def test_b5(u):
""" Test b5 space-group and equivalents """
from numpy import dot
from numpy.random import randint
from pylada.crystal import Structure, which_site
x, y = u, 0.25-u
lattice = 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")
assert which_site(lattice[6].pos + [0.5, -0.5, 2], lattice) == 6
for i, atom in enumerate(lattice):
assert which_site(atom.pos, lattice) == i
for j in xrange(10):
newpos = dot(lattice.cell, randint(10, size=(3,)) - 5)
assert which_site(atom.pos + newpos, lattice) == i, (atom.pos, newpos, i)
def test_b5(u):
""" Test b5 space-group and equivalents """
from numpy import dot
from numpy.random import randint
from pylada.crystal import Structure, which_site
x, y = u, 0.25 - u
lattice = 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")
assert which_site(lattice[6].pos + [0.5, -0.5, 2], lattice) == 6
for i, atom in enumerate(lattice):
assert which_site(atom.pos, lattice) == i
for j in xrange(10):
newpos = dot(lattice.cell, randint(10, size=(3, )) - 5)
assert which_site(atom.pos + newpos,
lattice) == i, (atom.pos, newpos, i)
def test_position_to_atomic_site_correspondence(u):
from numpy import dot
from numpy.random import randint
from pylada.crystal import which_site
lattice = get_a_b5_lattice(u)
assert which_site(lattice[6].pos + [0.5, -0.5, 2], lattice) == 6
for i, atom in enumerate(lattice):
assert which_site(atom.pos, lattice) == i
for j in range(10):
newpos = dot(lattice.cell, randint(10, size=(3,)) - 5)
assert which_site(atom.pos + newpos, lattice) == i, (atom.pos, newpos, i)
def test_position_to_atomic_site_correspondence(u):
from numpy import dot
from numpy.random import randint
from pylada.crystal import which_site
lattice = get_a_b5_lattice(u)
assert which_site(lattice[6].pos + [0.5, -0.5, 2], lattice) == 6
for i, atom in enumerate(lattice):
assert which_site(atom.pos, lattice) == i
for j in range(10):
newpos = dot(lattice.cell, randint(10, size=(3, )) - 5)
assert which_site(atom.pos + newpos,
lattice) == i, (atom.pos, newpos, i)
def test():
from numpy import all, abs, dot, identity
from pylada.dftcrystal import Crystal, External
from pylada.crystal import which_site
orig = Crystal(227, 5.43).add_atom(0.125, 0.125, 0.125, 'Si')
b = External(copy=orig.eval())
assert all(abs(orig.eval().cell - b.initial.cell) < 1e-8)
assert len(b.initial) == 2
assert repr(b) == repr( eval(repr(b), {'External': External}) )
assert len(b.print_input().splitlines()) == 2
assert b.print_input().splitlines()[0] == 'EXTERNAL'
assert b.print_input().splitlines()[1] == 'END EXTERNAL'
# check that symmetries as extracted are ok.
for atom in b.initial:
for op in orig.symmetry_operators:
assert all(abs(identity(3, dtype='float64') - dot(op[:3].T, op[:3])) < 1e-8)
assert which_site(dot(op[:3], atom.pos) + op[3], b.initial) != -1
# Check that running structure through crystal works
c = b.eval()
assert all(abs(c.cell - b.cell) < 1e-8)
assert len(c) == 2
assert all(abs(abs(c[0].pos) - [0.67875]*3) < 1e-8)
assert all(abs(abs(c[1].pos) - [0.67875]*3) < 1e-8)
assert all(abs(c[0].pos + c[1].pos) < 1e-8)
def inequivalent_sites(lattice):
""" Returns a list containing only one site index per inequivalent sub-lattice. """
from pylada.crystal import which_site
result = set( i for i in range(len(lattice.sites)) )
for i, site in enumerate(lattice.sites):
if i not in result: continue
for op in lattice.space_group:
j = which_site( op(site.pos), lattice )
if j != i and j in result: result.remove(j)
return result
def _spin(self, position):
""" Returns formatted spin. """
from pylada.crystal import which_site
from pylada.error import ValueError
# find sublattice
sublattice = which_site(position, self.lattice)
if sublattice == -1: raise ValueError('Could not find atomic site')
# create spin and adds it to group.
return spin(position - self.lattice[sublattice].pos, sublattice)
def test_rotations():
from numpy import all, dot, zeros
from numpy.linalg import inv
from pylada.crystal import binary, supercell, HFTransform, space_group, \
which_site
from pylada.enum 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)
def get_cells(n):
for i in xrange(1, n):
yield [[i, 0, 0], [0, 0.5, 0.5], [0, -0.5, 0.5]]
for i in xrange(1, n):
yield [[i, 0, 0], [0, i, 0], [0, 0, 1]]
for i in xrange(1, n):
yield [[i, 0, 0], [0, i, 0], [0, 0, i]]
yield dot(lattice.cell, [[1, 0, 0], [0, 1, 0], [0, 0, 2]])
for cell in get_cells(8):
# 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])
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])
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 and equivalents """
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.cppwrappers import space_group, Structure, equivalent, \
transform
from pylada.math import Rotation
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)
assert equivalent(structure, other, cartesian=False)
assert equivalent(other, structure, cartesian=False)
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)
assert equivalent(structure, other, cartesian=False)
assert equivalent(other, structure, cartesian=False)
# try random rotation, translations, atom swap
structure[0], structure[-1] = structure[-1], structure[0]
for u in xrange(10):
axis = random_sample((3,))
axis /= norm(axis)
rotation = Rotation( pi*random(), axis)
rotation[3] = random_sample((3,))
other = transform(structure, rotation)
for u in xrange(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)
assert equivalent(other, other2, cartesian=False)
assert equivalent(other2, other, cartesian=False)
