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wrightOmegaq(Z) performs floating point evaluation of the Wright omega function. Z is an array and may be complex. If Z is an array of symbolic values, it is converted to double-precision for computation and then recast as symbolic.
wrightOmegaq is up three to four orders of magnitude faster than wrightOmega for double-precision arrays. Additionally, it has much less numeric error, properly evaluates values greater than 2^28, supports single-precision evaluation, and handles NaN inputs.
References
- P.W. Lawrence, R.M. Corless, and D.J. Jeffrey, “Algorithm 917: Complex Double-Precision Evaluation of the Wright omega Function,” ACM Transactions on Mathematical Software, Vol. 38, No. 3, Article 20, pp. 1–17, Apr. 2012. [http://dx.doi.org/10.1145/2168773.2168779]
- R.M. Corless and D.J. Jeffrey, “The Wright omega Function,” In: Artificial Intelligence, Automated Reasoning, and Symbolic Computation, Joint International Conferences, AISC 2002 and Calculemus 2002, Marseille, France, July 2002, (Jacques Calmet, Belaid Benhamou, Olga Caprotti, Laurent Henocque, and Volker Sorge, Eds.), Berlin: Springer-Verlag, pp. 76–89, 2002. [http://orcca.on.ca/TechReports/2000/TR-00-12.html]
Andrew D. Horchler, horchler @ gmail . com, biorobots.case.edu
Created: 7-12-12, Revision: 1.0, 3-12-13
This version tested with Matlab 9.0.0.341360 (R2016a)
Mac OS X 10.11.4 (Build: 15E65), Java 1.7.0_75-b13
Compatibility maintained back through Matlab 7.4 (R2007a)
Acknowledgment of support: This material is based upon work supported by the National Science Foundation under Grant No. 1065489. Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Copyright © 2012–2017, Andrew D. Horchler
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