Monte Carlo Simulation Code

Hello! Can anyone help me out please!!!

I just started using matlab and I have to create a program that caculates the value of pi using the equation ? = ?/ ? 2 . First I need to calculate the value of A within a given radius of 4, and then im given this information: to estimate the area of a circle, we first note that we have a way to determine whether or not a point (x, y) is inside a circle that is centered at the origin and has radius r. Specifically, the distance from the origin to (x, y) is given by: ???????? = √? 2 + ? 2. If this distance is less than or equal to a radius r, then the point (x, y) is within the circle.

My program has to calculate the amount of sqaures that are within the circle because that eqauls the are. Can anyone help??

[Alejandra Bremuantz]

This is what I have so far !!

clear

%pi = area/(r^2);

r=4;

areasq = x*y;

x=0;

y=0;

d=sqrt((x^2)+(y^2));

counter=0;

for r==4

if ((x^2)+(y^2)<1)

counter=counter+1

end

end

counter

[Yidnekachew A sima]

function [estimatepi,c] = estimatepi9(tol)

x=rand;

y=rand;

c=0;

hits=rand;

n= 0;

hit=[];

error=[];

estimatepi=[];

tol=0.0001;

error = abs(pi-estimatepi)-tol;

while error>tol

n=n+1;

x=rand;

y=rand;

hit=(x-0.5).^2+(y.^2)<=1;

for c=1:n;

hits=sum(hit);

estimatepi=4*hits/n;

end

end

end

I am geting un empty set for this file can anyone help?

[Image Analyst]

You need to index hit so that it's a vector.

Answer 1

[Image Analyst]

You need to set x and y to rand(), not zero.

You should know that all Monte Carlo simulations use random numbers, and nowhere in your program do you call rand().

You should also do the loop some number of times, not just once like r==4 would do

for counter = 1 : 10000000  % Try 10 million times.
    x = r * rand
    y = r * rand
    % etc.
    % DO NOT increment counter in the loop!
end

[Alejandra Bremuantz]

Thank you so much for your respone!

The thing is that the guidelines of the assignment don't let me use a random number generator.

I have to place the center of the circle at the origin so x=0 and y=0 and then set the value of r=4. Only if the distance is equal to or less than the raidus the sqaure is inside of the circle.