Re: [Help-gsl] monotone interpolation

[Christian Krueger]

Ok, the implementation was easier than expected; I adopted the code for 
the Akima-spline to large extent.

I just figured out, that GSL considers itself to be almost complete 
(which it is not IMHO), cf. 
http://www.gnu.org/software/gsl/design/gsl-design.html#SEC2

Therefore, a new feature should not come with any issues (bugs, code 
layout, naming convention, and so on). And this is the point where I 
might need your help, please. Either from you directly or you redirect 
me to someone one else. Furthermore, it would be the first time for me 
to contribute to such a huge project.

-------
For the actual problem, *monotone spline interpolation*, there are three 
different solutions known to me:

(a) M.Steffen, "A simple method for monotonic interpolation in one 
dimension", Astron. Astrophys. 239, 443-450 (1990).

(b) H.T.Huynh, "Accurate Monotone Cubic Interpolation", SIAM J. Numer. 
Anal. 30, 57-100 (1993).

(c) Fritsch, F. N.; Carlson, R. E., "Monotone Piecewise Cubic 
Interpolation", SIAM J. Numer. Anal. 17 (2), 238–246 (1980).

For solution (c), there is also an article available on wikipedia and as 
it was the first one known to me, this one is implemented at the moment.

I don't know which of those is the "best" or to prefer in a certain 
situation. However, I will implement (a) or (b) (or both) soon since I 
am not 100% satisfied with (c); it sometimes produces more wiggles than 
Akima's method. So, I hope one of the other two suits my problem better.

Apart from that, to be most comprehensive, all three methods could go to 
GSL, but it might be frowned upon flooding GSL with new stuff. Does 
anybody of you have experience with some of those methods?

Any comments are appreciated! Thank you!

/Christian


On 03/02/2012 02:52 PM, Rhys Ulerich wrote:
> > The other one in that graph *might* be close to the one on wiki?
> > http://en.wikipedia.org/wiki/Monotone_cubic_interpolation
> >
> > However, I would prefer to have a GSL implementation.
>
> I suspect a GSL implementation would look enough like
> http://bzr.savannah.gnu.org/lh/gsl/trunk/annotate/head:/interpolation/cspline.c
> that those data structures could be used as a fruitful starting point.
>
> - Rhys