手写数字识别项目代码——卷积神经网络LeNet-5模型


'''
#2018-06-25 272015 June Monday the 26 week, the 176 day SZ
手写字体识别程序文件1:
这个程序使用了卷积神经网络LeNet - 5模型。
定义了前向传播的过程以及神经网络中的参数,无论训练还是测试,都可以直接调用inference这个函数
NUM_LABELS =10 #标签数目

#regularizer正则化矩阵,变量属性:维度,shape;
#tf.get_variable创建过滤器的权重变量和偏置项变量。[CONV1_SIZE, CONV1_SIZE, NUM_CHANNELS, CONV1_DEEP]是参数变量,
CONV1_SIZE代表过滤器尺寸,NUM_CHANNELS当前层的深度,CONV1_DEEP过滤器的深度。

tf.nn.conv2d函数实现卷积前向传播算法;input_tensor当前层节点矩阵(四维矩阵,第一维代表一个输入batch,表示第几张图片。后面三个维度代表一个节点矩阵
conv1_weights,卷积层的权重,
strides=[1,1,1,1]不同维度上的步长,
padding= 'SAME'填充的方法:全零填充,VALID不添加全零填充。全零填充保证前向传播结果和当前层矩阵大小保持一致。
conv1 = tf.nn.conv2d(input_tensor, conv1_weights, strides=[1,1,1,1],padding= 'SAME')

tf.nn.bias_add函数给每个节点添加偏置项。
tf.truncated_normal_initializer 从截断的正态分布中输出随机值。


seed:一个Python整数。用于创建随机种子。查看 tf.set_random_seed 行为。  

tf.nn.relu() 激活函数实现去线性化 

tf.variable_scope使用不同的命名空间隔离不同层的变量,让每一层中的变量命名只需要考虑在当前层的作用,不需要担心重名的问题。

pool1 = tf.nn.max_pool(relu1, ksize=[1,2,2,1], strides = [1,2,2,1],padding='SAME')实现最大池化层前向传播过程。
ksize提供过滤器尺寸,但是第一个和第四个元素都必须为1,strides提供步长,但是第一个和第四个元素都必须为1,padding填充方法

神经网络结果加上激活函数和偏置项:f(Wx +b); f(x)是激活函数,b是偏置项
每个神经元的输出经过非线性函数,整个模型就不是非线性了。这个非线性函数就是激活函数。
三个常见激活函数:ReLU激活函数,Sigmoid激活函数,tanh函数;
'''

import tensorflow as tf 

#定义输入,输出,隐藏层1的节点个数
INPUT_NODE = 784 #28*28的图片
OUTPUT_NODE = 10 #输出10个结点,十种分类结果,对应0-9数字

IMAGE_SIZE = 28
NUM_CHANNELS = 1 #黑白图片是1,彩色图片是3;;当前层的深度
NUM_LABELS =10 #标签数目

#第一层卷积层的尺寸和深度
CONV1_DEEP =32 #过滤器深度
CONV1_SIZE = 5 #过滤器尺寸

#第二层卷积层的尺寸和深度
CONV2_DEEP = 64 
CONV2_SIZE = 5

#全连接层结点个数
FC_SIZE = 512

#定义卷积神经网络的前向传播过程,dropout提升模型可靠性并且防止过拟合。只在训练时候使用。参数train区分训练过程和测试过程
def inference(input_tensor, train, regularizer):
	#声明第一层卷积层的变量'layer1 - conv1'并且实现前向传播的过程;使用全0填充,输入28*28*1,输出28*28*32
	with tf.variable_scope('layer1 - conv1'):
		#声明第一层卷积层的变量并且实现前向传播的过程,输入28*28*1的原始图片像素矩阵,使用全零填充,输出28*28*32矩阵。
		conv1_weights = tf.get_variable('weight', [CONV1_SIZE, CONV1_SIZE, NUM_CHANNELS, CONV1_DEEP],
			initializer = tf.truncated_normal_initializer(stddev=0.1))
		#[CONV1_DEEP]过滤器的深度,也是下一层节点矩阵的深度。
		conv1_biases = tf.get_variable(	'bias', [CONV1_DEEP], initializer= tf.constant_initializer(0.0))
		#使用边长为5,深度为32的过滤器,过滤器移动步长为1,使用全0填充。 使用全零填充:输出边长=输入边长/步长 28/1=28
		conv1 = tf.nn.conv2d(input_tensor, conv1_weights, strides=[1,1,1,1],padding= 'SAME')
		relu1 = tf.nn.relu(tf.nn.bias_add(conv1, conv1_biases))

