数值计算·第十三集：共轭梯度法（Numpy版）

ps:这是按照自己的理解写的程序，代码比较糙。献丑了，望海涵！

#FR method
'''
min f(x) = 2x1^2+x2^2

A = [[4,0],[0,2]]

'''

#original function
#x is col vector
import numpy as np

def func(x,A):
    return 0.5*(x.T@A@x)

def func_der(x,A):
    return A@x

def func_beta(beta1,beta2):
    if beta1.T@beta1 != 0:
        return (beta2.T@beta2)/(beta1.T@beta1)
    else:
        return 0

def conjugate_gradient(x0,A):
    
    flag = True
    eps = 1e-1
    g1 = np.zeros((x0.shape[0],1))
    d1 = np.zeros((x0.shape[0],1))
    
    while flag:
        #print('x0 = ',x0)
        #print('g1 = ',g1)

        g = func_der(x0,A)
        
        #print('g = ',g)
        d = -g
        #print('d = ',d)

        beta = func_beta(g1,g)
        #print('beta = ',beta)
        
        if np.linalg.norm(g)