python代码中线性回归的梯度下降

import numpy as np

X = np.array(...)  # 输入变量
y = np.array(...)  # 输出变量

theta = np.zeros(X.shape[1])  # 初始化模型参数
alpha = 0.01  # 学习率
iterations = 1000  # 迭代次数

def compute_cost(X, y, theta):
    m = len(y)
    predictions = X.dot(theta)
    cost = (1/(2*m)) * np.sum(np.square(predictions - y))
    return cost

def gradient_descent(X, y, theta, alpha, iterations):
    m = len(y)
    cost_history = np.zeros(iterations)
    for i in range(iterations):
        predictions = X.dot(theta)
        errors = predictions - y
        theta = theta - (alpha/m) * X.T.dot(errors)
        cost_history[i] = compute_cost(X, y, theta)
    return theta, cost_history

theta_final, cost_history = gradient_descent(X, y, theta, alpha, iterations)

import matplotlib.pyplot as plt

plt.plot(range(iterations), cost_history)
plt.xlabel('Iterations')
plt.ylabel('Cost')
plt.title('Cost vs. Iterations')
plt.show()