Buffon's needle simulation in python

Question

import numpy as np
import matplotlib.pylab as plt

class Buffon_needle_problem:

    def __init__(self,x,y,n,m):
        self.x = x #width of the needle
        self.y =         


        

Answer 1

The sampling of the needle's alignment should be a uniform cosine. See the following link for the method: http://pdg.lbl.gov/2012/reviews/rpp2012-rev-monte-carlo-techniques.pdf

Also, there were a few logical problems with the program. Here is a working version.

#!/bin/python
import numpy as np

def sample_cosine():
  rr=2.
  while rr > 1.:
    u1=np.random.uniform(0,1.)
    u2=np.random.uniform(0,1.)
    v1=2*u1-1.
    rr=v1*v1+u2*u2
  cc=(v1*v1-u2*u2)/rr
  return cc

class Buffon_needle_problem:

     def __init__(self,x,y,n,m):
        self.x = float(x)  #width of the needle
        self.y = float(y)  #witdh of the space
        self.r = [] #coordinated of the centre of the needle
        self.z = [] #measure of the alignment of the needle
        self.n = n  #no of throws
        self.m = m  #no of simulations
        self.p = self.x/self.y
        self.pi_approx = []

    def samples(self):
        # throwing the needles
        for i in range(self.n):
            self.r.append(np.random.uniform(0,self.y))
            C=sample_cosine()
            self.z.append(C*self.x/2.)
        return [self.r,self.z]

    def simulation(self):
        # m simulation
        for j in range(self.m):
            self.r=[]
            self.z=[]
            self.samples()
            # n throw
            hits = 0 #setting the success to 0
            for i in range(self.n):
                #condition for a hit
                if self.r[i]+self.z[i]>=self.y or self.r[i]-self.z[i]<0.:
                    hits += 1
                else:
                    continue
            est =self.p*float(self.n)/float(hits)
            self.pi_approx.append(est)
        return self.pi_approx

y = Buffon_needle_problem(1,2,80000,5)

print (y.simulation())