Can we vectorize this kind of for loop?

The for loop is as follows:

    N=2;T=3;
    Trials=rand(N,T);
    for i=1:N
        for j=1:T
            AverageValue=mean2(Trials);
            Trials(i,j)=Trials(i,j)-AverageValue;
        end
    end

The difficult is that 'AverageValue' changes its value according to each updated 'Trials'.

===========================================

Updated version with 'mean2' replaced by 'trapz':

    N=4;T=5;
    Trials=rand(N,T);
    for i=1:N
        for j=1:T
            IntValue=trapz(trapz(Trials(1:3,2:5)));
            Trials(i,j)=Trials(i,j)+IntValue;
        end
    end

Please help, thank you!

Answer 1

[Matt J]

I agree with Sean's general point, that for-loops needn't be vectorized at all costs. However, you can make this particular for-loop much more efficient (for large N and T) by incrementally updating AverageValue:

    N=2;T=3;
    Trials=rand(N,T);

   AverageValue=mean2(Trials);
   coeff=1-1/N/T;    

    for i=1:N
        for j=1:T

             Trials(i,j)=Trials(i,j)-AverageValue;

             AverageValue=AverageValue*coeff;

        end
    end

[Matt J]

And therefore, I guess you could vectorize it as follows

 Averages=mean2(Trials)*reshape(coeff.^(0:N*T-1),T,N).';

 Trials = Trials - Averages;

[Tuan]

Thank Matt J so much for your answer. It works. I would like to know if this principle can be applied for other function than mean2, e.g., an integral function of 'Trials'?

[Matt J]

It should be readily applicable to any linear operation, which mean2 is. It might also be applicable to some non-linear operations if the response to a change in one Trial(i,j) has a simple incremental effect on the output. That would have to be considered on a case-by-case basis, though.

[Tuan]

Thank Matt J for your reply. As commented by Jan, I have updated the more complicated code by replacing 'mean2' by 'trapz'. Could you please help me to vectorize it. Thank again.

[Matt J]

I would have to see how trapz is being used. In the meantime, please Accept-click my answer, since it seems to fulfill your posted question.

Answer 2

[Sean de Wolski]

I wouldn't bother vectorizing this.

My Thoughts on FOR-loops

[Tuan]

Thank Sean! I agree that for loop is not bad. However, for my code (it is not the simple code that I wrote above), for loop really takes time. This is why I seek a vectorized version ... Thank!

[Jan]

@Tuan: Do not post simplified versions of the code, when you ask for an optimization. Then important details are missing.

[Tuan]

Dear Jan, I have updated the more complicated code by replacing 'mean2' by 'trapz'. I hope to receive your help. Thank you.