{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "subject-wagon",
   "metadata": {},
   "source": [
    "# EasyVVUQ - Vector Quantities of Interest"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protective-intervention",
   "metadata": {},
   "source": [
    "**Author**: Vytautas Jancauskas, LRZ (jancauskas@lrz.de)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "elect-tract",
   "metadata": {},
   "source": [
    "It is often the case that simulation outputs are vector valued and represent changes over time in whatever phenomenon that is simulated. Here we examine how to analyse these cases with EasyVVUQ. As an example we use the following model from epidemiology - [SIR](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model). It compartmentalises the population into the following groups: ($S$)usceptible, ($I$)nfected and ($R$)emoved. There are four input parameters to out model. They are initial number of susceptible people $S_0$, initial number of infected people $I_0$, transmission rate $\\beta$ and recovery rate $\\gamma$. The system is governed by three differential equations below. The number of suspectible people is reduced by them getting infected (and thus moving to $I$) at rate specified by $\\beta$. The number of infected people increases similarly. Finally the number of recovered people increases depending on the recovery rate and the number of people currently infected."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "neither-sierra",
   "metadata": {},
   "source": [
    "$${\\frac  {dS}{dt}}=-{\\frac  {\\beta SI}{N}}$$\n",
    "\n",
    "$${\\displaystyle {\\frac {dI}{dt}}={\\frac {\\beta SI}{N}}-\\gamma I}$$\n",
    "\n",
    "$${\\displaystyle {\\frac {dR}{dt}}=\\gamma I}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "scientific-shareware",
   "metadata": {},
   "source": [
    "The simulation is run as shown below, where ```input_file``` is a JSON file of the following format: ```{\"outfile\": \"$outfile\", \"S0\": $S0, \"I0\": $I0, \"beta\": $beta, \"gamma\": $gamma, \"iterations\": $iterations}```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "german-upper",
   "metadata": {},
   "source": [
    "```sir <input_file>```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "religious-problem",
   "metadata": {},
   "source": [
    "Lets try and run it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "pressed-recipe",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:25.930406Z",
     "start_time": "2021-06-09T08:57:25.534388Z"
    }
   },
   "outputs": [],
   "source": [
    "!echo '{\"outfile\": \"output.csv\", \"S0\": 997, \"I0\": 3, \"beta\": 0.2, \"gamma\": 0.04, \"iterations\": 100}' > input.json"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bearing-force",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:27.202480Z",
     "start_time": "2021-06-09T08:57:25.931781Z"
    }
   },
   "outputs": [],
   "source": [
    "!./sir input.json"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "organizational-framework",
   "metadata": {},
   "source": [
    "The simulation code outputs a CSV file with a specified name. We can try opening it up and printing the first 10 lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "according-timer",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:27.563489Z",
     "start_time": "2021-06-09T08:57:27.204218Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S,I,R,r0,t\r\n",
      "996.4018,3.47784108,0.1391136432,4982.009,1\r\n",
      "995.7087475755611,4.0312978050411745,0.300365555401647,4978.543737877805,2\r\n",
      "994.905980318425,4.672165937353743,0.4872521928957967,4974.5299015921255,3\r\n",
      "993.9763679472093,5.4140230672294996,0.7038131155849767,4969.8818397360465,4\r\n",
      "992.9001871310173,6.27247777694467,0.9547122266627635,4964.500935655087,5\r\n",
      "991.654756898651,7.2654467105291545,1.2453300950839297,4958.273784493255,6\r\n",
      "990.2140324288114,8.413460157063296,1.5818685013664615,4951.070162144058,7\r\n",
      "988.548155936764,9.739995672478827,1.9714683282656145,4942.740779683821,8\r\n",
