def plot_permutation_groups(base_structure, output_name):
rotations, translations = get_symmetry_operations(base_structure)
displacement_set = base_structure.frac_coords
list_data = []
for index in range(2, 10 + 1):
for hnf in tqdm(generate_all_superlattices(index)):
dsperm = DerivativeStructurePermutation(hnf, displacement_set,
rotations, translations)
perms = [
Permutation(g)
for g in dsperm.get_symmetry_operation_permutations()
]
gens = get_generators(perms)
G = PermutationGroup(gens)
data = {
"index": index,
"hnf": hnf,
"generators": gens,
"group": G,
"order": G.order(),
"orbits": G.orbits(),
}
list_data.append(data)
df = pd.DataFrame(list_data)
sns.swarmplot(x="index", y="order", data=df)
plt.title(output_name)
plt.savefig(output_name + ".png")
return df
def test_number_of_snf():
# confirm table-3
num_hnf_expected = [
1, 7, 13, 35, 31, 91, 57, 155, 130, 217, 133, 455, 183, 399, 403, 651
]
num_snf_expected = [1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4]
max_index = len(num_hnf_expected)
for index, hnf_expected, snf_expected in zip(range(1, max_index + 1),
num_hnf_expected,
num_snf_expected):
list_HNF = generate_all_superlattices(index)
assert len(list_HNF) == hnf_expected
list_SNF = set()
for hnf in list_HNF:
snf, _, _ = smith_normal_form(hnf)
dag = tuple(snf.diagonal())
list_SNF.add(dag)
assert len(list_SNF) == snf_expected
def test_generate_all_superlattices():
# https://oeis.org/A001001
num_expected = [
1,
7,
13,
35,
31,
91,
57,
155,
130,
217,
133,
455,
183,
399,
403,
651,
307,
910,
381,
1085,
741,
931,
553,
2015,
806,
1281,
1210,
1995,
871,
2821,
993,
2667,
1729,
2149,
1767,
4550,
1407,
2667,
2379,
4805,
1723,
5187,
1893,
4655,
4030,
3871,
2257,
8463,
2850,
5642,
3991,
6405,
2863,
]
max_index = len(num_expected)
for index, expected in zip(range(1, max_index + 1), num_expected):
list_HNF = generate_all_superlattices(index)
assert len(list_HNF) == expected