MATLAB: Monte Carlo Simulation Code

estimationmonte carlopisimulation

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??

Best Answer

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

Related Solutions

MATLAB: MATLAB: I’m having trouble calculating the probability to estimate pi. Any help is appreciated.

You have made a decent start. Issues with your code:

1) You use counter for two separate conflicting things. One is the loop counter, and another is the number of "hits" within the unit quarter circle. Use two different variables. E.g., keep the loop counter and have another variable called hits ... set hits = 0 at the start and then inside the loop have hits = hits + 1.

2) Move all of your Est_pi stuff out of the loop and put it after the loop is finished. The estimated probability is simply hits/n. Then apply your formula for the estimate of pi.

3) Change the loop indexing to start at 1 instead of 0.

MATLAB: I am new to Maltlab, i wanted to use a while loop to calculate pi using Montecarlo method. the code below is not giving me any answer can anyone help please.

Lilay - part of the problem is that estimatepi is set to an empty array. This variable is next used in the calculation of error which ends up being [] and so the comparison with tol fails...and the code in the while loop never gets executed. Just set estimatepi to zero and that should allow you to pass the while loop condition.

Next you need to consider the random numbers, x and y. I think the point of using this Monte Carlo approach is that with the more random numbers generated and the more that fall in the circle (of radius 1) then the better the estimate for pi. That means we need to generate n random variables:

n=n+1;
x=rand(n,1);
y=rand(n,1);

We need to count those random numbers (points) that fall in our circle of radius 1. I see that you almost have the calculation correct but I don't understand why you are subtracting 0.5 from the x values. I think that you can simplify this line to just

numHits=sum((x.^2 + y.^2)<=1);

sum is used to count the number "hits" within the circle. The for loop doesn't add anything (as it never uses c) and so it can be ignored. The estimate on pi is fine but you also need to re-calculate the error

estimatepi=4*numHits/n;
error = abs(pi-estimatepi);

I don't think that you need the - tol. Try adding the above changes and see what happens.

Something else to note: tol is an input parameter but then you set it to 0.0001. Either remove the assignment or the input parameter. As for the other local variables set outside of the while loop

x=rand;
y=rand;
c=0;
hits=rand;
n= 0;
 
hit=[];

ask yourself if they are necessary. Also what is the c that this function returns?

Best Answer

Related Solutions

MATLAB: MATLAB: I’m having trouble calculating the probability to estimate pi. Any help is appreciated.

MATLAB: I am new to Maltlab, i wanted to use a while loop to calculate pi using Montecarlo method. the code below is not giving me any answer can anyone help please.

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