MathLab/exercises/day1_task.py

"""
Day 1 - 感知机 练习

任务：实现 感知机 的核心算法
"""

import numpy as np
import matplotlib.pyplot as plt


class 感知机:
    """感知机 类"""
    
    def __init__(self, learning_rate: float = 0.01):
        self.learning_rate = learning_rate
        self.weights = None
        self.bias = None
    
    def forward(self, X: np.ndarray) -> np.ndarray:
        """前向传播
        
        Args:
            X: 输入数据，shape: [n_samples, n_features]
            
        Returns:
            预测结果，shape: [n_samples]
        """
        # TODO: 实现 f(x) = sign(w · x + b)
        raise NotImplementedError
    
    def compute_loss(self, X: np.ndarray, y: np.ndarray) -> float:
        """计算损失"""
        # TODO: 实现损失函数
        raise NotImplementedError
    
    def update(self, X_i: np.ndarray, y_i: int):
        """更新参数
        
        Args:
            X_i: 单个样本，shape: [n_features]
            y_i: 标签，值域 (-1, 1)
        """
        # TODO: 实现梯度下降更新
        raise NotImplementedError
    
    def fit(self, X: np.ndarray, y: np.ndarray, max_iter: int = 100):
        """训练模型"""
        # TODO: 实现训练循环
        raise NotImplementedError


def plot_concept():
    """可视化概念"""
    # 生成二维数据
    np.random.seed(42)
    X = np.random.randn(100, 2)
    y = np.sign(X[:, 0] + X[:, 1] - 0.5) * 1
    
    # 绘制散点图
    plt.figure(figsize=(8, 6))
    scatter = plt.scatter(X[:, 0], X[:, 1], c=y, cmap="bwr", s=100, edgecolors="black")
    plt.xlabel("x1")
    plt.ylabel("x2")
    plt.title("Day 1 - 感知机 可视化")
    plt.colorbar(scatter)
    plt.grid(True, alpha=0.3)
    plt.savefig("./plots/day1_concept.png", dpi=150)
    print(f"✅ 可视化已保存：plots/day1_concept.png")


if __name__ == "__main__":
    plot_concept()