approximate the value of π using the following algorithm based on geometric probability. This algorithm is an example of the so called monte carlo method

Question

Luxsanan Ramanusam 2016-4-6

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https://ww2.mathworks.cn/matlabcentral/answers/277464-approximate-the-value-of-using-the-following-algorithm-based-on-geometric-probability-this-algor

回答： sam0037 2016-4-12

I have written the code for the estimation of pi but I don't understand ow to put hits and misses in my coding and how to ake the code loop.

Code:

clf
clear all
% MC estimate of pi
n=10000
x=rand([1 n])
y=rand ([1 n])
figure(1)
for i = 1:n
    plot(x(i), y(i), 'b+')
    hold on 
end
% plot(x, y, 'r+')
c=0
s=0
for i=1:n
    s=s+1
    if x(i)^2 +y(i)^2 <=1 % inside circle 
        c=c+1
          % hold on 
      else % else outside circle
          plot (x(i), y(i), 'r+')
      end
  end
  p=c/s
  pi_=p*4

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Answer 1

sam0037 2016-4-12

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Hi,

The code seems to work fine for computing PI using Hit & Miss Monte Carlo algorithm. In this code the variable 'c' is the number of hits and the variable 's' is the total number of samples i.e. hits + misses.

This code can be optimized further in terms of performance in MATLAB using vectorization. This link mentions how this can be done. However for illustration purpose I have taken the liberty to modify the code as below to show how to compute hits and misses using both vectorization and looping techniques. If this is not what you were looking for then kindly elaborate on the query.

% MC estimate of pi
clear all;
clc;
%%initialize random points
n=10000;
x=rand([1 n]);
y=rand ([1 n]);
%%compute using vectorization
radii = sqrt(x.^2+y.^2);
hits = sum(radii<=1);
misses = n-hits;
pi_mc = 4*(hits/n); 
fprintf('\nUsing Vectorization:: HITS = %d, MISSES = %d, PI = %f\n',hits,misses,pi_mc);
%%compute using a loop
c=0;
s=0;
for i=1:n
    s=s+1;
    if x(i)^2 +y(i)^2 <=1 % inside circle 
        c=c+1;
    end
end
p=c/s;
pi_=p*4;
fprintf('\nUsing Loop:: HITS = %d, MISSES = %d, PI = %f\n',c,s-c,pi_);