Untitled.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distance</th>\n",
       "      <th>accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>290.3</td>\n",
       "      <td>59.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>302.1</td>\n",
       "      <td>54.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>287.1</td>\n",
       "      <td>62.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>282.7</td>\n",
       "      <td>65.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>299.1</td>\n",
       "      <td>52.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   distance  accuracy\n",
       "0     290.3      59.5\n",
       "1     302.1      54.7\n",
       "2     287.1      62.4\n",
       "3     282.7      65.4\n",
       "4     299.1      52.8"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "pga=pd.read_csv('./data/pga.csv')\n",
    "pga.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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iA8ItMU97L9tomtnLgPXAM4BT3D2olldAqL9Bu7sLSd/QTYWU1FpqaYwZGItS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\nEQD+P2o4isRg2a9uAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe69a2c3048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data preprocessing\n",
    "# Normalize the data\n",
    "pga['distance']=(pga['distance']-pga['distance'].mean())/pga['distance'].std()\n",
    "pga['accuracy']=(pga['accuracy']-pga['accuracy'].mean())/pga['accuracy'].std()\n",
    "pga.head()\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(pga['distance'],pga['accuracy'])\n",
    "plt.xlabel('normalized distance')\n",
    "plt.ylabel('normalized accuracy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4.49711161658e-17\n",
      "[-0.60759882]\n"
     ]
    }
   ],
   "source": [
    "# Use linear model to model this data.\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import numpy as np\n",
    "\n",
    "lr=LinearRegression()\n",
    "lr.fit(pga.distance[:,np.newaxis],pga['accuracy'])  # Another way is using pga[['distance']]\n",
    "theta0=lr.intercept_\n",
    "theta1=lr.coef_\n",
    "print(theta0)\n",
