def test_composition(self):
nu, nv, nw, n_atm = 2, 3, 4, 2
np.random.seed(13)
c = 0.7
A_r = occupational.composition(nu, nv, nw, n_atm, value=c)
delta = c * (1 + A_r)
sigma = 2 * delta - 1
np.testing.assert_array_almost_equal(sigma, (2 * (A_r > 0) - 1))
np.random.seed(13)
u = np.random.rand(nu, nv, nw, n_atm)
np.testing.assert_array_almost_equal(delta, u.flatten() <= c)
c = np.array([0.6, 0.4])
A_r = occupational.composition(nu, nv, nw, n_atm, value=c)
delta = (c * (1 + A_r.reshape(nu, nv, nw, n_atm))).flatten()
sigma = 2 * delta - 1
np.testing.assert_array_almost_equal(sigma, (2 * (A_r > 0) - 1))
def test_transform(self):
nu, nv, nw, n_atm = 2, 3, 4, 2
np.random.seed(13)
c = 0.7
A_r = occupational.composition(nu, nv, nw, n_atm, value=c)
H = np.random.randint(0, 4 * nu, size=(16))
K = np.random.randint(0, 5 * nv, size=(16))
L = np.random.randint(0, 6 * nw, size=(16))
A_k, i_dft = occupational.transform(A_r, H, K, L, nu, nv, nw, n_atm)
A_r = A_r.reshape(nu, nv, nw, n_atm)
A_k = A_k.reshape(nu, nv, nw, n_atm)
n_uvw = nu * nv * nw
np.testing.assert_array_almost_equal(A_k[0,0,0,:], \
np.mean(A_r, axis=(0,1,2))*n_uvw)
w = i_dft % nw
v = i_dft // nw % nv
u = i_dft // nw // nv % nu
np.testing.assert_array_equal(u, np.mod(H, nu))
np.testing.assert_array_equal(v, np.mod(K, nv))
np.testing.assert_array_equal(w, np.mod(L, nw))
def test_transform(self):
nu, nv, nw, n_atm = 2, 3, 4, 2
np.random.seed(13)
c = 0.1
Ux, Uy, Uz = displacive.expansion(nu, nv, nw, n_atm, value=c)
c = 0.7
A_r = occupational.composition(nu, nv, nw, n_atm, value=c)
H = np.random.randint(0, 4 * nu, size=(16))
K = np.random.randint(0, 5 * nv, size=(16))
L = np.random.randint(0, 6 * nw, size=(16))
p = 2
U_r = displacive.products(Ux, Uy, Uz, p)
n_prod = U_r.shape[0] // (nu * nv * nw * n_atm)
U_k, A_k, i_dft = nonmagnetic.transform(U_r, A_r, H, K, L, nu, nv, nw,
n_atm)
A_r = np.tile(A_r, n_prod)
U_r = U_r.reshape(n_prod, nu, nv, nw, n_atm)
A_r = A_r.reshape(n_prod, nu, nv, nw, n_atm)
U_k = U_k.reshape(n_prod, nu, nv, nw, n_atm)
A_k = A_k.reshape(n_prod, nu, nv, nw, n_atm)
n_uvw = nu * nv * nw
V_r = U_r * A_r
np.testing.assert_array_almost_equal(U_k[:,0,0,0,:], \
np.mean(U_r, axis=(1,2,3))*n_uvw)
np.testing.assert_array_almost_equal(A_k[:,0,0,0,:], \
np.mean(V_r, axis=(1,2,3))*n_uvw)
w = i_dft % nw
v = i_dft // nw % nv
u = i_dft // nw // nv % nu
np.testing.assert_array_equal(u, np.mod(H, nu))
np.testing.assert_array_equal(v, np.mod(K, nv))
np.testing.assert_array_equal(w, np.mod(L, nw))
def test_disordered(self):
folder = os.path.abspath(os.path.join(directory, '..', 'data'))
uc_dict = crystal.unitcell(folder=folder,
filename='CaTiOSiO4.cif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
mom = uc_dict['moment']
atm = uc_dict['atom']
n_atm = uc_dict['n_atom']
nu, nv, nw = 2, 3, 4
constants = crystal.parameters(folder=folder, filename='CaTiOSiO4.cif')
A = crystal.cartesian(*constants)
C = crystal.cartesian_moment(*constants)
