diff --git a/function.py b/function.py
index 694e6d4..9a3d930 100644
--- a/function.py
+++ b/function.py
@@ -32,14 +32,14 @@ def sigmoid(z):
     """计算sigmoid函数"""
     return 1 / (1 + np.exp(-z))
 
-def train_logreg(X, y, learning_rate=0.01, iterations=1000):
+def train_logreg(X, y, learning_rate=0.01, iterations=1000，l2_penalty=0.01):
     """对率回归训练函数。"""
     weights = np.zeros(X.shape[1])
     
     for _ in range(iterations):
         z = np.dot(X, weights)
         predictions = sigmoid(z)
-        gradient = np.dot(X.T, (predictions - y)) / y.size
+        gradient = np.dot(X.T, (predictions - y)) / y.size + l2_penalty * weights  # 添加L2正则化项
         weights -= learning_rate * gradient
     
     return weights
@@ -84,6 +84,18 @@ def load_data(filepath):
     return data_array[:, :-1], data_array[:, -1]
 
 def preprocess_data(X, y):
+    """数据预处理，合并特征23的值，并删除特征3和特征24~28，以及特征缩放。"""
+    # 合并特征23的值和删除特征
+    X, y = preprocess_data_base(X, y)
+    
+    # 特征缩放：标准化特征
+    X_mean = np.mean(X, axis=0)
+    X_std = np.std(X, axis=0)
+    X = (X - X_mean) / X_std
+    
+    return X, y
+
+def preprocess_data_base(X, y):
     """数据预处理，合并特征23的值，并删除特征3和特征24~28。"""
     # 合并特征23的值：将2（死亡）和3（安乐死）合并为0（死亡）
     y = np.where(y == 2, 0, y)  # 将值2替换为0
@@ -101,8 +113,8 @@ if __name__ == "__main__":
     # 数据预处理
     X, y = preprocess_data(X, y)
 
-    # 训练模型
-    weights = train_logreg(X, y)
+     # 训练模型
+    weights = train_logreg(X, y, learning_rate=0.01, l2_penalty=0.01)
 
     # 加载测试数据并进行预处理
     X_test, y_test = load_data("./data/horse-colic.test")