ex1-linear regression/ex1-one-variable.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 线性回归（单变量）\n",
    "预测food truck的收益值。\n",
    "ex1data1.txt：数据集，第一列表示城市人数，第二列该城市的food truck收益"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Population   Profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = 'ex1data1.txt'\n",
    "data = pd.read_csv(path, header=None, names=['Population', 'Profit'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>97.000000</td>\n",
       "      <td>97.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.159800</td>\n",
       "      <td>5.839135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.869884</td>\n",
       "      <td>5.510262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.026900</td>\n",
       "      <td>-2.680700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.707700</td>\n",
       "      <td>1.986900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.589400</td>\n",
       "      <td>4.562300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.578100</td>\n",
       "      <td>7.046700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.203000</td>\n",
       "      <td>24.147000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Population     Profit\n",
       "count   97.000000  97.000000\n",
       "mean     8.159800   5.839135\n",
       "std      3.869884   5.510262\n",
       "min      5.026900  -2.680700\n",
       "25%      5.707700   1.986900\n",
       "50%      6.589400   4.562300\n",
       "75%      8.578100   7.046700\n",
       "max     22.203000  24.147000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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jAGCnhGZ2TOgEAA6abS05V0o5vZ1jAACwH213neZ/s81jAACw72zZnlFK+YYk35jkuaWUf7zmqi9NcqifAwMAgGHR1NN8R5LJ3u3uXHP8C0n+er8GBQAAw2TL0Fxr/b0kv1dK+aVa66cGNCYAABgqTe0Z/2ut9Q1Jfq6UUtdfX2s907eRAQDAkGhqz/jl3r8/1e+BAADAsGoKzT+Z5FuTvKLWen4A4wEAgKHTFJpfUEr5b5KcKaX8apKy9spa64f7NjIAABgSTaH5XyT5oSQzSX5m3XU1ycv7MSgAABgmTatn/HqSXy+l/Eit9U0DGhMAAAyVpkpzkqTW+qZSypkk39w79Lu11vf0b1gAADA8trWNdinlXyX5wSQf6339YO8YAADse9uqNCf575OcrLV2k6SU8o4kf5Tkn/VrYAAAMCy2VWnuec6ay8/e64EAAMCw2m6l+V8l+aNSyvuysuzcN0eVGQCAA6IxNJdSSpIPJPn6JH81K6H5fK31/+vz2AAAYCg0huZaay2l/Gat9euS3DuAMQHsOwuLS5m/ei0zUxOZnhxvezgA7NB22zM+VEr5q7XWP9zuDy6lvD3JK5N8ttb6Nb1jX5bk15LcneThJH+z1np1RyMGGDEXL1/J+dm5jHU6We52c+HsiZw5eaztYQGwA9s9EfBbshKc/6SUMldK+UgpZa7hPr+U5NvXHfuhJL9Ta/2qJL/T+x5g31pYXMr52blcX+7miaUbub7czbnZuSwsLrU9NAB2YLuV5u/Y6Q+utb6/lHL3usPfleRlvcvvSPK7Sc7v9GcDjIr5q9cy1unkerpPHRvrdDJ/9Zo2DYARsmVoLqUcSfIDSY4n+UiSt9Vab+zi8Z5fa300SWqtj5ZSnreLnwUw9GamJrLc7d5ybLnbzczUREsjAuB2NLVnvCPJqawE5u9I8tN9H1FPKeV1pZRLpZRLjz322KAeFmBPTU+O58LZEzky1smd44dzZKyTC2dPqDIDjJim9owX1Vr/6yQppbwtyR/s8vE+U0p5Qa/K/IIkn93shrXWtyR5S5KcOnWq7vJxAVpz5uSxnD5+1OoZACOsqdK8vHphl20Zq+5N8tre5dcmubgHPxNg6E1PjufFdz1HYAYYUU2V5heXUr7Qu1ySTPS+L1lZwvlLN7tjKeVXsnLS39FSynySH03yE0n+bSnl+5P8WZK/scvxAwBA320Zmmuth273B9daX73JVd96uz8TAADasN11mgEA4MASmgEAoIHQDAAADYRmAABoIDQDAEADobnPFhaX8uAjj2dhcantoQAAcJua1mlmFy5evpLzs3MZ63Sy3O3mwtkTOXPyWNvDAvaBhcUlOwwCDJDQ3CcLi0s5PzuX68vdXE83SXJudi6njx/1Bw7YFW/IAQZPe0afzF+9lrHOrdM71ulk/uq1lkYE7Adr35A/sXQj15e7OTc7pwUMoM+E5j6ZmZrIcrd7y7HlbjczUxMtjQjYD7whB2iH0Nwn05PjuXD2RI6MdXLn+OEcGevkwtkTWjOAXfGGHKAdepr76MzJYzl9/KiTdYA9s/qG/Ny6nmavLwD9JTT32fTkuD9mwJ7yhhxg8IRmgBHkDTnAYOlpBgCABkIzAAA0EJoBAKCB0AwAAA2EZgAAaCA0AwBAA6EZAAAaCM0AANBAaAb2hYXFpTz4yONZWFxqeygA7EN2BARG3sXLV3J+di5jnU6Wu91cOHsiZ04ea3tYAOwjKs3ASFtYXMr52blcX+7miaUbub7czbnZORVnAPaU0AwH1H5pZ5i/ei1jnVtfysY6ncxfvdbSiADYj7RnwAG0n9oZZqYmstzt3nJsudvNzNRESyMCYD9SaYYDZr+1M0xPjufC2RM5MtbJneOHc2SskwtnT2R6crztoQGwj6g0wwhaWFzK/NVrmZma2HE4XG1nuJ6nq7Or7QyjGjTPnDyW08eP3vacAEAToRlGzG5bK/ZrO8P05LiwDEDfaM+AEbIXrRXaGQBg51SaYYTsVWuFdgYA2BmhGUbIXrZWaGcAgO3TnjFk9svaucNuVOdZawUAtEOleYjsp7Vzh9moz7PWCgAYPJXmIbHf1s4dVvtlnqcnx/Piu54jMAPAgAjNQ8JWwINhngdvVFthAGAt7RlDYr+unTtszPNgjXorDACsUmkeEk7wGgzzPDj7pRUGABKV5qFy5uSxvOgFX