Fwd: 'for' loop vectorization

[Francesco Potorti`]

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.

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