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from itertools import combinations
import numpy as np
import pytest
from operation import MagneticOperation, remainder1_symmetry_operation
from magnetic_hall import MagneticHallSymbol
from transform import Transformation, get_standard_hall_number
from load import get_spg_table, get_msg_table
def test_magnetic_operations():
tc = MagneticOperation.from_linear_translation_time_reversal(
translation=np.array([0, 0, 1 / 2]), time_reversal=True
)
tc2 = tc * tc
assert tc2 == MagneticOperation.from_linear_translation_time_reversal(
translation=np.array([0, 0, 1])
)
# Translation by (0, 0, -1/2) is equivalent to that by (0, 0, 1/2)
assert remainder1_symmetry_operation(tc.inverse()) == tc
@pytest.mark.parametrize(
"hall_symbol,order_expected", [
("P 31 2 1c' (0 0 4)", 2 * 6), # 151.32 (type-IV)
("P 6c 2c' -1'", 24), # 194.265 (type-III)
("F 4d 2 3 1'", 2 * 96), # 210.53 (type-II)
]
)
def test_magnetic_hall_symbol(hall_symbol, order_expected):
mhs = MagneticHallSymbol(hall_symbol)
order_actual = len(mhs.coset)
assert order_actual == order_expected
def test_transformation():
spg_table = get_spg_table()
for hall_number in range(1, 530 + 1):
print(hall_number)
choice = spg_table[hall_number]['choice']
number = spg_table[hall_number]['number']
hall_symbol = spg_table[hall_number]['hall_symbol']
coset_expected = MagneticHallSymbol(hall_symbol).coset
hall_number_std = get_standard_hall_number(number)
hall_symbol_std = spg_table[hall_number_std]['hall_symbol']
coset_std = MagneticHallSymbol(hall_symbol_std).coset
# Transform from ITA standard setting to alternative setting
from_std = Transformation.to_standard(hall_number, choice, number).inverse()
coset_actual = from_std.transform_coset(coset_std)
assert set(coset_actual) == set(coset_expected)
def test_magnetic_hall_table():
# Test MSG table with ITA standard settings
msg_table = get_msg_table()
count = 0
for number in range(1, 230 + 1):
print(f"No. {number}")
hall_number_std = get_standard_hall_number(number)
serial_and_symbols = list(msg_table[hall_number_std].items())
hs_sg = MagneticHallSymbol(serial_and_symbols[0][1]) # type-I
list_msg = []
for bns_number, hall_symbol in serial_and_symbols:
print(f" {bns_number}: {hall_symbol}")
mhs = MagneticHallSymbol(hall_symbol)
assert len(mhs.coset) % len(hs_sg.coset) == 0
index = len(mhs.coset) // len(hs_sg.coset)
# For type-I and type-III, index == 1
# For type-II and type-IV, index == 2
assert (index == 1) or (index == 2)
list_msg.append(set(mhs.coset))
count += 1
# check no duplicates
for i, j in combinations(range(len(list_msg)), r=2):
if list_msg[i] == list_msg[j]:
print(serial_and_symbols[i], serial_and_symbols[j])
assert False
assert count == 1651
def test_all_msg_table():
msg_table = get_msg_table()
spg_table = get_spg_table()
for hall_number in range(1, 530 + 1):
number = spg_table[hall_number]['number']
choice = spg_table[hall_number]['choice']
hall_number_std = get_standard_hall_number(number)
# Transformation from ITA standard settings to the other settings
trns = Transformation.to_standard(hall_number, choice, number).inverse()
for bns_number, mhall_symbol in msg_table[hall_number_std].items():
mhs = MagneticHallSymbol(mhall_symbol)
coset = trns.transform_coset(mhs.coset)
# Check the order of coset
assert len(mhs.coset) % len(coset) == 0
if hall_number in [
434,
437,
445,
451,
453,
459,
461,
]:
# seven rhombohedral space groups
assert len(mhs.coset) // len(coset) == 3
else:
assert len(mhs.coset) == len(coset)
for op in coset:
print(hall_number, bns_number, np.around(op.linear).astype(int))
assert np.isclose(np.abs(np.linalg.det(op.linear)), 1)
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