def test15():
latt = Crystal3DLattice(a=4.0, b=4.0, c=4.0, alpha=90, beta=90, gamma=90)
print(latt)
recip_latt = Crystal3DLattice(a1=latt.b1, a2=latt.b2, a3=latt.b3)
print(recip_latt)
assert_equal(latt.a1, recip_latt.b1)
assert_equal(latt.a2, recip_latt.b2)
assert_equal(latt.a3, recip_latt.b3)
def test18():
a = np.sqrt(3) * aCC
dlattice = Crystal3DLattice(a=a,
b=a,
c=2 * r_CC_vdw,
alpha=90,
beta=90,
gamma=120)
dlattice_from_matrix = Crystal3DLattice(cell_matrix=dlattice.matrix)
assert_equal(dlattice, dlattice_from_matrix)
assert_true(np.allclose(dlattice.matrix, dlattice_from_matrix.matrix))
def test8():
a = np.sqrt(3) * aCC
latt = Crystal3DLattice(a=a,
b=a,
c=2 * r_CC_vdw,
alpha=90,
beta=90,
gamma=120)
print(latt)
a1 = latt.a1
a2 = latt.a2
a3 = latt.a3
xfrm = transformation_matrix(angle=-np.pi / 6)
rotangle = -np.pi / 6
for v in (a1, a2, a3):
v.rotate(angle=rotangle)
latt.rotate(angle=rotangle, axis='z')
print(latt)
assert_equal(latt.a1, a1)
assert_equal(latt.a2, a2)
assert_equal(latt.a3, a3)
assert_true(np.allclose(latt.orientation_matrix, xfrm))
def test13():
latt = Crystal3DLattice(a=4.0, b=4.0, c=4.0, alpha=90, beta=90, gamma=90)
print(latt)
p = [2.1, 0.9, 0.5]
assert_true(
np.allclose(latt.wrap_fractional_coordinate(p), Point(
(0.1, 0.9, 0.5))))
def test7():
latt = Crystal3DLattice(a=4.0, b=8.0, c=2.0, alpha=90, beta=90, gamma=120)
assert_true(np.allclose(latt.a, 4.0))
assert_true(np.allclose(latt.b, 8.0))
assert_true(np.allclose(latt.c, 2.0))
assert_true(np.allclose(latt.alpha, 90.))
assert_true(np.allclose(latt.beta, 90.))
assert_true(np.allclose(latt.gamma, 120.))
def test14():
latt = Crystal3DLattice(a=4.0, b=4.0, c=4.0, alpha=90, beta=90, gamma=90)
print(latt)
a = latt.a1
b = latt.a2
c = latt.a3
G = np.matrix([[a.dot(a), a.dot(b), a.dot(c)],
[b.dot(a), b.dot(b), b.dot(c)],
[c.dot(a), c.dot(b), c.dot(c)]])
assert_true(np.allclose(latt.metric_tensor, G))
def test9():
a = np.sqrt(3) * aCC
latt = Crystal3DLattice(a=a,
b=a,
c=2 * r_CC_vdw,
alpha=90,
beta=90,
gamma=120)
print(latt)
hex_latt = \
Crystal3DLattice.hexagonal(a, 2 * r_CC_vdw)
print(hex_latt)
assert_equal(latt, hex_latt)
def test3():
a = 5.0
angle = 90
basis = ['C', 'C']
coords = [[0, 0, 0], [1 / 2, 1 / 2, 1 / 2]]
latt1 = Crystal3DLattice.cubic(a)
latt2 = \
Crystal3DLattice(a=a, b=a, c=a, alpha=angle, beta=angle, gamma=angle)
assert_equal(latt1, latt2)
cell1 = UnitCell(lattice=latt1, basis=basis[:], coords=coords[:])
cell2 = UnitCell(lattice=latt2, basis=basis[:], coords=coords[:])
assert_equal(cell1, cell2)
latt3 = Crystal3DLattice.cubic(10.0)
assert_not_equal(latt1, latt3)
