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monte_carlo_pi_approximation.py
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monte_carlo_pi_approximation.py
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#! /usr/bin/env python3
#Import libraries
import matplotlib.pyplot as plt
from matplotlib import animation
from matplotlib import style
import numpy as np
import math
from random import random, randint
class monte_carlo_pi:
def __init__(self, n_points, x_inside, y_inside, x_outside, y_outside, points_inside, points_outside):
#self.x = x
#self.y = y
#self.r = r
#self.fig = fig
self.n_points = n_points
self.x_inside = x_inside
self.y_inside = y_inside
self.x_outside = x_outside
self.y_outside = y_outside
self.points_inside = points_inside
self.points_outside = points_outside
def monte_carlo(self, n_points):
points_inside = 0
points_outside = 0
y = 0
x = 0
r = np.zeros((self.n_points))
self.x_inside = np.zeros((self.n_points))
self.y_inside = np.zeros((self.n_points))
self.x_outside = np.zeros((self.n_points))
self.y_outside = np.zeros((self.n_points))
for i in range(1, self.n_points):
points_outside += 1
x = 2*random() - 1
y = 2*random() - 1
r = x**2 + y**2
if r <= 1:
points_inside = points_inside + 1
self.x_inside[i] = x
self.y_inside[i] = y
elif r > 1:
self.x_outside[i] = x
self.y_outside[i] = y
self.pi = 4*points_inside/self.n_points
return self.pi
def monte_plot(self, x_inside, y_inside, x_outside, y_outside):
#print(str(pi))
x_min = -1.1
x_max = 1.1
y_min = -1.1
y_max = 1.1
xlim = ((x_min, x_max))
ylim = ((y_min, y_max))
style.use('seaborn-dark')
circle = plt.Circle((0, 0), radius=1, fill=False, linewidth = 0.1)
self.fig = plt.figure(figsize=(10,5))
ax1 = self.fig.add_subplot(121, xlim = xlim, ylim = ylim)
title = ax1.set_title('', fontsize=20)
ax1.legend(prop=dict(size=15), loc='lower left', shadow=True, ncol=2)
ax1.set_xlabel('$x$', fontsize=10)
ax1.set_ylabel('$y$', fontsize=10)
ax1.xaxis.set_tick_params(labelsize=10)
ax1.yaxis.set_tick_params(labelsize=10)
ax1.set_title("Pi approximation= %f" % self.pi)
ax1.plot(self.x_inside,self.y_inside,'b.')
ax1.plot(self.x_outside,self.y_outside,'r.')
self.ax2 = self.fig.add_subplot(122, xlim = xlim, ylim = ylim)
self.inside, = self.ax2.plot([], [], c='r')
self.outside, = self.ax2.plot([], [], c='b')
self.ax2.add_artist(circle)
self.title = self.ax2.set_title('', fontsize=12)
self.ax2.legend(prop=dict(size=15), loc='lower left', shadow=True, ncol=2)
self.ax2.set_xlabel('$x$', fontsize=10)
self.ax2.set_ylabel('$y$', fontsize=10)
self.ax2.xaxis.set_tick_params(labelsize=10)
self.ax2.yaxis.set_tick_params(labelsize=10)
def init(self):
self.inside.set_data([], [])
self.outside.set_data([], [])
self.title.set_text('')
return self.inside, self.outside,
def update_pi(self, i):
n_points = 100
self.points_inside = 0
self.points_outside = 0
x = 2*random() - 1
y = 2*random() - 1
r = (x**2 + y**2)
#plt.title("Pi approximation= %f" % (4*points_inside /float(n_points)))
count = 0
for i in range(1, n_points):
if r <= 1:
self.points_inside += 1
count += 1
plt.plot(x,y,'r.-')
#x_inside = x
#y_inside = y
self.pi = ((4 * self.points_inside) / (i))
return self.points_inside
return self.pi
else:
self.points_outside += 1
count += 1
plt.plot(x,y,'b.-')
#x_outside = x
#y_outside = y
self.pi = ((4 * self.points_inside) / (i))
return self.points_outside
return self.pi
self.ax2.set_title("Pi approximation = {}".format(self.pi))
#pi = ((4 * self.points_inside) / (self.points_inside + self.points_outside))
#self.ax2.set_title("Pi approximation = {}".format(pi))
def animate(self, points_inside, points_outside):
#self.ax2.set_title("Pi approximation= %f" % (4 * (self.points_inside + 1) / ((self.points_inside + self.points_outside) + 1)))
#pi = ((4 * self.points_inside + 1) / (self.points_inside + self.points_outside + 1))
#self.ax2.set_title("Pi approximation = {}".format(pi))
self.animate_update = plt.matplotlib.animation.FuncAnimation(self.fig, self.update_pi, init_func=self.init, frames=n_points, interval=1, repeat=False)
#animate.save('animation.gif',writer='imagemagick', fps=60, dpi=80)
self.animate_update.save('pi.mp4', fps=120,extra_args=['-vcodec', 'libx264'])
plt.show()
print('Done')
#if __name__ == '__main__':
# init()
# animate(i)
n_points = 1000
x_inside = 0
y_inside = 0
x_outside = 0
y_outside = 0
points_inside = 0
points_outside = 0
m = monte_carlo_pi(n_points, x_inside, y_inside, x_outside, y_outside, points_inside, points_outside)
m.monte_carlo(n_points)
m.monte_plot(x_inside, y_inside, x_outside, y_outside)
m.init()
m.animate(points_inside, points_outside)