# +60k Lines on one plot - Too slow

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Ömer Yaman on 25 Jun 2022
Commented: Ömer Yaman on 27 Jun 2022
Dear all,
I need to plot more than 60k lines. I'm doing it in a for loop. It takes too much time, about 170 seconds with the rest of the code. Is there any quicker way?
And also saveas(fig ... command takes too much time as well. About 60 seconds. I would like to save my plot as a png. file.
What are your suggestions to reduce time cost.
Best Regards,
Ömer Yaman on 25 Jun 2022
At that moment, I have my code on the computer that I have in my university. I'will share the plot asap from here.
Task is given to me is like that, I have about 60500 different points which has 6 different value for different time domain. I am supposed to visualize that the generated lines (for each point for 6 different increasing values, basicaly y=mx+n) has slopes that it should not be higher than a certain amount of mean slope value among all slopes and should not be lower too.
Calculations are correct but the time cost is too much. I'm seeking more optimized coding to save time.

Adam Danz on 25 Jun 2022
Edited: Adam Danz on 25 Jun 2022
Another idea is to plot your 60k lines as a 2D density plot (initially suggested in this thread).
Pros:
• 1 graphics object, light weight plot
• simple to compute & simple to plot
• you can see the density patterns created by overlapping lines etc.
• If there is a strong median curve, you'll see it in the plot
Cons:
• Single curves won't appear in the plot (but you wouldn't see many single curves anyway with 60k lines)
• Outliers may become difficult or impossible to see
Example
Create 10k line series that follow a general pattern with varying amounts of noise. I'll use the same x-coordinates but this works just as well if the x-values vary too.
gaus = @(x,mu,sig,amp,vo)amp*exp(-(((x-mu).^2)/(2*sig.^2)))+vo;
x = 0:850;
n = 1e4;
y = zeros(n,numel(x));
rng('default') % to reproduce these results
for i = 1:n
mu = rand(1)*175+300;
sig = rand(1)*100+150;
amp = randn(1)*20+30;
vo = rand(1)*10;
y(i,:) = gaus(x,mu,sig,amp,vo);
end
Now, let's plot 50 random lines to see what they look like. Use randperm to do the random selection.
figure
m = 50;
selection = randperm(n,m);
plot(x, y(selection,:))
title(sprintf('%d random curves from %d',m,n))
axis tight Plot the 2D density using histogram2()
% Replicate the X-vector (skip this if your x values vary for each curve)
xRep = repmat(x, n, 1);
% plot the bivariate historgram
figure
h = histogram2(xRep(:),y(:),'DisplayStyle','tile','ShowEmptyBins','on');
title('Bivariate density of curves')
cb = colorbar();
ylabel(cb,'Number of curves') Alternatively, you could turn off the empty bins to see the shape of the entire dataset
figure
h = histogram2(xRep(:),y(:),'DisplayStyle','tile');
title('...ignoring empty bins')
cb = colorbar();
ylabel(cb,'Number of curves') ##### 2 CommentsShowHide 1 older comment
Ömer Yaman on 27 Jun 2022
Thank you, I will go with this solution.

dpb on 25 Jun 2022
Edited: dpb on 25 Jun 2022
This is way too much data to plot on single figure realistically, of course it's going to take time.
But, the use of a loop and plot is the slowest way possible -- you're computing/drawing every single line individually instead of using the power of MATLAB in being vectorized...
y=[slopes(:,1)*energy+slopes(i,2)].'; % generate y(i,j) by column
hL=plot(energy,y); % plot the result
Here on a not terribly upscale system,
>> tic,y=m*e;toc
Elapsed time is 0.001305 seconds.
>> tic,hL=plot(e,y);toc
Elapsed time is 15.350194 seconds.
>> delete(hL)
>> close
although it took the renderer quite some additional time to actually draw and display the figure -- and at least as long to delete 60K graphics handles.
Since there are only some 1-2K pixels on a monitor anyway, 60K points is some 60X the possible density to be able to display; I would strongly suggest decimating the y array by at least a factor of 10 and likely you'll be unable to see any difference in the result at factors approaching 100X.
Ömer Yaman on 25 Jun 2022

Image Analyst on 25 Jun 2022
Plot just a subsample of the curves. You'll never be able to see all 60k lines anyway, so just pick, say 1000 of them at random and plot those. You'll probably still get the general idea of what all the data would look like if you could have plotted them.
Ömer Yaman on 27 Jun 2022
Thank you for your help, I will keep the math but reduce the number of lines which is plotted.

R2020a

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