	#声明第二层池化层的前向传播过程,选用最大池化层,池化层过滤器边长为2,全零填充,移动步长2,输入为上一层输出:28*28*32,这层输出:14*14*32
	with tf.name_scope('layer2-pool1'):
		pool1 = tf.nn.max_pool(relu1, ksize=[1,2,2,1], strides = [1,2,2,1],padding='SAME')

	#第三层卷积层前向传播过程,输出14*14*64的矩阵
	with tf.variable_scope('layer3-conv2'):
		conv2_weights = tf.get_variable(
			'weight', [CONV2_SIZE, CONV2_SIZE, CONV1_DEEP,CONV2_DEEP],
			initializer = tf.truncated_normal_initializer(stddev=0.1))
		conv2_biases = tf.get_variable(
			'bias', [CONV2_DEEP], initializer= tf.constant_initializer(0.0))
		#使用边长为5,深度为64的过滤器,过滤器移动步长为1,使用全0填充。
		conv2 = tf.nn.conv2d(pool1, conv2_weights, strides=[1,1,1,1],padding= 'SAME')
		relu2 = tf.nn.relu(tf.nn.bias_add(conv2, conv2_biases))

	#实现第四层:池化层的前向传播过程。过滤器尺寸:2*2;步长2*2;输出7*7*64的矩阵
	with tf.name_scope('layer4-pool2'):
		pool2 = tf.nn.max_pool(relu2, ksize=[1,2,2,1], strides = [1,2,2,1],padding='SAME')
		
	#池化层输出转为第五层全连接层的输入格式:多维矩阵转一维向量
	pool_shape = pool2.get_shape().as_list()  #得到维度,维度也包含了batch中数据的个数
	#计算矩阵拉成向量后的长度,长度就是矩阵长宽高的乘积;pool1_shape[0]为一个batch中数据的个数
	nodes = pool_shape[1] * pool_shape[2] * pool_shape[3]
	#把第四层池化层输出变成一个batch的向量
	reshaped = tf.reshape(pool2, [pool1_shape[0], nodes])

	#声明第五层全连接层的变量并且实现前向传播过程。输入是一个拉直的向量7*7*64=3136,长度3136,输出是长度为512的向量。
	#这里引入了dropout,随机把全连接层的部分节点输出变为0,从而避免过拟合。
	with tf.variable_scope('layer5-fc1'):
		fc1_weights = tf.get_variable('weight', [nodes, FC_SIZE],initializer = tf.truncated_normal_initializer(stddev=0.1))
		#只有全连接层的权重需要加入正则化
		if regularizer != None:
			tf.add_to_collection('losses', regularizer(fc1_weights))
		fc1_biases = tf.get_variable('bias', [FC_SIZE],initializer=tf.constant_initializer(0.1))
		fc1 = tf.nn.relu(tf.matmul(reshaped, fc1_weights) + fc1_biases)
		if train: fc1 = tf.nn.dropout(fc1, 0.5)

	#声明第六层全连接层变量并且实现前向传播过程。输入512长度向量,输出长度为10的向量。这一层的输出通过softmax之后就得到了最后的分类结果。
	with tf.variable_scope('layer6-fc2'):
		fc2_weights = tf.get_variable('weight', [FC_SIZE, NUM_LABELS], initializer = tf.truncated_normal_initializer(stddev=0.1))
		if regularizer != None:
			tf.add_to_collection('losses', regularizer(fc2_weights))
		fc2_biases = tf.get_variable('bias',[NUM_LABELS],initializer=tf.constant_initializer(0.1))
		logit = tf.matmul(fc1, fc2_weights) + fc2_biases

	#返回第六层的输出
	return logit 

###########################################以下是训练部分###########################################

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
import mnist_inference
import os