def __init__(self,
bond=aCC,
a=np.sqrt(3) * aCC,
c=2 * r_CC_vdw,
gamma=60,
basis=['C', 'C'],
coords=[[0, 0, 0], [aCC, 0, 0]],
cartesian=True):
lattice = Crystal3DLattice(a=a,
b=a,
c=c,
alpha=90.,
beta=90.,
gamma=gamma)
lattice.rotate(angle=-np.pi / 6, axis='z')
super().__init__(lattice, basis, coords, cartesian)
def test20():
a = np.sqrt(3) * aCC
orientation_matrix = rotation_matrix(angle=-np.pi / 6, axis=zhat)
dlattice = Crystal3DLattice(a=a,
b=a,
c=2 * r_CC_vdw,
alpha=90,
beta=90,
gamma=120,
orientation_matrix=orientation_matrix)
rlattice = \
Reciprocal3DLattice(a_star=dlattice.reciprocal_lattice.a_star,
b_star=dlattice.reciprocal_lattice.b_star,
c_star=dlattice.reciprocal_lattice.c_star,
alpha_star=dlattice.reciprocal_lattice.alpha_star,
beta_star=dlattice.reciprocal_lattice.beta_star,
gamma_star=dlattice.reciprocal_lattice.gamma_star)
print('\ndlattice.reciprocal_lattice.matrix:\n{}'.format(
dlattice.reciprocal_lattice.matrix))
print('\nrlattice.matrix:\n{}'.format(rlattice.matrix))
print('\ndlattice.matrix:\n{}'.format(dlattice.matrix))
print('\nrlattice.reciprocal_lattice.matrix:\n{}'.format(
rlattice.reciprocal_lattice.matrix))
print('\ndlattice.reciprocal_lattice.matrix:\n{}'.format(
dlattice.reciprocal_lattice.matrix))
pmg_rlattice = \
pmg.Lattice.from_parameters(dlattice.reciprocal_lattice.a_star,
dlattice.reciprocal_lattice.b_star,
dlattice.reciprocal_lattice.c_star,
dlattice.reciprocal_lattice.alpha_star,
dlattice.reciprocal_lattice.beta_star,
dlattice.reciprocal_lattice.gamma_star)
print('\npmg_rlattice.matrix:\n{}'.format(pmg_rlattice.matrix))
print('\nrlattice.matrix:\n{}'.format(rlattice.matrix))
print('\npmg_rlattice.reciprocal_lattice.matrix:\n{}'.format(
pmg_rlattice.reciprocal_lattice.matrix))
print('\nrlattice.reciprocal_lattice.matrix:\n{}'.format(
rlattice.reciprocal_lattice.matrix))
assert_true(np.allclose(rlattice.matrix, pmg_rlattice.matrix))
assert_true(
np.allclose(dlattice.reciprocal_lattice.matrix, pmg_rlattice.matrix))
assert_true(np.allclose(rlattice.matrix, pmg_rlattice.matrix))
def test19():
a = np.sqrt(3) * aCC
dlattice = Crystal3DLattice(a=a,
b=a,
c=2 * r_CC_vdw,
alpha=90,
beta=90,
gamma=120)
print('\ndlattice.matrix:\n{}'.format(dlattice.matrix))
print('\ndlattice.reciprocal_lattice.matrix:\n{}'.format(
dlattice.reciprocal_lattice.matrix))
a1 = dlattice.a1
a2 = dlattice.a2
a3 = dlattice.a3
V = dlattice.volume
b1 = a2.cross(a3) / V
b2 = a3.cross(a1) / V
b3 = a1.cross(a2) / V
a_star = b1.length
b_star = b2.length
c_star = b3.length
alpha_star = np.degrees(b2.angle(b3))
beta_star = np.degrees(b3.angle(b1))
