On 2/5/2013 11:17 AM, Christian wrote:
> Hello,
> does there exist something like an approach for vectorization loops (2,
> 3 or 4 nested loops)?
...
Completely general, no, most have to be analyzed based on the
characteristics of what is in the loop(s) and the loop structure itself...
> Example for discussion:
>
> n=3;
> a=rand(n,n);
> for i=1:n
> for j=1:n
> b = b + a(i,j)*a(j,i); % command
> end
> end
> b
>
> Okay, the innermost loop is absolutely no problem, but what's with the
> outer one.
Consider what the above operations do...for this particular case,
s=x'.*x; s=sum(s(:);
which can be written in several other ways...
s=sum(sum(x'.*x));
s=sum(dot(x'.*x));
>> x=rand(3);
>> s=0;for i=1:3,for j=1:3,s=s+x(i,j)*x(j,i);end,end,s
s =
3.1787
>> s=x'.*x; s=sum(s(:))
s =
3.1787
>> s=sum(sum(x'.*x))
s =
3.1787
>> s=sum(dot(x',x))
s =
3.1787
>>
So, the key is in recognizing the algebraic expression and often on how
it relates to linear algebra, etc., ...

