Data cloning into 3D matrix

Question

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.

Answer 1

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

A=rand(200,200);
for i=1:15
  B(:,:,i)=A;
end

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.

Answer 2

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.