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_construction(self):
E = np.eye(4).tolist()
L = Lattice(E)
self.assertEqual(L.dimension(), 4)
self.assertListEqual(L.base()[:, 0].tolist(), [1, 0, 0, 0])
# not matrix
E = "adfda"
self.assertRaises(ValueError, Lattice, E)
# det E = 0
E = [[1, 0, 0], [0, 0, 0], [0, 0, 1]]
self.assertRaises(ValueError, Lattice, E)
# 0 dimension
E = []
self.assertRaises(ValueError, Lattice, E)
def test_construction(self):
E = np.eye(4).tolist()
L = Lattice(E)
self.assertEqual(L.dimension(), 4)
self.assertListEqual(L.base()[:, 0].tolist(), [1, 0, 0, 0])
# not matrix
E = "adfda"
self.assertRaises(ValueError, Lattice, E)
# det E = 0
E = [[1, 0, 0], [0, 0, 0], [0, 0, 1]]
self.assertRaises(ValueError, Lattice, E)
# 0 dimension
E = []
self.assertRaises(ValueError, Lattice, E)