gamma_star = np.degrees(b1.angle(b2))
assert_true(np.allclose(a_star, dlattice.reciprocal_lattice.a_star))
assert_true(np.allclose(b_star, dlattice.reciprocal_lattice.b_star))
assert_true(np.allclose(c_star, dlattice.reciprocal_lattice.c_star))
assert_true(np.allclose(alpha_star,
dlattice.reciprocal_lattice.alpha_star))
assert_true(np.allclose(beta_star, dlattice.reciprocal_lattice.beta_star))
assert_true(np.allclose(gamma_star,
dlattice.reciprocal_lattice.gamma_star))
rlattice = Reciprocal3DLattice(a_star=a_star,
b_star=b_star,
c_star=c_star,
alpha_star=alpha_star,
beta_star=beta_star,
gamma_star=gamma_star)
print('\nrlattice.matrix:\n{}'.format(rlattice.matrix))
print('\nrlattice.reciprocal_lattice.matrix:\n{}'.format(
rlattice.reciprocal_lattice.matrix))
rlattice_from_rlattice_matrix = \
Reciprocal3DLattice(cell_matrix=rlattice.matrix)
print('\nrlattice_from_rlattice_matrix.matrix:\n{}'.format(
rlattice_from_rlattice_matrix.matrix))
print('\nrlattice_from_rlattice_matrix.reciprocal_lattice.matrix:\n{}'.
format(rlattice_from_rlattice_matrix.reciprocal_lattice.matrix))
assert_equal(rlattice, rlattice_from_rlattice_matrix)
assert_true(
np.allclose(rlattice.matrix, rlattice_from_rlattice_matrix.matrix))
rlattice_from_dlattice_rlattice_matrix = \
Reciprocal3DLattice(cell_matrix=dlattice.reciprocal_lattice.matrix)
print('\nrlattice_from_dlattice_rlattice_matrix.matrix:\n{}'.format(
rlattice_from_dlattice_rlattice_matrix.matrix))
print(
'\nrlattice_from_dlattice_rlattice_matrix.reciprocal_lattice.'
'matrix:\n{}'.format(
rlattice_from_dlattice_rlattice_matrix.reciprocal_lattice.matrix))
def test12():
a = np.sqrt(3) * aCC
cubic_latt = Crystal3DLattice(a=a, b=a, c=a, alpha=90, beta=90, gamma=90)
assert_equal(cubic_latt, Crystal3DLattice.cubic(a))
def test11():
a = np.sqrt(3) * aCC
dlattice = Crystal3DLattice(a=a,
b=a,
c=2 * r_CC_vdw,
alpha=90,
beta=90,
gamma=120)
orientation_matrix = rotation_matrix(angle=np.pi / 6, axis=zhat)
rlattice = \
Reciprocal3DLattice(a_star=dlattice.reciprocal_lattice.a_star,
b_star=dlattice.reciprocal_lattice.b_star,
c_star=dlattice.reciprocal_lattice.c_star,
alpha_star=dlattice.reciprocal_lattice.alpha_star,
beta_star=dlattice.reciprocal_lattice.beta_star,
gamma_star=dlattice.reciprocal_lattice.gamma_star,
orientation_matrix=orientation_matrix)
print('\ndlattice.reciprocal_lattice.matrix:\n{}'.format(
dlattice.reciprocal_lattice.matrix))
print('\nrlattice.matrix:\n{}'.format(rlattice.matrix))
print('\ndlattice.matrix:\n{}'.format(dlattice.matrix))
print('\nrlattice.reciprocal_lattice.matrix:\n{}'.format(
rlattice.reciprocal_lattice.matrix))