    "print(theta1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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w3TuZRmFBEQBCgoN44QeDCA4SHnxnHaUVlW6XZEydXlm2k5VZB/nd+L4kx9no\nazdZUASI+FbNee6WAaTnHeO/P97mdjnG1Co1+xB/WbyDGwd0ZGKKPdbUbRYUAeTqPnHcNTyJ17/K\nZlG6TeJrvNPB46U8+PZ64ls1548397NbYb2ABUWAeezaXgzoFM0j722yKT6M16msUn46ZwOHTpYx\n/baLiQpv5nZJBguKgBMaEsRLt15MkAhT/7mOknK7XmG8x4v/zuTLzCJ+N74v/eKj3S7HOCwoAlDn\nNhE8//2BbN1/jF/Pt/EVxjt8mVnI35Zm8p2L45k02K5LeBMLigA1plcsP7miO++m5TJ7zV63yzEB\nLufQSX7yznqSY1vw+wl2XcLbWFAEsIeu6sHI5HY8uSCDDTlH3C7HBKiS8kqm/jONiirl1dtTiAgN\ncbskcwYLigAWHCS8MGkQsVFhTH0zzR6hapqcqvLLeZvJ2HeM578/kKR2NnW4N7KgCHCtI0OZcXsK\nR06VMe2tdZRV2PMrTNN5Y9UePliXx8NX9eDK3nFul2POwYLC0KdjS/70vQGszT7MUx9luF2OCRAr\ns4p46qMtXNU7lh9f0d3tckwtrDPQADB+QEcy8o7y6vJd9Gzfktsv7eJ2ScaPZRed4IG31tEtJpK/\nfn8gQfZIU69mZxTmG4+O68UVvWL57YIMVmYVuV2O8VPHSsq5541UROC1Hw22QXU+wILCfCM4SPjb\npIF0i4nkgbfWsavwuNslGT9TUVnFT95ZT3bRCabfdjEJbSPcLsl4wILCfEtUeDP+PnkwwUHCPbNS\nOXKyzO2SjJ9QVZ76aAtfbC/kdzf1ZVi3dm6XZDzkUVCISLaIbBaRDSKS6qxrIyKLRSTTeW1dY/vH\nRSRLRLaLyNga6/8gIjkiUutP1XPtb5pG5zYRvHr7JeQePsWUN9NsWnLTIP6xMps3Vu1hyqiu3DbU\nroH5kvqcUYxR1YGqmuK8fwxYqqrJwFLnPSLSB5gE9AXGAdNF5PQTR/4FDKmtkTr2N01kcGIbnr2l\nP2t2H+KRdzdRVaVul2R82OIt+Ty9cAvj+rbnsXH2pDpfcyFdTzcBs5zlWcCEGutnq2qpqu4GsnDC\nQVW/VtW65rc+5/6mad00MJ5HxvZkwcZ9/HnxdrfLMT5q/d7D/OSd9fSPj7Y7nHyUp0GhwBIRSROR\nKc66uBpf+geA06Nl4oGcGvvmOus8daH7mwb0wOhuTBrcmZc/38mbX+9xuxzjY3YVHueu19cSExXG\na5MH0zw7HdUyAAAPEklEQVTUOgd8kafjKEaoap6IxAKLReRbj0hTVRWRJu2bcAJrCkBCQkJTNh1Q\nRITfT+hHYXEpT36YTtvIUK67qIPbZRkfUFBcwo9mriFIhDfuGkJMVJjbJZnz5NEZharmOa8FwDyq\nu4LyRaQDgPNa4GyeB9ScI7iTs85THu2vqjNUNUVVU2JiYurx8aa+QoKrn2ExqHMrfjp7A6t2HnS7\nJOPljpWUc8fMtRw6UcbMOwaTaHM4+bQ6g0JEIkUk6vQycA2QDiwAJjubTQY+dJYXAJNEJExEkoBk\nYE09arrQ/U0jaB4azMw7BpPQNoIpb6SSnnfU7ZKMlzpVVsndr68ls6CY6bddzIDOrdwuyVwgT84o\n4oAVIrKR6i/shaq6CHgGuFpEMoGrnPeoagYwF9gCLAKmqWolgIj8SURygQgRyRWR3zrrx4vIU3Xt\nb9zVKiKUN+4aQsvmzbj976vJzC92uyTjZcoqqpj6zzRS9xzmr98fyOiesW6XZBqAqPr+bY8pKSma\nmprqdhkBI7voBLe8ugoB3p16GV3aWreCqR51/dDsDSzcvJ9nvnMRk4bYtUNvJyJpNYY8nJONzDb1\nltgukn/ePZSyyipu/b/V7Dtyyu2SjMsqq5RH3tvEws37+eV1vSwk/IwFhTkvPdtH8cZdQzh2qpxJ\nM75m/1ELi0BVVaX81/ubmLc+j19c04Mpo7q5XZJpYBYU5rz179SKN+4ewuETZRYWAaqqSnli/mbe\nS8vloSuTefCKZLdLMo3AgsJckEEJrZl19xAOHi/jBxYWAaWySnnsg028syaHaWO68dOrLCT8lQWF\nuWAXJ7Rm1l1DKDpexsRXV5Fz6KTbJZlGVlFZxS/e3cjc1Fx+cmUyv7imJyI2NYe/sqAwDeKSLq15\n656hHDtVwS2vrLJnWfix8soqHpqzgXnr83hkbE9+dnUPCwk/Z0FhGsyAzq2YPeVSyiurmPjq12zd\nf8ztkkwDO1VWyb1vpLJwU/XdTdPG2LOuA4EFhWlQvTu0ZM59lxESJEx8dRWrd9l0H/7i6Mlybv/7\napbtKOSPN19kdzcFEAsK0+C6x7bg/QeGERMVxu0z1/BpxgG3SzIXKP9YCd+fsYpNuUd5+daLuXWo\njZMIJBYUplHEt2rOe1OH0adDS+7/Zxr/tCnKfdb2A8Xc/PJK9h46ycw7BtvswQHIgsI0mjaRobx9\n71BG9YjhV/PT+ePHW+1JeT7mq6wivvfKV1RUKXPvu4wRyfac60BkQWEaVURoCK/9KIUfXprAjOW7\nmPb2OkrKbY5HX/Buag6T/7GGDtHhzJs2nH7x0W6XZFxiQWEaXUhwEE/f1I9fXd+bRRkHmPjqKhuY\n58Uqq5Tff7SFR97bxNCktrw7dRjxrZq7XZZxkQWFaRIiwj0juzLj9hR2FhznxhdXkrbnkNtlmTMc\nKynn7llreW3Fbu4Ylsjrdw4munkzt8syLrOgME3q6j5xzJs2nMiwYH4wYzVvr96LP0x17w+2HTjG\n+BdXsCKziD/efBG/Hd+XkGD7ijAWFMYFPeKi+HDacIZ2bcMv523m5+9u5FSZXbdw0/z1eUx4eSUn\nyyp5Z8qldvur+RYLCuOKVhGhvH7nEB66Mpl5zpfUTpv2o8mVlFfyxLzN/HTOBgZ0asVHPxnB4MQ2\nbpdlvIwFhXFNcJDw8NU9mHXnEAqKS7jhhRXMWWtdUU1lR34x419awVur93Lf5V15656hxEaFu12W\n8UIWFMZ1o3rE8MlDoxjYuRX/9f5mHnhrHUdOlrldlt9SVd5clc2NL67g0Ily3rhrCI9f29uuR5hz\nCnG7AGMA2keH8897hjJj+S7+/Nl21u09zDPf6c+YXrFul+ZX9h05xX+9v4kvM4sY1SOGP98ygJio\nMLfLMl7Oo58QIpItIptFZIOIpDrr2ojIYhHJdF5b19j+cRHJEpHtIjK2xvpLnM/JEpEX5CxzE4tI\nooicctraICKvNMSBGu8XHCTcP7ob8x4YTnTzZtz5+lp+8e5Gjp4qd7s0n6eqvJuaw9jnl5O25zC/\nn9CPWXcOtpAwHqnPueYYVR2oqinO+8eApaqaDCx13iMifYBJQF9gHDBdRIKdff4XuBdIdv4Zd462\ndjptDVTVqfU6IuPzLuoUzb9+PIIHRnfjg3W5XP2XZXy8eb9duzhP2UUnuO211Tzy3iZ6tY/ik4dG\n8sNLu9gzJIzHLqRT8iZglrM8C5hQY/1sVS1V1d1AFjBERDoALVX1a63+f/wbNfYx5lvCQoJ5dFwv\n5j0wnHYtwnjgrXXc9fpae3pePZSUV/LSvzMZ+/xyNuce5Q8392POlMvo0jbS7dKMj/E0KBRYIiJp\nIjLFWRenqvud5QNAnLMcD+TU2DfXWRfvLJ+5/mySnG6nZSIy0sMajR8a0LkVCx4czq+u783q3Ye4\n6i/L+Mtn2zlRWuF2aV5LVfks4wDX/HU5z322gyt7x7Lk55dz29AuBAXZWYSpP08vZo9Q1TwRiQUW\ni8i2mn9UVRWRhuoX2A8kqOpBEbkEmC8ifVX1W49LcwJrCkBCgg0O8mchwUHcM7Ir1/fvwH9/vI0X\n/p3FnNQcHhnbi5sHxRNsX37fSM87yjOfbGNFVhE94lrw1j1DGd7dZnw1F8ajMwpVzXNeC4B5wBAg\n3+lOwnktcDbPAzrX2L2Tsy7PWT5z/ZltlarqQWc5DdgJ9DjLdjNUNUVVU2JiYjw5DOPjOkQ354Uf\nDOL9+y+jfctwfvHuRq7923I+zTgQ8NcvsotO8ON31nPDiyvI2HeU39zYh4U/GWkhYRpEnUEhIpEi\nEnV6GbgGSAcWAJOdzSYDHzrLC4BJIhImIklUX7Re43RTHRORS527nX5UY5+a7cWcvvgtIl2d/Xdd\nwDEaP3NJlzbMe2A4L906iIpK5b4305jw8koWb8kPuOdd7Cw8zs/mbuDKvyxjyZZ8fnxFd5Y9OoY7\nhyfRzMZFmAbiSddTHDDPuUMiBHhbVReJyFpgrojcDewBJgKoaoaIzAW2ABXANFU9PZHPA8DrQHPg\nE+cfRGQ8kKKqTwKjgKdEpByoAqaqqk0zar4lKEi4oX9HxvVtz/vrcnnp8yzufSOVnnFR3D+6G9f3\n7+DXX5Qbco7w2pe7WLh5P2EhQdwxLJH7RnUltqWNrDYNT/zhlD0lJUVTU1PdLsO4qKKyio827Wf6\nF1nsyD9ObFQYtw3twq1DE/xmrEBZRRWLt+Qzc+Vu0vYcJioshFsvTeDekV1p18I/jtE0LRFJqzHk\n4dzbWVAYf1JVpSzbUcjrX2WzbEchzYKFK3vFMXFwJ0Ylx/jkNBW7Co8zZ20O76/Lpeh4GQltIrhz\neCLfu6QTUeH2rAhz/jwNCpvCw/iVoCBhTK9YxvSKZWfhcd5evZf56/NYlHGAmKgwrr+oA9dd1IGU\nLq29+lbRfUdOsXDTfhZs3MfmvKOEBAlX9o5l0uAERvWIsTu9TJOyMwrj98oqqvh8ewHvp+XyxY5C\nyiqqiI0KY0zPWEb3jGF4cjtauvzLvKKyis15R/l8WwFLtxWQsa/6bvABnaK5oX9HbhrU0WZ2NQ3O\nup6MOYvjpRUs3ZrPovQDrMgsori0guAgoV/HlqQktmFwYhv6d4qmQ3R4o05xUVxSTnreMTbmHmH1\nroOszT7M8dIKggRSurRhTK9YrruovY2iNo3KgsKYOpRXVrF+7xGW7yhkTfYhNuQcoayiCoBWEc3o\n3b4l3WNb0KVtBF3aRtIhOpyYqDDaRIbWeUeVqlJcWkH+0RLyj5WSd+Qku4pOsKvwBFkFx9lddOKb\nbbvFRDK0a1su7dqWkd3b0ToytFGP25jT7BqFMXVoFhzEkKQ2DEmqfqJbaUUl6XnH2LLvKFv2H2PL\n/mLmb8ijuOQ/pwtpERZC89BgIkKDaRYcRJUqqtXdXMUl5RwvreDMIR2hwUF0aRtBz7govntxPP3i\no+kXH213LBmvZ0FhjCMsJJhLurTmki7fzJiPqnLkZDl7Dp3kwNESio6XUnS8lGOnKjhVXsHJskrK\nK6sIEkFEaBYstAxvRouwEKKbNyO2ZRjtW4bTIbo58a2b20Vo45MsKIyphYjQOjK0ujuoc93bG+OP\nfO+mcmOMMU3KgsIYY0ytLCiMMcbUyoLCGGNMrSwojDHG1MqCwhhjTK0sKIwxxtTKgsIYY0yt/GKu\nJxEppPope+erHVDUQOX4gkA7XrBjDhR2zPXTRVVj6trIL4LiQolIqicTY/mLQDtesGMOFHbMjcO6\nnowxxtTKgsIYY0ytLCiqzXC7gCYWaMcLdsyBwo65Edg1CmOMMbWyMwpjjDG1sqAARORpEdkkIhtE\n5DMR6eh2TY1NRJ4VkW3Occ8TkVZu19TYROQWEckQkSoR8es7Y0RknIhsF5EsEXnM7Xoam4jMFJEC\nEUl3u5amICKdReRzEdni/G/6ocZsz4Ki2rOq2l9VBwIfAU+6XVATWAz0U9X+wA7gcZfraQrpwHeA\n5W4X0phEJBh4GbgW6AP8QET6uFtVo3sdGOd2EU2oAvi5qvYBLgWmNeZ/YwsKQFWP1XgbCfj9hRtV\n/UxVTz8M+mugk5v1NAVV3aqq292uowkMAbJUdZeqlgGzgZtcrqlRqepy4JDbdTQVVd2vquuc5WJg\nKxDfWO3Zo1AdIvIH4EfAUWCMy+U0tbuAOW4XYRpMPJBT430uMNSlWkwjE5FEYBCwurHaCJigEJEl\nQPuz/OkJVf1QVZ8AnhCRx4EHgd80aYGNoK5jdrZ5gurT2LeasrbG4skxG+MvRKQF8D7w0zN6RhpU\nwASFql7l4aZvAR/jB0FR1zGLyB3ADcCV6if3Sdfjv7M/ywM613jfyVln/IiINKM6JN5S1Q8asy27\nRgGISHKNtzcB29yqpamIyDjgUWC8qp50ux7ToNYCySKSJCKhwCRggcs1mQYkIgL8Hdiqqn9p9Pb8\n5IfkBRGR94GeQBXVs9BOVVW//gUmIllAGHDQWfW1qk51saRGJyI3Ay8CMcARYIOqjnW3qsYhItcB\nzwPBwExV/YPLJTUqEXkHGE31TKr5wG9U9e+uFtWIRGQE8CWwmervLYBfqurHjdKeBYUxxpjaWNeT\nMcaYWllQGGOMqZUFhTHGmFpZUBhjjKmVBYUxxphaWVAYY4yplQWFMcaYWllQGGOMqdX/Az8mAjff\ntcb7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe687b080f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0      0.314379\n",
      "1      1.693777\n",
      "2     -0.059695\n",
      "3     -0.574047\n",
      "4      1.343083\n",
      "5      1.471671\n",
      "6      1.553499\n",
      "7     -0.948121\n",
      "8      0.022134\n",
      "9     -0.340251\n",
      "10     1.062527\n",
