MATLAB: How to plot billions of points efficiently

figureMATLABplot

I have 3 billions of 2D points to be plotted, which requires a lot of memory. Thus, I can only do this on a server, which has about 1TB memory. But the server does not have a decent graphics card, thus export of figures uses CPU to render and takes more than 5 hours. But this procedure needs to be done many times, because I need to change the scale of axes according to the shape of the scatter diagrams. My desktop has a decent graphics card. Could I utilize the desktop's ability when data can not fit into its memory?
Here is an example of my figures.

Best Answer

Here is one way to subsample the data to produce almost identical plots:
% Fake data:
X = 10.^randn(2e4,1);
Y = 10.^randn(2e4,1);
figure()
scatter(X,Y,'filled')
set(gca,'xscale','log','yscale','log','title','AllData')
% Merge data points:
Xb = log10(X);
Yb = log10(Y);
Xf = 0.05; % adjust factor to suit

Yf = 0.05; % adjust factor to suit
Xb = Xf*round(Xb/Xf);
Yb = Yf*round(Yb/Yf);
[~,idx] = unique([Xb,Yb],'rows');
figure()
scatter(X(idx),Y(idx),'filled')
set(gca,'xscale','log','yscale','log','title','SubData')
The number of points plotted:
>> numel(X) % AllData
ans =  20000
>> nnz(idx) % SubData
ans =  6653
You can also see that all extrema are still clearly visible.
PS: you might be able to save some memory by putting the merging onto one line:
[~,idx] = unique([Xf*round(log10(X)/Xf),Yf*round(log10(Y)/Yf)],'rows');
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