Re: Reducing for loop

[Oliver Heimlich]

Am 25.03.2015 um 21:09 schrieb Dr.-Ing. Dieter Jurzitza:
> Dear listmembers,
> I am using a for loop as follows. I have an array, say A, containing numelem
> elements.
>
> Now I want to fill array B with elements as follows:
>
> B(1)=A(1)
>
> for i=2:numelem
>     B(i)=B(i-1)+A(i);
> endfor
>
> In order to get this vectorized I tried to write something like
>
> B(1)=A(1) # IMHO no way around ...
>
> # apparently does not work ...
> for i=2:n
>     B=A(i)+B(i-1);
> endfor
>
> What am I doing wrong here? Apparently using the indexed left - side array on
> the right side is causing trouble ... Many thanks for any explanation in
> advance,
> take care

Dieter,

after vectorization you will have no for-loop anymore. Instead you have 
a single assignment, which updates the whole array at once.

> for i=2:numelem
>     B(i)=B(i-1)+A(i);
> endfor

Lets solve this step by step. If you did B=B+A, this would compute the 
sum of B and A element-wise and be equivalent to:
for i=1:numelem
    B(i)=B(i)+A(i);
endfor

You do not want the sum of n elements, but the sum of n-1 elements. You 
can achieve this by working on subsets of the arrays with range indices:

B(2:end) = B(2:end) + A(2:end);
… which is equivalent to …
for i=2:numelem
    B(i)=B(i)+A(i);
endfor

Last, you want to shift indices of the first addend, which is also possible:

B(2:end) = B((2:end) - 1) + A(2:end);
or alternatively
B(2:end) = B(1:end - 1) + A(2:end);

and not forget: B(1)=A(1);