(3,b,h,R2xxo,Trqq),
Symmetry(3,b,h,R1000,t0),
Symmetry(3,b,h,I,Tsss)
]
else:
raise ValueError('ITA number not supported.')
```