def test_2D(self):
# square
E = np.array([[2, 0], [0, 2]])
L = Lattice(E)
PG1 = L.point_group()
# centered rectangle
E = np.array([[1., -1.], [1.5, 1.5]])
L = Lattice(E)
self.assertEqual(L.dimension(), 2)
PG_expected = [
[[1, 0], [0, 1]],
[[-1, 0], [0, -1]],
[[1, 0], [0, -1]],
[[-1, 0], [0, 1]]
]
PG2 = L.point_group()
for Q in PG2.matrices():
self.assertTrue(Q.tolist() in PG_expected)
self.assertTrue(PG1.hassubgroup(PG2))
# hexagonal
E = [[2., 1.], [0., 1.73205081]]
L = Lattice(E)
self.assertEqual(L.Laue_group().order(), 6)
self.assertEqual(L.point_group().order(), 12)
# a random lattice
E = 10 * np.random.rand(2, 2)
while la.det(E) <= 0:
E = 10 * np.random.rand(2, 2)
L = Lattice(E)
# lattice_group, point_group relationship
PG = L.point_group().matrices()
LG = L.lattice_group().matrices()
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.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(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_2D(self):
# square
E = np.array([[2, 0], [0, 2]])
L = Lattice(E)
PG1 = L.point_group()
# centered rectangle
E = np.array([[1., -1.], [1.5, 1.5]])
L = Lattice(E)
self.assertEqual(L.dimension(), 2)
PG_expected = [[[1, 0], [0, 1]], [[-1, 0], [0, -1]], [[1, 0], [0, -1]],
[[-1, 0], [0, 1]]]
PG2 = L.point_group()
for Q in PG2.matrices():
self.assertTrue(Q.tolist() in PG_expected)
self.assertTrue(PG1.hassubgroup(PG2))
# hexagonal
E = [[2., 1.], [0., 1.73205081]]
L = Lattice(E)
self.assertEqual(L.Laue_group().order(), 6)
self.assertEqual(L.point_group().order(), 12)
# a random lattice
E = 10 * np.random.rand(2, 2)
while la.det(E) <= 0:
E = 10 * np.random.rand(2, 2)
L = Lattice(E)
# lattice_group, point_group relationship
PG = L.point_group().matrices()
LG = L.lattice_group().matrices()
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.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(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))
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))