[SciPy-Dev] Hankel transforms, again

[Robert Kern]

On Fri, Feb 14, 2014 at 9:45 AM, Tom Grydeland <tom.grydeland at gmail.com> wrote:
> Hi developers,
>
> This is a repost of a message from December 2008 which gave no useful answers.  Since then, I’ve had 4-5 requests for the code from people who had a need for it.  It’s not a massive demand, but enough that perhaps you’ll consider my offer again.
>
> Since the previous posting, I’ve also included alternative filters thanks to Fan-Nian Kong that are shorter and more accurate when the function makes significant changes in more limited intervals. I’m not including the code (since it is mostly thousands of lines of tables), but I will provide the files to anyone who’s interested.

Yes, I think we'd be interested. Please do make a PR. Before you do,
please double-check the licensing on the new code that you have added.
It does look like Anderson's original code is in the public domain
(the paper being published as part of Anderson's work at the USGS as a
federal employee), so that part is in the clear. Just so we are clear,
the lack of copyright statements (work by US federal employees aside)
usually means that you have *no license* to redistribute the work, not
that there are no restrictions on redistribution.

Thanks!

> —— original message below ———
>
> When I recently needed a Hankel transform I was unable to find one in
> Scipy.  I found one in MATLAB though[1], written by Prof. Brian
> Borchers at New Mexico Tech. The code is based on a previous FORTRAN
> implementation by W. L. Anderson [2], and the MATLAB code is not
> marked with any copyright statements.  Hankel transforms of the first
> and second order can be computed through digital filtering.
>
> I have rewritten the code in Python/numpy, complete with tests and
> acknowledgements of the origins, and my employer has agreed that I can
> donate the code to Scipy.  I believe this should be of interest.
> Hankel transforms arise often in acoustics and other systems with
> cylinder symmetry.  If you want it, I would like a suggestion where it
> belongs (with other integral transforms, probably) and how I should
> shape the tests to make them suitable for inclusion.
>
> The tests I currently have use Hankel transforms of five different
> functions with known analytical transforms and compares the
> transformed values to the numerically evaluated analytical
> expressions.  Currently plots are generated, but for automated testing
> I suppose something else would be better.  Pointing me at an example
> is sufficient.
>
> [1]
> http://infohost.nmt.edu/~borchers/hankel.html
>
> [2] Anderson, W. L., 1979, Computer Program Numerical Integration of
> Related Hankel Transforms of Orders 0 and 1 by Adaptive Digital
> Filtering. Geophysics, 44(7):1287-1305.
>
> Best regards,
>
> --
> Tom Grydeland
>   <Tom.Grydeland@(norut.no|gmail.com)>
>
>
>
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-- 
Robert Kern