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monocrystal.pyx
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monocrystal.pyx
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#cython: boundscheck=False, wraparound=False, nonecheck=False, cdivision=True
#cython: language_level=3
import numpy as np
cimport numpy as np
from cython.parallel import prange
cimport cython
from disorder.material import tables
from libc.math cimport M_PI, cos, sin, exp, sqrt, fabs, fmod, remainder
cpdef (double, double, double) transform(double x,
double y,
double z,
Py_ssize_t sym,
Py_ssize_t op) nogil:
if (sym == 0):
if (op == 0): return x,y,z
elif (op == 1): return -x,-y,z
elif (op == 2): return -x,y,-z
elif (op == 3): return x,-y,-z
elif (op == 4): return z,x,y
elif (op == 5): return z,-x,-y
elif (op == 6): return -z,-x,y
elif (op == 7): return -z,x,-y
elif (op == 8): return y,z,x
elif (op == 9): return -y,z,-x
elif (op == 10): return y,-z,-x
elif (op == 11): return -y,-z,x
elif (op == 12): return y,x,-z
elif (op == 13): return -y,-x,-z
elif (op == 14): return y,-x,z
elif (op == 15): return -y,x,z
elif (op == 16): return x,z,-y
elif (op == 17): return -x,z,y
elif (op == 18): return -x,-z,-y
elif (op == 19): return x,-z,y
elif (op == 20): return z,y,-x
elif (op == 21): return z,-y,x
elif (op == 22): return -z,y,x
elif (op == 23): return -z,-y,-x
elif (op == 24): return -x,-y,-z
elif (op == 25): return x,y,-z
elif (op == 26): return x,-y,z
elif (op == 27): return -x,y,z
elif (op == 28): return -z,-x,-y
elif (op == 29): return -z,x,y
elif (op == 30): return z,x,-y
elif (op == 31): return z,-x,y
elif (op == 32): return -y,-z,-x
elif (op == 33): return y,-z,x
elif (op == 34): return -y,z,x
elif (op == 35): return y,z,-x
elif (op == 36): return -y,-x,z
elif (op == 37): return y,x,z
elif (op == 38): return -y,x,-z
elif (op == 39): return y,-x,-z
elif (op == 40): return -x,-z,y
elif (op == 41): return x,-z,-y
elif (op == 42): return x,z,y
elif (op == 43): return -x,z,-y
elif (op == 44): return -z,-y,x
elif (op == 45): return -z,y,-x
elif (op == 46): return z,-y,-x
else: return z,y,x
elif (sym == 1):
if (op == 0): return x,y,z
elif (op == 1): return -x,-y,z
elif (op == 2): return -x,y,-z
elif (op == 3): return x,-y,-z
elif (op == 4): return z,x,y
elif (op == 5): return z,-x,-y
elif (op == 6): return -z,-x,y
elif (op == 7): return -z,x,-y
elif (op == 8): return y,z,x
elif (op == 9): return -y,z,-x
elif (op == 10): return y,-z,-x
elif (op == 11): return -y,-z,x
elif (op == 12): return -x,-y,-z
elif (op == 13): return x,y,-z
elif (op == 14): return x,-y,z
elif (op == 15): return -x,y,z
elif (op == 16): return -z,-x,-y
elif (op == 17): return -z,x,y
elif (op == 18): return z,x,-y
elif (op == 19): return z,-x,y
elif (op == 20): return -y,-z,-x
elif (op == 21): return y,-z,x
elif (op == 22): return -y,z,x
else: return y,z,-x
elif (sym == 2):
if (op == 0): return x,y,z
elif (op == 1): return -x-y,x,z
elif (op == 2): return y,-x-y,z
elif (op == 3): return -x,-y,z
elif (op == 4): return x+y,-x,z
elif (op == 5): return -y,x+y,z
elif (op == 6): return y,x,-z
elif (op == 7): return x,-x-y,-z
elif (op == 8): return -x-y,y,-z
elif (op == 9): return -y,-x,-z
elif (op == 10): return -x,x+y,-z
elif (op == 11): return x+y,-y,-z
elif (op == 12): return -x,-y,-z
elif (op == 13): return x+y,-x,-z
elif (op == 14): return -y,x+y,-z
elif (op == 15): return x,y,-z
elif (op == 16): return -x-y,x,-z
elif (op == 17): return y,-x-y,-z
elif (op == 18): return -y,-x,z
elif (op == 19): return -x,x+y,z
elif (op == 20): return x+y,-y,z
elif (op == 21): return y,x,z
elif (op == 22): return x,-x-y,z
else: return -x-y,y,z
