efficient normalization of matrix columns?

[Joachim De Beule]

Hi all,

1) I have the following function that normalizes the columns in a sparse 
matrix X and returns the result as a sparse matrix Xn:

function Xn = normalizeX (X)
    norms = sqrt(sumsq(X));
    [i,j,v] = find (X);
    [n, m] = size(X);
    v = v./full(norms(j'))';
    Xn = sparse(i,j,v,n,m);
endfunction

On my computer, this function takes about 0.7 seconds when applied to a random 
(sparse) matrix of 1000 by 1000.

It uses a huge amount of memory however, and becomes unfeasible to use on 
really large matrices (I need to apply it to matrices of size 3206978  by 
18846)

2) On the other hand, the following function performs better on memory, but 
takes over 27 seconds to terminate on the same random matrix as mentioned 
above:

function Xn = normalizeX (X)
   norms = sqrt(sumsq(X));
   for c = 1:size(X)(2)
      Xn(:,c) = X(:,c)./norms(c);
   endfor
endfunction

3) In short, it seems that it is not possible to normalize a large sparse 
matrix in octave, either because it requires too much memory or else because 
it takes too long too compute. Any ideas?


Thanks, Joachim.