import numpy as np
import matplotlib.pyplot as plt
from X1 import random_points, compute_curveData
from X2 import draw_axis

# # (1) 定义x和y坐标数据
# x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
# y = np.array([1, 2, 3, 5, 8, 13, 21, 34, 55, 89])
#
# # (2) 定义多项式阶数m，这里以3阶多项式为例
# m = 2
#
# # 使用x的幂次来构造A矩阵
# A = np.vander(x, m + 1)
#
# # (3) 计算拟合系数theta，使用最小二乘法的正规方程
# theta = np.linalg.inv(A.T @ A) @ A.T @ y
# print(theta)
# # (4) 使用theta和x的幂次计算拟合曲线
# x_fit = np.linspace(min(x), max(x), 100)
# A_fit = np.vander(x_fit, m + 1)
# y_fit = A_fit @ theta
#
# # 创建图形对象并绘制拟合曲线和样本点
# fig, ax = plt.subplots()
# ax.plot(x_fit, y_fit, label=f'Polynomial Fit of degree {m}')
# ax.scatter(x, y, color='red', label='Sample Points')
# ax.set_xlabel('X')
# ax.set_ylabel('Y')
# ax.legend()
# plt.show()


# 编程4.5-----------------------------------------

# m次多项式的最小二乘法
def least_square_method(m, sampleData):
    x = sampleData[:,0]
    y = sampleData[:,1]

    # (2) 多项式阶数m，这里以3阶多项式为例
    # 使用x的幂次来构造A矩阵
    A = np.vander(x, m + 1)

    # (3) 计算拟合系数theta，使用最小二乘法的正规方程
    theta = np.linalg.inv(A.T @ A) @ A.T @ y

    # (4) 使用theta和x的幂次计算拟合曲线
    x_fit = np.linspace(min(x), max(x), 100)
    A_fit = np.vander(x_fit, m + 1)
    y_fit = A_fit @ theta

    plt.plot(x_fit, y_fit)
    plt.show()

    # 计算残差平方和
    residuals = y - A @ theta
    residuals_squared_sum = residuals.T @ residuals
    # 计算均方误差
    degrees_of_freedom = len(y) - (m + 1)
    mean_squared_error = residuals_squared_sum / degrees_of_freedom
    # 计算协方差矩阵
    covariance_matrix = np.linalg.inv(A.T @ A) * mean_squared_error

    return theta, covariance_matrix


def curve_draw_line(curveData,sampleData):
    x_fit = curveData[:,0]
    y_fit = curveData[:,1]
    x = sampleData[:,0]
    y = sampleData[:,1]
    # 创建图形对象并绘制拟合曲线和样本点
    ax = draw_axis(0, 1000,step=250)
    ax.plot(x_fit, y_fit, label=f'FitCurve')
    ax.scatter(x, y, color='red', label='SampleData')
    # ax.set_xlabel('X')
    # ax.set_ylabel('Y')
    plt.legend()
    plt.show()

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, 150, 250, 350, 450, 550, 650, 700, 750, 850])
    # y = np.array([6, 30, 90, 160, 220, 340, 490, 620, 730, 1000])
    # x = np.array([10, 100, 200, 300, 400, 500, 600, 700, 800, 900])
    # y = np.array([10, 20, 30, 50, 80, 130, 210, 340, 550, 890])
    # x = np.array([0, 10, 20, 30, 40, 50, 60, 70, 80, 90])
    # y = np.array([1, 2, 1, 5, 8, 13, 21, 34, 55, 89])
    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(LimitNum, 1, theta, m, )
    # print("curveData",curveData)
    curve_draw_line(curveData,sampleData)

# 编程4.5 END-----------------------------------------