Interpolate a 3D-Matrix using interp1

I try to interpolate a 3D Matrix using interp1. I think it should be easy but i just don't get it.

I have a 3d-matrix and a vector in z direction. I wan't to get an interpolated 2d Matrix for any value in the z direction. For Example:

    matrix(1:3,1:3,1) = 1
    matrix(1:3,1:3,2) = 2
    z(1,1,1:2) = [10,20]
    interp1(z,matrix,15)

so I thought interp1 would return a 3x3 Matrix with the values 1.5 but i just get an error.

Thanks a lot!

Answer 1

[Matt J]

    V=reshape(matrix,[],2).'; 
    VI = interp1(z,V,15);
    ans =  reshape(VI,3,3),

You could also use griddedInterpolant instead

 F=griddedInterpolant({1:3,1:3,z},matrix);
 ans= F({1:3,1:3,15});

It's hard to say which would be more efficient, in general. griddedInterpolant is a newer and better optimized function, but interp1 takes advantage of the 1D nature of the interpolation.

Answer 2

[Glynn]

Using the same example above, what if the xi in interp1(x,Y,xi), is a 2-d matrix the same size as the first two dimensions of 'matrix'? I keep getting OOM issues when trying to solve: x is a (1,3)array Y is a (2030,873,3) matrix xi is a (2030,873) matrix

[Matt J]

interp1(x,Y,xi) will interpolate each column of Y at all points specified in xi. In your case, that means it is trying to generate a resulting array containing (2030*873)^2 values. Thus your out-of-memory errors.

You cannot use interp1(x,Y,xi) to do 1D interpolation at a different set of points in every column of Y. You would have to do that as a multi-dimensional interpolation.

[Glynn]

Okay got it, thanks, makes sense. So should I be using interp3 instead? I'm confused as how to set that up with my particular example. Any help is appreciated.

[Matt J]

Yes, you could use interp3, though I think griddedInterpolant is easier to work with. I don't actually have a clear picture how your xi are supposed to be interpreted. If you are interpolating in a 3D array, like Y, then the locations at which you interpolate must consist of (xx,yy,zz) coordinate triplets.