scipy.special.voigt_profile

scipy.special.voigt_profile(x, sigma, gamma, out=None) = <ufunc 'voigt_profile'>

Voigt profile.

The Voigt profile is a convolution of a 1-D Normal distribution with standard deviation sigma and a 1-D Cauchy distribution with half-width at half-maximum gamma.

If sigma = 0, PDF of Cauchy distribution is returned. Conversely, if gamma = 0, PDF of Normal distribution is returned. If sigma = gamma = 0, the return value is Inf for x = 0, and 0 for all other x.

Parameters

xarray_like

Real argument

sigmaarray_like

The standard deviation of the Normal distribution part

gammaarray_like

The half-width at half-maximum of the Cauchy distribution part

outndarray, optional

Optional output array for the function values

Returns

scalar or ndarray

The Voigt profile at the given arguments

See also

wofz

Faddeeva function

Notes

It can be expressed in terms of Faddeeva function

\[V(x; \sigma, \gamma) = \frac{Re[w(z)]}{\sigma\sqrt{2\pi}},\]

\[z = \frac{x + i\gamma}{\sqrt{2}\sigma}\]

where \(w(z)\) is the Faddeeva function.

References

1

https://en.wikipedia.org/wiki/Voigt_profile

scipy.special.modfresnelm scipy.special.erf_zeros