I am working with MATLAB, and I would have the following problem. I have the following matrix of random numbers rand(200,200) and I need to create a 3D matrix with the following structure 3D_mat(r,s,p) with 15 layers (p=15), where each layer will contain the given data rand(200,200). Perhaps, it is easy task, but I am MATLAB beginner.

  • $\begingroup$ It is very unlikely that you can call a variable 3D_mat (cannot start with a number) $\endgroup$ – Laurent Duval Aug 18 '16 at 22:03
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    $\begingroup$ This is actually a duplicate of stackoverflow.com/questions/16746999/… (modulo replacing 1d arrays by 2d arrays), which also includes some timings. $\endgroup$ – Christian Clason Aug 18 '16 at 22:17
  • $\begingroup$ @Christian Clason Yes, and link you point at is "so 2013" $\endgroup$ – Laurent Duval Aug 23 '16 at 6:27
  • $\begingroup$ Same data for 15 layers? Or each layer with different random numbers? $\endgroup$ – Memming Sep 20 '16 at 19:28

This is probably not the most efficient way to do this in MATLAB, but the following works for me in Octave:

for i=1:15

And, I think it should work fine in MATLAB as well. If your dimensions get a lot bigger or you have to create the 3D matrix frequently, there are probably much more efficient was to accomplish this.

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    $\begingroup$ You can also use repmat: B=repmat(A,1,1,15). If the dimensions are a lot bigger, it would make sense to not construct B at all and instead use broadcasting (look for bsxfun in the online help) whenever you need to do something with B. $\endgroup$ – Christian Clason Aug 18 '16 at 13:46
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    $\begingroup$ @ Christian Clason To maintain compatibility with older versions of MATLAB, it is better to use repmat(A,[1,1,15]) which will work in new and old versions of MATLAB. $\endgroup$ – Mark L. Stone Aug 18 '16 at 15:18

Here are three options: with repmat or bsxfun, two functions evoked by @Christian Clason. On some versions of Matlab (notably older than 2013, as can be seen from https://stackoverflow.com/questions/16746999/most-efficient-way-for-repeating-a-vector-in-matlab), bsxfun was faster, and if not the case, is believed to use less memory (useful if you get much bigger than $200\times 200\times15$). The last one plays with indexing.

nRow = 200;
nCol = 200;
nDep = 15;

r = rand(nRow,nCol);
o = zeros(nRow,nCol,nDep); % Not bad to initialize

% Choose one
o = repmat(r,1,1,nDep); % repmat version
o = bsxfun(@times,ones(1, 1 , nDep),r); % bsxfun version
o = r(:,:,ones(1, 1 , nDep)); % multiple-indexing version

In my case (Matlab2013b), repmat is $2/3$ faster than the two others, for several matrix sizes and repetition depth (including yours). According to some testimonies, since a novel coding of repmat exist in Matlab2013b and above, bsxfun indeed can be slower.

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    $\begingroup$ Actually, I wasn't recommending to use bsxfun for creating o -- that would completely defeat the purpose. Instead, when you want to do (e.g.) D=o.*C, you do D=bsxfun(@times,C,r) (and similarly for other operations). But as I said, I doubt you'll see much difference for the sizes in this example. $\endgroup$ – Christian Clason Aug 18 '16 at 22:11
  • $\begingroup$ @Christian Clason Actually, I never used bsxfun before, that was an opportunity for me to try it. I'll be aware of its convenience in the future $\endgroup$ – Laurent Duval Aug 18 '16 at 22:16

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