MATLAB Help Given the matlab code that uses Monte Carlo method to estimate pi an

Question

MATLAB Help

Given the matlab code that uses Monte Carlo method to estimate pi and the difference from true value for the fixed number of random points:

a=10; % the experiment event number
r=1; %the circle radius
c=0; % sucessful event number
for i=1:a
s=-r+1*r*rand();
t=-r+1*r*rand();
pi_sim(i)=4*c/a
pi_dif(i)=pi-pi_sim(i)
if ((s.^2+t.^2)<=r^2)
    c = c+1
end
end

Question:    With the given MATLAB code, time the execution of the code for various numbers of points, and plot the precision vs the computational cost.

Explanation / Answer

a=0; % the experiment event number
c=0; % sucessful event number
r =1; % redius of the circle
min_tries = 100;

pi_prev = 1000;
precision = 0.001;

while (true)
    s = 2 * r * (rand() - 0.5); %get a point between -1 to +1
    t = 2 * r * (rand() - 0.5);
  
    a = a+1;
    pi_sim = 4 * c / a;
    pi_diff = abs(pi_prev - pi_sim);
    pi_prev = pi_sim;
  
    if (pi_diff <= precision && a>min_tries)
        break;
    end

    if ((s.^2+t.^2)<=r^2)
        c = c+1;
    end  
end

fprintf("estimated value of pi is %f", pi_prev);

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