"""
====================
Voigt Profile Fitter
====================
Module API
^^^^^^^^^^
"""
from . import model
import numpy as np
from ...spectrum.moments import moments
import types
try:
import scipy.special
scipyOK = True
except ImportError:
scipyOK = False
[docs]def voigt(xarr, amp, xcen, sigma, gamma, normalized=False):
"""
Normalized Voigt profile
z = (x+i*gam)/(sig*sqrt(2))
V(x,sig,gam) = Re(w(z))/(sig*sqrt(2*pi))
The area of V in this definition is 1.
If normalized=False, then you can divide the integral of V by
sigma*sqrt(2*pi) to get the area.
Original implementation converted from
http://mail.scipy.org/pipermail/scipy-user/2011-January/028327.html
(had an incorrect normalization and strange treatment of the input
parameters)
Modified implementation taken from wikipedia, using the definition.
http://en.wikipedia.org/wiki/Voigt_profile
Parameters
----------
xarr : np.ndarray
The X values over which to compute the Voigt profile
amp : float
Amplitude of the voigt profile
if normalized = True, amp is the AREA
xcen : float
The X-offset of the profile
sigma : float
The width / sigma parameter of the Gaussian distribution
gamma : float
The width / shape parameter of the Lorentzian distribution
normalized : bool
Determines whether "amp" refers to the area or the peak
of the voigt profile
"""
if scipyOK:
z = ((xarr.value-xcen) + 1j*gamma) / (sigma * np.sqrt(2))
V = amp * np.real(scipy.special.wofz(z))
if normalized:
return V / (sigma*np.sqrt(2*np.pi))
else:
return V
else:
raise ImportError("Couldn't import scipy, therefore cannot do "
"voigt profile stuff")
[docs]def voigt_fwhm(sigma, gamma):
"""
Approximation to the Voigt FWHM from wikipedia
http://en.wikipedia.org/wiki/Voigt_profile
Parameters
----------
sigma : float
The width / sigma parameter of the Gaussian distribution
gamma : float
The width / shape parameter of the Lorentzian distribution
"""
return 0.5346 * 2 * gamma + np.sqrt(0.2166*(2*gamma)**2 + sigma**2*8*np.log(2))
[docs]def voigt_moments(self, *args, **kwargs):
"""
Get the spectral moments from the moments package. Use the gaussian width
for the lorentzian width (not a great guess!)
"""
m = moments(*args,**kwargs)
return list(m) + [m[-1]]
[docs]def voigt_fitter():
"""
Generator for voigt fitter class
"""
myclass = model.SpectralModel(voigt, 4,
parnames=['amplitude', 'shift', 'gwidth',
'lwidth'],
parlimited=[(False, False), (False, False),
(True, False), (True, False)],
parlimits=[(0, 0), (0, 0), (0, 0), (0, 0)],
shortvarnames=('A', r'\Delta x',
r'\sigma_G', r'\sigma_L'),
centroid_par='shift',
fwhm_func=voigt_fwhm,
fwhm_pars=['gwidth','lwidth'],
guess_types=['amplitude', 'center', 'width',
'width'],
)
myclass.__name__ = "voigt"
try:
myclass.moments = types.MethodType(voigt_moments, myclass,
myclass.__class__)
except TypeError: # indicates py3 is being used
# http://stackoverflow.com/questions/10729909/convert-builtin-function-type-to-method-type-in-python-3?lq=1
myclass.moments = voigt_moments.__get__(myclass)
return myclass
