本文是初學keras這兩天來，自己仿照addition_rnn.py，寫的一個例項，資料處理稍微有些不同，但是準確性相比addition_rnn.py 差一點，下面直接貼程式碼，
解釋和註釋都在程式碼裡邊。

<span style="font-family: Arial, Helvetica, sans-serif;">#coding:utf-8</span>

from keras.models import  Sequential
from keras.layers.recurrent import LSTM
from utils import  log
from numpy import random
import numpy as np
from  keras.layers.core import RepeatVector, TimeDistributedDense, Activation

'''
先用lstm實現一個計算加法的keras版本, 根據addition_rnn.py改寫
size: 500
10次: test_acu = 0.3050  base_acu= 0.3600
30次: rest_acu = 0.3300  base_acu= 0.4250
size: 50000
10次: test_acu: loss: 0.4749 - acc: 0.8502 - val_loss: 0.4601 - val_acc: 0.8539
      base_acu: loss: 0.3707 - acc: 0.9008 - val_loss: 0.3327 - val_acc: 0.9135
20次: test_acu: loss: 0.1536 - acc: 0.9505 - val_loss: 0.1314 - val_acc: 0.9584
      base_acu: loss: 0.0538 - acc: 0.9891 - val_loss: 0.0454 - val_acc: 0.9919
30次: test_acu: loss: 0.0671 - acc: 0.9809 - val_loss: 0.0728 - val_acc: 0.9766
      base_acu: loss: 0.0139 - acc: 0.9980 - val_loss: 0.0502 - val_acc: 0.9839
'''

log = log()
#defination the global variable
training_size = 50000
hidden_size = 128
batch_size = 128
layers = 1

maxlen = 7
single_digit = 3


def generate_data():
    log.info("generate the questions and answers")
    questions = []
    expected = []
    seen = set()
    while len(seen) < training_size:
        num1 = random.randint(1, 999) #generate a num [1,999]
        num2 = random.randint(1, 999)
        #用set來儲存又有排序,來保證只有不同資料和結果
        key  = tuple(sorted((num1,num2)))
        if key in seen:
            continue
        seen.add(key)
        q = '{}+{}'.format(num1,num2)
        query = q + ' ' * (maxlen - len(q))
        ans = str(num1 + num2)
        ans = ans + ' ' * (single_digit + 1 - len(ans))
        questions.append(query)
        expected.append(ans)
    return questions, expected

class CharacterTable():
    '''
    encode: 將一個str轉化為一個n維陣列
    decode: 將一個n為陣列轉化為一個str
    輸入輸出分別為
    character_table =  [' ', '+', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
    如果一個question = [' 123+23']
    那個改question對應的陣列就是(7,12):
    同樣expected最大是一個四位數[' 146']:
    那麼ans對應的陣列就是[4,12]
    '''
    def __init__(self, chars, maxlen):
        self.chars = sorted(set(chars))
        '''
        >>> b = [(c, i) for i, c in enumerate(a)]
        >>> dict(b)
        {' ': 0, '+': 1, '1': 3, '0': 2, '3': 5, '2': 4, '5': 7, '4': 6, '7': 9, '6': 8, '9': 11, '8': 10}
        得出的結果是無序的,但是下面這種方式得出的結果是有序的
        '''
        self.char_index = dict((c, i) for i, c in enumerate(self.chars))
        self.index_char = dict((i, c) for i, c in enumerate(self.chars))
        self.maxlen = maxlen

    def encode(self, C, maxlen):
        X = np.zeros((maxlen, len(self.chars)))
        for i, c in enumerate(C):
            X[i, self.char_index[c]] = 1
        return X

    def decode(self, X, calc_argmax=True):
        if calc_argmax:
            X = X.argmax(axis=-1)
        return ''.join(self.index_char[x] for x in X)

chars = '0123456789 +'
character_table = CharacterTable(chars,len(chars))

questions , expected = generate_data()

log.info('Vectorization...') #失量化
inputs = np.zeros((len(questions), maxlen, len(chars))) #(5000, 7, 12)
labels = np.zeros((len(expected), single_digit+1, len(chars))) #(5000, 4, 12)

log.info("encoding the questions and get inputs")
for i, sentence in enumerate(questions):
    inputs[i] = character_table.encode(sentence, maxlen=len(sentence))
#print("questions is ", questions[0])
#print("X is ", inputs[0])
log.info("encoding the expected and get labels")
for i, sentence in enumerate(expected):
    labels[i] = character_table.encode(sentence, maxlen=len(sentence))
#print("expected is ", expected[0])
#print("y is ", labels[0])