elif (sym == 3):
if (op == 0): return x,y,z
elif (op == 1): return -x-y,x,z
elif (op == 2): return y,-x-y,z
elif (op == 3): return -x,-y,z
elif (op == 4): return x+y,-x,z
elif (op == 5): return -y,x+y,z
elif (op == 6): return -x,-y,-z
elif (op == 7): return x+y,-x,-z
elif (op == 8): return -y,x+y,-z
elif (op == 9): return x,y,-z
elif (op == 10): return -x-y,x,-z
else: return y,-x-y,-z
elif (sym == 4):
if (op == 0): return x,y,z
elif (op == 1): return -x-y,x,z
elif (op == 2): return y,-x-y,z
elif (op == 3): return -y,-x,-z
elif (op == 4): return -x,x+y,-z
elif (op == 5): return x+y,-y,-z
elif (op == 6): return -x,-y,-z
elif (op == 7): return x+y,-x,-z
elif (op == 8): return -y,x+y,-z
elif (op == 9): return y,x,z
elif (op == 10): return x,-x-y,z
else: return -x-y,y,z
elif (sym == 5):
if (op == 0): return x,y,z
elif (op == 1): return -x-y,x,z
elif (op == 2): return y,-x-y,z
elif (op == 3): return -x,-y,-z
elif (op == 4): return x+y,-x,-z
else: return -y,x+y,-z
elif (sym == 6):
if (op == 0): return x,y,z
elif (op == 1): return -x,-y,z
elif (op == 2): return -y,x,z
elif (op == 3): return y,-x,z
elif (op == 4): return -x,y,-z
elif (op == 5): return x,-y,-z
elif (op == 6): return y,x,-z
elif (op == 7): return -y,-x,-z
elif (op == 8): return -x,-y,-z
elif (op == 9): return x,y,-z
elif (op == 10): return y,-x,-z
elif (op == 11): return -y,x,-z
elif (op == 12): return x,-y,z
elif (op == 13): return -x,y,z
elif (op == 14): return -y,-x,z
else: return y,x,z
elif (sym == 7):
if (op == 0): return x,y,z
elif (op == 1): return -x,-y,z
elif (op == 2): return -y,x,z
elif (op == 3): return y,-x,z
elif (op == 4): return -x,-y,-z
elif (op == 5): return x,y,-z
elif (op == 6): return y,-x,-z
else: return -y,x,-z
elif (sym == 8):
if (op == 0): return x,y,z
elif (op == 1): return -x,-y,z
elif (op == 2): return -x,y,-z
elif (op == 3): return x,-y,-z
elif (op == 4): return -x,-y,-z
elif (op == 5): return x,y,-z
elif (op == 6): return x,-y,z
else: return -x,y,z
elif (sym == 9):
if (op == 0): return x,y,z
elif (op == 1): return -x,y,-z
elif (op == 2): return -x,-y,-z
else: return x,-y,z
elif (sym == 10):
if (op == 0): return x,y,z
else: return -x,-y,-z
else:
return x,y,z
cdef double round2even(double x) nogil:
x -= remainder(x, 1.0)
return x
cdef double complex iexp(double y) nogil:
return cos(y)+1j*sin(y)
cdef bint iszero(double a) nogil:
cdef double atol = 1e-04
return fabs(a) <= atol
cdef bint nuclear(double h, double k, double l, int centering) nogil:
cdef bint cond = 0
cdef int H, K, L
H, K, L = int(round2even(h)), int(round2even(k)), int(round2even(l))
if (centering == 0):
cond = 0
elif (centering == 1):
cond = (H % 1 == 0) & (K % 1 == 0) & (L % 1 == 0)
elif (centering == 2):
cond = ((H+K+L) % 2 == 0)
elif (centering == 3):
cond = ((H+K) % 2 == 0) \
& ((K+L) % 2 == 0) \
& ((L+H) % 2 == 0)
elif (centering == 4):
cond = ((-H+K+L) % 3 == 0)
elif (centering == 5):
cond = ((H+K) % 2 == 0)
elif (centering == 6):
cond = ((K+L) % 2 == 0)
elif (centering == 7):
cond = ((L+H) % 2 == 0)
return cond
@cython.binding(True)
def magnetic(double [::1] Sx,
double [::1] Sy,
double [::1] Sz,
double [::1] occupancy,
double [::1] U11,
double [::1] U22,
double [::1] U33,
double [::1] U23,
double [::1] U13,
double [::1] U12,
double [::1] ux,
double [::1] uy,
double [::1] uz,
ions,
h_range,
k_range,
l_range,
long [::1] indices,
symop,
double [:,:] W,
double [:,:] B,
double [:,:] R,
double [:,:] D,
double [:,:,:] T,
double [:] weights,
Py_ssize_t nh,
Py_ssize_t nk,
Py_ssize_t nl,
Py_ssize_t nu,
Py_ssize_t nv,
Py_ssize_t nw,
Py_ssize_t Nu,
Py_ssize_t Nv,
Py_ssize_t Nw,
double [::1] g):
"""
Magnetic scattering intensity.
