import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# 样本数据
path="C:\\Users\\Zeng Zhong Yan\\Desktop\\py.vs\\.vscode\\数学建模\\梯度下降法材料包\\LinearRegression.xlsx"
# 读取excel文件
dataframe = pd.read_excel(path, header=0)
data=np.array(dataframe)
X=data[:,0].reshape(-1,1)
y=data[:,1]
X_bias = np.insert(X, 0, 1, axis=1)
learning_rate = 0.01
batch_size = 128 # 小批量大小
theta = np.ones(X_bias.shape[1]) # 包括截距和特征系数
#小批量递归下降
num1 =[0,2,10,50,100,500,1000]
global num_iterations
# 包括截距和特征系数
plt.figure(figsize=(24,8))
plt.subplot(2,4,1)
plt.scatter(X,y,color='blue',s=1)
fig1=plt.plot(X,y,'.',color='blue',label='Iris Data')
plt.legend(loc=3, borderaxespad=0., bbox_to_anchor=(0.01, 0.85))
for i in range(len(num1)):
num_iterations=num1[i]
theta = np.zeros(X_bias.shape[1])
X_bias = np.insert(X, 0, 1, axis=1)
for _ in range(num_iterations):
# 随机选择一个小批量样本
batch_indices = np.random.choice(len(X_bias), batch_size, replace=False)
X_batch = X_bias[batch_indices]
y_batch = y[batch_indices]
gradient = X_batch.T.dot(X_batch.dot(theta) - y_batch) / len(X_batch)
theta -= learning_rate * gradient
plt.subplot(2,4,i+2)
plt.scatter(X,y,color='blue',s=1)
Y=theta[1]*X+theta[0]
plt.plot(X,Y,color='r')
plt.xlabel("X")
plt.ylabel("Y")
fig3=plt.plot(X,Y,'white',label="iterations={}".format(num_iterations))
fig1=plt.plot(X,y,'.',color='blue',label='Iris Data')
fig2=plt.plot(X,Y,'r',label='Regression Curve')
plt.legend(loc=3, borderaxespad=0., bbox_to_anchor=(0.01, 0.75))
plt.savefig('C:\\Users\\Zeng Zhong Yan\\Desktop\\py.vs\\.vscode\\数学建模\\梯度下降法材料包\\梯度下降法效果图.png', dpi=500, bbox_inches='tight')
plt.show()
