最小二乘法的python插值代码

以下是使用最小二乘法进行插值的Python代码示例：

import numpy as np

# 定义最小二乘法函数
def least_squares(x, y, n):
    x_matrix = np.mat([[i**j for j in range(n+1)] for i in x])
    y_matrix = np.mat(y).T
    xTx = x_matrix.T * x_matrix
    if np.linalg.det(xTx) == 0.0:
        print("This matrix is singular, cannot do inverse")
        return
    w = xTx.I * (x_matrix.T * y_matrix)
    return w

# 定义插值函数
def interpolate(x, y, n, x_new):
    w = least_squares(x, y, n)
    x_new_matrix = np.mat([[i**j for j in range(n+1)] for i in x_new])
    y_new_matrix = x_new_matrix * w
    y_new = [y_new_matrix[i, 0] for i in range(len(x_new))]
    return y_new

# 示例
x = [1, 2, 3, 4, 5]
y = [1, 4, 9, 16, 25]
n = 2 # 二次插值
x_new = [1.5, 2.5, 3.5, 4.5]
y_new = interpolate(x, y, n, x_new)
print(y_new) # 输出：[2.25, 6.25, 12.25, 20.25]