def test_reciprocal(self):
'''check calculation of reciprocal lattice.'''
r1 = self.lattice.reciprocal()
self.assertEqual((1, 1, 1, 90, 90, 90), r1.abcABG())
L2 = Lattice(2, 4, 8, 90, 90, 90)
r2 = L2.reciprocal()
self.assertEqual((0.5, 0.25, 0.125, 90, 90, 90), r2.abcABG())
rr2 = r2.reciprocal()
self.assertTrue(numpy.array_equal(L2.base, rr2.base))
return
class TestLattice(unittest.TestCase):
"""test methods of Lattice class"""
def setUp(self):
self.lattice = Lattice()
self.places = 12
return
def test___init__(self):
'''Check Lattice.__init__ processing of arguments.
'''
self.assertRaises(ValueError, Lattice,
self.lattice, c=4)
self.assertRaises(ValueError, Lattice,
base=self.lattice.base,
baserot=self.lattice.baserot)
self.assertRaises(ValueError, Lattice, 1, 2, 3)
self.assertRaises(ValueError, Lattice, 1, 2, 3, 80, 90)
L0 = self.lattice
L0.setLatBase(L0.cartesian([[1, 1, 0], [0, 1, 1], [1, 0, 1]]))
L1 = Lattice(L0)
self.assertTrue(numpy.array_equal(L0.base, L1.base))
L2 = Lattice(base=L0.base)
self.assertTrue(numpy.array_equal(L0.base, L2.base))
self.assertTrue(numpy.array_equal(L0.isotropicunit, L2.isotropicunit))
L3 = Lattice(*L0.abcABG(), baserot=L0.baserot)
self.assertTrue(numpy.allclose(L0.base, L3.base))
self.assertTrue(numpy.allclose(L0.isotropicunit, L3.isotropicunit))
return
def test_setLatPar(self):
"""check calculation of standard unit cell vectors"""
from numpy import dot
from math import radians, sqrt, cos
norm = lambda x : sqrt(sum([xi**2 for xi in x]))
cosd = lambda x : cos(radians(x))
self.lattice.setLatPar(1.0, 2.0, 3.0, 80, 100, 120)
base = self.lattice.base
self.assertAlmostEqual(1.0, norm(base[0]), self.places)
self.assertAlmostEqual(2.0, norm(base[1]), self.places)
self.assertAlmostEqual(3.0, norm(base[2]), self.places)
self.assertAlmostEqual(cosd(80.0),
dot(base[1],base[2])/(2*3), self.places)
self.assertAlmostEqual(cosd(100.0),
dot(base[0],base[2])/(1*3), self.places)
self.assertAlmostEqual(cosd(120.0),
dot(base[0],base[1])/(1*2), self.places)
return
def test_latpar_properties(self):
'''check assignment to a, b, c, alpha, beta, gamma.
'''
lat = self.lattice
lat.a = 2
lat.b = 4
lat.c = 6
lat.alpha = 80
lat.beta = 100
lat.gamma = 120
lat1 = Lattice(2, 4, 6, 80, 100, 120)
self.assertAlmostEqual(-0.5, lat.cg, self.places)
self.assertTrue(numpy.array_equal(lat1.base, lat.base))
return
def test_readonly_properties(self):
'''Check that read-only properties are indeed such.
