MethodLevelAnomalyReport.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# #SOA #health #anomalies #analysis #regression_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Anomaly dimensions\n",
    "Level: System, service, method\n",
    "Measure: BusinessErrorCount, TotalTime, AvgDuration\n",
    "Time: grouped by hour\n",
    "\n",
    "Anomaly measures\n",
    "AnomalyStrength: Value/prediction ratio if greater than threshold, othewrise empty value or 0\n",
    "\n",
    "HyperParameters\n",
    "WindowSize: (default 5) how many hours to consider in training before now\n",
    "AnomalyThreshold: (default 3.5) Value/prediction ratio to alert.\n",
    "BusinessErrorCountThreshold: \n",
    "TotalTimeThreshold:\n",
    "AvgDurationThreshold:\n",
    "\n",
    "Futher improvements\n",
    "Increse granularity to 15m instead of 1 hour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import datetime\n",
    "from sklearn import linear_model\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>INTERVAL_START</th>\n",
       "      <th>ServiceContractMethod</th>\n",
       "      <th>SucceededCount</th>\n",
       "      <th>BusinessErrorCount</th>\n",
       "      <th>TotalTime</th>\n",
       "      <th>AvgDuration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2017-03-08</td>\n",
       "      <td>BillingDomain/CreditCardGateway/v001/ServiceCo...</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>3.167293</td>\n",
       "      <td>0.2120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2017-03-08</td>\n",
       "      <td>BillingDomain/CreditCardGateway/v001/ServiceCo...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.015595</td>\n",
       "      <td>0.0160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2017-03-08</td>\n",
       "      <td>BillingDomain/CreditCardGateway/v001/ServiceCo...</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>6.661867</td>\n",
       "      <td>0.5005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2017-03-08</td>\n",
       "      <td>BillingDomain/CreditCardGateway/v001/ServiceCo...</td>\n",
       "      <td>14</td>\n",
       "      <td>2</td>\n",
       "      <td>2.558621</td>\n",
       "      <td>0.1595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2017-03-08</td>\n",
       "      <td>BillingDomain/CreditCardGateway/v001/ServiceCo...</td>\n",
       "      <td>717</td>\n",
       "      <td>0</td>\n",
       "      <td>1.154967</td>\n",
       "      <td>0.0015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  INTERVAL_START                              ServiceContractMethod  \\\n",
       "0     2017-03-08  BillingDomain/CreditCardGateway/v001/ServiceCo...   \n",
       "1     2017-03-08  BillingDomain/CreditCardGateway/v001/ServiceCo...   \n",
       "2     2017-03-08  BillingDomain/CreditCardGateway/v001/ServiceCo...   \n",
       "3     2017-03-08  BillingDomain/CreditCardGateway/v001/ServiceCo...   \n",
       "4     2017-03-08  BillingDomain/CreditCardGateway/v001/ServiceCo...   \n",
       "\n",
       "   SucceededCount  BusinessErrorCount  TotalTime  AvgDuration  \n",
       "0              15                   0   3.167293       0.2120  \n",
       "1               1                   0   0.015595       0.0160  \n",
       "2              14                   0   6.661867       0.5005  \n",
       "3              14                   2   2.558621       0.1595  \n",
       "4             717                   0   1.154967       0.0015  "
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_pickle('preprocessed_data.pickle')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def getMethodLevelAnomalies(data, time, WindowSize=5, AnomalyThreshold=3.5,BusinessErrorCountThreshold=2,TotalTimeThreshold=10000,AvgDurationThreshold=2):\n",
    "    #friday evening + Meshuggah Clockworks :)\n",
    "    report_structure = []\n",
    "\n",
    "    data_filtered = data[(data['INTERVAL_START'] >= datetime.datetime.strptime(time, \"%Y-%m-%d %H:%M:00\") - datetime.timedelta(hours=WindowSize)) \n",
    "                             & (data['INTERVAL_START'] <= time)]\n",
    "    data_grouped = data_filtered.groupby('ServiceContractMethod')\n",
    "    for name, method_group in data_grouped:\n",
    "        time_method_group = method_group.groupby('INTERVAL_START')\n",
    "\n",
    "        #BusinessErrorCount measure\n",
    "        time_method_group_measure = time_method_group.agg({'BusinessErrorCount' : np.sum})\n",
    "        time_method_group_measure = time_method_group_measure.reset_index()\n",
    "        if(time_method_group_measure.size > (WindowSize*2) ):\n",
    "            regression_model = linear_model.LinearRegression()\n",
    "            regression_model.fit(X = pd.DataFrame(time_method_group_measure.index[:-1]),y = time_method_group_measure[\"BusinessErrorCount\"][:-1])\n",
    "            train_prediction = regression_model.predict(X = pd.DataFrame(time_method_group_measure.index))\n",
    "            regression_prediction = train_prediction[-1]\n",
    "            mean_prediction = time_method_group_measure[\"BusinessErrorCount\"][:-1].mean()\n",
    "            if(mean_prediction<BusinessErrorCountThreshold):\n",
    "                continue\n",
    "            prediction = max(regression_prediction,mean_prediction)\n",
    "            AnomalyStrength = list(time_method_group_measure['BusinessErrorCount'])[-1]/prediction\n",
    "            if(AnomalyStrength<0): \n",
    "                AnomalyStrength=0\n",
    "            if(AnomalyStrength>AnomalyThreshold):\n",
    "                report_structure.append({'INTERVAL_START':time,'Level':'Method','object':name,'Measure':'BusinessErrorCount','AnomalyStrength':AnomalyStrength})\n",
    "                time_method_group_measure.plot(title=name,color=\"black\")\n",
    "                plt.plot(pd.DataFrame(time_method_group_measure.index), train_prediction, color=\"blue\")\n",
    "\n",
    "    data_filtered = data[(data['INTERVAL_START'] >= datetime.datetime.strptime(time, \"%Y-%m-%d %H:%M:00\") - datetime.timedelta(hours=WindowSize)) \n",
    "                             & (data['INTERVAL_START'] <= time)]\n",
    "    data_grouped = data_filtered.groupby('ServiceContractMethod')\n",
    "    for name, method_group in data_grouped:\n",
    "        time_method_group = method_group.groupby('INTERVAL_START')\n",
    "\n",
    "        #TotalTime measure\n",
    "        time_method_group_measure = time_method_group.agg({'TotalTime' : np.sum})\n",
    "        time_method_group_measure = time_method_group_measure.reset_index()\n",
    "        if(time_method_group_measure.size > (WindowSize*2) ):\n",
    "            regression_model = linear_model.LinearRegression()\n",
    "            regression_model.fit(X = pd.DataFrame(time_method_group_measure.index[:-1]),y = time_method_group_measure[\"TotalTime\"][:-1])\n",
    "            train_prediction = regression_model.predict(X = pd.DataFrame(time_method_group_measure.index))\n",
    "            regression_prediction = train_prediction[-1]\n",
    "            mean_prediction = time_method_group_measure[\"TotalTime\"][:-1].mean()\n",
    "            if(mean_prediction<TotalTimeThreshold):\n",
    "                continue\n",
    "            prediction = max(regression_prediction,mean_prediction)\n",
