def test_get_hkl_from_q(self):
lat = ( 5.0, 10.0, 20.0)
lat_inverse = (0.2, 0.1, 0.05)
angles = tuple( np.deg2rad( [90, 90, 90]))
(a,b,c) = make_reciprocal_lattice(lat, angles)
rec = vectors_to_matrix(a,b,c)
hkl = get_hkl_from_q(column([0.2, 0, 0])*2*pi, rec)
assert np.allclose(vector(hkl), vector([1,0,0])), "get_hkl_from_q (1,0,0)."
#Sanity check
for i in xrange(10):
val = column(np.random.rand(3))
q = get_q_from_hkl(val, a, b, c)
hkl = get_hkl_from_q(q, rec)
assert np.allclose(vector(hkl), vector(val)), "get_hkl_from_q vs get_q_from_hkl for random values."
def test_make_lattice_vectors(self):
"cystal_calc module: make_lattice_vectors()"
#Make up a lattice - orthorombic
lat = ( 5.0, 10.0, 20.0)
angles = tuple( np.deg2rad( [90, 90, 90]))
#Make the expected matrix
M = np.identity(3)
for x in xrange(3): M[x,x] = lat[x]
(a,b,c,V) = make_lattice_vectors(lat, angles)
res = (vectors_to_matrix(a,b,c))
assert np.allclose(M, res), "Simple orthorombic lattice"
assert self.check_matrix_lengths(res, lat), "orthorombic: vectors are correct length."
#Monoclinic example
angles = tuple( np.deg2rad( [45, 90, 90]))
M[:,2] = np.sqrt(2)/2 * vector( 0, 20, 20 ) #Value by inspection
(a,b,c,V) = make_lattice_vectors(lat, angles)
res = (vectors_to_matrix(a,b,c))
assert np.allclose(M, res), "Monoclinic lattice"
assert self.check_matrix_lengths(res, lat), "Monoclinic: vectors are correct length."
#Rhombohedral example
angles = tuple( np.deg2rad( [45, 45, 45]))
M = np.identity(3)
for x in xrange(3): M[x,x] = lat[x]
M[:,1] = np.sqrt(2)/2 * vector( 10, 10, 0 ) #Value by inspection
M[:,2] = vector( 14.14213562, 5.85786438, 12.87188506 ) #Value came from program
(a,b,c,V) = make_lattice_vectors(lat, angles)
res = (vectors_to_matrix(a,b,c))
assert np.allclose(M, res), "Rhombohedral lattice"
assert self.check_matrix_lengths(res, lat), "Rhombohedral: vectors are correct length."
#Triclinic example
angles = tuple( np.deg2rad( [30, 45, 60]))
M = np.identity(3)
for x in xrange(3): M[x,x] = lat[x]
M[:,1] = vector( 5, 8.66025404, 0 ) #Value came from program
M[:,2] = vector( 14.14213562, 11.83503419, 7.74157385 ) #Value came from program
(a,b,c,V) = make_lattice_vectors(lat, angles)
res = (vectors_to_matrix(a,b,c))
assert np.allclose(M, res), "Triclinic lattice"
assert self.check_matrix_lengths(res, lat), "Triclinic: vectors are correct length."
def test_get_q_from_hkl(self):
lat = ( 5.0, 10.0, 20.0)
lat_inverse = (0.2, 0.1, 0.05)
angles = tuple( np.deg2rad( [90, 90, 90]))
(a,b,c) = make_reciprocal_lattice(lat, angles)
q = get_q_from_hkl(column([1., 0, 0]), a, b, c)
assert np.allclose(vector(q), a), "Simple get_q_from_hkl a."
q = get_q_from_hkl(column([1., 0, 0]), a, b, c)
assert np.allclose(vector(q), vector([2*pi/5, 0, 0])), "Simple get_q_from_hkl a, comparing to value."
q = get_q_from_hkl(column([0, 1., 0]), a, b, c)
assert np.allclose(vector(q), b), "Simple get_q_from_hkl b."
q = get_q_from_hkl(column([0, 0, 1.]), a, b, c)
assert np.allclose(vector(q), c), "Simple get_q_from_hkl c."
q = get_q_from_hkl(column([1, 2, 3.]), a, b, c)
assert np.allclose(vector(q), a+2*b+3*c), "get_q_from_hkl (1,2,3)."
hkl = np.ones( (3, 12) )
q = get_q_from_hkl(hkl, a, b, c)
assert q.shape == (3, 12), "get_q_from_hkl correct shape."
def make_reciprocal_lattice(lattice_lengths, lattice_angles):
"""Generate a reciprocal lattice matrix.
Parameters:
lattice_lengths: tuple. the DIRECT lattice lengths a,b,c in Angstroms.
lattice_angles: tuple. the DIRECT lattice lengths alpha, beta, gamma, in radians.
alpha = angle between b and c; beta = angle between a and c; gamma = angle between b and c
Returns:
(a_star, b_star, c_star): the 3 reciprocal lattice vectors.
"""
#First, get the direct space lattice vectors
(a,b,c, V) = make_lattice_vectors(lattice_lengths, lattice_angles)
#With cross-products, calculate the reciprocal vectors
a_star = 2 * np.pi * np.cross(vector(b),vector(c)) / V
b_star = 2 * np.pi * np.cross(vector(c),vector(a)) / V
c_star = 2 * np.pi * np.cross(vector(a),vector(b)) / V
return (a_star, b_star, c_star)
