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#导入模块
from sympy import *
import sympy as sp #将导入的模块重新定义一个名字以便后续的程序进行使用
from numpy import *
import numpy as npdef main():#本例是利用共轭梯度法进行最优化x1,x2,alpha symbols(x1,x2,…共轭梯度法 代码
#导入模块
from sympy import *
import sympy as sp #将导入的模块重新定义一个名字以便后续的程序进行使用
from numpy import *
import numpy as npdef main():#本例是利用共轭梯度法进行最优化x1,x2,alpha symbols(x1,x2,alpha,real True)f_fun x1**2 25*x2**2x np.mat(np.array([[2],[2]]))x0 np.mat(np.array([[2],[2]]))f_diff_x01 sp.diff(f_fun,x1).subs({x1:x0[0,0],x2:x0[1,0]})f_diff_x02 sp.diff(f_fun,x2).subs({x1:x0[0,0],x2:x0[1,0]})f_diff_array np.array([[f_diff_x01],[f_diff_x02]])f_diff_mat np.mat(f_diff_array)d -f_diff_matx_fun x alpha*df (x_fun[0,0])**2 25*(x_fun[1,0])**2f_diff_alpha sp.diff(f,alpha)alpha_solver (solve([f_diff_alpha],[alpha]))[alpha]x_solver x alpha_solver*df_diff_x11 float(sp.diff(f_fun,x1).subs({x1:x_solver[0,0],x2:x_solver[1,0]}))f_diff_x12 float(sp.diff(f_fun,x2).subs({x1:x_solver[0,0],x2:x_solver[1,0]}))f_diff_array np.array([[f_diff_x11],[f_diff_x12]])f_diff_mat np.mat(f_diff_array)print(-------------------第一次--------------------)print(alpha:\n%s,\nx(1):\n%s,\nf_diff_1:\n%s\n%(alpha_solver ,x_solver,f_diff_mat))beta float(((f_diff_x11)**2 (f_diff_x12)**2)/((f_diff_x01)**2 (f_diff_x02)**2))d (-f_diff_matbeta*d)print(beta,d)x_fun x_solver alpha*df (x_fun[0, 0]) ** 2 25 * (x_fun[1, 0]) ** 2f_diff_alpha sp.diff(f,alpha)alpha_solver (solve([f_diff_alpha],[alpha]))[alpha]x_solver x alpha_solver*df_diff_x11 float(sp.diff(f_fun,x1).subs({x1:x_solver[0,0],x2:x_solver[1,0]}))f_diff_x12 float(sp.diff(f_fun,x2).subs({x1:x_solver[0,0],x2:x_solver[1,0]}))f_diff_array np.array([[f_diff_x11],[f_diff_x12]])f_diff_mat np.mat(f_diff_array)print(-------------------第二次--------------------)print(alpha:\n%s,\nx(1):\n%s,\nf_diff_1:\n%s\n%(alpha_solver ,x_solver,f_diff_mat))if __name__ __main__:main()
运行结果 ------------------------第1次迭代---------------------
alpha:
0.02003071803404582x:
[[1.91987712786382][-0.00307180340458224]]负梯度
[[3.83975425572763][-0.153590170229112]]beta:
0.0014743712744378474d:
[[-3.84565174082538][0.00615304278532730]]判断条件
14.76730268476948------------------------第2次迭代---------------------
alpha:
0.4992332268370619x:
[[-4.66293670342566e-15][3.21053947316408e-15]]负梯度
[[-9.32587340685131e-15][1.60526973658204e-13]]beta:
0.0014743712744378474d:
[[ 9.32587341e-15][-1.60526974e-13]]判断条件
2.585588118666227e-26进程已结束,退出代码0
