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：
代码语言：javascript复制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。
以上就是本文的全部内容，希望对大家的学习有所帮助。
