text: # LSTM for international airline passengers problem with regression framing
  import numpy
  import matplotlib.pyplot as plt
  from pandas import read_csv
  import math
  from keras.models import Sequential
  from keras.layers import Dense
  from keras.layers import LSTM
  from sklearn.preprocessing import MinMaxScaler
  from sklearn.metrics import mean_squared_error
  # convert an array of values into a dataset matrix
  def create_dataset(dataset, look_back=1):
  	dataX, dataY = [], []
  	for i in range(len(dataset)-look_back-1):
  		a = dataset[i:(i+look_back), 0]
  		dataX.append(a)
  		dataY.append(dataset[i + look_back, 0])
  	return numpy.array(dataX), numpy.array(dataY)
  # fix random seed for reproducibility
  numpy.random.seed(7)
  # load the dataset
  dataframe = read_csv('airline-passengers.csv', usecols=[1], engine='python')
  dataset = dataframe.values
  dataset = dataset.astype('float32')
  # normalize the dataset
  scaler = MinMaxScaler(feature_range=(0, 1))
  dataset = scaler.fit_transform(dataset)
  # split into train and test sets
  train_size = int(len(dataset) * 0.67)
  test_size = len(dataset) - train_size
  train, test = dataset[0:train_size,:], dataset[train_size:len(dataset),:]
  # reshape into X=t and Y=t+1
  look_back = 1
  trainX, trainY = create_dataset(train, look_back)
  testX, testY = create_dataset(test, look_back)
  # reshape input to be [samples, time steps, features]
  trainX = numpy.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))
  testX = numpy.reshape(testX, (testX.shape[0], 1, testX.shape[1]))
  # create and fit the LSTM network
  model = Sequential()
  model.add(LSTM(4, input_shape=(1, look_back)))
  model.add(Dense(1))
  model.compile(loss='mean_squared_error', optimizer='adam')
  model.fit(trainX, trainY, epochs=100, batch_size=1, verbose=2)
  # make predictions
  trainPredict = model.predict(trainX)
  testPredict = model.predict(testX)
  # invert predictions
  trainPredict = scaler.inverse_transform(trainPredict)
  trainY = scaler.inverse_transform([trainY])
  testPredict = scaler.inverse_transform(testPredict)
  testY = scaler.inverse_transform([testY])
  # calculate root mean squared error
  trainScore = math.sqrt(mean_squared_error(trainY[0], trainPredict[:,0]))
  print('Train Score: %.2f RMSE' % (trainScore))
  testScore = math.sqrt(mean_squared_error(testY[0], testPredict[:,0]))
  print('Test Score: %.2f RMSE' % (testScore))
  # shift train predictions for plotting
  trainPredictPlot = numpy.empty_like(dataset)
  trainPredictPlot[:, :] = numpy.nan
  trainPredictPlot[look_back:len(trainPredict)+look_back, :] = trainPredict
  # shift test predictions for plotting
  testPredictPlot = numpy.empty_like(dataset)
  testPredictPlot[:, :] = numpy.nan
  testPredictPlot[len(trainPredict)+(look_back*2)+1:len(dataset)-1, :] = testPredict
  # plot baseline and predictions
  plt.plot(scaler.inverse_transform(dataset))
  plt.plot(trainPredictPlot)
  plt.plot(testPredictPlot)
  plt.show()
  