def test(cell, numops):
""" Test structure initialization. """
from numpy import all, abs, dot, array
from numpy.linalg import inv, det
from pylada.crystal.cppwrappers import cell_invariants, Structure
from pylada.math import is_integer
ops = cell_invariants(cell)
if isinstance(cell, Structure): cell = cell.cell.copy()
assert len(ops) == numops
for op in ops:
assert op.shape == (4, 3)
assert all(abs(op[3, :]) < 1e-8)
transformation = dot(dot(inv(cell), op[:3]), cell)
assert is_integer(transformation)
assert abs(abs(det(transformation)) - 1e0) < 1e-8
if numops != 48:
allops = cell_invariants(
array([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]]))
failed = 0
for op in allops:
transformation = dot(dot(inv(cell), op[:3]), cell)
if not (is_integer(transformation)
and abs(abs(det(transformation)) - 1e0) < 1e-8):
failed += 1
assert failed == 48 - numops
def test_gruber():
from numpy import dot
from numpy.linalg import inv
from pylada.math import gruber, is_integer
from pylada.error import internal, input
cell = [[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]]
lim = 5
for a00 in [-1, 1]:
for a10 in xrange(-lim, lim+1):
for a11 in [-1, 1]:
for a20 in xrange(-lim, lim+1):
for a21 in xrange(-lim, lim+1):
for a22 in [-1, 1]:
a = [[a00, 0, 0], [a10, a11, 0], [a20, a21, a22]]
g = gruber(dot(cell, a))
assert is_integer(dot(inv(cell), g))
assert is_integer(dot(inv(g), cell))
try: gruber([[0, 0, 0], [1, 2, 0], [4, 5, 6]])
except input: pass
else: raise Exception()
try: gruber([[1, 0, 0], [1, 1, 0], [4, 5, 1]], itermax=2)
except internal: pass
else: raise Exception()
def test_gruber():
from numpy import dot
from numpy.linalg import inv
from pylada.math import gruber, is_integer
from pylada.error import internal, input
cell = [[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]]
lim = 5
for a00 in [-1, 1]:
for a10 in xrange(-lim, lim+1):
for a11 in [-1, 1]:
for a20 in xrange(-lim, lim+1):
for a21 in xrange(-lim, lim+1):
for a22 in [-1, 1]:
a = [[a00, 0, 0], [a10, a11, 0], [a20, a21, a22]]
testcell = dot(cell, a)
g = gruber(testcell)
print testcell
print g
assert is_integer(dot(inv(cell), g))
assert is_integer(dot(inv(g), cell))
try: gruber([[0, 0, 0], [1, 2, 0], [4, 5, 6]])
except input: pass
else: raise Exception()
try: gruber([[1, 0, 0], [1, 1, 0], [4, 5, 1]], itermax=2)
except internal: pass
else: raise Exception()
def test_primitive():
""" Tests whether primitivization works. """
from numpy import abs, dot
from numpy.linalg import inv
from pylada.crystal.cppwrappers import supercell, Structure, are_periodic_images as api, \
primitive, is_primitive
from pylada.math import is_integer
lattice = Structure( 0.0, 0.5, 0.5,
0.5, 0.0, 0.5,
0.5, 0.5, 0.0, scale=2.0, m=True ) \
.add_atom(0, 0, 0, "As") \
.add_atom(0.25, 0.25, 0.25, ['In', 'Ga'], m = True)
assert is_primitive(lattice)
for cell in itercells(10):
structure = supercell(lattice, dot(lattice.cell, cell))
assert not is_primitive(structure)
structure = primitive(structure, 1e-8)
assert is_primitive(structure)
assert abs(structure.volume - lattice.volume) < 1e-8
assert len(structure) == len(lattice)
assert is_integer(dot(structure.cell, inv(lattice.cell)))
assert is_integer(dot(lattice.cell, inv(structure.cell)))
invcell = inv(lattice.cell)
for atom in structure:
assert api(lattice[atom.site].pos, atom.pos, invcell) and \
atom.type == lattice[atom.site].type and \
getattr(lattice[atom.site], 'm', False) == getattr(atom, 'm', False) and \
(getattr(atom, 'm', False) or atom.site == 0)
def test_isinteger():
from numpy import array
from pylada.math import is_integer
from pylada.error import TypeError
assert is_integer(array([0, 1, 0, 2]))
assert is_integer(array([0L, 1, 0, 2]))
assert is_integer(array([0, 1.0, 0.0, 2.0]))
assert not is_integer(array([0, 1.1, 0.0, 2.0]))
try:
is_integer([5, 6, 7])
except TypeError:
pass
else:
raise Exception()
def decoration(A, B, lattice):
""" Adds changes to the motif. """
from numpy import dot
from numpy.linalg import inv
from pylada.crystal.cppwrappers import SmithTransform
from pylada.math import is_integer
basis(A, B)
return
smith = SmithTransform(lattice, A)
