prediction_time_series_pain.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction of time-series \n",
    "\n",
    "We use LSTM network for regression methods of time-series.\n",
    "\n",
    "For other ways of time-series analysis and prediction see.\n",
    "https://github.com/2wavetech/Time-Series-Analysis-and-Prediction\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       "      <th>basisPeakSteps</th>\n",
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       "      <th>handsAndFingerPain</th>\n",
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       "      <th>aroundEyesPain</th>\n",
       "      <th>shoulderNeckPain</th>\n",
       "      <th>...</th>\n",
       "      <th>walk</th>\n",
       "      <th>roadBike</th>\n",
       "      <th>mountainBike</th>\n",
       "      <th>swimming</th>\n",
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       "      <th>alpiSki</th>\n",
       "      <th>downSki</th>\n",
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       "    </tr>\n",
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      ],
      "text/plain": [
       "   Unnamed: 0  basisPeakSteps  steps  denivelation  kneePain  \\\n",
       "0  2015-11-19             0.0    0.0           0.0       0.0   \n",
       "1  2015-11-20             0.0    0.0           0.0       0.0   \n",
       "2  2015-11-21             0.0    0.0           0.0       0.0   \n",
       "3  2015-11-22             0.0    0.0           0.0       0.0   \n",
       "4  2015-11-23             0.0    0.0           0.0       0.0   \n",
       "5  2015-11-24             0.0    0.0           0.0       0.0   \n",
       "6  2015-11-25             0.0    0.0           0.0       5.7   \n",
       "7  2015-11-26             0.0    0.0           0.0       5.0   \n",
       "8  2015-11-27             0.0    0.0           0.0       5.0   \n",
       "9  2015-11-28             0.0    0.0           0.0       6.0   \n",
       "\n",
       "   handsAndFingerPain  foreheadAndEyesPain  forearmElbowPain  aroundEyesPain  \\\n",
       "0                 0.0                  0.0               0.0             0.0   \n",
       "1                 0.0                  0.0               0.0             0.0   \n",
       "2                 0.0                  0.0               0.0             0.0   \n",
       "3                 0.0                  0.0               0.0             0.0   \n",
       "4                 0.0                  0.0               0.0             0.0   \n",
       "5                 0.0                  0.0               0.0             0.0   \n",
       "6                 3.0                  3.0               0.0             0.0   \n",
       "7                 2.8                  3.9               0.0             0.0   \n",
       "8                 2.8                  3.9               0.0             0.0   \n",
       "9                 2.0                  2.0               0.0             0.0   \n",
       "\n",
       "   shoulderNeckPain  ...  walk  roadBike  mountainBike  swimming  surfing  \\\n",
       "0               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "1               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "2               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "3               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "4               0.0  ...   0.0       1.0           0.0       0.0      0.0   \n",
       "5               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "6               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "7               0.0  ...   1.0       0.0           0.0       0.0      0.0   \n",
       "8               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "9               0.0  ...   0.0       0.0           0.0       0.0      0.0   \n",
       "\n",
       "   climbing  viaFerrata  alpiSki  downSki  eyeRelatedActivities  \n",
       "0       0.0         0.0      0.0      0.0                   0.0  \n",
       "1       0.0         0.0      0.0      0.0                   0.0  \n",
       "2       0.0         0.0      0.0      0.0                   0.0  \n",
       "3       0.0         0.0      0.0      0.0                   0.0  \n",
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       "6       0.0         0.0      0.0      0.0                   7.0  \n",
       "7       0.0         0.0      0.0      0.0                   0.0  \n",
       "8       0.0         0.0      0.0      0.0                   0.0  \n",
       "9       0.0         0.0      0.0      0.0                 105.0  \n",
       "\n",
       "[10 rows x 34 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "import pandas as pd\n",
    "import csv\n",
    "#import plotly.plotly as py\n",
    "#import plotly.graph_objs as go\n",
    "\n",
    "\n",