5rLjzyek3c9J8eff2fbQ9qX2jiRbjfbXo+q/bhdNwAHl9A8RA7iR9nbDZN7HToHuUbxMP9e+xnmtcIAsJ8IzUNi7UfZq5W5c7NzOX386L6tym03TA5z6GwybL/XtSH5A5/8XF/ndbUV5ty6x9ivz2cA9jeheUj0+6PsYWsP2G6YHLbQuVPD1KKw9s3HkzdvpluT5Zu1r/NqTWkA9guheUj086PsYazUbjdM7iZ0DsMbhWFpUdjozcd6/QrztusGYD+wesaQ6NeqDsO6gsF2w+Tths6Ll6/k9D335Xvfen9O33Nf7r18ZW8GvkPDslrHRutTr6ffGAA2p9I8RPrxUfYwtQestd1+19vpix22lo5haFHY6M3H4U5yqNPJHYf0GwNAE6F5yOz1R9nD0h6wke2GyZ2GzmF8o9B2i8Jmbz7aDvMAMCqE5n1u2Fcw2G6Y3EnoHOY3Cm3a7M3HsDwXAGCYCc0HwDC0BwzSsL9RaFPbFW8AGFVC8wFx0MLSQXujAAD0l9DMvnXQ3igAAP1jybkDamFxKQ8+8njrS88BAIwCleYDaBg3OwEAGGYqzQfMsG52AgAwzITmA2ajneFW1zAGAGBjQvMW9mPf70Fdw3g//i4BgMHR07yJ/dr3exDXMN6vv0sAYHBKrbXtMTQ6depUvXTp0sAeb2FxKafvuS/Xl5+uyB4Z6+SD51++b8LlwuLSgVjD+CD8LgGAvVNKeaDWemr9ce0ZGxj1vt/ttCJMT47nxXc9Z98Hx1H/XQIAw0F7xgZGue9XK8KtRvl3CQAMD5XmDaz2/R4Z6+TO8cM5MtYZib7fQS8nNwon143S73IU5nOYmT8A+kmleRNnTh7L6eNHR6rvd7UV4Xqerqwe6pTMX72W6cnxPe1jHqWK9ij8LkdpPoeR+QOg34TmLUxPjg9lwNrMRq0IX1y6mYeufD4PL3xxz0LF2or2akA/NzuX08ePDu18DfPvchTnc5iYPwAGQXvGPjI9OZ4feeWLnnH8x9/z0Zz79b1r2zjoJ9ftdRvAQZ/P3TJ/AAyCSnODUVuabWHxyWccO1Q6Sbn12GqouJ3/poN8cl0/2gAO8nzuBfMHwCC0UmkupTxcSvlIKeVyKWVwCzDv0MXLV3L6nvvyvW+9P6fvuS/3Xr7S9pC2tLC4lDe/75PPOH6jezM3u7eux72bUDFKJ9ftpX6daHlQ53OvmD8ABqHNSvO31Fo/1+Ljb2kU+yTnr17LHYc6Wbpxa9XtH738v8xXTH/Jnu4CuNcn141CRX+jEy13U7FfaxROVhxm5g+AftOesYl+BqR+2ehj6vHDnfytl74w05Pjex4q9urkulFZ+aDfbQDDfLLiKDB/APRTWycC1iS/VUp5oJTyupbGsKVR7JPc6GPqn/zrT1eUB7EL4E5Pkhv02tK7oQ0AAA6utirNp2utny6lPC/Jb5dSPlFrff/aG/TC9OuS5IUvfOHAB7gakPaypWEQ2vyY+nYqxqNW0dcGAAAHUyuhudb66d6/ny2lvCvJS5K8f91t3pLkLUly6tSp+owfMgCjGpDa+Jj6dnvAR7WiPyrPBQBgbwy8PaOU8qxSyp2rl5N8W5KHBj2O7RpES8N+cLtr5Wp5AABGQRuV5ucneVcpZfXx/69a6//TwjhaMQqrRNyO3VSMd1rR369zCAAMr4GH5lrrnyZ58aAfdxiMyioRt2O3PeDbbXnYz3MIAAyvUmsr7cI7curUqXrp0tDugbItC4tLOX3Pfbm+/HQ19shYJx88//J9VS3tZxX4oMwhANCeUsoDtdZT64+3teTcgXO7Pb+jZjs94Dtdlm7VQZlDAGD42NxkQEZxlYi9trC4lHfe/2d58/v+OHccOvSM9oqmKrU5BADaIjT30foQOIrrPu+Vi5ev5Nyvzz21xffSjRtJnl6W7gOf/Fxjr3I/59DJhQDAVoTmPtnshLVRXPd5t1bXcF4NzGuNdTr56Ke/sO01nvsxh04uBACa6Gnug622hj6I6z5v1Iu8aqXdou6oV3mzObydXulR2sYbAGiPSnMfjNrW0P20sLiUz197Mk/evPmM68YPl1w4eyJf/eXP3nWv8u1Wi/2uAIDtEJr7wAlrK9YG2W5NDneSibHDefJmN6//luP5Wy994VPBdDe9yre7hXfS3u9KDzUAjBahuQ/200l/txvuNgqy44c7efNr/kq++su/NNOT40+1U8xMTeyqV3k31eI2fld6qAFg9AjNW9hNNXA/nPS3m3C3UZC941Anz54Yy/Tk+KY/+3bmabfV4kH+rnZTFQcA2uNEwE1cvHwlp++5L9/71vtz+p77cu/lKzv+GaN80t9uT5DbKsju9cl3q9XiI2Od3Dl+OEfGOjuuFg/qd2WDFgAYTSrNG1AN3P0Jclu1PTz4yON7fvLdqFT29bsDwGgSmjewn1ZUuN0Wk70Id5sF2X4Fx+nJ8aH//eynfncAOEiE5g3sl2rgbnqS9yrcbRRkD3pwHJWqOADwtFJrbXsMjU6dOlUvXbo00Me89/KVZ4S6psA5TMuILSwu5fQ99+X68tPh/8hYJx88//Idr4LRr/+mYZovAIAkKaU8UGs9tf64SvMmdloN3E5Vd5Ahca9aTPrZ8jAK7RQAAInQvKXthrrtnDg46LV5bdoBALB3LDm3B5qWEdvrJda2Yy+WYdupvVimDwBgGKk074Gmqu5mrRIf/fTn8+yJO/pWlbVpBwDA3hCa90DTahAbherrN27m7//ypRzudLJ8s5sf/c6vzmu+/it2/NhN7RCD6hveT8v0AQCsJzTvka2qutOT4/mRV74oP/buj2XsUMmNmzU3u90s3UyWcjNJ8sO/+VBSkte8dPvBedB90lvZL8v0AQBsRE/zHtpsK+aLl6/kTe/5WMY6Jcs3uvm7p+/O+OFDz7j/j737Y9vuc26jT3orbfRQAwAMikpzn60Nt6ve/sGH011XlU2SsUNl2+0Mw9gOYdMOAGC/Umnus41W1rjjUCd/75u+8hm3vdmt225nGNZ2iM2q7QAAo0xobrCwuJQHH3n8ttseNgu3f++bvjL/8lVfkzsOd/Ks8UM7bmfQDgEAMDi20d7CXp1ot9WW3LvdDMRmIgAAe2ezbbSF5k0sLC7l9D333dKLfGSskw+ef7lwCwCwT20Wmp0IuIm9PtFuUOslAwCw9/Q0b2JYT7QDAGDwhOZNjOKJdrs9aREAgI1pz9jCoNYd3ot+52HaHRAAYL8Rmhv0uxd5L8Lu2g1UVnuwz83O5fTxo0NdGQcAGBXaM1q0V1thb7SByupJiwAA7J7Q3KK9CrtOWgQA6C+huUV7FXZH8aRFAIBRoqd5G/q1Mclq2F2/W+DtPMagTloEADiIhOYGTSfq7TZQ72XYtYEKAEB/CM1baFqVYq+WeRN2AQCGm9C8ha220k6y62Xe1lapVx9v/WVhGgCgfULzFrY6UW+zFS7mr17bVtBdW6W+fuNmaq2ZGDt8y2WblAAADAerZ2xhq1UpnnXHoVxfvjVQX1/u5ll3HGr8uevXZ16+WXOjm2dcvt11mwEA2FsqzQ02O1Hvi0/ezPihkqWb9anbjh8q+eKTNxt/5kZtH5tZbQfRpgEA0B6heRs2OlFvZmoipVOSNaG5dMq21ljeqO1jMzYpAQBon/aM27SbDUXW33fsUMnhTp5x2SYlAADDodRam2/VslOnTtVLly61PYwN7WadZqtnAAAMl1LKA7XWU+uPa8/Ypd2ssbz+vptd3ql+7WAIAHBQCc37zF5tuAIAwNP0NI+AhcWlPPjI441Lz61fys6SdQAAe0OlecjtpHK81Q6G2jQAAG6fSvMQ22nleKsdDAEAuH1Ccx+ttlV88jNPbKu9Yr3VyvFaq5XjjexmGbzbtd3WEQCAUaY9o09W2yqSle21xw+VlE7Z0Yl5t1M53mwHw35w0iEAcLHNlJkAAA7USURBVFCoNPfB2raK68sroXfpZt3xiXmrlePxwyVfMnYo44fLtirH05PjefFdz+l7hdlJhwDAQSE098FGbRWrtmqv2MjK1jMlKb1/h8ROW0cAAEaZ0NwHG7VVrNrJiXmr1dylG9385ydvZunG8FRznXQIABwkQnMfrD0h78jYyhSPHyo5MtbJj7zyRZm/em1bwXc31dx+n6DXxkmHAABtcSJgHywsLuUrpp+V97z+r+WLT97Ms+44lC8+eTMPXfl83vSej237xLnbreYO6gS9QZ50CADQJpXmbdpu5fadH/pUvuEn7str3vqhvPLnPpBPLXwxx59/Z2amJvKm//tjOzpx7naquYM+QW8QJx0CALRNpXkbtlu5feeHPpUf/s2HkiRP3lg5dm527qlq7Prd+g6Vkvd94rP5lr/8vE1D506ruXYFBADYeyrNDbZbuV1YXMqPvfujz7j/oU55KvCub7X44pM388Z3fzSn77kv916+sukYdlLNdYIeAMDeE5obbPdkvPmr1zJ26JnTuXyzPlUhXm21eNYdh566fnHp5p62UDhBDwBg72nPaLDdyu3M1ERu1vqM+//od77oqcC62mrxvk98Nm9890ezuHTzqdvtZQvFVi0dC4tLTtwDANghleYG6yu344dL/uHLjm95u2fdcSh3HCr5l9/9NXnNS7/iGbf7lr/8vNzo3hqw97qFYqOWjouXr+T0Pffle996f2NLCAAATyt1g+rosDl16lS9dOlSq2NYWFzKO+//s7z5fZ/MHYc2PyFwfSV3s8ruvZev5NwAloVbO67T99z31LbeSXJkrJMPnn/5gag4q7ADANtRSnmg1npq/XHtGTvwv//uJ7N0o5ulGyvBc3VljLUhbHpy/Knvt1p1Y9BrHB/kVTUGtW41ALB/tdKeUUr59lLKfyylfLKU8kNtjGGndro733ZW3RjkGscHdVWNQa9bDQDsTwMPzaWUQ0nenOQ7krwoyatLKS8a9Dh2aqehczdbYPfDQV1VY9h+DwDAaGqjPeMlST5Za/3TJCml/GqS70rysRbGsm2roXN9H/JmoXMYK7sHcdvrYfw9AACjp43QfCzJI2u+n0/y0vU3KqW8LsnrkuSFL3zhYEbWYCehc6che1DW9lwfBMP6ewAARksboblscOwZS3jUWt+S5C3JyuoZ/R7Udu0kdB7Eyu4w8nsAAHarjdA8n+SuNd/PJPl0C+MYiINW2R1Wfg8AwG60sXrGHyb5qlLKXyil3JHke5Lc28I4AABgWwZeaa613iilvD7Jf0hyKMnba60fHfQ4AABgu1rZ3KTW+t4k723jsQEAYKda2dwEAABGidAMAAANhOYdWlhcyoOPPG4bZgCAA6SVnuZRdfHylZxft0nGmZPH2h4WAAB9ptK8TQuLSzk/O5fry908sXQj15e7OTc7p+IMAHAACM3bNH/1WsY6t07XWKeT+avXWhoRAACDIjRv08zURJa73VuOLXe7mZmaaGlEAAAMitC8TdOT47lw9kSOjHVy5/jhHBnr5MLZE7ZmBgA4AJwIuANnTh7L6eNHM3/1WmamJgRmAIADQqV5h6Ynx/Piu56TJJaeAwA4IFSab4Ol5wAADhaV5h2y9BwAwMEjNO/QqCw9Z+dCAIC9oz1jh0Zh6TntIwAAe0uleYeGfek57SMAAHtPpfk2DPPSc6vtI9fzdDV8tX1kmMYJADBKhObbND05PpQhdBTaRwAARo32jH1m2NtHAABGkUrzPjTM7SMAAKNIaN6nhrV9BABgFGnPAACABkIzAAA0EJoBAKCB0AwAAA2EZgAAaCA0AwBAA6EZAAAaCM0AANBAaAYAgAZCMwAANBCaAQCggdC8hYXFpTz4yONZWFxqeygAALTocNsDGFYXL1/J+dm5jHU6We52c+HsiZw5eaztYQEA0AKV5g0sLC7l/Oxcri9388TSjVxf7ubc7JyKMwDAASU0b2D+6rWMdW6dmrFOJ/NXr7U0IgAA2iQ0b2BmaiLL3e4tx5a73cxMTbQ0IgAA2iQ0b2B6cjwXzp7IkbFO7hw/nCNjnVw4eyLTk+NtDw0AgBY4EXATZ04ey+njRzN/9VpmpiYEZgCAA0xo3sL05LiwDACA9gwAAGgiNAMAQAOhGQAAGgjNAADQQGgGAIAGQjMAADQQmgEAoIHQDAAADYRmAABoIDQDAEADoRkAABoIzQAA0EBoBgCABkIzAAA0EJoBAKBBqbW2PYZGpZTHknyqhYc+muRzLTzuQWF++88c95f57T9z3F/mt//Mcf/t9Rx/Ra31uesPjkRobksp5VKt9VTb49ivzG//meP+Mr/9Z477y/z2nznuv0HNsfYMAABoIDQDAEADoXlrb2l7APuc+e0/c9xf5rf/zHF/md/+M8f9N5A51tMMAAANVJoBAKDBgQ/NpZSHSykfKaVcLqVc2uD6Ukr530opnyylzJVS/kob4xxVpZS/1Jvb1a8vlFLesO42LyulfH7Nbf5FW+MdFaWUt5dSPltKeWjNsS8rpfx2KeWPe/9ObXLfby+l/Mfec/qHBjfq0bHJ/P5kKeUTvdeBd5VSnrPJfbd8TWHFJnP8xlLKlTWvBa/Y5L6eww02md9fWzO3D5dSLm9yX8/hbSil3FVKeV8p5eOllI+WUn6wd9xr8R7YYn5bey0+8O0ZpZSHk5yqtW64vl/vRfsfJXlFkpcm+de11pcOboT7RynlUJIrSV5aa/3UmuMvS/JPa62vbGtso6aU8s1JFpP8cq31a3rHLiT581rrT/RegKdqrefX3e9Qkv+U5L9LMp/kD5O8utb6sYH+Bwy5Teb325LcV2u9UUq5J0nWz2/vdg9ni9cUVmwyx29Mslhr/akt7uc5vA0bze+66386yedrrT++wXUPx3O4USnlBUleUGv9cCnlziQPJPnuJH8nXot3bYv5nUlLr8UHvtK8Dd+VlRedWmv9UJLn9H6R7Ny3JvmTtYGZ21NrfX+SP193+LuSvKN3+R1ZeXFZ7yVJPllr/dNa65NJfrV3P9bYaH5rrb9Va73R+/ZDWXnh5jZt8hzeDs/hbdhqfkspJcnfTPIrAx3UPlNrfbTW+uHe5SeSfDzJsXgt3hObzW+br8VCc1KT/FYp5YFSyus2uP5YkkfWfD/fO8bOfU82f5H+hlLKg6WUf19K+epBDmofeX6t9dFk5cUmyfM2uI3n8974u0n+/SbXNb2msLXX9z52ffsmH2t7Du/eNyX5TK31jze53nN4h0opdyf52iT3x2vxnls3v2sN9LX48F78kBF3utb66VLK85L8dinlE7136KvKBvc52D0tt6GUckeSM0n+2QZXfzgrW1Yu9tphfjPJVw1yfAeI5/MulVJ+OMmNJO/c5CZNryls7ueTvCkrz8k3JfnprPxRXMtzePdena2rzJ7DO1BKmUwym+QNtdYvrBTym++2wTHP4w2sn981xwf+WnzgK8211k/3/v1skndl5SOTteaT3LXm+5kknx7M6PaV70jy4VrrZ9ZfUWv9Qq11sXf5vUnGSilHBz3AfeAzq61DvX8/u8FtPJ93oZTy2iSvTPKauskJIdt4TWETtdbP1Fpv1lq7SX4xG8+d5/AulFIOJ/kfkvzaZrfxHN6+UspYVgLdO2utv9E77LV4j2wyv629Fh/o0FxKeVavuTyllGcl+bYkD6272b1J/nZZ8fVZOXHi0QEPdT/YtLJRSvkvej12KaW8JCvPy4UBjm2/uDfJa3uXX5vk4ga3+cMkX1VK+Qu96v/39O5Hg1LKtyc5n+RMrfU/b3Kb7bymsIl154u8KhvPnefw7vy3ST