Column-wise inexing of matrix

Consider the following

A = magic(4);
indx = [1 1 3 2;4 2 1 1; 1 3 2 1];
A(indx)

Because of linear indexing the code above returns:

ans =

    16    16     9     5
     4     5    16    16
    16     9     5    16

But I would like it to return the equivalent of

    [A(indx(:,1),1) A(indx(:,2),2) A(indx(:,3),3) A(indx(:,4),4)]
    
    ans =

    16     2     6     8
     4    11     3    13
    16     7    10    13

What is the most efficient, scalable way of doing this? Thiking of larger matrices.

Answer 1

[James Tursa]

One way that is scalable and matches your example:

A(indx + (0:size(indx,2)-1)*size(A,1))

This uses implicit expansion. On earlier versions of MATLAB you would have to use bsxfun or repmat to get the same result.

Should work as long as indx columns match the columns of A that you want extracted. If not, then you would need to modify the row indexing vector I used to match the actual column indexing you wanted.

[Guillaume]

You may want to use sub2ind instead. It does exactly the same calculations as James' code, possibly a smidge slower because it'll validate the inputs. The advantage is that it's clearer to the reader what is going on:

A(sub2ind(size(A), indx, repmat(1:size(indx, 2), size(indx, 1), 1)))

Otherwise, please write a comment after that line of code so readers understand what it does.

[James Tursa]

You have your row & column indexing reversed. It should be

A(sub2ind(size(A), indx, repmat(1:size(indx, 2), size(indx, 1), 1)))

[Guillaume]

Indeed!