# assert_equal(dlattice.reciprocal_lattice, rlattice)
assert_true(
np.allclose(dlattice.reciprocal_lattice.matrix, rlattice.matrix))
assert_true(
np.allclose(dlattice.matrix, rlattice.reciprocal_lattice.matrix))
# print('\n{}'.format(np.linalg.inv(dlattice.matrix)))
# print(np.linalg.inv(dlattice.matrix) * dlattice.matrix)
# print(np.linalg.inv(dlattice.matrix).T)
# print(dlattice.reciprocal_lattice.matrix)
# print(dlattice.reciprocal_lattice.b1)
# print(dlattice.reciprocal_lattice.b2)
# print(dlattice.reciprocal_lattice.b3)
# print(rlattice.matrix)
# print(rlattice.b1)
# print(rlattice.b2)
# print(rlattice.b3)
assert_equal(dlattice.reciprocal_lattice, rlattice)
assert_equal(dlattice.reciprocal_lattice.b1, rlattice.b1)
assert_equal(dlattice.reciprocal_lattice.b2, rlattice.b2)
assert_equal(dlattice.reciprocal_lattice.b3, rlattice.b3)
assert_true(
np.allclose(dlattice.reciprocal_lattice.matrix, rlattice.matrix))
assert_true(
np.allclose(dlattice.reciprocal_lattice.metric_tensor,
rlattice.metric_tensor))
pmg_dlattice = pmg.Lattice(dlattice.matrix)
print('\npmg_dlattice.matrix:\n{}'.format(pmg_dlattice.matrix))
print('\ndlattice.matrix:\n{}'.format(dlattice.matrix))
print('\npmg_dlattice.reciprocal_lattice.matrix:\n{}'.format(
pmg_dlattice.reciprocal_lattice.matrix))
print('\ndlattice.reciprocal_lattice.matrix:\n{}'.format(
dlattice.reciprocal_lattice.matrix))
assert_true(np.allclose(dlattice.a, pmg_dlattice.a))
assert_true(np.allclose(dlattice.b, pmg_dlattice.b))
assert_true(np.allclose(dlattice.c, pmg_dlattice.c))
assert_true(np.allclose(np.asarray(dlattice.a1), pmg_dlattice.matrix[0]))
assert_true(np.allclose(np.asarray(dlattice.a2), pmg_dlattice.matrix[1]))
assert_true(np.allclose(np.asarray(dlattice.a3), pmg_dlattice.matrix[2]))
assert_true(np.allclose(dlattice.matrix, pmg_dlattice.matrix))
assert_true(
np.allclose(dlattice.ortho_matrix.T,
pmg.Lattice(dlattice.ortho_matrix.T).matrix))
assert_true(
np.allclose(
pmg.Lattice(dlattice.matrix).metric_tensor,
dlattice.metric_tensor))
assert_true(
np.allclose(
pmg.Lattice(dlattice.ortho_matrix.T).metric_tensor,
dlattice.metric_tensor))
assert_true(
np.allclose(pmg.Lattice(dlattice.matrix).matrix, dlattice.matrix))
assert_true(
np.allclose(
pmg.Lattice(dlattice.ortho_matrix.T).matrix, dlattice.matrix))
# print('latt_from_inv_latt_matrix_transpose:\n{}\n'.format(
# latt_from_inv_latt_matrix_transpose.matrix))
# print('rlattice.reciprocal_lattice.matrix:\n{}'.format(
# rlattice.reciprocal_lattice.matrix))
assert_true(
np.allclose(
pmg.Lattice(dlattice.matrix).matrix,
rlattice.reciprocal_lattice.matrix))
