import warnings
import numpy as np
from scipy.integrate import IntegrationWarning, quad, quad_vec
# Load the C library
import os.path
from pathlib import Path
import ctypes
# # Commands to manually generate
# gcc -Wall -fPIC -c voigt.c
# gcc -shared -o libvoigt.so voigt.o
dllabspath = Path(os.path.dirname(os.path.abspath(__file__))) # Path to libraries directory
try:
libfile = [str(i) for i in dllabspath.glob('ext_voigtlib.*.so')][0] # Select first (and only) library
lib = ctypes.CDLL(libfile) # Load the library
lib.func.restype = ctypes.c_double # Specify the expected result type
lib.func.argtypes = (ctypes.c_int, ctypes.c_double) # Specify the type of the input parameters
cvoigt = lib.func # Create alias for the specific function used in functions below
except IndexError: # File does not exist
warnings.warn("Could not locate the external C library. Further use of `clib` will fail!")
# Parameters for `voigt_approx_nobg` and other approx. Voigt functions
params = np.array([[-1.2150, -1.3509, -1.2150, -1.3509],
[1.2359, 0.3786, -1.2359, -0.3786],
[-0.3085, 0.5906, -0.3085, 0.5906],
[0.0210, -1.1858, -0.0210, 1.1858]])
sqrt_ln2 = np.sqrt(np.log(2))
sqrt_pi = np.sqrt(np.pi)
A, B, C, D = params
__all__ = ['voigt_approx_nobg', 'voigt_approx', 'double_voigt_approx_nobg', 'double_voigt_approx',
'voigt_nobg', 'voigt', 'double_voigt_nobg', 'double_voigt']
[docs]def voigt_approx_nobg(x, a, b, s, g):
"""Voigt function (efficient approximation) with no background (Base approx. Voigt function)
This is the base for all other approximated Voigt functions. Not implemented in any models yet as initial tests
exhibited slow convergence.
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a : float
Amplitude of the Lorentzian.
b : float
Central line core.
s : float
Sigma (for Gaussian).
g : float
Gamma (for Lorentzian).
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt_approx : Approximated Voigt function with background added
double_voigt_approx_nobg : Two approximated Voigt functions added together
double_voigt_approx : Two approximated Voigt functions and a background added together
voigt_nobg : Base Voigt function with no background
voigt : Voigt function with background added
double_voigt_nobg : Two Voigt functions added together
double_voigt : Two Voigt function and a background added together
Notes
-----
This algorithm is taken from A. B. McLean et al. [1]_.
References
----------
.. [1] A. B. McLean, C. E. J. Mitchell and D. M. Swanston, "Implementation of an efficient analytical
approximation to the Voigt function for photoemission lineshape analysis," Journal of Electron Spectroscopy and
Related Phenomena, vol. 69, pp. 125-132, 1994. https://doi.org/10.1016/0368-2048(94)02189-7
"""
fwhm_g = 2 * s * np.sqrt(2 * np.log(2))
fwhm_l = 2 * g
xx = (x - b) * 2 * sqrt_ln2 / fwhm_g
xx = xx[..., np.newaxis]
yy = fwhm_l * sqrt_ln2 / fwhm_g
yy = yy[..., np.newaxis]
v = np.sum((C * (yy - A) + D * (xx - B)) / ((yy - A) ** 2 + (xx - B) ** 2), axis=-1)
return fwhm_l * a * sqrt_pi / fwhm_g * v
[docs]def voigt_approx(x, a, b, s, g, d):
"""Voigt function (efficient approximation) with background
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a : float
Amplitude of the Lorentzian.
b : float
Central line core.
s : float
Sigma (for Gaussian).
g : float
Gamma (for Lorentzian).
d : float
Background.
