How to vectorize computing all pairwise vectors in a pointcloud?

I have an m points x n dimensions array xy of Cartesian coordinates. In my case, n is 2, but this should generalize to at least three dimensions. My goal is get the all the vectors created by combinatorial pairs of points. I can do this with nested for loops (see below), how can I vectorize this operation? I can get the vector magnitudes with pdist2(xy,xy), but not the vector angles.

[m,n] = size(xy); 
V = zeros(m,m,n);
for im1 = 1:m
  for im2 = 1:m
    V(im1,im2,:) = xy(im1,:) - xy(im2,:);
  end
end

Answer 1

[Burke Rosen]

After further review, I reduced it down to:

[m,n] = size(xy); 
V = zeros(m,m,n);
for im = 1:m
    V(:,im,:) = xy - xy(im,:); %2016b bsxfun syntax
end

Can it be vectorized any further?

Answer 2

[Lowey]

If I understand your question correctly, the meshgrid function may be of help.

 im1 = 1:m;
 im2 = 1:m;
 [X, Y] = meshgrid(im1, im2);

The elements in X and their corresponding elements in Y give all possible combinations

Answer 3

[Walter Roberson]

V = pdist(xy);