Matlab getting incredibely slow when plotting

Hi!

I'm working on a bifurcation diagram plotting project.

I've written two very similar codes for that, one is plotting the logistic, the other one the Gauss iterative map.

Although the two codes are very similar, the first one (logistic) finishes plotting in 10 seconds, meanwhile it takes 50 seconds for Matlab to plot the Gauss one, and it often freezes after that and the figure can't be closed. I couldn't find a real difference between the codes, what might be the issue with the Gauss one?

Here are the scripts:

Logistic:

Resolution = 100000;
Transients = 512;
SavedPoints = 128;

r = linspace(0,4,Resolution);
x = 0.5*ones(1,Resolution);

% Transient iterations v1
tic
for i=1:Resolution
    for j=1:Transients
        x(i) = r(i)*x(i)*(1-x(i));
    end
end
toc

figure(2); hold on;
for i=1:SavedPoints
    for j=1:Resolution
       x(j) = r(j)*x(j)*(1-x(j));
    end
    
    p2=plot(r,x);
    set(p2,'LineStyle','none','Marker','.','MarkerSize',0.5,'Color',[0 0 0]);
end

The Gauss:

Resolution=1000;
%a=linspace(0,5,N+1);
a=4.90;
b=linspace(-1,1,Resolution);
x=ones(Resolution);
T=512; 
tic
for t=1:T
    for i=1:Resolution
        x(i)=exp(-1*a*x(i)^2)+b(i);
    end
end
toc
SavedPoints=128;
figure(3); hold on;
tic
for it=1:SavedPoints
    for i=1:Resolution
        x(i)=exp(-1*a*x(i)^2)+b(i);
    end
    
    p2=plot(b,x);
    set(p2,'LineStyle','none','Marker','.','MarkerSize',0.1,'Color',[0,0,0]);
end
toc

Thank you for your answers!

M

[Walter Roberson]

I would expect that exp() would be slower than multiplications.

I am still investigating on the graphics speed... I do see what you mean.

Answer 1

[Walter Roberson]

For the first one you have

x = 0.5*ones(1,Resolution);

which is a row vector.

For the second one you have

x=ones(Resolution);

which is a square array.

[Walter Roberson]

Note: you get marginally better performance if you vectorize,

    x = exp(-a*x.^2) + b;

[Mihály Makovsky]

Hi! If I use x=ones(1, Resolution) in the second code as well, it gets 100 times faster than if I use x=ones(Resolution)! (0.5 seconds vs 50 seconds!). Very probably, computations and plotting is optimized on vectors, and not arrays, this might be the reason for this strange behavior.

Thank you for spotting this tiny difference!

[Walter Roberson]

It is not a matter of "optimization"

When you plot() a 2d array, one line is created for each column. So you were creating 1000 lines each plot() call, each with 1000 points. And you were doing that 128 times, so you were ending up with 128000 line objects of 1000 points each.