What are efficient ways to extract lower dimensional slices from a high-dimensional array ?

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gg 2011-12-14

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I am looking for an efficient way to extract sub-arrays from a larger array. There are (at least) two standard solutions both having certain disadvantages.

First solution: Use a loop Disadvantage: Might be slow if nidx (see code below) is large

Second solution: use sub2ind Disadvantage: Interim indices created are large if nidx * ndim3 is large

Any other (especially better) ideas?

Kind regards, gg

   %create 3dim testarray
   ndim1 = 3;
   ndim2 = 4;
   ndim3 = 5;
   testarr = rand([ndim1,ndim2,ndim3]);
   %pick some indices into the first two dimensions
   nidx = 10;
   idx1 = randi([1,ndim1],[nidx,1]);
   idx2 = randi([1,ndim2],[nidx,1]);
   %now extract slices from testarr according to the indices
   %First solution: by loop
   newarr = zeros(nidx, ndim3);
   for kidx = 1:nidx
      newarr(kidx,:) = testarr(idx1(kidx), idx2(kidx), :);
   end
   %Second solution using sub2ind
   refidx1 = repmat(idx1, [ndim3,1]);
   refidx2 = repmat(idx2, [ndim3,1]);
   tmp = repmat((1:ndim3),[nidx, 1]);
   refidx3 = tmp(:);
   lidx = sub2ind(size(testarr), refidx1, refidx2, refidx3);
   newarr_alt = reshape(testarr(lidx), nidx, ndim3);
   %are they equal this time?
   isequal(newarr, newarr_alt)

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James Tursa 2011-12-14

Copying the data can easily dominate the run time over the calculations involved, particularly for something as simple as squaring elements or setting elements to a value. E.g., a mex routine can often significantly outperform m-code for these cases.

gg 2011-12-16

Now I understand! Yes, of course you are completely right. But then on a MEX level this problem doesn't arise. Andrei's way of doing index arithmetic is the way to do it in C, isn't it?

So I was really asking (not entirely precise obviously) on a MATLAB intrinsic way of doing it, without using MEX.

Note that if you are using Andrei's method you create an index (somewhat implicitely though). So even if you do in situ calculations you may need to allocate memory for this index. Actually it is not clear to me under what conditions, which solution is the "best". Except for MEX maybe which seems to be straightforward and thus quick. I have never used it but then there might be overheads involved as well?

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Answer 1

Andrei Bobrov 2011-12-14

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在 MATLAB Online 中打开

s = size(testarr);
m = prod(s(1:2));
out = testarr(bsxfun(@plus,idx2*(s(1)-1)+idx1,0:m:(s(3)-1)*m))

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gg 2011-12-14

Andrei,

Thanks!

I consider this an optimissed variant of sub2ind. It does suffer from creating an auxiliary index as well. Although the size is only ndim3 as opposed to ndim3 * nidx, which is certainly a huge improvement. It will be interesting to compare speed.

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