      "986.6229648025937,11.27183768247915,2.4223418355647803,4933.11482401297,9\r\n"
     ]
    }
   ],
   "source": [
    "!head output.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "japanese-canvas",
   "metadata": {},
   "source": [
    "Finally lets plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "moral-booking",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:28.350065Z",
     "start_time": "2021-06-09T08:57:27.565838Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "df = pd.read_csv('output.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "introductory-cambodia",
   "metadata": {},
   "source": [
    "As we can see it shows the number of infected people increasing at first and then decreasing as the number of people who have recovered rises. Number of susceptible and recovered people also changes in a way that makes intuitive sense."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "sudden-boring",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:28.435209Z",
     "start_time": "2021-06-09T08:57:28.350940Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x139479f10>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df['S'], label='S')\n",
    "plt.plot(df['I'], label='I')\n",
    "plt.plot(df['R'], label='R')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "collectible-bread",
   "metadata": {},
   "source": [
    "So let us see what EasyVVUQ can tell us about the distribution of the number of infected people over time. We will not go into the details of the EasyVVUQ API this time. Only where it differs from the [basic concepts](./basic_tutorial.ipynb) tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "flexible-password",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:30.588513Z",
     "start_time": "2021-06-09T08:57:28.437128Z"
    }
   },
   "outputs": [],
   "source": [
    "import easyvvuq as uq\n",
    "import chaospy as cp\n",
    "import os\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "victorian-dallas",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:30.592929Z",
     "start_time": "2021-06-09T08:57:30.590057Z"
    }
   },
   "outputs": [],
   "source": [
    "params = {\n",
    "    \"S0\": {\"type\": \"float\", \"default\": 997}, \n",
    "    \"I0\": {\"type\": \"float\", \"default\": 3}, \n",
    "    \"beta\": {\"type\": \"float\", \"default\": 0.2}, \n",
    "    \"gamma\": {\"type\": \"float\", \"default\": 0.04, \"min\": 0.0, \"max\": 1.0},\n",
    "    \"iterations\": {\"type\": \"integer\", \"default\": 100},\n",
    "    \"outfile\": {\"type\": \"string\", \"default\": \"output.csv\"}\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "meaning-berry",
   "metadata": {},
   "source": [
    "Encoder is the same as in the basic concepts tutorial, essentially. However, since the simulation outputs a CSV file with the evolution of output variables over time we want the ```SimpleCSV``` decoder. The arguments to it should be self explanatory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "owned-preliminary",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:30.598048Z",
     "start_time": "2021-06-09T08:57:30.595407Z"
    }
   },
   "outputs": [],
   "source": [
    "encoder = uq.encoders.GenericEncoder(template_fname='sir.template', delimiter='$', target_filename='input.json')\n",
    "decoder = uq.decoders.SimpleCSV(target_filename='output.csv', output_columns=['I'])\n",
    "actions = uq.actions.local_execute(encoder, os.path.abspath('sir') + ' input.json', decoder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "neutral-marina",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:30.630175Z",
     "start_time": "2021-06-09T08:57:30.599889Z"
    }
   },
   "outputs": [],
   "source": [
    "campaign = uq.Campaign(name='sir', params=params, actions=actions)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "searching-interpretation",
   "metadata": {},
   "source": [
    "We assume that the infection rate $\\beta$ is uniformly distributed between 0.15 and 0.25 and the recovery rate $\\gamma$ is normally distributed with mean 0.04 and small variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "native-order",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:30.633520Z",
