a question on for loop statement

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?

[Luna]

Is T variable very large?

[madhan ravi]

Luna T is 1000

[Adam Danz]

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]

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.

Answer 1

[Jos (10584)]

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

[madhan ravi]

Answer using filter() was posted earlier but the OP claimed that it wasn't fast enough as the for loop.

[Adam Danz]

Nice solution, Jos! I hadn't thought of that. It's quite fast and simple.

I ran both versions through a speed tests where each version was executed 100,000 times and then the median speeds were compared. The loop method is 1.6 times faster (p<0.001, Wilcox signed rank) on my machine with a difference of 0.004 milliseconds.

[Jos (10584)]

Thanks Adam :-) Did you exclude the copying of u and the add the initial (weird?) offset to u(1) directly? That would speed things up a little, I presume.

@madhan, sorry, I missed that post, apparently ....

[Adam Danz]

Yea, the speed test was just between the loop and your single line that executes filter(). I'd bet that the filter() function uses a loop, too.

[Jos (10584)]

Internally filter uses a loop, for sure. I also expect error checks etc, that are omitted in the matlab for-loop. But still, it is pretty fast, and nice of course :-)

[ektor]

So, the filter is at least as fast as the for loop?

[Adam Danz]

No, the loop is still faster. As Jos mentioned, there's overhead computations in filter() that aren't needed in your loop.

It's a MYTH that loops are always slower than alternatives.

If you want something neat and tidy, use Jos' solution. If you want something that will save you fractions of microseconds and something you already understand, use your loop.

[Jos (10584)]

btw, regarding execution time, you should also include the pre-allocation of the array :-D

[Luna]

+1 Jos :)