Parameters
----------
Sx, Sy, Sz : 1d array
Magnetic spin vector components.
occupancy : 1d array
Unit cell site occupancies.
U11, U22, U33, U23, U13, U12 : 1d array
Unit cell anisotropic displacemnt parameters.
ux, uy, uz : 1d array
Unit cell ion positions.
ions : 1d array
Unit cell ions.
h_range, k_range, l_range : 2-tuple or 2-list
Extents of :math:`h`, :math:`k`, and :math:`l` (min, max) pairs.
indices : 1d array, int
Array of reciprocal space volume indices.
symop : 2-tuple or 2-list, int
Symmetry operator identifier and number of operators.
W : 2d array, 3x3
Reciprocal space projection matrix.
B : 2d array, 3x3
Reciprocal lattice to Cartesian wavevector transformation matrix.
R : 2d array, 3x3
Cartesian axis rotation matrix between real and reciprocal space.
D : 2d array, 3x3
Crystal axis to Cartesian transformation matrix for atomic displacement
parameters.
T : 3d array
Twin transformation matrices. Last two axes are of size 3x3.
weights: 1d array
Twin mass fractions.
nh, nk, nl : int
Number of reciprocal space grid points.
nu, nv, nw : int
Number of supercell grid points.
Nu, Nv, Nw : int
Number of supercell grid points based on reciprocal space resolution.
g : 1d array
Magnetic g-factor.
Returns
-------
I : 1d array
Magnetic scattering intensity.
"""
cdef Py_ssize_t n_atm = len(ions)
cdef Py_ssize_t n_hkl = indices.shape[0]
cdef Py_ssize_t sym = symop[0]
cdef Py_ssize_t n_ops = symop[1]
cdef Py_ssize_t n_vars = weights.shape[0]
cdef Py_ssize_t n_uvw = nu*nv*nw
cdef Py_ssize_t n = n_uvw*n_atm
cdef double factor
if (n == 0):
factor = 0
else:
factor = 1.0/n
cdef double x_, y_, z_
cdef double h_, k_, l_
cdef double x, y, z
cdef double h, k, l
cdef double Qh, Qk, Ql
cdef double Qx, Qy, Qz
cdef double Qx_norm, Qy_norm, Qz_norm, Q
cdef double complex phase_factor, factors, dw_factors
cdef double [::1] Uxx = np.zeros(n_atm, dtype=float)
cdef double [::1] Uyy = np.zeros(n_atm, dtype=float)
cdef double [::1] Uzz = np.zeros(n_atm, dtype=float)
cdef double [::1] Uyz = np.zeros(n_atm, dtype=float)
cdef double [::1] Uxz = np.zeros(n_atm, dtype=float)
cdef double [::1] Uxy = np.zeros(n_atm, dtype=float)
cdef double [::1] K2 = 2/np.copy(g, order='C')-1
cdef double form_factor, j0, j2, s_, s_sq, occ
cdef double [::1] A0 = np.zeros(n_atm, dtype=float)
cdef double [::1] B0 = np.zeros(n_atm, dtype=float)
cdef double [::1] C0 = np.zeros(n_atm, dtype=float)
cdef double [::1] D0 = np.zeros(n_atm, dtype=float)
cdef double [::1] A2 = np.zeros(n_atm, dtype=float)