5Ra53f6ErP4e3r/d16W5KP11p/Zs1VXov3wGbz2+prca31wH4l+cokD/a+Pprkh3vHfyDJD/QulyRvTvInST6SlTMxWx/7KH0l+ZKshOBnrzm2do5f35v/B7PS1P+NbY952L+y8gbk0STLWalYfH+S6SS/k+SPe/9+We+2X57kvWvu+4qsnLX9J6vPeV/bmt9PZqUH8XLv6xfWz+9mrym+tj3H/0fvdXYuKwHiBevnuPe95/BtzG/v+C+tvvauua3n8O3N8V/LSkvF3JrXhVd4Le77/Lb2Wnzgl5wDAIAmB7o9AwAAtkNoBgCABkIzAAA0EJoBAKCB0AwAAA2EZoABK6XcLKVcLqU8VEr5d6WUL9njn/93Sik/13Cbl5VSvnHN9z9QSvnbezkOgP1EaAYYvGu11pO11q9J8mRW1i0ftJcleSo011p/odb6yy2MA2AkCM0A7fr9JMeTpJTyj3vV54dKKW/oHbu7lPKJUso7SilzpZRfX61Ml1IeXt1yvpRyqpTyu+t/eCnlO0sp95dS/qiU8v+WUp5fSrk7K0H9f+5VvL+plPLGUso/7d3nZCnlQ73He1cpZap3/HdLKfeUUv6glPKfSinf1P/pARgOQjNAS0oph5N8R5KPlFK+Lsn/mOSlSb4+yd8vpXxt76Z/Kclbaq0nknwhyf+0g4f5QJKvr7V+bZJfTXKu1vpwkl9I8rO9ivfvr7vPLyc533u8jyT50TXXHa61viTJG9YdB9jXhGaAwZsopVxOcinJnyV5W1a2jH1XrfWLtdbFJL+RZLWS+0it9YO9y/9n77bbNZPkP5RSPpLkf0ny1VvduJTy7CTPqbX+Xu/QO5J885qb/Ebv3weS3L2DcQCMtMNtDwDgALpWaz259kAppWxx+7rJ9zfydPHjyCb3/TdJfqbWem8p5WVJ3rizoT7DUu/fm/E3BDhAVJoBhsP7k3x3KeVLSinPSvKqrPQ7J8kLSynf0Lv86qy0XCTJw0m+rnf57CY/99lJrvQuv3bN8SeS3Ln+xrXWzye5uqZf+fuS/N762wEcNEIzwBCotX44yS8l+YMk9yd5a631j3pXfzzJa0spc0m+LMnP947/WJJ/XUr5/axUfjfyxiT/rnebz605/u4kr1o9EXDdfV6b5Cd7j3cyyY/v5r8NYD8ota7/1A+AYdFb6eI9veXpAGiJSjMAADRQaQYAgAYqzQAA0EBoBgCABkIzAAA0EJoBAKCB0AwAAA2EZgAAaPD/A4xzCLBZJqAAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 代价函数\n",
    "\n",
    "![](img/cost.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>Ones</th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Population   Profit\n",
       "0     1      6.1101  17.5920\n",
       "1     1      5.5277   9.1302\n",
       "2     1      8.5186  13.6620\n",
       "3     1      7.0032  11.8540\n",
       "4     1      5.8598   6.8233"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 新增一例，x0\n",
    "data.insert(0, 'Ones', 1)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = data.shape[1]\n",
    "X = data.iloc[:, 0:cols-1]\n",
    "Y = data.iloc[:, cols-1:cols]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>Ones</th>\n",
       "      <th>Population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>6.1101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5.5277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>8.5186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>7.0032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5.8598</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ones  Population\n",
       "0     1      6.1101\n",
       "1     1      5.5277\n",
       "2     1      8.5186\n",
       "3     1      7.0032\n",
       "4     1      5.8598"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Profit\n",
       "0  17.5920\n",
       "1   9.1302\n",
       "2  13.6620\n",
       "3  11.8540\n",
       "4   6.8233"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.matrix(X.values)\n",
    "Y = np.matrix(Y.values)\n",
    "theta = np.matrix(np.array([0, 0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((97, 2), (97, 1), (1, 2))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, Y.shape, theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 代价函数\n",
    "def computeCost(X, Y, theta):\n",
    "    inner = np.power((X * theta.T) - Y, 2)\n",
    "    return np.sum(inner) / (2 * len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.072733877455676"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computeCost(X, Y, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 梯度下降\n",
    "\n",
    "![](img/gradient.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 梯度下降\n",
    "def gradientDescent(X, Y, theta, alpha, iters):\n",
    "    temp = np.matrix(np.zeros(theta.shape))\n",
    "    parameters = int(theta.shape[1])\n",
    "    cost = np.zeros(iters)\n",
    "    \n",
    "    for i in range(iters):\n",
    "        error = X * theta.T - Y\n",
    "        \n",
    "        for j in range(parameters):\n",