# create map of atoms.
indices = [-1] * len(A)
for i, atom in enumerate(A):
u = smith.index(atom.pos - lattice[atom.site].pos, atom.site)
indices[u] = i
# transform A according to all possible atom-atom translations.
for atom in A:
if atom.site != A[0].site: continue # only primitive translations.
trans = atom.pos - A[0].pos
B = A.copy()
for index in indices:
vec = A[index].pos + trans - lattice[A[index].site].pos
assert is_integer(dot(inv(lattice.cell),
vec)) # vector should be on lattice
B[indices[smith.index(vec, A[index].site)]] = A[index]
basis(A, B)
def decoration(A, B, lattice):
""" Adds changes to the motif. """
from numpy import dot
from numpy.linalg import inv
from pylada.crystal.cppwrappers import SmithTransform
from pylada.math import is_integer
basis(A, B)
return
smith = SmithTransform(lattice, A)
# create map of atoms.
indices = [-1] * len(A)
for i, atom in enumerate(A):
u = smith.index(atom.pos-lattice[atom.site].pos, atom.site)
indices[u] = i
# transform A according to all possible atom-atom translations.
for atom in A:
if atom.site != A[0].site: continue # only primitive translations.
trans = atom.pos - A[0].pos
B = A.copy()
for index in indices:
vec = A[index].pos + trans - lattice[A[index].site].pos
assert is_integer(dot(inv(lattice.cell), vec)) # vector should be on lattice
B[ indices[smith.index(vec, A[index].site)] ] = A[index]
basis(A, B)
def test(cell, numops):
""" Test structure initialization. """
from numpy import all, abs, dot, array
from numpy.linalg import inv, det
from pylada.crystal.cppwrappers import cell_invariants, Structure
from pylada.math import is_integer
ops = cell_invariants(cell)
if isinstance(cell, Structure): cell = cell.cell.copy()
assert len(ops) == numops
for op in ops:
assert op.shape == (4, 3)
assert all(abs(op[3, :]) < 1e-8)
transformation = dot(dot(inv(cell), op[:3]), cell)
assert is_integer(transformation)
assert abs(abs(det(transformation))-1e0) < 1e-8
if numops != 48:
allops = cell_invariants(array([[0,0.5,0.5],[0.5,0,0.5],[0.5,0.5,0]]))
failed = 0
for op in allops:
transformation = dot(dot(inv(cell), op[:3]), cell)
if not (is_integer(transformation) and abs(abs(det(transformation))-1e0) < 1e-8):
failed += 1
assert failed == 48 - numops
def test_isinteger(): from numpy import array from pylada.math import is_integer from pylada.error import TypeError assert is_integer(array([0, 1, 0, 2])) assert is_integer(array([0L, 1, 0, 2])) assert is_integer(array([0, 1.0, 0.0, 2.0])) assert not is_integer(array([0, 1.1, 0.0, 2.0])) try: is_integer([5, 6, 7]) except TypeError: pass else: raise Exception()