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Chapter 7. Monte Carlo Methods to Compute Pi. Circle formed within a square, with unit radius so that square has sides 2*2. Ratio of the area of the circle to the square given by Points within square chosen randomly Score kept of how many points happen to lie within circle

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Chapter 7

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Chapter 7

Chapter 7


Monte carlo methods to compute pi

Monte Carlo Methods to Compute Pi

  • Circle formed within a square, with unit radius so that square has sides 2*2. Ratio of the area of the circle to the square given by

  • Points within square chosen randomly

  • Score kept of how many points happen to lie within circle

  • Fraction of points within the circle will be pi/4, given a sufficient number of randomly selected samples


Monte carlo methods to compute pi1

Monte Carlo Methods to Compute Pi


Monte carlo methods to compute pi2

Monte Carlo Methods to Compute Pi

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

int main(int argc, char* argv[])

{ double niter = 100000000;

double x,y;

int i;

int count=0;

double z;

double pi;

srand(time(NULL));

for (i=0; i<niter; ++i)

{ //get random points

x = (double)random()/RAND_MAX;

y = (double)random()/RAND_MAX;

z = sqrt((x*x)+(y*y));

if (z<=1)

{

++count;

}

}

pi = ((double)count/(double)niter)*4.0;

printf("Pi: %f\n", pi);

}


Monte carlo methods to compute pi3

Monte Carlo Methods to Compute Pi

feng.gu@service0:~/csc229> ./pi

Pi: 3.141370


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