def test_translations(cell):
from numpy import abs, all
from pylada.crystal import binary, supercell, HFTransform
from pylada.decorations import Transforms
lattice = binary.zinc_blende()
lattice[0].type = ['Si', 'Ge']
lattice[1].type = ['Si', 'Ge', 'C']
# create random structure
structure = supercell(lattice, cell)
hft = HFTransform(lattice, structure)
# these are all the translations
translations = Transforms(lattice).translations(hft)
assert translations.shape == (len(structure) // len(lattice) - 1,
len(structure))
# compute each translation and gets decorations
for atom in structure:
if atom.site != 0:
continue
# create translation
trans = atom.pos - lattice[0].pos
if all(abs(trans) < 1e-8):
continue
# figure out its index
index = hft.index(trans) - 1
for site in structure:
pos = site.pos - lattice[site.site].pos
i = hft.index(pos, site.site)
j = hft.index(pos + trans, site.site)
assert translations[index, i] == j
def test_toarray():
""" Tests label exchange """
from random import choice
from numpy import all, zeros
from pylada.crystal import binary, supercell, HFTransform
from pylada.decorations import Transforms
lattice = binary.zinc_blende()
lattice[0].type = ['Si', 'Ge']
lattice[1].type = ['Si', 'Ge', 'C']
transforms = Transforms(lattice)
lattice = transforms.lattice
for u in range(11):
structure = supercell(lattice, get_cell())
for atom in structure:
atom.type = choice(atom.type)
hft = HFTransform(lattice, structure)
a = transforms.toarray(hft, structure)
b = zeros(len(structure), dtype='int')
for atom in structure:
site = lattice[atom.site]
b[hft.index(atom.pos - site.pos,
atom.site)] = site.type.index(atom.type) + 1
assert all(a == b)
def test_supercell_indices():
from pytest import raises
from random import randint
from numpy import all, abs, dot, array
from pylada.crystal import HFTransform, Structure, supercell
unitcell = array([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]])
lattice = Structure(unitcell).add_atom(0, 0, 0, "Si")
supercell = supercell(
lattice, dot(lattice.cell, [[3, 0, 5], [0, 0, -1], [-2, 1, 2]]))
a = HFTransform(unitcell, supercell)
assert all(abs(a.transform - [[0, 2, 0], [1, 5, -1], [-2, -4, 0]]) < 1e-8)
assert all(abs(a.quotient - [1, 1, 3]) < 1e-8)
all_indices = set()
for atom in supercell:
indices = a.indices(atom.pos)
index = a.index(atom.pos)
assert index not in all_indices, (index, all_indices)
assert all(indices >= 0)
assert all(indices <= a.quotient)
assert index == a.flatten_indices(*indices)
all_indices.add(index)
for i in range(20):
vec = dot(
supercell.cell,
array([randint(-20, 20),
randint(-20, 20),
randint(-20, 20)],
dtype="float64"))
vec += atom.pos
assert all(abs(a.indices(vec) - indices) < 1e-8)
with raises(ValueError):
a.indices(vec + [0.1, 0.1, 0])
assert index == a.index(vec)
with raises(ValueError):
a.index(vec + [0.1, 0.1, 0])
assert len(all_indices) == len(supercell)
def test_deformed_b5(u):
from pytest import raises
from random import randint
from numpy import all, abs, dot, array, concatenate
from pylada.crystal import HFTransform, supercell
lattice = b5(u)
supercell = supercell(lattice,
dot(lattice.cell, [[2, 2, 0], [0, 2, 2], [4, 0, 4]]))
a = HFTransform(lattice.cell, supercell)
assert all(abs(a.transform - [[-1, 1, 1], [1, -1, 1], [5, -3, -1]]) < 1e-8)
assert all(abs(a.quotient - [2, 2, 8]) < 1e-8)
all_indices = set()
others = set()
for atom in supercell:
indices = a.indices(atom.pos - lattice[atom.site].pos)
index = a.index(atom.pos - lattice[atom.site].pos, atom.site)
assert index not in all_indices, (index, all_indices)
assert all(indices >= 0)
assert all(indices <= a.quotient)
all_indices.add(index)
assert str(concatenate((indices, [atom.site]))) not in others