# print('rlattice.reciprocal_lattice.matrix:\n{}'.format(
# rlattice.reciprocal_lattice.matrix))
# print('pmg.Lattice(np.linalg.inv(dlattice.matrix).T).'
# 'reciprocal_lattice_crystallographic.matrix:\n{}'
# .format(pmg.Lattice(np.linalg.inv(dlattice.matrix).T)
# .reciprocal_lattice_crystallographic.matrix))
# print('pmg.Lattice.from_parameters(...):\n{}\n'.format(
# rezero_array(pmg.Lattice.from_parameters(
# dlattice.reciprocal_lattice.a_star,
# dlattice.reciprocal_lattice.b_star,
# dlattice.reciprocal_lattice.c_star,
# dlattice.reciprocal_lattice.alpha_star,
# dlattice.reciprocal_lattice.beta_star,
# dlattice.reciprocal_lattice.gamma_star)
# .reciprocal_lattice_crystallographic.matrix)))
# print('dlattice.ortho_matrix:\n{}'.format(dlattice.ortho_matrix))
# print('np.linalg.inv(dlattice.matrix).T:\n{}'.format(np.linalg.inv(
# dlattice.matrix).T))
# print('rlattice.reciprocal_lattice.ortho_matrix:\n{}'
# .format(rlattice.reciprocal_lattice.ortho_matrix))
# print('rlattice.reciprocal_lattice.ortho_matrix:\n{}\n'.
# format(rlattice.reciprocal_lattice.ortho_matrix))
# print('dlattice.reciprocal_lattice.ortho_matrix:\n{}'.format(
# dlattice.reciprocal_lattice.ortho_matrix))
# print('rlattice.ortho_matrix:\n{}'.format(
# rlattice.ortho_matrix))
# print('rlattice.ortho_matrix:\n{}\n'.format(
# rlattice.ortho_matrix))
assert_true(
np.allclose(dlattice.ortho_matrix,
rlattice.reciprocal_lattice.ortho_matrix))
assert_true(
np.allclose(dlattice.reciprocal_lattice.ortho_matrix,
rlattice.ortho_matrix))
assert_equal(dlattice, rlattice.reciprocal_lattice)
assert_equal(dlattice.reciprocal_lattice, rlattice)
print(dlattice.matrix * rlattice.matrix.T)
assert_true(np.allclose(dlattice.matrix * rlattice.matrix.T, np.eye(3)))
def test10():
a = np.sqrt(3) * aCC
dlattice = Crystal3DLattice(a=a,
b=a,
c=2 * r_CC_vdw,
alpha=90,
beta=90,
gamma=120)
rlattice = \
Reciprocal3DLattice(cell_matrix=dlattice.reciprocal_lattice.matrix)
# print('\n{}'.format(np.linalg.inv(dlattice.matrix)))
# print(np.linalg.inv(dlattice.matrix) * dlattice.matrix)
# print(np.linalg.inv(dlattice.matrix).T)
# print(dlattice.reciprocal_lattice.matrix)
# print(dlattice.reciprocal_lattice.b1)
# print(dlattice.reciprocal_lattice.b2)
# print(dlattice.reciprocal_lattice.b3)
# print(rlattice.matrix)
assert_equal(dlattice, rlattice.reciprocal_lattice)
assert_equal(dlattice.reciprocal_lattice, rlattice)
assert_equal(dlattice.reciprocal_lattice.b1, rlattice.b1)
assert_equal(dlattice.reciprocal_lattice.b2, rlattice.b2)
assert_equal(dlattice.reciprocal_lattice.b3, rlattice.b3)
assert_true(
np.allclose(dlattice.reciprocal_lattice.matrix, rlattice.matrix))
assert_true(
np.allclose(dlattice.reciprocal_lattice.metric_tensor,
rlattice.metric_tensor))
assert_true(
np.allclose(dlattice.ortho_matrix,
rlattice.reciprocal_lattice.ortho_matrix))
assert_true(
np.allclose(dlattice.reciprocal_lattice.ortho_matrix,
rlattice.ortho_matrix))
assert_true(np.allclose(dlattice.matrix * rlattice.matrix.T, np.eye(3)))