    "filepath = \"C:/Users/lyubo/Documents/DATA_networks/patients_data/MonsterMizer-master/MonsterMizerOpenData/\"#'C:/Users/tupikina/Documents/Python_Scripts/MonsterMizer-master'\n",
    "\n",
    "df = pd.read_csv(filepath +'data_patients.csv')\n",
    "df.head(10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Method using LSTM\n",
    "\n",
    "We rephrase the problem as a regression problem for prediction of time-series using LSTM network for regression.\n",
    "\n",
    "Given the time-series of pain level P(t), what is the expected pain level next day? \n",
    "\n",
    "We can write a simple function to convert our single column of data P(t) into a two-column dataset: the first column containing this month's P(t) and the second column containing next month's (t+1) pain to be predicted.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas\n",
    "import math\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import LSTM\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use TensorFlow backend.\n",
    "\n",
    "We fix the random number seed to ensure our results are reproducible.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fix random seed for reproducibility\n",
    "seed = numpy.random.seed(7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preprocess data to needed format \n",
    "\n",
    "LSTMs are sensitive to the scale of the input data, specifically when the sigmoid (default) or tanh activation functions are used. It can be a good practice to rescale the data to the range of 0-to-1, also called normalizing. We can easily normalize the dataset using the MinMaxScaler preprocessing class from the scikit-learn library.\n",
    "\n",
    "Initially we have the array *pain* non-rescaled from 0 to 5 (with some missing values), while *activity* is rescaled from 0 to 1.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calculating time series for pain\n",
      "nonzero steps 1118\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "\n",
    "'''tp.plot_timeseries(data, datatime, var_names)'''\n",
    "#array = df.values\n",
    "#print(type(dataframe.values))\n",
    "#print(array.shape)\n",
    "print('calculating time series for pain')\n",
    "\n",
    "pain = df.kneePain.values #array[:,3]\n",
    "activity = df.walk.values #array[:,1] or for walk \n",
    "steps = df.steps.values\n",
    "\n",
    "array = np.zeros((3,np.shape(pain)[0]))\n",
    "array[0,:] = pain\n",
    "array[1,:] = steps\n",
    "print('nonzero steps', np.count_nonzero(array[1,:]))\n",
    "#print(array[0,7])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normalize the dataset\n",
    "We normalise and cut dataset (exclude first elements which are zero records)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nonzero elements 1431\n",
      "nonzero elements 1118\n",
      "first nonzero element 6\n",
      "cut array 1454\n",
      "cutting 287 zero values for array\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data_range = (0, 1)\n",
    "scaler = MinMaxScaler(feature_range=data_range)        # scaler can also de-normalize the dataset by scaler.inverse_transform(), useful for actual prediction\n",
    "# scaling works by the formula X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))\n",
    "# now we scale array with several variables in it\n",
    "#array_scaled = scaler.fit_transform(array)  #pain.reshape(-1, 1)# scaler.fit_transform(pain_array) # for 2D array\n",
    "\n",
    "plt.title('non-rescaled data')\n",
    "plt.plot(array[0,:])\n",
    "plt.plot(array[1,:])\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#print('total shape', array_scaled[0,:].shape)\n",
    "# here we check that we get only nonzero elements in rescaled data if we have nonzero element in original dat\n",
    "print('nonzero elements', np.count_nonzero(array[0,:]))\n",
    "print('nonzero elements', np.count_nonzero(array[1,:]))\n",
    "#print('nonzero elements', np.count_nonzero(array_scaled[0,:]))\n",
    "#print('nonzero elements', np.count_nonzero(array_scaled[1,:]))\n",
    "\n",
    "\n",
    "n_nnz = (array[0,:]!=0).argmax(axis=0)\n",
    "print('first nonzero element', (array[0,:]!=0).argmax(axis=0))\n",
    "print('cut array', np.shape(array)[1] - n_nnz)\n",
    "\n",
    "print('cutting 287 zero values for array')\n",
    "cut_array = np.zeros((3, np.shape(array)[1] - n_nnz))\n",
    "cut_array[0,:] = array[0,n_nnz:np.shape(array)[1]]\n",
    "#cut_array[1,:] = array[1,287:1431]\n",
    "\n",
    "plt.title('cut data')\n",
    "plt.plot(cut_array[0,:])\n",
    "plt.plot(cut_array[1,:])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lyubo\\Anaconda3\\envs\\default\\lib\\site-packages\\ipykernel_launcher.py:5: RuntimeWarning: invalid value encountered in true_divide\n",
      "  \"\"\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "normalised\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "array_scaled = cut_array\n",
