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
