機(jī)器學(xué)習(xí)中的優(yōu)化算法！

import numpy as npimport pandas as pdimport matplotlib.pyplot as pltimport time%matplotlib inlinefrom mpl_toolkits.mplot3d import Axes3Dclass Rosenbrock():    def __init__(self):        self.x1 = np.arange(-100, 100, 0.0001)        self.x2 = np.arange(-100, 100, 0.0001)        #self.x1, self.x2 = np.meshgrid(self.x1, self.x2)        self.a = 1        self.b = 1        self.newton_times = 1000        self.answers = []        self.min_answer_z = []

    # 準(zhǔn)備數(shù)據(jù)    def data(self):        z = np.square(self.a - self.x1) + self.b * np.square(self.x2 - np.square(self.x1))        #print(z.shape)        return z
    # 隨機(jī)牛頓    def snt(self,x1,x2,z,alpha):        rand_init = np.random.randint(0,z.shape[0])        x1_init,x2_init,z_init = x1[rand_init],x2[rand_init],z[rand_init]        x_0 =np.array([x1_init,x2_init]).reshape((-1,1))        #print(x_0)

        for i in range(self.newton_times):            x_i = x_0 - np.matmul(np.linalg.inv(np.array([[12*x2_init**2-4*x2_init+2,-4*x1_init],[-4*x1_init,2]])),np.array([4*x1_init**3-4*x1_init*x2_init+2*x1_init-2,-2*x1_init**2+2*x2_init]).reshape((-1,1)))            x_0 = x_i            x1_init = x_0[0,0]            x2_init = x_0[1,0]        answer = x_0        return answer

    # 繪圖    def plot_data(self,min_x1,min_x2,min_z):        x1 = np.arange(-100, 100, 0.1)        x2 = np.arange(-100, 100, 0.1)        x1, x2 = np.meshgrid(x1, x2)        a = 1        b = 1        z = np.square(a - x1) + b * np.square(x2 - np.square(x1))        fig4 = plt.figure()        ax4 = plt.axes(projection='3d')        ax4.plot_surface(x1, x2, z, alpha=0.3, cmap='winter')  # 生成表面， alpha 用于控制透明度        ax4.contour(x1, x2, z, zdir='z', offset=-3, cmap="rainbow")  # 生成z方向投影，投到x-y平面        ax4.contour(x1, x2, z, zdir='x', offset=-6, cmap="rainbow")  # 生成x方向投影，投到y(tǒng)-z平面        ax4.contour(x1, x2, z, zdir='y', offset=6, cmap="rainbow")  # 生成y方向投影，投到x-z平面        ax4.contourf(x1, x2, z, zdir='y', offset=6, cmap="rainbow")  # 生成y方向投影填充，投到x-z平面，contourf()函數(shù)        ax4.scatter(min_x1,min_x2,min_z,c='r')        # 設(shè)定顯示范圍        ax4.set_xlabel('X')        ax4.set_ylabel('Y')        ax4.set_zlabel('Z')        plt.show()
    # 開始    def start(self):        times = int(input("請(qǐng)輸入需要隨機(jī)優(yōu)化的次數(shù)："))        alpha = float(input("請(qǐng)輸入隨機(jī)優(yōu)化的步長(zhǎng)"))        z = self.data()        start_time = time.time()        for i in range(times):            answer = self.snt(self.x1,self.x2,z,alpha)            self.answers.append(answer)        min_answer = np.array(self.answers)        for i in range(times):            self.min_answer_z.append((1-min_answer[i,0,0])**2+(min_answer[i,1,0]-min_answer[i,0,0]**2)**2)        optimal_z = np.min(np.array(self.min_answer_z))        optimal_z_index = np.argmin(np.array(self.min_answer_z))        optimal_x1,optimal_x2 = min_answer[optimal_z_index,0,0],min_answer[optimal_z_index,1,0]        end_time = time.time()        running_time = end_time-start_time        print("優(yōu)化的時(shí)間:%.2f秒!" % running_time)        self.plot_data(optimal_x1,optimal_x2,optimal_z)if __name__ == '__main__':    snt = Rosenbrock()    snt.start()