數值計算·第十二集：梯度下降法（Numpy版）

ps:這是按照自己的理解寫的程序，代碼比較糙。獻醜了，望海涵！

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

A = [[4,0],[0,2]]
'''
#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 gradient_descent(x0,A):
    
    eps = 1e-1
    step = 0.3
    
    flag = True
    while(flag):
        
        g = func_der(x0,A)
        
        d = -g
        
        if np.linalg.norm(d)<eps:
            flag = False
        
        x = x0 + step*d
        
        x0 = x.copy()
        print('x0 = ',x0)
        
    print('The optimal value is {}'.format(x0))
    

        
A = np.array([[4,0],[0,2]])
x0 = np.array([[2],[2]])

gradient_descent(x0,A)