qsotools.voigt.voigt

qsotools.voigt. voigt ( a , u )

Compute the Voigt function.

a: float

The lorentzian FWHM divided by the gaussian FWHM of the line.

u: array of floats

The frequency offsets from the frequency at the line centre, in units of the FWHM frequency of the doppler broadening.

Returns voigt function H(a,u).

Notes

This is a Taylor approximation to the Voigt function valid for 0 < a < 0.1. (Harris 1948, ApJ, 108, 112). Relative error with respect to voigt_de is < 10^-4.9 for a < 0.1, gets worse for larger a (since it’s an expansion in a).

Examples

>>> uvals = numpy.arange(-25, 25, 1./100)
>>> a = 0.01
>>> y1 = voigt(a, uvals)
>>> y2 = numpy.fromfile('data/idl_voigt.txt', sep=' ')
>>> numpy.allclose(y1, y2, rtol=1e-8)
True
>>> uvals = numpy.linspace(-25, 25, 40)
>>> a = 1e-5
>>> y1 = voigt(a, uvals)
>>> y2 = [voigtslow(a,u) for u in uvals]
>>> all(mp.almosteq(i, j, 1e-5) for i,j in zip(y1,y2))
True
>>> a = 0.1
>>> y1 = voigt(a, uvals)
>>> y2 = [voigtslow(a,u) for u in uvals]
>>> all(mp.almosteq(i, j, 1e-5) for i,j, in zip(y1,y2))
True