    "            AnomalyStrength = list(time_method_group_measure['TotalTime'])[-1]/prediction\n",
    "            if(AnomalyStrength<0): \n",
    "                AnomalyStrength=0\n",
    "            if(AnomalyStrength>AnomalyThreshold):\n",
    "                report_structure.append({'INTERVAL_START':time,'Level':'Method','object':name,'Measure':'TotalTime','AnomalyStrength':AnomalyStrength})\n",
    "                time_method_group_measure.plot(title=name,color=\"black\")\n",
    "                plt.plot(pd.DataFrame(time_method_group_measure.index), train_prediction, color=\"blue\")\n",
    "\n",
    "    data_filtered = data[(data['INTERVAL_START'] >= datetime.datetime.strptime(time, \"%Y-%m-%d %H:%M:00\") - datetime.timedelta(hours=WindowSize)) \n",
    "                             & (data['INTERVAL_START'] <= time)]\n",
    "    data_grouped = data_filtered.groupby('ServiceContractMethod')\n",
    "    for name, method_group in data_grouped:\n",
    "        time_method_group = method_group.groupby('INTERVAL_START')\n",
    "\n",
    "        #AvgDuration measure\n",
    "        time_method_group_measure = time_method_group.agg({'AvgDuration' : np.mean})\n",
    "        time_method_group_measure = time_method_group_measure.reset_index()\n",
    "        if(time_method_group_measure.size > (WindowSize*2) ):\n",
    "\n",
    "            regression_model = linear_model.LinearRegression()\n",
    "            regression_model.fit(X = pd.DataFrame(time_method_group_measure.index[:-1]),y = time_method_group_measure[\"AvgDuration\"][:-1])\n",
    "            train_prediction = regression_model.predict(X = pd.DataFrame(time_method_group_measure.index))\n",
    "            regression_prediction = train_prediction[-1]\n",
    "            mean_prediction = time_method_group_measure[\"AvgDuration\"][:-1].mean()\n",
    "            if(mean_prediction<AvgDurationThreshold):\n",
    "                continue\n",
    "            prediction = max(regression_prediction,mean_prediction)\n",
    "            AnomalyStrength = list(time_method_group_measure['AvgDuration'])[-1]/prediction\n",
    "            if(AnomalyStrength<0): \n",
    "                AnomalyStrength=0\n",
    "            if(AnomalyStrength>AnomalyThreshold):\n",
    "                report_structure.append({'INTERVAL_START':time,'Level':'Method','object':name,'Measure':'AvgDuration','AnomalyStrength':AnomalyStrength})\n",
    "                time_method_group_measure.plot(title=name,color=\"black\")\n",
    "                plt.plot(pd.DataFrame(time_method_group_measure.index), train_prediction, color=\"blue\")\n",
    "    \n",
    "    return report_structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
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UqFE0atSIrKwsvv76axYtWsSBAwfIz89n3759lcYYrJns3Lkz69atS8zGS4Ol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\n9dVXufXWW7nmmmtq/YeOk9GuXbv47W9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113230828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7duyzjsLCtb133HEHY8eO5eqrryYzM5MTTzyRv/71rwBcddVVrFu3joKCAjIz\nMykuLm7WehCJEyXDIiLSLB999BGzZ8/mi1/8YoOfMfNd0j799NMsW7aMt99+mw8//JDZs2fTv3//\ner+zYcMGduzYwQcffMC0adOYMGEC27ZtA+AHP/gBb7/9Nq+99hpvv/0277//Pj/96U8BuO+++xg8\neDCbN2/mn//8J3fffTcAb775JiUlJbzyyits376dhQsXMmTIkGYv59y5c3nppZfqkvfEsBUrVrBq\n1Sq2bt3Kl7/8ZW644QY2b97MjTfeyAUXXMDWrVvrPv/oo48ybdo0duzYwccff8w//vEPLr744gbn\n+dBDDzFjxgyee+451q5dy44dO5gwYcJ+67UhZWVljBs3jm3btlFQUFD33RkzZpCVlcX8+fPZvn07\nEydObPZ6EIkLJcMiIp2cmR3w34H46le/Sr9+/ejduzeLFy9uVkLVrVs3duzYwapVq3DOccwxxzBg\nwIB6P9u9e3duvfVWunTpwnnnncchhxzCmjVrAJg2bRr3338/vXv3plevXtx888089thjdfNYv349\nFRUVdOnShdNOOw2ALl268Mknn/D3v/+d2tpasrKyGDp0aN38Zs+eTb9+/er+8vPz94nnRz/6EX36\n9KFHjx77DOvduzc9evRgwYIFDB8+nHHjxpGRkcGll15KTk7OPu1/r7nmGnJycsjIyGD79u0AHHHE\nEQ2ur1mzZvG9732P7Oxsevbsyc9//nNmz57Nnj17mlzXAKeffjrnnHMOZsaVV17Ja6+9ts94PdhF\npGFKhkVEOjnn3AH/HYi5c+eyZcsWPvnkE379619zxhlnUFVV1eh3Ro8ezbe+9S0mTJjAwIED+cY3\nvkF1dXW9n+3fvz8ZGXsPRz179qS6upqNGzfy0Ucf8fnPf74ucT3vvPPYvHkzADfddBNHH300Z599\nNp/+9KeZNGkSAEcffTS//OUvuf322xkwYADjxo1jw4YNddMfO3YsW7ZsqftbsmTJPvEMGjRovxjD\nwz744AOys7P3GZ+dnb3PjYXhZg2JGvH169c3uL6Sp5mdnc2//vWvJtdzwsCBA+te9+zZk48//rjZ\nibRI3CkZFhGRRiWSaTPjoosuokuXLpSXl9OrVy8++uijus+FE06Ab33rW7z88su8/vrrrFmzhl/8\n4hctmu9hhx1Gz549ef311+sS1w8//LCuCcUhhxxCcXEx77zzDmVlZUyePLmubfCll17KCy+8QGVl\nJQA//OFa/z+2AAAgAElEQVQPmz3f+mrSw8OOPPJI3n333X3Gr1u3jqOOOqrezx9zzDEMHjyYJ598\nssF5HnnkkXWxAlRWVtKtWzcGDBiw33revXs3GzduPKDlEZG9lAyLiEizzZ07lw8//JBjjz2WESNG\n8Pvf/56amhrefvttpk+fXve5l19+mZdeeona2loOPvhgDjroILp06dKieZkZ119/PTfccENd8vf+\n++/z9NNPA7BgwQLeeecdwCfGXbt2pUuXLrz55ps8++yzfPLJJ3Tv3p2DDz64xfNuzPnnn89bb73F\n448/zu7du5k9ezZvvPEGBQUFDX7nvvvu42c/+xkPP/wwO3bswDnHsmXL+MY3vgHAZZddxv3338+7\n775LdXU1t9xyC5deeikZGRkMHz6cjz/+mD/96U/U1tZy55138sknnzQaY/hqwMCBA1m7dm3bLLxI\nGlIyLCIijUr0RNC7d29uvfVWZsyYwbHHHsuNN95It27dGDhwINdeey1XXHFF3Xe2b9/O9ddfT79+\n/Rg6dCiHHXZYs2/eCtdk3nPPPXz605/m1FNPpU+fPpx99tm8+eabALz11lucddZZHHrooZx22mlM\nmDCBM844g127dnHzzTdz+OGHc+SRR7Jx48a6m+vAtxkO9zOcmZnJpk2b9pt3ffEA9OvXj/nz51Nc\nXMxhhx1GcXExCxYsoG/fvg1O4+KLL2b27NlMnz6do446ioEDB/KTn/yECy+8EIDrrruOK6+8kjPO\nOIOjjz6anj178l//9V8AZGZmUlpayvjx4xk0aBCHHnpovU05Gor55ptv5mc/+xn9+vVj8uTJjX5P\nJI5MjeolDszMqaxLZ2RmurlJItdQOQyGq52FpDXVDIuIiIhIbCkZFhEREZHYUjIsIiIiIrGlZFhE\nREREYkvJsIiIiIjElpJhEREREYmtrlEHICISZ9nZ2XpCmEQu+fHSInGifoYlFtTPsIhIy6mfYYkD\nNZMQERERkdhSMiwiIiIisaVkWERERERiS8mwiIiIiMSWkmERERHZz86dO6MOQaRDKBkWERGR/cyc\nOTPqEEQ6hLpWk1hQ12oiIs3nnGPEiBG89tpr6lpN0p5qhkVERGQfy5cvp6amJuowRDqEkmERERHZ\nR0lJCUVFRVGHIdIh1ExCYkHNJEREmqeqqoqcnBwqKiro27evmklI2lPNsKQMMxtkZs+Y2Soz+5uZ\nfScY3tfMnjazNWa20Mx6Rx2riEiqmjZtGoWFhfTp0yfqUEQ6hGqGJWWY2UBgoHPuVTM7BHgFuBC4\nFtjsnLvXzH4I9HXO3Zz0XdUMi4g0oba2lmHDhjFv3jxGjBiBmalmWNKeaoYlZTjnNjjnXg1eVwNv\nAIPwCfHDwcceBr4aTYQiIqmtrKyMwYMHM2LEiKhDEekwSoYlJZnZEGAE8GdggHOuCnzCDBweXWQi\nIqmrtLRUN85J7HSNOgCRlgqaSDwBfNc5V21mzWr/cPvtt9e9zsvLIy8vr13iExFJRWvWrOGVV17h\nC1/4wj77S5F0pzbDklLMrCswH/iTc+5XwbA3gDznXFXQrvhZ59yxSd9Tm2ERkUZ897vf5ZBDDuGu\nu+6qG6Y2wxIHSoYlpZjZDGCTc+57oWGTgC3OuUm6gU5EpOV27txJVlYWK1euJCsrq264kmGJAzWT\nkJRhZqcBlwN/M7OVgAN+BEwC5pjZdcA64GvRRSkiknpmzpxJbm7uPomwSFyoZlhiQTXDIiL1c84x\nYsQIiouLGTNmzD7jVDMscaDeJERERGJs+fLl1NTUkJ+fH3UoIpFQMiwiIhJjJSUlFBUVkZGhlEDi\nSc0kJBbUTEJEZH9VVVXk5ORQUVFR7+OX1UxC4kCngSIiIjE1bdo0CgsL602EReJCNcMSC6oZFhHZ\nV21tLcOGDWPevHkNPn5ZNcMSB6oZFhERiaGysjIGDx7cYCIsEhdKhkVERGKotLSUoqKiqMMQiZya\nSUgsqJmEiMhea9asYdSoUVRWVtKjR48GP6dmEhIHqhkWERGJmdLSUsaPH99oIiwSF6oZllhQzbCI\niLdz506ysrJYuXJlk49fVs2wxIFqhkVERGJk5syZ5ObmNpkIi8SFkmEREZGYcM5RUlLChAkTog5F\npNNQMiwiIhITy5cvp6amhvz8/KhDEek0lAyLiIjERElJCUVFRWRk6PAvkqAb6CQWdAOdiMRdVVUV\nOTk5VFRUNPvxy7qBTuJAp4YiIiIxMG3aNAoLC5udCIvEhWqGJRZUMywicVZbW8uwYcOYN29eix6/\nrJphiQPVDIuIiKS5srIyBg8e3KJEWCQulAyLiIikudLSUoqKiqIOQ6RTUjMJiQU1kxCRuFqzZg2j\nRo2isrKyxY9fVjMJiQPVDIuIiKSx0tJSxo8f3+JEWCQuVDMssaCaYRGJo507d5KVlcXKlStb9fhl\n1QxLHKhmWEREJE3NnDmT3NzcViXCInGhZFhERCQNOecoKSlhwoQJUYci0qkpGRYREUlDy5cvp6am\nhvz8/KhDEenUlAyLiIikoZKSEoqKisjI0KFepDG6gU5iQTfQiUicVFVVkZOTQ0VFxQE9flk30Ekc\n6HRRREQkzUybNo3CwsIDSoRF4kI1wxILqhkWkbiora1l2LBhzJs374Afv6yaYYkD1QyLiIikkbKy\nMgYPHnzAibBIXCgZFhERSSOlpaUUFRVFHYZIylAzCYkFNZMQkThYs2YNo0aNorKysk0ev6xmEhIH\nqhkWERFJE6WlpYwfP75NEmGRuFDNsMSCaoZFJN3t3LmTrKwsVq5c2WaPX1bNsMSBaoZFRETSwMyZ\nM8nNzW2zRFgkLpQMS8ows+lmVmVmr4WG3WZm/zCzvwZ/50YZo4hIFJxzlJSUMGHChKhDEUk5SoYl\nlTwEnFPP8MnOuZOCv//t6KBERKK2fPlyampqyM/PjzoUkZSjZFhShnNuGbC1nlFqzyYisVZSUkJR\nUREZGTqsi7SUthpJBxPM7FUzm2ZmvaMORkSkI1VVVfGnP/2Ja665JupQRFKSkmFJdaXA0c65EcAG\nYHLE8YiIdKhp06ZRWFhInz59og5FJCV1jToAkQPhnNsYejsVKGvos7fffnvd67y8PPLy8totLhGR\njlBbW8sDDzzAvHnz2mR6S5cuZenSpW0yLZFUoX6GJaWY2RCgzDl3YvB+oHNuQ/D6RuBk59y4er6n\nfoZFJO089dRTFBcXU15e3i7TVz/DEgeqGZaUYWazgDygv5mtA24DRpvZCGAP8C7wH5EFKCLSwUpL\nSykqKoo6DJGUppphiQXVDItIulmzZg2jRo2isrKy3R6/rJphiQPdQCciIpKCSktLGT9+fLslwiJx\noZphiQXVDItIOtm5cydZWVmsXLmyXR+/rJphiQPVDIuIiKSYmTNnkpub266JsEhcKBkWERFJIc45\nSkpKmDBhQtShiKQFJcMiIiIpZPny5dTU1JCfnx91KCJpQcmwiIhICikpKaGoqIiMDB3CRdqCbqCT\nWNANdCKSDqqqqsjJyaGioqJDHr+sG+gkDnRaKSIikiKmTZtGYWFhhyTCInGhmmGJBdUMi0iqq62t\nZdiwYcybN48RI0Z0yDxVMyxxoJphERGRFFBWVsbgwYM7LBEWiQslwyIiIimgtLSUoqKiqMMQSTtq\nJiGxoGYSIpLK1qxZw6hRo6isrOzQxy+rmYTEgWqGRUREOrnS0lLGjx/foYmwSFyoZlhiQTXDIpKq\ndu7cSVZWFitXruzwxy+rZljiQDXDIiIindjMmTPJzc3t8ERYJC6UDIuIiHRSzjlKSkqYMGFC1KGI\npC0lwyIiIp3U8uXLqampIT8/P+pQRNKWkmEREZFOqqSkhKKiIjIydLgWaS+6gU5iQTfQiUiqqaqq\nIicnh4qKisgev6wb6CQOdKopIiLSCU2bNo3CwsLIEmGRuFDNsMSCaoZFJJXU1tYybNgw5s2bF+nj\nl1UzLHGgmmEREZFOpqysjMGDB0eaCIvEhZJhERGRTiZx45yItD81k5BYUDMJEUkVq1evJi8vj8rK\nysgfv6xmEhIHqhkWERHpRKZMmcL48eMjT4RF4kI1wxILqhkWkVRQXV1NdnY2K1eu7BSPX1bNsMSB\naoZFREQ6iVmzZpGbm9spEmGRuFAyLCIi0gk45ygpKWHChAlRhyISK0qGRUREOoHy8nJqamrIz8+P\nOhSRWFEyLCIi0gmUlpZSVFRERoYOzSIdSTfQSSzoBjoR6cyqqqrIycmhoqKiUz1+WTfQSRzo9FNE\nYqm8vJzTTjuNd999N+pQRJg6dSqFhYWdKhEWiQslwyISO5s2beKyyy4jJyeH3NxcVq1aFXVIEmO1\ntbU88MADunFOJCJKhkUkVvbs2cPVV1/NZZddxvTp07n77rs588wzefnll6MOTWKqrKyMrKwsRowY\nEXUoIrHUNeoAREQ6UnFxMR9++CF33nknAFdeeSWZmZmcf/75zJkzh7y8vGgDlNgpKSmhqKgo6jBE\nYks30Eks6AY6Ad9O+OKLL2bFihUMHjx4n3HPPvssY8eOZfr06RQUFEQUocTN6tWrycvLo7KyslM+\nflk30EkcqJmEpAwzm25mVWb2WmhYXzN72szWmNlCM+sdZYzSeSXaCU+fPn2/RBhg9OjRLFiwgOuv\nv55HH300gggljqZMmcL48eM7ZSIsEheqGZaUYWanA9XADOfcZ4Nhk4DNzrl7zeyHQF/n3M31fFc1\nwzG2Z88eCgoKOOGEE5g0aVKjn3399dc599xzufnmm3VDk7Sr6upqsrOzWblyZad9/LJqhiUOVDMs\nKcM5twzYmjT4QuDh4PXDwFc7NChJCcnthBtz/PHH8/zzz3P//fdz5513opMoaS+zZs0iNze30ybC\nInGhG+gk1X3KOVcF4JzbYGaHRx2QdC7l5eVMnjyZFStW0K1bt2Z9Z+jQobzwwgucc845bN26leLi\nYsxUOSZtxzlHSUkJxcXFUYciEnuqGRaRtNVUO+HGHHHEESxdupTly5fz7//+7+zevbudopQ4Ki8v\np6amhvz8/KhDEYk91QxLqqsyswHOuSozGwj8s6EP3n777XWv8/Ly1IVWmgv3J3zBBRe0ahr9+vVj\n0aJFXHTRRYwdO5aZM2fqRidpE6WlpRQVFZGR0bnqpJYuXcrSpUujDkOkQ+kGOkkpZjYEKHPOnRi8\nnwRscc5N0g10Enbvvfcyd+5cli5d2uzmEQ3ZtWsX48aNY8eOHTz11FP06tWrjaKUOKqqqiInJ4eK\niopO//hl3UAncdC5TklFGmFms4DlwHAzW2dm1wL3AGPMbA1wVvBeYi7RTvjxxx8/4EQYoEePHsye\nPZtBgwYxZswYtm5Nvo9TpPmmTp1KYWFhp0+EReJCNcMSC6oZjo9NmzZx0kknMWXKlFY3j2jInj17\nmDhxIkuWLGHhwoUMHDiwTacv6a+2tpahQ4dSVlaWEo9fVs2wxIFqhkUkbbRFO+HGZGRkcN9991FY\nWEhubi7vvvtum89D0ltZWRlZWVkpkQiLxIVuoBORtNGS/oRby8y49dZb6dOnD7m5uSxcuJDjjjuu\n3eYn6aWkpISioqKowxCREDWTkFhQM4n0V15ezsUXX8yKFSta3I1aaz3yyCPcdNNNzJ8/n5EjR3bI\nPCV1rV69mry8PCorK1OmVxI1k5A4UM2wiKS8A+lP+EBceeWVZGZmcv755zNnzhx11yeNmjJlCuPH\nj0+ZRFgkLlQzLLGgmuH0tWfPHgoKCjjhhBOYNGlSJDE8++yzjB07lunTp1NQUBBJDNK5VVdXk52d\nzcqVK1Pq8cuqGZY40A10IpLSOqKdcFNGjx7NggULuP7663n00Ucji0M6r1mzZpGbm5tSibBIXKiZ\nhIikrER/witWrGiT/oQPxMknn8ySJUs499xz2bZtGxMmTIg0Huk8nHOUlJRQXFwcdSgiUg8lwyKS\nkqJqJ9yY448/nueff77uwRy33HILZrrCHHfl5eXU1NSQn58fdSgiUg81kxCRlNPe/QkfiKFDh/LC\nCy8wZ84cJk6ciNqqS2lpKUVFRWRk6JAr0hnpBjqJBd1Al17uvfde5s6dy9KlSyNvHtGQLVu2cMEF\nF3Dcccfx4IMP0qVLl6hDkghUVVWRk5NDRUVFSj5+WTfQSRzoNFVEUkqinfDjjz/eaRNhgH79+rFo\n0SLWrVvH2LFj2bVrV9QhSQSmTp1KYWFhSibCInGhmmGJBdUMp4dNmzZx0kknMWXKlE7XPKIhu3bt\nYty4cezYsYOnnnqKXr16RR2SdJDa2lqGDh1KWVlZyj5+WTXDEgeqGRaRlNCZ2wk3pkePHsyePZtB\ngwbV3Vgn8VBWVkZWVlbKJsIicaFkWERSQmfoT7i1unbtyrRp0zj11FPJy8tjw4YNUYckHaCkpISi\noqKowxCRJqiZhMSCmkmktvLyci6++GJWrFjRabpRaw3nHHfeeSczZsxg0aJFDBkyJOqQpJ2sXr2a\nvLw8KisrU/rxy2omIXGgfoZFpFPrjP0Jt5aZceutt9KnTx9yc3NZuHAhxx13XNRhSTuYMmUK48eP\nT+lEWCQuVDMssaCa4dS0Z88eCgoKOOGEE5g0aVLU4bSpRx55hJtuuon58+czcuTIqMORNlRdXU12\ndjYrV65M+ccvq2ZY4kA1wyLSaaVyO+GmXHnllWRmZnL++eczZ84c8vLyog5J2sisWbPIzc1N+URY\nJC5UMyyxoJrh1JMu7YSb8uyzzzJ27FimT59OQUFB1OHIAXLOMWLECIqLixkzZkzU4Rww1QxLHKg3\nCRHpdNKpnXBTRo8ezYIFC7j++ut59NFHow5HDlB5eTk1NTXk5+dHHYqINJOaSYhIp5Kq/QkfiJNP\nPpklS5Zw7rnnsm3bNiZMmBB1SNJKpaWlFBUVkZGhuiaRVKFmEhILaiaROu69917mzp3L0qVLO/Xj\nlttDRUUFY8aM4ZprruGWW27BTFenU0lVVRU5OTlUVFSkzeOX1UxC4kA1wyLSaZSXlzN58mRWrFgR\nu0QYYOjQobzwwgucc845bN26leLiYiXEKWTq1KkUFhamTSIsEheqGZZYUM1w57dp0yZOOukkpkyZ\nEpvmEQ3ZsmULF1xwAccddxwPPvggXbp0iTokaUJtbS1Dhw6lrKwsrR6/rJphiQM1ahKRyMWxnXBj\n+vXrx6JFi1i3bh1jx45l165dUYckTSgrKyMrKyutEmGRuFAyLCKRS+f+hFvrkEMOYf78+TjnKCgo\nYOfOnVGHJI0oKSmhqKgo6jBEpBXUTEJiQc0kOq+49CfcWrW1tXz9619n9erVLFiwgL59+0YdkiRZ\nvXo1eXl5VFZWpt3jl9VMQuJANcMiEpk49SfcWl27dmXatGmceuqpjBo1ig0bNkQdkiSZMmUK48eP\nT7tEWCQuVDMssaCa4c5nz549FBQUcMIJJzBp0qSow+n0nHPceeedPPzwwyxevJghQ4ZEHZIA1dXV\nZGdns3LlyrR8/LJqhiUO1LWaiERC7YRbxsy49dZb6dOnD7m5uSxcuJDjjjsu6rBib9asWeTm5qZl\nIiwSF0qGRaTDLVu2LNb9CR+Ib3/72/Tp04czzzyT+fPnM3LkyKhDii3nHCUlJRQXF0cdiogcACXD\nItKhNm3axLhx49RO+ABceeWVZGZmcv755zNnzhzy8vKiDimWysvLqampIT8/P+pQROQA6AY6Eekw\ne/bs4aqrrlJ/wm3gwgsvZPbs2VxyySWUlZVFHU4slZaWUlRUREaGDqUiqUw30Eks6Aa6zmHSpEnM\nmzePpUuXqnlEG1mxYgUFBQUUFxdzxRVXRB1ObFRVVZGTk0NFRUVaP35ZN9BJHKiZhIh0iGXLlnH/\n/fernXAbO/nkk1myZAnnnnsu27ZtY8KECVGHFAtTp06lsLAwrRNhkbhQMiwi7U7thNvX8ccfz/PP\nP8+YMWPYunUrt9xyC2aqzGsvtbW1PPDAA2qeIpImlAxLWjCzd4FtwB7gX865U6KNSBLUTrhjDB06\nlBdeeIFzzjmHrVu3UlxcrIS4nZSVlZGVlcWIESOiDqVdqWWZxIXaDEtaMLO1wOedc1sbGK82wxFR\nO+GOtWXLFi644AKOO+44HnzwQbp06RJ1SGnnrLPO4tprr+Xyyy+PLAbn4OOP4aOP9v7t3Nm27z/6\nCJxTm2FJf0qGJS2YWQUw0jm3uYHxSoYjsGzZMgoLC1mxYoWaR3Sg6upqLrroInr37s3MmTP1mOA2\ntHr1avLy8qisrGxwvToHu3a1fXKa/L57d+jZc+9fr177vq9vWEveH3wwdOumZFjSn5JhSQtBzfAW\nwAEPOuemJo1XMtzBNm3axEknncSUKVPUPCICu3btYty4cezYsYOnnnqKXr16RR1Sp9BQotrcZPS5\n517CuZ4MG3ZCo59vKlFt6n1zEtWuHdDQUb1JSByozbCkiy855zaY2eHAIjN7wzm3LPyB22+/ve51\nXl6eHlTQjtROOHo9evRg9uzZfP3rX2fMmDEsWLCAvn37Rh1WoxKJanvUorYkUU0e1qsX9OkDXbp8\nzKOPPswvfnE72dnRJ6rtYenSpSxdujTqMEQ6lGqGJe2Y2W3ADufc5NAw1Qx3ILUT7jz27NnDxIkT\nWbx4MU8//TQDBw5s1XRakqgeSLKanKge6KX+tkxUH3zwQf74xz/yhz/8oXUTSEGqGZY4UDIsKc/M\negIZzrlqM+sFPA3c4Zx7OvQZJcMdRO2EO15TierOnY5Zs/7Ac8+t4Jvf/D4HHdS/VYlqt25tm5im\nUo2qc44RI0ZQXFzMmDFjog6nwygZljjopLsdkRYZADxlZg5fpmeGE2HpOOpPeH/NvZmqtXf7N69G\n1ejZ8yKOPno4kyfPZezYr5CVdRhHHrlvItqrV8PJamdOVDtCeXk5NTU15OfnRx2KiLSxGO/aJF04\n5yqA9O7wMwWkYjvh5nRPdaBJamtvpurTpz1qVI/nkUf+yk03ncD8+fMZOXJke6/itFFaWkpRUREZ\nGRlRhyIibUzNJCQW1Eyi/bV1O+G26Ee1pd1TtfUd/4m/ztbV79y5c7n++uuZM2eObiRthqqqKnJy\ncqioqIjd45fVTELiQDXDItJiyZf+X3jhFe69dxEPPvh7nn22W5v1ANCaRLVv3+Z//uCDO1+i2hEu\nvPBCMjMzueSSS5g+fToFBQVRh9SpTZ06lcLCwtglwiJxoZphiYU41Qy3VYf/ze2e6qCDdrNx47tk\nZR3GwIG92+zGqs5Yo5puVqxYQUFBAcXFxVxxxRVRh9Mp1dbWMnToUMrKytL+8cv1Uc2wxIFqhkU6\n0IF2+N/SRLW1bVSbm6ju2bOHL3+5gBNPPJFJkyZFvXqlhU4++WSWLFnCueeey1tvvcWoUaMYNmwY\ngwYNomuc75YLKSsrIysrK5aJsEhcqGZYYqE5NcOdpcP/A33fkXf9qz/h9FBRUcFdd93F22+/zdq1\na6mqqmLw4MEMGzas7u/oo4+ue927d++oQ+4wZ511Ftdeey2XX3551KFEQjXDEgdKhiUWzMxdfLFr\nNFmtqfH9qLblzVPpfOlf/Qmnr127dlFZWcnatWtZu3Yt77zzTt3rtWvX0r17930S5XCynE61yqtX\nryYvL4/Kykp69OgRdTiRUDIscaBkWGLBzNzvfudik6i2t02bNnHSSScxZcqUlOlGTdqGc45NmzY1\nmCinU63yd7/7XQ455BDuuuuuqEOJjJJhiQMlwxILcbqBrr35dsJfVjthqVe4Vjk5UU6lWuXq6mqy\ns7NZuXIlWVlZUYcTGSXDEgdKhiUWlAy3HbUTltZKpVrlBx98kD/+8Y/84Q9/6LB5dkZKhiUOlAxL\nLCgZbhtqJyztqbPUKjvnGDFiBMXFxYwZM6ZNppmqlAxLHCgZllhQMnzg1E5YohSuVa4vUW7LWuVl\ny5Zx3XXXsXr16tg/flnJsMSBkmGJBSXDB0bthKWzS9Qq15cot7RWedy4cZxyyinccMMNES5R56Bk\nWOJAybDEgpm5F198kZEjR3aaG3RSidoJSyprSa3y0KFDmTNnDhUVFXr8MkqGJR6UDEssmJk78cQT\nee+998