voigt function algorithm for GSL attached: First contact

[Jochen Küpper]

michael crescimanno <mcrescim@cc.ysu.edu> writes:

>    I have enjoyed using GSL and recently for a project needed a routine to
> compute the voigt function and its first moment. 

Thanks for your effort.

Could you please post the reference you used for the calculation?

The standard way to calculate the Voigt-profile fast used to be
Humlicek's formulas, whose references I attach. Maybe you wanna
incorporate them into gsl as well?

I do have C code for some of these lying around and can look it
up/send it along if somebody wants to incorporate it into GSL.

,----
| @Article{Humlicek:FSNUPB:29,
|   author       = {J. Huml\'{\i}\v{c}ek and V. Kapi\v{c}ka},
|   title        = {The evaluation of spectrum line profiles: The {Voigt} function
|                   and its derivatives},
|   journal      = {Folia Fac. Sci. Nat. Univ. Purk. Brun.},
|   pages        = 5,
|   year         = 1979,
|   volume       = {Physica 29},
|   annote       = {Algorithmus zur Berechnung der komplexen Voigt-Funktion aus 20
|                   Termen einer adaptierten Gauss-Hermite-Integration mit
|                   Programm in FORTRAN, max. relativer Fehler ist < 10^-6, der
|                   absolute Fehler < 10^-7}
| }
| 
| @Article{Humlicek:JQSRT21:306,
|   author       = {J. Huml\'{\i}\v{c}ek},
|   title        = {An efficient method for evaluation of the complex probability
|                   function: The {Voigt} function and its derivatives},
|   journal      = {J. Quant. Spectrosc. Radiat. Transfer},
|   pages        = 309,
|   year         = 1979,
|   volume       = 21,
|   annote       = {Algorithmus zur Berechnung der komplexen Voigt-Funktion aus 12
|                   Termen einer adaptierten Gauss-Hermite-Integration und
|                   Bereichsunterscheidung mit Programm in FORTRAN, max. relativer
|                   Fehler des komplexen Teils < 5*10^-6, der des reellen Teils <
|                   2*10^-6}
| }
| 
| @Article{Humlicek:JQSRT27:437,
|   author       = {J. Huml\'{\i}\v{c}ek},
|   title        = {Optimized computation of the {V}oigt and complex probability
|                   functions},
|   journal      = {J. Quant. Spectrosc. Radiat. Transfer},
|   pages        = 437,
|   year         = 1982,
|   volume       = 27,
|   annote       = {Schneller Algorithmus zur Berechnung der komplexen
|                   Voigt-Funktion mit 4 Bereichsunterscheidungen mit Programm in
|                   FORTRAN, max. relativer Fehler des komplexen und reellen Teils
|                   < 1*10^-4}
| }
| 
| @Article{Humlicek:SFSNUPB11:241,
|   author       = {J. Huml\'{\i}\v{c}ek},
|   title        = {An optimized approximation to {V}oigt spectrum line profiles},
|   journal      = {Scripta Fac. Sci. Nat. Univ. Purk. Brun.},
|   pages        = 241,
|   year         = 1981,
|   volume       = 11,
|   annote       = {Schneller Algorithmus zur Berechnung der komplexen
|                   Voigt-Funktion mit 4-termiger Formel, max. relativer Fehler
|                   des komplexen und reellen Teils < 3*10^-4}
| }
`----

Greetings,
Jochen
-- 
Einigkeit und Recht und Freiheit                http://www.Jochen-Kuepper.de
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        (Part 3 you find in my messages before fall 2003.)
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