def Laue_group(self):
'''
:return: get the Laue group in :math:`SO(3)` of a 3D lattice, in :math:`SO(2)` of a 2D lattice.
:rtype: :py:class:`MatrixGroup <structrans.crystallography.MatrixGroup>`
:raises AttributeError: Laue groups for other than 2D and 3D lattices are not implemented yet.
'''
if not self.dimension() in [2, 3]:
raise AttributeError('Laue groups for other than 2D and 3D lattices are not implemented yet.')
if self.__LaueGroup is None and self.dimension() == 3:
self.__LaueGroup = MatrixGroup(np.array([Q for Q in CUBIC_LAUE_GROUP.matrices() if self.inpointgroup(Q)]))
if self.__LaueGroup.order() == 4:
hexgroup = MatrixGroup(np.array([Q for Q in HEX_LAUE_GROUP.matrices() if self.inpointgroup(Q)]))
if hexgroup.order() > self.__LaueGroup.order():
self.__LaueGroup = hexgroup
if self.__LaueGroup is None and self.dimension() == 2:
self.__LaueGroup = MatrixGroup(np.array([Q for Q in SQUARE_GROUP.matrices() if self.inpointgroup(Q)]))
if self.__LaueGroup.order() == 2:
hexGroup = MatrixGroup(np.array([Q for Q in HEX2D_GROUP.matrices() if self.inpointgroup(Q)]))
if hexGroup.order() > self.__LaueGroup.order():
self.__LaueGroup = hexGroup
return self.__LaueGroup
def Laue_group(self):
'''
:return: get the Laue group in :math:`SO(3)` of a 3D lattice, in :math:`SO(2)` of a 2D lattice.
:rtype: :py:class:`MatrixGroup <structrans.crystallography.MatrixGroup>`
:raises AttributeError: Laue groups for other than 2D and 3D lattices are not implemented yet.
'''
if not self.dimension() in [2, 3]:
raise AttributeError(
'Laue groups for other than 2D and 3D lattices are not implemented yet.'
)
if self.__LaueGroup is None and self.dimension() == 3:
self.__LaueGroup = MatrixGroup(
np.array([
Q for Q in CUBIC_LAUE_GROUP.matrices()
if self.inpointgroup(Q)
]))
if self.__LaueGroup.order() == 4:
hexgroup = MatrixGroup(
np.array([
Q for Q in HEX_LAUE_GROUP.matrices()
if self.inpointgroup(Q)
]))
if hexgroup.order() > self.__LaueGroup.order():
self.__LaueGroup = hexgroup
if self.__LaueGroup is None and self.dimension() == 2:
self.__LaueGroup = MatrixGroup(
np.array([
Q for Q in SQUARE_GROUP.matrices() if self.inpointgroup(Q)
]))
if self.__LaueGroup.order() == 2:
hexGroup = MatrixGroup(
np.array([
Q for Q in HEX2D_GROUP.matrices()
if self.inpointgroup(Q)
]))
if hexGroup.order() > self.__LaueGroup.order():
self.__LaueGroup = hexGroup
return self.__LaueGroup
def test_groups(self):
L = Lattice(np.eye(4))
self.assertRaises(AttributeError, L.Laue_group)
self.assertRaises(AttributeError, L.point_group)
self.assertRaises(AttributeError, L.special_lattice_group)
self.assertRaises(AttributeError, L.lattice_group)
# fcc with a = 2
E = [[1., 0., 1.], [1., 1., 0.], [0., 1., 1.]]
L = Lattice(E)
Q = [[0., 1., 0.], [1., 0., 0.], [0., 0., -1.]]
self.assertTrue(L.inpointgroup(Q))
self.assertEqual(L.Laue_group().order(), 24)
self.assertEqual(L.point_group().order(), 48)
self.assertEqual(L.special_lattice_group().order(), 24)
self.assertEqual(L.lattice_group().order(), 48)
PG1 = L.point_group()
self.assertTrue(PG1.hassubgroup(PG1))
# monoclinic
E = [[2., 0., 0.20934382], [0., 3., 0.], [0., 0., 3.99451814]]
L = Lattice(E)
self.assertFalse(L.inpointgroup(Q))
self.assertEqual(L.Laue_group().order(), 2)
self.assertEqual(L.point_group().order(), 4)
self.assertEqual(L.special_lattice_group().order(), 2)
self.assertEqual(L.lattice_group().order(), 4)
PG2 = L.point_group()
self.assertTrue(PG1.hassubgroup(PG2))
# hexagonal, a = 2, c = 3
E = [[2., 1., 0.], [0., np.sqrt(3), 0.], [0., 0., 3.]]
L = Lattice(E)
self.assertEqual(L.Laue_group().order(), 12)
self.assertEqual(L.point_group().order(), 24)
self.assertEqual(L.special_lattice_group().order(), 12)
self.assertEqual(L.lattice_group().order(), 24)
for Q in HEX_LAUE_GROUP.matrices():
self.assertTrue(L.inpointgroup(Q))
PG3 = L.point_group()
self.assertFalse(PG1.hassubgroup(PG3))
# rounding tolerance of floating numbers
E = [[2., 1., 0.], [0., 1.73205081, 0.], [0., 0., 3.]]
