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  1. import numpy as np
  2.  
  3. #ガウス=ルジャンドルのアルゴリズム。N回繰り返す
  4. def GaussRegendre(N):
  5.     #初項
  6.     a = 1.0
  7.     b = np.sqrt(2) / 2
  8.     t = 1 / 4
  9.     p = 1
  10.  
  11.     for i in range(N): #iが0からN-1までの間以下を繰り返す
  12.         #漸化式に従い、次の項を計算
  13.         a_new = (a + b) / 2
  14.         b_new = np.sqrt(a * b)
  15.         t_new = t - p * (a - a_new)**2
  16.         p_new = 2 * p
  17.  
  18.         #古い値を新しい値に置き換え
  19.         a = a_new
  20.         b = b_new
  21.         t = t_new
  22.         p = p_new
  23.  
  24.     pi = (a + b)**2 / (4 * t) #円周率の計算
  25.     return pi
  26.  
  27. #出力
  28. print("GaussRegendre(1) = " + str(GaussRegendre(1)))
  29. print("GaussRegendre(2) = " + str(GaussRegendre(2)))
  30. print("GaussRegendre(3) = " + str(GaussRegendre(3)))
Success #stdin #stdout 0.15s 28568KB
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GaussRegendre(1) = 3.1405792505221686
GaussRegendre(2) = 3.141592646213543
GaussRegendre(3) = 3.141592653589794
https://ideone.com/XM8wWG
language:
Python 3 (python  3.9.5)
created:
1 year ago
visibility:
public

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