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Re: [Bug-gsl] Contribution: Hermite polynomials, functions etc.

From: Patrick Alken
Subject: Re: [Bug-gsl] Contribution: Hermite polynomials, functions etc.
Date: Sun, 06 Apr 2014 21:16:16 -0600
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:24.0) Gecko/20100101 Thunderbird/24.4.0

Hi Konrad,

  Just curious, since there is a simple relationship between the 2
flavors (probablist and physicist) (ie: Eqs 3 and 4 of your
specfunc-hermite.texi), why not code up just 1 of them and then for the
other flavor just use eqs 3-4?

  I'm guessing the algorithm for computing both is the same, but using
different starting values for the recurrence? I'm asking whether there
is an efficiency reason to have a full implementation of both methods?


On 04/06/2014 07:45 PM, Konrad wrote:
> Hi Rhys and all,
> since finishing the Hermite polynomials and functions, I got around to
> including their zeros. Building on that, I also wrote two small
> Gauss-Hermite quadrature routines, which similarly to the existing
> Gauss-Legendre routines do not accept errors bounds.
> Please find attached the code (gsl_sf_hermite.c,
> gsl_integration_hermite.c), header (gsl_sf_hermite.h,
> gsl_integration_hermite.h), test (test_hermite.c, test_hermite_quad.c)
> and documentation (specfunc-hermite.texi, integration-hermite.texi) files.
> In gsl_integration_hermite.c, the correct header file has to be called
> once the other routines are included in the GSL.
> Cheers,
> Konrad
> P.S.: As always, please notify me if any bugs are found etc.
> Am 11.03.2014 21:29, schrieb Rhys Ulerich:
>> Hi Konrad,
>> Just pinging you to let you know I've not lost track of getting these
>> into the GSL.  I'm about three months past due on my thesis, and so
>> this  has been back-burnered.  I still plan to take care of it once
>> I'm able.
>> - Rhys
>> On Mon, Dec 9, 2013 at 3:17 PM, Konrad <address@hidden> wrote:
>>> Hi Rhys and all,
>>> finally I got around to finishing up on the issues with my contribution.
>>> So please find attached the documentation (specfunc-hermite.texi),
>>> header file (gsl_sf_hermite.h), precision tests (test_hermite.c) and of
>>> course the main code (gsl_sf_hermite.c).
>>> As in my last message on the documentation I should mention the
>>> following points.
>>> The introduction is a little longer than in most other chapters, this is
>>> on purpose since I figured that it is easier for one of you to throw
>>> parts of it out than to extend it. So feel free to shorten it, the only
>>> piece of information I find noteworthy is the fact that the Hermite
>>> functions are eigenfunctions of the Fourier transform. This makes them
>>> very useful and is often forgotten.
>>> Since I'm not very well versed in Texinfo, I couldn't get the greek
>>> character psi on the index, so if somebody knows how to fix this, please
>>> do, the corresponding line is commented right now.
>>> Also, the attached file can be compiled on its own, but I've added
>>> comments where the part relevant for the GSL-manual begins and ends.
>>> The other files are hopefully sufficiently similar to the GSL-standards.
>>> Especially, the functions now include rough estimates of the numerical
>>> errors. Also, some overflow control is implemented throughout the code
>>> that could be exploited further in the future if necessary.
>>> Hope this helps, please feel to contact me with any issues that may arise!
>>> Cheers,
>>> Konrad
>>>>> There's a piece of code I'd like to contribute to your great library.
>>>>> It consists of a few functions to compute Hermite polynomials, Hermite
>>>>> functions and their respective derivatives, please see the attachment
>>>>> gsl_hermite.c.
>>>> Thank you!  From a quick pass there are a couple of little things:
>>>> 1) We need a set of gsl_sf_hermite.h declarations.  Should this just
>>>> be all non-static functions declared within your gsl_hermite.c file?
>>>> Should the single-point functions like gsl_sf_hermite_prob and
>>>> gsl_sf_hermite_prob_der be publicly exposed too?
>>>> 2) We need to get the test cases in gsl_hermite_test.c using the GSL
>>>> test infrastructure.  You can see an example of this within
>>>> specfunc/test_airy.c.  I think getting the test code ported over
>>>> should be relatively quick but I'm uncertain what tolerances to use
>>>> given the printf statements in your gsl_hermite_test.c code.
>>>> 3) We'll need to add documentation for the new functions.  These will
>>>> resemble content like doc/specfunc-airy.texi.  Much of the necessary
>>>> content appears in your email and can be written once we've got a
>>>> gsl_sf_hermite.h in hand from item 1.
>>>> These three things don't have to happen all in one commit, but we
>>>> should get them in place before the next release.  I must admit I
>>>> don't know when that is planned.
>>>> The code looks very nice from a quick browse.  Thank you again.
>>>> - Rhys

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