Faster way to calculate pairwise distance?

I have a matrix p x n, with row vector as coordinate in space. I need to calculate distance between all pairs of these coordinates. Since my p is very large(~50,000), I want to write the code without using any for loop and using only built-in function. I have reduced the code till 1 for loop, still it takes lot of time. I have only signal processing toolbox available with me.

My code looks like this:

if true
  Y = a + rand(50000,5)*(b-a);
for i=1:p-1
  j=i+1:p
      D(j,i) = sqrt(sum(bsxfun(@minus,Y(i,:),Y(j,:)).^2,2));
end
end

Any help would be much appreciated.

[Matt Kindig]

Well the first thing you could do is pre-allocate D, by inserting this line prior to the for loop:

D = zeros(p-1,p);

However, Shashank is right--you will run into major issues with memory soon.

Answer 1

[Shashank Prasanna]

pdist

http://www.mathworks.com/help/stats/pdist.html

But part of the statistics toolbox.

Alternatively you could generate all pairwise combinations of row using

nchoosek

And then calculate distance as above. But you may hit the memory wall, as the nchoosek output will be huge.