log.info("total inputs is %s"%str(inputs.shape))
log.info("total labels is %s"%str(labels.shape))

log.info("build model")
model = Sequential()
'''
LSTM(output_dim, init='glorot_uniform', inner_init='orthogonal',
                 forget_bias_init='one', activation='tanh',
                 inner_activation='hard_sigmoid',
                 W_regularizer=None, U_regularizer=None, b_regularizer=None,
                 dropout_W=0., dropout_U=0., **kwargs)
output_dim: 輸出層的維數,或者可以用output_shape
init:
    uniform(scale=0.05) :均勻分佈，最常用的。Scale就是均勻分佈的每個資料在-scale~scale之間。此處就是-0.05~0.05。scale預設值是0.05；
    lecun_uniform:是在LeCun在98年發表的論文中基於uniform的一種方法。區別就是lecun_uniform的scale=sqrt(3/f_in)。f_in就是待初始化權值矩陣的行。
    normal：正態分佈（高斯分佈)。
    Identity ：用於2維方陣，返回一個單位陣.
    Orthogonal：用於2維方陣，返回一個正交矩陣. lstm預設
    Zero：產生一個全0矩陣。
    glorot_normal：基於normal分佈，normal的預設 sigma^2=scale=0.05，而此處sigma^2=scale=sqrt(2 / (f_in+ f_out))，其中，f_in和f_out是待初始化矩陣的行和列。
    glorot_uniform：基於uniform分佈，uniform的預設scale=0.05，而此處scale=sqrt( 6 / (f_in +f_out)) ，其中，f_in和f_out是待初始化矩陣的行和列。
W_regularizer , b_regularizer  and activity_regularizer:
    官方文件: http://keras.io/regularizers/
    from keras.regularizers import l2, activity_l2
    model.add(Dense(64, input_dim=64, W_regularizer=l2(0.01), activity_regularizer=activity_l2(0.01)))

    加入規則項主要是為了在小樣本資料下過擬合現象的發生,我們都知道,一半在訓練過程中解決過擬合現象的方法主要中兩種,一種是加入規則項(權值衰減), 第二種是加大資料量
    很顯然,加大資料量一般是不容易的,而加入規則項則比較容易,所以在發生過擬合的情況下,我們一般都採用加入規則項來解決這個問題.

'''
model.add(LSTM(hidden_size, input_shape=(maxlen, len(chars)))) #(7,12) 輸入層
'''
keras.layers.core.RepeatVector(n)
       把1維的輸入重複n次。假設輸入維度為(nb_samples, dim)，那麼輸出shape就是(nb_samples, n, dim)
       inputshape: 任意。當把這層作為某個模型的第一層時，需要用到該引數（元組，不包含樣本軸）。
       outputshape：(nb_samples,nb_input_units)
'''
model.add(RepeatVector(single_digit + 1))
#表示有多少個隱含層
for _ in range(layers):
    model.add(LSTM(hidden_size, return_sequences=True))
'''
TimeDistributedDense:
官方文件:http://keras.io/layers/core/#timedistributeddense

keras.layers.core.TimeDistributedDense(output_dim,init='glorot_uniform', activation='linear', weights=None
W_regularizer=None, b_regularizer=None, activity_regularizer=None, W_constraint=None, b_constraint=None,
input_dim=None, input_length=None)
這是一個基於時間維度的全連線層。主要就是用來構建RNN(遞迴神經網路)的，但是在構建RNN時需要設定return_sequences=True。
for example:
# input shape: (nb_samples, timesteps,10)
model.add(LSTM(5, return_sequences=True, input_dim=10)) # output shape: (nb_samples, timesteps, 5)
model.add(TimeDistributedDense(15)) # output shape:(nb_samples, timesteps, 15)
W_constraint:
    from keras.constraints import maxnorm
    model.add(Dense(64, W_constraint =maxnorm(2))) #限制權值的各個引數不能大於2
'''
model.add(TimeDistributedDense(len(chars)))
model.add(Activation('softmax'))
'''
關於目標函式和優化函式,參考另外一片博文: http://blog.csdn.net/zjm750617105/article/details/51321915
'''
model.compile(loss='categorical_crossentropy',
              optimizer='adam',
              metrics=['accuracy'])

# Train the model each generation and show predictions against the validation dataset
for iteration in range(1, 3):
    print()
    print('-' * 50)
    print('Iteration', iteration)
    model.fit(inputs, labels, batch_size=batch_size, nb_epoch=2,
              validation_split = 0.1)
    # Select 10 samples from the validation set at random so we can visualize errors
model.get_config()