# 递推最小二乘法——python程序

```            ```
# data 第一列为标记值
# data 后几列为特征向量
# initialTheta 为需要求得的theta
import numpy as np
import sklearn.datasets
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
import matplotlib as mpl
import matplotlib.pyplot as plt
import warnings

###################
## data 第一列为真值，后面所有列为特征
## initialTheta 估算的权值初值
## featureNum 特征的个数
def RLS_Fun(data, initialTheta, featureNum):
Theta = initialTheta
P = 10 ** 6 * np.eye(featureNum)
lamda = 1
for i in range(len(data)):
featureMatrix = data[i][1:]
featureMatrix = featureMatrix.reshape(featureMatrix.shape[0], 1)
y_real = data[i][0]
K = np.dot(P, featureMatrix) / (lamda + np.dot(np.dot(featureMatrix.T, P), featureMatrix))
Theta = Theta + np.dot(K, (y_real - np.dot(featureMatrix.T, Theta)))
P = np.dot((np.eye(featureNum) - np.dot(K, featureMatrix.T)), P)
return Theta

if __name__ == '__main__':
warnings.filterwarnings(action='ignore')
x = np.array(dataInitial.data)
y = np.array(dataInitial.target)
y = y.reshape((y.shape[0], 1))
x_train, x_test, y_train, y_test = train_test_split(x, y, train_size=0.7, random_state=0)
data = np.concatenate((y_train, x_train), axis=1)
featureNum = np.shape(x)[1]  # 有几个特征
initialTheta = 0.5 * np.ones((featureNum, 1))
Theta = RLS_Fun(data, initialTheta, featureNum)
y_pred = np.dot(x_test, Theta)
mse = mean_squared_error(y_test, y_pred)
print('均方误差：', mse)
t = np.arange(len(y_pred))
mpl.rcParams['font.sans-serif'] = ['simHei']
mpl.rcParams['axes.unicode_minus'] = False
plt.figure(facecolor='w')
plt.plot(t, y_test, 'r-', lw=2, label='真实值')
plt.plot(t, y_pred, 'g-', lw=2, label='估计值')
plt.legend(loc='best')
plt.title('波士顿房价预测', fontsize=18)
plt.xlabel('样本编号', fontsize=15)
plt.ylabel('房屋价格', fontsize=15)
plt.grid()
plt.show()

```
```

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