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Example Code

import numpy as np

import math

import matplotlib.pyplot as plt;

EVN=100000;

posX, posY = (np.random.rand(EVN)-0.5, np.random.rand(EVN)-0.5)

poxInCirx, poxInCiry =([],[])

[(poxInCirx.append(posX[x]), poxInCiry.append(posY[x]) ) for x in range(EVN) if math.hypot(posX[x],posY[x]) <=0.5]

plt.plot(posX,posY, 'r.')

plt.plot(poxInCirx,poxInCiry, 'go')

plt.axes().set_aspect('equal')

print("Monte Carlo Pi=", len(poxInCirx)/EVN*4)

print("Error of Monte Carlo Pi=", (len(poxInCirx)/EVN*4-math.pi)/math.pi*100)

plt.text(-0.15, -0.6, r'EVN=%d' %EVN, fontsize=20)

plt.show()

Note and Comments

import numpy as np

import math

import matplotlib.pyplot as plt; 匯入圖形函式庫Matplotlib中的pyplot資料庫

EVN=100000; 宣告要產生多少數據點

posX, posY = (np.random.rand(EVN)-0.5, np.random.rand(EVN)-0.5) 產生兩組-0.5到0.5的亂數, 每組有EVN個亂數點.

poxInCirx, poxInCiry =([],[]) 產生兩組X跟Y的集合,用來存放半徑小於0.5

[(poxInCirx.append(posX[x]), poxInCiry.append(posY[x]) ) for x in range(EVN) if math.hypot(posX[x],posY[x]) <=0.5]

將位於圓內的亂數點用append加到poxInCirx, poxInCiry數組內. math.hypot(x,y)函數將回傳(x*x+y*y)的根號值

plt.plot(posX,posY, 'r.') 以(posX,posY) 爲數據點,2維作圖顏色爲紅色r, 數據點以.表示

plt.plot(poxInCirx,poxInCiry, 'go') 以(poxInCirx,poxInCiry) 爲數據點,2維作圖. 顏色爲綠色g, 數據點以o表示

plt.axes().set_aspect('equal') 將圖的X軸與Y軸設爲相同比例

print("Monte Carlo Pi=", len(poxInCirx)/EVN*4)

print("Error of Monte Carlo Pi=", (len(poxInCirx)/EVN*4-math.pi)/math.pi*100)

plt.text(-0.15, -0.6, r'EVN=%d' %EVN, fontsize=20) 將文字EVN=10000設置在-0.15, -0.6的位置

plt.show() 圖形設定完畢,開始作圖

Lesson 6 01: 蒙地卡羅方法求Pi值