python实现最速下降法

深碍√TFBOYSˉ_ 2023-01-03 11:29 187阅读 0赞

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本文实例为大家分享了python实现最速下降法的具体代码，供大家参考，具体内容如下

代码：

from sympy import *
    import numpy as np
    def backtracking_line_search(f,df,x,x_k,p_k,alpha0):
      rho=0.5
      c=10**-4
      alpha=alpha0
      replacements1=zip(x,x_k)
      replacements2=zip(x,x_k+alpha*p_k)
      f_k=f.subs(replacements1)
      df_p=np.dot([df_.subs(replacements1) for df_ in df],p_k)
      while f.subs(replacements2)>f_k+c*alpha*df_p:
        alpha=rho*alpha
        replacements2 = zip(x, x_k +alpha * p_k)
      return alpha
    def stepest_line_search(f,x,x0,alpha0):
      df = [diff(f, x_) for x_ in x]
      x_k=x0
      alpha=alpha0
      replacements=zip(x,x_k)
      len_df = sqrt(np.sum([df_.subs(replacements) ** 2 for df_ in df]))
      while len_df>1e-6:
        p_k=-1*np.array([df_.subs(replacements) for df_ in df])
        alpha = backtracking_line_search(f, df, x, x_k, p_k, alpha)
        x_k=x_k+alpha*p_k
        replacements = zip(x, x_k)
        len_df=np.sum([df_.subs(replacements)**2 for df_ in df])
      return x_k
    if __name__=="__main__":
      init_printing(use_unicode=True)
      x1 = symbols("x1")
      x2 = symbols("x2")
      x = np.array([x1, x2])
      f = 100 * (x2 - x1 ** 2)**2 + (1 - x1) ** 2
      ans=stepest_line_search(f, x, np.array([1.2, 1]), 1)
      print "the minimal value in point:",ans

分析：

这个采用的是backtracking line search来寻找alpha。

![Image 1][]

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