def _get_transformation_string_from_Pp(P: Union[List[List[float]],
np.ndarray],
p: List[float]) -> str:
P = np.array(P).transpose()
P_string = transformation_to_string(P, components=("a", "b", "c"))
p_string = transformation_to_string(np.zeros((3, 3)), p)
return P_string + ";" + p_string
def test_transformation_to_string(self):
m = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
t = [0, 0, 0]
s = "x,y,z"
ms = "mx,my,mz"
abc = "a,b,c"
self.assertEqual(s, transformation_to_string(m, t))
self.assertEqual(ms, transformation_to_string(m, t, c="m"))
self.assertEqual(
abc, transformation_to_string(m, t, components=("a", "b", "c"))
)
m = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
t = [11, 12, 13]
s = "x+2y+3z+11,4x+5y+6z+12,7x+8y+9z+13"
self.assertEqual(s, transformation_to_string(m, t))
m = [
[-1 / 2, -2 / 3, -3 / 4],
[-5 / 6, -6 / 7, -7 / 8],
[-8 / 9, -9 / 10, -10 / 11],
]
t = [-11 / 12, -12 / 13, -13 / 14]
s = "-x/2-2y/3-3z/4-11/12,-5x/6-6y/7-7z/8-12/13,-8x/9-9y/10-10z/11-13/14"
self.assertEqual(s, transformation_to_string(m, t))
def _parse_wyckoff(b):
"""Parses compact binary representation into list of Wyckoff sites."""
if len(b) == 0:
return None
wyckoff_sites = []
def get_label(idx):
if idx <= 25:
return chr(97 + idx) # returns a-z when idx 0-25
return "alpha" # when a-z labels exhausted, use alpha, only relevant for a few space groups
o = 0 # offset
n = 1 # nth Wyckoff site
num_wyckoff = b[0]
while len(wyckoff_sites) < num_wyckoff:
m = b[1 + o] # multiplicity
label = str(b[2 + o] * m) + get_label(num_wyckoff - n)
sites = []
for j in range(m):
s = b[
3 + o + (j * 22):3 + o + (j * 22) +
22] # data corresponding to specific Wyckoff position
translation_vec = [s[0] / s[3], s[1] / s[3], s[2] / s[3]]
matrix = [
[s[4], s[7], s[10]],
[s[5], s[8], s[11]],
[s[6], s[9], s[12]],
]
matrix_magmom = [
[s[13], s[16], s[19]],
[s[14], s[17], s[20]],
[s[15], s[18], s[21]],
]
# store string representation, e.g. (x,y,z;mx,my,mz)
wyckoff_str = "({};{})".format(
transformation_to_string(matrix, translation_vec),
transformation_to_string(matrix_magmom, c="m"),
)
sites.append({
"translation_vec": translation_vec,
"matrix": matrix,
"matrix_magnetic": matrix_magmom,
"str": wyckoff_str,
})
# only keeping string representation of Wyckoff sites for now
# could do something else with these in future
wyckoff_sites.append({
"label": label,
"str": " ".join([s["str"] for s in sites])
})
n += 1
o += m * 22 + 2
return wyckoff_sites
def _parse_wyckoff(b):
'''Parses compact binary representation into list of Wyckoff sites.'''
if len(b) == 0:
return None
wyckoff_sites = []
def get_label(idx):
if idx <= 25:
return chr(97+idx) # returns a-z when idx 0-25
else:
return 'alpha' # when a-z labels exhausted, use alpha, only relevant for a few space groups
o = 0 # offset
n = 1 # nth Wyckoff site
num_wyckoff = b[0]
while len(wyckoff_sites) < num_wyckoff:
m = b[1+o] # multiplicity
label = str(b[2+o]*m)+get_label(num_wyckoff-n)
sites = []
for j in range(m):
s = b[3+o+(j*22):3+o+(j*22)+22] # data corresponding to specific Wyckoff position
translation_vec = [s[0]/s[3], s[1]/s[3], s[2]/s[3]]
matrix = [[s[4], s[5], s[6]],
[s[7], s[8], s[9]],
[s[10], s[11], s[12]]]
matrix_magmom = [[s[13], s[14], s[15]],
[s[16], s[17], s[18]],
[s[19], s[20], s[21]]]
# store string representation, e.g. (x,y,z;mx,my,mz)
wyckoff_str = "({};{})".format(transformation_to_string(matrix, translation_vec),
transformation_to_string(matrix_magmom, c='m'))
sites.append({'translation_vec': translation_vec,
'matrix': matrix,
'matrix_magnetic': matrix_magmom,
'str': wyckoff_str})
# only keeping string representation of Wyckoff sites for now
# could do something else with these in future
wyckoff_sites.append({'label': label,
'str': ' '.join([s['str'] for s in sites])})
n += 1
o += m*22 + 2
return wyckoff_sites
def test_transformation_to_string(self):
m = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
t = [0, 0, 0]
s = 'x,y,z'
ms = 'mx,my,mz'
abc = 'a,b,c'
self.assertEqual(s, transformation_to_string(m, t))
self.assertEqual(ms, transformation_to_string(m, t, c='m'))
self.assertEqual(abc, transformation_to_string(m, t, components=('a', 'b', 'c')))
m = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
t = [11, 12, 13]
s = 'x+2y+3z+11,4x+5y+6z+12,7x+8y+9z+13'
self.assertEqual(s, transformation_to_string(m, t))
m = [[-1 / 2, -2 / 3, -3 / 4], [-5 / 6, -6 / 7, -7 / 8], [-8 / 9, -9 / 10, -10 / 11]]
t = [-11 / 12, -12 / 13, -13 / 14]
s = '-x/2-2y/3-3z/4-11/12,-5x/6-6y/7-7z/8-12/13,-8x/9-9y/10-10z/11-13/14'
self.assertEqual(s, transformation_to_string(m, t))
def test_transformation_to_string(self):
m = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
t = [0, 0, 0]
s = 'x,y,z'
ms = 'mx,my,mz'
abc = 'a,b,c'
self.assertEqual(s, transformation_to_string(m, t))
self.assertEqual(ms, transformation_to_string(m, t, c='m'))
self.assertEqual(abc, transformation_to_string(m, t, components=('a', 'b', 'c')))
m = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
t = [11, 12, 13]
s = 'x+2y+3z+11,4x+5y+6z+12,7x+8y+9z+13'
self.assertEqual(s, transformation_to_string(m, t))
m = [[-1 / 2, -2 / 3, -3 / 4], [-5 / 6, -6 / 7, -7 / 8], [-8 / 9, -9 / 10, -10 / 11]]
t = [-11 / 12, -12 / 13, -13 / 14]
s = '-x/2-2y/3-3z/4-11/12,-5x/6-6y/7-7z/8-12/13,-8x/9-9y/10-10z/11-13/14'
self.assertEqual(s, transformation_to_string(m, t))
def as_xyz_string(self):
"""
Returns a string of the form 'x, y, z', '-x, -y, z',
'-y+1/2, x+1/2, z+1/2', etc. Only works for integer rotation matrices
"""
# test for invalid rotation matrix
if not np.all(np.isclose(self.rotation_matrix,
np.round(self.rotation_matrix))):
warnings.warn('Rotation matrix should be integer')
return transformation_to_string(self.rotation_matrix, translation_vec=self.translation_vector, delim=", ")
def as_xyz_string(self):
"""
Returns a string of the form 'x, y, z', '-x, -y, z',
'-y+1/2, x+1/2, z+1/2', etc. Only works for integer rotation matrices
"""
xyz = ['x', 'y', 'z']
strings = []
# test for invalid rotation matrix
if not np.all(np.isclose(self.rotation_matrix,
np.round(self.rotation_matrix))):
warnings.warn('Rotation matrix should be integer')
return transformation_to_string(self.rotation_matrix, translation_vec=self.translation_vector, delim=", ")
def _parse_transformation(b):
"""Parses compact binary representation into transformation between OG and BNS settings."""
if len(b) == 0:
return None
# capital letters used here by convention,
# IUCr defines P and p specifically
P = [[b[0], b[3], b[6]], [b[1], b[4], b[7]], [b[2], b[5], b[8]]]
p = [b[9] / b[12], b[10] / b[12], b[11] / b[12]]
P = np.array(P).transpose()
P_string = transformation_to_string(P, components=("a", "b", "c"))
p_string = (f"{Fraction(p[0]).limit_denominator()},"
f"{Fraction(p[1]).limit_denominator()},"
f"{Fraction(p[2]).limit_denominator()}")
return P_string + ";" + p_string
def _parse_transformation(b):
'''Parses compact binary representation into transformation between OG and BNS settings.'''
if len(b) == 0:
return None
# capital letters used here by convention,
# IUCr defines P and p specifically
P = [[b[0], b[1], b[2]], [b[3], b[4], b[5]], [b[6], b[7], b[8]]]
p = [b[9] / b[12], b[10] / b[12], b[11] / b[12]]
P = np.array(P).transpose()
P_string = transformation_to_string(P, components=('a', 'b', 'c'))
p_string = "{},{},{}".format(
Fraction(p[0]).limit_denominator(),
Fraction(p[1]).limit_denominator(),
Fraction(p[2]).limit_denominator())
return P_string + ";" + p_string
def _parse_transformation(b):
'''Parses compact binary representation into transformation between OG and BNS settings.'''
if len(b) == 0:
return None
# capital letters used here by convention,
# IUCr defines P and p specifically
P = [[b[0], b[1], b[2]],
[b[3], b[4], b[5]],
[b[6], b[7], b[8]]]
p = [b[9]/b[12], b[10]/b[12], b[11]/b[12]]
P = np.array(P).transpose()
P_string = transformation_to_string(P, components=('a', 'b', 'c'))
p_string = "{},{},{}".format(Fraction(p[0]).limit_denominator(),
Fraction(p[1]).limit_denominator(),
Fraction(p[2]).limit_denominator())
return P_string + ";" + p_string
def _get_transformation_string_from_Pp(P, p):
# type: (List[List[float]], List[float]) -> str
P = np.array(P).transpose()
P_string = transformation_to_string(P, components=('a', 'b', 'c'))
p_string = transformation_to_string(np.zeros((3, 3)), p)
return P_string+";"+p_string