jLy+Oss87irLPOYvjw4ZhpP98YtROWdJdcq/ypT32Kr33ta1GH1SkoGZY4UDIssZBoJrFh\nwwaWLFnC4sWLWbRoERkZGXWJcX5+PgMGDIg61E5F7YRF4k3JsMSBkmGJhfraDDvnePPNN1m0aBGL\nFy9m6dKlZGdn1yXHZ5xxBr169Yoo4uipnbCIKBmWOFAyLLHQnBvoamtrefnll+uS41deeYWRI0fW\nJcdxa2+sdsIiomRY4kDJsMRCa3qTqK6u5vnnn2fx4sUsXrw4Vu2N1U5YREDJsMSDkmGJhbboWi0u\n7Y3VTlhEEpQMSxwoGZZYaOt+htO1vbHaCYtImJJhiQMlwxIL7f3QjXRpb6x2wiISpmRY4kDJsMRC\nRz+BLhXbG6udsIgkUzIscaBkWGIh6scxd/b2xmonLCL1UTIscaBkWGIh6mQ4LNHeOJEYR93eWO2E\nRaQhSoYlDpQMSyx0pmQ4WaK9cSI57uj2xmonLCINUTIscaBkWGKhMyfDyaqrq3nhhRfqbsZrz/bG\naicsIo1RMixxoGRYYiGVkuFkGzZs4JlnnqlLjs2sTdobq52wiDRFybDEgZJhiYVUTobD2qq9sdoJ\ni0hzKBmWOFAyLLGQLslwsta2N1Y7YRFpDiXDEgdKhiUW0jUZTtac9sbl5eVqJywizaJkWOJAybDE\nQlyS4WT1tTfetWsXv/nNb9ROWESapGRY4kDJsMRCXJPhsER7440bN3L66adHHY6IpAAlwxIHSoYl\nFpQMi4i0nJJhiYOMqAMQEREREYmKkmERERERiS0lw5IWzOxcM1ttZm+a2Q+jjkdERERSg5JhSXlm\nlgH8N3AOcDxwmZnlRBtV57V06dKoQ+g0tC720rrYS+tCJF6UDEs6OAV4yzlX6Zz7F/A4cGHEMXVa\nOglkga0AAAMvSURBVNDvpXWxl9bFXloXIvGiZFjSwVHAe6H3/wiGiYiIiDRKybCkg/q6/VE/aiIi\nItIk9TMsKc/MTgVud86dG7y/GXDOuUmhz6igi4i0gvoZlnSnZFhSnpl1AdYA+cB64CXgMufcG5EG\nJiIiIp1e16gDEDlQzrndZvYt4Gl805/pSoRFRESkOVQzLCIiIiKxpRvoJO3pgRyemU03syozey3q\nWKJmZoPM7BkzW2VmfzOz70QdU1TMrIeZ/cXMVgbr4raoY4qamWWY2V/NbF7UsUTJzN41s/8LysZL\nUccj0l5UMyxpLXggx5v49sQfACuAS51zqyMNLAJmdjpQDcxwzn026niiZGYDgYHOuVfN7BDgFeDC\nOJYLADPr6Zz7KGh/Xw58xzkX2+THzG4EPg9kOue+EnU8UTGztcDnnXNbo45FpD2pZljSnR7IEXDO\nLQN0UAOccxucc68Gr6uBN4hx39TOuY+Clz3w95LEtpbEzAYB5wPToo6lEzCUJ0gMqJBLutMDOaRR\nZjYEGAH8JdpIohM0C1gJbAAWOedWRB1ThO4HbiLGJwQhDlhoZivM7PqogxFpL0qGJd3pgRzSoKCJ\nxBPAd4Ma4lhyzu1xzv0/YBDwBTM7LuqYomBmFwBVwVUDo/79R5x8yTk3El9TPiFoaiWSdpQMS7r7\nB5AVej8I33ZYYs7MuuIT4Uecc3OjjqczcM5tB5YC50YcSlROA74StJV9DBhtZjMijikyzrkNwf+N\nwFP4ZmciaUfJsKS7FcCnzSzbzLoDlwJxvkNctV17/QZY5Zz7VdSBRMnMDjOz3sHrg4GzgFjeSOic\n+5FzLss5Nwy/r3jGOXdV1HFFwcx6BldOMLNewNnA36ONSqR9KBmWtOac2w0kHsjxOvB4XB/IYWaz\ngOXAcDNbZ2bXRh1TVMzsNOBy4Myg26i/mllca0OPAJ41s1fx7aYXOuf+GHFMEr0BwLKgLfmfgTLn\n3NMRxyTSLtS1moiIiIjElmqGRURERCS2lAyLiIiISGwpGRYRERGR2FIyLCIiIiKxpWRYRERERGJL\nybCIiIiIxJaSYRERERGJLSXDIiIiIhJb/x92VSaXEHd6dgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1132a04a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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stJiecxkiIlKYJUuWsHjxYs4888y0iyKdgAK1MuTuq9z9mfh6K/AiUAucDcyK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\niIiUKQVqIiIiImXq/wcq4oxAJrR32wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1132c8320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BlYiItBt64Ke0Zer+kxzq/hORtmr16tUcfPDBrFmzhp49e2ZdnB3U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\nILKYvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1180412b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SV1fHo48+mu9sSBFSgCYiItJNrr32Wk488cR8Z0OKkAI0ERGRbuDuzJkzhzPO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\nAvP/ATh5MB9uWcd3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11804f6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bgHnu/nsz+zfgUHe/wswuBM51991/3Q81b4mI1Gfnzp0MHTqUefPmMXLkyNp0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\nj4iItLnnn3+ebt26MX78+Hx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lqnpVW5aIiEgd1KenkzKzCcBUd58YP18LeLIzs5np4IqI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187cbe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FDAqzUzVZJgMPmFmNma0ElgOnhNdyM1tlZtXAA2FZgHOAv4Xpe4EpsW3dG6b/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\nhXPOuQZ5oHDOOdeg/w87VgvL8eSg1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119807748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VLfxMNoPuHZQnC1ax+onHpFzaNGXKlPbt2tpaamtrU1UVEcmZ6dOnc++99+ak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\niHRIgUJERDqkQCEiIh1SoBARkQ79fw1kIyPiWRwEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ac2f128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dR5xdXldNu/sP3b2bu/cCxgDPufuXgeeBi0Nv44BHw+d/hO+E35+LdR8TWlX3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aeb17f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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h7lB6LCUIWWBmvYEbgY8nv93SOLNmzWp8XlZWRllZWUeEJiLSJS1atIghQ4Y0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\n0L7KPQ1PAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11af6acf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9W2Io8dMTxcXFzJ07l9/85jdcddVVEUclTUX32UlzZlYAPO2cGxw8vxHo45yb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\nqMM5IipjxZNadjLTccBmM3v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Sa+qgHENm9nkze8/M3jez/4g6nqiY2YNmtsHMFkcdS9R0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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11afeef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IeXn5jBxZwPDh+QwceESrhNRZVWRVVT0bNmzgnHM+y4cfdq36MtgB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\nRESSSolGRESSSolGRESSSolGRESS6v8DlSiHR2PK9zkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b072278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rc24JsKORQfcD32rncEREOo2nnnqK888/n65du0YdSqeWksm1MWY2EVjnnFsR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\nU3IVERFpZUquIiIirez/AwhMGJ+SMnpwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b0a9860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KOKffONCihnn+U+B4M5sbfdHMavBlhp+EG9ev8Al1Mf3kIJf5v/hPlS91zh2G/0Q60k6A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\nBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b177978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SGOnuGwDcfT3wzhTaJiKSV4rxOpZGYaoADgeud/fDgTcJMZ5Og0Sk16upqVGM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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b1b0c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2bRojR47cYpxKxLmpRCwiItvkmWeeoVevXhx66KFph9IlKRGLiMg2qaqqYvz4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\n/wE8saFIeiv6tAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b293588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "now='2017-09-15 00:00:00'\n",
    "result = getMethodLevelAnomalies(data,now)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AnomalyStrength</th>\n",
       "      <th>INTERVAL_START</th>\n",
       "      <th>Level</th>\n",
       "      <th>Measure</th>\n",
       "      <th>object</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.204545</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.962264</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.639679</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>FORIS/IL/NationalCorporateInternetHelper/INati...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>108.645560</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.529246</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>18.910492</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>24.416972</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/OTSP/v001/IOTSPWcf GetPriceBasePeriod</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>40.447859</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/OTSP/v001/IOTSPWcf MakeBill</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.060741</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.861559</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>FORIS/IL/NationalCorporateInternetHelper/IPort...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   AnomalyStrength       INTERVAL_START   Level             Measure  \\\n",
