How to programmatically select which array dimension to address

I've run across this issue a few times, and I'm wondering if there's an elegant way to handle it.

Say I have a function that reorders the vectors/pages/etc of an N-D array along a specified dimension, but we don't really know how many dimensions this arbitrary array might have. How can I address the elements of the array? I can think of two solutions, neither of which seem particularly ideal.

On one hand, I could presume a maximum number of dimensions and just handle it with explicit cases. It wouldn't take that many cases to cover most practical scenarios. Let's say I presume a maximum of 5-D:

function outpict=reorderarray(myarray,whichdim)
	sz=size(myarray);
	reorderedVector=randi(sz(whichdim),[1 sz(whichdim)]);
	switch whichdim
		case 1
			outpict=myarray(reorderedVector,:,:,:,:);
		case 2
			outpict=myarray(:,reorderedVector,:,:,:);
		case 3
			outpict=myarray(:,:,reorderedVector,:,:);
		case 4
			outpict=myarray(:,:,:,reorderedVector,:);
		case 5
			outpict=myarray(:,:,:,:,reorderedVector);
		% we could go on ...
	end
end

Alternatively, I could build the expression as a character array and use eval(). This seems like something I should avoid.

Is there a better way to do something like this?

[Stephen23]

"How can I address the elements of the array?"

Define the indices in a cell array, then use a comma-separated list:

https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html

https://www.mathworks.com/matlabcentral/answers/320713-how-to-operate-on-comma-separated-lists

"It wouldn't take that many cases to cover most practical scenarios."

Or you could use a simple comma-separated list to obtain the general solution for any number of dimensions:

https://www.mathworks.com/matlabcentral/answers/757464-how-can-i-extract-a-slice-from-a-multidimensional-array

https://www.mathworks.com/matlabcentral/answers/340858-selecting-data-from-a-dynamically-named-nd-array

https://www.mathworks.com/matlabcentral/answers/564101-accessing-the-nth-dimension-in-a-variable-sized-multidimensional-array

https://www.mathworks.com/matlabcentral/answers/332592-i-want-to-index-across-multiple-dimensions-using-a-vector-as-opposed-to-comma-notation

[DGM]

Oof. I admit, I had struggled to find a good search query and could've done a better job. Thank you.

Answer 1

[Walter Roberson]

img = imread('flamingos.jpg');
imshow(reorderarray(img, 2));

imshow(reorderarray(img, 3));

imshow(reorderarray(img, 7));

function outpict = reorderarray(myarray,whichdim)
	sz = size(myarray);
        sz(end+1:whichdim) = 1;    %in case asked for a dimension past the typical
        idx = repmat({':'}, 1, length(sz));
        idx{whichdim} = randperm(sz(whichdim));
        outpict = myarray(idx{:});
end

[DGM]

Auugh! It works!

I had run across a similar example in a very old book, but in the printing, the curly braces were parentheses. I just figured it was some old syntax that no longer worked. I didn't even think that of course it would be a cell array. I should've been paying attention.

Many thanks to you, Stephen, and John.

Answer 2

[John Chilleri]

Hello,

I wouldn't suggest this to be an elegant solution, but it has worked so far for a number of test cases.

   
    % A is myarray
    % wdim is whichdim
    % ordering is reorderedVector

function C = reorderarray(A,wdim,ordering)
    sz = size(A);          % Acquire size
    pA = 1:length(sz);     % Create permutation vector
    pA(1) = wdim;          % Swap desired dimension with first dimension
    pA(wdim) = 1;
    sz2 = sz;              % Track permuted size
    sz2(1) = sz(wdim);
    sz2(wdim) = sz(1);
    B1 = permute(A,pA);    % Permute matrix so desired dimension is first
    B2 = B1(ordering,:);   % Reorder rows and restructure as 2D array
    B3 = reshape(B2,sz2);  % Reshape back into original permuted shape
    C = permute(B3,pA);    % Undo the permutation
end

I'll note that the process makes sense intuitively, but I wouldn't guarantee its correctness. The reshape restoring order seems to work because MATLAB has consistent methods of indexing across functions.

Thanks!

[DGM]

That works, but in my tests, it performs poorly in terms of execution time -- especially as array size increases. For a sample 100x10x10x10x10 array, it requires more than twice the time compared to the methods I described, and doubling the array size quintuples the time, whereas it only doubles it for the aforementioned methods.

I was actually surprised that the eval() method is actually slightly the fastest of the three. I've had it drilled into my head to avoid using eval(), but I'm not sure if this isn't a good use for it.