      "11    -0.503908\n",
      "12    -0.422079\n",
      "13     0.513106\n",
      "14    -0.585737\n",
      "15     0.033823\n",
      "16    -0.983191\n",
      "17     0.478036\n",
      "18     0.267620\n",
      "19     0.255930\n",
      "20     1.308013\n",
      "21    -0.796154\n",
      "22     0.852110\n",
      "23    -0.012936\n",
      "24    -0.574047\n",
      "25    -1.158538\n",
      "26    -2.000204\n",
      "27    -0.281802\n",
      "28     3.213453\n",
      "29    -0.667566\n",
      "         ...   \n",
      "167    1.822365\n",
      "168   -0.655876\n",
      "169   -0.667566\n",
      "170   -0.071385\n",
      "171    0.688453\n",
      "172   -0.468839\n",
      "173    1.085907\n",
      "174    0.384518\n",
      "175    1.798985\n",
      "176    0.606624\n",
      "177   -0.761084\n",
      "178    0.630004\n",
      "179   -0.422079\n",
      "180   -0.913052\n",
      "181    0.618314\n",
      "182   -0.422079\n",
      "183   -0.655876\n",
      "184   -0.819533\n",
      "185    0.010444\n",
      "186    0.010444\n",
      "187    1.249564\n",
      "188    1.401532\n",
      "189    0.431277\n",
      "190    0.887180\n",
      "191    0.045513\n",
      "192    1.191115\n",
      "193   -0.188283\n",
      "194   -0.270112\n",
      "195   -0.083075\n",
      "196   -1.462473\n",
      "Name: distance, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#calculating cost-function for each theta1\n",
    "#计算平均累积误差\n",
    "def cost(x,y,theta0,theta1):\n",
    "    J=0\n",
    "    for i in range(len(x)):\n",
    "        mse=(x[i]*theta1+theta0-y[i])**2\n",
    "        J+=mse\n",
    "    return J/(2*len(x))\n",
    "\n",
    "theta0=100\n",
    "theta1s = np.linspace(-3,2,100)\n",
    "costs=[]\n",
    "for theta1 in theta1s:\n",
    "    costs.append(cost(pga['distance'],pga['accuracy'],theta0,theta1))\n",
    "plt.plot(theta1s,costs)\n",
    "plt.show()\n",
    "print(pga.distance)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "5.579133854071898\n"
     ]
    }
   ],
   "source": [
    "#调整theta\n",
    "def partial_cost_theta0(x,y,theta0,theta1):\n",
    "    #我们的模型时线性拟合函数：y=theta1*x + theta0，而不是sigmoid函数，当非线性时我们可以用sigmoid\n",
    "    #直接多整个x series操作，省的一个一个计算，最终求sum 再平均\n",
    "    h=theta1*x+theta0  \n",
    "    diff=(h-y)\n",