       "0         9.204545  2017-09-15 00:00:00  Method  BusinessErrorCount   \n",
       "1         3.962264  2017-09-15 00:00:00  Method  BusinessErrorCount   \n",
       "2         8.639679  2017-09-15 00:00:00  Method           TotalTime   \n",
       "3       108.645560  2017-09-15 00:00:00  Method           TotalTime   \n",
       "4        10.529246  2017-09-15 00:00:00  Method           TotalTime   \n",
       "5        18.910492  2017-09-15 00:00:00  Method           TotalTime   \n",
       "6        24.416972  2017-09-15 00:00:00  Method           TotalTime   \n",
       "7        40.447859  2017-09-15 00:00:00  Method           TotalTime   \n",
       "8         4.060741  2017-09-15 00:00:00  Method           TotalTime   \n",
       "9         4.861559  2017-09-15 00:00:00  Method         AvgDuration   \n",
       "\n",
       "                                              object  \n",
       "0  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "1  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2  FORIS/IL/NationalCorporateInternetHelper/INati...  \n",
       "3  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "4  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "5  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "6         SUPS/OTSP/v001/IOTSPWcf GetPriceBasePeriod  \n",
       "7                   SUPS/OTSP/v001/IOTSPWcf MakeBill  \n",
       "8  marti/workflow/services/IProcessFacade StartOC...  \n",
       "9  FORIS/IL/NationalCorporateInternetHelper/IPort...  "
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(result)\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "#without debug output, could be run on realtime\n",
    "def getMethodLevelAnomalies(data, time, WindowSize=5, AnomalyThreshold=3.5,BusinessErrorCountThreshold=4,TotalTimeThreshold=10000,AvgDurationThreshold=2):\n",
    "    report_structure = []\n",
    "\n",
    "    data_filtered = data[(data['INTERVAL_START'] >= datetime.datetime.strptime(time, \"%Y-%m-%d %H:%M:00\") - datetime.timedelta(hours=WindowSize)) \n",
    "                             & (data['INTERVAL_START'] <= time)]\n",
    "    data_grouped = data_filtered.groupby('ServiceContractMethod')\n",
    "    for name, method_group in data_grouped:\n",
    "        time_method_group = method_group.groupby('INTERVAL_START')\n",
    "\n",
    "        #BusinessErrorCount measure\n",
    "        time_method_group_measure = time_method_group.agg({'BusinessErrorCount' : np.sum})\n",
    "        time_method_group_measure = time_method_group_measure.reset_index()\n",
    "        if(time_method_group_measure.size > (WindowSize*2) ):\n",
    "            regression_model = linear_model.LinearRegression()\n",
    "            regression_model.fit(X = pd.DataFrame(time_method_group_measure.index[:-1]),y = time_method_group_measure[\"BusinessErrorCount\"][:-1])\n",
    "            train_prediction = regression_model.predict(X = pd.DataFrame(time_method_group_measure.index))\n",
    "            regression_prediction = train_prediction[-1]\n",
    "            mean_prediction = time_method_group_measure[\"BusinessErrorCount\"][:-1].mean()\n",
    "            if(mean_prediction<BusinessErrorCountThreshold):\n",
    "                continue\n",
    "            prediction = max(regression_prediction,mean_prediction)\n",
    "            AnomalyStrength = list(time_method_group_measure['BusinessErrorCount'])[-1]/prediction\n",
    "            if(AnomalyStrength>20):\n",
    "                AnomalyStrength=20\n",
    "            if(AnomalyStrength<0): \n",
    "                AnomalyStrength=0\n",
    "            if(AnomalyStrength>AnomalyThreshold):\n",
    "                report_structure.append({'INTERVAL_START':time,'Level':'Method','object':name,'Measure':'BusinessErrorCount','AnomalyStrength':AnomalyStrength})\n",
    "\n",
    "    data_filtered = data[(data['INTERVAL_START'] >= datetime.datetime.strptime(time, \"%Y-%m-%d %H:%M:00\") - datetime.timedelta(hours=WindowSize)) \n",
    "                             & (data['INTERVAL_START'] <= time)]\n",
    "    data_grouped = data_filtered.groupby('ServiceContractMethod')\n",
    "    for name, method_group in data_grouped:\n",
    "        time_method_group = method_group.groupby('INTERVAL_START')\n",
    "\n",
    "        #TotalTime measure\n",
    "        time_method_group_measure = time_method_group.agg({'TotalTime' : np.sum})\n",
    "        time_method_group_measure = time_method_group_measure.reset_index()\n",
    "        if(time_method_group_measure.size > (WindowSize*2) ):\n",
    "            regression_model = linear_model.LinearRegression()\n",
    "            regression_model.fit(X = pd.DataFrame(time_method_group_measure.index[:-1]),y = time_method_group_measure[\"TotalTime\"][:-1])\n",
    "            train_prediction = regression_model.predict(X = pd.DataFrame(time_method_group_measure.index))\n",
    "            regression_prediction = train_prediction[-1]\n",
    "            mean_prediction = time_method_group_measure[\"TotalTime\"][:-1].mean()\n",
    "            if(mean_prediction<TotalTimeThreshold):\n",
    "                continue\n",
    "            prediction = max(regression_prediction,mean_prediction)\n",
    "            AnomalyStrength = list(time_method_group_measure['TotalTime'])[-1]/prediction\n",
    "            if(AnomalyStrength>30):\n",
    "                AnomalyStrength=30\n",
    "            if(AnomalyStrength<0): \n",
    "                AnomalyStrength=0\n",
    "            if(AnomalyStrength>AnomalyThreshold):\n",
    "                report_structure.append({'INTERVAL_START':time,'Level':'Method','object':name,'Measure':'TotalTime','AnomalyStrength':AnomalyStrength})\n",
    "\n",
    "    data_filtered = data[(data['INTERVAL_START'] >= datetime.datetime.strptime(time, \"%Y-%m-%d %H:%M:00\") - datetime.timedelta(hours=WindowSize)) \n",
    "                             & (data['INTERVAL_START'] <= time)]\n",
    "    data_grouped = data_filtered.groupby('ServiceContractMethod')\n",
    "    for name, method_group in data_grouped:\n",
    "        time_method_group = method_group.groupby('INTERVAL_START')\n",
    "\n",
    "        #AvgDuration measure\n",
    "        time_method_group_measure = time_method_group.agg({'AvgDuration' : np.mean})\n",
    "        time_method_group_measure = time_method_group_measure.reset_index()\n",
    "        if(time_method_group_measure.size > (WindowSize*2) ):\n",
    "\n",
    "            regression_model = linear_model.LinearRegression()\n",
    "            regression_model.fit(X = pd.DataFrame(time_method_group_measure.index[:-1]),y = time_method_group_measure[\"AvgDuration\"][:-1])\n",
    "            train_prediction = regression_model.predict(X = pd.DataFrame(time_method_group_measure.index))\n",
    "            regression_prediction = train_prediction[-1]\n",
    "            mean_prediction = time_method_group_measure[\"AvgDuration\"][:-1].mean()\n",
    "            if(mean_prediction<AvgDurationThreshold):\n",
    "                continue\n",
    "            prediction = max(regression_prediction,mean_prediction)\n",
    "            AnomalyStrength = list(time_method_group_measure['AvgDuration'])[-1]/prediction\n",
    "            if(AnomalyStrength>30):\n",
