Re: interp2d discussion

[jeremy theler <jeremy@talador.com.ar>]

On Friday 10 January 2014 18:55:37 Patrick Alken wrote:
> On 01/10/2014 05:27 PM, jeremy theler wrote:
> > Hi all,
> > 
> > I consider the addition of these routines to GSL as a major breakthrough.
> > 
> > Now I have three questions about generalization:
> >  1. can these 2D interpolation routines be extended to scattered (i.e.
> >  non-
> > 
> > rectangular) data?
> 
> Not currently, but this can always be done with least-squares models.
> I'm not aware of any available software that interpolates on nonuniform
> grids - do you know of any?


I think I saw a python numerical library (whose name I forgot) that performed 
some kind of scattered-data interpolation. I think it used a weigthed average 
of first n neighbors. What I do in these cases is a nearest-neighbors search 
using a k-dimensional tree to sort the data. Some simple 2D examples can be 
seen in

http://www.talador.com.ar/jeremy/wasora/realbook/._realbook010.html

For two dimensional functions such as f(x,y) I once tried to do a 3-nearest 
neighbors search, fit a plane as z = a*x + b*y + c an then evaluate the plane 
z at the desired (x,y) location, but that approach had more problems than 
advantages.

Actually, wasora is a piece of software I am writing that acts as a high-level 
interface to GSL for most of its features (except multidim interpolation for 
now, and ODE/DAE systems for which it uses SUNDIALS). Some examples of the GSL 
manual are rewritten as wasora inputs in

http://www.talador.com.ar/jeremy/wasora/realbook/._realbook015.html

If someone wants to try, comments are welcome.

 
> >  2. can these 2D interpolation routines be extended to n dimensions?
> 
> Once the 2D code is imported I'd like to make at least a 3D linear
> interpolater, which should be straightforward.

Good. Are n dimensions straightforward also?

--
jeremy