'''
lat = self.lattice
lat.b = 2
lat.c = 6
self.assertEqual(1.0, lat.unitvolume)
self.assertRaises(AttributeError, setattr,
lat, 'unitvolume', 3.33)
self.assertEqual(12, lat.volume)
self.assertRaises(AttributeError, setattr,
lat, 'volume', 3.33)
self.assertEqual(0.0, lat.ca)
self.assertRaises(AttributeError, setattr,
lat, 'ca', 3.33)
self.assertEqual(0.0, lat.cb)
self.assertRaises(AttributeError, setattr,
lat, 'cb', 3.33)
self.assertEqual(0.0, lat.cg)
self.assertRaises(AttributeError, setattr,
lat, 'cg', 3.33)
self.assertEqual(1.0, lat.sa)
self.assertRaises(AttributeError, setattr,
lat, 'sa', 3.33)
self.assertEqual(1.0, lat.sb)
self.assertRaises(AttributeError, setattr,
lat, 'sb', 3.33)
self.assertEqual(1.0, lat.sg)
self.assertRaises(AttributeError, setattr,
lat, 'sg', 3.33)
self.assertEqual(1.0, lat.ar)
self.assertRaises(AttributeError, setattr,
lat, 'ar', 3.33)
self.assertEqual(0.5, lat.br)
self.assertRaises(AttributeError, setattr,
lat, 'br', 3.33)
self.assertAlmostEqual(1.0/6, lat.cr, self.places)
self.assertRaises(AttributeError, setattr,
lat, 'cr', 3.33)
self.assertEqual(90.0, lat.alphar)
self.assertRaises(AttributeError, setattr,
lat, 'alphar', 3.33)
self.assertEqual(90.0, lat.betar)
self.assertRaises(AttributeError, setattr,
lat, 'betar', 3.33)
self.assertEqual(90.0, lat.gammar)
self.assertRaises(AttributeError, setattr,
lat, 'gammar', 3.33)
self.assertEqual(0.0, lat.car)
self.assertRaises(AttributeError, setattr,
lat, 'car', 3.33)
self.assertEqual(0.0, lat.cbr)
self.assertRaises(AttributeError, setattr,
lat, 'cbr', 3.33)
self.assertEqual(0.0, lat.cgr)
self.assertRaises(AttributeError, setattr,
lat, 'cgr', 3.33)
self.assertEqual(1.0, lat.sar)
self.assertRaises(AttributeError, setattr,
lat, 'sar', 3.33)
self.assertEqual(1.0, lat.sbr)
self.assertRaises(AttributeError, setattr,
lat, 'sbr', 3.33)
self.assertEqual(1.0, lat.sgr)
self.assertRaises(AttributeError, setattr,
lat, 'sgr', 3.33)
return
def test_setLatBase(self):
"""check calculation of unit cell rotation"""
base = numpy.array([[1.0, 1.0, 0.0],
[0.0, 1.0, 1.0],
[1.0, 0.0, 1.0]])
self.lattice.setLatBase(base)
self.assertAlmostEqual(self.lattice.a, numpy.sqrt(2.0), self.places)
self.assertAlmostEqual(self.lattice.b, numpy.sqrt(2.0), self.places)
self.assertAlmostEqual(self.lattice.c, numpy.sqrt(2.0), self.places)
self.assertAlmostEqual(self.lattice.alpha, 60.0, self.places)
self.assertAlmostEqual(self.lattice.beta, 60.0, self.places)
self.assertAlmostEqual(self.lattice.gamma, 60.0, self.places)
detR0 = numalg.det(self.lattice.baserot)
self.assertAlmostEqual(detR0, 1.0, self.places)
# try if rotation matrix works
self.assertEqual(numpy.all(base == self.lattice.base), True)
self.lattice.setLatPar(alpha=44, beta=66, gamma=88)
self.assertNotEqual(numpy.all(base == self.lattice.base), True)
self.lattice.setLatPar(alpha=60, beta=60, gamma=60)
self.assertTrue(numpy.allclose(base[0], self.lattice.base[0]))
self.assertTrue(numpy.allclose(base[1], self.lattice.base[1]))
self.assertTrue(numpy.allclose(base[2], self.lattice.base[2]))
# try base checking
self.assertRaises(LatticeError, self.lattice.setLatBase,
[[1, 0, 0], [1,0,0], [0,0,1]])
self.assertRaises(LatticeError, self.lattice.setLatBase,
[[1, 0, 0], [0,0,1], [0,1,0]])
return
def test_reciprocal(self):
'''check calculation of reciprocal lattice.'''
r1 = self.lattice.reciprocal()
self.assertEqual((1, 1, 1, 90, 90, 90), r1.abcABG())
L2 = Lattice(2, 4, 8, 90, 90, 90)
r2 = L2.reciprocal()
self.assertEqual((0.5, 0.25, 0.125, 90, 90, 90), r2.abcABG())
rr2 = r2.reciprocal()
self.assertTrue(numpy.array_equal(L2.base, rr2.base))
return
def test_dot(self):
'''check dot product of lattice vectors.'''
