用python写一个BP神经网络程序

好的，下面是一个简单的BP神经网络示例代码：

import numpy as np

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        
        # 初始化权重
        self.W1 = np.random.randn(self.input_size, self.hidden_size)
        self.W2 = np.random.randn(self.hidden_size, self.output_size)
        
        # 初始化偏置
        self.b1 = np.zeros((1, self.hidden_size))
        self.b2 = np.zeros((1, self.output_size))
        
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    def sigmoid_derivative(self, x):
        return x * (1 - x)
    
    def forward(self, X):
        # 隐藏层
        self.z1 = np.dot(X, self.W1) + self.b1
        self.a1 = self.sigmoid(self.z1)
        
        # 输出层
        self.z2 = np.dot(self.a1, self.W2) + self.b2
        self.a2 = self.sigmoid(self.z2)
        
        return self.a2
    
    def backward(self, X, y, output):
        # 计算输出层的误差
        self.output_error = y - output
        self.output_delta = self.output_error * self.sigmoid_derivative(output)
        
        # 计算隐藏层的误差
        self.hidden_error = np.dot(self.output_delta, self.W2.T)
        self.hidden_delta = self.hidden_error * self.sigmoid_derivative(self.a1)
        
        # 更新权重和偏置
        self.W1 += np.dot(X.T, self.hidden_delta)
        self.W2 += np.dot(self.a1.T, self.output_delta)
        self.b1 += np.sum(self.hidden_delta, axis=0)
        self.b2 += np.sum(self.output_delta, axis=0)
        
    def train(self, X, y, epochs):
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, output)
            
    def predict(self, X):
        return self.forward(X)
            
# 测试代码
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [1], [1], [0]])

nn = NeuralNetwork(2, 3, 1)
nn.train(X, y, 10000)

print(nn.predict(X))

这个BP神经网络包含一个输入层、一个隐藏层和一个输出层。输入层有2个神经元，隐藏层有3个神经元，输出层有1个神经元。这个神经网络可以用来解决异或问题。