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-maximumgamma
.If
sigma = 0
, PDF of Cauchy distribution is returned. Conversely, ifgamma = 0
, PDF of Normal distribution is returned. Ifsigma = gamma = 0
, the return value isInf
forx = 0
, and0
for all otherx
.- 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