Thread Subject: Recursive Relation without using for loops

Hallo,

I have a recursive relation , I want to compute the elemenst of the series (W) without using for loops.
Here is the version with for loops.

-----------------------------------------------------------
% P is defined before

total=100;
time=100000;

W=zeros(total,time);

% First element

W(1,:)=1;


% Others are constructed using recursive relation
  
for m=2:total

    sum=zeros(1,time);
    
    for r=1:m-1
            sum(1,:)=sum(1,:)+W(r,:)*mean(P(m,:).*W(r,:))/mean(W(r,:).*W(r,:));
        
    end
     
    W(m,:)=W(m,:)-sum(1,:);

end

------------------------------------------------------------
This is indeed inefficient, takes hours to compute
Any suggestions will be appreciated

Thanks,

Selim

"selim selim" <fthsel@example.com> wrote in message <gcn4ir$54o$1@fred.mathworks.com>...
> Hallo,
>
> I have a recursive relation , I want to compute the elemenst of the series (W) without using for loops.
> Here is the version with for loops.

Sorry I can't see any recursion in your algo/problem. On the other hand this array manipulation could be vectorized.

Bruno

This may very well be vectorizable, but you should also look at what your loops are doing to see if they can be improved. Since you you don't describe P, I ran a much shorter version of your code with a random P. I noticed that the resultant W is one column repeated over and over. There is no need to manipulate a matrix like this when you can do all you need with a vector. These simple changes get the same value for W, but not repeated in a matrix:


total = 100;
time = 100000;
P = round(rand(total,time)*20);

W = zeros(total,1);
W(1,:) = 1;

for m=2:total
    sum = 0;
    for r=1:m-1
        sum = sum + W(r,:)*mean(P(m,:).*W(r,:))/mean(W(r,:).^2);
    end
    W(m,:) = W(m,:)-sum;
end



This runs in 16 seconds on my machine. I didn't run the full matrix version, but if you say it was taking hours then you should see quite an improvement.

"Matt Fig" <spamanon@yahoo.com> wrote in message <gco8g2$rts$1@fred.mathworks.com>...
> This may very well be vectorizable, but you should also look at what your loops are doing to see if they can be improved. Since you you don't describe P, I ran a much shorter version of your code with a random P. I noticed that the resultant W is one column repeated over and over. There is no need to manipulate a matrix like this when you can do all you need with a vector. These simple changes get the same value for W, but not repeated in a matrix:
>
>
> total = 100;
> time = 100000;
> P = round(rand(total,time)*20);
>
> W = zeros(total,1);
> W(1,:) = 1;
>
> for m=2:total
> sum = 0;
> for r=1:m-1
> sum = sum + W(r,:)*mean(P(m,:).*W(r,:))/mean(W(r,:).^2);
> end
> W(m,:) = W(m,:)-sum;
> end

One thing that you should do is to NEVER
define a variable named sum, or any other
commonly used function name. This will
prevent you from being able to use those
functions. Look at what happens if you
do:

x = 1:.1:10;
sum = 5;

Can you now form the sum of the elements
in x? Try it.

sum(x)
??? Subscript indices must either be real positive integers or logicals.

John