    "                AnomalyStrength=30\n",
    "            if(AnomalyStrength<0): \n",
    "                AnomalyStrength=0\n",
    "            if(AnomalyStrength>AnomalyThreshold):\n",
    "                report_structure.append({'INTERVAL_START':time,'Level':'Method','object':name,'Measure':'AvgDuration','AnomalyStrength':AnomalyStrength})\n",
    "    \n",
    "    return report_structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "now='2017-09-15 00:00:00'\n",
    "result = getMethodLevelAnomalies(data,now)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AnomalyStrength</th>\n",
       "      <th>INTERVAL_START</th>\n",
       "      <th>Level</th>\n",
       "      <th>Measure</th>\n",
       "      <th>object</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.204545</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.962264</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.639679</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>FORIS/IL/NationalCorporateInternetHelper/INati...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>30.000000</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.529246</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>18.910492</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>24.416972</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/OTSP/v001/IOTSPWcf GetPriceBasePeriod</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>30.000000</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/OTSP/v001/IOTSPWcf MakeBill</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.060741</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.861559</td>\n",
       "      <td>2017-09-15 00:00:00</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>FORIS/IL/NationalCorporateInternetHelper/IPort...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   AnomalyStrength       INTERVAL_START   Level             Measure  \\\n",
       "0         9.204545  2017-09-15 00:00:00  Method  BusinessErrorCount   \n",
       "1         3.962264  2017-09-15 00:00:00  Method  BusinessErrorCount   \n",
       "2         8.639679  2017-09-15 00:00:00  Method           TotalTime   \n",
       "3        30.000000  2017-09-15 00:00:00  Method           TotalTime   \n",
       "4        10.529246  2017-09-15 00:00:00  Method           TotalTime   \n",
       "5        18.910492  2017-09-15 00:00:00  Method           TotalTime   \n",
       "6        24.416972  2017-09-15 00:00:00  Method           TotalTime   \n",
       "7        30.000000  2017-09-15 00:00:00  Method           TotalTime   \n",
       "8         4.060741  2017-09-15 00:00:00  Method           TotalTime   \n",
       "9         4.861559  2017-09-15 00:00:00  Method         AvgDuration   \n",
       "\n",
       "                                              object  \n",
       "0  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "1  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2  FORIS/IL/NationalCorporateInternetHelper/INati...  \n",
       "3  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "4  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "5  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "6         SUPS/OTSP/v001/IOTSPWcf GetPriceBasePeriod  \n",
       "7                   SUPS/OTSP/v001/IOTSPWcf MakeBill  \n",
       "8  marti/workflow/services/IProcessFacade StartOC...  \n",
       "9  FORIS/IL/NationalCorporateInternetHelper/IPort...  "
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(result)\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['2017-09-14 00:00:00', '2017-09-14 01:00:00', '2017-09-14 02:00:00', '2017-09-14 03:00:00', '2017-09-14 04:00:00', '2017-09-14 05:00:00', '2017-09-14 06:00:00', '2017-09-14 07:00:00', '2017-09-14 08:00:00', '2017-09-14 09:00:00', '2017-09-14 10:00:00', '2017-09-14 11:00:00', '2017-09-14 12:00:00']\n"
     ]
    }
   ],
   "source": [
    "def perdelta(start, end, delta):\n",
    "    curr = start\n",
    "    while curr <= end:\n",
    "        yield curr\n",
    "        curr += delta\n",
    "        \n",
    "def generateDateRangeByHour(fromt,tot):\n",
    "    result = []\n",
    "    for dt in perdelta(datetime.datetime.strptime(fromt, \"%Y-%m-%d %H:%M:00\"),\n",
    "                       datetime.datetime.strptime(tot, \"%Y-%m-%d %H:%M:00\"),\n",
    "                       timedelta(hours=1)):\n",
    "        result.append(str(dt))\n",
    "    return result\n",
    "\n",
    "\n",
    "print(generateDateRangeByHour('2017-09-14 00:00:00','2017-09-14 12:00:00'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "#batch data processing. Could take a lot of time, for me 10 minutes.\n",
    "#complexity: methodCount * hoursCount\n",
    "def analysePeriod(data,fromt,tot):\n",
    "    result = []\n",
    "    times = generateDateRangeByHour(fromt,tot)\n",
    "    for now in times:\n",
    "        result = result + getMethodLevelAnomalies(data,now)\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = analysePeriod(data,'2017-09-14 06:00:00','2017-09-16 00:00:00') #move to 16 00:00\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AnomalyStrength</th>\n",
       "      <th>Level</th>\n",
       "      <th>Measure</th>\n",
       "      <th>object</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INTERVAL_START</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-09-14 06:00:00</th>\n",
       "      <td>3.537736</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 07:00:00</th>\n",
       "      <td>3.736842</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 08:00:00</th>\n",
       "      <td>3.863636</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 08:00:00</th>\n",
       "      <td>8.750000</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartCh...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 08:00:00</th>\n",
       "      <td>7.086245</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>marti/sales/services/IRequestDirectory Workflo...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 09:00:00</th>\n",
       "      <td>4.262295</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 09:00:00</th>\n",
       "      <td>20.000000</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 09:00:00</th>\n",
       "      <td>3.782584</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 10:00:00</th>\n",
       "      <td>4.485940</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>billing/AccountsReceivable/IFinancialData GetH...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 12:00:00</th>\n",
       "      <td>20.000000</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>SUPS/StateIn/v001/IStateInWcf QueryAccountInfo...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 12:00:00</th>\n",
       "      <td>5.018821</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>Foris.IL.BulkServiceOperations/2009/01/IFacade...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 12:00:00</th>\n",
       "      <td>9.358493</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/StateIn/v001/IStateInWcf QueryAccountInfo...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 12:00:00</th>\n",
       "      <td>5.796677</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/StateIn/v001/IStateInWcf QueryPhoneInform...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 13:00:00</th>\n",
