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44 lines
1.4 KiB
Python
44 lines
1.4 KiB
Python
"""
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@author: MatteoRaso
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"""
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from numpy import pi, sqrt
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from random import uniform
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def pi_estimator(iterations: int):
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"""An implementation of the Monte Carlo method used to find pi.
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1. Draw a 2x2 square centred at (0,0).
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2. Inscribe a circle within the square.
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3. For each iteration, place a dot anywhere in the square.
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3.1 Record the number of dots within the circle.
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4. After all the dots are placed, divide the dots in the circle by the total.
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5. Multiply this value by 4 to get your estimate of pi.
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6. Print the estimated and numpy value of pi
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"""
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circle_dots = 0
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# A local function to see if a dot lands in the circle.
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def circle(x: float, y: float):
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distance_from_centre = sqrt((x ** 2) + (y ** 2))
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# Our circle has a radius of 1, so a distance greater than 1 would land outside the circle.
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return distance_from_centre <= 1
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circle_dots = sum(
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int(circle(uniform(-1.0, 1.0), uniform(-1.0, 1.0))) for i in range(iterations)
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)
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# The proportion of guesses that landed within the circle
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proportion = circle_dots / iterations
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# The ratio of the area for circle to square is pi/4.
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pi_estimate = proportion * 4
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print("The estimated value of pi is ", pi_estimate)
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print("The numpy value of pi is ", pi)
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print("The total error is ", abs(pi - pi_estimate))
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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