     "start_time": "2021-06-09T08:57:30.630961Z"
    }
   },
   "outputs": [],
   "source": [
    "vary = {\n",
    "    \"beta\": cp.Uniform(0.15, 0.25),\n",
    "    \"gamma\": cp.Normal(0.04, 0.01),\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "engaging-spoke",
   "metadata": {},
   "source": [
    "For this tutorial we will use Polynomial Chaos Expansion method. However, both [SCSampler](https://easyvvuq.readthedocs.io/en/dev/easyvvuq.sampling.html#module-easyvvuq.sampling.stochastic_collocation) and [QMCSampler](https://easyvvuq.readthedocs.io/en/dev/easyvvuq.sampling.html#module-easyvvuq.sampling.qmc) would work as well and might be preferable depending on the case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cosmetic-stake",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:30.761510Z",
     "start_time": "2021-06-09T08:57:30.634548Z"
    }
   },
   "outputs": [],
   "source": [
    "campaign.set_sampler(uq.sampling.PCESampler(vary=vary, polynomial_order=5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "governing-warrant",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:30.785220Z",
     "start_time": "2021-06-09T08:57:30.762311Z"
    }
   },
   "outputs": [],
   "source": [
    "execution = campaign.execute()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "junior-proxy",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:31.042069Z",
     "start_time": "2021-06-09T08:57:31.036748Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'ready': 24, 'active': 12, 'finished': 0, 'failed': 0}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "execution.progress()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "regulated-semester",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:35.750226Z",
     "start_time": "2021-06-09T08:57:31.043481Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 36/36 [00:04<00:00,  8.51it/s]\n"
     ]
    }
   ],
   "source": [
    "execution.collate(progress_bar=True)\n",
    "result = campaign.analyse(qoi_cols=['I'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "descending-resident",
   "metadata": {},
   "source": [
    "We can now see the results of the analysis. One thing to try would be to plot the first order sobol indices over time. This shows us how much influence the two parameters (```beta``` and ```gamma```) have over the number of people infected over time ```t```. The ```higher orders``` line is meant to represent the influence of the interactions between the input variables. However it is negligible in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "pressing-sister",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:35.908776Z",
     "start_time": "2021-06-09T08:57:35.765529Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='t', ylabel='First Order Sobol Index'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "result.plot_sobols_first('I', xlabel='t')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "exposed-paraguay",
   "metadata": {},
   "source": [
    "Finally we can try and visualize certain aspects of the distribution for our quantity of interest (number of infected people) over time. In this plot we will plot the mean value, standard deviation and 0.01 and 0.99 quantiles. This is with respect to the input variable distributions we have specified in the ```vary``` dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "corrected-titanium",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:36.072288Z",
     "start_time": "2021-06-09T08:57:35.917531Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='t', ylabel='I'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "result.plot_moments('I', xlabel='t')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "overhead-wright",
   "metadata": {},
   "source": [
    "If you want to access all of this data for processing you can use the following methods. Due to large output I have not evaluated these cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "destroyed-darkness",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:36.076580Z",
