小波变换的可遗忘因子最小二乘代码
时间: 2023-07-22 20:20:39 浏览: 50
以下是小波变换的可遗忘因子最小二乘的 Python 代码实现:
```python
import numpy as np
import pywt
from scipy.optimize import minimize
def wavelet_lsf(x, y, wavelet, level):
# 进行小波变换
coeffs = pywt.wavedec(y, wavelet, level=level)
# 求可遗忘因子最小二乘
def func(params):
a = params[0]
b = params[1:]
fitted = a * pywt.waverec(coeffs[:-1] + [b * coeffs[-1]], wavelet)
residuals = y - fitted
return np.sum(residuals ** 2)
a0 = np.mean(y)
b0 = np.ones(len(coeffs[-1]))
x0 = np.hstack((a0, b0))
result = minimize(func, x0)
# 返回拟合结果
a = result.x[0]
b = result.x[1:]
fitted = a * pywt.waverec(coeffs[:-1] + [b * coeffs[-1]], wavelet)
return fitted
```
其中,`x` 和 `y` 分别为自变量和因变量,`wavelet` 是小波基函数的名称(如 `db4`),`level` 是小波变换的层数。函数返回拟合的结果。