# 随机梯度下降函数
# training_data 是一个 (x, y) 元组的列表，表示训练输入和其对应的期# 望输出。
# 变量 epochs 迭代期数量
# 变量 mini_batch_size 采样时的小批量数据的大小。
# eta 是学习速率， η
# 如果给出了可选参数 test_data，那么程序会在每个训练器后评估网络，并# 打印出部分进展def SGD(self, training_data, epochs, mini_batch_size, eta,test_data=None):"""Train the neural network using mini-batch stochasticgradient descent.  The "training_data" is a list of tuples"(x, y)" representing the training inputs and the desiredoutputs.  The other non-optional parameters are
self-explanatory. If "test_data" is provided then the network will be evaluated against the test data after each epoch, and partial progress printed out. This is useful for tracking progress, but slows things down substantially."""# 获得测试集大小if test_data: n_test = len(test_data)n = len(training_data)for j in xrange(epochs):# 打乱训练集random.shuffle(training_data)# 获得最小数据集 mini_batchmini_batches = [training_data[k:k+mini_batch_size]for k in xrange(0, n, mini_batch_size)]# for mini_batch in mini_batches:# 训练模型self.update_mini_batch(mini_batch, eta)# 打印跟踪if test_data:print "Epoch {0}: {1} / {2}".format(j, self.evaluate(test_data), n_test)else:print "Epoch {0} complete".format(j)    def update_mini_batch(self, mini_batch, eta):
"""Update the network's weights and biases by applying gradient descent using backpropagation to a single mini batch. The "mini_batch" is a list of tuples "(x, y)", and "eta"is the learning rate."""nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:# 利用反向传播算法，快速计算代价函数的梯度delta_nabla_b, delta_nabla_w = self.backprop(x, y)nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]# 利用梯度下降算法公式self.weights = [w-(eta/len(mini_batch))*nwfor w, nw in zip(self.weights, nabla_w)]self.biases = [b-(eta/len(mini_batch))*nbfor b, nb in zip(self.biases, nabla_b)]