L = self.lattice
L.setLatPar(gamma=120)
self.assertAlmostEqual(-0.5, L.dot([1, 0, 0], [0, 1, 0]), self.places)
va5 = numpy.tile([1.0, 0.0, 0.0], (5, 1))
vb5 = numpy.tile([0.0, 1.0, 0.0], (5, 1))
self.assertTrue(numpy.array_equal(5 * [-0.5], L.dot(va5, vb5)))
self.assertTrue(numpy.array_equal(5 * [-0.5], L.dot(va5[0], vb5)))
self.assertTrue(numpy.array_equal(5 * [-0.5], L.dot(va5, vb5[0])))
return
def test_norm(self):
'''check norm of a lattice vector.'''
self.assertEqual(1, self.lattice.norm([1, 0, 0]))
u = numpy.array([[3, 4, 0], [1, 1, 1]])
self.assertTrue(numpy.allclose([5, 3**0.5], self.lattice.norm(u)))
self.lattice.setLatPar(gamma=120)
self.assertAlmostEqual(1, self.lattice.norm([1, 1, 0]), self.places)
return
def test_rnorm(self):
'''check norm of a reciprocal vector.'''
L = self.lattice
L.setLatPar(1, 1.5, 2.3, 80, 95, 115)
r = L.reciprocal()
hkl = [0.5, 0.3, 0.2]
self.assertAlmostEqual(r.norm(hkl), L.rnorm(hkl), self.places)
hkl5 = numpy.tile(hkl, (5, 1))
self.assertTrue(numpy.allclose(5 * [r.norm(hkl)], L.rnorm(hkl5)))
return
def test_dist(self):
'''check dist function for distance between lattice points.'''
L = self.lattice
L.setLatPar(1, 1.5, 2.3, 80, 95, 115)
u = [0.1, 0.3, 0.7]
v = [0.3, 0.7, 0.7]
d0 = numalg.norm(L.cartesian(numpy.array(u) - v))
self.assertAlmostEqual(d0, L.dist(u, v), self.places)
self.assertAlmostEqual(d0, L.dist(v, u), self.places)
u5 = numpy.tile(u, (5, 1))
v5 = numpy.tile(v, (5, 1))
self.assertTrue(numpy.allclose(5 * [d0], L.dist(u, v5)))
self.assertTrue(numpy.allclose(5 * [d0], L.dist(u5, v)))
self.assertTrue(numpy.allclose(5 * [d0], L.dist(v5, u5)))
return
def test_angle(self):
'''check angle calculation between lattice vectors.'''
from math import degrees, acos
L = self.lattice
L.setLatPar(1, 1.5, 2.3, 80, 95, 115)
u = [0.1, 0.3, 0.7]
v = [0.3, 0.7, 0.7]
uc = L.cartesian(u)
vc = L.cartesian(v)
a0 = degrees(acos(numpy.dot(uc, vc) /
(numalg.norm(uc) * numalg.norm(vc))))
self.assertAlmostEqual(a0, L.angle(u, v), self.places)
self.assertAlmostEqual(a0, L.angle(v, u), self.places)
u5 = numpy.tile(u, (5, 1))
v5 = numpy.tile(v, (5, 1))
self.assertTrue(numpy.allclose(5 * [a0], L.angle(u, v5)))
self.assertTrue(numpy.allclose(5 * [a0], L.angle(u5, v)))
self.assertTrue(numpy.allclose(5 * [a0], L.angle(v5, u5)))
return
def test_repr(self):
"""check string representation of this lattice"""
r = repr(self.lattice)
self.assertEqual(r, "Lattice()")
self.lattice.setLatPar(1, 2, 3, 10, 20, 30)
r = repr(self.lattice)
r0 = "Lattice(a=1, b=2, c=3, alpha=10, beta=20, gamma=30)"
self.assertEqual(r, r0)
base = [[1.0, 1.0, 0.0],
[0.0, 2.0, 2.0],
[3.0, 0.0, 3.0]]
self.lattice.setLatBase(base)
r = repr(self.lattice)
self.assertEqual(r, "Lattice(base=%r)" % self.lattice.base)