Tensorflow 里通过softmax后再计算交叉熵有2个函数：
1 softmax_cross_entropy_with_logits_v2
2 sparse_softmax_cross_entropy_with_logits

均涉及两个参数，logits 和 labels ，logits 一般是神经网络的输出，是一个batch乘待分类类型数的二维张量。而labels是已知的标注，同样shape的张量。第二个函数的labels是稀疏表示的labels，因而是一维张量。

设logits1=[ [0.2, 0.1, 0.9]] ,labels1=[[0, 0, 1]],通过softmax_cross_entropy_with_logits_v2(logits=logits1,labels=labels1)的计算过程如下：
对[0.2, 0.1, 0.9]运算softmax ,得到 sm= [0.25519383 0.23090893 0.51389724] ，然后，
交叉熵=  — （ log（sm[0]）*labels1[0][0] + log（sm[1]）*labels1[0][1] + log（sm[2]）*labels1[0][2] ）.请看下面的代码例子，分别使用提供的两个函数算交叉熵，还有通过自己调用softmax算，然后直接根据上式计算，三者计算结果一致。

import tensorflow as tf
import math

input_data = tf.Variable([ [0.2, 0.1, 0.9] , [0.2, 0.1, 0.9], [0.7, 0.4, 0.1]], dtype=tf.float32)
labels1=[[0, 0, 1], [0, 1, 0] , [1, 0, 0]]
output = tf.nn.softmax_cross_entropy_with_logits_v2(logits=input_data, labels=labels1 )
labels2 = tf.argmax(labels1,1 ) 
output1 = tf.nn.sparse_softmax_cross_entropy_with_logits(logits=input_data, labels=labels2 )
sm = tf.nn.softmax ( input_data )

with tf.Session() as sess:
    init = tf.global_variables_initializer()
    sess.run(init)
    our = sess.run(output)
    print('softmax_cross_entropy_with_logits_v2:\n', our)
    our1 = sess.run(output1)
    print('sparse_softmax_cross_entropy_with_logits:\n', our)    
    inp= sess.run( input_data )
    smv = sess.run( sm )
    print( 'softmax output:\n', smv )
    l2 = sess.run( labels2 )
    print ('argmax output(sparse labels)', l2 ) 
    for k  in range(len(inp) ) :
        x = 0.0 
        for i in range(len(inp[0])) :
            x += math.log( smv[k][i] ) *  labels1[k][i]
        x = -x 
        print( 'softmax_cross_entropy_with_logits by my computing for input ' , k ,':',  x )
        #print( 'tensorflow == myComputing?' , math.fabs( x - our[k] ) < 0.001 ) 
        
    

输出结果：

softmax_cross_entropy_with_logits_v2:
 [0.6657319 1.4657319 0.8283902]
sparse_softmax_cross_entropy_with_logits:
 [0.6657319 1.4657319 0.8283902]
softmax output:
 [[0.25519383 0.23090893 0.51389724]
 [0.25519383 0.23090893 0.51389724]
 [0.4367518  0.3235537  0.23969449]]
argmax output(sparse labels) [2 1 0]
softmax_cross_entropy_with_logits by my computing for input  0 : 0.6657319553780278
softmax_cross_entropy_with_logits by my computing for input  1 : 1.4657318873121323
softmax_cross_entropy_with_logits by my computing for input  2 : 0.8283901795553891

有四种方法计算交叉熵，在正常情况下他们的值相等，但遇到极小值值时，会不一样：
    #4 methods to calculate cross entropy , First without clip to ynew ,
    #Second cliped manually
    #Third/Forth with clip inside themself , but the clip area is not clear
    cross_entropy1 = -tf.reduce_mean( tf.reduce_sum( y_*tf.log(ynew), 1 ) )
    ynew1 = tf.clip_by_value(ynew,1e-36,1.0)
    cross_entropy2 = -tf.reduce_mean( tf.reduce_sum( y_*tf.log(ynew1), 1 ) )
    cross_entropy3 = tf.reduce_mean (tf.nn.softmax_cross_entropy_with_logits_v2( logits = y3n , labels=y_ ) )
    cross_entropy4 = tf.reduce_mean (tf.nn.sparse_softmax_cross_entropy_with_logits(\
        logits = y3n , labels=tf.argmax(y_,1) ) )
cross_entropy1会溢出，cross_entropy3使用softmax_cross_entropy_with_logits_v2得到的交叉熵在极端下也是非常的大（6.72853e+30），而当我们用 cross_entropy2方法，将输入的分量限制在（1e-36,1.0)时，得到的交叉熵是个可继续训练的值（82.89307）
请看下面的代码：

#file crossEntroyTest.py

import tensorflow as tf
import math

print('exp(lar)' , math.exp( - 6.72853e+30 ) )
print(1.2e+3) 

def testCrossEbtropyNormalData() :
    y_ = tf.Variable(  [[0. , 0., 0., 0., 1., 0., 0., 0., 0., 0.],\
         [0., 0., 1. ,0., 0., 0., 0. ,0., 0., 0.]])
    ynew = tf.Variable( [[0.09775153, 0.10184532, 0.10208829, 0.0985443, \
                          0.09175218, 0.10402172,\
      0.10551486, 0.09878179, 0.10147586 ,0.09822416],\
     [0.09767619, 0.10240721, 0.09688035, 0.09931276, \
      0.09407537, 0.10758881,\
      0.10283026, 0.09836568, 0.10210507, 0.09875835]]) #ynew= tf.nn.softmax( y3n ) ,
                                                        #calculated by englishHndUsingCnn.py in NN training
    y3n = tf.Variable( [[-0.02758069,  0.01344561 , 0.01582842, \
                         -0.0195034,  -0.09091826,  0.03459012,\
       0.04884226, -0.01709634 , 0.00981142 ,-0.02275741],\
     [-0.02703298,  0.02026634, -0.03521407, -0.0104167,\
      -0.06459457,  0.06962582,\
       0.02438892, -0.01999882,  0.01731157, -0.01601485]])
                       
