Exp8-Prediction-Batch 264 with model optimization 12 hours.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 435,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pandas import DataFrame\n",
    "from pandas import Series\n",
    "from pandas import concat\n",
    "from pandas import read_csv\n",
    "from pandas import datetime\n",
    "from sklearn.metrics import median_absolute_error\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import LSTM\n",
    "from math import sqrt\n",
    "from matplotlib import pyplot\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hardcode all variables\n",
    "predict_batch_size_exp = 1\n",
    "epoch_exp = 200\n",
    "neurons_exp = 5\n",
    "predict_values_exp = 12\n",
    "lag_exp=24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {},
   "outputs": [],
   "source": [
    "# frame a sequence as a supervised learning problem\n",
    "def timeseries_to_supervised(data, lag=1):\n",
    "    df = DataFrame(data)\n",
    "    columns = [df.shift(i) for i in range(1, lag+1)]\n",
    "    columns.append(df)\n",
    "    df = concat(columns, axis=1)\n",
    "    df.fillna(0, inplace=True)\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a differenced series\n",
    "def difference(dataset, interval=1):\n",
    "    diff = list()\n",
    "    for i in range(interval, len(dataset)):\n",
    "        value = dataset[i] - dataset[i - interval]\n",
    "        diff.append(value)\n",
    "    return Series(diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "metadata": {},
   "outputs": [],
   "source": [
    "# invert differenced value\n",
    "def inverse_difference(history, yhat, interval=1):\n",
    "    return yhat + history[-interval]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scale train and test data to [-1, 1]\n",
    "def scale(train, test):\n",
    "    # fit scaler\n",
    "    scaler = MinMaxScaler(feature_range=(-1, 1))\n",
    "    scaler = scaler.fit(train)\n",
    "    # transform train\n",
    "    train = train.reshape(train.shape[0], train.shape[1])\n",
    "    train_scaled = scaler.transform(train)\n",
    "    # transform test\n",
    "    test = test.reshape(test.shape[0], test.shape[1])\n",
    "    test_scaled = scaler.transform(test)\n",
    "    return scaler, train_scaled, test_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {},
   "outputs": [],
   "source": [
    "# inverse scaling for a forecasted value\n",
    "def invert_scale(scaler, X, value):\n",
    "    new_row = [x for x in X] + [value]\n",
    "    array = np.array(new_row)\n",
    "    array = array.reshape(1, len(array))\n",
    "    inverted = scaler.inverse_transform(array)\n",
    "    return inverted[0, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit an LSTM network to training data\n",
    "\n",
    "from keras.layers import Activation, Dense, BatchNormalization, TimeDistributed\n",
    "\n",
    "def fit_lstm(train, batch_size, nb_epoch, neurons):\n",
    "    X, y = train[:, 0:-1], train[:, -1]\n",
    "    X = X.reshape(X.shape[0], 1, X.shape[1])\n",
    "    model = Sequential()\n",
    "    model.add(LSTM(neurons_exp, dropout = 0.1 ,batch_input_shape=(batch_size, X.shape[1], X.shape[2]), stateful=True))\n",
    "    \n",
    "    \n",
    "    model.add(BatchNormalization())\n",
    "    model.add(Dense(50))\n",
    "    model.add(Activation('relu'))\n",
    "    model.add(Dense(50))\n",
    "    model.add(Activation('tanh'))\n",
    "    model.add(Dense(1))\n",
    "    \n",
    "    model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "    for i in range(nb_epoch):\n",
    "        model.fit(X, y, epochs=1, batch_size=batch_size, verbose=1, shuffle=False)\n",
    "        model.reset_states()\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make a one-step forecast with new model with batch size 1\n",
    "def forecast_lstm(model, batch_size, X):\n",
    "    X = X.reshape(1, 1, len(X))\n",
    "    # re-define model\n",
    "    new_model = Sequential()\n",
    "    new_model.add(LSTM(neurons_exp, dropout = 0.1 , batch_input_shape=(batch_size, X.shape[1], X.shape[2]), stateful=True))\n",
    "    new_model.add(BatchNormalization())\n",
    "    new_model.add(Dense(50))\n",
    "    new_model.add(Activation('relu'))\n",
    "    new_model.add(Dense(50))\n",
    "    new_model.add(Activation('tanh'))\n",
    "   \n",
    "    new_model.add(Dense(1))\n",
    "    # copy weights\n",
    "    old_weights = model.get_weights()\n",
    "    new_model.set_weights(old_weights)\n",
    "    # compile model\n",
    "    new_model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "    \n",
    "    \n",
    "    #print(X)\n",
    "    yhat = new_model.predict(X, batch_size=1)\n",
    "    return yhat[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Air temperature | ('C)</th>\n",
       "      <th>Pressure | (atm)</th>\n",
       "      <th>Wind speed | (m/s)</th>\n",
       "      <th>Wind direction | (deg)</th>\n",
       "      <th>Power generated by system | (kW)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DateTime</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2007-01-01 00:00:00</th>\n",
       "      <td>10.926</td>\n",
       "      <td>0.979103</td>\n",
       "      <td>9.014</td>\n",
       "      <td>229</td>\n",
       "      <td>33688.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 01:00:00</th>\n",
       "      <td>9.919</td>\n",
       "      <td>0.979566</td>\n",
       "      <td>9.428</td>\n",
       "      <td>232</td>\n",
       "      <td>37261.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 02:00:00</th>\n",
       "      <td>8.567</td>\n",
       "      <td>0.979937</td>\n",
       "      <td>8.700</td>\n",
       "      <td>236</td>\n",
       "      <td>30502.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 03:00:00</th>\n",
       "      <td>7.877</td>\n",
       "      <td>0.980053</td>\n",
       "      <td>8.481</td>\n",
       "      <td>247</td>\n",
       "      <td>28419.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 04:00:00</th>\n",
       "      <td>7.259</td>\n",
       "      <td>0.979867</td>\n",
       "      <td>8.383</td>\n",
