Making some minor contributions to GSL
linas@austin.ibm.com
linas@austin.ibm.com
Wed Jan 14 00:57:00 GMT 2004
On Tue, Jan 13, 2004 at 03:56:00PM -0700, Gerard Jungman wrote:
> On Tue, 2004-01-13 at 11:17, linas@austin.ibm.com wrote:
> >
> > I have some code that might be appropriate for inclusion with GSL,
> > and was curious to gauge interest, and understand the hurdles
> > involved.
> >
> > Polygamma functions, Abramowitz & Stegun chapter 6.4 -- these
> > are derivatives of the gamma (factorial) function. The algo
> > I have is fairly straightforward ... and is accurate to about
> > 1e-14 or so for "small" orders and arguments. (The "multiplication
> > theorm" breaks down above order 30 or 40 or so, i.e. for arguments
> > greater than a 100 or 200 or so. I'm not sure why.)
>
> I have never made a study of robustness of the GSL
> implementation, in gsl_sf_psi_n(). There are only
How embarassing. When I looked for it, I didn't find it,
so I wrote my own implementation ...
> the test cases in specfunc/test_sf.c. Is there
> a specific deficiency in the GSL implementation?
The only "deficiency" is that the GSL implementation generates
a "domain error" when gsl_sf_psi_n (1,x) is called with
negative x. The psi's should be perfectly well defined
for negative, non-integer x's.
You may find it reassuring that your gsl_sf_psi_n (1,x) agrees
with mine to better than 1e-14 across the board, from very close
to the pole at x=0 (1e-6) to at least 1e+6. I beleive that
most of this error is from my own algo, which wasn't tuned.
It might make you feel better to also know that your algo is
faster than what I came up with, a lot faster in some cases,
especially for large x.
> If you have some test cases that break it, please
> send them so I can check it out. If you have code
> that can plug a hole in the current implementation,
> then that would be greatly appreciated.
Well, now that I know it exists ... it seems to be quite fine.
=====
Another minor suggestion/comment: It would be nice to have
a function that returns Riemann zeta -1, which provides better
accuracy for the intermediate/larger values values of the argument.
Note also, (numerically) convergent sums involving zeta are more
likely to use it in the form of (zeta - 1), which falls off very
nicely. At least, that's the way I like it ...
--linas
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