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This article mainly introduces python how to use Monte Carlo method to find the relevant knowledge of pi, the content is detailed and easy to understand, the operation is simple and fast, has a certain reference value, I believe everyone will read this python how to use Monte Carlo method to find the pi article will have some gains, let's take a look at it.

Monte Carlo method for calculating pi

Introduction:

Monte Carlo method (Monte Carlo method), also known as statistical simulation method, is a kind of very important numerical calculation method which was proposed in the middle of 1940s due to the development of science and technology and the invention of electronic computer. A method of solving many computational problems using random numbers (or more commonly pseudo-random numbers). The answer is deterministic algorithms. Monte Carlo methods are widely used in financial engineering, macroeconomics, computational physics (such as particle transport calculations, quantum thermodynamic calculations, aerodynamic calculations) and other fields.

In fact, the geometric scheme (P= shaded area (or interval or volume)/total area (or interval or volume)) in high school mathematics is a Monte Carlo method.

import numpy as npimport matplotlib.pyplot as pltfrom matplotlib.patches import Circle

#Number of points cast n = 10,000

#Circle information r = 1.0 #Radius a, b = (0., 0.) #Center

#square region boundary x_min, x_max = a-r, a+ry_min, y_max = b-r, b+r

#Random points x = np.random.uniform(x_min, x_max, n) #Uniform distribution y = np.random.uniform(y_min, y_max, n)

#Calculate the distance d = np.sqrt((x-a)**2 + (y-b)**2)

#count the number of points that fall inside the circle res = sum(np.where(d < r, 1, 0))

#Calculate an approximation of pi (essence of Monte Carlo method: approximation of true values with statistics) pi = 4 * res / n

print('pi: ', pi)

spi = 3.1415926535print ('here the approximate pi and 10-bit pi accuracy is: ', (spi - pi)/spi )

#Draw a graph to see fig = plt.figure() axes = fig.add_subplot(111) axes.plot(x, y,'ro',markersize = 1)plt.axis ('equal ') #Prevent image distortion

circle = Circle(xy=(a,b), radius=r, alpha=0.5)axes.add_patch(circle)

plt.show()

Implementation results:

pi: 3.1224 Here the approximate pi is 0.006109211351324613 to the 10-digit pi accuracy.

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