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt_approx_nobg : Base approximated Voigt function with no background
double_voigt_approx_nobg : Two approximated Voigt functions added together
double_voigt_approx : Two approximated Voigt functions and a background added together
voigt_nobg : Base Voigt function with no background
voigt : Voigt function with background added
double_voigt_nobg : Two Voigt functions added together
double_voigt : Two Voigt function and a background added together
"""
return voigt_approx_nobg(x, a, b, s, g) + d
[docs]def double_voigt_approx_nobg(x, a1, b1, s1, g1, a2, b2, s2, g2):
"""Double Voigt function (efficient approximation) with no background
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a1 : float
Amplitude of the Lorentzian of 1st Voigt function.
b1 : float
Central line core of 1st Voigt function.
s1 : float
Sigma (for Gaussian) of 1st Voigt function.
g1 : float
Gamma (for Lorentzian) of 1st Voigt function.
a2 : float
Amplitude of 2st Voigt function.
b2 : float
Central line core of 2st Voigt function.
s2 : float
Sigma (for Gaussian) of 2st Voigt function.
g2 : float
Gamma (for Lorentzian) of 2st Voigt function.
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt_approx_nobg : Base approximated Voigt function with no background
voigt_approx : Approximated Voigt function with background added
double_voigt_approx : Two approximated Voigt functions and a background added together
voigt_nobg : Base Voigt function with no background
voigt : Voigt function with background added
double_voigt_nobg : Two Voigt functions added together
double_voigt : Two Voigt function and a background added together
"""
return voigt_approx_nobg(x, a1, b1, s1, g1) + voigt_approx_nobg(x, a2, b2, s2, g2)
[docs]def double_voigt_approx(x, a1, b1, s1, g1, a2, b2, s2, g2, d):
"""Double Voigt function (efficient approximation) with background
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a1 : float
Amplitude of the Lorentzian of 1st Voigt function.
b1 : float
Central line core of 1st Voigt function.
s1 : float
Sigma (for Gaussian) of 1st Voigt function.
g1 : float
Gamma (for Lorentzian) of 1st Voigt function.
a2 : float
Amplitude of 2st Voigt function.
b2 : float
Central line core of 2st Voigt function.
s2 : float
Sigma (for Gaussian) of 2st Voigt function.
g2 : float
Gamma (for Lorentzian) of 2st Voigt function.
d : float
Background.
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt_approx_nobg : Base approximated Voigt function with no background
voigt_approx : Approximated Voigt function with background added
double_voigt_approx_nobg : Two approximated Voigt functions added together
voigt_nobg : Base Voigt function with no background
voigt : Voigt function with background added
double_voigt_nobg : Two Voigt functions added together
double_voigt : Two Voigt function and a background added together
"""
return voigt_approx_nobg(x, a1, b1, s1, g1) + voigt_approx_nobg(x, a2, b2, s2, g2) + d
[docs]def voigt_nobg(x, a, b, s, g, clib=True):
"""Voigt function with no background (Base Voigt function)
This is the base of all the other Voigt functions.
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a : float
Amplitude.
b : float
Central line core.
s : float
Sigma (for Gaussian).
g : float
Gamma (for Lorentzian).
clib : bool, optional, default = True
Whether to use the complied C library or a slower Python version. If using the C library, the accuracy
of the integration is reduced to give the code a significant speed boost. Python version can be used when
speed is not a priority. Python version will remove deviations that are sometimes present around the wings
due to the reduced accuracy.
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt : Voigt function with background added
double_voigt_nobg : Two Voigt functions added together
double_voigt : Two Voigt function and a background added together
Notes
-----
More information on the Voigt function can be found here: https://en.wikipedia.org/wiki/Voigt_profile
"""
warnings.filterwarnings("ignore", category=IntegrationWarning)
u = x - b
if clib:
i = [quad(cvoigt, -np.inf, np.inf, args=(v, s, g), epsabs=1.49e-1, epsrel=1.49e-4)[0] for v in u]
else:
i = quad_vec(lambda y: np.exp(-y**2 / (2 * s**2)) / (g**2 + (u - y)**2), -np.inf, np.inf)[0]
const = g / (s * np.sqrt(2 * np.pi**3))
return a * const * np.array(i)
[docs]def voigt(x, a, b, s, g, d, clib=True):
"""Voigt function with background
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a : float
Amplitude.