    "\n",
    "# normalize the dataset in alternative way: devide by the maximum array element:\n",
    "array_scaled[0, :] =  cut_array[0, :]* 1./max(cut_array[0, :]) ##X_std = (X ) / (X.max(axis=0))\n",
    "array_scaled[1, :] =  cut_array[1, :]* 1./max(cut_array[1, :]) ##X_std = (X ) / (X.max(axis=0))\n",
    "\n",
    "print('normalised')\n",
    "\n",
    "plt.title('cut rescaled data')\n",
    "plt.plot(array_scaled[0,:])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# split into train and test sets\n",
    "\n",
    "A simple method that we can use is to split the ordered dataset into train and test datasets. The code below calculates the index of the split point and separates the data into the training datasets with 67% of the observations that we can use to train our model, leaving the remaining 33% for testing the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "974 480\n"
     ]
    }
   ],
   "source": [
    "# split into train and test sets\n",
    "\n",
    "train_size = int(len(array_scaled[0,:]) * 0.67)\n",
    "test_size = len(array_scaled[0,:]) - train_size\n",
    "\n",
    "\n",
    "train, test = array_scaled[0,0:train_size], array_scaled[0,train_size:len(array_scaled[0,:])]\n",
    "print(len(train), len(test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can define a function to create a new dataset, as described above.\n",
    "\n",
    "The function takes two arguments: the dataset, which is a NumPy array that we want to convert into a dataset, and the look_back, which is the number of previous time steps to use as input variables to predict the next time period in this case defaulted to 1.\n",
    "\n",
    "This default will create a dataset where X is the pain level at a given time (t) and Y is the pain level at the next time (t + 1).\n",
    "\n",
    "It can be configured, and we will by constructing a differently shaped dataset in the next section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert an array of values into a dataset matrix\n",
    "def create_dataset(data, look_back=1):\n",
    "    dataX, dataY = [], []\n",
    "    i_range = len(data) - look_back - 1\n",
    "    print(i_range)\n",
    "    for i in range(0, i_range):\n",
    "        dataX.append(data[i:(i+look_back)])    # index can move down to len(dataset)-1\n",
    "        dataY.append(data[i + look_back])      # Y is the item that skips look_back number of items\n",
    "    \n",
    "    return numpy.array(dataX), numpy.array(dataY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1449\n",
      "shape of datax (1449, 4) (1449,)\n"
     ]
    }
   ],
   "source": [
    "look_back = 4\n",
    "\n",
    "dataX, dataY = create_dataset(array_scaled[0,:], look_back=look_back)\n",
    "print('shape of datax', np.shape(dataX), np.shape(dataY))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X shape: (1449, 4)\n",
      "Y shape: (1449,)\n",
      "Xt-3     Xt-2      Xt-1      Xt        Y\n",
      "---------------------------------------------\n",
      "for look back steps 4\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.8769230769230769 0.7692307692307693 0.7692307692307693 0.9230769230769231 0.6\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7692307692307693 0.7692307692307693 0.9230769230769231 0.6 0.7692307692307693\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7692307692307693 0.9230769230769231 0.6 0.7692307692307693 0.7230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.9230769230769231 0.6 0.7692307692307693 0.7230769230769231 0.7230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6 0.7692307692307693 0.7230769230769231 0.7230769230769231 0.5692307692307692\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7692307692307693 0.7230769230769231 0.7230769230769231 0.5692307692307692 0.5384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7230769230769231 0.7230769230769231 0.5692307692307692 0.5384615384615384 0.6923076923076923\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7230769230769231 0.5692307692307692 0.5384615384615384 0.6923076923076923 0.7692307692307693\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5692307692307692 0.5384615384615384 0.6923076923076923 0.7692307692307693 0.6923076923076923\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5384615384615384 0.6923076923076923 0.7692307692307693 0.6923076923076923 0.6153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6923076923076923 0.7692307692307693 0.6923076923076923 0.6153846153846154 0.6153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7692307692307693 0.6923076923076923 0.6153846153846154 0.6153846153846154 0.6153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6923076923076923 0.6153846153846154 0.6153846153846154 0.6153846153846154 0.6153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6153846153846154 0.6153846153846154 