171 lines
5.8 KiB
Python
171 lines
5.8 KiB
Python
import math
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import random
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# import matplotlib.pyplot as plt # 注：matplotlib严格来说是第三方库，此处仅用于可视化，可移除
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# 1. 基础数学工具（替代NumPy的部分功能）
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def dot_product(a, b):
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"""计算两个向量的点积"""
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return sum(x * y for x, y in zip(a, b))
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def vector_add(a, b):
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"""向量加法"""
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return [x + y for x, y in zip(a, b)]
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def vector_subtract(a, b):
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"""向量减法"""
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return [x - y for x, y in zip(a, b)]
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def scalar_multiply(scalar, vector):
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"""标量乘以向量"""
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return [scalar * x for x in vector]
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def mean(x):
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"""计算平均值"""
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return sum(x) / len(x)
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# 2. 激活函数（引入非线性）
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def relu(x):
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"""ReLU激活函数"""
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return max(0, x)
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def relu_derivative(x):
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"""ReLU导数（用于反向传播）"""
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return 1 if x > 0 else 0
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def tanh(x):
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"""tanh激活函数"""
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return math.tanh(x)
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def tanh_derivative(x):
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"""tanh导数"""
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return 1 - math.tanh(x) ** 2
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# 3. 神经网络类（多层感知器）
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class SimpleNN:
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def __init__(self, input_size=3, hidden_size=8, output_size=1):
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# 初始化权重和偏置（随机值）
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self.weights1 = [
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[random.uniform(-0.5, 0.5) for _ in range(input_size)]
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for _ in range(hidden_size)
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]
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self.biases1 = [random.uniform(-0.5, 0.5) for _ in range(hidden_size)]
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self.weights2 = [
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[random.uniform(-0.5, 0.5) for _ in range(hidden_size)]
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for _ in range(output_size)
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]
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self.biases2 = [random.uniform(-0.5, 0.5) for _ in range(output_size)]
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# 学习率
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self.learning_rate = 0.001
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def forward(self, x):
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"""前向传播计算"""
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# 隐藏层计算
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self.hidden = []
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for i in range(len(self.weights1)):
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activation = dot_product(self.weights1[i], x) + self.biases1[i]
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self.hidden.append(relu(activation)) # 应用ReLU激活
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# 输出层计算
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output = []
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for i in range(len(self.weights2)):
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activation = dot_product(self.weights2[i], self.hidden) + self.biases2[i]
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output.append(activation) # 输出层不使用激活函数
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return output[0]
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def backward(self, x, y, y_pred):
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"""反向传播计算梯度"""
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# 输出层误差
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output_error = y - y_pred
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# 隐藏层误差
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hidden_errors = [0] * len(self.hidden)
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for i in range(len(hidden_errors)):
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for j in range(len(self.weights2)):
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hidden_errors[i] += self.weights2[j][i] * output_error
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# 更新输出层权重和偏置
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for i in range(len(self.weights2)):
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for j in range(len(self.weights2[i])):
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self.weights2[i][j] += self.learning_rate * output_error * self.hidden[j]
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self.biases2[i] += self.learning_rate * output_error
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# 更新隐藏层权重和偏置
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for i in range(len(self.weights1)):
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for j in range(len(self.weights1[i])):
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self.weights1[i][j] += self.learning_rate * hidden_errors[i] * relu_derivative(self.hidden[i]) * x[j]
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self.biases1[i] += self.learning_rate * hidden_errors[i] * relu_derivative(self.hidden[i])
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def train(self, X, y, epochs=1000):
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"""训练模型"""
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for epoch in range(epochs):
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total_loss = 0
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for i in range(len(X)):
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# 前向传播
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y_pred = self.forward(X[i])
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# 计算损失（MSE）
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loss = (y[i] - y_pred) ** 2
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total_loss += loss
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# 反向传播更新
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self.backward(X[i], y[i], y_pred)
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# 打印训练进度
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if (epoch + 1) % 100 == 0:
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avg_loss = total_loss / len(X)
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print(f"Epoch {epoch+1}/{epochs}, Loss: {avg_loss:.6f}")
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# 4. 生成非线性数据（模拟多输入非线性关系）
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def generate_data(num_samples=1000):
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X = []
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y = []
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for _ in range(num_samples):
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# 3个输入特征
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x1 = random.uniform(-2, 2)
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x2 = random.uniform(-2, 2)
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x3 = random.uniform(-2, 2)
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# 非线性目标函数：y = x1² + sin(x2) + x3³ + 噪声
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target = x1**2 + math.sin(x2) + x3**3 + random.gauss(0, 0.1)
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X.append([x1, x2, x3])
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y.append(target)
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return X, y
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# 5. 主程序
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if __name__ == "__main__":
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# 生成训练数据
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X_train, y_train = generate_data(500)
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# 创建并训练模型
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model = SimpleNN(input_size=3, hidden_size=16)
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model.train(X_train, y_train, epochs=100)
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# 测试模型
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X_test, y_test = generate_data(100)
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y_pred = [model.forward(x) for x in X_test]
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# 计算测试集误差
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test_loss = mean([(y_test[i] - y_pred[i])**2 for i in range(len(y_test))])
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print(f"\n测试集平均损失: {test_loss:.6f}")
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# 示例预测
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sample_input = [100.2, -0.8, 0.5]
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prediction = model.forward(sample_input)
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print(f"\n输入 {sample_input} 的预测结果: {prediction:.4f}")
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print(f"实际值参考: {sample_input[0]**2 + math.sin(sample_input[1]) + sample_input[2]**3:.4f}")
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# （可选）可视化结果（需要matplotlib）
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try:
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plt.scatter(y_test, y_pred, alpha=0.6)
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plt.xlabel("真实值")
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plt.ylabel("预测值")
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plt.title("纯Python神经网络预测结果")
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plt.plot([min(y_test), max(y_test)], [min(y_test), max(y_test)], 'r--')
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plt.show()
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except:
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pass # 如果没有matplotlib则跳过可视化
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