     "start_time": "2021-06-09T08:57:36.073217Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'beta': array([0.89204991, 0.89185266, 0.89149001, 0.89096097, 0.89026466,\n",
       "        0.88940042, 0.88836788, 0.88716713, 0.88579887, 0.88426465,\n",
       "        0.88256715, 0.88071051, 0.87870074, 0.87654612, 0.87425765,\n",
       "        0.87184944, 0.86933898, 0.86674715, 0.86409788, 0.8614171 ,\n",
       "        0.85873111, 0.85606382, 0.85343316, 0.85084649, 0.84829549,\n",
       "        0.84575091, 0.84315795, 0.84043276, 0.83746062, 0.83409584,\n",
       "        0.83016322, 0.82546019, 0.81975914, 0.81280885, 0.80433458,\n",
       "        0.7940368 , 0.78158862, 0.76663314, 0.74878204, 0.72761773,\n",
       "        0.7027023 , 0.67359755, 0.63990145, 0.60130728, 0.55769073,\n",
       "        0.50922621, 0.45652411, 0.40076392, 0.34377714, 0.28801728,\n",
       "        0.23636068, 0.19172748, 0.15659244, 0.13253095, 0.11995903,\n",
       "        0.11815331, 0.12551813, 0.13997798, 0.15935905, 0.18167041,\n",
       "        0.20525921, 0.22885867, 0.25156611, 0.272786  , 0.29216284,\n",
       "        0.30951812, 0.32479749, 0.33802971, 0.34929615, 0.35870914,\n",
       "        0.366397  , 0.37249406, 0.37713427, 0.38044717, 0.38255565,\n",
       "        0.38357479, 0.38361138, 0.38276395, 0.38112306, 0.37877176,\n",
       "        0.37578605, 0.37223548, 0.36818363, 0.36368866, 0.35880377,\n",
       "        0.3535776 , 0.34805468, 0.34227574, 0.33627808, 0.33009582,\n",
       "        0.32376017, 0.31729967, 0.3107404 , 0.30410619, 0.29741875,\n",
       "        0.29069789, 0.28396159, 0.27722619, 0.27050651, 0.26381593]),\n",
       " 'gamma': array([0.10795009, 0.108081  , 0.1082452 , 0.10844475, 0.10868198,\n",
       "        0.10895947, 0.10928011, 0.10964712, 0.11006411, 0.11053511,\n",
       "        0.1110646 , 0.11165763, 0.11231979, 0.11305739, 0.11387752,\n",
       "        0.11478817, 0.11579846, 0.11691886, 0.11816155, 0.11954088,\n",
       "        0.12107397, 0.12278152, 0.12468883, 0.12682701, 0.12923442,\n",
       "        0.13195833, 0.13505678, 0.13860045, 0.14267476, 0.14738191,\n",
       "        0.15284307, 0.15920061, 0.16662051, 0.17529499, 0.18544537,\n",
       "        0.19732504, 0.21122225, 0.22746203, 0.24640622, 0.26844958,\n",
       "        0.29400941, 0.32350472, 0.35731988, 0.39574695, 0.43890161,\n",
       "        0.48661152, 0.53828507, 0.59278447, 0.64834747, 0.70261752,\n",
       "        0.75283613, 0.79620725, 0.8303664 , 0.85381512, 0.86616865,\n",
       "        0.86813485, 0.86125663, 0.84753487, 0.8290625 , 0.80775511,\n",
       "        0.78520285, 0.76262477, 0.74089032, 0.72057421, 0.70202081,\n",
       "        0.68540466, 0.67078107, 0.65812541, 0.64736233, 0.63838646,\n",
       "        0.63107668, 0.62530575, 0.6209464 , 0.61787514, 0.61597451,\n",
       "        0.6151342 , 0.61525151, 0.61623137, 0.61798614, 0.62043516,\n",
       "        0.62350436, 0.62712574, 0.63123693, 0.6357807 , 0.64070456,\n",
       "        0.64596039, 0.65150402, 0.65729496, 0.66329612, 0.66947349,\n",
       "        0.67579593, 0.68223496, 0.68876457, 0.69536099, 0.70200259,\n",
       "        0.70866968, 0.71534439, 0.72201054, 0.7286535 , 0.73526013])}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.sobols_first('I')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "contrary-wound",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:36.084115Z",
     "start_time": "2021-06-09T08:57:36.077428Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.4778336 ,   4.03404206,   4.68171534,   5.43612205,\n",
       "         6.31505352,   7.3392123 ,   8.5326462 ,   9.92322633,\n",
       "        11.54316403,  13.42955585,  15.62493745,  18.17781631,\n",
       "        21.14313804,  24.58262204,  28.56487862,  33.16519322,\n",
       "        38.46483541,  44.54972656,  51.50828773,  59.42829956,\n",
       "        68.39265292,  78.47396641,  89.72820311, 102.18763148,\n",
       "       115.85371859, 130.69076976, 146.62126765, 163.52384337,\n",