0.6153846153846154 0.6153846153846154 0.6153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6153846153846154 0.6153846153846154 0.6153846153846154 0.6153846153846154 0.7692307692307693\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6153846153846154 0.6153846153846154 0.6153846153846154 0.7692307692307693 0.6153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6153846153846154 0.6153846153846154 0.7692307692307693 0.6153846153846154 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6153846153846154 0.7692307692307693 0.6153846153846154 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7692307692307693 0.6153846153846154 0.46153846153846156 0.46153846153846156 0.3076923076923077\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6153846153846154 0.46153846153846156 0.46153846153846156 0.3076923076923077 0.38461538461538464\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.3076923076923077 0.38461538461538464 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.3076923076923077 0.38461538461538464 0.43076923076923074 0.38461538461538464\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.3076923076923077 0.38461538461538464 0.43076923076923074 0.38461538461538464 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.38461538461538464 0.43076923076923074 0.38461538461538464 0.43076923076923074 0.6923076923076923\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.38461538461538464 0.43076923076923074 0.6923076923076923 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.38461538461538464 0.43076923076923074 0.6923076923076923 0.46153846153846156 0.6923076923076923\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.6923076923076923 0.46153846153846156 0.6923076923076923 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6923076923076923 0.46153846153846156 0.6923076923076923 0.43076923076923074 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.6923076923076923 0.43076923076923074 0.46153846153846156 0.7384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6923076923076923 0.43076923076923074 0.46153846153846156 0.7384615384615384 0.6461538461538462\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.46153846153846156 0.7384615384615384 0.6461538461538462 0.9076923076923078\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.7384615384615384 0.6461538461538462 0.9076923076923078 0.6615384615384615\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.7384615384615384 0.6461538461538462 0.9076923076923078 0.6615384615384615 0.9230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6461538461538462 0.9076923076923078 0.6615384615384615 0.9230769230769231 1.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.9076923076923078 0.6615384615384615 0.9230769230769231 1.0 0.8923076923076922\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6615384615384615 0.9230769230769231 1.0 0.8923076923076922 0.6923076923076923\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.9230769230769231 1.0 0.8923076923076922 0.6923076923076923 0.6923076923076923\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 1.0 0.8923076923076922 0.6923076923076923 0.6923076923076923 0.5384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.8923076923076922 0.6923076923076923 0.6923076923076923 0.5384615384615384 0.5384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6923076923076923 0.6923076923076923 0.5384615384615384 0.5384615384615384 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6923076923076923 0.5384615384615384 0.5384615384615384 0.5230769230769231 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5384615384615384 0.5384615384615384 0.5230769230769231 0.49230769230769234 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5384615384615384 0.5230769230769231 0.49230769230769234 0.43076923076923074 0.38461538461538464\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.49230769230769234 0.43076923076923074 0.38461538461538464 0.38461538461538464\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.43076923076923074 0.38461538461538464 0.38461538461538464 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.38461538461538464 0.38461538461538464 0.46153846153846156 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.38461538461538464 0.38461538461538464 0.46153846153846156 0.4461538461538461 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.38461538461538464 0.46153846153846156 0.4461538461538461 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.4461538461538461 0.46153846153846156 0.46153846153846156 0.5384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.46153846153846156 0.46153846153846156 0.5384615384615384 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.5384615384615384 0.49230769230769234 0.6\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.5384615384615384 0.49230769230769234 0.6 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5384615384615384 