BATCH_SIZE = 100  #每批次取100个;一个批次中训练个数。
LEARNING_RATE_BASE = 0.8 #学习率初始值
LEARNING_RATE_DECAY = 0.99 #学习率衰减率
REGULARIZATION_RATE = 0.0001 #正则化系数
TRAINING_STEPS = 30000 #训练轮数
MOVING_AVERAGE_DECAY = 0.99 #滑动平均衰减率,控制模型更新的速度,让模型在测试数据上更健壮
MODEL_SAVE_PATH = 'D:\\ST\\Python_work\\program\\手写识别'
MODEL_NAME = "mnist_model"

def train(mnist):
    # 定义输入输出placeholder。placeholder定义了一个位置,程序运行时候给这个位置提供数据。这个机制提供输入数据,输入为思维矩阵
    x = tf.placeholder(tf.float32, [ 
    	BATCH_SIZE, 							#第一维表示一个batch中样例的个数
    	mnist_inference.IMAGE_SIZE,			#第二,三维表示图片的尺寸
    	mnist_inference.IMAGE_SIZE,
    	mnist_inference.NUM_CHANNELS],    	 #第四维表示图片深度,黑白图片,深度1,彩色图片,深度3
    	name='x-input')
    #把输入训练数据格式调整为一个四维矩阵,并把调整后的数据传入sess.run的过程
    reshaped_xs = np.reshape(xs, (
    	BATCH_SIZE, 							#第一维表示一个batch中样例的个数
    	mnist_inference.IMAGE_SIZE,			#第二,三维表示图片的尺寸
    	mnist_inference.IMAGE_SIZE,
    	mnist_inference.NUM_CHANNELS,    	 #第四维表示图片深度,黑白图片,深度1,彩色图片,深度3
    	))
    y_ = tf.placeholder(tf.float32, [None, mnist_inference.OUTPUT_NODE], name='y-input')

    regularizer = tf.contrib.layers.l2_regularizer(REGULARIZATION_RATE) #L2范数正则化
    y = mnist_inference.inference(x, regularizer) #预测值
    global_step = tf.Variable(0, trainable=False) #定义存储训练轮数的变量
    
    # 定义损失函数、学习率、滑动平均操作以及训练过程。
    variable_averages = tf.train.ExponentialMovingAverage(MOVING_AVERAGE_DECAY, global_step)
    variables_averages_op = variable_averages.apply(tf.trainable_variables())
    cross_entropy = tf.nn.sparse_softmax_cross_entropy_with_logits(logits=y, labels=tf.argmax(y_, 1))
    cross_entropy_mean = tf.reduce_mean(cross_entropy)
    loss = cross_entropy_mean + tf.add_n(tf.get_collection('losses')) #总损失=交叉熵损失和正则化损失
    learning_rate = tf.train.exponential_decay(
        LEARNING_RATE_BASE, #基础学习率
        global_step,		#当前迭代轮数
        mnist.train.num_examples / BATCH_SIZE, #过完所有训练数据需要的迭代次数
        LEARNING_RATE_DECAY, 					#学习率衰减速度
        staircase=True)
    train_step = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)
    #每次循环需要通过反向传播来更新参数,又要更新参数的每一个滑动平均值
    with tf.control_dependencies([train_step, variables_averages_op]):
        train_op = tf.no_op(name='train')
        
    # 初始化TensorFlow持久化类。
    saver = tf.train.Saver()
    #初始化会话,开始训练过程
    with tf.Session() as sess:
        tf.global_variables_initializer().run()

        for i in range(TRAINING_STEPS):
            xs, ys = mnist.train.next_batch(BATCH_SIZE)
            _, loss_value, step = sess.run([train_op, loss, global_step], feed_dict={x: xs, y_: ys})
            if i % 1000 == 0: #每1000轮输出一次损失,保存模型,实现持久化
                print("After %d training step(s), loss on training batch is %g." % (step, loss_value))
                saver.save(sess, os.path.join(MODEL_SAVE_PATH, MODEL_NAME), global_step=global_step) #


def main(argv=None):
    mnist = input_data.read_data_sets('D:\\ST\\Python_work\\program\\手写识别', one_hot=True)
    train(mnist)

if __name__ == '__main__':
    main()

'''

