Fwd: 'for' loop vectorization

[John W. Eaton]

On 25-Oct-2007, Francesco Potorti` wrote:

| This mail does not contain references to previous mails on the subject,
| as I am writing without being subscribed to this list.
| 
| I do not know if this piece of information can add anything to the
| discussion, but I can make two observations.  First is that I managed to
| obtain a humble 10% improvement over triu.m by vectorising it like this:
| 
| octave> n=5000; a=ones(n,n);
| octave> function z=vtriu(z) n=rows(z); z((1:n)'*ones(1,n)>ones(n,1)*(1:n))=0; 
end
| octave> t=cputime;b=triu(a);cputime-t
| ans =  1.7081
| octave> t=cputime;c=vtriu(a);cputime-t
| ans =  1.5081
| octave> all(all(b==c))
| ans =  1
| 
| The idea is that I build a vector of the matrix indices that are under
| the diagonal, and then I zero them.
| Maybe some variation on this concept could make triu and tril faster.
| 
| Second is an observation on the proposed cumulative max function using
| triu: it requires space proportional to n^2 for a vector of length n, so
| it is not abvious that is worth optimising, because it cannot be used
| for big vectors, that is, vectors of length n such that n^2 does not fit
| into memory.

I don't think it is worth it for just 10%.

jwe