大数据分析 - 绘制 S=x0^2+x1^2 梯度下降学习情况的函数图形

绘制 S=x0^2+x12 梯度下降学习情况的函数图形

import numpy as np
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
from pylab import mpl
mpl.rcParams['font.sans-serif'] = ['Microsoft YaHei'] #汉字显示

def f(x,y):
    return x**2 + (y/1.7)**2

def numerical_gradient_no_batch(f,x):
    h = 1e-4 #0.0001
    grad = np.zeros_like(x) #生成和X形状相同的数组
    
    for idx in range(x.size):
        tmp_val = x[idx]
        # f(x+h)的计算
        x[idx] = tmp_val + h
        fxh1 = f(x)
        
         # f(x-h)的计算
        x[idx] = tmp_val - h
        fxh2 = f(x)
        grad[idx] = (fxh1 - fxh2)/(2*h)
        x[idx] = tmp_val #还原值
        
    return grad

def numerical_gradient(f,X):
    if X.ndim == 1:
        return numerical_gradient_no_batch(f,X)
    else:
        grad = np.zeros_like(X)
        for idx,x in enumerate(X):
            grad[idx] = numerical_gradient_no_batch(f,x)
        
    return grad


def function_2(x):
        return np.sum(x ** 2)
    

def gradient_descent(f,init_x,lr=0.01,step_num=100):
    x = init_x
    x_history = []
    for i in range(step_num):
        x_history.append(x.copy())
        grad = numerical_gradient(f,x)
        x -= lr*grad
    return x,np.array(x_history)

if __name__ == '__main__':
    init_x= np.array([-3.0,4.0])

    lr = 0.1
    step_num = 10000
    
    x,x_history = gradient_descent(function_2,init_x,lr=lr,step_num=step_num)
    print(x_history)
    
    fig1 = plt.figure()
    ax = Axes3D(fig1)
    ax.scatter(x_history[:,0],x_history[:,1],np.array(x_history[:,0]**2 + x_history[:,1**2]),c='r')
    ax.set_xlabel('x0')
    ax.set_ylabel('01')
    ax.set_title('函数图形')
    
   
    plt.xlim([-3.5,3.5])           
    plt.ylim([-4.5,4.5])           
    plt.xlabel('x0')
    plt.ylabel('x1')
    plt.show()

运价结果

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