Access all k-th elements of a n-dimensional array, where the k indexes are defined in a (n-1)-dimensional array.

I have a 3-dimensional N-by-M-by-L array of values A, e.g.

A(:,:,1) = [1 2 3;
            4 5 6;
            7 8 9];
A(:,:,2) = [10 11 12;
            13 14 15
            16 17 18];

I also have a N-by-M matrix containing indexes idx, e.g.

idx = [1 2 1;
       2 1 1;
       2 2 2];

where the indexes are in the range [1 to L].

I would like to create the N-by-M matrix B such that B(i,j) = A(i,j,idx(i,j)), e.g.

   B = [1 11 3;
       13 5 6;
       16 17 18].

I can see that it could be done easily with nested for loops, but i was wondering if there is a vectorized (and possibly faster) way to achieve this.

Answer 1

[Stephen23]

>> S = size(A);
>> [R,C,~] = ndgrid(1:S(1),1:S(2),1);
>> X = sub2ind(S,R,C,idx);
>> B = A(X)
B =
    1   11    3
   13    5    6
   16   17   18