Successfully downloaded train-images-idx3-ubyte.gz 9912422 bytes.
Extracting D:\ST\Python_work\program\手写识别\train-images-idx3-ubyte.gz
Successfully downloaded train-labels-idx1-ubyte.gz 28881 bytes.
Extracting D:\ST\Python_work\program\手写识别\train-labels-idx1-ubyte.gz
Successfully downloaded t10k-images-idx3-ubyte.gz 1648877 bytes.
Extracting D:\ST\Python_work\program\手写识别\t10k-images-idx3-ubyte.gz
Successfully downloaded t10k-labels-idx1-ubyte.gz 4542 bytes.
Extracting D:\ST\Python_work\program\手写识别\t10k-labels-idx1-ubyte.gz
2018-06-25 19:14:55.952000: I C:\tf_jenkins\home\workspace\rel-win\M\windows\PY\35\tensorflow\core\platform\cpu_feature_guard.cc:137] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX AVX2
After 1 training step(s), loss on training batch is 2.96337.
After 1001 training step(s), loss on training batch is 0.21122.
After 2001 training step(s), loss on training batch is 0.195296.
After 3001 training step(s), loss on training batch is 0.147966.
After 4001 training step(s), loss on training batch is 0.121113.
After 5001 training step(s), loss on training batch is 0.104925.
After 6001 training step(s), loss on training batch is 0.0969063.
After 7001 training step(s), loss on training batch is 0.0967676.
After 8001 training step(s), loss on training batch is 0.0805094.
After 9001 training step(s), loss on training batch is 0.0758026.
After 10001 training step(s), loss on training batch is 0.0662473.
After 11001 training step(s), loss on training batch is 0.0667674.
After 12001 training step(s), loss on training batch is 0.0615224.
After 13001 training step(s), loss on training batch is 0.0548805.
After 14001 training step(s), loss on training batch is 0.0576472.
After 15001 training step(s), loss on training batch is 0.0558432.
After 16001 training step(s), loss on training batch is 0.050817.
After 17001 training step(s), loss on training batch is 0.04974.
After 18001 training step(s), loss on training batch is 0.0424435.
After 19001 training step(s), loss on training batch is 0.0423194.
After 20001 training step(s), loss on training batch is 0.0413847.
After 21001 training step(s), loss on training batch is 0.0433296.
After 22001 training step(s), loss on training batch is 0.0370582.
After 23001 training step(s), loss on training batch is 0.0422068.
After 24001 training step(s), loss on training batch is 0.0377206.
After 25001 training step(s), loss on training batch is 0.0377879.
After 26001 training step(s), loss on training batch is 0.0397268.
After 27001 training step(s), loss on training batch is 0.035891.
After 28001 training step(s), loss on training batch is 0.0405907.
After 29001 training step(s), loss on training batch is 0.0337722.
[Finished in 479.9s]
'''

'''
'''
###########################################我的问题代码训练部分###########################################

我的问题代码2
源码地址:
https://github.com/caicloud/tensorflow-tutorial/tree/master/Deep_Learning_with_TensorFlow

#2018-06-25 272015 June Monday the 26 week, the 176 day SZ
手写字体识别程序文件1:
定义了神经网络的训练过程

'''
import os
import tensorflow as tf 
from tensorflow.examples.tutorials.mnist import input_data

#加载mnist_inference.py中定义的常量和前向传播的函数
import mnist_inference

#配置神经网络的参数
BATCH_SIZE = 100
LEARNING_RATE_BASE = 0.8 
LEARNING_RATE_DECAY = 0.99
REGULARAZTION_RATE = 0.0001
TRAINING_STEPS = 30000
MOVING_AVERAGE_DECAY = 0.99
#模型保存路径和文件名
MODEL_SAVE_PATH = 'D:\\ST\\Python_work\\program\\手写识别'
MODEL_NAME = 'model.ckpt'

def train(mnist):
    #定义输入输出placeholder.
    x = tf.placeholder(tf.float32, [None, mnist_inference.INPUT_NODE],name = 'x-input')
    y_ = tf.placeholder(tf.float32, [None, mnist_inference.OUTPUT_NODE], name = 'y-input')

    regularizer = tf.contrib.layers.l2_regularizer(REGULARAZTION_RATE)
    #直接使用mnist_inference.py中定义的前向传播过程
    y = mnist_inference.inference(x, regularizer)
    global_step = tf.Variable(0, trainable = False)

