Faddeyeva985.jl

This package exports a single function approximating the Faddeyeva Function (sometimes called Faddeeva). The algorithm was developed by Mofreh R. Zaghloul at the United Arab Emirates University and is translated to Julia here.

The published description states a relative accuracy better than 4e-5 over wide ranges of inputs. My testing indicates relative error is slightly greater than 4e-5 at some points in the same ranges, but never greater than 5e-5.

The Faddeyeva function arises in a handful of physical problems. For example, it is needed to evaluate the Voigt profile for molecular absorption lines in radiative transfer applications/modeling.

If you use it for research, cite the original paper:

• Mofreh R. Zaghloul. 2017. Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function. ACM Trans. Math. Softw. 44, 2, Article 22 (October 2017), 9 pages. DOI: https://doi.org/10.1145/3119904

The module can be installed from Julia's general registry with ]add Faddeyeva985

The function has two methods. One takes a complex argument and returns the full complex result.

julia> using Faddeyeva985
julia> faddeyeva(1 + 2im)
0.2184926141618737 + 0.09299780803270477im

The other takes a complex argument split into its parts and returns only the real part of the result. This spares some calculations.

julia> faddeyeva(1, 2)
0.2184926141618737

A highly accurate version of the function is available through erfcx in SpecialFunctions.jl, but it's slower.