    "            term = np.multiply(error, X[:, j])\n",
    "            temp[0, j] = temp[0, j] - alpha / len(X) * np.sum(term)\n",
    "        \n",
    "        theta = temp\n",
    "        cost[i] = computeCost(X, Y, theta)\n",
    "    \n",
    "    return theta, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-3.24140214,  1.1272942 ]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = 0.01\n",
    "iters = 1000\n",
    "g, cost = gradientDescent(X, Y, theta, alpha, iters)\n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.515955503078912"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 计算训练模型的误差\n",
    "computeCost(X, Y, g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画出拟合图像\n",
    "x = np.linspace(data.Population.min(), data.Population.max(), 100)\n",
    "f = g[0, 0] + g[0, 1] * x\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.xlabel('Population')\n",
    "plt.ylabel('Profit')\n",
    "l1 = plt.plot(x, f, label='Prediction', color='red')\n",
    "l2 = plt.scatter(data.Population, data.Profit, label='Traing Data', )\n",
    "plt.legend(loc='best')\n",
    "plt.title('Predicted Profit vs Population Size')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VxABdjaOOgq22ghNPhHffLbsaSZIklcAAXY26OvjLX+DTT3OYdiiHJElSp2OArtbgwXDGGXDrrXDJJWVXI0mSpFZmgF4UJ5wAO+wAP/whvP562dVIkiSpFRmgF0VdHVx6aX5/+OEwe3ap5UiSJKn1GKAX1cCB8PvfwwMPwLnnll2NJEmSWokBenEccQR85Svw05/C88+XXY0kSZJagQF6cUTARRdBz55w2GEwc2bZFUmSJKnGDNCLq39/OP98eOKJPDuHJEmSOjQDdEv4xjfgoIPgl7+EMWPKrkaSJEk1ZIBuKeedB/36wSGHwGeflV2NJEmSasQA3VL69IHLLssPE/7oR2VXI0mSpBoxQLekYcPgxz+GP/0J/v73squRJElSDRigW9qvfgWbbgpHHgkTJ5ZdjSRJklqYAbqlde8OV14JU6fCt7/tKoWSJEkdjAG6FgYPht/9Du6+G845p+xqJEmS1IIM0LXy3e/C3nvnVQqffLLsaiRJktRCDNC10rBKYZ8+cPDB8PnnZVckSZKkFmCArqW+feGvf4XnnoOf/KTsaiRJktQCDNC1tuuucOKJ8L//69R2kiRJHYABujWccQYMGZJn5XjzzbKrkSRJ0mIwQLeG7t3h6qthxgw46KD8KkmSpHbJAN1aBg2CCy+Ef/4TfvGLsquRJEnSIjJAt6aDDoLvfCcP6bj77rKrkSRJ0iIwQLe2c86BDTaAb37Tpb4lSZLaIQN0a+vRA669FqZMgUMPhVmzyq5IkiRJVTBAl2H99eG88+C+++A3vym7GkmSJFXBAF2Www+HQw6B006DBx8suxpJkiQVZIAuSwScfz6stVZe6vu998quSJIkSQUYoMvUuzdcdx18+GGeoWPmzLIrkiRJ0kIYoMu2ySa5J/r+++HUU8uuRpIkSQthgG4Lvv1tOOqoPD/0LbeUXY0kSZIWwADdVvzhDzBkCBx2GLz6atnVSJIkaT4M0G3FkkvCiBH5/de/DtOmlVuPJEmSmmWAbkvWWAMuvxzGjoXjjy+7GkmSJDXDAN3WfOUr8LOfwUUXwSWXlF2NJEmSmjBAt0X/9V8wbBh873swblzZ1UiSJKkRA3Rb1KULXHUVrLACfPWrMHly2RVJkiSpwgDdVvXtC9dfD++8Awce6CIrkiRJbUShAB0RfytyTC1syy3zIiv33AMnn1x2NZIkSQK6Frxug8Y7EdEF2Lzly9E8Dj8cxoyBs86CzTaDgw8uuyJJkqRObYE90BFxckRMATaOiE8q2xTgfeDmVqlQ8Lvfwfbbw3e+k6e4kyRJUmkWGKBTSmeklHoDZ6aUlq5svVNKy6eUHFPQWpZYAq67DpZfHvbbDz74oOyKJEmSOq2iDxHeGhE9ASLi0Ij4XUSsXsO61FS/fnDjjfDuu7D//j5UKEmSVJKiAfp84LOI2AQ4CXgDuKxmVal59fVw4YVw//3wk5+UXY0kSVKnVDRAz0wpJWAf4JyU0jlA79qVpfk67DA44QQ4+2y49NKyq5EkSep0igboKRFxMvBN4LbKLBxL1K4sLdCZZ+aVCo8+Gh55pOxqJEmSOpWiAfoAYDpwRErpXWAV4MyaVaUFa3iocI018kOFr71WdkWSJEmdRqEAXQnNVwDLRMRwYFpKyTHQZVpuObjllvww4V57wSeflF2RJElSp1B0JcL9gZHAN4D9gccj4uu1LEwFrLMOjBgBzz8PBx0Es2aVXZEkSVKHV3QIx8+ALVJK30opHQZsCfy/2pWlwoYNg/POg9tvh5NOKrsaSZKkDq/oUt51KaX3G+1Ppnj4Vq0dcwyMH59XLBw8OK9YKEmSpJooGqDvjIi7gKsq+wcAt9emJC2S//kfeOEFOPZYWHtt2HHHsiuSJEnqkBbYixwRa0fENimlnwAXABsDmwCPARe2Qn0qqmtXuOYaGDQIvvY1ePnlsiuSJEnqkBY2DONsYApASumGlNJ/pJROJPc+n13r4lSlZZbJM3NEwFe+ApMnl12RJElSh7OwAD0wpfRU04MppVHAwJpUpMWz1lpw003wxhuwzz4wbVrZFUmSJHUoCwvQSy7g3FItWYha0LbbwmWXwaOPwre+BbNnl12RJElSh7GwAP1ERBzV9GBEHAmMrk1JahH775+X/L72WvjpT8uuRpIkqcNY2CwcPwRujIhDmBOY64FuwH61LEwt4Ec/yst8n3kmDBwI3/te2RVJkiS1ewsM0Cml94CtI2InYMPK4dtSSvfVvDItvgg45xx46y04/ngYMCAv+y1JkqRFVmge6JTS/cD9Na5FtdC1K1x1VZ4X+sAD4cEHob6+7KokSZLaLVcT7Ax69oRbb4V+/fL0dq+9VnZFkiRJ7ZYBurNYcUW44w6YMQP22AM++KDsiiRJktolA3Rnst56cPPNeY7o4cNh6tSyK5IkSWp3DNCdzXbb5SW/n3giL/n9xRdlVyRJktSuGKA7o733hj//Ge66Cw4/3IVWJEmSqlBoFo5FFRGvA1OAWcDMlFJ9k/M7AjcDDU+13ZBS+mUta1LFEUfA++/DySdD377w+9/nae8kSZK0QDUN0BU7pZQW9MTawyml4a1Qh5r6z//MIfr3v88PGZ58ctkVSZIktXmtEaDVVkXAWWfBpElwyim5J/o73ym7KkmSpDat1mOgE3B3RIyOiKPnc83QiHgyIu6IiA1qXI+aqquDv/wlT2333e/CjTeWXZEkSVKbVusAvU1KaQiwB3BcRGzf5PwYYPWU0ibAucBNzd0kIo6OiFERMWrSpEm1rbgzWmIJuO462HJLOOgguM+V2iVJkuanpgE6pfRO5fV94EZgyybnP0kpfVp5fzuwRESs0Mx9Lkwp1aeU6vv27VvLkjuvhtUKBw3Ks3Q89ljZFUmSJLVJNQvQEdEzIno3vAd2BZ5pck3/iDz1Q0RsWalncq1q0kIsvzz84x+w0kp5SMfYsWVXJEmS1ObUsgd6ReCRiHgSGAncllK6MyKOiYhjKtd8HXimcs0fgANTSqmGNWlh+veHe++FZZaBXXeF8ePLrkiSJKlNifaWV+vr69OoUaPKLqPje+kl2H77PFPHww/DWmuVXZEkSVKriojRTdcxAVci1PwMGpSHc3zxBQwbBm+9VXZFkiRJbYIBWvO34YZ5ue+PPoJddoH33iu7IkmSpNIZoLVgm28Ot98OEybAl78MH35YdkWSJEmlMkBr4bbZBm6+GV54IT9Y+NFHZVckSZJUGgO0itlll7xK4dNP5xD973+XXZEkSVIpDNAqbs894frr4cknDdGSJKnTMkCrOsOHww03wLhxsNtu8PHHZVckSZLUqgzQqt7w4bkneuzY3BNtiJYkSZ2IAVqLZq+94LrrcojebTf45JOyK5IkSWoVBmgtun32gWuvhdGjDdGSJKnTMEBr8ey7bw7Ro0Y5JlqSJHUKBmgtvv32m9MTPWwYTJ5cdkWSJEk1Y4BWy9hvvzxP9DPPwE47uey3JEnqsAzQajlf+Qrcdhu88grssAO8/XbZFUmSJLU4A7Ra1rBhcNdd8M47sP328PrrZVckSZLUogzQannbbgv33gsffZRD9EsvlV2RJElSizFAqza22ALuvx8+/zyH6OeeK7siSZKkFmGAVu1ssgk8+CBE5DHRY8aUXZEkSdJiM0CrttZfHx56CHr2hB13hAceKLsiSZKkxWKAVu2tvTY8+igMGAC77w433VR2RZIkSYvMAK3Wscoq8PDDsOmm8LWvwSWXlF2RJEnSIjFAq/X06QP33AO77AJHHAFnnll2RZIkSVUzQKt19eoFt9wCBxwAJ50E//mfkFLZVUmSJBXWtewC1Al16wZXXAHLLQf//d8weTL86U/Q1X8cJUlS22diUTm6dIE//hH69oXTT4dJk+Cqq6BHj7IrkyRJWiCHcKg8EfDLX8K55+ZhHTvvnIO0JElSG2aAVvm+/324/np48knYemt45ZWyK5IkSZovA7Tahv32g3vvhQ8/hKFDYeTIsiuSJElqlgFabcfWW8M//5ln6thxxzysQ5IkqY0xQKttWXddeOyxvAT4vvvCBReUXZEkSdJcDNBqe1ZcER54IC/7fcwxcMopMHt22VVJkiQBBmi1Vb16wc03w1FHwRln5IVXPvus7KokSZIM0GrDunbNQzjOOivP0rHDDjBxYtlVSZKkTs4ArbYtAn70I7jpJhg/HrbcEsaNK7sqSZLUiRmg1T7svTc88kh+v+228Pe/l1uPJEnqtAzQaj823TTPD90wQ8dZZ0FKZVclSZI6GQO02peVVsozdHzta/CTn+SHDL/4ouyqJElSJ2KAVvvTowdccw38/Odw8cWw664waVLZVUmSpE7CAK32qa4OTj8dLr8cHn8c6uthzJiyq5IkSZ2AAVrt2yGH5IcLU4JttoErrii7IkmS1MEZoNX+bb45jBqVp7g79FD48Y9h5syyq5IkSR2UAVodQ79+cM89cNxx8D//A3vsAZMnl12VJEnqgAzQ6jiWWALOOw8uuggeegi22AKeeqrsqiRJUgdjgFbHc+SR8OCDMG0aDB0K115bdkWSJKkDMUCrY9pqKxg9GjbZBA44AH74Q+eLliRJLcIArY6rYdGVE06Ac86BHXeECRPKrkqSJLVzBmh1bN26wdln54VXnn4aNtssP2woSZK0iAzQ6hz23x+eeAJWXDGvXHj66TB7dtlVSZKkdsgArc5jvfXyqoUHHwynngrDhzvVnSRJqpoBWp1Lz57wt7/B+efDvffCkCEwcmTZVUmSpHbEAK3OJwKOOQYefTS/32YbOPNMh3RIkqRCDNDqvOrrYexY2GcfOOkk2HNPeO+9squSJEltnAFandtyy8F11+UhHQ8+mOeNdpYOSZK0AAZoqWFIx8iR0KdPnqXjlFNgxoyyK5MkSW2QAVpqsNFGMGoUfOc7cMYZsMMO8PrrZVclSZLaGAO01FiPHnDhhXD11fDss7DppnDttWVXJUmS2hADtNScAw7IDxiut15+/81vwscfl12VJElqAwzQ0vysuSY88gicdhpcdRVsvHF+0FCSJHVqBmhpQbp2hV/8Is8Z3a0b7LRTnvJu+vSyK5MkSSUxQEtFfOlLeUjHUUflRVe+9CV45pmyq5IkSSUwQEtF9eoFF1wAf/87vPMObL45/O53rmAoSVInY4CWqrXXXrn3ebfd4Ec/gp13hldfLbsqSZLUSgzQ0qLo1w9uvhkuuigP7dhoIzjvPHujJUnqBAzQ0qKKgCOPzL3R220Hxx9vb7QkSZ2AAVpaXAMGwB132BstSVInYYCWWkLj3ujtt7c3WpKkDswALbWkAQPg9tvh4ovn9Eafey7MmlV2ZZIkqYUYoKWWFgFHHAHPPpt7o3/wA9h2W3j66bIrkyRJLcAALdXKqqvm3ujLL4eXX4YhQ+DnP4dp08quTJIkLQYDtFRLEXDIIfD883DoofDrX8PGG8P995ddmSRJWkQGaKk1LL88XHIJ3HNPnp1j553zMI/Jk8uuTJIkVckALbWmYcPyWOiTT4a//Q0GD4Yrr4SUyq5MkiQVZICWWttSS8FvfgOjR8Oaa+YhHrvuCi+8UHZlkiSpAAO0VJaNN4ZHH82LrjzxRJ7y7pRTYOrUsiuTJEkLYICWytSlCxx3HLz4Yu6JPuOMPKzjhhsc1iFJUhtlgJbagn798kOGjzwCyy0HX/sa7LEHvPRS2ZVJkqQmDNBSW7LNNnls9DnnwGOPwYYb5rmjP/us7MokSVKFAVpqa7p2zasXvvAC7L9/njt68GC49lqHdUiS1AYYoKW2qn//PNXdgw/mYR0HHJCXBh89uuzKJEnq1AzQUlvXEJovvDD3Sm+xRV6EZeLEsiuTJKlTqmmAjojXI+LpiBgXEaOaOR8R8YeIeDkinoqIIbWsR2q3unSBo47KDxX++Mdw+eWwzjp51o5p08quTpKkTqU1eqB3SiltmlKqb+bcHsCgynY0cH4r1CO1X8ssA//93/Dcc7DLLnne6MGDYcQIx0dLktRKyh7CsQ9wWcr+BSwbESuVXJPU9q29Ntx4I9x7L/TuDd/4Bmy3XZ65Q5Ik1VStA3QC7o6I0RFxdDPnVwHearQ/oXJMUhE77wxjx8IFF8Arr8DWW8NXv+qy4JIk1VCtA/Q2KcWw420AABcoSURBVKUh5KEax0XE9k3ORzOfmee/Q0fE0RExKiJGTZo0qRZ1Su1Xly5w9NHw8stw+unwj3/ABhvAMcf4oKEkSTVQ0wCdUnqn8vo+cCOwZZNLJgADGu2vCrzTzH0uTCnVp5Tq+/btW6typfatZ8+86Morr8Cxx8LFF+ehHqeeClOmlF2dJEkdRs0CdET0jIjeDe+BXYFnmlz2d+CwymwcWwEfp5TsMpMWR79+cO65MH48DB+ee6XXWgv+939hxoyyq5Mkqd2rZQ/0isAjEfEkMBK4LaV0Z0QcExHHVK65HXgVeBn4M/C9GtYjdS5rrw3XXAMjR+YhHd//Pqy3Hlx2GcyaVXZ1kiS1W5Ha2dRX9fX1adSoeaaUlrQgKcEdd+QhHmPH5iB92ml59o66sifjkSSpbYqI0