2/3d interpolation from a regular grid to another regular grid

- krigging in package fields, which also requires irregular spaced data

That kriging requires irregularly spaced data sounds new to me ;) It
cannot be, you misread something (I feel free to say that even if I
never used that package).
It can be tricky doing kriging, though, if you're not comfortable with
a little bit of geostatistics. You have to infer a variogram model for
each data set; you possibly run into non-stationarity or anisotropy,
which are indeed very well treated (maybe at best) by kriging in one
of its forms, but ... it takes more than this list to help you then;
basically kriging requires modelling, so it is often very difficult to
set up an automatic procedure. I can reccomend kriging if the spatial
variability of your data (compared to grid refinement) is quite
important.

In other simple cases, a wheighted mean using the (squared) inverse of
the distance as wheight and a spherical neighbourhood could be the
simpliest way to perform the interpolation.

- krigging in package fields, which also requires irregular spaced  
data

That kriging requires irregularly spaced data sounds new to me ;) It
cannot be, you misread something (I feel free to say that even if I
never used that package).

Of Krigging I only know the name and general intent so I gladly line  
up to your opinion.
I just read the description in ?Krig in the package fields which says:
" Fits a surface to irregularly spaced data. "
But there are probably other Krigging methods I overlooked.

It can be tricky doing kriging, though, if you're not comfortable with
a little bit of geostatistics. You have to infer a variogram model for
each data set; you possibly run into non-stationarity or anisotropy,
which are indeed very well treated (maybe at best) by kriging in one
of its forms, but ... it takes more than this list to help you then;
basically kriging requires modelling, so it is often very difficult to
set up an automatic procedure. I can reccomend kriging if the spatial
variability of your data (compared to grid refinement) is quite
important.

This was the impression I had too: that Krigging is an art in itself  
and that it requires you to know much about your data. My problem is  
simpler: the variability is not very large between grid points (it is  
oceanic current velocity data so it is highly auto-correlated  
spatially) and I can get grids fine enough for variability to be low  
anyway. So it is really purely numerical.

In other simple cases, a wheighted mean using the (squared) inverse of
the distance as wheight and a spherical neighbourhood could be the
simpliest way to perform the interpolation.

Yes, that would be largely enough for me. I had C routines for 2D  
polynomial interpolation of a similar cases and low order polynomes  
gave good results. I just hoped that R had that already coded  
somewhere in an handy and generic function rather than having to  
recode it myself in a probably highly specialized and not reusable  
manner.

Thank you very much for you answer and if someone knows a function  
doing what is described above, that would be terrific.

JiHO
---
http://jo.irisson.free.fr/

I just read the description in ?Krig in the package fields which says:
" Fits a surface to irregularly spaced data. "

Yes, that is the most general case. Regular data location is a subset
of irregular. Anyway, kriging, just one g, after the name of Danie
Krige, the south african statistician who first applied such method
for minig survey.

My problem is simpler

...

So it is really purely numerical.

...

I just hoped that R had that already coded ...

Of course R has ... ;) If your grids are really as simple as the
example you posted above, and you have a really little variability,
all you need is a "moving average", the arithmetic mean of the two
nearest points belonging to grid1 and grid2 respectively. I assume
that your regularly shaped grids are values stored in matrix objects.

The functions comes from the "diff.default" code (downloading the R
source code, I assure, is worth):

my.interp <- function(x, lag = 1)
{
    r <- unclass(x)  # don't want class-specific subset methods
    i1 <- -1:-lag
    r <- (r[i1] + r[-length(r):-(length(r)-lag+1)])/2
    class(r) <- oldClass(x)
    return(r)
}

Finally,

g1 <- apply(grid1val,1,my.interp)
g2 <- apply(grid2val,2,my.interp)

give the interpolations on gridFinal, provided that all gridFinal
points are within the grid1 and grid2 ones.

If you want the mean from 4 points, you apply once more with lag=3,
cbind/rbind to the result columns/rows o NAs, and you calculate the
mean of the points of the two matrixes.
This is the simplest (and quickest) moving average that you can do.
For more complicated examples, and for 3d, you have to go a little
further, but the principle holds.

ScionForbai

I just read the description in ?Krig in the package fields which  
says:
" Fits a surface to irregularly spaced data. "

Yes, that is the most general case. Regular data location is a subset
of irregular. Anyway, kriging, just one g, after the name of Danie
Krige, the south african statistician who first applied such method
for minig survey.

ooops. sorry about the typo.

My problem is simpler

...

So it is really purely numerical.

...

I just hoped that R had that already coded ...

Of course R has ... ;) If your grids are really as simple as the
example you posted above, and you have a really little variability,
all you need is a "moving average", the arithmetic mean of the two
nearest points belonging to grid1 and grid2 respectively. I assume
that your regularly shaped grids are values stored in matrix objects.

The functions comes from the "diff.default" code (downloading the R
source code, I assure, is worth):

I can imagine it is indeed. I use the source of packages functions  
very often.

my.interp <- function(x, lag = 1)
{
    r <- unclass(x)  # don't want class-specific subset methods
    i1 <- -1:-lag
    r <- (r[i1] + r[-length(r):-(length(r)-lag+1)])/2
    class(r) <- oldClass(x)
    return(r)
}

Finally,

g1 <- apply(grid1val,1,my.interp)
g2 <- apply(grid2val,2,my.interp)

give the interpolations on gridFinal, provided that all gridFinal
points are within the grid1 and grid2 ones.

If you want the mean from 4 points, you apply once more with lag=3,
cbind/rbind to the result columns/rows o NAs, and you calculate the
mean of the points of the two matrixes.
This is the simplest (and quickest) moving average that you can do.
For more complicated examples, and for 3d, you have to go a little
further, but the principle holds.

Thanks very much. I'll test this soon (and it looks like the vector  
operation might even be directly translatable in Fortran which is  
nice since I'll need to do it in Fortran too).

Thanks again.

JiHO
---
http://jo.irisson.free.fr/