第5.2节_回归.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 读入学习数据\n",
    "train = np.loadtxt('click.csv', delimiter=',', skiprows=1)\n",
    "train_x = train[:,0]\n",
    "train_y = train[:,1]\n",
    "\n",
    "# 绘图\n",
    "\n",
    "plt.plot(train_x, train_y, 'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 参数初始化\n",
    "theta0 = np.random.rand()\n",
    "theta1 = np.random.rand()\n",
    "\n",
    "# 预测函数\n",
    "def f(x):\n",
    "    return theta0 + theta1 * x\n",
    "\n",
    "# 目标函数\n",
    "def E(x, y):\n",
    "    return 0.5 * np.sum((y - f(x)) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 标准化\n",
    "mu = train_x.mean()\n",
    "sigma = train_x.std()\n",
    "def standardize(x):\n",
    "    return (x - mu) / sigma\n",
    "\n",
    "train_z = standardize(train_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "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(train_z, train_y, 'o')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第1次: theta0 = 9.026, theta1 = 1.899, 差值 = 76235.6995\n",
      "第2次: theta0 = 17.429, theta1 = 3.731, 差值 = 73216.7658\n",
      "第3次: theta0 = 25.663, theta1 = 5.526, 差值 = 70317.3819\n",
      "第4次: theta0 = 33.733, theta1 = 7.285, 差值 = 67532.8136\n",
      "第5次: theta0 = 41.641, theta1 = 9.009, 差值 = 64858.5141\n",
      "第6次: theta0 = 49.391, theta1 = 10.698, 差值 = 62290.1170\n",
      "第7次: theta0 = 56.987, theta1 = 12.354, 差值 = 59823.4283\n",
      "第8次: theta0 = 64.430, theta1 = 13.976, 差值 = 57454.4206\n",
      "第9次: theta0 = 71.724, theta1 = 15.566, 差值 = 55179.2255\n",
      "第10次: theta0 = 78.873, theta1 = 17.125, 差值 = 52994.1282\n",
      "第11次: theta0 = 85.878, theta1 = 18.652, 差值 = 50895.5607\n",
      "第12次: theta0 = 92.744, theta1 = 20.148, 差值 = 48880.0965\n",
      "第13次: theta0 = 99.472, theta1 = 21.615, 差值 = 46944.4447\n",
      "第14次: theta0 = 106.065, theta1 = 23.052, 差值 = 45085.4447\n",
      "第15次: theta0 = 112.527, theta1 = 24.461, 差值 = 43300.0611\n",
      "第16次: theta0 = 118.860, theta1 = 25.841, 差值 = 41585.3787\n",
      "第17次: theta0 = 125.065, theta1 = 27.194, 差值 = 39938.5977\n",
      "第18次: theta0 = 131.147, theta1 = 28.519, 差值 = 38357.0292\n",
      "第19次: theta0 = 137.107, theta1 = 29.819, 差值 = 36838.0908\n",
      "第20次: theta0 = 142.948, theta1 = 31.092, 差值 = 35379.3024\n",
      "第21次: theta0 = 148.672, theta1 = 32.340, 差值 = 33978.2821\n",
      "第22次: theta0 = 154.282, theta1 = 33.562, 差值 = 32632.7421\n",
      "第23次: theta0 = 159.779, theta1 = 34.761, 差值 = 31340.4855\n",
      "第24次: theta0 = 165.166, theta1 = 35.935, 差值 = 30099.4023\n",
      "第25次: theta0 = 170.446, theta1 = 37.086, 差值 = 28907.4660\n",
      "第26次: theta0 = 175.620, theta1 = 38.214, 差值 = 27762.7303\n",
      "第27次: theta0 = 180.691, theta1 = 39.319, 差值 = 26663.3262\n",
      "第28次: theta0 = 185.660, theta1 = 40.402, 差值 = 25607.4585\n",