0.49230769230769234 0.6 0.43076923076923074 0.5846153846153845\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.6 0.43076923076923074 0.5846153846153845 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.6 0.43076923076923074 0.5846153846153845 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.5846153846153845 0.46153846153846156 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5846153846153845 0.46153846153846156 0.46153846153846156 0.46153846153846156 0.5076923076923077\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.46153846153846156 0.5076923076923077 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.5076923076923077 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.5076923076923077 0.46153846153846156 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5076923076923077 0.46153846153846156 0.46153846153846156 0.46153846153846156 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.46153846153846156 0.49230769230769234 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.49230769230769234 0.49230769230769234 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.49230769230769234 0.49230769230769234 0.5230769230769231 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.49230769230769234 0.5230769230769231 0.49230769230769234 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.5230769230769231 0.49230769230769234 0.4461538461538461 0.5384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.49230769230769234 0.4461538461538461 0.5384615384615384 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.4461538461538461 0.5384615384615384 0.43076923076923074 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.5384615384615384 0.43076923076923074 0.49230769230769234 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5384615384615384 0.43076923076923074 0.49230769230769234 0.49230769230769234 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.49230769230769234 0.49230769230769234 0.5230769230769231 0.5076923076923077\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.49230769230769234 0.5230769230769231 0.5076923076923077 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.5230769230769231 0.5076923076923077 0.43076923076923074 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.5076923076923077 0.43076923076923074 0.46153846153846156 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5076923076923077 0.43076923076923074 0.46153846153846156 0.4461538461538461 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.46153846153846156 0.4461538461538461 0.46153846153846156 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.4461538461538461 0.46153846153846156 0.4461538461538461 0.5076923076923077\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.46153846153846156 0.4461538461538461 0.5076923076923077 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.4461538461538461 0.5076923076923077 0.46153846153846156 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.5076923076923077 0.46153846153846156 0.49230769230769234 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5076923076923077 0.46153846153846156 0.49230769230769234 0.5230769230769231 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.49230769230769234 0.5230769230769231 0.0 0.5538461538461539\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.5230769230769231 0.0 0.5538461538461539 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.0 0.5538461538461539 0.5230769230769231 0.5076923076923077\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.5538461538461539 0.5230769230769231 0.5076923076923077 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5538461538461539 0.5230769230769231 0.5076923076923077 0.5230769230769231 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.5076923076923077 0.5230769230769231 0.46153846153846156 0.5538461538461539\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5076923076923077 0.5230769230769231 0.46153846153846156 0.5538461538461539 0.5384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.46153846153846156 0.5538461538461539 0.5384615384615384 0.5538461538461539\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.5538461538461539 0.5384615384615384 0.5538461538461539 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5538461538461539 0.5384615384615384 0.5538461538461539 0.5230769230769231 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5384615384615384 0.5538461538461539 0.5230769230769231 0.5230769230769231 0.5538461538461539\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5538461538461539 0.5230769230769231 0.5230769230769231 0.5538461538461539 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.5230769230769231 0.5538461538461539 0.4461538461538461 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.5538461538461539 0.4461538461538461 0.46153846153846156 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5538461538461539 