    #定义损失函数,学习率,滑动平均操作以及训练过程
    variable_averages = tf.train.ExponentialMovingAverage(MOVING_AVERAGE_DECAY, global_step)
    variables_averages_op = variable_averages.apply(tf.trainable_variables())
    cross_entropy = tf.nn.sparse_softmax_cross_entropy_with_logits(y, tf.argmax(y_, 1))
    cross_entropy_mean = tf.reduce_mean(cross_entropy)
    loss = cross_entropy_mean +tf.add_n(tf.get_collection('losses'))
    learning_rate = tf.train.exponential_decay(LEARNING_RATE_BASE, global_step, mnist.train.num_examples / BATCH_SIZE, LEARNING_RATE_DECAY)
    train_step = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step = global_step)
    with tf.control_dependencies([train_step, variables_averages_op]):
        train_op = tf.no_op(name='train')

    #初始化tf持久化类
    saver = tf.train.Saver()
    with tf.Session() as sess:
        tf.initialize_all_variables().run()
        tf.global_variables_initializer().run()

        #在训练过程中不再测试模型在验证数据上的表现,验证和测试的过程有一个独立程序完成
        for i in range(TRAINING_STEPS):
            xs, ys = mnist.train.next_batch(BATCH_SIZE)
            _, loss_value, step = sess.run([train_op, loss, global_step], feed_dict = {x:xs, y_:ys})

            #每1000轮保存一次模型
            if i % 1000 ==0:
                #输出当前损失函数
                print('After %d training step(s) , loss on training batch is %g'%(step, loss_value))
                #保存模型,文件尾部加上训练轮数
                saver.save(sess, os.path.join(MODEL_SAVE_PATH, MODEL_NAME), global_step = global_step)

def main(argv = None):
    mnist = input_data.read_data_sets('D:\\ST\\Python_work\\program\\手写识别', one_hot = True)
    train(mnist)

if __name__ == '__main__':
    tf.app.run()


'''

###########################################以下是预测部分###########################################

#老师代码3
import time
import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
import mnist_inference
import mnist_train

# 加载的时间间隔。每十秒加载一次最新模型,并在测试数据上测试最新模型的正确率
EVAL_INTERVAL_SECS = 50

def evaluate(mnist):
    with tf.Graph().as_default() as g:

        x = tf.placeholder(tf.float32, [None, mnist_inference.INPUT_NODE], name='x-input')
        y_ = tf.placeholder(tf.float32, [None, mnist_inference.OUTPUT_NODE], name='y-input')
        #准备验证数据集
        validate_feed = {x: mnist.validation.images, y_: mnist.validation.labels}
        #预测值,用封装好的函数来计算前向传播的结果
        y = mnist_inference.inference(x, None)
        #正确预测,使用前向传播结果计算正确率。tf.argmax(y_, 1)得到输入样例的预测类别
        correct_prediction = tf.equal(tf.argmax(y, 1), tf.argmax(y_, 1))
        accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
        #变量重命名的方式加载模型,这样不用调用求滑动平均的函数来获取平均值了。
        variable_averages = tf.train.ExponentialMovingAverage(mnist_train.MOVING_AVERAGE_DECAY)
        variables_to_restore = variable_averages.variables_to_restore()
        saver = tf.train.Saver(variables_to_restore)

        while True:
            with tf.Session() as sess:
            	#MODEL_SAVE_PATH = 'D:\\ST\\Python_work\\program\\手写识别'
            	#checkpoint文件自动找到目录中最新模型的文件名
                ckpt = tf.train.get_checkpoint_state(mnist_train.MODEL_SAVE_PATH)
                #print(ckpt)  #None找不到该文件,我明明看到有这个文件呢。
                if ckpt and ckpt.model_checkpoint_path:
                	#加载模型
                    saver.restore(sess, ckpt.model_checkpoint_path)
                    #通过文件名得到模型保存时迭代的轮数
                    global_step = ckpt.model_checkpoint_path.split('/')[-1].split('-')[-1]
                    accuracy_score = sess.run(accuracy, feed_dict=validate_feed)
                    print("After %s training step(s), validation accuracy = %g" % (global_step, accuracy_score))
                else:
                    print('No checkpoint file found')
                    return
            time.sleep(EVAL_INTERVAL_SECS)



def main(argv=None):
    mnist = input_data.read_data_sets('D:\\ST\\Python_work\\program\\手写识别', one_hot=True)
    evaluate(mnist)

if __name__ == '__main__':
    main()