D = crystal.cartesian_displacement(*constants)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
U11, U22, U33, U23, U13, U12 = disp.T
U = np.row_stack(displacive.cartesian(U11, U22, U33, U23, U13, U12, D))
Ux, Uy, Uz = displacive.expansion(nu, nv, nw, n_atm, U)
A_r = occupational.composition(nu, nv, nw, n_atm, occ)
delta = (occ * (1 + A_r.reshape(nu, nv, nw, n_atm))).flatten()
mu1, mu2, mu3 = mom.T
mu = np.row_stack(magnetic.cartesian(mu1, mu2, mu3, C))
Sx, Sy, Sz = magnetic.spin(nu, nv, nw, n_atm, mu)
crystal.disordered(delta,
Ux,
Uy,
Uz,
Sx,
Sy,
Sz,
rx,
ry,
rz,
nu,
nv,
nw,
atm,
A,
folder + '/disordered_CaTiOSiO4.cif',
folder=folder,
filename='CaTiOSiO4.cif',
ulim=[0, nu],
vlim=[0, nv],
wlim=[0, nw])
UC_dict = crystal.unitcell(folder=folder,
filename='disordered_CaTiOSiO4.cif',
tol=1e-4)
Atm = UC_dict['atom']
np.testing.assert_array_equal(atms == Atm, True)
os.remove(folder + '/disordered_CaTiOSiO4.cif')
uc_dict = crystal.unitcell(folder=folder,
filename='CuMnO2.mcif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
mom = uc_dict['moment']
atm = uc_dict['atom']
n_atm = uc_dict['n_atom']
nu, nv, nw = 2, 3, 4
constants = crystal.parameters(folder=folder, filename='CuMnO2.mcif')
A = crystal.cartesian(*constants)
C = crystal.cartesian_moment(*constants)
D = crystal.cartesian_displacement(*constants)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
Uiso = disp.flatten()
Ux, Uy, Uz = displacive.expansion(nu, nv, nw, n_atm, Uiso)
A_r = occupational.composition(nu, nv, nw, n_atm, occ)
delta = (occ * (1 + A_r.reshape(nu, nv, nw, n_atm))).flatten()
mu1, mu2, mu3 = mom.T
mu = np.row_stack(magnetic.cartesian(mu1, mu2, mu3, C))
Sx, Sy, Sz = magnetic.spin(nu, nv, nw, n_atm, mu)
crystal.disordered(delta,
Ux,
Uy,
Uz,
Sx,
Sy,
Sz,
rx,
ry,
rz,
nu,
nv,
nw,
atm,
A,
folder + '/disordered_CuMnO2.mcif',
folder=folder,
filename='CuMnO2.mcif',
ulim=[0, nu],
vlim=[0, nv],
wlim=[0, nw])
UC_dict = crystal.unitcell(folder=folder,
filename='disordered_CuMnO2.mcif',
tol=1e-4)
Atm = UC_dict['atom']
np.testing.assert_array_equal(atms == Atm, True)
os.remove(folder + '/disordered_CuMnO2.mcif')
def test_occupational(self):
a, b, c, alpha, beta, gamma = 5, 6, 7, np.pi / 2, np.pi / 3, np.pi / 4
inv_constants = crystal.reciprocal(a, b, c, alpha, beta, gamma)
a_, b_, c_, alpha_, beta_, gamma_ = inv_constants
h_range, nh = [-1, 1], 5
k_range, nk = [0, 2], 11
l_range, nl = [-1, 0], 5
nu, nv, nw, n_atm = 2, 5, 4, 2
u = np.array([0.2, 0.1])
v = np.array([0.3, 0.4])
w = np.array([0.4, 0.5])
atm = np.array(['Fe', 'Mn'])
occupancy = np.array([0.75, 0.5])
U11 = np.array([0.5, 0.3])
U22 = np.array([0.6, 0.4])
U33 = np.array([0.4, 0.6])
U23 = np.array([0.05, -0.03])
U13 = np.array([-0.04, 0.02])
U12 = np.array([0.03, -0.02])
twins = np.eye(3).reshape(1, 3, 3)
variants = np.array([1.0])
W = np.eye(3)
T = space.debye_waller(h_range, k_range, l_range, nh, nk, nl, U11, U22,