       "      <td>3.695652</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>11.764706</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>20.000000</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>20.000000</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>20.000000</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v002/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>6.266667</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>13.347826</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>7.566138</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>10.769231</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>7.228261</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>15.849057</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 14:00:00</th>\n",
       "      <td>5.429316</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>billing/AccountsReceivable/IFinancialData GetH...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 15:00:00</th>\n",
       "      <td>5.166448</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>marti/sales/services/IDocumentDirectory GetDoc...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 16:00:00</th>\n",
       "      <td>3.703704</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 17:00:00</th>\n",
       "      <td>3.880597</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartCh...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 21:00:00</th>\n",
       "      <td>5.185185</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 21:00:00</th>\n",
       "      <td>4.166667</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 22:00:00</th>\n",
       "      <td>4.194685</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>FORIS/UMRS/CRM/ICRM GetPeData</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-14 22:00:00</th>\n",
       "      <td>3.543598</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>9.204545</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>3.962264</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>8.639679</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>FORIS/IL/NationalCorporateInternetHelper/INati...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>30.000000</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>10.529246</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>18.910492</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>24.416972</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/OTSP/v001/IOTSPWcf GetPriceBasePeriod</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>30.000000</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>SUPS/OTSP/v001/IOTSPWcf MakeBill</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>4.060741</td>\n",
       "      <td>Method</td>\n",
       "      <td>TotalTime</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>4.861559</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>FORIS/IL/NationalCorporateInternetHelper/IPort...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>4.027061</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>OrderManagement.BusinessProcess.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>4.099558</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>6.449415</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>8.670972</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>9.049849</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 00:00:00</th>\n",
       "      <td>12.474829</td>\n",
       "      <td>Method</td>\n",
       "      <td>AvgDuration</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartOC...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 01:00:00</th>\n",
       "      <td>4.183007</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>Foris.OrderManagement.Workflow2.Services/v001/...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-15 01:00:00</th>\n",
       "      <td>17.819549</td>\n",
       "      <td>Method</td>\n",
       "      <td>BusinessErrorCount</td>\n",
       "      <td>marti/workflow/services/IProcessFacade StartDe...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     AnomalyStrength   Level             Measure  \\\n",
       "INTERVAL_START                                                     \n",
       "2017-09-14 06:00:00         3.537736  Method  BusinessErrorCount   \n",
       "2017-09-14 07:00:00         3.736842  Method  BusinessErrorCount   \n",
       "2017-09-14 08:00:00         3.863636  Method  BusinessErrorCount   \n",
       "2017-09-14 08:00:00         8.750000  Method  BusinessErrorCount   \n",
       "2017-09-14 08:00:00         7.086245  Method         AvgDuration   \n",
       "2017-09-14 09:00:00         4.262295  Method  BusinessErrorCount   \n",
       "2017-09-14 09:00:00        20.000000  Method  BusinessErrorCount   \n",
       "2017-09-14 09:00:00         3.782584  Method         AvgDuration   \n",
       "2017-09-14 10:00:00         4.485940  Method         AvgDuration   \n",
       "2017-09-14 12:00:00        20.000000  Method  BusinessErrorCount   \n",
       "2017-09-14 12:00:00         5.018821  Method           TotalTime   \n",
       "2017-09-14 12:00:00         9.358493  Method           TotalTime   \n",
       "2017-09-14 12:00:00         5.796677  Method           TotalTime   \n",
       "2017-09-14 13:00:00         3.695652  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00        11.764706  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00        20.000000  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00        20.000000  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00        20.000000  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00         6.266667  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00        13.347826  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00         7.566138  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00        10.769231  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00         7.228261  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00        15.849057  Method  BusinessErrorCount   \n",
       "2017-09-14 14:00:00         5.429316  Method         AvgDuration   \n",
       "2017-09-14 15:00:00         5.166448  Method         AvgDuration   \n",
       "2017-09-14 16:00:00         3.703704  Method  BusinessErrorCount   \n",
       "2017-09-14 17:00:00         3.880597  Method  BusinessErrorCount   \n",
       "2017-09-14 21:00:00         5.185185  Method  BusinessErrorCount   \n",
       "2017-09-14 21:00:00         4.166667  Method  BusinessErrorCount   \n",
       "2017-09-14 22:00:00         4.194685  Method  BusinessErrorCount   \n",
       "2017-09-14 22:00:00         3.543598  Method         AvgDuration   \n",
       "2017-09-15 00:00:00         9.204545  Method  BusinessErrorCount   \n",
       "2017-09-15 00:00:00         3.962264  Method  BusinessErrorCount   \n",
       "2017-09-15 00:00:00         8.639679  Method           TotalTime   \n",
       "2017-09-15 00:00:00        30.000000  Method           TotalTime   \n",
       "2017-09-15 00:00:00        10.529246  Method           TotalTime   \n",
       "2017-09-15 00:00:00        18.910492  Method           TotalTime   \n",