L = Lattice(E)
self.assertEqual(L.Laue_group().order(), 12)
self.assertEqual(L.point_group().order(), 24)
self.assertEqual(L.special_lattice_group().order(), 12)
self.assertEqual(L.lattice_group().order(), 24)
Q = HEX_LAUE_GROUP.matrices()[6]
self.assertTrue(L.inpointgroup(Q))
# a random lattice
E = 4 * np.random.rand(3, 3)
while la.det(E) <= 0:
E = 4 * np.random.rand(3, 3)
L = Lattice(E)
# lattice_group, point_group relationship
PG = L.point_group().matrices()
LG = L.lattice_group().matrices()
LGlist = [m.tolist() for m in LG]
LaueG = [m.tolist() for m in L.Laue_group().matrices()]
SLG = [m.tolist() for m in L.special_lattice_group().matrices()]
for Q in PG:
self.assertEqual(L, Lattice(Q.dot(L.base())))
self.assertTrue(np.array_equal(Q.T.dot(Q), np.eye(3)))
self.assertTrue(L.inpointgroup(Q))
if Q.tolist() in LaueG:
self.assertTrue(la.det(Q) == 1)
else:
self.assertTrue(la.det(Q) == -1)
# QE = EM
M = np.rint(la.inv(E).dot(Q.dot(E)))
self.assertTrue(M.tolist() in LGlist)
self.assertTrue(L.inlatticegroup(M))
for M in LG:
self.assertEqual(L, Lattice(L.base().dot(M)))
if M.tolist() in SLG:
self.assertTrue(la.det(M) == 1)
else:
self.assertTrue(la.det(M) == -1)
# QE = EM
Q = E.dot(M).dot(la.inv(E))
self.assertTrue(L.inpointgroup(Q))
def test_groups(self):
L = Lattice(np.eye(4))
self.assertRaises(AttributeError, L.Laue_group)
self.assertRaises(AttributeError, L.point_group)
self.assertRaises(AttributeError, L.special_lattice_group)
self.assertRaises(AttributeError, L.lattice_group)
# fcc with a = 2
E = [[1., 0., 1.], [1., 1., 0.], [0., 1., 1.]]
L = Lattice(E)
Q = [[0., 1., 0.], [1., 0., 0.], [0., 0., -1.]]
self.assertTrue(L.inpointgroup(Q))
self.assertEqual(L.Laue_group().order(), 24)
self.assertEqual(L.point_group().order(), 48)
self.assertEqual(L.special_lattice_group().order(), 24)
self.assertEqual(L.lattice_group().order(), 48)
PG1 = L.point_group()
self.assertTrue(PG1.hassubgroup(PG1))
# monoclinic
E = [[2., 0., 0.20934382], [0., 3., 0.], [0., 0., 3.99451814]]
L = Lattice(E)
self.assertFalse(L.inpointgroup(Q))
self.assertEqual(L.Laue_group().order(), 2)
self.assertEqual(L.point_group().order(), 4)
self.assertEqual(L.special_lattice_group().order(), 2)
self.assertEqual(L.lattice_group().order(), 4)
PG2 = L.point_group()
self.assertTrue(PG1.hassubgroup(PG2))
# hexagonal, a = 2, c = 3
E = [[2., 1., 0.], [0., np.sqrt(3), 0.], [0., 0., 3.]]
L = Lattice(E)
self.assertEqual(L.Laue_group().order(), 12)
self.assertEqual(L.point_group().order(), 24)
self.assertEqual(L.special_lattice_group().order(), 12)
self.assertEqual(L.lattice_group().order(), 24)
for Q in HEX_LAUE_GROUP.matrices():
self.assertTrue(L.inpointgroup(Q))
PG3 = L.point_group()
self.assertFalse(PG1.hassubgroup(PG3))
# rounding tolerance of floating numbers
E = [[2., 1., 0.], [0., 1.73205081, 0.], [0., 0., 3.]]
L = Lattice(E)
self.assertEqual(L.Laue_group().order(), 12)
self.assertEqual(L.point_group().order(), 24)
self.assertEqual(L.special_lattice_group().order(), 12)
self.assertEqual(L.lattice_group().order(), 24)
Q = HEX_LAUE_GROUP.matrices()[6]
self.assertTrue(L.inpointgroup(Q))
# a random lattice
E = 4 * np.random.rand(3, 3)
while la.det(E) <= 0:
E = 4 * np.random.rand(3, 3)
L = Lattice(E)
# lattice_group, point_group relationship
PG = L.point_group().matrices()
LG = L.lattice_group().matrices()
LGlist = [m.tolist() for m in LG]
LaueG = [m.tolist() for m in L.Laue_group().matrices()]
SLG = [m.tolist() for m in L.special_lattice_group().matrices()]
for Q in PG:
self.assertEqual(L, Lattice(Q.dot(L.base())))
self.assertTrue(np.array_equal(Q.T.dot(Q), np.eye(3)))
self.assertTrue(L.inpointgroup(Q))
if Q.tolist() in LaueG:
self.assertTrue(la.det(Q) == 1)
else:
self.assertTrue(la.det(Q) == -1)
# QE = EM
M = np.rint(la.inv(E).dot(Q.dot(E)))
self.assertTrue(M.tolist() in LGlist)
self.assertTrue(L.inlatticegroup(M))
for M in LG:
self.assertEqual(L, Lattice(L.base().dot(M)))
if M.tolist() in SLG:
self.assertTrue(la.det(M) == 1)
else:
self.assertTrue(la.det(M) == -1)
# QE = EM
Q = E.dot(M).dot(la.inv(E))
self.assertTrue(L.inpointgroup(Q))