U33, U23, U13, U12, a_, b_, c_)
A = crystal.cartesian(a, b, c, alpha, beta, gamma)
B = crystal.cartesian(a_, b_, c_, alpha_, beta_, gamma_)
R = crystal.cartesian_rotation(a, b, c, alpha, beta, gamma)
D = crystal.cartesian_displacement(a, b, c, alpha, beta, gamma)
A_r = occupational.composition(nu, nv, nw, n_atm, value=occupancy)
index_parameters = space.mapping(h_range, k_range, l_range, nh, nk, nl,
nu, nv, nw)
h, k, l, H, K, L, indices, inverses, operators = index_parameters
Qh, Qk, Ql = crystal.vector(h, k, l, B)
Qx, Qy, Qz = crystal.transform(Qh, Qk, Ql, R)
Qx_norm, Qy_norm, Qz_norm, Q = space.unit(Qx, Qy, Qz)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
phase_factor = scattering.phase(Qx, Qy, Qz, ux, uy, uz)
scattering_length = scattering.length(atm, Q.size)
A_k, i_dft = occupational.transform(A_r, H, K, L, nu, nv, nw, n_atm)
factors = space.prefactors(scattering_length, phase_factor, occupancy)
factors *= T
I_ref = occupational.intensity(A_k, i_dft, factors)
reduced_params = space.reduced(h_range, k_range, l_range, nh, nk, nl,
nu, nv, nw)
indices, reverses, symops, Nu, Nv, Nw = reduced_params
symop = symmetry.laue_id(symops)
I = monocrystal.occupational(A_r, occupancy, U11, U22, U33, U23, U13,
U12, ux, uy, uz, atm, h_range, k_range,
l_range, indices, symop, W, B, R, D,
twins, variants, nh, nk, nl, nu, nv, nw,
Nu, Nv, Nw)
np.testing.assert_array_almost_equal(I, I_ref)
def test_intensity(self):
a, b, c, alpha, beta, gamma = 5, 6, 7, np.pi / 2, np.pi / 3, np.pi / 4
inv_constants = crystal.reciprocal(a, b, c, alpha, beta, gamma)
a_, b_, c_, alpha_, beta_, gamma_ = inv_constants
h_range, nh = [-1, 1], 5
k_range, nk = [0, 2], 11
l_range, nl = [-1, 0], 5
nu, nv, nw, n_atm = 2, 5, 4, 2
u = np.array([0.2, 0.1])
v = np.array([0.3, 0.4])
w = np.array([0.4, 0.5])
atm = np.array(['Fe', 'Mn'])
occupancy = np.array([0.75, 0.5])
U11 = np.array([0.5, 0.3])
U22 = np.array([0.6, 0.4])
U33 = np.array([0.4, 0.6])
U23 = np.array([0.05, -0.03])
U13 = np.array([-0.04, 0.02])
U12 = np.array([0.03, -0.02])
T = space.debye_waller(h_range, k_range, l_range, nh, nk, nl, U11, U22,
U33, U23, U13, U12, a_, b_, c_)
A = crystal.cartesian(a, b, c, alpha, beta, gamma)
B = crystal.cartesian(a_, b_, c_, alpha_, beta_, gamma_)
R = crystal.cartesian_rotation(a, b, c, alpha, beta, gamma)
A_r = occupational.composition(nu, nv, nw, n_atm, value=occupancy)
index_parameters = space.mapping(h_range, k_range, l_range, nh, nk, nl,
nu, nv, nw)
h, k, l, H, K, L, indices, inverses, operators = index_parameters
Qh, Qk, Ql = crystal.vector(h, k, l, B)
Qx, Qy, Qz = crystal.transform(Qh, Qk, Ql, R)
Qx_norm, Qy_norm, Qz_norm, Q = space.unit(Qx, Qy, Qz)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
phase_factor = scattering.phase(Qx, Qy, Qz, ux, uy, uz)
scattering_length = scattering.length(atm, Q.size)
A_k, i_dft = occupational.transform(A_r, H, K, L, nu, nv, nw, n_atm)
factors = space.prefactors(scattering_length, phase_factor, occupancy)
