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Re: Mathieu functions ready for alpha testing
- From: Brian Gough <bjg at network-theory dot co dot uk>
- To: Lowell Johnson <ldj00 at sio dot midco dot net>
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Tue, 2 Dec 2003 20:14:58 +0000
- Subject: Re: Mathieu functions ready for alpha testing
- References: <200311281805.54834.ldj00@sio.midco.net>
Lowell Johnson writes:
> Mathieu function routines have been committed on the mathieu-1-4
> CVS branch under the specfunc directory. They presently handle the
> angular functions and the radial functions of type 1, integer order
> and real arguments only. These limitations are based in part on
> the current lack of support for complex arguments in the GSL Bessel
> and Hankel function routines. Also the highest order is currently
> limited to 100. I haven't spent much time testing the argument
> limits.
Cool. Good work.
I don't know much about these functions but here are some comments:
Clean compile with -Wall. No memory problems noted by various testing
tools either. Good.
According to the GSL Design document avoid using malloc inside the
functions, or returning a * pointer to malloced memory block. Instead
have a suitable array argument passed in by the caller.
Test values -- best practice would be to "fail-safe" here, by not
using the output of the function as an expected value. Otherwise some
of the tests may slip through into a released version.
The ACM TOMS papers ought to discuss testing somewhere (I would hope)
http://math.nist.gov/toms/cgi-bin/TOMSsearch?string=mathieu
I also found J. Phys. A: Math. Gen. 34 (2001) 35413551
http://www.cbpf.br/~portugal/Mathieu.pdf
For multi-precision calculations Maxima, GP-Pari and Emacs Calc are
good choices.