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Remark on “Algorithm 916: Computing the Faddeyeva and Voigt Functions”: Efficiency Improvements and Fortran Translation

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Mofreh R. ZaghloulAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 42, Issue 3

Article No.: 26, Pages 1 - 9

https://doi.org/10.1145/2806884

Published: 23 May 2016 Publication History

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Abstract

This remark describes efficiency improvements to Algorithm 916 [Zaghloul and Ali 2011]. It is shown that the execution time required by the algorithm, when run at its highest accuracy, may be improved by more than a factor of 2. A better accuracy vs efficiency tradeoff scheme is also implemented; this requires the user to supply the number of significant figures desired in the computed values as an extra input argument to the function. Using this tradeoff, it is shown that the efficiency of the algorithm may be further improved significantly while maintaining reasonably accurate and safe results that are free of the pitfalls and complete loss of accuracy seen in other competitive techniques.

The current version of the code is provided in Matlab and Scilab in addition to a Fortran translation prepared to meet the needs of real-world problems where very large numbers of function evaluations would require the use of a compiled language. To fulfill this last requirement, a recently proposed reformed version of Humlíček's w4 routine, shown to maintain the claimed accuracy of the algorithm over a wide and fine grid, is implemented in the present Fortran translation for the case of four significant figures. This latter modification assures the reliability of the code in the solution of practical problems requiring numerous evaluation of the function for applications requiring low-accuracy computations (<10⁻⁴).

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M. R. Zaghloul. 2015. A simple reform for treating the loss of accuracy of humliceck's W4 algorithm near the real axis. arXiv:1505.05596v1 [astro-ph.IM].

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Cited By

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Zaghloul MLe Bourlot J(2025)A highly efficient Voigt program for line profile computationJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/j.jqsrt.2024.109234330(109234)Online publication date: Jan-2025
https://doi.org/10.1016/j.jqsrt.2024.109234
Thompson I(2024)Algorithm 1046: An Improved Recurrence Method for the Scaled Complex Error FunctionACM Transactions on Mathematical Software10.1145/368879950:3(1-18)Online publication date: 21-Aug-2024
https://dl.acm.org/doi/10.1145/3688799
de Campos MRomero Sda Silva Lde Castro J(2024)Shape Anisotropy and Magnetic Texture Determination in Anisotropic and Isotropic Alnico MagnetsJOM10.1007/s11837-024-06586-3Online publication date: 14-May-2024
https://doi.org/10.1007/s11837-024-06586-3
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Index Terms

Remark on “Algorithm 916: Computing the Faddeyeva and Voigt Functions”: Efficiency Improvements and Fortran Translation
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
    2. Numerical analysis
      1. Arbitrary-precision arithmetic
  2. Mathematical software
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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Published In

ACM Transactions on Mathematical Software Volume 42, Issue 3

June 2016

208 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2935754

Editor:
Michael A. Heroux
Sandia National Laboratories, USA

Issue’s Table of Contents

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Publication History

Published: 23 May 2016

Accepted: 01 July 2015

Revised: 01 June 2015

Received: 01 January 2015

Published in TOMS Volume 42, Issue 3

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Zaghloul MLe Bourlot J(2025)A highly efficient Voigt program for line profile computationJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/j.jqsrt.2024.109234330(109234)Online publication date: Jan-2025
https://doi.org/10.1016/j.jqsrt.2024.109234
Thompson I(2024)Algorithm 1046: An Improved Recurrence Method for the Scaled Complex Error FunctionACM Transactions on Mathematical Software10.1145/368879950:3(1-18)Online publication date: 21-Aug-2024
https://dl.acm.org/doi/10.1145/3688799
de Campos MRomero Sda Silva Lde Castro J(2024)Shape Anisotropy and Magnetic Texture Determination in Anisotropic and Isotropic Alnico MagnetsJOM10.1007/s11837-024-06586-3Online publication date: 14-May-2024
https://doi.org/10.1007/s11837-024-06586-3
Zaghloul M(2024)Efficient numerical algorithms for multi-precision and multi-accuracy calculation of the error functions and Dawson integral with complex argumentsNumerical Algorithms10.1007/s11075-023-01727-297:2(869-887)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s11075-023-01727-2
Zaghloul M(2024)Efficient multiple-precision computation of the scaled complementary error function and the Dawson integralNumerical Algorithms10.1007/s11075-023-01608-895:3(1291-1308)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1007/s11075-023-01608-8
Zaghloul MAlrawas L(2023)Calculation of Fresnel integrals of real and complex arguments up to 28 significant digitsNumerical Algorithms10.1007/s11075-023-01654-296:2(489-506)Online publication date: 14-Sep-2023
https://doi.org/10.1007/s11075-023-01654-2
Mahler AWilliams JSu NYang W(2022)Localized orbital scaling correction for periodic systemsPhysical Review B10.1103/PhysRevB.106.035147106:3Online publication date: 28-Jul-2022
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Yan XCai HZhang WHao LYao PLi XZou SZhu SHe X(2019)Anomalous mix induced by a collisionless shock wave in an inertial confinement fusion hohlraumNuclear Fusion10.1088/1741-4326/ab32cf59:10(106016)Online publication date: 21-Aug-2019
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Schippers S(2018)Analytical expression for the convolution of a Fano line profile with a gaussianJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/j.jqsrt.2018.08.003219(33-36)Online publication date: Nov-2018
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Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function

Algorithm 916: Computing the Faddeyeva and Voigt Functions

Remark on “Algorithm 680: Evaluation of the Complex Error Function”: Cause and Remedy for the Loss of Accuracy Near the Real Axis

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Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function

Algorithm 916: Computing the Faddeyeva and Voigt Functions

Remark on “Algorithm 680: Evaluation of the Complex Error Function”: Cause and Remedy for the Loss of Accuracy Near the Real Axis

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