Python 梯度下降

code:http://www.pianshen.com/article/9815275222/

import random
import numpy as np
import matplotlib.pyplot as plt
 
 
"""
最速下降法
Rosenbrock函数
函数 f(x)=100*(x(2)-x(1).^2).^2+(1-x(1)).^2
梯度 g(x)=(-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1)),200*(x(2)-x(1)^2))^(T)
"""
 
 
def goldsteinsearch(f,df,d,x,alpham,rho,t):
    '''
    线性搜索子函数
    数f，导数df，当前迭代点x和当前搜索方向d
    '''
    flag = 0
 
    a = 0
    b = alpham
    fk = f(x)
    gk = df(x)
 
    phi0 = fk
    dphi0 = np.dot(gk, d)
    # print(dphi0)
    alpha=b*random.uniform(0,1)
 
    while(flag==0):
        newfk = f(x + alpha * d)
        phi = newfk
        # print(phi,phi0,rho,alpha ,dphi0)
        if (phi - phi0 )<= (rho * alpha * dphi0):
            if (phi - phi0) >= ((1 - rho) * alpha * dphi0):
                flag = 1
            else:
                a = alpha
                b = b
                if (b < alpham):
                    alpha = (a + b) / 2
                else:
                    alpha = t * alpha
        else:
            a = a
            b = alpha
            alpha = (a + b) / 2
    return alpha
 
 
def rosenbrock(x):
    # 函数:f(x) = 100 * (x(2) - x(1). ^ 2). ^ 2 + (1 - x(1)). ^ 2
    return 100*(x[1]-x[0]**2)**2+(1-x[0])**2
 
 
def jacobian(x):
    # 梯度g(x) = (-400 * (x(2) - x(1) ^ 2) * x(1) - 2 * (1 - x(1)), 200 * (x(2) - x(1) ^ 2)) ^ (T)
    return np.array([-400*x[0]*(x[1]-x[0]**2)-2*(1-x[0]),200*(x[1]-x[0]**2)])
 
 
 
def steepest(x0):
 
    print('初始点为:')
    print(x0,'\n')
    imax = 20000
    W = np.zeros((2, imax))
    epo=np.zeros((2, imax))
    W[:, 0] = x0
    i = 1
    x = x0
    grad = jacobian(x)
    delta = sum(grad ** 2)  # 初始误差
 
    f=open("最速.txt",'w')
 
    while i < imax and delta > 10 ** (-5):
        p = -jacobian(x)
        x0 = x
        alpha = goldsteinsearch(rosenbrock, jacobian, p, x, 1, 0.1, 2)
        x = x + alpha * p
        W[:, i] = x
        if i % 5 == 0:
 
            epo[:,i] =np.array((i,delta))
            f.write(str(i)+"        "+str(delta)+"\n")
            print(i,np.array((i,delta)))
        grad = jacobian(x)
        delta = sum(grad ** 2)
        i = i + 1
 
    print("迭代次数为:", i)
    print("近似最优解为:")
    print(x, '\n')
    W = W[:, 0:i]  # 记录迭代点
 
    return [W,epo]
 
if __name__=="__main__":
    X1 = np.arange(-1.5, 1.5 + 0.05, 0.05)
    X2 = np.arange(-3.5, 4 + 0.05, 0.05)
    [x1, x2] = np.meshgrid(X1, X2)
    f = 100 *(x2 - x1 ** 2) ** 2 + (1 - x1) ** 2  # 给定的函数
    plt.contour(x1, x2, f, 20)  # 画出函数的20条轮廓线
 
    x0 = np.array([-1.2, 1])
    list_out = steepest(x0)
    W=list_out[0]
 
    epo=list_out[1]
 
    plt.plot(W[0, :], W[1, :], 'g*-')  # 画出迭代点收敛的轨迹
 
    plt.show()