    "    partial=diff.sum()/len(diff)\n",
    "    return partial\n",
    "partial0=partial_cost_theta0(pga.distance,pga.accuracy,1,1)\n",
    "def partial_cost_theta1(x,y,theta0,theta1):\n",
    "    h=theta1*x+theta0#我们的模型时线性拟合函数：y=theta1*x + theta0，而不是sigmoid函数，当非线性时我们可以用sigmoid\n",
    "    diff=(h-y)*x\n",
    "    partial=diff.sum()/len(diff)\n",
    "    return partial\n",
    "partial1=partial_cost_theta1(pga.distance,pga.accuracy,0,5)\n",
    "print(partial0)\n",
    "print(partial1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta1 = -0.6046983166379608\n",
      "-0.5976256382464712\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6874622e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gradient_descent(x,y,alpha=0.1,theta0=0,theta1=0):  #设置默认参数\n",
    "    #计算成本\n",
    "    #调整权值\n",
    "    #计算错误代价，判断是否收敛或者达到最大迭代次数\n",
    "    most_iterations=1000\n",
    "    convergence_thres=0.000001 \n",
    "    \n",
    "    \n",
    "    c=cost(x,y,theta0,theta1)\n",
    "    costs=[c]\n",
    "    cost_pre=c+convergence_thres+1.0\n",
    "    \n",
    "    counter=0\n",
    "    while( (np.abs(c-cost_pre)>convergence_thres) & (counter<most_iterations) ):\n",
    "        \n",
    "        update0=alpha*partial_cost_theta0(x,y,theta0,theta1)\n",
    "        update1=alpha*partial_cost_theta1(x,y,theta0,theta1)\n",
    "        \n",
    "        theta0-=update0\n",
    "        theta1-=update1\n",
    "\n",
    "        cost_pre=c\n",
    "        c=cost(x,y,theta0,theta1)\n",
    "        costs.append(c)\n",
    "        counter+=1\n",
    "    return  {'theta0': theta0, 'theta1': theta1, \"costs\": costs}\n",
    "\n",
    "print(\"Theta1 =\", gradient_descent(pga.distance, pga.accuracy)['theta1'])\n",
    "costs=gradient_descent(pga.distance,pga.accuracy,alpha=.01)['costs']\n",
    "print(gradient_descent(pga.distance, pga.accuracy,alpha=.01)['theta1'])\n",
    "plt.scatter(range(len(costs)),costs)\n",
    "plt.show()\n",
    "\n",
    "# result=gradient_descent(pga.distance, pga.accuracy,alpha=.01)\n",
    "# print(\"Theta0 =\", result['theta0'])\n",
    "# print(\"Theta1 =\",  result['theta1'])\n",
    "# costs=result['costs']\n",
    "# plt.scatter(range(len(costs)),costs)\n",
    "# plt.show()"
   ]
  },
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