cdef double [::1] B2 = np.zeros(n_atm, dtype=float)
cdef double [::1] C2 = np.zeros(n_atm, dtype=float)
cdef double [::1] D2 = np.zeros(n_atm, dtype=float)
cdef double [::1] a0 = np.zeros(n_atm, dtype=float)
cdef double [::1] b0 = np.zeros(n_atm, dtype=float)
cdef double [::1] c0 = np.zeros(n_atm, dtype=float)
cdef double [::1] a2 = np.zeros(n_atm, dtype=float)
cdef double [::1] b2 = np.zeros(n_atm, dtype=float)
cdef double [::1] c2 = np.zeros(n_atm, dtype=float)
I_np = np.zeros(n_hkl, dtype=float)
cdef double [::1] I = I_np
Sx_np = np.copy(Sx, order='C')
Sy_np = np.copy(Sy, order='C')
Sz_np = np.copy(Sz, order='C')
Sx_np = Sx_np.reshape(nu,nv,nw,n_atm)
Sy_np = Sy_np.reshape(nu,nv,nw,n_atm)
Sz_np = Sz_np.reshape(nu,nv,nw,n_atm)
cdef double h_min_, k_min_, l_min_
cdef double h_max_, k_max_, l_max_
cdef double h_step_, k_step_, l_step_
h_min_, k_min_, l_min_ = h_range[0], k_range[0], l_range[0]
if (nh == 1):
h_max_ = h_range[0]
h_step_ = 0
else:
h_max_ = h_range[1]
h_step_ = (h_max_-h_min_)/(nh-1)
if (nk == 1):
k_max_ = k_range[0]
k_step_ = 0
else:
k_max_ = k_range[1]
k_step_ = (k_max_-k_min_)/(nk-1)
if (nl == 1):
l_max_ = l_range[0]
l_step_ = 0
else:
l_max_ = l_range[1]
l_step_ = (l_max_-l_min_)/(nl-1)
cdef Py_ssize_t Fu = Nu // nu
cdef Py_ssize_t Fv = Nv // nv
cdef Py_ssize_t Fw = Nw // nw
cdef double f_H, f_K, f_L
cdef double f_Nu = float(Nu)
cdef double f_Nv = float(Nv)
cdef double f_Nw = float(Nw)
Sx_k_np = idft(Sx_np, Nu, Nv, Nw).flatten()*n_uvw
Sy_k_np = idft(Sy_np, Nu, Nv, Nw).flatten()*n_uvw
Sz_k_np = idft(Sz_np, Nu, Nv, Nw).flatten()*n_uvw
cdef double complex [::1] Sx_k = Sx_k_np
cdef double complex [::1] Sy_k = Sy_k_np
cdef double complex [::1] Sz_k = Sz_k_np
cdef Py_ssize_t F_uvw = Fu*Fv*Fw
cdef Py_ssize_t N_uvw = Nu*Nv*Nw
cdef double complex prod_x, prod_y, prod_z
cdef double complex Fx, Fy, Fz
cdef double complex Fx_perp, Fy_perp, Fz_perp
cdef double complex Q_norm_dot_F
cdef double Fx_perp_real, Fy_perp_real, Fz_perp_real
cdef double Fx_perp_imag, Fy_perp_imag, Fz_perp_imag
cdef Py_ssize_t H, K, L, iH, iK, iL
cdef Py_ssize_t i_dft, i_ind, j_dft
cdef Py_ssize_t op, var
cdef Py_ssize_t i, j
cdef Py_ssize_t u, v, w
cdef double M_TAU = 2*np.pi
cdef double complex M_I = 1j
cdef double inv_M_SP = 1/(4*np.pi)
for j in range(n_atm):
ion = ions[j]
if (tables.j0.get(ion) is None):
A0[j], a0[j], \
B0[j], b0[j], \
C0[j], c0[j], \
D0[j] = 0, 0, 0, 0, 0, 0, 0
A2[j], a2[j], \
B2[j], b2[j], \
C2[j], c2[j], \