factors *= T
I = occupational.intensity(A_k, i_dft, factors)
n_hkl = Q.size
n_xyz = nu * nv * nw * n_atm
i, j = np.triu_indices(n_xyz, 1)
k, l = np.mod(i, n_atm), np.mod(j, n_atm)
m = np.arange(n_xyz)
n = np.mod(m, n_atm)
rx_ij = rx[j] - rx[i]
ry_ij = ry[j] - ry[i]
rz_ij = rz[j] - rz[i]
bc = scattering.length(atm, 1)
T = T.reshape(n_hkl, n_atm)
A_i, A_j, A_m = A_r[i], A_r[j], A_r[m]
c_k, c_l, c_n = occupancy[k], occupancy[l], occupancy[n]
b_k, b_l, b_n = bc[k], bc[l], bc[n]
T_k, T_l, T_n = T[:, k], T[:, l], T[:, n]
I_ref = ((c_n**2*(b_n*b_n.conj()).real*A_m**2*T_n**2).sum(axis=1)\
+ 2*(c_k*c_l*(b_k*b_l.conj()).real*A_i*A_j*T_k*T_l*\
np.cos(Qx[:,np.newaxis]*rx_ij+\
Qy[:,np.newaxis]*ry_ij+\
Qz[:,np.newaxis]*rz_ij)).sum(axis=1))/n_xyz
np.testing.assert_array_almost_equal(I, I_ref)
def test_structure(self):
a, b, c, alpha, beta, gamma = 5, 6, 7, np.pi / 2, np.pi / 3, np.pi / 4
inv_constants = crystal.reciprocal(a, b, c, alpha, beta, gamma)
a_, b_, c_, alpha_, beta_, gamma_ = inv_constants
h_range, nh = [-1, 1], 5
k_range, nk = [0, 2], 11
l_range, nl = [-1, 0], 5
nu, nv, nw, n_atm = 2, 5, 4, 2
u = np.array([0.2, 0.1])
v = np.array([0.3, 0.4])
w = np.array([0.4, 0.5])
atm = np.array(['Fe', 'Mn'])
occupancy = np.array([0.75, 0.5])
U11 = np.array([0.5, 0.3])
U22 = np.array([0.6, 0.4])
U33 = np.array([0.4, 0.6])
U23 = np.array([0.05, -0.03])
U13 = np.array([-0.04, 0.02])
U12 = np.array([0.03, -0.02])
T = space.debye_waller(h_range, k_range, l_range, nh, nk, nl, U11, U22,
U33, U23, U13, U12, a_, b_, c_)
A = crystal.cartesian(a, b, c, alpha, beta, gamma)
B = crystal.cartesian(a_, b_, c_, alpha_, beta_, gamma_)
R = crystal.cartesian_rotation(a, b, c, alpha, beta, gamma)
A_r = occupational.composition(nu, nv, nw, n_atm, value=occupancy)
index_parameters = space.mapping(h_range, k_range, l_range, nh, nk, nl,
nu, nv, nw)
h, k, l, H, K, L, indices, inverses, operators = index_parameters
Qh, Qk, Ql = crystal.vector(h, k, l, B)
Qx, Qy, Qz = crystal.transform(Qh, Qk, Ql, R)
Qx_norm, Qy_norm, Qz_norm, Q = space.unit(Qx, Qy, Qz)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
phase_factor = scattering.phase(Qx, Qy, Qz, ux, uy, uz)
scattering_length = scattering.length(atm, Q.size)
A_k, i_dft = occupational.transform(A_r, H, K, L, nu, nv, nw, n_atm)
factors = space.prefactors(scattering_length, phase_factor, occupancy)
factors *= T
F, prod = occupational.structure(A_k, i_dft, factors)
n_hkl = Q.size
n_xyz = nu * nv * nw * n_atm
m = np.arange(n_xyz)
n = np.mod(m, n_atm)
rx_m = rx[m]
ry_m = ry[m]
rz_m = rz[m]
bc = scattering.length(atm, 1)
T = T.reshape(n_hkl, n_atm)
A_m = A_r[m]
c_n = occupancy[n]
b_n = bc[n]
T_n = T[:, n]
prod_ref = (c_n*b_n*A_m*T_n*np.exp(1j*(Qx[:,np.newaxis]*rx_m+\
Qy[:,np.newaxis]*ry_m+\
Qz[:,np.newaxis]*rz_m)))
F_ref = prod_ref.sum(axis=1)
prod_ref = prod_ref.reshape(n_hkl, nu * nv * nw,
n_atm).sum(axis=1).flatten()
