def test_zb():
from numpy import all, abs, dot
from pylada.crystal import space_group, transform, binary
structure = binary.zinc_blende()
ops = space_group(structure)
assert len(ops) == 24
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
for atom in structure:
atom.type = ['A', 'B']
ops = space_group(structure)
assert len(ops) == 48
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
def test_zb():
from numpy import all, abs, dot
from pylada.crystal import space_group, transform, binary
structure = binary.zinc_blende()
ops = space_group(structure)
assert len(ops) == 24
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
for atom in structure:
atom.type = ['A', 'B']
ops = space_group(structure)
assert len(ops) == 48
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
def test_fcc():
""" Test fcc space-group """
from numpy import all, abs, dot
from pylada.crystal import space_group, Structure, transform
structure = Structure([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]],
m=True).add_atom(0, 0, 0, "Si", m=True)
ops = space_group(structure)
assert len(ops) == 48
for op in ops:
assert op.shape == (4, 3)
assert all(abs(op[3, :]) < 1e-8)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
assert getattr(other, 'm', False)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
assert getattr(atom, 'm', False)
def test_fcc():
""" Test fcc space-group """
from numpy import all, abs, dot
from pylada.crystal import space_group, Structure, transform
structure = Structure([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]],
m=True).add_atom(0, 0, 0, "Si", m=True)
ops = space_group(structure)
assert len(ops) == 48
for op in ops:
assert op.shape == (4, 3)
assert all(abs(op[3,:]) < 1e-8)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
assert getattr(other, 'm', False)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
assert getattr(atom, 'm', False)
def test_b5(u):
""" Test b5 space-group """
from random import random, randint
from numpy import all, abs, dot, pi
from numpy.linalg import inv, norm
from numpy.random import random_sample
from pylada.crystal import space_group, Structure, transform
from pylada.crystal import which_site
x, y = u, 0.25 - u
structure = Structure([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]]) \
.add_atom(5.000000e-01, 5.000000e-01, 5.000000e-01, "A") \
.add_atom(5.000000e-01, 2.500000e-01, 2.500000e-01, "A") \
.add_atom(2.500000e-01, 5.000000e-01, 2.500000e-01, "A") \
.add_atom(2.500000e-01, 2.500000e-01, 5.000000e-01, "A") \
.add_atom(8.750000e-01, 8.750000e-01, 8.750000e-01, "B") \
.add_atom(1.250000e-01, 1.250000e-01, 1.250000e-01, "B") \
.add_atom( x, x, x, "X") \
.add_atom( x, y, y, "X") \
.add_atom( y, x, y, "X") \
.add_atom( y, y, x, "X") \
.add_atom( -x, -x, -x, "X") \
.add_atom( -x, -y, -y, "X") \
.add_atom( -y, -x, -y, "X") \
.add_atom(-y, -y, -x, "X")
ops = space_group(structure)
assert len(ops) == 48
invcell = inv(structure.cell)
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
sites = []
for i, atom in enumerate(structure):
pos = dot(op[:3], atom.pos) + op[3]
j = which_site(pos, structure, invcell)
assert j != -1
sites.append(j)
assert len(set(sites)) == len(structure)
structure[0], structure[-1] = structure[-1], structure[0]
ops = space_group(structure)
assert len(ops) == 48
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
sites = []
for i, atom in enumerate(structure):
pos = dot(op[:3], atom.pos) + op[3]
j = which_site(pos, structure, invcell)
assert j != -1, (i, atom, op)
sites.append(j)
assert len(set(sites)) == len(structure)
# try random rotation, translations, atom swap
structure[0], structure[-1] = structure[-1], structure[0]
for u in range(10):
axis = random_sample((3, ))