0.4461538461538461 0.46153846153846156 0.49230769230769234 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.46153846153846156 0.49230769230769234 0.5230769230769231 0.5230769230769231\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.49230769230769234 0.5230769230769231 0.5230769230769231 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.5230769230769231 0.5230769230769231 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.5230769230769231 0.46153846153846156 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5230769230769231 0.46153846153846156 0.46153846153846156 0.46153846153846156 0.47692307692307695\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.46153846153846156 0.47692307692307695 0.5384615384615384\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.47692307692307695 0.5384615384615384 0.5076923076923077\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.47692307692307695 0.5384615384615384 0.5076923076923077 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.47692307692307695 0.5384615384615384 0.5076923076923077 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.5384615384615384 0.5076923076923077 0.46153846153846156 0.46153846153846156 0.46153846153846156\n",
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      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4153846153846154 0.43076923076923074 0.47692307692307695 0.43076923076923074 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.47692307692307695 0.43076923076923074 0.43076923076923074 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.47692307692307695 0.43076923076923074 0.43076923076923074 0.43076923076923074 0.4\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.43076923076923074 0.43076923076923074 0.4 0.4\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.43076923076923074 0.4 0.4 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.4 0.4 0.43076923076923074 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4 0.4 0.43076923076923074 0.43076923076923074 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4 0.43076923076923074 0.43076923076923074 0.46153846153846156 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.43076923076923074 0.46153846153846156 0.46153846153846156 0.47692307692307695\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.46153846153846156 0.46153846153846156 0.47692307692307695 0.46153846153846156\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.46153846153846156 0.47692307692307695 0.46153846153846156 0.4153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.47692307692307695 0.46153846153846156 0.4153846153846154 0.4153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.47692307692307695 0.46153846153846156 0.4153846153846154 0.4153846153846154 0.49230769230769234\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.46153846153846156 0.4153846153846154 0.4153846153846154 0.49230769230769234 0.47692307692307695\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4153846153846154 0.4153846153846154 0.49230769230769234 0.47692307692307695 0.47692307692307695\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4153846153846154 0.49230769230769234 0.47692307692307695 0.47692307692307695 0.47692307692307695\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.49230769230769234 0.47692307692307695 0.47692307692307695 0.47692307692307695 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.47692307692307695 0.47692307692307695 0.47692307692307695 0.4461538461538461 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.47692307692307695 0.47692307692307695 0.4461538461538461 0.4461538461538461 0.43076923076923074\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.47692307692307695 0.4461538461538461 0.4461538461538461 0.43076923076923074 0.4153846153846154\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.4461538461538461 0.43076923076923074 0.4153846153846154 0.47692307692307695\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.43076923076923074 0.4153846153846154 0.47692307692307695 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.43076923076923074 0.4153846153846154 0.47692307692307695 0.4461538461538461 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4153846153846154 0.47692307692307695 0.4461538461538461 0.4461538461538461 0.4461538461538461\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.47692307692307695 0.4461538461538461 0.4461538461538461 0.4461538461538461 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.4461538461538461 0.4461538461538461 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.4461538461538461 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.4461538461538461 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n",
      "%.2f   %.2f    %.2f    %.2f    %.2f 0.0 0.0 0.0 0.0 0.0\n"
     ]
    }
   ],
   "source": [
    "print(\"X shape:\", dataX.shape)\n",
