# interpolate over a multi-dimensional function

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I want to use interpn to interpolate the values of function V:R^4->R^3. I.e. size(V) = [C C C C 3], but interpn requires that the last dimension be of size 1.

So instead of doing:

anew = interpn(C, M, Y, K, V, a(:,1), a(:,2), a(:,3), a(:,4));

I have to do this:

anew = zeros(size(a_cmyk));

for i=1:4

anew(:,i) = interpn(C, M, Y, K, V(:,:,:,:,i),a(:,1), a(:,2), a(:,3), a(:,4));

end

And it really slows me down. Am I doing something wrong? Is there a way around this?

##### 0 Comments

### Answers (3)

the cyclist
on 6 Apr 2011

Alec
on 7 Apr 2011

It seems interpn only works with scalar functions. If you issue

open interpn

you can see where it parses the input it expects that you have as many X1,X2,... as dimensions in V. So V has to be a scalar function: R^n --> R. You'll have to interpolate each coordinate function independently.

In your original post, you write that V is a function from R^4 --> R^3, but then in the code V seems to be a function from R^4 --> R^4 (you're looping from 1 to 4 rather than 1 to 3). Was that just a typo?

In the example you posted in the comment. V is a function from R^3 to R^4. So you'll have to interpolate each of the 4 coordinate functions separately, perhaps like this:

c = 1:100;

m = 1:100;

y = 1:100;

V = rand([100 100 100 4]);

[C M Y] = ndgrid(c,m,y);

vals = zeros([size(1:50) 4]);

for ii = 1:4

vals(:,:,ii) = interpn(C,M,Y,V(:,:,:,ii), 1:50,1:50,1:50);

end

(Note: vals here has size(vals) = [ 1 50 4] because the 50 interpolated points are defined on a "grid" that only has one row )

As far as performance, the for loop isn't really a "bad" for loop in terms of matlab optimization. Presuming the number of coordinates is much much smaller than the number of data points or interpolated points.

##### 1 Comment

the cyclist
on 7 Apr 2011

If I am not mistaken, this is pretty much the same coding strategy that Lior included with her original question.

See my answer, posted (time-wise) just after yours, in which I think I have the correct vectorization of the last dimension. Performance wise, I am not sure if it will be faster or not, but it is worth a shot.

the cyclist
on 7 Apr 2011

Lior,

Putting this as a new answer, because I did not have a perfect understanding of what you were trying to do before.

I am going to put this code in without explanation, because I think you are going to understand what it is doing. If you do not, add a comment, and I will try to explain a bit what is happening. The code that does what you want is the one commented "Four planes".

c = 1:20;

m = 1:20;

y = 1:20;

z = 1:4;

V = rand([20 20 20 4]);

[C M Y Z] = ndgrid(c,m,y,z);

% One plane:

ci = 1:10;

mi = 1:10;

yi = 1:10;

zi = ones(1,10);

vals = interpn(C,M,Y,Z,V,ci,mi,yi,zi);

% Four planes:

ci = repmat(1:10,[1 4]);

mi = repmat(1:10,[1 4]);

yi = repmat(1:10,[1 4]);

zi = [ones(1,10), 2*ones(1,10), 3*ones(1,10), 4*ones(1,10)];

vals = interpn(C,M,Y,Z,V,ci,mi,yi,zi);

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