how to repeat a loop until a condition is met than draw histogramm

what i want is to generate 2 uniforms randoms numbers 'u1' and 'u2' and evaluate the magnetude of the 2 nummbers .if the magnetude "d<1" it is transformed and scalled by u1 to finally draw a histogramm of the outpout result.

the pgroramm is looks like this .

repeat 
u1=2*rand()-1;
u2=2*rand()-1; 
d=(u1.^2)+(u2.^2);
until 0<d<1
G=sqrt((-2*log(d))/d);
return G*u1

Answer 1

[Yongjian Feng]

Just use a while loop?

Try:

done = false;
while ~done
    u1=2*rand()-1;
    u2=2*rand()-1; 
    d=(u1.^2)+(u2.^2);
    done = d > 0 && d < 1;
end
d
G=sqrt((-2*log(d))/d);
G*u1

[ad lyn]

and what's about the histogram? i need to draw the histogram of (G*u1) so i can get a gaussian distribution

Answer 2

[Image Analyst]

You're not going to be able to generate many points before you get a squared distance of less than 1 and need to quit. I ran it several times and it was always done in the first pass - just was able to get one point. Nonetheless, you need to index your distance so you have an array of distances that you can pass into the histogram() function. Here is how you'd do it:

loopCounter = 1;
maxIterations = 100000; % Failsafe
% Preallocate space
distanceSquared = zeros(1, maxIterations);
while loopCounter <= maxIterations
	u1=2*rand()-1;
	u2=2*rand()-1;
	distanceSquared(loopCounter) = (u1.^2)+(u2.^2);
	
	% See if we need to quit.  Quit when distanceSquared is less than 1.
	if distanceSquared(loopCounter) < 1
		% Crop off unused.
		distanceSquared = distanceSquared(1 : loopCounter);
		break;
	end
	loopCounter = loopCounter + 1;
end
caption = sprintf('Was able to generate %d distances.\n', loopCounter);
fprintf('%s\n', caption);
% Compute G from distanceSquared:
G = sqrt((-2*log(distanceSquared)) ./ distanceSquared);
histogram(G);
grid on;
title(caption);
xlabel('G');
ylabel('Count');