np.testing.assert_array_almost_equal(F, F_ref)
np.testing.assert_array_almost_equal(prod, prod_ref)
def random_occupancies(self, nu, nv, nw, n_atm, occupancy):
return occupational.composition(nu, nv, nw, n_atm, occupancy)
def test_intensity(self):
a, b, c, alpha, beta, gamma = 5, 6, 7, np.pi / 2, np.pi / 3, np.pi / 4
inv_constants = crystal.reciprocal(a, b, c, alpha, beta, gamma)
a_, b_, c_, alpha_, beta_, gamma_ = inv_constants
h_range, nh = [-1, 1], 5
k_range, nk = [0, 2], 11
l_range, nl = [-1, 0], 5
nu, nv, nw, n_atm = 2, 5, 4, 2
u = np.array([0.2, 0.1])
v = np.array([0.3, 0.4])
w = np.array([0.4, 0.5])
atm = np.array(['Fe', 'Mn'])
occupancy = np.array([0.75, 0.5])
U11 = np.array([0.5, 0.3])
U22 = np.array([0.6, 0.4])
U33 = np.array([0.4, 0.6])
U23 = np.array([0.05, -0.03])
U13 = np.array([-0.04, 0.02])
U12 = np.array([0.03, -0.02])
A = crystal.cartesian(a, b, c, alpha, beta, gamma)
B = crystal.cartesian(a_, b_, c_, alpha_, beta_, gamma_)
R = crystal.cartesian_rotation(a, b, c, alpha, beta, gamma)
U = np.row_stack((U11, U22, U33, U23, U13, U12))
Ux, Uy, Uz = displacive.expansion(nu, nv, nw, n_atm, value=U)
A_r = occupational.composition(nu, nv, nw, n_atm, value=occupancy)
index_parameters = space.mapping(h_range, k_range, l_range, nh, nk, nl,
nu, nv, nw)
h, k, l, H, K, L, indices, inverses, operators = index_parameters
Qh, Qk, Ql = crystal.vector(h, k, l, B)
Qx, Qy, Qz = crystal.transform(Qh, Qk, Ql, R)
Qx_norm, Qy_norm, Qz_norm, Q = space.unit(Qx, Qy, Qz)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
phase_factor = scattering.phase(Qx, Qy, Qz, ux, uy, uz)
scattering_length = scattering.length(atm, Q.size)
p = 3
coeffs = displacive.coefficients(p)
H_nuc, K_nuc, L_nuc, cond = space.condition(H,
K,
L,
nu,
nv,
nw,
centering='P')
U_r = displacive.products(Ux, Uy, Uz, p)
Q_k = displacive.products(Qx, Qy, Qz, p)
U_k, A_k, i_dft = nonmagnetic.transform(U_r, A_r, H, K, L, nu, nv, nw,
n_atm)
factors = space.prefactors(scattering_length, phase_factor, occupancy)
I, F_nuc = nonmagnetic.intensity(U_k,
A_k,
Q_k,
coeffs,
cond,
p,
i_dft,
factors,
subtract=False)
n_hkl = Q.size
n_xyz = nu * nv * nw * n_atm
i, j = np.triu_indices(n_xyz, 1)
k, l = np.mod(i, n_atm), np.mod(j, n_atm)
m = np.arange(n_xyz)
n = np.mod(m, n_atm)
rx_ij = rx[j] - rx[i]
ry_ij = ry[j] - ry[i]
rz_ij = rz[j] - rz[i]
bc = scattering.length(atm, 1)
U_r = U_r.reshape(coeffs.shape[0], n_xyz)
Q_k = Q_k.reshape(coeffs.shape[0], n_hkl)
U_i, U_j, U_m = U_r[:, i], U_r[:, j], U_r[:, m]
A_i, A_j, A_m = A_r[i], A_r[j], A_r[m]
c_k, c_l, c_n = occupancy[k], occupancy[l], occupancy[n]
b_k, b_l, b_n = bc[k], bc[l], bc[n]
exp_iQ_dot_V_m = np.dot(coeffs * (U_m + A_m * U_m).T, Q_k).T
exp_iQ_dot_V_i = np.dot(coeffs * (U_i + A_i * U_i).T, Q_k).T
exp_iQ_dot_V_j = np.dot(coeffs * (U_j + A_j * U_j).T, Q_k).T
I_ref = ((c_n**2*(b_n*b_n.conj()).real*\
(exp_iQ_dot_V_m*exp_iQ_dot_V_m.conj()).real).sum(axis=1)\
+ 2*(c_k*c_l*(b_k*b_l.conj()).real*
