vectorizing four nested for loops

If I have a one-dimensional array A of size n and I need to create a new two-dimensional array R from the elements of array A, I can do it using two nested loops:

for i = 1:n
  for j = 1:n
      R(i,j) = A(i) + A(j);
  end
end

Or I can use vectorization:

[i, j]=ndgrid(1:n);
R = A(i)+A(j);

If array A becomes a n by n matrix and I need to create a four dimensional array R I can still use nested loops:

for i = 1:n
  for j = 1:n
      for k = 1:n
          for l = 1:n
              r(i,j, k, l) = a(i, j) + a(k, l);
          end
      end
  end
end

Is there a way to replace these four nested loops and use vectorization? Thanks for your help!

Answer 1

[Geoff]

Try this:

[i,j] = ndgrid(1:n*n);
r = reshape(a(i)+a(j), [n n n n]);

[Andrei Bobrov]

+1

[Max]

Thanks a lot for your help, Geoff. Would it be possible to modify your code to accommodate a slightly different manipulation with the matrices in the nested loop:

r(i,j,k,l)=a(i,j)+a(k,l)+a(i+k,j+l) for all i+k<=n and j+l<=n

Thanks!

[Geoff]

Awwwk!! Um, I dunno. You're talking about chucking in some kind of triangular term. I have trouble thinking about that in 4 dimensions. Remember that brevity should not always be chosen over clarity.

[Max]

Yeah, I shouldn't have simplified the problem in the first place. That's my bad. Thanks for your help anyway!

Answer 2

[Andrei Bobrov]

variant

R = bsxfun(@plus,a,reshape(a,1,1,n,n))

[Max]

Thanks a lot, Andrei!