c1Nxey/OaXOIAL23DOvaHj99fnBwwMPhM02g5tvdg5pSZKqYICWOpOIPM3dk0/CFVfAZ5/BvvvCllvCnXcapCVJKsAALXVGXbrAwQfnBw3/8heYNAn22CMvxnL//QZpSZIWwAAtdWZdu8Lhh8OLL8If/wivvZYXZ9luO7jrLoO0JEnNMEBLgm7d8tzRL7+cp8B74w3YfXf40pfgllsM0pIkNWKAljTHUkvl6e5efhkuvBA++AD23js/bDhiBMyeXXaFkiSVzgAtaV7du8NRR8ELL8Cll8Lnn+cp7zbaCK680nmkJUmdmgFa0vwtsQR861vw3HNw1VV5Fo9DDsnzSF9wAUybVnaFkiS1OgO0pIVrmDf6qafyPNLLLgvHHAOrrw6/+Q189FHZFUqS1GoM0JKKq6vL80iPHAn33QdDhsDPfgYDBsB//Ae8+WbZFUqSVHMGaEnVi4CddsrLgz/5JOy3H/zhD7DWWnDYYfD002VXKElSzRigJS2ejTeGv/0NXnklz+Bxww352J57uiiLJKlDMkBLahmrrw6//30exvGrX8GoUXlRlk03zasd+sChJKmDMEBLall9+uRx0W++CRdfnI8deWQeJ/3zn8M775RbnyRJi8kALak2llwSjjgCxo3LDxxus02esWP11fNUeCNHll2hJEmLxAAtqbYaHji86SZ46aU8TvqWW/Iy4VtvDddcAzNmlF2lJEmFGaAltZ611srjpCdMgHPOgfffz/NLr746nHpqPi5JUhtngJbU+pZeGn7wA3jxxdwbvdlm+cHDgQPzlHh33w2zZ5ddpSRJzTJASypPXR0MHw633Zanwfvxj+GRR2C33WDddeGss2Dy5LKrlCRpLgZoSW3DGmvAb3+bh3FccQX07w8/+Qmssgp861vwr385p7QkqU0wQEtqW7p3h4MPhocfhqeeyjN53HADDB2aF2g5+2z44IOyq5QkdWIGaElt10YbwR//mOeOvuAC6NEDTjwx90rvvz/cdRfMmlV2lZKkTsYALant690bjj4aHn8890p/73t5bundd89DP37xC3j99bKrlCR1EgZoSe3LRhvlqfDefhuuvRbWXx9OPx3WXBO+/GW4+mqXDZck1ZQBWlL71L07fOMbcOeduff5tNPyQi0HHZQfQDz66DyO2gcPJUktzAAtqf1bbbW8EMurr8I//gF77w1XXgnbb58Xbzn11ByuJUlqAQZoSR1HXR3ssgtcdhm8+y787W+w9trw61/DOuvAVlvlhxKdW1qStBgM0JI6pl694NBD86qGb70FZ54Jn30Gxx0HK60E++4LI0bA55+XXakkqZ0xQEvq+FZeOa9y+NRTMG5cXkb88cfzGOp+/XLQvuUWmD697EolSe2AAVpS57LJJnmJ8LfegnvuyQ8d3nFHHjfdv39euOXuu2HmzLIrlSS1UQZoSZ1T164wbBhceCFMnAi33ZZD9IgRsNtueZjHscfCAw+4WIskaS4GaEnq1g323BP++ld4/3248cYcri+7DHbaCQYMyMM+HnzQMC1JMkBL0lyWXDI/YHj11TlMX301fOlL8Oc/w4475p7po47Kwz4cMy1JnZIBWpLmp2dPOOCA3CM9aRJcd12eJu+aa3KPdd++cPDBcP31MHVq2dVKklpJpHa2Sld9fX0aNWpU2WVI6symT4d774UbboCbb4YPPsg917vtBl/9Kuy1Fyy3XNlVSpIWU0SMTinVz3PcAC1Ji2HmTHjkkRymb7gB3n4bunSBbbfNQXr4cFh33bKrlCQtAgO0JNXa7NkwalTulb7lFnj66Xx80KAcpvfaC7bZBpZYotw6JUmFGKAlqbW98QbcemsO0/ffD198AcsuC7vvnsP07rtDnz5lVylJmg8DtCSV6dNP4R//yGH6ttvyDB9duuQe6T33zGF6440houxKJUkVBmhJaitmz4Ynnshh+tZb4ckn8/H+/fODiLvtBl/+MqywQrl1SlInZ4CWpLbqnXfy8uF33ZVfP/ww90TX1+ee6d13hy23zKsnSpJajQFaktqDWbPyg4h33QV33gmPP557rJddNs9BvdtueZXENdYou1JJ6vAM0JLUHn30EdxzTw7Td92Vp8mDHKCHDYOdd87biiuWW6ckdUAGaElq71KC8ePzIi733gsPPAAff5zPbbjhnEC9ww6wzDKllipJHYEBWpI6mlmzYMyYOYH6kUdg2rQ8u0d9/ZxAPXQo9OhRdrWS1O4YoCWpo5s+HR57LIfp++7L46dnzcoLt2yxBWy/fd623toeakkqwAAtSZ3NlCnw8MN5e+ihPHXejBlQVwebbgrbbZcD9XbbQd++ZVcrSW2OAVqSOrvPPsu90g89lLfHHoPPP8/nBg+e00O93XYwYEC5tUpSG2CAliTN7YsvYPToOYH6kUfgk0/yuVVXzUM9hg7Nr5tuCt26lVuvJLUyA7QkacFmzYKnnspDPh57DP75T3jzzXxuySXzg4kNgXroUKfOk9ThGaAlSdV7++0cphsC9ZgxuecaYM01c5Bu2DbaKD+wKEkdhAFakrT4pk2DsWNzmG4I1RMn5nPdu+ehHltsMWdbd9380KIktUMGaElSy0sJ3ngDRo7M2xNP5HHVU6fm80svDZtvPneoXm01iCi3bkkqwAAtSWods2bB88/PCdRPPAFPPpmn0IM8ZV5DmB4yBDbbLD+0aKiW1MYYoCVJ5Zk+PT+g2DhUjx+fe7ABVlghD//YbLO8DRkCgwY5/ENSqeYXoLuWUYwkqZPp3n1Or3ODTz/NoXrMmDyueuxYOPvsOT3VPXvCJpvMCdWbbQYbbJDvJUklsgdaktR2fPEFPPfcnEA9diyMG5fDNuRZPtZfP8/4sfHG+XWjjWDllR0CIqnFOYRDktQ+zZ4Nr7wyd6h++ml455051yy33Jww3bBtuGF+iFGSFpFDOCRJ7VNdXR4PPWgQ7L//nOMffpiDdOPtsstgypQ516y++ryhep11HAYiabEYoCVJ7VOfPrDDDnlr0DCtXtNgfeedMHNmvqauDtZaCwYPnrOtvz6stx707l3Ob5HUrhigJUkdRwQMHJi3vfaac3z6dHjhBXj22Tz7x/jxeaz1HXfMeWgR8nR6DYG6ccDu27e1f4mkNswALUnq+Lp3zw8dbrzx3MdnzIBXX507VI8fDxddNGcxGMjT7A0enIeRrLNO3gYNyj3ZSy3Vur9FUul8iFCSpKZmz4YJE+YO1ePHw0svwXvvzbkuAgYMmBOoG4frgQPzrCGS2i0fIpQkqai6urzk+GqrwW67zX3uk09ykH7pJXjxxby99BJceSV8/PGc67p2hTXWmBOoG3qs11wzP9zYrVvr/iZJLcYALUlSNZZeGjbfPG+NpQQffDBvsH7xRbjvPvj88znX1tXl8dYNgbpha9jv08d5raU2zAAtSVJLiMgPG/btC1tvPfe52bNh4sQ83rrpduutcw8LgRzSGwfqhm3gwNwrvuSSrfazJM3LAC1JUq3V1cEqq+Rtu+3mPT91Krz22rzh+tlnc8CePn3u6/v1y8NAmttWWw2WXdYebKmGDNCSJJWtZ8+8yMuGG857rnHv9RtvzL09/XQO2NOmzf2Z3r3nH65XXx1WXBG6dGmd3yZ1QAZoSZLasoX1XqcEkybNG64btkcfhX//e+7PdOkCK6+cx2Gvumq+d8P7hm2llXzQUZoPA7QkSe1ZRB7S0a8fbLFF89d88kkO02++mV/ffjtP0zdhAjz1FNx2G3z22byfW3HFuUN146C9yio5hPfqVdvfJ7VBBmhJkjq6pZeGjTbKW3NSylPwTZgwd7hu2F59FR56CD76aN7P9uoF/fvnHuumW+Pjyy/vuGx1GAZoSZI6u4j84OGyyzY/DrvB1