       "      <td>256</td>\n",
       "      <td>27370.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     Air temperature | ('C)  Pressure | (atm)  \\\n",
       "DateTime                                                        \n",
       "2007-01-01 00:00:00                  10.926          0.979103   \n",
       "2007-01-01 01:00:00                   9.919          0.979566   \n",
       "2007-01-01 02:00:00                   8.567          0.979937   \n",
       "2007-01-01 03:00:00                   7.877          0.980053   \n",
       "2007-01-01 04:00:00                   7.259          0.979867   \n",
       "\n",
       "                     Wind speed | (m/s)  Wind direction | (deg)  \\\n",
       "DateTime                                                          \n",
       "2007-01-01 00:00:00               9.014                     229   \n",
       "2007-01-01 01:00:00               9.428                     232   \n",
       "2007-01-01 02:00:00               8.700                     236   \n",
       "2007-01-01 03:00:00               8.481                     247   \n",
       "2007-01-01 04:00:00               8.383                     256   \n",
       "\n",
       "                     Power generated by system | (kW)  \n",
       "DateTime                                               \n",
       "2007-01-01 00:00:00                           33688.1  \n",
       "2007-01-01 01:00:00                           37261.9  \n",
       "2007-01-01 02:00:00                           30502.9  \n",
       "2007-01-01 03:00:00                           28419.2  \n",
       "2007-01-01 04:00:00                           27370.3  "
      ]
     },
     "execution_count": 444,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''' Loading data '''\n",
    "import pandas as pd\n",
    "series = pd.read_excel('AL_WIND_07_12.xlsx',index_col=\"DateTime\")\n",
    "series.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Power generated by system | (kW)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DateTime</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2007-01-01 00:00:00</th>\n",
       "      <td>33688.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 01:00:00</th>\n",
       "      <td>37261.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 02:00:00</th>\n",
       "      <td>30502.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 03:00:00</th>\n",
       "      <td>28419.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01 04:00:00</th>\n",
       "      <td>27370.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     Power generated by system | (kW)\n",
       "DateTime                                             \n",
       "2007-01-01 00:00:00                           33688.1\n",
       "2007-01-01 01:00:00                           37261.9\n",
       "2007-01-01 02:00:00                           30502.9\n",
       "2007-01-01 03:00:00                           28419.2\n",
       "2007-01-01 04:00:00                           27370.3"
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''Drop all the features as we will not be having any in production'''\n",
    "del series['Air temperature | (\\'C)']\n",
    "del series['Pressure | (atm)']\n",
    "del series['Wind speed | (m/s)']\n",
    "del series['Wind direction | (deg)']\n",
    "series.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Power generated by system | (kW)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DateTime</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-12-31 08:00:00</th>\n",
       "      <td>5802.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31 09:00:00</th>\n",
       "      <td>6110.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31 10:00:00</th>\n",
       "      <td>6251.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31 11:00:00</th>\n",
       "      <td>6899.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31 12:00:00</th>\n",
       "      <td>4514.49</td>\n",
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      "text/plain": [
       "                     Power generated by system | (kW)\n",
       "DateTime                                             \n",
       "2012-12-31 08:00:00                           5802.11\n",
       "2012-12-31 09:00:00                           6110.57\n",
       "2012-12-31 10:00:00                           6251.34\n",
       "2012-12-31 11:00:00                           6899.17\n",
       "2012-12-31 12:00:00                           4514.49"
      ]
     },
     "execution_count": 446,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range(0,11):\n",
    "  series = series[:-1]\n",
    "series.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {},
   "outputs": [],
   "source": [
    "# transform data to be stationary\n",
    "raw_values = series.values\n",
    "diff_values = difference(raw_values, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {},
   "outputs": [],
   "source": [
    "# transform data to be supervised learning\n",
    "supervised = timeseries_to_supervised(diff_values, lag_exp)\n",
    "supervised_values = supervised.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split data into train and test-sets\n",
    "train, test = supervised_values[0:-predict_values_exp], supervised_values[-predict_values_exp:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\envs\\tensorflow35\\lib\\site-packages\\sklearn\\utils\\validation.py:475: DataConversionWarning: Data with input dtype object was converted to float64 by MinMaxScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    }
   ],
   "source": [
    "# transform the scale of the data\n",