       "       181.23458606, 199.55197143, 218.24513987, 237.06470706,\n",
       "       255.75488712, 274.06555177, 291.76296652, 308.63828094,\n",
       "       324.51329838, 339.24349061, 352.71856713, 364.86111453,\n",
       "       375.62389166, 384.98633302, 392.95071792, 399.53834415,\n",
       "       404.78592878, 408.74236162, 411.46586385, 413.02155449,\n",
       "       413.47939812, 412.91249216, 411.39564756, 409.00421782,\n",
       "       405.81313627, 401.89612761, 397.32506563, 392.16945484,\n",
       "       386.49601832, 380.36837781, 373.84681454, 366.98810159,\n",
       "       359.84539945, 352.46820727, 344.90236319, 337.19008678,\n",
       "       329.37005755, 321.47752329, 313.54443255, 305.5995859 ,\n",
       "       297.66880097, 289.77508687, 281.93882404, 274.17794602,\n",
       "       266.50812042, 258.94292658, 251.49402806, 244.17133841,\n",
       "       236.98317926, 229.93642984, 223.0366674 , 216.28829859,\n",
       "       209.69468132, 203.25823762, 196.98055751, 190.86249422,\n",
       "       184.9042513 , 179.10546191, 173.46526081, 167.98234963,\n",
       "       162.6550557 , 157.4813851 , 152.45907035, 147.58561312,\n",
       "       142.85832243, 138.27434872, 133.83071424, 129.52433996,\n",
       "       125.35206945, 121.31068996, 117.396951  , 113.60758069])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.describe('I', 'mean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "biblical-saint",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:36.092045Z",
     "start_time": "2021-06-09T08:57:36.085146Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.13081930e-02, 2.11560354e-01, 3.67777061e-01, 5.68492124e-01,\n",
       "       8.24044420e-01, 1.14691458e+00, 1.55210823e+00, 2.05758473e+00,\n",
       "       2.68472560e+00, 3.45882970e+00, 4.40961189e+00, 5.57166667e+00,\n",
       "       6.98483857e+00, 8.69441463e+00, 1.07510228e+01, 1.32100846e+01,\n",
       "       1.61306351e+01, 1.95733000e+01, 2.35972171e+01, 2.82557340e+01,\n",
       "       3.35908224e+01, 3.96263450e+01, 4.63605930e+01, 5.37588577e+01,\n",
       "       6.17471385e+01, 7.02083075e+01, 7.89820280e+01, 8.78693628e+01,\n",
       "       9.66423075e+01, 1.05057574e+02, 1.12873064e+02, 1.19864881e+02,\n",
       "       1.25842595e+02, 1.30660906e+02, 1.34226572e+02, 1.36500409e+02,\n",
       "       1.37494923e+02, 1.37268669e+02, 1.35918592e+02, 1.33571532e+02,\n",
       "       1.30375825e+02, 1.26493586e+02, 1.22094009e+02, 1.17347705e+02,\n",
       "       1.12421962e+02, 1.07476667e+02, 1.02660572e+02, 9.81076004e+01,\n",
       "       9.39330242e+01, 9.02295425e+01, 8.70636263e+01, 8.44728002e+01,\n",
       "       8.24646905e+01, 8.10185006e+01, 8.00890700e+01, 7.96129967e+01,\n",
       "       7.95157804e+01, 7.97187921e+01, 8.01451251e+01, 8.07238318e+01,\n",
       "       8.13924958e+01, 8.20983823e+01, 8.27985372e+01, 8.34592011e+01,\n",
       "       8.40548441e+01, 8.45670392e+01, 8.49833179e+01, 8.52960937e+01,\n",
       "       8.55016939e+01, 8.55995188e+01, 8.55913271e+01, 8.54806402e+01,\n",
       "       8.52722529e+01, 8.49718369e+01, 8.45856236e+01, 8.41201536e+01,\n",
       "       8.35820817e+01, 8.29780275e+01, 8.23144641e+01, 8.15976363e+01,\n",
       "       8.08335031e+01, 8.00277000e+01, 7.91855163e+01, 7.83118844e+01,\n",
       "       7.74113774e+01, 7.64882151e+01, 7.55462733e+01, 7.45890979e+01,\n",
       "       7.36199211e+01, 7.26416791e+01, 7.16570304e+01, 7.06683749e+01,\n",
       "       6.96778727e+01, 6.86874620e+01, 6.76988771e+01, 6.67136650e+01,\n",
       "       6.57332016e+01, 6.47587064e+01, 6.37912566e+01, 6.28318001e+01])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.describe('I', 'std')"
   ]
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  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "demanding-quick",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:36.100836Z",
     "start_time": "2021-06-09T08:57:36.093842Z"
    },
    "scrolled": true
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.30371256,   3.63791935,   4.00562838,   4.41013295,\n",
