Module « scipy.special »

Fonction voigt_profile - module scipy.special

Signature de la fonction voigt_profile

Description

voigt_profile.__doc__

voigt_profile(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

voigt_profile(x, sigma, gamma, out=None)

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
----------
x : array_like
    Real argument
sigma : array_like
    The standard deviation of the Normal distribution part
gamma : array_like
    The half-width at half-maximum of the Cauchy distribution part
out : ndarray, optional
    Optional output array for the function values

Returns
-------
scalar or ndarray
    The Voigt profile at the given arguments

Notes
-----
It can be expressed in terms of Faddeeva function

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

where :math:`w(z)` is the Faddeeva function.

See Also
--------
wofz : Faddeeva function

References
----------
.. [1] https://en.wikipedia.org/wiki/Voigt_profile