"Desort" a matrix. Undo a sorting in Matlab

Question

This question is basically an extension of that question.

I have a matrix A in Matlab and want to sort that matrix along one dimension:

A = rand(3,3,5); [B idx] = sort(A,3);

Now idx is a matrix containing the "sorted" indices. How can i get back the matrix A using only B and idx?

The answer of the original question doesn't work for matrices, unfortunately.

Answer 1

You need to sort the indices idxto get back the original indices. Rest of the work would involve getting the formatted row and column indices corresponding to all those dim-3 indices. The implementation would look something like this -

[~,dim3idx] = sort(idx,3);

[m,n,r] = size(B);
[rowidx,colidx,~] = ndgrid(1:m,1:n,1:r);

Aout = B(sub2ind(size(B),rowidx,colidx,dim3idx))

Please note that for performance, one can get the linear indices generated by sub2ind alternatively with bsxfun directly from the size parameters and thus also avoid ndgrid, like so -

Aout = B(bsxfun(@plus,bsxfun(@plus,(1:m)',m*(0:n-1)),m*n*(dim3idx-1)))