((exp_iQ_dot_V_i*exp_iQ_dot_V_j.conj()*\
np.cos(Qx[:,np.newaxis]*rx_ij+\
Qy[:,np.newaxis]*ry_ij+\
Qz[:,np.newaxis]*rz_ij)).real+
(exp_iQ_dot_V_i*exp_iQ_dot_V_j.conj()*\
np.sin(Qx[:,np.newaxis]*rx_ij+\
Qy[:,np.newaxis]*ry_ij+\
Qz[:,np.newaxis]*rz_ij)).imag
)).sum(axis=1))/n_xyz
np.testing.assert_array_almost_equal(I, I_ref)
def test_structure(self):
a, b, c, alpha, beta, gamma = 5, 6, 7, np.pi / 2, np.pi / 3, np.pi / 4
inv_constants = crystal.reciprocal(a, b, c, alpha, beta, gamma)
a_, b_, c_, alpha_, beta_, gamma_ = inv_constants
h_range, nh = [-1, 1], 5
k_range, nk = [0, 2], 11
l_range, nl = [-1, 0], 5
nu, nv, nw, n_atm = 2, 5, 4, 2
u = np.array([0.2, 0.1])
v = np.array([0.3, 0.4])
w = np.array([0.4, 0.5])
atm = np.array(['Fe', 'Mn'])
occupancy = np.array([0.75, 0.5])
U11 = np.array([0.5, 0.3])
U22 = np.array([0.6, 0.4])
U33 = np.array([0.4, 0.6])
U23 = np.array([0.05, -0.03])
U13 = np.array([-0.04, 0.02])
U12 = np.array([0.03, -0.02])
A = crystal.cartesian(a, b, c, alpha, beta, gamma)
B = crystal.cartesian(a_, b_, c_, alpha_, beta_, gamma_)
R = crystal.cartesian_rotation(a, b, c, alpha, beta, gamma)
U = np.row_stack((U11, U22, U33, U23, U13, U12))
Ux, Uy, Uz = displacive.expansion(nu, nv, nw, n_atm, value=U)
A_r = occupational.composition(nu, nv, nw, n_atm, value=occupancy)
index_parameters = space.mapping(h_range, k_range, l_range, nh, nk, nl,
nu, nv, nw)
h, k, l, H, K, L, indices, inverses, operators = index_parameters
Qh, Qk, Ql = crystal.vector(h, k, l, B)
Qx, Qy, Qz = crystal.transform(Qh, Qk, Ql, R)
Qx_norm, Qy_norm, Qz_norm, Q = space.unit(Qx, Qy, Qz)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
phase_factor = scattering.phase(Qx, Qy, Qz, ux, uy, uz)
scattering_length = scattering.length(atm, Q.size)
p = 3
coeffs = displacive.coefficients(p)
H_nuc, K_nuc, L_nuc, cond = space.condition(H,
K,
L,
nu,
nv,
nw,
centering='P')
U_r = displacive.products(Ux, Uy, Uz, p)
Q_k = displacive.products(Qx, Qy, Qz, p)
U_k, A_k, i_dft = nonmagnetic.transform(U_r, A_r, H, K, L, nu, nv, nw,
n_atm)
factors = space.prefactors(scattering_length, phase_factor, occupancy)
F, F_nuc, \
prod, prod_nuc, \
V_k, V_k_nuc, \
even, bragg = nonmagnetic.structure(U_k, A_k, Q_k, coeffs, cond,
p, i_dft, factors)
n_hkl = Q.size
n_xyz = nu * nv * nw * n_atm
m = np.arange(n_xyz)
n = np.mod(m, n_atm)
rx_m = rx[m]
ry_m = ry[m]
rz_m = rz[m]
bc = scattering.length(atm, 1)
U_r = U_r.reshape(coeffs.shape[0], n_xyz)
Q_k = Q_k.reshape(coeffs.shape[0], n_hkl)
U_m = U_r[:, m]
A_m = A_r[m]
c_n = occupancy[n]
b_n = bc[n]
exp_iQ_dot_V_m = np.dot(coeffs * (U_m + A_m * U_m).T, Q_k).T
prod_ref = (c_n*b_n*exp_iQ_dot_V_m*np.exp(1j*(Qx[:,np.newaxis]*rx_m+\
Qy[:,np.newaxis]*ry_m+\
Qz[:,np.newaxis]*rz_m)))
F_ref = prod_ref.sum(axis=1)
prod_ref = prod_ref.reshape(n_hkl, nu * nv * nw,
n_atm).sum(axis=1).flatten()
np.testing.assert_array_almost_equal(F, F_ref)
np.testing.assert_array_almost_equal(prod, prod_ref)