from __future__ import annotations
import numpy as np
from numba import jit
from scipy.special import kn
[docs]
@jit(nopython=True, nogil=True)
def scattering_factor(k2, p):
return (
p[0, 0] / (p[1, 0] + k2)
+ p[2, 0] * np.exp(-p[3, 0] * k2)
+ p[0, 1] / (p[1, 1] + k2)
+ p[2, 1] * np.exp(-p[3, 1] * k2)
+ p[0, 2] / (p[1, 2] + k2)
+ p[2, 2] * np.exp(-p[3, 2] * k2)
)
[docs]
@jit(nopython=True, nogil=True)
def potential(r, p):
return (
p[0, 0] * np.exp(-p[1, 0] * r) / r
+ p[2, 0] * np.exp(-p[3, 0] * r**2.0)
+ p[0, 1] * np.exp(-p[1, 1] * r) / r
+ p[2, 1] * np.exp(-p[3, 1] * r**2.0)
+ p[0, 2] * np.exp(-p[1, 2] * r) / r
+ p[2, 2] * np.exp(-p[3, 2] * r**2.0)
)
[docs]
@jit(nopython=True, nogil=True)
def potential_derivative(r, p):
dvdr = (
-p[0, 0] * (1 / r + p[1, 0]) * np.exp(-p[1, 0] * r) / r
- 2 * p[2, 0] * p[3, 0] * r * np.exp(-p[3, 0] * r**2)
- p[0, 1] * (1 / r + p[1, 1]) * np.exp(-p[1, 1] * r) / r
- 2 * p[2, 1] * p[3, 1] * r * np.exp(-p[3, 1] * r**2)
- p[0, 2] * (1 / r + p[1, 2]) * np.exp(-p[1, 2] * r) / r
- 2 * p[2, 2] * p[3, 2] * r * np.exp(-p[3, 2] * r**2)
)
return dvdr
[docs]
def projected_potential(r, p):
v = (
2 * p[0, 0] * kn(0, p[1, 0] * r)
+ np.sqrt(np.pi / p[3, 0]) * p[2, 0] * np.exp(-p[3, 0] * r**2.0)
+ 2 * p[0, 1] * kn(0, p[1, 1] * r)
+ np.sqrt(np.pi / p[3, 1]) * p[2, 1] * np.exp(-p[3, 1] * r**2.0)
+ 2 * p[0, 2] * kn(0, p[1, 2] * r)
+ np.sqrt(np.pi / p[3, 2]) * p[2, 2] * np.exp(-p[3, 2] * r**2.0)
)
return v
[docs]
@jit(nopython=True, nogil=True)
def projected_scattering_factor(k2, p):
pi = np.array(np.pi, dtype=np.float32)
f = (
4 * np.pi * p[0, 0] / (4 * pi**2 * k2 + p[1, 0] ** 2)
+ np.sqrt(np.pi / p[3, 0])
* p[2, 0]
* np.pi
/ p[3, 0]
* np.exp(-(pi**2) * k2 / p[3, 0])
+ 4 * np.pi * p[0, 1] / (4 * pi**2 * k2 + p[1, 1] ** 2)
+ np.sqrt(np.pi / p[3, 1])
* p[2, 1]
* np.pi
/ p[3, 1]
* np.exp(-(pi**2) * k2 / p[3, 1])
+ 4 * np.pi * p[0, 2] / (4 * pi**2 * k2 + p[1, 2] ** 2)
+ np.sqrt(np.pi / p[3, 2])
* p[2, 2]
* np.pi
/ p[3, 2]
* np.exp(-(pi**2) * k2 / p[3, 2])
)
return f
