After a certain time for loop speed slow down?

Question

Alberto Paniate 2020-10-6

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https://ww2.mathworks.cn/matlabcentral/answers/606191-after-a-certain-time-for-loop-speed-slow-down

评论： Asad (Mehrzad) Khoddam 2020-10-6

Hi, I am creating a program with a for loop. As I have asked in another question I have learned to speed this process with vector and ok. But I would like to know why this thing happen.

Take this code:

A = zeros(1000,1000);
E0=10;
for k = 1:1000
    k
    for j = 1:1000
        A(k,j)=E0*exp(-65*((k-500)^2+(j-500)^2)) *exp(-1i *6.5*((k-500)^2+(j-500)^2)); %gaussiana
    end
end

On my computer the first 500 k are really fast, then after about 500, it is very slow, almost 0.8 sec for one k. Why?

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Asad (Mehrzad) Khoddam 2020-10-6

How much RAM do you have? Matlab may write the variables on hard disk when memory is low

Rik 2020-10-6

编辑：Rik 2020-10-6

在 MATLAB Online 中打开

Really strange, especially since the two values for the inner and outer loop don't seem to have an interchangeable effect.

I slightly modified your code and reproduced your finding on R2020b, R2015a, and R2011a (all Windows 10). The peaks for 1,1 and 501,501 are reproducible acros runs and releases (the latter is much more prominent on R2020b).

A = zeros(1000,1000);
E0=10;
k1_list=1:10:1000;
k2_list=1:10:1000;
t=NaN(size(A));
for k1 = k1_list
    for k2 = k2_list
        h_tic=tic;
        for repeats=1:5%make a single line take enough time for tic,toc
            A(k1,k2)=E0*exp(-65*((k1-500)^2+(k2-500)^2)) *exp(-1i *6.5*((k1-500)^2+(k2-500)^2));
        end
        t(k1,k2)=toc(h_tic);
    end
end
figure(1),clf(1),set(gcf,'menu','none','toolbar','none')
[K1,K2]=ndgrid(k1_list,k2_list);
surf(K1,K2,t(k1_list,k2_list),'EdgeAlpha',0.3)
v=regexp(version,'(R[0-9ab]+)','tokens');v=v{1};title(v)
view(-20,40),xlabel('k1'),ylabel('k2'),colormap('jet'),set(gca,'ZLim',[0 3e-3]),caxis([-2e-3 2e-3])

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Answer 1

Asad (Mehrzad) Khoddam 2020-10-6

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https://ww2.mathworks.cn/matlabcentral/answers/606191-after-a-certain-time-for-loop-speed-slow-down#answer_506416

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You can create A without having two nested loops:

E0=10;
[km, jm] = meshgrid(1:1000, 1:1000);
A= E0*exp(-65*((km - 500).^2 + (jm - 500).^2)) .*exp(-1i *6.5*((km - 500).^2 + (jm - 500).^2));

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Rik 2020-10-6

As Alberto mentioned in his question, he does know how to vectorize this, but the slowdown is not explained.

Asad (Mehrzad) Khoddam 2020-10-6

Yes, you are right. This may be because of the internal storage of variables and accessing them. it has exp functions on imaginary variables that may have varying spped for differnt arguments

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