def orthogonal():
"""
Returns orthogonal symmetry operators
(100)_sa mirroring - RD
(010)_sa mirroring - TD
RD = [[ 1., 0., 0.],
[ 0., -1., 0.],
[ 0., 0., 1.]]
TD = [[-1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]]
v`[sa] = RD[sa,sa] * v[sa]
"""
from cs import reflect, vector_ang
import numpy as np
rxz = reflect(th=0) # rxz xz-plane reflection, v`<- [rxz]v
r = vector_ang(u=[0, 0, 1], th=90)
# matrix that rotates about z-axis by 90degree
ryz = np.zeros((3, 3))
for i in range(3):
for j in range(3):
ryz[i, j] = 0.
for k in range(3):
for l in range(3):
ryz[i, j] = ryz[i, j] + r[k, i] * rxz[k, l] * r[l, j]
RD = rxz
TD = ryz
return RD, TD
def orthogonal():
"""
Returns orthogonal symmetry operators
(100)_sa mirroring - RD
(010)_sa mirroring - TD
RD = [[ 1., 0., 0.],
[ 0., -1., 0.],
[ 0., 0., 1.]]
TD = [[-1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]]
v`[sa] = RD[sa,sa] * v[sa]
"""
from cs import reflect, vector_ang
import numpy as np
rxz = reflect(th = 0) # rxz xz-plane reflection, v`<- [rxz]v
r = vector_ang(u=[0,0,1], th=90)
# matrix that rotates about z-axis by 90degree
ryz = np.zeros((3,3))
for i in range(3):
for j in range(3):
ryz[i,j] = 0.
for k in range(3):
for l in range(3):
ryz[i,j] = ryz[i,j] + r[k,i] * rxz[k,l] * r[l,j]
RD = rxz
TD = ryz
return RD, TD
def rot_vectang(self, th, r):
""" Rotate the given rotation matrix r [ca<-sa] by a
random axis with th degree.
"""
from cs import vector_ang
import numpy as np
delta, phi = self.rot_axis()
v = self.polar2vect(delta, phi)
rot = vector_ang(u=v, th=th)
newr = np.dot(rot, r)
return newr
def rot_vectang(self, th, r):
""" Rotate the given rotation matrix r [ca<-sa] by a
random axis with th degree.
"""
from cs import vector_ang
import numpy as np
delta, phi = self.rot_axis()
v = self.polar2vect(delta, phi)
rot = vector_ang(u=v, th=th)
newr = np.dot(rot, r)
return newr