MATLAB: Reduce dimensionality using indices

dimensionalityindexing

Hi all.
I have what I tink should be a fairly simple question but I just can't work it out. In one of my scripts I have a three-dimensional array A like this:
A(:,:,1) =
       2     4     8
       5     6     3
      10     3     6
A(:,:,2) =
       7     6     3
       9     2     9
      10     2     3
A(:,:,3) =
       9     4     7
       3     2     5
      10     3     4
I also have a 2D matrix d which looks sth like this:
d =
       1     2     3
       1     1     3
       2     1     1
Now, what I want to reduce A to two dimensions using the third dimension elements indicated by d. The result should be:
AA =
       2     6     7
       5     6     5
      10     3     6
Surely there's a clever way to do this without loops? I fiddled around with a combination of meshgrid and d but that got ugly really quickly…
EDIT : I should have made clear that this is just an example and I don't necessarily know the dimensions of A. It will always be true that
size(A,1) == size(d,1)
size(A,2) == size(d,2)
but A may be 5x5x13.
Thanks so much for your help.

Best Answer

Convert sub indices into linear indices:
% some data
  A = ceil(10*rand(3,4,3)) % A has an arbitrary size
  d = ceil(size(A,3)*rand(size(A,1),size(A,2))) % d is the subindex in the 3rd dimension
% engine
  Nrc = size(d) ;
  [r,c] = ndgrid(1:Nrc(1), 1:Nrc(2)) ; %r,c, specify the subindices in the 1st and 2nd dimension
  ix = sub2ind(size(A),r, c, d) % convert to linear indices
  B = A(ix) % retrieve from A
% check
  x = 2 ; y = 3 ;
  A(x,y,d(x,y)) == B(x,y)
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