D2[j] = 0, 0, 0, 0, 0, 0, 0
else:
A0[j], a0[j], \
B0[j], b0[j], \
C0[j], c0[j], \
D0[j] = tables.j0.get(ion)
A2[j], a2[j], \
B2[j], b2[j], \
C2[j], c2[j], \
D2[j] = tables.j2.get(ion)
U = np.array([[U11[j], U12[j], U13[j]],
[U12[j], U22[j], U23[j]],
[U13[j], U23[j], U33[j]]])
Up = np.dot(np.dot(D, U), D.T)
Uxx[j] = Up[0,0]
Uyy[j] = Up[1,1]
Uzz[j] = Up[2,2]
Uyz[j] = Up[1,2]
Uxz[j] = Up[0,2]
Uxy[j] = Up[0,1]
for i in prange(n_hkl, nogil=True):
i_ind = indices[i]
w = i_ind % nl
v = i_ind // nl % nk
u = i_ind // nl // nk % nh
h_ = h_min_+h_step_*u
k_ = k_min_+k_step_*v
l_ = l_min_+l_step_*w
x = W[0,0]*h_+W[0,1]*k_+W[0,2]*l_
y = W[1,0]*h_+W[1,1]*k_+W[1,2]*l_
z = W[2,0]*h_+W[2,1]*k_+W[2,2]*l_
for var in range(n_vars):
x_ = T[var,0,0]*x+T[var,0,1]*y+T[var,0,2]*z
y_ = T[var,1,0]*x+T[var,1,1]*y+T[var,1,2]*z
z_ = T[var,2,0]*x+T[var,2,1]*y+T[var,2,2]*z
for op in range(n_ops):
h, k, l = transform(x_, y_, z_, sym, op)
f_H, f_K, f_L = h*Nu, k*Nv, l*Nw
H = int(round2even(f_H))
K = int(round2even(f_K))
L = int(round2even(f_L))
iH = (H % Nu+Nu) % Nu
iK = (K % Nv+Nv) % Nv
iL = (L % Nw+Nw) % Nw
if (iH < Fu and not iszero(fmod(f_H, f_Nu)) and Nu-iH > Fu):
iH = iH+Fu
if (iK < Fv and not iszero(fmod(f_K, f_Nv)) and Nv-iK > Fv):
iK = iK+Fv
if (iL < Fw and not iszero(fmod(f_L, f_Nw)) and Nw-iL > Fw):
iL = iL+Fw
i_dft = iL+Nw*(iK+Nv*iH)
Qh = M_TAU*(B[0,0]*h+B[0,1]*k+B[0,2]*l)
Qk = M_TAU*(B[1,0]*h+B[1,1]*k+B[1,2]*l)
Ql = M_TAU*(B[2,0]*h+B[2,1]*k+B[2,2]*l)
Qx = R[0,0]*Qh+R[0,1]*Qk+R[0,2]*Ql
Qy = R[1,0]*Qh+R[1,1]*Qk+R[1,2]*Ql
Qz = R[2,0]*Qh+R[2,1]*Qk+R[2,2]*Ql
Q = sqrt(Qx*Qx+Qy*Qy+Qz*Qz)
if iszero(Q):
Qx_norm, Qy_norm, Qz_norm = 0, 0, 0
else:
Qx_norm, Qy_norm, Qz_norm = Qx/Q, Qy/Q, Qz/Q
s_ = Q*inv_M_SP
s_sq = s_*s_
prod_x = 0
prod_y = 0
prod_z = 0
for j in range(n_atm):
occ = occupancy[j]
j0 = A0[j]*exp(-a0[j]*s_sq)\
+ B0[j]*exp(-b0[j]*s_sq)\
+ C0[j]*exp(-c0[j]*s_sq)\
+ D0[j]
j2 = (A2[j]*exp(-a2[j]*s_sq)\
+ B2[j]*exp(-b2[j]*s_sq)\
+ C2[j]*exp(-c2[j]*s_sq)\
+ D2[j])*s_sq
form_factor = j0+K2[j]*j2
if (form_factor < 0):
form_factor = 0
phase_factor = iexp(Qx*ux[j]+Qy*uy[j]+Qz*uz[j])
dw_factors = exp(-0.5*(Uxx[j]*Qx*Qx+\
Uyy[j]*Qy*Qy+\
Uzz[j]*Qz*Qz)-\
(Uyz[j]*Qy*Qz+\
Uxz[j]*Qx*Qz+\
Uxy[j]*Qx*Qy))
factors = occ*form_factor*phase_factor*dw_factors
j_dft = j+n_atm*i_dft
prod_x = prod_x+factors*Sx_k[j_dft]
prod_y = prod_y+factors*Sy_k[j_dft]
prod_z = prod_z+factors*Sz_k[j_dft]
Fx = prod_x
Fy = prod_y
Fz = prod_z
Q_norm_dot_F = Qx_norm*Fx+Qy_norm*Fy+Qz_norm*Fz