       "2017-09-15 00:00:00        24.416972  Method           TotalTime   \n",
       "2017-09-15 00:00:00        30.000000  Method           TotalTime   \n",
       "2017-09-15 00:00:00         4.060741  Method           TotalTime   \n",
       "2017-09-15 00:00:00         4.861559  Method         AvgDuration   \n",
       "2017-09-15 00:00:00         4.027061  Method         AvgDuration   \n",
       "2017-09-15 00:00:00         4.099558  Method         AvgDuration   \n",
       "2017-09-15 00:00:00         6.449415  Method         AvgDuration   \n",
       "2017-09-15 00:00:00         8.670972  Method         AvgDuration   \n",
       "2017-09-15 00:00:00         9.049849  Method         AvgDuration   \n",
       "2017-09-15 00:00:00        12.474829  Method         AvgDuration   \n",
       "2017-09-15 01:00:00         4.183007  Method  BusinessErrorCount   \n",
       "2017-09-15 01:00:00        17.819549  Method  BusinessErrorCount   \n",
       "\n",
       "                                                                object  \n",
       "INTERVAL_START                                                          \n",
       "2017-09-14 06:00:00  Foris.OrderManagement.Workflow2.Services/v001/...  \n",
       "2017-09-14 07:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-14 08:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 08:00:00  marti/workflow/services/IProcessFacade StartCh...  \n",
       "2017-09-14 08:00:00  marti/sales/services/IRequestDirectory Workflo...  \n",
       "2017-09-14 09:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 09:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-14 09:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 10:00:00  billing/AccountsReceivable/IFinancialData GetH...  \n",
       "2017-09-14 12:00:00  SUPS/StateIn/v001/IStateInWcf QueryAccountInfo...  \n",
       "2017-09-14 12:00:00  Foris.IL.BulkServiceOperations/2009/01/IFacade...  \n",
       "2017-09-14 12:00:00  SUPS/StateIn/v001/IStateInWcf QueryAccountInfo...  \n",
       "2017-09-14 12:00:00  SUPS/StateIn/v001/IStateInWcf QueryPhoneInform...  \n",
       "2017-09-14 13:00:00  Foris.OrderManagement.Workflow2.Services/v001/...  \n",
       "2017-09-14 14:00:00  Foris.OrderManagement.Workflow2.Services/v001/...  \n",
       "2017-09-14 14:00:00  Foris.OrderManagement.Workflow2.Services/v001/...  \n",
       "2017-09-14 14:00:00  Foris.OrderManagement.Workflow2.Services/v001/...  \n",
       "2017-09-14 14:00:00  Foris.OrderManagement.Workflow2.Services/v002/...  \n",
       "2017-09-14 14:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 14:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 14:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 14:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 14:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 14:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 14:00:00  billing/AccountsReceivable/IFinancialData GetH...  \n",
       "2017-09-14 15:00:00  marti/sales/services/IDocumentDirectory GetDoc...  \n",
       "2017-09-14 16:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 17:00:00  marti/workflow/services/IProcessFacade StartCh...  \n",
       "2017-09-14 21:00:00  Foris.OrderManagement.Workflow2.Services/v001/...  \n",
       "2017-09-14 21:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-14 22:00:00                      FORIS/UMRS/CRM/ICRM GetPeData  \n",
       "2017-09-14 22:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-15 00:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-15 00:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-15 00:00:00  FORIS/IL/NationalCorporateInternetHelper/INati...  \n",
       "2017-09-15 00:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-15 00:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-15 00:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-15 00:00:00         SUPS/OTSP/v001/IOTSPWcf GetPriceBasePeriod  \n",
       "2017-09-15 00:00:00                   SUPS/OTSP/v001/IOTSPWcf MakeBill  \n",
       "2017-09-15 00:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-15 00:00:00  FORIS/IL/NationalCorporateInternetHelper/IPort...  \n",
       "2017-09-15 00:00:00  OrderManagement.BusinessProcess.Services/v001/...  \n",
       "2017-09-15 00:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-15 00:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-15 00:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-15 00:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-15 00:00:00  marti/workflow/services/IProcessFacade StartOC...  \n",
       "2017-09-15 01:00:00  Foris.OrderManagement.Workflow2.Services/v001/...  \n",
       "2017-09-15 01:00:00  marti/workflow/services/IProcessFacade StartDe...  "
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(result)\n",
    "df = df.set_index('INTERVAL_START')\n",
    "df.head(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "writer = pd.ExcelWriter('output.xlsx')\n",
    "df.to_excel(writer,'Sheet1')\n",
    "writer.save()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11b981470>"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BIq5i5XUDUF4uYctc2nD1ahGrqD2rdN8TAL7zHeDXv45+8DIgN1iNjXL+Rt1u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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117d82f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe id=\"igraph\" scrolling=\"no\" style=\"border:none;\" seamless=\"seamless\" src=\"https://plot.ly/~aydar.tech/2.embed\" height=\"525px\" width=\"100%\"></iframe>"
      ],
      "text/plain": [
       "<plotly.tools.PlotlyDisplay object>"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import plotly \n",
    "import plotly.plotly as py\n",
    "import plotly.graph_objs as go\n",
    "\n",
    "plotly.tools.set_credentials_file(username='aydar.tech', api_key='Ify4HOzEdTSWSXOnm7wX')\n",
    "\n",
    "layout= go.Layout(\n",
    "    title= 'SystemAnomalyAnalysis',\n",
    "    hovermode= 'closest',\n",
    "    xaxis= dict(\n",
    "        title= 'DateTime',\n",
    "        zeroline= False,\n",
    "    ),\n",
    "    yaxis=dict(\n",
    "        title= 'AnomalyStrength',\n",
    "    )\n",
    ")\n",
    "\n",
    "group=df.groupby('Measure').get_group('AvgDuration')\n",
    "AvgDurationAnomaly = go.Scatter(\n",
    "    x = group.index,\n",
    "    text= group['object'],\n",
    "    y = group['AnomalyStrength'],\n",
    "    name = 'AvgDurationAnomaly',\n",
    "    mode = 'markers',\n",
    ")\n",
    "group=df.groupby('Measure').get_group('BusinessErrorCount')\n",
    "BusinessErrorCountAnomaly = go.Scatter(\n",
    "    x = group.index,\n",
    "    text= group['object'],\n",
    "    y = group['AnomalyStrength'],\n",
    "    name = 'BusinessErrorCountAnomaly',\n",
    "    mode = 'markers',\n",
    ")\n",
    "group=df.groupby('Measure').get_group('TotalTime')\n",
    "TotalTimeAnomaly = go.Scatter(\n",
    "    x = group.index,\n",
    "    text= group['object'],\n",
    "    y = group['AnomalyStrength'],\n",
    "    name = 'TotalTimeAnomaly',\n",
    "    mode = 'markers',\n",
    ")\n",
    "\n",
    "data = [AvgDurationAnomaly,BusinessErrorCountAnomaly,TotalTimeAnomaly]\n",
    "\n",
    "fig = go.Figure(data=data, layout=layout)\n",
    "py.iplot(fig, filename='SystemAnomalyAnalysis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}