assert_true(
np.allclose(dlattice.metric_tensor * rlattice.metric_tensor,
np.eye(3)))
pmg_dlattice = pmg.Lattice(dlattice.matrix)
print('\npmg_dlattice.matrix:\n{}'.format(rezero_array(
pmg_dlattice.matrix)))
print('\ndlattice.matrix:\n{}'.format(rezero_array(dlattice.matrix)))
print('\npmg_dlattice.reciprocal_lattice.matrix:\n{}'.format(
rezero_array(pmg_dlattice.reciprocal_lattice.matrix)))
print('\ndlattice.reciprocal_lattice.matrix:\n{}'.format(
rezero_array(dlattice.reciprocal_lattice.matrix)))
assert_true(np.allclose(dlattice.a, pmg_dlattice.a))
assert_true(np.allclose(dlattice.b, pmg_dlattice.b))
assert_true(np.allclose(dlattice.c, pmg_dlattice.c))
assert_true(np.allclose(np.asarray(dlattice.a1), pmg_dlattice.matrix[0]))
assert_true(np.allclose(np.asarray(dlattice.a2), pmg_dlattice.matrix[1]))
assert_true(np.allclose(np.asarray(dlattice.a3), pmg_dlattice.matrix[2]))
assert_true(np.allclose(dlattice.matrix, pmg_dlattice.matrix))
pmg_dlattice = pmg.Lattice.from_parameters(dlattice.a, dlattice.b,
dlattice.c, dlattice.alpha,
dlattice.beta, dlattice.gamma)
print('\npmg_dlattice.matrix:\n{}'.format(rezero_array(
pmg_dlattice.matrix)))
print('\ndlattice.matrix:\n{}'.format(rezero_array(dlattice.matrix)))
print('\npmg_dlattice.reciprocal_lattice.matrix:\n{}'.format(
rezero_array(pmg_dlattice.reciprocal_lattice.matrix)))
print('\ndlattice.reciprocal_lattice.matrix:\n{}'.format(
rezero_array(dlattice.reciprocal_lattice.matrix)))
assert_true(np.allclose(dlattice.a, pmg_dlattice.a))
assert_true(np.allclose(dlattice.b, pmg_dlattice.b))
assert_true(np.allclose(dlattice.c, pmg_dlattice.c))
assert_true(np.allclose(np.asarray(dlattice.a1), pmg_dlattice.matrix[0]))
assert_true(np.allclose(np.asarray(dlattice.a2), pmg_dlattice.matrix[1]))
assert_true(np.allclose(np.asarray(dlattice.a3), pmg_dlattice.matrix[2]))
assert_true(np.allclose(dlattice.matrix, pmg_dlattice.matrix))
assert_true(
np.allclose(dlattice.ortho_matrix.T,
pmg.Lattice(dlattice.ortho_matrix.T).matrix))
assert_true(
np.allclose(
pmg.Lattice(dlattice.matrix).metric_tensor,
dlattice.metric_tensor))
assert_true(
np.allclose(
pmg.Lattice(dlattice.ortho_matrix.T).metric_tensor,
dlattice.metric_tensor))
assert_true(
np.allclose(pmg.Lattice(dlattice.matrix).matrix, dlattice.matrix))
assert_true(
np.allclose(
pmg.Lattice(dlattice.ortho_matrix.T).matrix, dlattice.matrix))
assert_true(
np.allclose(
pmg.Lattice(dlattice.matrix).matrix,
rlattice.reciprocal_lattice.matrix))
pmg_rlattice = \
pmg.Lattice.from_parameters(dlattice.reciprocal_lattice.a_star,
dlattice.reciprocal_lattice.b_star,
dlattice.reciprocal_lattice.c_star,
dlattice.reciprocal_lattice.alpha_star,
dlattice.reciprocal_lattice.beta_star,
dlattice.reciprocal_lattice.gamma_star)
print('\npmg_rlattice:\n{}'.format(rezero_array(pmg_rlattice.matrix)))
print('\nrlattice:\n{}'.format(rezero_array(rlattice.matrix)))
assert_true(
np.allclose(dlattice.reciprocal_lattice.matrix, rlattice.matrix))