Bugfix/fix asymptotic bessel

Makes the following corrections to multiprecision bessel function implementation:

• Include second series scaling with exp(-z) in asymptotic calculation of I
• Correct normalization of besinorm
• Make precision-dependent condition for selecting Taylor series or asymptotic approximation for I and K

The first change is the only one to affect the rest of the IW2D-scripts in their current form, as the normalized K and I are not used, and precision is hard coded. The first change is particularly important for small Re(z). All changes are based on the work of Amos: AMOS, D. E, Computation of Bessel functions of complex argument. SAND83-0086, Sandia National Laboratories, Albuquerque, N.M. (May 1983).

requested review from @nimounet

assigned to @esvik

assigned to @nimounet

Ah my bad, forgot that the bash script should also be in this merge request. Will finish that now

Many thanks! Maybe worth adding a few plots to show the Bessel function behaviour before and after the bug fix (compared to scipy, for instance), w.r.t |z|? (if those plots are readily available)

added 3 commits

• 50c3273e - add test commands
• df223dfe - fix correct precision dependancy
• ba88688e - change input paramteres and upload expected output

Compare with previous version

Here are a sample of files showing the output of the bessel function before and after the fix. Each plot is at an fixed angle in the complex plane. The switch from Taylor expansion to asymptotic happens at |z|=60. Most important to note regarding this merge request is the pi=0.50 / pi=0.49 cases, where the large error before the fix has been fixed after.

0.05pi

0.16 pi

0.25 pi

0.33 pi

0.50 pi

Here are the results of running roundchamber.cc before and after the fix, for one finite dielectric layer. This case has been implemented as a test case. Note that the figure showing relative diffrence is only plotted from the region where there actually is a diffrence. For most frequencies, the results before and after the fix are identical.

@nimounet The merge request should now be fully ready (I hope). The test I wrote runs as intended, so I think I did everything correct there as well. Feel free to add any further comments or requests you might have, or merge the request if it looks good.

Excellent work!

Please have a look at the (mostly minor) comments.

added 1 commit

• 3862c93c - address MR comments

Compare with previous version

I have noted your comment about imagj and addressed the other two. I left the full reference to Amos as a comment, as I did not find a place in readme.md where I felt it was natural to cite it (and because it is a quite minor point that most users do not need to know).

mentioned in issue #2

I agree on all grounds. thanks!

resolved all threads

approved this merge request

merged

mentioned in commit dbd892f6