Fx_perp = Fx-Q_norm_dot_F*Qx_norm
Fy_perp = Fy-Q_norm_dot_F*Qy_norm
Fz_perp = Fz-Q_norm_dot_F*Qz_norm
Fx_perp_real, Fx_perp_imag = Fx_perp.real, Fx_perp.imag
Fy_perp_real, Fy_perp_imag = Fy_perp.real, Fy_perp.imag
Fz_perp_real, Fz_perp_imag = Fz_perp.real, Fz_perp.imag
I[i] += (Fx_perp_real*Fx_perp_real+Fx_perp_imag*Fx_perp_imag\
+ Fy_perp_real*Fy_perp_real+Fy_perp_imag*Fy_perp_imag\
+ Fz_perp_real*Fz_perp_real+Fz_perp_imag*Fz_perp_imag)\
* factor*weights[var]
return I_np
@cython.binding(True)
def occupational(double [::1] A_r,
double [::1] occupancy,
double [::1] U11,
double [::1] U22,
double [::1] U33,
double [::1] U23,
double [::1] U13,
double [::1] U12,
double [::1] ux,
double [::1] uy,
double [::1] uz,
atms,
h_range,
k_range,
l_range,
long [::1] indices,
symop,
double [:,:] W,
double [:,:] B,
double [:,:] R,
double [:,:] D,
double [:,:,:] T,
double [:] weights,
Py_ssize_t nh,
Py_ssize_t nk,
Py_ssize_t nl,
Py_ssize_t nu,
Py_ssize_t nv,
Py_ssize_t nw,
Py_ssize_t Nu,
Py_ssize_t Nv,
Py_ssize_t Nw,
source='neutron'):
"""
Occupational diffuse scattering intensity.
Parameters
----------
A_r : 1d array
Relative occupancy parameter.
occupancy : 1d array
Unit cell site occupancies.
U11, U22, U33, U23, U13, U12 : 1d array
Unit cell anisotropic displacemnt parameters.
ux, uy, uz : 1d array
Unit cell atom, ion, or isotope positions.
atms : 1d array
Unit cell atoms, ions, or isotopes.
h_range, k_range, l_range : 2-tuple or 2-list
Extents of :math:`h`, :math:`k`, and :math:`l` (min, max) pairs.
indices : 1d array, int
Array of reciprocal space volume indices.
symop : 2-tuple or 2-list, int
Symmetry operator identifier and number of operators.
W : 2d array, 3x3
Reciprocal space projection matrix.
B : 2d array, 3x3
Reciprocal lattice to Cartesian wavevector transformation matrix.
R : 2d array, 3x3
Cartesian axis rotation matrix between real and reciprocal space.
D : 2d array, 3x3
Crystal axis to Cartesian transformation matrix for atomic displacement
parameters.
T : 3d array
Twin transformation matrices. Last two axes are of size 3x3.
weights: 1d array
Twin mass fractions.
nh, nk, nl : int
Number of reciprocal space grid points.
nu, nv, nw : int
Number of supercell grid points.
Nu, Nv, Nw : int
Number of supercell grid points based on reciprocal space resolution.
source : str
Radiation source ``'neutron'``, ``'x-ray'``, or ``'electron'``.
Default ``'neutron'``.
Returns
-------
I : 1d array
Occupational diffuse scattering intensity.