others.add(str(concatenate((indices, [atom.site]))))
for i in range(20):
vec = dot(
supercell.cell,
array([randint(-20, 20),
randint(-20, 20),
randint(-20, 20)],
dtype="float64"))
vec += atom.pos - lattice[atom.site].pos
assert all(abs(a.indices(vec) - indices) < 1e-8)
with raises(ValueError):
a.indices(vec + [0.1, 0.1, 0])
assert index == a.index(vec, atom.site)
with raises(ValueError):
a.index(vec + [0.1, 0.1, 0])
assert len(all_indices) == len(supercell)
def test_indices():
from random import randint
from numpy import all, abs, dot, array
from pytest import raises
from pylada.crystal import HFTransform
unitcell = array([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]])
supercell = array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
a = HFTransform(unitcell, supercell)
assert all(abs(a.transform - [[1, 1, -1], [0, 2, 0], [0, 0, 2]]) < 1e-8)
assert all(abs(a.quotient - [1, 2, 2]) < 1e-8)
for i in range(20):
vec = dot(
supercell,
array([randint(-20, 20),
randint(-20, 20),
randint(-20, 20)],
dtype="float64"))
vec += [0, -0.5, 0.5]
assert all(abs(a.indices(vec) - [0, 1, 1]) < 1e-8)
with raises(ValueError):
a.indices(vec + [0.1, 0.1, 0])
def test_labelexchange():
""" Tests label exchange """
from pylada.crystal import binary, supercell, HFTransform
from pylada.decorations import Transforms
lattice = binary.zinc_blende()
lattice[0].type = ['Si', 'Ge']
lattice[1].type = ['Si', 'Ge', 'C']
transforms = Transforms(lattice)
lattice = transforms.lattice
structure = supercell(lattice, [[8, 0, 0], [0, 0.5, 0.5], [0, -0.5, 0.5]])
species = [
'Ge', 'C', 'Si', 'C', 'Si', 'C', 'Si', 'Si', 'Ge', 'Si', 'Ge', 'Si',
'Ge', 'Si', 'Ge', 'Ge', 'Ge', 'C', 'Ge', 'Si', 'Si', 'Si', 'Si', 'Ge',
'Si', 'Ge', 'Si', 'Si', 'Si', 'C', 'Ge', 'Si'
]
for atom, s in zip(structure, species):
atom.type = s
hft = HFTransform(lattice, structure)
x = transforms.toarray(hft, structure)
results = [
21112222221111123331111231122131, # <- this is x
21112222221111122221111321133121,
21112222221111123332222132211232,
21112222221111121112222312233212,
21112222221111122223333123311323,
21112222221111121113333213322313,
12221111112222213331111231122131,
12221111112222212221111321133121,
12221111112222213332222132211232,
12221111112222211112222312233212,
12221111112222212223333123311323,
12221111112222211113333213322313
]
permutations = transforms.label_exchange(hft)
for a, b in zip(permutations(x), results[1:]):
assert int(str(a)[1:-1].replace(' ', '')) == b
def test_rotations(cell):
from numpy import all, dot, zeros
from numpy.linalg import inv
from pylada.crystal import binary, supercell, HFTransform, space_group, \
which_site
from pylada.decorations import Transforms
lattice = binary.zinc_blende()
lattice[0].type = ['Si', 'Ge']
lattice[1].type = ['Si', 'Ge', 'C']
sg = space_group(lattice)
invcell = inv(lattice.cell)
# create random structure
structure = supercell(lattice, cell)
hft = HFTransform(lattice, structure)
# these are all the translations
transforms = Transforms(lattice)
permutations = transforms.transformations(hft)
assert permutations.shape == (len(sg) - 1, len(structure))
operations = transforms.invariant_ops(structure)
assert any(operations)
# compute each translation and gets decorations
for index, (op, isgood) in enumerate(zip(sg[1:], operations)):
if not isgood:
continue
# Create rotation and figure out its index
permutation = zeros(len(structure), dtype='int') - 1
for atom in structure:
pos = dot(op[:3], atom.pos) + op[3]
newsite = which_site(pos, lattice, invcell)
i = hft.index(atom.pos - lattice[atom.site].pos, atom.site)
j = hft.index(pos - lattice[newsite].pos, newsite)
permutation[i] = j
assert all(permutation == permutations[index])
