[R] 2d approx

[roger koenker]

?interp in akima for f: R^2 -> R.

url:	www.econ.uiuc.edu/~roger        	Roger Koenker
email	rkoenker at uiuc.edu			Department of Economics
vox: 	217-333-4558				University of Illinois
fax:   	217-244-6678				Champaign, IL 61820

On Oct 14, 2004, at 8:09 PM, Vadim Ogranovich wrote:

> Hi,
>
> I am looking for a function that generalizes 'approx' to two (or more)
> dimensions. The references on the approx help page point toward 
> splines,
> but a) splines is what I am trying to avoid in the first place and b)
> splines (except for mgcv splines) seem to be one dimensional.
>
> Here is a more detailed account. Using mgcv:gam I fit an additive model
> xy.gam according to the formula y ~ s(x), which is a spline under the
> hood. If I now wish to compute model prediction for new data I could 
> use
> predict.gam(xy.gam, newdata). However newdata will first be expanded
> into a large matrix of coefficients with respect to the spline basis
> functions. For example if the length of newdata is 1e6 and the size of
> the basis is 100 than the matrix of coefficients is 100*1e6, i.e. huge.
> The predict.gam recognizes the problem and works around it by doing a
> piece-meal prediction, but this turns out to be too slow for my needs.
>
> One way around is to tabulate s(x) on a fine enough grid and use approx
> for prediction. Something like this (pseudo-code)
>
> x.grid <- seq(min(newdata), max(newdata), length=1000)
> y.grid <- predict.gam(xy.gam, x.grid)
>
> y.newdata <- approx(x.grid, y.grid, newdata)$y
>
>
> I didn't test this, but I expect it to be dramatically faster than
> predict.gam.
>
> Unfortunately I don't know how to extend it into 2D. Your suggestions
> are very welcome!
>
>
> Thanks,
> Vadim
>
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>
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