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64 lines
2.0 KiB
Python
64 lines
2.0 KiB
Python
import random
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class Point:
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def __init__(self, x: float, y: float) -> None:
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self.x = x
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self.y = y
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def is_in_unit_circle(self) -> bool:
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"""
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True, if the point lies in the unit circle
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False, otherwise
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"""
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return (self.x ** 2 + self.y ** 2) <= 1
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@classmethod
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def random_unit_square(cls):
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"""
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Generates a point randomly drawn from the unit square [0, 1) x [0, 1).
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"""
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return cls(x=random.random(), y=random.random())
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def estimate_pi(number_of_simulations: int) -> float:
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"""
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Generates an estimate of the mathematical constant PI (see https://en.wikipedia.org/wiki/Monte_Carlo_method#Overview).
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The estimate is generated by Monte Carlo simulations. Let U be uniformly drawn from the unit square [0, 1) x [0, 1). The probability that U lies in the unit circle is:
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P[U in unit circle] = 1/4 PI
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and therefore
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PI = 4 * P[U in unit circle]
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We can get an estimate of the probability P[U in unit circle] (see https://en.wikipedia.org/wiki/Empirical_probability) by:
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1. Draw a point uniformly from the unit square.
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2. Repeat the first step n times and count the number of points in the unit circle, which is called m.
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3. An estimate of P[U in unit circle] is m/n
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"""
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if number_of_simulations < 1:
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raise ValueError("At least one simulation is necessary to estimate PI.")
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number_in_unit_circle = 0
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for simulation_index in range(number_of_simulations):
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random_point = Point.random_unit_square()
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if random_point.is_in_unit_circle():
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number_in_unit_circle += 1
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return 4 * number_in_unit_circle / number_of_simulations
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if __name__ == "__main__":
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# import doctest
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# doctest.testmod()
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from math import pi
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prompt = "Please enter the desired number of Monte Carlo simulations: "
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my_pi = estimate_pi(int(input(prompt).strip()))
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print(f"An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}")
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