15-374b-class.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np               # numerical python\n",
    "import scipy as sp               # scientific python\n",
    "import matplotlib.pyplot as plt  # plotting library\n",
    "import pandas as pd              # panel data (spreadsheets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lists and arrays\n",
    "\n",
    "Like a column of numbers in a spreadsheet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "numbers = [1, 2, 3]\n",
    "\n",
    "#np.array(numbers)\n",
    "#t = np.linspace(0, 1, 5)\n",
    "#print(t)\n",
    "#print(t*2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "#t = np.linspace(0, 10, 50)\n",
    "#y = t**2\n",
    "#plt.plot(t, y)\n",
    "#y2 = t**3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DataFrames\n",
    "\n",
    "Similar to spreadsheets\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.000000</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.204082</th>\n",
       "      <td>0.041649</td>\n",
       "      <td>0.008500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.408163</th>\n",
       "      <td>0.166597</td>\n",
       "      <td>0.067999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.612245</th>\n",
       "      <td>0.374844</td>\n",
       "      <td>0.229496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.816327</th>\n",
       "      <td>0.666389</td>\n",
       "      <td>0.543991</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 y        y2\n",
       "time                        \n",
       "0.000000  0.000000  0.000000\n",
       "0.204082  0.041649  0.008500\n",
       "0.408163  0.166597  0.067999\n",
       "0.612245  0.374844  0.229496\n",
       "0.816327  0.666389  0.543991"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame({'time':t, 'y':y, 'y2':y2}).set_index('time')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='time'>"
      ]
     },
     "execution_count": 33,
     "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": [
    "data[['y', 'y2']].plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Same Row Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y2</th>\n",
       "      <th>new</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.000000</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.204082</th>\n",
       "      <td>0.041649</td>\n",
       "      <td>0.008500</td>\n",
       "      <td>0.050149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.408163</th>\n",
       "      <td>0.166597</td>\n",
       "      <td>0.067999</td>\n",
       "      <td>0.234596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.612245</th>\n",
       "      <td>0.374844</td>\n",
       "      <td>0.229496</td>\n",
       "      <td>0.604340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.816327</th>\n",
       "      <td>0.666389</td>\n",
       "      <td>0.543991</td>\n",
       "      <td>1.210380</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 y        y2       new\n",
       "time                                  \n",
       "0.000000  0.000000  0.000000  0.000000\n",
       "0.204082  0.041649  0.008500  0.050149\n",
       "0.408163  0.166597  0.067999  0.234596\n",
       "0.612245  0.374844  0.229496  0.604340\n",
       "0.816327  0.666389  0.543991  1.210380"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['new'] = data['y'] + data['y2']\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Different Row Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Slopes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13d4ab400>]"
      ]
     },
     "execution_count": 40,
     "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(np.diff(y))\n",
    "plt.plot(np.diff(y2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Areas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.0"
      ]
     },
     "execution_count": 43,
