scatter plot: tall arrays eating up all the memory

Question

I am working on tone mapping operators in HDR. My question is very simple. I want to scatter plot large arrays on Matlab 2015Ra with computer specs core i5 20GB RAM. Only the scatter plot eats up the whole memory (around 92% of 20GB). I need some suggestion to plot tall arrays. I know Matlab 2018 has binscatter function but I have lower version. Thank you. Sample Code:

a=randn(21026304,1);
scatter(a,a); 

Only this code eats up the all memory.

Answer 1

You can create a binscatter like function yourself with histcounts2! Histcounts bins the data into an NxN array which you can then visualize with imshow... this is pretty memory-efficient as every bin only takes up a couple of bytes, regardless of the input size.

% Some (correlated) data
x = randn(1e6,1);
y = randn(1e6,1)+x;

% Count 32x32 bins
[N,ax,ay] = histcounts2(x,y,32);

% Some gradient
cmap = [linspace(1,0,16);
    linspace(1,0.3,16);
    linspace(1,0.5,16)].';

% Show the histogram
imshow(...
    N,[],...                        % N contains the counts, [] indicated range min-max
    'XData', ax, 'YData', ay, ...   % Axis ticks
    'InitialMagnification', 800,... % Enlarge 8x
    'ColorMap', cmap...             % The colormap
);

colorbar;       
axis on;
title('bin-counts');