       "         4.85503629,   5.34427779,   5.8821608 ,   6.47338203,\n",
       "         7.12306239,   7.83677917,   8.62059944,   9.4811144 ,\n",
       "        10.4254743 ,  11.46142357,  12.59636755,  13.83723605,\n",
       "        15.1950249 ,  16.67957355,  18.30129156,  20.07584014,\n",
       "        22.01596356,  24.13195445,  26.43738786,  28.94645148,\n",
       "        31.67391876,  34.63511523,  37.845865  ,  41.32239329,\n",
       "        45.08115257,  49.13853658,  53.51045426,  58.21175389,\n",
       "        63.25551783,  68.65228261,  74.42754389,  80.65952874,\n",
       "        87.16126743,  93.95246604, 101.25998759, 108.74840971,\n",
       "       116.38209257, 124.25222664, 132.50047911, 140.98448035,\n",
       "       149.50249927, 157.94714529, 166.90407315, 175.5267385 ,\n",
       "       183.8345441 , 192.64259134, 201.57916814, 208.99226416,\n",
       "       217.26936135, 224.52289348, 229.70261182, 233.1524848 ,\n",
       "       231.10573143, 226.24387994, 219.7377034 , 216.35019436,\n",
       "       208.79487182, 199.89201136, 191.9786809 , 183.24272516,\n",
       "       174.8911105 , 166.79116213, 158.78210809, 151.22887879,\n",
       "       143.99893671, 136.97873835, 130.25560381, 123.81594242,\n",
       "       117.6016978 , 111.81998388, 106.22577492, 100.76070153,\n",
       "        95.59688376,  90.62699067,  85.92966635,  81.59311556,\n",
       "        77.49226797,  73.62090271,  69.90048565,  66.39431304,\n",
       "        62.87879837,  59.6481019 ,  56.59183562,  53.68678449,\n",
       "        50.92587039,  48.28028553,  45.75426565,  43.31201836,\n",
       "        40.99734465,  38.82241703,  36.76744362,  34.79004615,\n",
       "        32.98291427,  31.26620126,  29.58780737,  28.03067612])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.describe('I', '1%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "distinguished-greene",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-06-09T08:57:36.165232Z",
     "start_time": "2021-06-09T08:57:36.102023Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.65473544,   4.45159463,   5.42105695,   6.59995928,\n",
       "         8.03273578,   9.77237069,  11.88245812,  14.43937619,\n",
       "        17.53357297,  21.2718391 ,  25.77933367,  31.20140399,\n",
       "        37.70491606,  45.47868804,  54.73247024,  65.69375369,\n",
       "        78.60154364,  93.73168347, 111.27448377, 131.6344494 ,\n",
       "       154.7857425 , 180.86403334, 209.58681046, 241.43954559,\n",
       "       274.88582043, 309.82691674, 345.72971088, 382.13983461,\n",
       "       418.49281379, 453.56094937, 489.24298587, 517.06485735,\n",
       "       547.05623467, 568.58269584, 589.97745129, 605.24056993,\n",
       "       615.80919014, 624.13853541, 632.23797939, 637.78993505,\n",
       "       643.17971248, 646.1495388 , 647.29732844, 647.22908542,\n",
       "       644.68533053, 640.67413635, 640.04781522, 638.15402871,\n",
       "       636.31941958, 633.30742371, 629.6295947 , 623.59809917,\n",
       "       617.39323537, 612.19873087, 610.48310439, 606.38344966,\n",
       "       602.70792655, 596.66956347, 591.12890481, 586.73621   ,\n",
       "       582.17974134, 575.14420168, 568.66783872, 562.49386021,\n",
       "       557.14404893, 551.10398734, 545.40509088, 538.20147774,\n",
       "       532.15271447, 525.78873229, 517.77018519, 509.80511032,\n",
       "       502.58155003, 495.34759641, 487.36912554, 479.82915848,\n",
       "       471.76860154, 463.73045288, 456.12268072, 448.80372073,\n",
       "       441.58051555, 434.45455213, 427.42694505, 419.80808179,\n",
       "       412.09975428, 405.52141951, 397.96888624, 390.49863826,\n",
       "       383.2239695 , 377.25538331, 371.37972682, 364.39773588,\n",
       "       358.25220422, 351.3360762 , 344.50675675, 338.08728769,\n",
       "       331.76636824, 326.60428765, 321.52509349, 316.52755532])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.describe('I', '99%')"
   ]
  }
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