b : float
Central line core.
s : float
Sigma (for Gaussian).
g : float
Gamma (for Lorentzian).
d : float
Background.
clib : bool, optional, default = True
Whether to use the complied C library or a slower Python version. If using the C library, the accuracy
of the integration is reduced to give the code a significant speed boost. Python version can be used when
speed is not a priority. Python version will remove deviations that are sometimes present around the wings
due to the reduced accuracy.
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt_nobg : Base Voigt function with no background
double_voigt_nobg : Two Voigt functions added together
double_voigt : Two Voigt function and a background added together
Notes
-----
More information on the Voigt function can be found here: https://en.wikipedia.org/wiki/Voigt_profile
"""
return voigt_nobg(x, a, b, s, g, clib) + d
[docs]def double_voigt_nobg(x, a1, b1, s1, g1, a2, b2, s2, g2, clib=True):
"""Double Voigt function with no background
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a1 : float
Amplitude of 1st Voigt function.
b1 : float
Central line core of 1st Voigt function.
s1 : float
Sigma (for Gaussian) of 1st Voigt function.
g1 : float
Gamma (for Lorentzian) of 1st Voigt function.
a2 : float
Amplitude of 2st Voigt function.
b2 : float
Central line core of 2st Voigt function.
s2 : float
Sigma (for Gaussian) of 2st Voigt function.
g2 : float
Gamma (for Lorentzian) of 2st Voigt function.
clib : bool, optional, default = True
Whether to use the complied C library or a slower Python version. If using the C library, the accuracy
of the integration is reduced to give the code a significant speed boost. Python version can be used when
speed is not a priority. Python version will remove deviations that are sometimes present around the wings
due to the reduced accuracy.
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt_nobg : Base Voigt function with no background
voigt : Voigt function with background added
double_voigt : Two Voigt function and a background added together
Notes
-----
More information on the Voigt function can be found here: https://en.wikipedia.org/wiki/Voigt_profile
"""
return voigt_nobg(x, a1, b1, s1, g1, clib) + voigt_nobg(x, a2, b2, s2, g2, clib)
[docs]def double_voigt(x, a1, b1, s1, g1, a2, b2, s2, g2, d, clib=True):
"""Double Voigt function with background
Parameters
----------
x : ndarray
Wavelengths to evaluate Voigt function at.
a1 : float
Amplitude of 1st Voigt function.
b1 : float
Central line core of 1st Voigt function.
s1 : float
Sigma (for Gaussian) of 1st Voigt function.
g1 : float
Gamma (for Lorentzian) of 1st Voigt function.
a2 : float
Amplitude of 2st Voigt function.
b2 : float
Central line core of 2st Voigt function.
s2 : float
Sigma (for Gaussian) of 2st Voigt function.
g2 : float
Gamma (for Lorentzian) of 2st Voigt function.
d : float
Background.
clib : bool, optional, default = True
Whether to use the complied C library or a slower Python version. If using the C library, the accuracy
of the integration is reduced to give the code a significant speed boost. Python version can be used when
speed is not a priority. Python version will remove deviations that are sometimes present around the wings
due to the reduced accuracy.
Returns
-------
result : ndarray of shape `x.shape`
The value of the Voigt function here.
See Also
--------
voigt_nobg : Base Voigt function with no background
voigt : Voigt function with background added
double_voigt_nobg : Two Voigt functions added together
Notes
-----
More information on the Voigt function can be found here: https://en.wikipedia.org/wiki/Voigt_profile
"""
return double_voigt_nobg(x, a1, b1, s1, g1, a2, b2, s2, g2, clib) + d