Question

Write a matlab program that determines the value of pi using the monte carlo technique. do this for a loop of multiple fixed points. (i.e 100-10000) Plot the computed value of pi and the difference from the true value as this number increases. Time the execution of your code for various numbers of points, and plot the precision vs the computational cost.

Answer 1

MATLAB CODE

% Write a matlab program that determines the value of pi using the monte carlo
% technique. do this for a loop of multiple fixed points. (i.e 100-10000) Plot the
% computed value of pi and the difference from the true value as this number
% increases. Time the execution of your code for various numbers of points, and plot
% the precision vs the computational cost.
n = 1;
pimc = zeros(1,1);
exection_time = zeros(1,1);
for nTrial = 100:50:10000
tic
nHit = 0;
r = 1;
for i = 1:nTrial
x = r*rand();
y = r*rand();
if x^2 + y^2 <= (r)^2
nHit = nHit + 1;
end
end
pimc(n) = 4*nHit/nTrial;
exection_time(n) = toc;
n = n + 1;
end
figure(1)
plot(100:50:10000, pimc, 'LineWidth', 2);
xlabel('Number of trials', 'FontSize', 20)
ylabel('Monte carlo estimate of pi', 'FontSize', 20)
print -dpng figure1.png

figure(2)
plot(100:50:10000, pimc-pi, 'LineWidth', 2);
xlabel('Number of trials', 'FontSize', 20)
ylabel('pimc - pi', 'FontSize', 20)
print -dpng figure2.png

figure(3)
plot(exection_time, -log10(abs(pimc-pi)), 'LineWidth', 2);
xlabel('Execution time (s)', 'FontSize', 20)
ylabel('Precision', 'FontSize', 20)
print -dpng figure3.png