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