    cross_entropy = -tf.reduce_mean( tf.reduce_sum( y_*tf.log(ynew), 1 )    )
    cross_entropy1 = tf.reduce_mean (tf.nn.softmax_cross_entropy_with_logits_v2( logits = y3n , labels=y_ ) )
    cross_entropy2 = tf.reduce_mean (tf.nn.sparse_softmax_cross_entropy_with_logits(\
        logits = y3n , labels=tf.argmax(y_,1) ) )

    ynews = tf.nn.softmax( y3n )
    sum1 = tf.reduce_mean( tf.reduce_sum( ynews,1 )) 
    equalBool = tf.subtract( ynews , ynew )
    equalBool = tf.abs( equalBool )
    equalBool = tf.less( equalBool , 0.000001 ) 
    equalFloat = tf.cast( equalBool ,'float32')
    equNum = tf.reduce_sum( equalFloat ) 

    with tf.Session() as sess :
        sess.run( tf.global_variables_initializer() )
        r = sess.run( cross_entropy )
        print('crs' , r )
        print( 'crs1' , sess.run( cross_entropy1 ) )
        print( 'crs2' , sess.run( cross_entropy2 ) )
        ynewsR = sess.run( ynews )
        print('ynews:',  ynewsR )
        print('SoftMax' , sess.run( sum1) )  
        print('soft equal ?' , sess.run( equNum ) )
    '''
    crs 2.3614712
    crs1 2.3614712
    crs2 2.3614712
    ynews: [[0.09775153 0.10184532 0.10208829 0.0985443  0.09175218 0.10402172
      0.10551486 0.09878179 0.10147586 0.09822416]
     [0.09767619 0.10240721 0.09688035 0.09931276 0.09407537 0.10758881
      0.10283026 0.09836569 0.10210507 0.09875835]]
    SoftMax 1.0
    soft equal ? 20.0
    '''

def testCrossEbtropyAbnormalData() :
    y_ = tf.Variable(  [[0.,0.,0.,1.,0.,0.,0.,0.,0.,0.],
     [0.,0.,0.,0.,1.,0.,0.,0.,0.,0.]])
    ynew = tf.Variable(  [[0.,0.,0.,0.,0.,1.,0.,0.,0.,0.],
         [0.,0.,0.,0.,0.,1.,0.,0.,0.,0.]])
    y3n = tf.Variable( [[-2.4375510e+23 ,2.0621505e+22,-7.2626525e+23, 1.5664488e+31
,  3.5969707e+24, 1.5914237e+31,-3.2679661e+22, 2.5958722e+24
,  5.2547755e+23,-3.1578729e+31],
     [-2.0226255e+23,1.7113962e+22,-6.0270867e+23, 1.3000047e+31
,  2.9850567e+24, 1.3207314e+31,-2.7118364e+22, 2.1541442e+24
,  4.3611144e+23,-2.6207365e+31]])

    #4 methods to calculate cross entropy , First without clip to ynew ,
    #Second cliped manually
    #Third/Forth with clip inside themself , but the clip area is not clear
    cross_entropy1 = -tf.reduce_mean( tf.reduce_sum( y_*tf.log(ynew), 1 ) )
    ynew1 = tf.clip_by_value(ynew,1e-36,1.0)
    cross_entropy2 = -tf.reduce_mean( tf.reduce_sum( y_*tf.log(ynew1), 1 ) )
    cross_entropy3 = tf.reduce_mean (tf.nn.softmax_cross_entropy_with_logits_v2( logits = y3n , labels=y_ ) )
    cross_entropy4 = tf.reduce_mean (tf.nn.sparse_softmax_cross_entropy_with_logits(\
        logits = y3n , labels=tf.argmax(y_,1) ) )

    ynews = tf.nn.softmax( y3n )
    sum1 = tf.reduce_mean( tf.reduce_sum( ynews,1 )) 
    equalBool = tf.subtract( ynews , ynew )
    equalBool = tf.abs( equalBool )
    equalBool = tf.less( equalBool , 0.000001 ) 
    equalFloat = tf.cast( equalBool ,'float32')
    equNum = tf.reduce_sum( equalFloat ) 

    with tf.Session() as sess :
        sess.run( tf.global_variables_initializer() )
        print( 'crs1' , sess.run( cross_entropy1 ) )
        print( 'crs2' , sess.run( cross_entropy2 ) )
        print( 'crs3' , sess.run( cross_entropy3 ) )
        print( 'crs4' , sess.run( cross_entropy4 ) )
        ynewsR = sess.run( ynews )
        print('ynews:',  ynewsR )
        print('SoftMax' , sess.run( sum1) )  
        print('soft equal ?' , sess.run( equNum ) )
    '''
    soft equal ? 20.0
    crs1 nan
    crs2 82.89307
    crs3 6.72853e+30
    crs4 6.72853e+30
    ynews: [[0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
     [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]]
    SoftMax 1.0
    soft equal ? 20.0
    '''
                           
testCrossEbtropyNormalData()
testCrossEbtropyAbnormalData()