a question on for loop statement

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ektor
ektor on 16 May 2019
Commented: Luna on 17 May 2019
Dear all,
I have this for loop
T=1000;
k=0.1;
u=rand(T,1);
a = zeros(T,1);
a(1) =u(1)+ k*0.01;
for t=2:T
a(t) = u(t,1) + k*a(t-1);
end
Is there a faster way of obtaining a? Maybe if I avoid loop?
  4 Comments
Adam Danz
Adam Danz on 16 May 2019
Edited: Adam Danz on 16 May 2019
This is the tricky part: *a(t-1)
Short answer to "is there a faster way": Probably not.
There's probably a way to avoid the loop by replacing it with a convoluted, unreadable, jumble of functions but I doubt it will be as fast and it will not be as intuitive. If your loop works for you, keep it. It's simple, clean, and fast.
Luna
Luna on 16 May 2019
I agree with Adam I have tried with both T = 1000 and T = 1000000.
The time perfomances are below:
T = 1000 -> Elapsed time is 0.051244 seconds.
T = 1000000 -> Elapsed time is 0.073614 seconds.
The for loop is already as fast as it could be and the simplest solution.

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Answers (1)

Jos (10584)
Jos (10584) on 16 May 2019
This is filtering.
T=10; % smaller example
k=0.1;
u=rand(T,1);
% your loop -> a
a = zeros(T,1);
a(1) =u(1)+ k*0.01; % i do not get this addition ...
for t=2:T
a(t) = u(t,1) + k*a(t-1);
end
% filtering -> aa
uu = u ;
uu(1) = uu(1) + k*0.01 ; % implement offset?
aa = filter(1, [1 -k], uu) ;
% do they produce the same result?
isequal(a, aa) % YES
  9 Comments
Jos (10584)
Jos (10584) on 17 May 2019
btw, regarding execution time, you should also include the pre-allocation of the array :-D

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