    "print(\"Y shape:\", dataY.shape)\n",
    "   \n",
    "print(\"Xt-3     Xt-2      Xt-1      Xt        Y\")\n",
    "print(\"---------------------------------------------\")\n",
    "print('for look back steps', look_back)\n",
    "\n",
    "\n",
    "for i in range(len(dataX)): \n",
    "    print('%.2f   %.2f    %.2f    %.2f    %.2f', dataX[i,0],dataX[i,1],dataX[i,2],dataX[i,3], dataY[i])\n",
    "#    print('%.2f   %.2f    %.2f    %.2f    %.2f' % (dataX[i][0][0], dataX[i][1][0], dataX[i][2][0], dataX[i][3][0], dataY[i][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X shape: (1449, 1, 4)\n"
     ]
    }
   ],
   "source": [
    "# Reshape to (samples, timestep, features)\n",
    "dataX = numpy.reshape(dataX, (dataX.shape[0], 1, dataX.shape[1]))\n",
    "\n",
    "print(\"X shape:\", dataX.shape) #X shape: (1455, 1, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "972\n",
      "478\n"
     ]
    }
   ],
   "source": [
    "# Let's use this function to prepare the train and test datasets for modeling.\n",
    "\n",
    "# reshape into X=t and Y=t+1\n",
    "look_back = 1\n",
    "trainX, trainY = create_dataset(train, look_back)      # trainX is input, trainY is expected output\n",
    "testX, testY = create_dataset(test, look_back)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The LSTM network expects the input data (X) to be provided with a specific array structure in the form of 3D: [samples, time steps, features], or in other words, 3D tensor with shape (batch_size, timesteps, input_dim), or optionally, 2D tensors with shape (batch_size, output_dim).\n",
    "\n",
    "Currently, our data is in the form: [samples, features] and we are framing the problem as one time step for each sample. We can transform the prepared train and test input data into the expected structure using numpy.reshape() as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original trainX shape: (972, 1)\n",
      "New trainX shape: (972, 1, 1)\n",
      "trainY shape: (972,)\n",
      "trainY example: 0.7692307692307693\n"
     ]
    }
   ],
   "source": [
    "# reshape input to be [samples, time steps, features]\n",
    "print(\"Original trainX shape:\", trainX.shape)\n",
    "trainX = numpy.reshape(trainX, (trainX.shape[0], look_back, trainX.shape[1]))     # timestep = 1, input_dim = trainX.shape[1]\n",
    "testX = numpy.reshape(testX, (testX.shape[0], look_back, testX.shape[1]))\n",
    "print(\"New trainX shape:\", trainX.shape)\n",
    "print(\"trainY shape:\", trainY.shape)\n",
    "print(\"trainY example:\", trainY[0])\n",
    "\n",
    "#Old input Original trainX shape: (976, 1, 1)\n",
    "#New trainX shape: (976, 1, 1)\n",
    "#trainY shape: (976, 1)\n",
    "#trainY example: [0.0]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LSTM fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/50\n",
      " - 4s - loss: 0.0149\n",
      "Epoch 2/50\n",
      " - 3s - loss: 0.0033\n",
      "Epoch 3/50\n",
      " - 2s - loss: 0.0028\n",
      "Epoch 4/50\n",
      " - 2s - loss: 0.0026\n",
      "Epoch 5/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 6/50\n",
      " - 3s - loss: 0.0024\n",
      "Epoch 7/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 8/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 9/50\n",
      " - 2s - loss: 0.0025\n",
      "Epoch 10/50\n",
      " - 3s - loss: 0.0024\n",
      "Epoch 11/50\n",
      " - 3s - loss: 0.0024\n",
      "Epoch 12/50\n",
      " - 3s - loss: 0.0023\n",
      "Epoch 13/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 14/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 15/50\n",
      " - 3s - loss: 0.0024\n",
      "Epoch 16/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 17/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 18/50\n",
      " - 3s - loss: 0.0023\n",
      "Epoch 19/50\n",
      " - 3s - loss: 0.0024\n",
      "Epoch 20/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 21/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 22/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 23/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 24/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 25/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 26/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 27/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 28/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 29/50\n",
      " - 2s - loss: 0.0024\n",
      "Epoch 30/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 31/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 32/50\n",
      " - 3s - loss: 0.0023\n",
