Re: cumulative maximum (was: 'for' loop vectorization)

[Hermann Schwarting]

Am Dienstag, 23. Oktober 2007 schrieb Jordi Gutiérrez Hermoso:

> On 23/10/2007, Hermann Schwarting <address@hidden> wrote:
> > The more I think about it, it looks like I can't vectorize this.
> > It's a bit similar to a cumulative maximum, which can't be
> > vectorized either, I think.
>
> It can be, but my vectorisation runs slower than the unvectorised
> code. :-(
>
>      a = max(triu(repmat(a(:),1,length(a))))
>
> The triu call is the bottleneck, it seems, which mystifies me.

I was wrong. Here is a recursive version of cummax that needs O(log2 
n) recursions and is faster than a naïve implementation. The use of 
triu() is prohibitive if the input is a large vector, because of 
memory consumption.


function X = cummax( X )

n = length(X);
if n == 2,
        X(2) = max(X);
elseif n > 2,
        X(2:2:n) = cummax( max( X(1:2:n-1), X(2:2:n) ));
        X(3:2:n) = max( X(3:2:n), X(2:2:n-1) );
end


Kind regards,
Hermann