"""
cdef bint neutron = source == 'neutron'
cdef Py_ssize_t n_atm = len(atms)
cdef Py_ssize_t n_hkl = indices.shape[0]
cdef Py_ssize_t sym = symop[0]
cdef Py_ssize_t n_ops = symop[1]
cdef Py_ssize_t n_vars = weights.shape[0]
cdef Py_ssize_t n_uvw = nu*nv*nw
cdef Py_ssize_t n = n_uvw*n_atm
cdef double factor
if (n == 0):
factor = 0
else:
factor = 1.0/n
cdef double x_, y_, z_
cdef double h_, k_, l_
cdef double x, y, z
cdef double h, k, l
cdef double Qh, Qk, Ql
cdef double Qx, Qy, Qz
cdef double complex phase_factor, factors, dw_factors
cdef double [::1] Uxx = np.zeros(n_atm, dtype=float)
cdef double [::1] Uyy = np.zeros(n_atm, dtype=float)
cdef double [::1] Uzz = np.zeros(n_atm, dtype=float)
cdef double [::1] Uyz = np.zeros(n_atm, dtype=float)
cdef double [::1] Uxz = np.zeros(n_atm, dtype=float)
cdef double [::1] Uxy = np.zeros(n_atm, dtype=float)
cdef double Q, s_, s_sq
cdef double occ
cdef double complex scattering_length
cdef double complex [::1] b = np.zeros(n_atm, dtype=complex)
cdef double [::1] a1 = np.zeros(n_atm, dtype=float)
cdef double [::1] b1 = np.zeros(n_atm, dtype=float)
cdef double [::1] a2 = np.zeros(n_atm, dtype=float)
cdef double [::1] b2 = np.zeros(n_atm, dtype=float)
cdef double [::1] a3 = np.zeros(n_atm, dtype=float)
cdef double [::1] b3 = np.zeros(n_atm, dtype=float)
cdef double [::1] a4 = np.zeros(n_atm, dtype=float)
cdef double [::1] b4 = np.zeros(n_atm, dtype=float)
cdef double [::1] c = np.zeros(n_atm, dtype=float)
I_np = np.zeros(n_hkl, dtype=float)
cdef double [::1] I = I_np
A_r_np = np.copy(A_r, order='C')
A_r_np = A_r_np.reshape(nu,nv,nw,n_atm)
cdef double h_min_, k_min_, l_min_
cdef double h_max_, k_max_, l_max_
cdef double h_step_, k_step_, l_step_
h_min_, k_min_, l_min_ = h_range[0], k_range[0], l_range[0]
if (nh == 1):
h_max_ = h_range[0]
h_step_ = 0
else:
h_max_ = h_range[1]
h_step_ = (h_max_-h_min_)/(nh-1)
if (nk == 1):
k_max_ = k_range[0]
k_step_ = 0
else:
k_max_ = k_range[1]
k_step_ = (k_max_-k_min_)/(nk-1)
if (nl == 1):
l_max_ = l_range[0]
l_step_ = 0
else:
l_max_ = l_range[1]
l_step_ = (l_max_-l_min_)/(nl-1)
cdef Py_ssize_t Fu = Nu // nu
cdef Py_ssize_t Fv = Nv // nv
cdef Py_ssize_t Fw = Nw // nw
cdef double f_H, f_K, f_L
cdef double f_Nu = float(Nu)
cdef double f_Nv = float(Nv)
cdef double f_Nw = float(Nw)
A_k_np = idft(A_r_np, Nu, Nv, Nw).flatten()*n_uvw
cdef double complex [::1] A_k = A_k_np
cdef Py_ssize_t F_uvw = Fu*Fv*Fw
cdef Py_ssize_t N_uvw = Nu*Nv*Nw
cdef double complex prod
cdef double complex F
cdef double F_real, F_imag
cdef Py_ssize_t H, K, L, iH, iK, iL
cdef Py_ssize_t i_dft, i_ind, j_dft
