import numpy as np
import matplotlib.pyplot as plt


def gradient_descent_poly_fit(sampleData, degree, learning_rate=0.001, iterations=50000):
    def error_function(y_pred, y): # 定义误差函数error_function()
        return y_pred - y
    def gradient(degree,error,x_normalized,sampleNum,learning_rate): # 定义梯度函数gradient()
        # 对每个参数计算梯度
        for i in range(degree + 1):
            # 计算损失函数对参数的偏导数（梯度）
            gradient = np.dot(error, x_normalized**i) * 2 / sampleNum
            # 梯度下降更新参数
            theta[i] -= learning_rate * gradient
        return theta


    x = sampleData[:,0]
    y = sampleData[:,1]
    # 初始化参数（多项式系数）为0
    theta = np.zeros(degree + 1)
    sampleNum = len(x)  # 样本数量

    # 归一化x以改善数值稳定性
    x_normalized = (x - x.mean()) / x.std()
    # 迭代梯度下降
    for _ in range(iterations):
        # 通过当前参数计算多项式的值
        y_pred = np.polyval(theta[::-1], x_normalized)

        # 计算预测值与真实值之间的误差
        error = error_function(y_pred, y)
        # 计算梯度并更新theta
        theta = gradient(degree,error,x_normalized,sampleNum,learning_rate)

    return theta, x_normalized

# 设置一个较小的学习率和较多的迭代次数
learning_rate = 0.001
iterations = 50000
degree = 4

x = np.array([0, 100, 200, 300, 400, 500, 600, 700, 800, 900])
y = np.array([10, 20, 10, 50, 80, 130, 210, 340, 550, 890])
sampleData = np.array(list(zip(x, y)))
# 运行梯度下降算法
theta, x_normalized = gradient_descent_poly_fit(sampleData, degree, learning_rate, iterations)

# 用拟合的参数计算多项式的值
x_fit_normalized = np.linspace(x_normalized.min(), x_normalized.max(), 100)
y_fit = np.polyval(theta[::-1], x_fit_normalized)

# 反归一化x_fit
x_fit = x_fit_normalized * x.std() + x.mean()

# 绘制原始数据点和拟合的多项式
plt.scatter(x, y, color='red', label='Sample Data')
plt.plot(x_fit, y_fit, label='Polynomial Fit')
plt.legend()
plt.show()

# 输出拟合参数
print(theta)
# if __name__ == '__main__':
#     LimitNum = 1000
#     sampleData = random_points(20,0, 1000)
#     # 这里为了便于观察使用设计好的数据
#     # x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
#     # y = np.array([1, 2, 1, 5, 8, 13, 21, 34, 55, 89])
#     # sampleData = np.array(list(zip(x, y)))	# 将两个一维数组拼接成二维数组
#     m = 3
#     theta, covariance_matrix = least_square_method(m, sampleData)
#     # print(theta)
#     curveData = compute_curveData(0,1000,1,theta,m)
#     # print("curveData",curveData)
#     draw_dots_and_line(curveData,sampleData,0,1000)