Linear Extrapolation with interp2
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Matlab's griddedInterpolant allows for linear interpolation with linear extrapolation in 2D space, i.e.,
griddedInterpolant(X,Y,V,'linear','linear');
However, it seems to be the case that interp2, which I believe uses griddedInterpolant under-the-hood, doesn't allow for this combination. If "linear" is selected as the interpolation method, then the extrapolation must be a scalar. Is there a way to use linear-linear inter-extrapolation with interp2?
4 Comments
John D'Errico
on 16 May 2020
My question is still valid for Michael to answer as to why. Regardless, you can't force interp2 to do what it is not written to do. Anyway, IF the interp2 call is just going to get sent into griddedInterpolant anyway, then the GPU call would still seem to be a problem, since then interp2 is just a wrapper.
Matt J
on 16 May 2020
I am curious of Michael's actual motives as well. Irrespectively, though, it is a frustrating problem for gpuArray users... I don't believe the gpuArray version of interp2 is a wrapper for anything. If a GPU version of griddedInterpolant existed, it would make sense for the Parallel Computing Toolbox developers to make it available to us.
Accepted Answer
Matt J
on 16 May 2020
Edited: Matt J
on 16 May 2020
The only remedy I can think of is to pre-pad the edges of the data V with linearly extrapolated values at distant X, Y. That way, you aren't doing any extrapolation anymore. All of your query points xq,yq will fall within the boundaries of the padded data, assuming you make the padded, X,Y distant enough to enclose them.
[V,x]=linearpad(V,x);
[V,x]=linearpad(fliplr(V),flip(x)); V=fliplr(V);
V=V.';
[V,y]=linearpad(V,y);
[V,y]=linearpad(fliplr(V),flip(y)); V=fliplr(V);
V=V.';
Vq=interp2(x,y,V,xq,yq,'linear');
function [D,z]=linearpad(D0,z0)
factor=1e6;
dz=z0(end)-z0(end-1);
dD=D(:,end)-D(:,end-1);
z=z0;
z(end+1)=z(end)+factor*dz;
D=D0;
D(:,end+1)=D(:,end) + factor*dD;
end
1 Comment
KD
on 26 Mar 2021
Edited: KD
on 26 Mar 2021
FYI this almost works but there are mistakes. There should be no fliplr after applying linearpad the second time in each direction, and in the function it should be D=D0(:,end)-D0(:,end-1); (not D=D...)
Otherwise works great - thanks!
This is my modified version:
[V,x]=linearpad(V,x);
[V,x]=linearpad(fliplr(V),flip(x));
V=V.';
[V,y]=linearpad(V,y);
[V,y]=linearpad(fliplr(V),flip(y));
V=V.';
Vq=interp2(x,y,V,xq,yq,'linear');
function [D,z]=linearpad(D0,z0)
factor=1e6;
dz=z0(end)-z0(end-1);
dD=D0(:,end)-D0(:,end-1);
z=z0;
z(end+1)=z(end)+factor*dz;
D=D0;
D(:,end+1)=D(:,end) + factor*dD;
end
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