'''
Successfully downloaded train-labels-idx1-ubyte.gz 28881 bytes.
Extracting D:\ST\Python_work\program\手写识别\train-labels-idx1-ubyte.gz
Successfully downloaded t10k-images-idx3-ubyte.gz 1648877 bytes.
Extracting D:\ST\Python_work\program\手写识别\t10k-images-idx3-ubyte.gz
Successfully downloaded t10k-labels-idx1-ubyte.gz 4542 bytes.
Extracting D:\ST\Python_work\program\手写识别\t10k-labels-idx1-ubyte.gz
2018-06-25 19:35:27.932000: I C:\tf_jenkins\home\workspace\rel-win\M\windows\PY\35\tensorflow\core\platform\cpu_feature_guard.cc:137] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX AVX2
No checkpoint file found
[Finished in 19.6s]
'''

'''
###########################################我的问题代码预测部分###########################################

#自己代码
'''
#2018-06-25 272015 June Monday the 26 week, the 176 day SZ
手写字体识别程序文件3:
定义了前向传播的过程以及神经网络中的参数
'''
import time 
import tensorflow as tf 
from tensorflow.examples.tutorials.mnist import input_data

#加载mnist_inference.py 和mnist_train.py中定义的常量和函数
import mnist_inference 
import mnist_train

#10秒加载一次最新的模型,并且在测试集上测试最新模型的正确率
EVAL_INTERVAL_SECS = 10

def evaluate(mnist):
	with tf.Graph().as_default() as g:
		#定义输入输出格式
		x = tf.placeholder(tf.float32, [None, mnist_inference.INPUT_NODE], name = 'x- input')
		y_ = tf.placeholder(tf.float32, [None, mnist_inference.OUTPUT_NODE], name = 'y- input')
		validate_feed = {x:mnist.validation.images, y_:mnist.validation.labels}

		#直接调用其他文档的函数进行计算前向传播结果
		y = mnist_inference.inference(x, None)

		#使用前向结果计算正确率
		correct_prediction = tf.equal(tf.argmax(y, 1), tf.argmax(y_, 1))
		accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

		#通过变量重命名的方式加载模型,这样在前向传播过程中就不要调用求滑动平均的函数来获取平均值了。这样可以完全共用
		#mnist_inference.py中定义的前向传播过程
		variable_averages = tf.train.ExponentialMovingAverage(mnist_train.MOVING_AVERAGE_DECAY)
		variables_to_restore = variable_averages.variables_to_restore()
		saver = tf.train.Saver(variables_to_restore)

		#每隔EVAL_INTERVAL_SECS秒调用一次计算正确率的过程来检测训练过程中正确率的变化
		while True:
			with tf.Session() as sess:
				#tf.train.get_checkpoint_state()会通过checkpoint文件自动找到目录中最新模型的文件名字
				ckpt = tf.train.get_checkpoint_state(mnist_train.MODEL_SAVE_PATH)
				if ckpt and ckpt.model_checkpoint_path:
					#加载模型
					saver.restore(sess, ckpt.model_checkpoint_path)
					#通过文件名字得到模型保存时候迭代的轮数
					global_step = ckpt.model_checkpoint_path.split('/')[-1].split('-')[-1]
					accuracy_score = sess.run(accuracy, feed_dict = validation_feed)
					print('After %s training steps, validation accuracy = %g'%(global_step, accuracy_score))
				else:
					print('no checkpoint file found')
					return time.sleep(EVAL_INTERVAL_SECS)

def main(argv=None):
	mnist = input_data.read_data_sets('D:\\ST\\Python_work\\program\\手写识别', one_hot = True)
	evaluate(mnist)

if __name__ == '__main__':
	tf.app.run()
'''




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转载自blog.csdn.net/btujack/article/details/81095970