MATLAB: Computing the pairwise distance matrix given a matrix of vectors

Question

I'm producing m amount of nx1 vectors, and storing them all in an nxm matrix A (each column is a vector). What I want is to now create an mxm matrix B where B(i,j) = norm(vi -vj). I have a naive solution using nested for loops, but this takes far too long; I came up with a solution using 3d arrays but since I'm producing ~9000 vectors and each one is ~100000 entries, there's no way I have the memory for a 100000x9000x9000 array. Is there any other way to compute this?

Naive solution:

 for i = 1:nvectors
  for j = i:nvectors
    dist = norm(vectorMatrix(:,i) - vectorMatrix(:,j));
    distanceMatrix(i,j) = dist;
    distanceMatrix(j,i) = distanceMatrix(i,j);
  end
 end

3d array solution:

 vectorMatrix = repmat(vectorMatrix, 1,1,nvectors);
 distanceMatrix(:,1,:) = vectorMatrix(:,:,1);
 distanceMatrix = repmat(distanceMatrix,1,nvectors,1);
 distanceMatrix = distanceMatrix - vectorMatrix;
 distanceMatrix = sqrt(sum(distanceMatrix.^2,1));

Answer 1

doc pdist

e.g.,

result = squareform(pdist(vectorMatrix'));

or drop the squareform if you are willing to do your own indexing calculation:

result = pdist(vectorMatrix');