cdef Py_ssize_t op, var
cdef Py_ssize_t i, j
cdef Py_ssize_t u, v, w
cdef double M_TAU = 2*np.pi
cdef double complex M_I = 1j
cdef double inv_M_SP = 1/(4*np.pi)
for j in range(n_atm):
atm = atms[j]
if neutron:
b[j] = tables.bc.get(atm)
else:
a1[j], b1[j], \
a2[j], b2[j], \
a3[j], b3[j], \
a4[j], b4[j], \
c[j] = tables.X.get(atm)
U = np.array([[U11[j], U12[j], U13[j]],
[U12[j], U22[j], U23[j]],
[U13[j], U23[j], U33[j]]])
Up = np.dot(np.dot(D, U), D.T)
Uxx[j] = Up[0,0]
Uyy[j] = Up[1,1]
Uzz[j] = Up[2,2]
Uyz[j] = Up[1,2]
Uxz[j] = Up[0,2]
Uxy[j] = Up[0,1]
for i in prange(n_hkl, nogil=True):
i_ind = indices[i]
w = i_ind % nl
v = i_ind // nl % nk
u = i_ind // nl // nk % nh
h_ = h_min_+h_step_*u
k_ = k_min_+k_step_*v
l_ = l_min_+l_step_*w
x = W[0,0]*h_+W[0,1]*k_+W[0,2]*l_
y = W[1,0]*h_+W[1,1]*k_+W[1,2]*l_
z = W[2,0]*h_+W[2,1]*k_+W[2,2]*l_
for var in range(n_vars):
x_ = T[var,0,0]*x+T[var,0,1]*y+T[var,0,2]*z
y_ = T[var,1,0]*x+T[var,1,1]*y+T[var,1,2]*z
z_ = T[var,2,0]*x+T[var,2,1]*y+T[var,2,2]*z
for op in range(n_ops):
h, k, l = transform(x_, y_, z_, sym, op)
f_H, f_K, f_L = h*Nu, k*Nv, l*Nw
H = int(round2even(f_H))
K = int(round2even(f_K))
L = int(round2even(f_L))
iH = (H % Nu+Nu) % Nu
iK = (K % Nv+Nv) % Nv
iL = (L % Nw+Nw) % Nw
if (iH < Fu and not iszero(fmod(f_H, f_Nu)) and Nu-iH > Fu):
iH = iH+Fu
if (iK < Fv and not iszero(fmod(f_K, f_Nv)) and Nv-iK > Fv):
iK = iK+Fv
if (iL < Fw and not iszero(fmod(f_L, f_Nw)) and Nw-iL > Fw):
iL = iL+Fw
i_dft = iL+Nw*(iK+Nv*iH)
Qh = M_TAU*(B[0,0]*h+B[0,1]*k+B[0,2]*l)
Qk = M_TAU*(B[1,0]*h+B[1,1]*k+B[1,2]*l)
Ql = M_TAU*(B[2,0]*h+B[2,1]*k+B[2,2]*l)
Qx = R[0,0]*Qh+R[0,1]*Qk+R[0,2]*Ql
Qy = R[1,0]*Qh+R[1,1]*Qk+R[1,2]*Ql
Qz = R[2,0]*Qh+R[2,1]*Qk+R[2,2]*Ql
prod = 0
for j in range(n_atm):
occ = occupancy[j]
if neutron:
scattering_length = b[j]
else:
Q = sqrt(Qx*Qx+Qy*Qy+Qz*Qz)
s_ = Q*inv_M_SP
s_sq = s_*s_
scattering_length = a1[j]*exp(-b1[j]*s_sq)\
+ a2[j]*exp(-b2[j]*s_sq)\
+ a3[j]*exp(-b3[j]*s_sq)\
+ a4[j]*exp(-b4[j]*s_sq)\
+ c[j]
phase_factor = iexp(Qx*ux[j]+Qy*uy[j]+Qz*uz[j])
dw_factors = exp(-0.5*(Uxx[j]*Qx*Qx+\
Uyy[j]*Qy*Qy+\
Uzz[j]*Qz*Qz)-\
(Uyz[j]*Qy*Qz+\
Uxz[j]*Qx*Qz+\
Uxy[j]*Qx*Qy))
factors = occ*scattering_length*phase_factor*dw_factors
j_dft = j+n_atm*i_dft
prod = prod+factors*A_k[j_dft]
F = prod
F_real, F_imag = F.real, F.imag
I[i] += (F_real*F_real+F_imag*F_imag)*factor*weights[var]
return I_np
@cython.binding(True)
def displacive(double [::1] U_r,
double complex [::1] coeffs,
double [::1] occupancy,
double [::1] ux,
double [::1] uy,
double [::1] uz,
atms,
h_range,
k_range,
l_range,