      "Epoch 33/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 34/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 35/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 36/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 37/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 38/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 39/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 40/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 41/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 42/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 43/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 44/50\n",
      " - 3s - loss: 0.0024\n",
      "Epoch 45/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 46/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 47/50\n",
      " - 2s - loss: 0.0023\n",
      "Epoch 48/50\n",
      " - 2s - loss: 0.0022\n",
      "Epoch 49/50\n",
      " - 2s - loss: 0.0022\n",
      "Epoch 50/50\n",
      " - 2s - loss: 0.0023\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.callbacks.History at 0x1fce33b08d0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create and fit the LSTM network\n",
    "from keras.layers import Dropout\n",
    "\n",
    "batch_size = 1\n",
    "timesteps = trainX.shape[1]\n",
    "input_dim = trainX.shape[2]\n",
    "\n",
    "model = Sequential()\n",
    "#model.add(LSTM(8, input_shape=(1, look_back)))    # 4 or 8 is the number of LSTM units or dimensions of output of LSTM layer, can be any integer. input_shape must show up in the first layer\n",
    "model.add(LSTM(4, batch_input_shape=(batch_size, timesteps, input_dim)))\n",
    "model.add(Dense(10))    # not necessary, but just want to try it\n",
    "#model.add(Dropout(0.8))\n",
    "model.add(Dense(1))\n",
    "model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "model.fit(trainX, trainY, epochs=50, batch_size=1, verbose=2)   # it turns out that epochs = 15 is enough, 100 is not necess"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the model is fit, we can estimate the performance of the model on the train and test datasets. This will give us a point of comparison for new models.\n",
    "\n",
    "Note that we invert the predictions before calculating error scores to ensure that performance is reported in the same units as the original data.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# make predictions\n",
    "trainPredict = model.predict(trainX, batch_size)\n",
    "testPredict = model.predict(testX, batch_size)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(478, 1)\n"
     ]
    }
   ],
   "source": [
    "# shift train predictions for plotting\n",
    "#trainPredictPlot = numpy.empty_like(dataset_scaled)\n",
    "#trainPredictPlot[:, :] = numpy.nan\n",
    "#print(trainPredictPlot[0])\n",
    "#trainPredictPlot[look_back:len(trainPredict)+look_back, :] = trainPredict\n",
    "\n",
    "# shift test predictions for plotting\n",
    "testPredictPlot = numpy.empty_like(array_scaled[0,:])#dataset_scaled)\n",
    "testPredictPlot[:] = numpy.nan\n",
    "print(np.shape(testPredict))\n",
    "testPredictPlot[len(trainPredict)+(look_back*2)+1:len(array_scaled[0,:])-1] = testPredict[:,0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# plot baseline and predictions\n",
    "#plt.plot(scaler.inverse_transform(dataset_scaled))\n",
    "plt.plot(array_scaled[0,:],'b', label='data')\n",
    "plt.plot(trainPredict,'r', label='trained')\n",
    "plt.plot(testPredictPlot, 'g', label='predicted')\n",
    "plt.legend(title ='Time-sereis')#['scaled','train','predicted'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distribution\n",
    "\n",
    "# Old predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns, numpy as np\n",
    "sns.set()\n",
    "\n",
    "\n",
    "# calculate the number of time steps where the time-series decrease or increase is predicted correctly\n",
    "\n",
    "# estimate error through distributions comparison \n",
    "#plotting\n",
    "\n",
    "\n",
    "\n",
    "#For removing NaN values use boolean indexing:\n",
    "\n",
    "nan_array = np.isnan(testPredictPlot)\n",
    "\n",
    "not_nan_array = ~ nan_array\n",
    "\n",
    "array2 = testPredictPlot[not_nan_array]\n",
    "\n",
    "f, ax = plt.subplots(figsize=(7, 7))\n",
    "#ax.set( yscale=\"log\")\n",
    "ax = sns.distplot(array2)\n",
    "\n",
    "\n",
    "print(np.mean(array2))\n",
    "print(np.median(array2))#\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# plot baseline and predictions\n",
    "#plt.plot(scaler.inverse_transform(dataset_scaled))\n",
    "plt.plot(dataset_scaled)\n",
    "plt.plot(trainPredictPlot)\n",
    "plt.plot(testPredictPlot)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction accuracy \n",
    "\n",
    "\n",
    "We estimate the accuracy for the pain level as number of cases when pain level is above the mean pain level $<P(t)>$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the number of false positive \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# calculate the number of false negative "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}