(And I really need to stop writing markdown and forget to trigger the beautification of it...)
On Friday, November 21, 2014 10:19:08 PM UTC+1, Tomas Lycken wrote: > > Hi Nils (and others), > > I just completed some work I've had lying around on [Interpolations.jl]( > https://github.com/tlycken/Interpolations.jl), a package which is meant > to eventually become `Grid.jl`s heir. The stuff I've done so far isn't even > merged into master yet (but it hopefully will be quite soon), so this is > really an early call, but I think there might be some infrastructure in > this package already that can be useful for lots of interpolation types. > Besides, it wouldn't be a bad thing to try to gather all of these different > methods in one place. > > `Interpolations.jl` currently only supports [B-splines on regular grids]( > http://en.wikipedia.org/wiki/B-spline#Cardinal_B-spline) (and only up to > quadratic order, although cubic is in the pipeline), but I would definitely > be interested in a collaboration effort to add e.g. Hermite splines of > various degrees as well. I would also like to at least investigate how > difficult it would be to generalize the approach used there to work on > irregular grids. > > There is quite a ways to feature parity with `Grid.jl`, but at least for > B-splines most of the basic infrastructure is there, and it's all been > designed to be easy to extend with new interpolation types. Feel free to > comment, file issues or pull requests with any ideas or functionality you'd > like to see. > > Regards, > > // Tomas > > On Friday, November 14, 2014 12:57:19 PM UTC+1, Nils Gudat wrote: >> >> Hi Tamas, >> >> Thanks for your input! Indeed it appears that shape preserving >> interpolation in higher dimensions is a somewhat tricky problem. Most of >> the literature I've found is in applied maths journals and not a lot seems >> to have been transferred to economics, although there's a paper by Cai >> and Judd >> <http://books.google.co.uk/books?id=xDhO6L_Psp8C&pg=PA499&lpg=PA499&dq=shape+preserving+interpolation+higher+dimensions&source=bl&ots=8yLHXvILy-&sig=ykAEER_ahDcCckTBZmfcq1cMQUU&hl=en&sa=X&ei=ktplVOjSDcPmav4M&ved=0CDgQ6AEwAg#v=onepage&q=shape%20preserving%20interpolation%20higher%20dimensions&f=false> >> >> in the Handbook of Computational Economics, Vol. 3. >> In any case this discussion is not about Julia anymore, but if it turns >> out I really have to write some form of shape-preserving higher dimensional >> interpolation algorithm I'll make sure to make it as general as possible so >> that it can potentially be added to some Julia interpolation package. >> >> Best, >> Nils >> >
