Journal of negative results in Octave?

[Jose Ramom Flores das Seixas]

I would like to know if there is something like The negative results Journal for octave functions?

The reason I ask is because I implemented a quadrature for strongly oscillating functions, quadgF, but after comparing it with octave function quadgk I found, to my disappointment, that my function was not generally faster than quadgk.

The quadgk and quadl functions allowed to integrate strongly oscillating functions, but they are slow for my needs: perform diffraction calculations. Browsing the bibliography on the subject, I found an article by L.F. Shampine, reference [1], which describes an algorithm that seemed easy to implement to me. In fact, the proposed algorithm is an improvement of the SSP method [2,3], which possibly Mr. Shampine did not know, since he does not mention it in his bibliography.

In his article, Professor Shampine talks about a function he implemented, quadgF, based on the algorithm, but as much as I looked for it I couldn't find it -quadgF.m-. So I implemented it as well as I could, trying to vectorize it as much as possible, and kept the name used in [1].

It is quite possible that the reason why Professor Shampine's function has disappeared from the radar is precisely what I found after writing my implementation, i.e. that, in general, has no advantages over general functions like quadgk.

Anyway, for if my implementation served someone, either because he/she improved it and got more speed, or to avoid wasting time doing what I already did, I send attached the function I wrote, quadgF.m, and a document, quadgF.pdf, describing the algorithm and my implementation, as well as an analysis that compares my function and quadgk.

Yours sincerely

Jose Ramom

References

1Shampine L.F., Integrating oscillatory functions in MATLAB, II. Electronic Transactions on Numerical Analysis, volume 39, pp 403-413, 2012.

2Stamnes J.J., Spjelkavik B. & Pedersen H.M., Evaluation of diffraction integrals using local phase and amplitude approximations. Opt. Acta 30, 207-222, 1983.

3Stamnes J.J., Waves in focal regions: propagation, diffraction and focusing of light, sound and water waves. Adam Hilger, 1986.

quadgF.m
Description: Text Data

quadgF.pdf
Description: Adobe PDF document