How can i vectorize this loop?

Hi, I have to compute the stucture functions of velocity increments of a velocity sample (vector v) of size 1X13'000'000. My code is the following

for li = 1:20000
    vl = v(1+li:end)-v(1:end-li);
    S_2(li) = mean(vl.^2);
    S_3(li) = mean(vl.^3);
    S_4(li) = mean(vl.^4);
    
end

Is it possible to vectorize this loop to speed up computation ?

Thanks for your answers

[William Alberg]

I don't know if you can vectorize that, since vl change size every iteration

You can still speed it up a bit by doing the following:

S_2 = nan(L,1);
S_3 = nan(L,1);
S_4 = nan(L,1);
for li = 1:L
    vl = v(1+li:end)-v(1:end-li);
	
	temp = vl.^2;
	S_2(li) = mean(temp);
	
	temp = temp .* vl;
	S_3(li) = mean(temp);
	
	temp = temp .* vl;
	S_4(li) = mean(temp);
end

[Rik]

@William, feel free to move that to the answer section.

@Julien, I don't see a way to use a convolution or the mov___ functions, which generally would do something like this. What are you using this for? There might be a way to do a different calculation that gets you the downstream result. A change of algorithm will speed up your code much more than optimizing your code.

[Julien Neuhaus]

@William, Thank you it works better like this.

@Rik I have to compute it in a project about turbulence in a fluid flow at university, but the solution from William is already a good optimization.

Thanks to you two

Answer 1

[William Alberg]

@Rik told me to move my comment to the answer section, i hope he ment copy-paste :)

I don't know if you can vectorize that, since vl change size every iteration

You can still speed it up a bit by doing the following:

S_2 = nan(L,1);
S_3 = nan(L,1);
S_4 = nan(L,1);
for li = 1:L
    vl = v(1+li:end)-v(1:end-li);
	
	temp = vl.^2;
	S_2(li) = mean(temp);
	
	temp = temp .* vl;
	S_3(li) = mean(temp);
	
	temp = temp .* vl;
	S_4(li) = mean(temp);
end

[Rik]

Yes, I did mean copy-pasting the contents of your comment. Actually moving posts between the answer and comment section has been on the wish-list for years now, so I doubt that will be possible any time soon.