题解 | 使用梯度下降的线性回归

import numpy as np
def linear_regression_gradient_descent(X, y, alpha, iterations):
    # 补全代码
    X = np.array(X, dtype=float)
    y = np.array(y, dtype=float).reshape(-1, 1) #(m, 1)

    m, n = X.shape

    # 初始化theta
    theta = np.zeros((n, 1), dtype=float)

    # 使用梯度下降迭代
    for _ in range(int(iterations)):
        error = X @ theta - y        #(m, 1)
        grad = (X.T @ error) / m     #(n, 1)
        theta = theta - alpha * grad #(n, 1)

    # 四舍五入到小数点后4位，并按题意返回 List
    theta = np.round(theta.flatten(), 4)    # (n,)
    return theta

# 主程序
if __name__ == "__main__":
    # 输入矩阵和向量
    matrix_inputx = input()
    array_y = input()
    alpha = input()
    iterations = input()

    # 处理输入
    import ast
    matrix = np.array(ast.literal_eval(matrix_inputx))
    y = np.array(ast.literal_eval(array_y)).reshape(-1,1)
    alpha = float(alpha)
    iterations = int(iterations)

    # 调用函数计算逆矩阵
    output = linear_regression_gradient_descent(matrix,y,alpha,iterations)
    
    # 输出结果
    print(output)