axis /= norm(axis)
rotation = rotation_matrix(pi * random(), axis)
translation = random_sample((3, ))
other = transform(structure, rotation, translation)
for u in range(10):
l, m = randint(0,
len(structure) - 1), randint(0,
len(structure) - 1)
a, b = other[l], other[m]
other[l], other[m] = b, a
invcell = inv(other.cell)
ops = space_group(other)
for z, op in enumerate(ops):
assert op.shape == (4, 3)
other2 = transform(other, op)
assert all(abs(dot(op[:3], other.cell) - other2.cell) < 1e-8)
for a, atom in zip(other, other2):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
sites = []
for i, atom in enumerate(other):
pos = dot(op[:3], atom.pos) + op[3]
j = which_site(pos, other, invcell)
if j == -1:
print((i, z))
print(atom)
print(op)
print(pos)
print(other)
raise Exception()
sites.append(j)
assert len(set(sites)) == len(other)
def test_b5(u):
""" Test b5 space-group """
from random import random, randint
from numpy import all, abs, dot, pi
from numpy.linalg import inv, norm
from numpy.random import random_sample
from pylada.crystal import space_group, Structure, transform
from pylada.crystal import which_site
x, y = u, 0.25 - u
structure = Structure([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]]) \
.add_atom(5.000000e-01, 5.000000e-01, 5.000000e-01, "A") \
.add_atom(5.000000e-01, 2.500000e-01, 2.500000e-01, "A") \
.add_atom(2.500000e-01, 5.000000e-01, 2.500000e-01, "A") \
.add_atom(2.500000e-01, 2.500000e-01, 5.000000e-01, "A") \
.add_atom(8.750000e-01, 8.750000e-01, 8.750000e-01, "B") \
.add_atom(1.250000e-01, 1.250000e-01, 1.250000e-01, "B") \
.add_atom( x, x, x, "X") \
.add_atom( x, y, y, "X") \
.add_atom( y, x, y, "X") \
.add_atom( y, y, x, "X") \
.add_atom( -x, -x, -x, "X") \
.add_atom( -x, -y, -y, "X") \
.add_atom( -y, -x, -y, "X") \
.add_atom(-y, -y, -x, "X")
ops = space_group(structure)
assert len(ops) == 48
invcell = inv(structure.cell)
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
sites = []
for i, atom in enumerate(structure):
pos = dot(op[:3], atom.pos) + op[3]
j = which_site(pos, structure, invcell)
assert j != -1
sites.append(j)
assert len(set(sites)) == len(structure)
structure[0], structure[-1] = structure[-1], structure[0]
ops = space_group(structure)
assert len(ops) == 48
for op in ops:
assert op.shape == (4, 3)
other = transform(structure, op)
assert all(abs(dot(op[:3], structure.cell) - other.cell) < 1e-8)
for a, atom in zip(structure, other):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
sites = []
for i, atom in enumerate(structure):
pos = dot(op[:3], atom.pos) + op[3]
j = which_site(pos, structure, invcell)
assert j != -1, (i, atom, op)
sites.append(j)
assert len(set(sites)) == len(structure)
# try random rotation, translations, atom swap
structure[0], structure[-1] = structure[-1], structure[0]
for u in range(10):
axis = random_sample((3,))
axis /= norm(axis)
rotation = rotation_matrix(pi * random(), axis)
translation = random_sample((3,))
other = transform(structure, rotation, translation)
for u in range(10):
l, m = randint(0, len(structure) - 1), randint(0, len(structure) - 1)
a, b = other[l], other[m]
other[l], other[m] = b, a
invcell = inv(other.cell)
ops = space_group(other)
for z, op in enumerate(ops):
assert op.shape == (4, 3)
other2 = transform(other, op)
assert all(abs(dot(op[:3], other.cell) - other2.cell) < 1e-8)
for a, atom in zip(other, other2):
assert all(abs(dot(op[:3], a.pos) + op[3] - atom.pos) < 1e-8)
assert a.type == atom.type
sites = []
for i, atom in enumerate(other):
pos = dot(op[:3], atom.pos) + op[3]
j = which_site(pos, other, invcell)
if j == -1:
print((i, z))
print(atom)
print(op)
print(pos)
print(other)
raise Exception()
sites.append(j)
assert len(set(sites)) == len(other)
