多找几个递推最小二乘法的python程序
时间: 2023-05-30 18:02:10 浏览: 90
以下是几个递推最小二乘法的Python程序:
1. 递推最小二乘法(TLS)的基本实现:
```python
import numpy as np
def TLS(X, y):
"""
递推最小二乘法(TLS)的基本实现
X: 数据矩阵
y: 目标向量
"""
n, p = X.shape
Q = np.zeros((n, n))
R = np.zeros((p, p))
b = np.zeros(p)
for i in range(n):
# 递推公式
x = X[i, :]
q = x - np.dot(Q[:i, :].T, x)
Q[i, :] = q / np.linalg.norm(q)
b += y[i] * Q[i, :]
R += np.outer(Q[i, :], x)
theta = np.linalg.solve(R, b)
return theta
```
2. 递推最小二乘法(TLS)的改进实现:
```python
import numpy as np
def TLS(X, y):
"""
递推最小二乘法(TLS)的改进实现
X: 数据矩阵
y: 目标向量
"""
n, p = X.shape
Q = np.zeros((n, n))
R = np.zeros((p, p))
b = np.zeros(p)
for i in range(n):
# 递推公式
x = X[i, :]
q = x - np.dot(Q[:i, :].T, x)
r = np.linalg.norm(q)
if r > 1e-12:
Q[i, :] = q / r
b += y[i] * Q[i, :]
R += np.outer(Q[i, :], x)
theta = np.linalg.solve(R, b)
return theta
```
3. 递推最小二乘法(TLS)的加速实现:
```python
import numpy as np
def TLS(X, y):
"""
递推最小二乘法(TLS)的加速实现
X: 数据矩阵
y: 目标向量
"""
n, p = X.shape
Q = np.zeros((n, n))
R = np.zeros((p, p))
b = np.zeros(p)
for i in range(n):
# 递推公式
x = X[i, :]
q = x - np.dot(Q[:i, :].T, x)
r = np.linalg.norm(q)
if r > 1e-12:
Q[i, :] = q / r
b += y[i] * Q[i, :]
for j in range(i):
qj = Q[j, :]
R[j, :] += qj * np.dot(qj, x)
R[i, :] = r * q
theta = np.linalg.solve(R, b)
return theta
```