Generate Random Numbers from a 2D Discrete Distribution

Random numbers from any 2D discrete probability distribution, at any resolution.
1.8K Downloads
Updated 10 Feb 2016

View License

Tristan Ursell
2D Random Number Generator for a Given Discrete Distribution
March 2012
[x0,y0]=pinky(Xin,Yin,dist_in,varargin);
'Xin' is a vector specifying the equally spaced values along the x-axis.
'Yin' is a vector specifying the equally spaced values along the y-axis.
'dist_in' (dist_in > 0) is a matrix with dimensions length(Yin) x length(Xin), whose values specify a 2D discrete probability distribution. The distribution does not need to be normalized.

'res' (res > 1) is a multiplicative increase in the resolution of chosen random number, using cubic spline interpolation of the values in 'dist_in'. Using the 'res' option can significantly slow down the code, due to the computational costs of interpolation, but allows one to generate more continuous values from the distribution.

[x0,y0] is the output doublet of random numbers consistent with dist_in.

The 'gendist' function required by this script, is included in this m-file.

Example with an anisotropic Gaussian at native resolution:

Xin=-10:0.1:10;
Yin=-5:0.1:5;

Xmat = ones(length(Yin),1)*Xin;
Ymat = Yin'*ones(1,length(Xin));

D1=1;
D2=3;
Dist=exp(-Ymat.^2/(2*D1^2)-Xmat.^2/(2*D2^2));

N=10000;

vals=zeros(2,N);
for i=1:N
[vals(1,i),vals(2,i)]=pinky(Xin,Yin,Dist);
end

figure;
hold on
imagesc(Xin,Yin,Dist)
colormap(gray)
plot(vals(1,:),vals(2,:),'r.')
xlabel('Xin')
ylabel('Yin')
axis equal tight
box on

Example with multiple peaks at 10X resolution:

Xin=-10:0.1:10;
Yin=-5:0.1:5;

Xmat = ones(length(Yin),1)*Xin;
Ymat = Yin'*ones(1,length(Xin));

D1=0.5;
D2=1;
Dist=exp(-(Ymat-3).^2/(4*D2^2)-(Xmat+6).^2/(2*D1^2))+exp(-(Ymat+2).^2/(2*D1^2)-(Xmat+1).^2/(2*D2^2))+exp(-(Ymat-1).^2/(2*D1^2)-(Xmat-2).^2/(2*D2^2));

N=10000;
res=10;
vals=zeros(2,N);
for i=1:N
[vals(1,i),vals(2,i)]=pinky(Xin,Yin,Dist,res);
end

figure;
hold on
imagesc(Xin,Yin,Dist)
colormap(gray)
plot(vals(1,:),vals(2,:),'r.')
xlabel('Xin')
ylabel('Yin')
axis equal tight
box on

Cite As

Tristan Ursell (2024). Generate Random Numbers from a 2D Discrete Distribution (https://www.mathworks.com/matlabcentral/fileexchange/35797-generate-random-numbers-from-a-2d-discrete-distribution), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2014a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
Find more on Random Number Generation in Help Center and MATLAB Answers
Acknowledgements

Inspired: Probabilistic Earthquake Location in 2D

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
1.3.0.0

na

1.2.0.0

bug fix

1.1.0.0

fixed negative values due to interpolation

1.0.0.0