     "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": [
    "t = np.linspace(0, 10, 50)\n",
    "y = t * 1\n",
    "plt.plot(t, y)\n",
    "# what should the area under the curve be?\n",
    "#np.trapz(y, x=t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Euler Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13d5dd4f0>]"
      ]
     },
     "execution_count": 46,
     "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": [
    "power = 20\n",
    "initial_temperature = 19\n",
    "outside_temperature = 19\n",
    "UA = 0.45\n",
    "mc = 266\n",
    "\n",
    "time = np.linspace(0, 3000, 300)\n",
    "temperature = np.empty(300)\n",
    "\n",
    "\n",
    "for i in range(0, 299):\n",
    "    dT_dt = (power - UA * (temperature[i] - outside_temperature))/mc\n",
    "    temperature[i+1] = temperature[i] + dT_dt * (time[i+1] - time[i])\n",
    "    \n",
    "plt.plot(time, temperature)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Read and Write Files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "#read_csv\n",
    "#write_csv\n",
    "data.to_excel('test.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# XLWings\n",
    "\n",
    "[XLWings](https://www.xlwings.org/)\n",
    "is a libray that allows you to automate excel with scripting commands."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "power_w = 20\n",
    "mc = 104 * 1.9\n",
    "UA = 0.54 \n",
    "T_out = 19\n",
    "\n",
    "def dT_dt(T, t):\n",
    "    return (power_w - UA * (T - T_out))/mc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "t = np.linspace(0,5000,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = odeint(dT_dt, T_out, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x115f50580>]"
      ]
     },
     "execution_count": 6,
     "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(t, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "box_data = pd.read_csv('modeling-4-data.csv', parse_dates=[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "box_data['time_seconds'] = box_data.index * 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "box_data.index = box_data['time_seconds']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x119cc4550>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TPrQ9T/R9Qm85dufCDlwV8zSaanM1b+56k5YhLe1SsRviG0KpsRSj2WjztRS1owxcB0xmE08nP02FqYL/DP+PzXdMjoiKgVuPn078REphCg/3fBgvD9s/VIf4hgCqGtMRUAauA58c+IRtZ7fxbP9naRnSUm85unAhjdCk0ggbQ6Wpknd2v0PXiK6MbmafI6nzHQkdNYxii8k39qK+2pWB25mDuQd5Z9c7XNniSq5tfa3ecnTDz7MmjVDFwBvF4sOLySrL4pFej1i9aOdyOPIO3GAwkJub65QmLqUkNzcXg8Fg8XvUIaYdKa8uZ9aGWYT5hfF/A/7Pbn/hHBEVQmk8xVXFzN83n0FNB9Evtp/d1g3xqTFwByynj4+PJz09HWdt22EwGIiPj7f4emXgduS1Ha9xsvAkH4798MIuxl1RWSiNZ8HBBRRUFvBwr4ftuu75311HrMb09vamZUv3CUuqEIqdSM5IZtHhRdzR6Q4GxDauA5kroLJQGkdxVTFfHPqCUQmj6Bze2a5rX4iBO6CBuxvKwO1AfkU+/7fx/2jTpA0ze83UW45D4OXhhafwVDvwBrLo8CKKq4q5r/t9dl/7fJWnox5iuhMqhGJjpJTM3jSbwspC3r/ifbdMGbwUQggMXgYVA28ApcZSPj/4OcPjh9MpvJPd1/f08CTIJ8ghDzHdDbUDtzHLTy5nXdo6ZvaaSfuw9nrLcSgMnmoqT0NYfHgxhZWF3NfN/rvv86h+KI6BMnAbUlxVzKvbX6VrRFfu6HSH3nIcDoOXQbWTrSdlxjI+O/AZg+MG0zWyq246VEtZx0CFUGzIu7vfJbc8l7dHvY2HUP9W/hE/Lz+1A68nS44uIb8yn792+6uuOoJ9glUIxQFQrmIjDuQcYNHhRdzY7kY6R9g3S8BZMHiqGHh9MJqMfHrgU/rH9qdHVA9dtYT4qhCKI6AM3AZUVFfwTPIzhPuF80ivR/SW47D4evmqLJR6sOb0GnLKc5jaaareUpxmqIOro0IoNuCtXW+RUpjCB2M+cPuCndoweBkorFC7OEtZfHgxCUEJDI4brLeUCy1lzdKswoM6ov7PW5kTBSdYeGghN7e7mUFNB+ktx6Hx81QxcEs5kneEned2Mrn9ZIcwzBDfEMzSTKmxVG8pbo3+vwkuxivbX8Hfy5+Hej6ktxSHR+WBW85XR77C19OX69tcr7cUQFVjOgoWG7gQwlMIsUsIsazm+9lCiAwhxO6aj6tsJ9M52JSxieSMZO7rfh+hhlC95Tg8Bi+DioFbQElVCctSljGuxTiHCcld6EjogA2t3In6xMBnAoeA4Itee01K+Yp1JTknJrOJV3e8SnxgPLd2uFVvOU6BwdOg+oFbwLKUZZRXlzO5/WS9pVzgvIEXVBborMS9sWgHLoSIByYA820rx3n5+eTPHM0/ysxeM/Hx9NFbjlPg5+WnduB1IKXk66Nf0zGsI10iuugt5wJhhjAAcstzdVbi3lgaQnkdeBIw/+H1GUKIvUKIj4UQl4wZCCGmCyG2CyG2O2uP3rqoNFXy1q636BTeibEtxuotx2nw9fSlWlar2Yq1sDt7N8fyjzGp/SSH6h8f7R8NwLmyczorcW/qNHAhxNXAOSnljj/86D2gNdADyARevdT7pZTzpJR9pJR9IiMjG6vXIVl8eDGZpZn8rfffHCJDwFlQPcHr5usjXxPgHcBVLR3riMnf259A70Bl4DpjidsMBq4VQqQCi4FRQogFUsosKaVJSmkGPgTsNxLEgSiqKuLDfR8yuOlg+sf211uOU+Hnpcaq1UZ+RT6rUldxTatr8Pf211vOn4jyj1IGrjN1GriU8mkpZbyUsgVwC7BOSnm7ECL2ostuAPbbSKND8/G+jymqLOLR3o/qLcXpUDvw2vnh+A8YzUYmtZ+kt5RLogxcfxpTifmyEKIHIIFUQL/eljqRVZrFgkMLmNBqgmoV2wDOT+UpN6lc8D9ilmaWHF1Cr6hetA1tq7ecSxLlH8WWzC16y3Br6mXgUsokIKnma7fvj/runncxSzMzes7QW4rjYjbD6U1waBlkH4KoztB9MsR2VzvwWth6diuni0/z1+76dh2sjWj/aHLKczCZTXh6eOotxy1RvVAayImCE3x//HumdJxCXGCc3nIcj7yTcOgn2PkZ5B4HT1+IbA/bP4K9i+GR/SoGXgtLjy4l2CfYobOaovyjMEkTeRV5RPq7ZoKCo6MMvIG8vvN1/L38ubfrvXpLcQykhMw9cHi59nHugPZ6fD+4YR50mAC+gXBqE3wyHvZ8iX/LgQCqn8YfyK/IZ83pNdzc7maHHsEX5R8FaKmEysD1QRl4A9iZtZOktCRm9pqpSuaLs2DX57Dzcyg4DcIDmg2CK1+EDldBaIvfX99sIMT1gU1vE9zuCkCVY/+RZSnLMJqNTGw7UW8ptXI+FzyrLIvOqJ73eqAMvJ5IKfnvjv8S5RfFlI5T9JajD5XFsPcr2LsE0rYAEloOh+FPQbvxEBB++fcKAYMfhq/vJPjUZkAZ+MVIKVl6bCldI7o6/MH4xTtwhT4oA68niWmJ7Mnew+yBsy/EcN2Gc4dh23zYsxiqiiG6C4x4GrpMhIh6ZEp0uBq8AwhM3w0oA7+YPdl7OF5wnNkDZ+stpU7CDGF4Ck9l4DqiDLyefLL/ExKCEriuzXV6S7Efx1bDxjcgdQN4+kDnidDvXojrre2o64uHJ/iF4llVTJB3kGpJehFLjy3Fz8uPcS3H6S2lTjw9PInwiyCrLEtvKW6LMvB6sC97H7uzdzOr3yy8PNzgf13BaVj1jJZNEtIMRv8Tet0JARGNv7chGCoKCfYNVjvwGkqqSliZupKrWl5FgHeA3nIsIto/Wu3AdcQNXMh6LDi0gEDvQIdpqm8z8lNh8zuw41PtUHL0P2HQQ+Dpbb01fIOhsojgADXd/DwrUldQXl3u8IeXFxPlH0VKYYreMtwWZeAWcq7sHL+k/sKtHW91mt1RvTCb4fga2PahFjIRHtBzCgx7EpokWH89QwiUnCXYN1rtwGv46cRPtA5pTdeIrnpLsZgo/yh+y/xNbxluizJwC1l8eDFmzNzW4Ta9pViXikLY8ZlWYJOfCgFRMOwJ6H0XhNiwQMkQDDlHCfYJVo/gQHpxOrvO7WJmr5kO1Ta2LmICYigxllBSVUKgT6DectwOZeAWUFFdwZKjSxiZMJL4oHi95VgHYwVseQ+SX4eKAmg+GEb/AzpcA152GEjhWxMD91EhFNAGggAO1za2LpoGNgUgoyTD4dMeXRFl4BawPGU5BZUFrpP3ffJXWPaoVuLediyMfBaa9rCvBkOIFgP30Q4xpZROtfO0JlJKlqcsp1dUrwuG6CycbyOhDFwf1PSBOpBSsuDQAjqEdaBPdB+95TSO0lz47n747BowV8PtS2HKEvubN2ghFHM1wV5+GM1GKkzu2w/lcN5hUgpTmNBqgt5S6s3FBq6wP2oHXgdbzm7heMFx/j343867Q5QSdn8Jv/wdKotg6GNanNtbx0IkX202drDQfgWLKovcrzCqhuUpy/ESXoxt7riNqy5HE98m+Hv5KwPXCWXgdbDg4ALCDGGMbzlebykNozQHvr8fjv0CCQPgmtchqqPeqrQQChcZeFUR0QHReirSBZPZxIqTKxgSN4QmhiZ6y6k3QgjiguKUgeuEMvBaOFV0ivXp63mg+wPON2neZIRdX0Dii1qmyfiXoe+94OEgUbPzBi61pxp3TSXcnrWdc+XneKLVE3pLaTBxAcrA9UIZeC18eehLvD28ubn9zXpLqR9n98E30yDniNbO9er/QoyD5RbXGHiIWQK4bSbK8pTl+Hv5MzxhuN5SGkxcUBxbz25164NovbB4OyaE8BRC7BJCLKv5PkwIsVoIcazms0v1Va00VfJTyk+MaT6GCD8rlI7bAylhywfw4Sht133LIpj2i+OZN/wvBm6uBtxzB15lqmLNqTVc0fwKp47/xwXGUVZdRkFlgd5S3I76PE/PBA5d9P0sYK2Usi2wtuZ7lyExLZHiqmLnKZsvy4NFt8KKJ6HVSLh/o9aP21F3RIYaA682Au5p4JvPbKbYWMy4Fo7fuKo2zmeinCk5o7MS98MiAxdCxAMTgPkXvXwd8FnN158BTuJ0lvH98e+JCYihf2x/vaXUTfZRmD9aK4UfNxdu+8o6DadsSU0IJaiqEoFwSwNffWo1Qd5BDIgdoLeURnHewNNL0nVW4n5YGgN/HXgSCLrotWgpZSaAlDJTCBFlbXF6kVWaxeYzm7mn6z14CAc59Lscp3+DLyeBhzfctQyaOYkZePuD8MSjqphAn0C3i4EbzUYS0xIZnjAcb2s2CdMBlQuuH3W6kxDiauCclHJHQxYQQkwXQmwXQmzPzs5uyC3szk8pP2GWZq5v7eAPFcfXwBc3gH8E3LvOecwbtNCO4aJyejfbgW87u42iqiKuaH6F3lIaTaBPICG+IWQUKwO3N5ZsLwcD1wohUoHFwCghxAIgSwgRC1Dz+ZIdiaSU86SUfaSUfSIjHX/wqZSSH47/QK+oXiQE26ALn7XYNh8WToKwVnD3Sghtrrei+mMIgYoitzTwNafW4Oflx+Cmg/WWYhXiAuNUCEUH6jRwKeXTUsp4KWUL4BZgnZTyduBHYGrNZVOBH2ym0o7syd5DalGq4x5emqph+eOw/DFoMxr+sgICnTR6db4nuK97NbQymU2sO72OoXFDMXgZ9JZjFVqHtOZY/jG9ZbgdjQnwzgXGCCGOAWNqvnd6vj/+PX5efoxt4YBlzeX5sPBGrWf3wBlw6+IL2RxOiSHkQgilsMp9xqrtzt5NbkUuY5qP0VuK1egU3ons8myyy5wjTOoq1KuQR0qZBCTVfJ0LjLa+JP0ory5nVeoqxjQf43hDG3KOw6LJkH8Krn0bet2ht6LGYwiBvJOE+Ia41Q58zak1+Hj4MDR+qN5SrEan8E4AHMw9yHB/5y1KcjYcPMXCvvya/islxhKuaX2N3lJ+T/ZR+OgKbQc+9UfXMG/4fU/wmpayro6UkjWn1zAobpDjbRIaQYewDngIDw7kHtBbiluhDPwiVqWuIswQRt/ovnpL+R8l57SwiYcXTFsNzQfprch61PQED/UNxWg2UlZdprcim7M/Zz9nS8+6VPgEwN/bn5bBLTmYe1BvKW6FMvAayoxlbEjfwJjmY/D08NRbjkZ5ASy8CUqyteKc8NZ6K7IuhmCoLCbcEAZATnmOzoJsz+rTq/ESXgyPd70wQ6fwTsrA7Ywy8BrWp6+nwlThOGXNlSWw8GbIOgiTv4C43norsj6+wYAkwssfcH0Dl1Ky5tQa+sf2J8Q3RG85VqdzRGeyy7PVjFM7ogy8hlWpq4j0i6RnVE+9pWgT4r+9BzJ2wM2fQFvXety+QE05fYSH1qrX1Q38aP5R0orTXKJ451JcfJCpsA/KwIFSY6ljhU/Wz4WjK7S+Jh0d7EDVmtSkQEbUJEO5uoGvPrUaD+HBqGaj9JZiE9qHtkcgOJR7qO6LFVZBGTha58EqcxXjWjpA+OTQMlj/EvSYAv3u1VuNbTnfE9xkwkt4ubyBrzm1ht7RvQmrifm7Gv7e/jQNbMrJwpN6S3EblIGjhU+i/KPoHtldXyHZR+C7+6BpL5jwX8dtBWstakaIeVQUEu4X7tIGfrLwJCcKT3BFM9cMn5ynZUhLThYpA7cXbm/gRVVFbMzYyJUtrtS382BFESy+TRs0PHkBeLtGiXWtnG95W5ZLhF+ESxt4YloigMuGT87TMqQlp4pOYZZmvaW4BW5v4ElpSRjNRq5scaV+IqSEHx+CvJNw86cQEqefFnviVxNKKMshwi+C3PJcffXYkMTTiXQM60hMQIzeUmxKi+AWlFeXk1WapbcUt8DtDXx16mpiAmLoFtFNPxFbP4SD38Po/4MWQ/TTYW98/LW+4GV5Lr0Dzy3PZU/2HkY2G6m3FJvTMqQlgIqD2wm3NvDy6nI2Z25mVMIo/YaxZuyAVc9Au3EwaKY+GvTEPwLKcgn3Cye3IheT2aS3Iqvza/qvSCQjE9zIwFUc3C64tYH/duY3Kk2VjEgYoY+Asjz4+i4IioXr3wMPN/zj8A+DUi2EYpZm8ivz9VZkdZLSkogJiKF9aGYrWi4AACAASURBVHu9pdiccEM4Qd5BagduJ9zQMf5HUnoSgd6B9InuY//FzWb4/n4oztTi3v6umVpWJwERFw4xAZeLg1dUV7A5czMj4kfo95RnR4QQtAxpSWphqt5S3AK3NXCT2URSWhJD44bqM5Nw05twdCVc+QLEu2CZvKX4h//OwF0tDr4lcwvl1eVuET45T4uQFiqEYifc1sD35ewjryJPn/BJ2lZY+zx0uh76Tbf/+o7EeQM3uKaBJ6YlEuAdQN8YB+pwaWNahrTkXNk5So2lektxedzWwJPSkvASXgyOs/NMwooirc9JSBxc+6brF+vUhX84VJUQ7h0IuJaBm6WZ9enrGRI3xOknz9eHlsHaQWZKQYrOSlwftzbw3tG97d8VbsWTUJgGE+dfKCV3a/zDtU9VZQR4B7iUge/P2U9OeY5+h+Q6cb6p1d6cvTorcX3qNHAhhEEIsVUIsUcIcUAI8VzN67OFEBlCiN01H1fZXq51OF10mhOFJ+z/F2vfN7BnEQx7Epr1t+/ajooLV2MmpSXhKTwZGuc6o9MsITYwlmj/aHaf2623FJfHkpmYlcAoKWWJEMIbSBZCrKj52WtSyldsJ882JKUlAdjXwAtOw7K/QXw/GPaE/dZ1dGp24JTlEm4Id6le0olpifSK7uWSvb/romdUT3ZnKwO3NXXuwKVGSc233jUfTj28MDEtkbahbYkPirfPgtWVsOQvIM0wcR541muWtGtzkYHHBMSQVeYaJdhpxWkcLzjuVtknF9MjqgdnS89ytvSs3lJcGoti4EIITyHEbuAcsFpKuaXmRzOEEHuFEB8LIUIv897pQojtQojt2dnZVpLdcAorC9l1bhcj4kfYZ0EpYfnfIGM7XP8uhLW0z7rOgv//QiixAbFklWW5RDXmhac8e/2eORg9onoAsOvcLp2VuDYWGbiU0iSl7AHEA/2EEF2A94DWQA8gE3j1Mu+dJ6XsI6XsExkZaSXZDWfTmU2YpIlh8cPss+DuhbBrAQx9HDpda581nQm/JoC4YODV5mpyK5y/mCcpLYk2TdqQEJygtxRdaB/aHj8vP2XgNqZeWShSygIgCRgnpcyqMXYz8CHQzwb6rM6G9A008W1C14iutl8sPxVWPAXNh8DIZ2y/njPi4Ql+oVCac6FTn7M/dhdWFrIja4fbZZ9cjJeHF10juqqDTBtjSRZKpBCiSc3XfsAVwGEhROxFl90A7LeNROthlmaSM5IZHDfY9qPTzCb4/kFAaKETRxjV5qjUlNOfN/DM0kydBTWO5IxkTNLktvHv83SP7M6R/COUV5frLcVlseQ0LRb4TAjhiWb4X0splwkhvhBC9EA70EwF7rOdTOtwIOcA+ZX59knrWvs8nEqG696F0Oa2X8+ZqanGjA3U9gTOvgNPTEsk3BBOl4guekvRlc4RnTFLM0fyjlyIiSusS50GLqXcC/xpVLuU8g6bKLIhGzI2IBAMbmrj6sv9S2Hj69Dnbug5xbZruQL+4ZCXQpB3EAHeAU5t4EaTkeSMZMa1GKfvhCdrYzZrPes9vCw+y+kc3hnQptQrA7cNbpXPtiF9A90iu9GkZhajTSg6Az/NhIT+MO4l263jSviHQ/o2hBDE+Mc4dQhlW9Y2So2lrhX/PpGo9aw/dxCEJ0xbbVEDtmj/aMIMYRzMPWgHke6JC20RaienPIf9ufttGz6REpY/BiYj3PA+ePnYbi1XoiaEgtlMTKBzG3hSWhIGTwMDYgfoLaXxlOXBt/fCF9dDdQVc/77Wu/676VBVVufbhRB0Cu/EgdwDdhDrnriNgW86swmAofE2NPCDP8CRn7WMk7BWtlvH1QhuCuZqKM0mNiDWaUMoUkoS0xIZ2HQgBi8nH0p9ajO8PxQOLIXhT8H9m6HHrXD9O5B7XGuHbAGdwzuTUpiiDjJthNsY+Ib0DUT4RdAhrINtFijLg5+fgNgeMOAB26zhqoTU5EoXphHjH0NeRR4V1RX6amoAR/KPcLb0rPNnnxz8AT67RnuCnLZa25B41/yD1GoEtBgKB7636FadwjtdOMhUWB+3MPBqczWbzmxiSNwQ2x0srf4/LQxw7VuqVL6+NKkx8ILTFzJRnLGkPjEtEYGw7VOeLTGbYNPbsOQuiOsF967TPv+R9uMh+5BW51AH5zsTqjCKbXALA9+Xs4+iqiLbxb9TkrRqy8EPQ6yO0+2dlZCanjSFacQGOG8qYVJaEt0iu12YLuRU5J6AD0fBL89qA7bv+E4rsLoU7cZpn4+srPO20f7RhBvC1UGmjXALA9+QvgFP4cnApgOtf/OqMi3rJKy1FitU1B9DCPiGQEGa0xbznC09y8Hcg84ZPjm7Hz4ep3XMvOljuOVL8Am4/PXhrSGiPRxdcflrahBC0D2yOzuydlhRsOI87mHgGRvoGdWTIJ8g69886UXtUfLaN8Hbz/r3dxeaJEBhOtH+0QBklTpXCGV92noA5zPwE4nw6VXg6Q13r4IuN1o2Jar9OEjdqE2YqoP+sf3JKMkgvTjdCoIVF+PyBp5VmsXhvMO2iUue2Q2b34ZeU6HFEOvf350ISYDCNHw8ffD38qeoqm5jcCQS0xNpFtSMliFO1G1y23xYcCMEx8HdKyGyneXvbX8VmI1a1lUd9I/VhpdsPbu1oUoVl8HlDXzjmY0A1o9/m4zw4wwIiIIxz1v33u5IkwQoSAMg2DeYwspCnQVZTqmxlK2ZWxmRMALhDDNOpYSkl7SahbZjYNov0KRZ/e4R309Lld3xaZ2XtgppRYRfBL9l/tYwvYrL4vIGviF9AzEBMbRp0sa6N978NpzdBxNeqWmJqmgUIfFQWQgVhYT4hFBY5TwGvjFjI0az0TnCJ2azVlWZNAe63waTF4JvA0KLHh7Q+y44vRnOHa71UiEE/WL6sTVzK1I69SwYh8OlDdxoMrI5czND44Zad2eUewKS5kLHa7QPReM5nwtekEawbzBFlc4TQklKSyLEN8Tx+32YqrWnxt/ehf73w3XvNC7ltccU8PSxaBc+IHYAuRW5HC843vD1FH/CpQ1817ldlBpLGRJnxfi0lFrWiacvjP+P9e7r7px/hC9MJ8QnxGli4NXman7N+JVhccPw8nDg/P/yAvjyZm3AyIinYdyL2i66MQREaBuYPV9CZUmtl56Pg28+s7lxayp+h0sb+G+Zv+EpPOkXY8VZE7sWQOoGGPsvCI6t+3qFZVxUjRniG+I0MfBd53ZRWFno2M2ris/CR2Pg5Aat0GzELMsyTSyh//1QUVjnLrxpYFPahrZlXdo666yrAFzcwLdkbqFLRBcCfQKtc8PyAlgzG5oNhF53WueeCo2ASO2ppuA0wT7BTrMDT0xLxNvDm8FxNm5R3FBKc+Dz66AwQyvOsfbvbUJfaDlM641irL39wRXNrmBn1k5yynOsq8GNcVkDL64qZn/u/guPblZh/Utaufz4l6y3g1FoeHhoB5mFWgy80lTp8P1QjCYjy1OWMyRuCAHetRS+6EVeCnxylVancNtX0NJGlcjDnoCSLNi9oNbLRjcbjURr+KWwDi5r4DuydmCWZvrHWMnAzx2GLR9oJ++x3a1zT8XvCW0OeSmE+IYAOPwufG3aWvIq8rip3U16S/kzadu00viSLJjyje3MG7TmVnF9YOv8Wi9rF9qOhKAE1p5aazstboYlMzENQoitQog9QogDQojnal4PE0KsFkIcq/l8mcYJ+rAlcwu+nr50j7KC2UoJK58C30AY9X+Nv5/i0kR2gJxjBHtraW2OHgf/5sg3xAbE2n7CU33JOaYdWBqaaA2pbGneoD2Ndr1Ja3CVe6KWywRXNL+CLZlbHP7P1lmwZAdeCYySUnYHegDjhBADgFnAWillW2BtzfcOw2+Zv9Ezqie+nr6Nv9nh5VrDqpHPQkB44++nuDSRHcBYRoixEnBsAz9VdIotZ7dwY9sbbT8guz4UndGqK4Un3LFU61tiD9pfpX2uozJzQssJVMtqvjn6jR1EuT51GrjUOJ8j5F3zIYHrgM9qXv8MuN4mChtATnkOxwuOWyf+bazQCh8iO0KfaY2/n+LyRGq92kNKtEMuRw6h/HD8BzyEBze0vUFvKf8jLwU+vlLrTX/bV/YdKhLaHKK7apudWmgf1p6BsQNZeGghVaYqO4lzXSyKgQshPIUQu4FzwGop5RYgWkqZCVDzOcp2MuvHxgytfN4qj7ab34KCU9rBperzbVsi2wMQXHgGcNwduJSSFSdX0D+mP1H+DvJrn3VA6yhYWQJTf4T4PvbX0GECnP4NSrJrveyuLneRXZ7N8pTazV5RNxYZuJTSJKXsAcQD/YQQXSxdQAgxXQixXQixPTu79j9Ya5GckWyd6TuFGbDhv9DxWmg13DriFJfHrwkExRKSfwpw3B34vpx9pJekc1Wrq/SWopG+Xcs2EZ7wlxWXHsJgDzpcBcg6wygDYwfSIawDnx34TJXWN5J6ZaFIKQuAJGAckCWEiAWo+XzuMu+ZJ6XsI6XsExkZ2Ui5dXN++s6gpoMaXz6/+h8gzTD239YRp6ibyA4EZB/FU3g67A7855M/4+Phw+hmo/WWAhk74YsbtOELd6+EKBuNDLSEmG4Q0Q52fKId/F8GIQS3driVE4Un2Jezz44CXQ9LslAihRBNar72A64ADgM/AlNrLpsK/GArkfVhf85+60zfObUZ9n8Dgx7W4nsK+xDVEZFzzGGLeUxmEytPrmRY/DDb9JevD1kHYcFE7cnlrmX6/54KAf3/Cmd2QdqWWi8d23wsvp6+/HjiRzuJc00s2YHHAolCiL3ANrQY+DJgLjBGCHEMGFPzve4kZyTjITwaN33HbIIVT0BwPAx51HriFHUT2V7LRPHyd8gd+NazW8mtyNU/fFKYAQtvAi8DTP3pf2Pp9Kb7rVr64uZ3ar0s0CeQUc1GseLkCnWY2QgsyULZK6XsKaXsJqXsIqV8vub1XCnlaCll25rPebaXWzcbMjbQNaLrhWKQBrFrgdYqduzz4ONvPXGKuonsCECw8HTIHfjPJ38mwDvAdvNVLaEsD76cpE3DmfINhLbQT8sf8fGHPn+Bw8sg72Stl17X+jqKqopISkuyjzYXxKUqMc/PJWxUY6GqMm1MWnw/6DzRatoUFnI+E8VkcrgdeKWpkrWn1jK62WgMXgZ9RBRlageWOcdg8ucQY3E+gf3od5/WZvbX2rt1DogdQJR/FEuPLbWTMNfDpQz8/L/koxJGNfwmWz+A4kwY85zqd6IHfk0gtCUhlaUOZ+DJ6ckUG4uZ0HKCPgJKsrX5lYVpcPs30LoRv+e2JDgW+t4DexZB9pHLXubp4cmkdpPYeGYjKQUpdhToOriUga87vY4WwS0aPpewPB82vAZtr4Tmg6wrTmE5Cf0ILs11uBDK8pPLCTOE0S/Wiu2JLaWqDBbdolVa3r5U6wDoyAx5FLz9IXFOrZfd3P5mfD19WXCo9kZYikvjMgZeVFXEtrPbGNlsZMPTB7fO18Z6jfq7dcUp6kd8X0IqSiiuKsYszXqrASCvIo+ktCTGtxxv/8EN1VXwzV8gYwfcOB+aWbHDpq0IiIABD8DB7yFzz2UvCzOEcXWrq/npxE8UVBTYUaBr4DIGnpyeTLWsbnj4pKoMtrwHbcdCbDfrilPUj/g+BJvNSCTFVcV6qwHgu2PfYTQbubndzfZd2FQN306Doyu1+avONMJv0AwtI2Vd7XUUUzpOocJUwaIji+wkzHVwHQPPSCbUN5SuEV0bdoNdX2i9vof8zbrCFPUnugshaA2iHGE2plmaWXJ0CX2i+9C6iZ2aQ4FWDLP8UTj0I1w5R4srOxOGEBjyCBz7RSuxvwxtQ9syIn4ECw8tpMxYZkeBzo9LGLiUkt8yf2NA7ICGdYYzGWHTW5AwAJo3In9cYR08vQltop1jpBTqf7i1MWMjGSUZTG4/2b4L//oK7Pwchj4OAx+079rWot90CIyGZX/T0h4vw73d7qWwspCvj3xtR3HOj0sY+PGC42SXZze8eGffN9rJ/lC1+3YU+sUNJLbaxLu739E9Dv71ka8JN4Tbt3R+23xI/Dd0u8W5z2R8AuCG9yHnCHx9p7ZZugTdIrsxIHYAnx74lFJjqZ1FOi8uYeDnJ10PiB1Q/zebzZD8GkR11uLfCofAN2EgD+YXcDDvEL+c+kU3HWdKzrA+fT0T207E29PbPovuWgjLH4N247UhxM6eztp6FFzzJqQkwup/XvayGT1nkF+Zz5wttWeuKP6HSxj4b5m/0SK4BbGBDZgSf3SFtjsY8qjz/0VxJVoM4eqSMtp4h/DmzjepNFXqIuObo98ghLDf4eXRX+DHh6DVSLj5U/Dysc+6tqbnFC2c8ts7cPzSI9W6R3Znerfp/HjiR35Oqb2joULD6Q3caDKyPWt7w4Y3SKm1i23SHDo7UGN+BfiH4RnXiycrPEkrTuODPR/YXYLRZOTbY98yLG5YwzYH9eXMLlhyl1ZdOXkBeOtU7WkrxjwPUZ3g+/uh9NKT6e/rdh89o3ryr9/+RVpxmp0FOh9Ob+BrTq+hvLq8YfHv1GTI2A6DH1bDGhyR1qMYmLaPa1uM45P9n3Ak7/JVfbZg1alV5FXkMan9JNsvVnIOFt0G/mFw2xJt/qqr4e2n5bGXF8APD16y5ayXhxdzh85FIJj16yyM5kvHzBUaTm3g2WXZzNkyh87hnRkW34DKtOT/QkAk9JhifXGKxtN6FEgTT4b2Jtg3mBe2vGC3AQBmaWb+3vm0adKGwXE2HlpsMsLXU7VK4Fu+hKBo266nJ9GdtTYVR1dqB7WXoGlgU/4x6B/szdnLe7vfs7NA58KpDfz5zc9TXl3OnKFz8Pao5wHTmd1wYp1WLebtZxuBisYR3xd8ggg5tZkHezzIrnO7WJ++3i5LJ55O5EThCe7peg8ewoZ/TaSEn2bC6U3agaU7FJH1/yu0GaPNmk1NvuQl41qMY2LbiczfN5+tmVvtLNB5cFoDP1t6lqT0JKZ1nUarkAYMb934OvgGQ181qNhh8fTWen4cW8MNra+jeXBz3tj5BiazyabLSin5YO8HNAtqxpUtrrTpWiTNhd0LYfgs6GbnKk+9EAImzoPQlrD4Njh36JKXPdX3KZoHN+fpDU+rMvvL4LQGvvWs9q/yyISR9X9z7gk4+INm3oZG9A1X2J6uN0JROt7HVvNwz4c5XnCcn0/aNkPhu+PfcSjvENO7Tbdt35PDP8P6uVoIb8Qs263jiPiHaR0VvQxak66yP48T8Pf25+VhL5Nbkcvbu9/WQaTj47QGviVzC6G+obQLbVf/N298Azy8of/91hemsC4dr9OyhDa9yZjmY2gV0oovD31ps+Wyy7J5Zdsr9InuwzWtbdh3pCBNy8aI7Q5Xv+aeKaxNmsHkhVqHxW/u1vq+/IGO4R2Z1H4SS44u4Xj+cR1EOjZOaeBSSrZkbqFvTN/6xyeLs7Q+xT1vd+3DIlfB0wsGPQRpWxBpW5jcfjL7c/ezL9v6w3CrzdX8c9M/qTRVMnvQbNvFvqvKtHRBswlu+gS8fG2zjjOQ0BeuekUr8ln+qFZY9wce6P4AAd4B/Gf7f9QU+z9gyVDjBCFEohDikBDigBBiZs3rs4UQGUKI3TUfdhsSeKroFFllWQ3L/d7xKZiqtMNLhXPQYwr4hcGGV7m29bX4e/mz+Mhiqy5hMpt4JvkZNmRs4Mm+T9I82EYDgs0mWHqv1hr2hvcg3I7NsRyV3lO1fi87P4eVT/0pvbCJoQkPdH+ATWc28f3x73US6ZhYEuCrBh6TUu4UQgQBO4QQq2t+9pqU8hXbybs05+Pf9TZwkxF2fAKtR0NEGxsoU9gEH3+tNena5wk8d4RrWl/Dd8e+4/7u9xMf1PBhvmZpZm/2XtadXsfa02s5XXyamb1mMrmDDZtWrf6HNi9y/MvO1RrW1oz6O1RXwOa3ITAKhj3xux/f2uFW1qWt48WtL9Irupft/oF1MiwZapwppdxZ83UxcAiIs7Ww2vgt8zei/aNpFtSsfm88vFwbl9bvXtsIU9iOftPBPxyS5nBX57vw9fTlkcRHKK8ub9Dttp/dzlVLr+KOFXfwxcEviA+K58WhL3JPVxu2bN3zlWZQ/aZD//tst44zIgSM/Td0m6z1D9/9+97gnh6ezBmipQurAp//Ua8gnxCiBdAT2FLz0gwhxF4hxMdCiNDLvGe6EGK7EGJ7dnZ2o8SC9qi7JXMLA5sOrP/kna3zIKSZalrljPgGweCZcHwN8XlpvDTsJY7mH+Wfm/5Z77joFwe/YNov0/AUnswdOpf1t6zngzEfcHWrq20kHkjfAT89DM2HaL29FX9GCLj2bS119IcH4dBPv/txTEAMswfNZn/uft7d/a5OIh0Liw1cCBEIfAs8IqUsAt4DWgM9gEzg1Uu9T0o5T0rZR0rZJzIystGC9+fup6iqiMFN61kdl7EDTm2E/tOhIT3DFfrT9x4IjoPlf2NoTH8e6vkQK06uYMnRJRbfYve53byy/RWGxw/n62u+ZkKrCQT7BNtQNJCXAl9O0vpi3/yplt+uuDRePlo1alwvWPIXrbnXRYxpPoYb297IR/s+YlXqKp1EOg4WGbgQwhvNvBdKKZcCSCmzpJQmKaUZ+BCwy6TXTWc2IRD1bx278U3wDYFeU20jTGF7fAJgwn/h3EHY+DrTuk5jUNNBvLztZYv6pJQZy3g2+Vli/GOYM2QOAd4BttdcmgsLbgJpgtu/hcDGb2JcHt8gmPINRHeCr26HlKTf/fjJvk/SIawDj69/nEcSHyGn/NKNsdwBS7JQBPARcEhK+d+LXr+4PdsNwH7ry/szmzI20Tm8M00MTSx/U+4JbSxV37vBYOPdlsK2tB8HnSfCr//BI3MPc4bMIdgnmIfXPVznX+RPDnxCWnEa/x7ybwJ97NAsyliuFakUpsOtiyGire3XdBX8msAd30N4G1h0KxxbfeFH/t7+LLxqITN7zSQ5I5kbf7yR5IxLl+S7OpbswAcDdwCj/pAy+LIQYp8QYi8wEnjUlkJBmzy/L2cfg+IG1e+Nm98BDy+tB4PC+bnqP1o4YvHthJvMvDXqLfIr83lgzQOXnalYZari6yNfMzxhOH1j+tpeo8kI30yD9G1w44fQrAHDRtwd/zC483sIa62FoDa/c+FH3p7e3NP1HhZNWESYIYz719zP0xueJrc8V0fB9seSLJRkKaWQUnaTUvao+fhZSnmHlLJrzevXSikzbS12a+ZWTNLEoKb1MPDSHK3XRLfJEBRjO3EK+xEQofXLLsuBJVPpHNqeV4a/wpH8Izy94elLjmBbmbqSvIo8butwm+31mU3w3X1wZLmWLtjpOtuv6aoERsHdK6HDBK351YbfH7W1DW3LogmLmN5tOitTVzLxx4lutRt3qkrMjWc2EuAdQLfIenRs2zpPyy8d9LDthCnsT9MecM0b2sH0+rkMix/Gk32fZF3aOt7e9fu+GVJKFh5aSKuQVg0bu1dfVj0D+7+FK57TDs0VjcM3EG7+DLreDGuf10z8oswjg5eBh3o+xNdXf31hN/6fbf+hylSlo2j74DQGLqVkU8Ym+sf0t7x1bFWpZuDtJ0BkA3qmKByb7rdAj9u16e0nErmtw23c2PZGPtz3IctTll+4bE/2Hg7mHmRKxyn1Tz2tL7sWwJb3tUrfIY/Ydi13wsMTrn9fO/9Y+3zN2ULG7y45vxu/pf0tfH7wc27/+XbOlp7VSbB9cBoDP1V0ijOlZ+oXPtm1QGuSP3im7YQp9OWqlyGyAyyZisg+wrP9n6V3dG/+sfEfF/qlLDy0kCDvINvmeYPW4XLZo9ByOIz5l23Xckc8veCmj7Ww1Il18HpX+OoOyE+9cInBy8CzA57ljZFvcLr4NFNXTOV00Wn9NNsYpzHwjWc2Alh+gGmq1qreEgZAswb0TFE4Bz4BMOVrrS3pwpvwLsvltRGvEekfyczEmezL3sfqU6uZ2HYi/t7+ttEgpfYU8PWdWnfBmz9VI/pshRBaFeuM7VqTs5QkeH8o7PxCe+KuYVSzUXx05UeUV5dz18q7OFNyRj/NNsRpDHzTmU00C2pGQlCCZW84+D0UnNbmXSpcmybN4LavtZ7SC28mVHjx5qg3KTWWctfKuzBLM7d0uMV2669/Gdb9Szson7pMy55Q2JbQ5tpotr8mQ1RH+HEGvNwalk7X0oaBzuGd+ejKj6ioruD+NfdTWFmos2jr4xQGXmWqYtvZbZYPLpZS6/kd3hbajbetOIVj0LQHTPocsg7A11NpF9SCuUPnYjQbGZ4wvFFNry6LlJp5J83ROiZe/77rTZJ3dEKbw19WwJ0/Qs8pcPBHeLsv/DADCtJoG9qWN0Zp4ZQZa2dcNs3UWXEKA9+RtYPy6nKGxA2x7A0n18PZvdru28Mp/hMV1qDtFXDN63BiLSy9h5FxQ/niqi/49+B/W38tY7nWFjbxBeh2izbPUv2u6YOHJ7QaDhNehZl7tGZ1e7+Ct3pB4ov0De/KS0NfYm/OXh5a95BLmbhT/MatO70Og6fB8vaxG9/QCj262bAtqMIx6XUnXPmidqD47d10D25FiK+Vx+ZlHYR5I2HfEhj9D7jhfdVfx1EIiobxL8FDO6HjtdrIuncHMLaogBcG/YttZ7cx8ceJ/Jr+q95KrYLDG7iUknVp6xjUdBB+XhZMj8/cWzNt/n73nnTizgx8AMa+oHWze38o7F8KlcWNv2/JOVj5NMwboRUR3f4tDH3MPcehOTpNEuCmj+CO78AnEJbey9Vr/sPHvWfh4+nDg2sfZNqqaaw9tZZDuYcwmpyzPa2w54iiPn36yO3bt9frPQdyDnDL8lv49+B/c10bCyravpkGR1fCowe0fgoK9+XUZvhuunaY7eEFQU21atzgWIjuAu3Ha5/rMuDSXC2jacv7UF0JPW6F0f/UqgQVjo/ZDAeWwqpnoSSLqvbj+Sq+HfPPhzZI+AAAEh9JREFUJJFXoQ1Tbh7cnL8P+Lt9Cr0agBBih5Syz59ed3QDf3Pnm3y0/yPWT1pfdwOr7CPw7gAtvWjM841QqnAZTNWQtkV7KitM0wZ6FJ2pyVSQYGgCTXtq7Usj2oHwgIpCbbdtNmrFIgd/0Mbwdb0Jhs9S05yclYpCSH4NdnwG5XmUh7fhWPvRnAqK4L0ziaSVpNOmSRvGNB/DDW1uIDYwtu572gmnNfAbfriBUEMoH1/5cd0XL/kLHPsFZu6FgPAGqlS4BSXntN+VtK1wZqcW15amiy4QWt9ubz/ocpM2RSeqg25yFVbEWKGlGW+brzUbAyoCY/i2yxWsMRWwI2cfQgiGxQ1jcofJDGo6yHYDri3EKQ38eP5xbvjxBmb1m8WUjlNqvzjrALw3GIb+TTtYUijqg7H8f6XZvoEQEKkOJt2BsjztCW3jm3B6EwBnmsTxTdPWfFudQ56xhHBDOCObjeSOjnfQqkkrXWRezsAdulxsReoKPIQHV7a4su6Lk+ZqjeAHzrC9MIXr4e2nQiPuiH+YdhbSbpz2JJa2jaanknn42DruN5ayNiScNeFBLD/2PUuPfsuV8SMY1/Z6BsQOsF1lbz1wWAOXUrLy5Er6xvQlwi+i9osz92oDG4bPUlVwCoWi/ggBcb21jwF/BWMF3ifXM+7Iz4xL20p+7mk+Dg7kW9NaVqQn4gG08m7CqIju3Nz6OmJajtalDsBhDfxg3kFOF59mWtdpdV+c9CIYQrTUQYVCoWgs3gZod6X2AYRWlfJY5l4eztjGjrRf2VVwjF3lmXxYlc/8M0n0SPJgZFQvRraaQPM247UwnB1wWAP/OeVnvDy8GN1sdO0XpiTBkZ9h5N9V2qBCobANPgHQfCDezQcygIcZAFBRSPqZHfx4dAnrzv7Gq3k7eDVvB022zCba04+23iF09AkjtmkfWrWdQKuIzlZvZ+yQh5ilxlLGLBnDgKYD+O+I/17+wvxTWlFFQCTcu85u/+opFArFH8k4t5+kw1+TcnYnZ4rTOCJMZHv+z7DjzR70N0TTNaIzoxJGEhrWTqtLMITUWYvQ4ENMIUQC8DkQA5iBeVLKN4QQYcBXQAsgFZgkpcy3/D/38nxz9BuKjcXc3eXuy19UXgCLb9PGV926SJm3QqHQlbioLkyJ6vK71/JKsjh3YhX7U9eSWHCY1RVn+PZMJnPSVzO6rIxeFZW0MXsQ7RdBhKc/fsIDAiIwBsZwws+f3Dri6nXuwGumz8dKKXcKIYKAHcD1wF1AnpRyrhBiFhAqpXyqtntZsgM3mo2M/3Y8CUEJfDLuk0tfVFkMX9wAZ3bDbV9BmzrCLAqFQuEASLOZY2kbWHJ0Cb+c20Ze9e8bawXigZeUlGLGeNGufP9d+xu2A68ZVpxZ83WxEOIQEAdcB4youewzIAmo1cAtYdmJZWSVZfGPgZfJ5S4vgC8nQ8ZOmPSZMm+FQuE0CA8P2jUfzrPNh/OMlGSWZpJalEp2WTbZ5dnklOdgMpvw8/ajY5P2xBpCAUFPLj3Ipl6HmEKIFkBPYAsQfX4SvZQyUwhxycYQQojpwHSAZs2a1Xr/MuP/t3fuMZIU9x3//ObVs7Mzs3tz+8jdGfM4neUQCzAQPxJjJ1GEfTiRiWIiJ1aC40iOjYniWBHBBkdWokgQ4iTCkYgcwIYImZhgAlYSjGMbYzuJzRnuATkfcOAQjmP39nb3ZmZ3p+fRv/xRtXtzuzt7uwe7cz33+0itrqmuqapvV/evq6u7fj3LrU/eygVDF3DZtsuWJqi8Ave8H8Z/7D6t9NO/upbqG4ZhnDaICFvzW9ma33rKeaz6xUURyQP3A59Q1fJq/6eqX1DVS1X10uHh4RXT3r7vdibmJrjuLdctfVr7zCNupuXRg/Bb98LPXLnaKhiGYfQkq+qBi0gaZ7zvUdWv+ugxEdnie99bgPFXU5HvHfoed//P3ew8dycXDl94fMPhvc5p/jMPO89xv36H+aQwDMNgdW+hCHAHsF9V29/pewi4GrjJrx88lQq8WH6RBw8+yO37bmfH4A6u+9nr3EPKl5+EXXfC0w+412x+6TNumrx9ssowDANY3Vso7wC+C+zDvUYI8GncOPhXgNcDLwJXqerkSnlt2j6gv3DLZUyF00zVyyiguPIvHzyfPy9eSPbgo8ihxxGN0HQ/vO1jRG+/lukoR7EvTTrZ/W9QqCqVsMlcvbVk21y9xVi5xivlGhPVOoUgxVAhQ2LRkFCkykSlztRsHQX60klGiwGjxSzFvjTPjlU4Ugk5f2uRgb404+WQeita+H8mlWCkkEVVOVIJyWdTDPSlOTpTJ2xEjBYDGi1dqMvUjCsnm0owWsxSa7aYqNRpdWj/hMBQPiCXSTJeCRFguJClGjaZnAmJFv1NgE39GYrZNBPVkGYrYrSYpS+zskOoVuTqPz231KF+sxUxUa1zbJltnfKaqIZMzTZQVfoySUYKAbVGxORMncFcmlL/0rZYTH+QZCgfUK01OTbXoJTPMNiXWXhVd17rUN7lNRO2GK/UCFKuvFTy5JM1FKjUmoyXazQjpdmKOFIJCZsRI4WAXJCi2Yr48SsVnj8yQ7SonSJVjlaPHz/tJETY3J9hUy5zwuvFm3IZBnNpJmeO79N8kGK4EFDxWjfnMwz2pQGYnmtwpBLSWtzYwPRsg8mZOgO5NCVfTi6TZKSQZabe5Gi1TqRKkEow7I/T8UpIo+0Ynqc812CiWqfYl2K0mHXnQDa14qSXSJWp2QYTlZBIlVwmyZu2DVDIphgvhzSXqfPJEKDUn6GUX/kYUYVq6PZNf5BiKB+QTCyfPinCcCFgIJemU46rOX5+8Y2j3fdGOHp2oL/5J69jsBVRilokFEqtFu+am2Nb0xnDfdE5fCt6M09GO3gi2kGYKtBoRUTq3nUvZtMkBHKZFCPFgNmwxeRsnVIuQy5IMl4Oma03l5QdpJyB7A9StCLl6Eyd8lyDzfmAwb70woHeipQj1ZCpmTrgDOtIMUut0WKi6g7mWiNirrHUeBuvPYVsisFcGul4+B9HBDb3Zyj1ByQEZupNxsshfZkkm3IZpucaC+3aCUWp1ppMzTbIphMM9KWZmmmccPFcL4rZFJlU8oQL5LbBPt4wml/ScRGBzfmAUi7DYtvRjI4b93kihelZF7e53xkUgErNGaJCNu07ACHlOXf+FPtSDOeDZTtNA33uYnhszhlygGrYZLwS0p9JLhi1WjNivFxDRBgtBmSWyauQTTOUz1CuNRgrh4yVa1RqS8/hxWzKpRfKmZ5r8PShY9SaEUP5DEFq7Z4knV0IqTVO3tbJhLtIztZbVMOT1/XV8r83/0r3DfhZZ79e/+rGa5iOshwOsxSiY+SkiRS2UO8foZoepr9YYrO/As7Wm4yVa2TTSUr9GaZnGwsHZbXWZKxSI5dJUcplmJytM1tvMlrIks8uHRmaq7d4pVyj1mghCKX+DAN9rrdYrh3v4YkIQ/nMQk+tGjojkE0nGS4EpJNCOplgtBiQD9JLygl8D3e0GCz0bCaq4ZJekuB6uO3ljJVrjFdqTM402D7cz0gxy9OHjjHXaDFSyBKkjx/8tUaL8XKICAwXAmbCFtOzdYbyAZlUgrFyjXQywU8NZBktZBf26UzbPh0uBKQ7TBRoRq73OxM2GSkGoDBeCckHKYYKAcll7iiOVuuUaw2G8q4XMVauETZXPhkSfn9vyi3t9SQSnNKJ+FrQaEWkEoKIoKonnNQtVSardY7OhP6uxnUOwqbrRXe6q1lMPkgxUggIUskTtDZbEY2WIgLZtLm0XS2Rv+olOvSGV4OqEjYjTtaEmVRioddda7Q6pq/7O6t2G7MYd/ftOomdjp9Lzi5134CfygcdDMMwznQ6TaXv/oCyYRiGcUqYATcMw4gpZsANwzBiihlwwzCMmGIG3DAMI6aYATcMw4gpZsANwzBiihlwwzCMmLKhE3lEpAIc2LACu8cQMNHtSmwAZ4LOM0EjmM7TnbNVdYk/7o3+Kv2B5WYT9Roisst09gZngkYwnXHFhlAMwzBiihlwwzCMmLLRBvwLG1xetzCdvcOZoBFMZyzZ0IeYhmEYxmuHDaEYhmHEFDPghmEYMWVDDLiIvEdEDojIcyJy/UaUuZ6IyE9EZJ+I7BaRXT6uJCLfEJFn/XpTW/pPee0HROTd3av5yojInSIyLiJPtcWtWZeIXOL3z3Micqus9HHDLtBB52dF5JBv090ickXbttjpFJGzROTbIrJfRJ4WkT/08T3Vnivo7Kn27IiqrusCJIGDwHlABtgDnL/e5a6zpp8AQ4vi/hK43oevB2724fO95gA41++LZLc1dND1TuBi4KlXowv4IfB23Jfj/h3Y2W1tq9D5WeCPl0kbS53AFuBiHy4Az3gtPdWeK+jsqfbstGxED/wtwHOq+ryq1oF7gfdtQLkbzfuAu3z4LuDKtvh7VTVU1ReA53D75LRDVR8DJhdFr0mXiGwBiqr6X+rOirvb/nNa0EFnJ2KpU1UPq+oTPlwB9gPb6LH2XEFnJ2KpsxMbYcC3Af/X9vslVt7BcUCBR0TkRyLyER83qqqHwR1UwIiPj7v+tera5sOL4+PAtSKy1w+xzA8txF6niJwDvBn4AT3cnot0Qo+2ZzsbYcCXG0eK+7uLP6+qFwM7gY+LyDtXSNuL+qGzrrjqvQ3YDlwEHAY+5+NjrVNE8sD9wCdUtbxS0mXi4qyzJ9tzMRthwF8Czmr7/Trg5Q0od91Q1Zf9ehx4ADckMuZvw/DrcZ887vrXquslH14cf1qjqmOq2lLVCPgHjg9zxVaniKRxRu0eVf2qj+659lxOZy+253JshAF/HNghIueKSAb4APDQBpS7LohIv4gU5sPA5cBTOE1X+2RXAw/68EPAB0QkEJFzgR24hyVxYU26/G15RUTe5p/i/07bf05b5o2a59dwbQox1enrdAewX1X/um1TT7VnJ5291p4d2aAnxVfgng4fBG7o9pPbV6nlPNxT7D3A0/N6gM3AN4Fn/brU9p8bvPYDnMZPtoEv4243G7geye+dii7gUtwJcxD4O/yM39Nl6aDzH4F9wF7cSb4lzjqBd+CGAPYCu/1yRa+15wo6e6o9Oy02ld4wDCOm2ExMwzCMmGIG3DAMI6aYATcMw4gpZsANwzBiihlwwzCMmGIG3DAMI6aYATe6iogMisg1PrxVRP6523VaT0TkURHpma+iG93FDLjRbQaBa8C5KFDV93e5PoYRG8yAG93mJmC7d7p/3/xHFkTkQyLyLyLyNRF5QUSuFZFPisiTIvLfIlLy6baLyMPeM+R3ReSNnQoSkatE5CkR2SMij/m4pIjcIiKPe891v9+W/jrv4H+PiNzk4y7y5e8VkQfmvdz5nvXNIvJDEXlGRC7z8X0icq9P/09AX1u5X/L12Scif7Q+u9foabo9FdSWM3sBzsF/WGFR+EM4X80FYBg4BnzUb/sbnNc5cNPBd/jwW4FvrVDWPmCbDw/69UeAG304AHbhHP3vBP4TyPltJb/eC7zLh/8M+FsffhT4nA9fAfyHD38SuNOHLwCauCnblwDfaKvbYLfbwpb4LalXewEwjHXk2+qc9FdE5BjwNR+/D7jAuxD9OeC+tq9fBSvk933gSyLyFWDeO9/lPq/5oZsBnIOjXwa+qKqzAKo6KSIDOEP7HZ/2LuC+tvzn8/wR7mIE7us/t/o89orIXh//PHCeiHwe+FfgkZPtDMNYjBlw43QmbAtHbb8j3LGbAKZV9aLVZKaqHxWRtwLvBXaLyEU4P9B/oKpfb08rIu9h7f6g5+vX4sRza0k+qjolIhcC7wY+DvwG8OE1lmec4dgYuNFtKrhhkjWjznH/CyJyFTjXot4oLouIbFfVH6jqnwITOL/QXwc+5n1KIyJv8G6CHwE+LCI5H19S1WPA1Pz4NvDbwHeWFHQijwEf9Hm8CTeMgogMAQlVvR/4DO4bnYaxJqwHbnQVVT0qIt/3Dy/3n0IWHwRuE5EbgTTum6t7OqS9RUR24Hrd3/Tp9uKGO57wfqCPAFeq6sO+h75LROrAvwGfxvnQ/ntv2J8Hfvck9bsN+KIfOtnNcV/w23z8fCfqU2uTbRiYO1nDMIy4YkMohmEYMcWGUIyeQ0RuAK5aFH2fqv5FN+pjGOuFDaEYhmHEFBtCMQzDiClmwA3DMGKKGXDDMIyYYgbcMAwjpvw/Y5LxqAfxL7wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "box_data[['T1', 'T2', 'T3']].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "T_obs = box_data['T3'].values\n",
    "t_obs = box_data.index.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0,   15,   30,   45,   60,   75,   90,  105,  120,  135,  150,\n",
       "        165,  180,  195,  210,  225,  240,  255,  270,  285,  300,  315,\n",
       "        330,  345,  360,  375,  390,  405,  420,  435,  450,  465,  480,\n",
       "        495,  510,  525,  540,  555,  570,  585,  600,  615,  630,  645,\n",
       "        660,  675,  690,  705,  720,  735,  750,  765,  780,  795,  810,\n",
       "        825,  840,  855,  870,  885,  900,  915,  930,  945,  960,  975,\n",
       "        990, 1005, 1020, 1035, 1050, 1065, 1080, 1095, 1110, 1125, 1140,\n",
       "       1155, 1170, 1185, 1200, 1215, 1230, 1245, 1260, 1275, 1290, 1305,\n",
       "       1320, 1335, 1350, 1365, 1380, 1395, 1410, 1425, 1440, 1455, 1470,\n",
       "       1485, 1500, 1515, 1530, 1545, 1560, 1575, 1590, 1605, 1620, 1635,\n",
       "       1650, 1665, 1680, 1695, 1710, 1725, 1740, 1755, 1770, 1785, 1800,\n",
       "       1815, 1830, 1845, 1860, 1875, 1890, 1905, 1920, 1935, 1950, 1965,\n",
       "       1980, 1995, 2010, 2025, 2040, 2055, 2070, 2085, 2100, 2115, 2130,\n",
       "       2145, 2160, 2175, 2190, 2205, 2220, 2235, 2250, 2265, 2280, 2295,\n",
       "       2310, 2325, 2340, 2355, 2370, 2385, 2400, 2415, 2430, 2445, 2460,\n",
       "       2475, 2490, 2505, 2520, 2535, 2550, 2565, 2580, 2595, 2610, 2625,\n",
       "       2640, 2655, 2670, 2685, 2700, 2715, 2730, 2745, 2760, 2775, 2790,\n",
       "       2805, 2820, 2835, 2850, 2865, 2880, 2895])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x119d07ee0>]"
      ]
     },
     "execution_count": 14,
     "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(t, T)\n",
    "plt.plot(t_obs, T_obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}