    "scaler, train_scaled, test_scaled = scale(train, test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 6s 120us/step - loss: 0.0184\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0152\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 25us/step - loss: 0.0150\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 20us/step - loss: 0.0147\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 20us/step - loss: 0.0144\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 22us/step - loss: 0.0141\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0141\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 20us/step - loss: 0.0142\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 21us/step - loss: 0.0140\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 20us/step - loss: 0.0139\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 21us/step - loss: 0.0138\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 21us/step - loss: 0.0137\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0136\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0136\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0135\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 2s 30us/step - loss: 0.0135\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0135\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0135\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0134\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0134\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0134\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0134\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 25us/step - loss: 0.0134\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0133\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0133\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0133\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 27us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 27us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0131\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0132\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0131\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 25us/step - loss: 0.0131\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0131\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0131\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 25us/step - loss: 0.0131\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 2s 29us/step - loss: 0.0131\n",
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      "52536/52536 [==============================] - 1s 27us/step - loss: 0.0131\n",
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      "52536/52536 [==============================] - 1s 25us/step - loss: 0.0130\n",
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      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 25us/step - loss: 0.0128: 0s - loss\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
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      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0127\n",
      "Epoch 1/1\n",
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      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 22us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 22us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 22us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 26us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0129\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 22us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 23us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 2s 30us/step - loss: 0.0128\n",
      "Epoch 1/1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "52536/52536 [==============================] - 1s 24us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 22us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 22us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 20us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 20us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 20us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 21us/step - loss: 0.0128\n",
      "Epoch 1/1\n",
      "52536/52536 [==============================] - 1s 21us/step - loss: 0.0128\n"
     ]
    }
   ],
   "source": [
    "# fit the model\n",
    "fit_batch_size_exp = 264\n",
    "lstm_model = fit_lstm(train_scaled, fit_batch_size_exp, epoch_exp, neurons_exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hour=1, Predicted=32194.827326, Expected=35723.600000\n",
      "Hour=2, Predicted=30875.971859, Expected=28221.500000\n",
      "Hour=3, Predicted=25730.511703, Expected=22650.000000\n",
      "Hour=4, Predicted=19966.024685, Expected=14845.100000\n",
      "Hour=5, Predicted=11596.577572, Expected=11449.700000\n",
      "Hour=6, Predicted=11334.957709, Expected=11637.200000\n",
      "Hour=7, Predicted=11347.123791, Expected=6465.350000\n",
      "Hour=8, Predicted=7449.639746, Expected=5802.110000\n",
      "Hour=9, Predicted=9463.258433, Expected=6110.570000\n",
      "Hour=10, Predicted=8279.471022, Expected=6251.340000\n",
      "Hour=11, Predicted=7981.391572, Expected=6899.170000\n",
      "Hour=12, Predicted=9291.055655, Expected=4514.490000\n"
     ]
    }
   ],
   "source": [
    "# walk-forward validation on the test data\n",
    "predictions = list()\n",
    "expectations = list()\n",
    "for i in range(len(test_scaled)):\n",
    "    # make one-step forecast\n",
    "    #print(test_scaled)\n",
    "    X, y = test_scaled[i, 0:-1], test_scaled[i, -1]\n",
    "    #print(X)\n",
    "    yhat = forecast_lstm(lstm_model, predict_batch_size_exp, X)\n",
    "    # invert scaling\n",
    "    yhat = invert_scale(scaler, X, yhat)\n",
    "    # invert differencing\n",
    "    yhat = inverse_difference(raw_values, yhat, len(test_scaled)+1-i)\n",
    "    # store forecast\n",
    "    predictions.append(yhat)\n",
    "    expected = raw_values[len(train) + i + 1]\n",
    "    expectations.append(expected)\n",
    "    print('Hour=%d, Predicted=%f, Expected=%f' % (i+1, yhat, expected))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Percent Error:  31.99698222228608\n"
     ]
    }
   ],
   "source": [
    "expectations = np.array(expectations)\n",
    "predictions = np.array(predictions)\n",
    "print(\"Mean Percent Error: \", (np.mean(np.abs((expectations - predictions) / expectations))*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# line plot of observed vs predicted\n",
    "pyplot.plot(raw_values[-predict_values_exp:])\n",
    "pyplot.plot(predictions)\n",
    "pyplot.show()"
   ]
  }
 ],
 "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": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}