import tensorflow as tf
# Basic idea
# Sample a bunch of points from uniform distribution in R2 into a square
# Draw a circle inside this square and count points falling into this square
# Area of circle is S = pi * r**2 => pi = S / r**2, since r = 1.0 => pi = S (area of circle)
# Area of circle is ratio of points falling inside circle multiplied to area of square (which is 4)
# For more detail, check https://en.wikipedia.org/wiki/Monte_Carlo_integration
pi_true = 3.1415926535897932384626433 # true value of pi
points_n = 1000000
radius = 1.0
area = (2 * radius) ** 2
points = tf.random_uniform([points_n, 2], minval = -1, maxval = 1) # random point coordinates sampled from uniform distribution
distance = tf.norm(points, axis = 1) # distance to each point
in_circle = tf.less(distance, 1) # points that lie inside circle
points_in_circle = tf.count_nonzero(in_circle) # number of points that lie inside circle
pi = 4 * (points_in_circle / points_n) # value of pi equals to four points that lie inside circle to all samples
sess = tf.Session()
pi_estimate = sess.run(pi)
print('Pi estimate: {}'.format(pi_estimate))
print('Accuracy ({} samples): {} %'.format(points_n, 100 * abs(pi_true - pi_estimate) / pi_true))Pi estimate: 3.14236
Accuracy (1000000 samples): 0.0244253948496507 %