Sample Code for Monte Carlo estimation of pi

[FallenApple]

Below is the partial code to plot the rejection/accept regions using monte carlo sampling. The context is to estimate pi and plotting is just one part of it.

I'm not sure how the ~ symbol can work.

scatter(samples(1,~reject),samples(2,~reject),'b.')
scatter(samples(1,reject),samples(2,reject),'rx')

I get the idea that ~ means "not". But reject is a different vector. How can the samples matrix detect logicals on vectors that aren't even subsets of the matrix?

The entire code and website I got it from is below.

% DISPLAY A CIRCLE INSCRIBED IN A SQUARE

figure;
a = 0:.01:2*pi;
x = cos(a); y = sin(a);
hold on
plot(x,y,'k','Linewidth',2)

t = text(0.5, 0.05,'r');
l = line([0 1],[0 0],'Linewidth',2);
axis equal
box on
xlim([-1 1])
ylim([-1 1])
title('Unit Circle Inscribed in a Square')

pause;
rand('seed',12345)
randn('seed',12345)
delete(l); delete(t);

% DRAW SAMPLES FROM PROPOSAL DISTRIBUTION
samples = 2*rand(2,100000) - 1;

% REJECTION
reject = sum(samples.^2) > 1;

% DISPLAY REJECTION CRITERION
scatter(samples(1,~reject),samples(2,~reject),'b.')
scatter(samples(1,reject),samples(2,reject),'rx')
hold off
xlim([-1 1])
ylim([-1 1])

piHat = mean(sum(samples.*samples)<1)*4;

title(['Estimate of \pi = ',num2str(piHat)]);

https://theclevermachine.wordpress.com/2012/09/10/rejection-sampling/

 

[Orodruin]

I suggest reading this: https://se.mathworks.com/help/matlab/math/matrix-indexing.html

If it is a tl;dr - scroll down directly to using logical arrays to access matrix elements.

 

[FallenApple]

I suggest reading this: https://se.mathworks.com/help/matlab/math/matrix-indexing.html

If it is a tl;dr - scroll down directly to using logical arrays to access matrix elements.

Ok I see. How silly of me.

reject = sum(samples.^2) > 1;
is just a vector of logicals. True or False. So it can be used for conditioning.