Kk5YL/9Nrz1Frz7bh6f3bCNHZuXR58yZd7PLrHEnEDdXODu339OT7qrO6qNM0BLkqRievacs9rignz66dzhumnQfu01eOyxPHa7Ob16zQnT/frloSSN9xtvyy/vA5FqdQZoSZLUsnr1grXXztuCzJiR58BuCNmTJsH77+ftvffy6+uvw8iR+dysWfPeIwJWWKH5cN23bw7Yyy+fr2l43717TX62Og8DtCRJKscSS8x5KHFhZs/OY7AbAnbToN2wjRmTXxsvq95Ur15zB+qG9ws61qNHy/1utXsGaEmS1PbV1c0Jt4MHL/z66dNh8uS8vHpzr43fv/xyfl1Q6F5qqTnf36cPLLdcsW3ZZaGrcaujsUUlSVLH0717nmZv5ZWLf2bGDPjww/kH7YbXDz+E55/PPeIffTTvQjZN9e6dg3TR0L3MMnlbeuk87tzZS9ocA7QkSRLkISUrrpi3akybNidMF9leemnO+88/X/C9u3TJQbohUDcO1829b+7c0kvbC97C/NOUJElaHEsuOWc6vmpNnz5vwP7kkzycpOG16fu334bnnpuzP3Pmwr+nZ895g3WvXrl3vOlrc8cav/bo0el7xQ3QkiRJZenePc+B3b//on0+pdwD3jhkzy94N30/cWKecnDKlPw6fXqx76yry0F6QSG76WvPnnlr/L7p1o56yWteaUR0AUYBb6eUhjc5tyNwM/Ba5dANKaVf1romSZKkDiEiP+C41FKLHsIbfPFFDtKNQ/WCXpsee/vtufc//bS67+/Wbf7h+tJLqx9aU0OtEfVPAMYDS8/n/MNNg7UkSZJaWbdueYaRPn1a5n6zZ8Nnn+VAPXVq9dunn+bXyZNzr3cbUtMAHRGrAl8Bfg38Ry2/S5IkSW1I46EeHUyt4/zZwEnA7AVcMzQinoyIOyJigxrXI0mSJC2WmgXoiBgOvJ9SGr2Ay8YAq6eUNgHOBW6az72OjohRETFq0qRJNahWkiRJKqaWPdDbAHtHxOvA1cDOEXF54wtSSp+klD6tvL8dWCIiVmh6o5TShSml+pRSfd++fWtYsiRJkrRgNQvQKaWTU0qrppQGAgcC96WUDm18TUT0j8gTCUbElpV6JteqJkmSJGlxtfqEexFxDEBK6U/A14FjI2Im8DlwYEoptXZNkiRJUlHR3vJqfX19GjVqVNllSJIkqYOLiNEppfqmx9vWpHqSJElSG2eAliRJkqpggJYkSZKqYICWJEmSqmCAliRJkqpggJYkSZKqYICWJEmSqmCAliRJkqpggJYkSZKqYICWJEmSqmCAliRJkqpggJYkSZKqECmlsmuoSkRMAt4o6etXAD4o6bvVemznjs827hxs587Bdu4cymrn1VNKfZsebHcBukwRMSqlVF92Haot27njs407B9u5c7CdO4e21s4O4ZAkSZKqYICWJEmSqmCArs6FZRegVmE7d3y2cedgO3cOtnPn0Kba2THQkiRJUhXsgZYkSZKqYIAuICJ2j4gXIuLliPhp2fVo0UXEgIi4PyLGR8SzEXFC5XifiPhHRLxUeV2u0WdOrrT9CxGxW3nVqxoR0SUixkbErZV927iDiYhlI2JERDxf+d/0UNu544mIEyt/Xz8TEVdFxJK2c/sXEX+JiPcj4plGx6pu14jYPCKerpz7Q0REa9RvgF6IiOgC/C+wB7A+cFBErF9uVVoMM4EfpZQGA1sBx1Xa86fAvSmlQcC9lX0q5w4ENgB2B/5Y+WdCbd8JwPhG+7Zxx3MOcGdKaT1gE3J7284dSESsAvwAqE8pbQh0Ibej7dz+XUpuo8YWpV3PB44GBlW2pvesCQP0wm0JvJxSejWl9AVwNbBPyTVpEaWUJqaUxlTeTyH/C3cVcpv+tXLZX4F9K+/3Aa5OKU1PKb0GvEz+Z0JtWESsCnwFuKjRYdu4A4mIpYHtgYsBUkpfpJT+je3cEXUFloqIrkAP4B1s53YvpfQQ8GGTw1W1a0SsBCydUnos5Yf6Lmv0mZoyQC/cKsBbjfYnVI6pnYuIgcBmwOPAiimliZBDNtCvcpnt3z6dDZwEzG50zDbuWNYEJgGXVIbqXBQRPbGdO5SU0tvAWcCbwETg45TS3djOHVW17bpK5X3T4zVngF645sbSOHVJOxcRvYDrgR+mlD5Z0KXNHLP927CIGA68n1IaXfQjzRyzjdu+rsAQ4PyU0mbAVCr/uXc+bOd2qDIGdh9gDWBloGdEHLqgjzRzzHZu/+bXrqW1twF64SYAAxrtr0r+z0dqpyJiCXJ4viKldEPl8HuV/xRE5fX9ynHbv/3ZBtg7Il4nD7naOSIuxzbuaCYAE1JKj1f2R5ADte3csewCvJZSmpRSmgHcAGyN7dxRVduuEyrvmx6vOQP0wj0BDIqINSKiG3kQ+99LrkmLqPJ07sXA+JTS7xqd+jvwrcr7bwE3Nzp+YER0j4g1yA8ojGytelW9lNLJKaVVU0oDyf97vS+ldCi2cYeSUnoXeCsi1q0cGgY8h+3c0bwJbBURPSp/fw8jP7tiO3dMVbVrZZjHlIjYqvLPx2GNPlNTXVvjS9qzlNLMiPg+cBf56d+/pJSeLbksLbptgG8CT0fEuMqxU4DfAtdGxJHkv7C/AZBSejYiriX/i3kmcFxKaVbrl60WYBt3PMcDV1Q6N14FDid3DNnOHURK6fGIGAGMIbfbWPKKdL2wndu1iLgK2BFYISImAL9g0f6ePpY8o8dSwB2Vrfb1uxKhJEmSVJxDOCRJkqQqGKAlSZKkKhigJUmSpCoYoCVJkqQqGKAlSZKkKhigJamNiIhPK68DI+LgFr73KU32/9mS95ekzsQALUltz0CgqgAdEV0WcslcATqltHWVNUmSKgzQktT2/BbYLiLGRcSJEdElIs6MiCci4qmI+C5AROwYEfdHxJXA05VjN0XE6Ih4NiKOrhz7LbBU5X5XVI419HZH5d7PRMTTEXFAo3s/EBEjIuL5iLiistIXEfHbiHiuUstZrf6nI0klcyVCSWp7fgr8OKU0HKAShD9OKW0REd2BRyPi7sq1WwIbppReq+wfkVL6MCKWAp6IiOtTSj+NiO+nlDZt5ru+CmwKbAKsUPnMQ5VzmwEbAO8AjwLbRMRzwH7AeimlFBHLtvivl6Q2zh5oSWr7dgUOqyw//ziwPDCocm5ko/AM8IOIeBL4FzCg0XXzsy1wVUppVkrpPeBBYItG956QUpoNjCMPLfkEmAZcFBFfBT5b7F8nSe2MAVqS2r4Ajk8pbVrZ1kgpNfRAT/2/iyJ2BHYBhqaUNgHGAksWuPf8TG/0fhbQNaU0k9zrfT2wL3BnVb9EkjoAA7QktT1TgN6N9u8Cjo2IJQAiYp2I6NnM55YBPkopfRYR6wFbNTo3o+HzTTwEHFAZZ90X2B4YOb/CIqIXsExK6Xbgh+ThH5LUqTgGWpLanqeAmZWhGJcC55CHT4ypPMg3idz729SdwDER8RTwAnkYR4MLgaciYkxK6ZBGx28EhgJPAgk4KaX0biWAN6c3cHNELEnuvT5x0X6iJLVfkVIquwZJkiSp3XAIhyRJklQFA7QkSZJUBQO0JEmSVAUDtCRJklQFA7QkSZJUBQO0JEmSVAUDtCRJklQFA7QkSZJUhf8PHuGsfC+2SoIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画出cost的走势\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Error vs Training Epoch')\n",
    "plt.plot(np.arange(iters), cost, 'r')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}