      "第29次: theta0 = 190.530, theta1 = 41.464, 差值 = 24593.4031\n",
      "第30次: theta0 = 195.302, theta1 = 42.504, 差值 = 23619.5043\n",
      "第31次: theta0 = 199.979, theta1 = 43.524, 差值 = 22684.1720\n",
      "第32次: theta0 = 204.562, theta1 = 44.523, 差值 = 21785.8788\n",
      "第33次: theta0 = 209.054, theta1 = 45.502, 差值 = 20923.1580\n",
      "第34次: theta0 = 213.456, theta1 = 46.461, 差值 = 20094.6009\n",
      "第35次: theta0 = 217.770, theta1 = 47.402, 差值 = 19298.8547\n",
      "第36次: theta0 = 221.998, theta1 = 48.323, 差值 = 18534.6201\n",
      "第37次: theta0 = 226.141, theta1 = 49.226, 差值 = 17800.6491\n",
      "第38次: theta0 = 230.201, theta1 = 50.111, 差值 = 17095.7434\n",
      "第39次: theta0 = 234.180, theta1 = 50.979, 差值 = 16418.7520\n",
      "第40次: theta0 = 238.079, theta1 = 51.829, 差值 = 15768.5694\n",
      "第41次: theta0 = 241.901, theta1 = 52.662, 差值 = 15144.1340\n",
      "第42次: theta0 = 245.646, theta1 = 53.478, 差值 = 14544.4263\n",
      "第43次: theta0 = 249.316, theta1 = 54.278, 差值 = 13968.4671\n",
      "第44次: theta0 = 252.912, theta1 = 55.062, 差值 = 13415.3158\n",
      "第45次: theta0 = 256.437, theta1 = 55.830, 差值 = 12884.0693\n",
      "第46次: theta0 = 259.891, theta1 = 56.583, 差值 = 12373.8601\n",
      "第47次: theta0 = 263.277, theta1 = 57.321, 差值 = 11883.8552\n",
      "第48次: theta0 = 266.594, theta1 = 58.045, 差值 = 11413.2546\n",
      "第49次: theta0 = 269.845, theta1 = 58.753, 差值 = 10961.2897\n",
      "第50次: theta0 = 273.031, theta1 = 59.448, 差值 = 10527.2226\n",
      "第51次: theta0 = 276.154, theta1 = 60.128, 差值 = 10110.3446\n",
      "第52次: theta0 = 279.214, theta1 = 60.795, 差值 = 9709.9750\n",
      "第53次: theta0 = 282.212, theta1 = 61.449, 差值 = 9325.4600\n",
      "第54次: theta0 = 285.151, theta1 = 62.090, 差值 = 8956.1717\n",
      "第55次: theta0 = 288.031, theta1 = 62.717, 差值 = 8601.5073\n",
      "第56次: theta0 = 290.853, theta1 = 63.333, 差值 = 8260.8877\n",
      "第57次: theta0 = 293.619, theta1 = 63.936, 差值 = 7933.7565\n",
      "第58次: theta0 = 296.330, theta1 = 64.526, 差值 = 7619.5797\n",
      "第59次: theta0 = 298.986, theta1 = 65.105, 差值 = 7317.8444\n",
      "第60次: theta0 = 301.590, theta1 = 65.673, 差值 = 7028.0577\n",
      "第61次: theta0 = 304.141, theta1 = 66.229, 差值 = 6749.7467\n",
      "第62次: theta0 = 306.641, theta1 = 66.774, 差值 = 6482.4567\n",
      "第63次: theta0 = 309.091, theta1 = 67.308, 差值 = 6225.7514\n",
      "第64次: theta0 = 311.492, theta1 = 67.832, 差值 = 5979.2117\n",
      "第65次: theta0 = 313.846, theta1 = 68.344, 差值 = 5742.4349\n",
      "第66次: theta0 = 316.152, theta1 = 68.847, 差值 = 5515.0344\n",
      "第67次: theta0 = 318.412, theta1 = 69.340, 差值 = 5296.6391\n",
      "第68次: theta0 = 320.626, theta1 = 69.823, 差值 = 5086.8922\n",
      "第69次: theta0 = 322.797, theta1 = 70.296, 差值 = 4885.4512\n",
      "第70次: theta0 = 324.924, theta1 = 70.759, 差值 = 4691.9874\n",
      "第71次: theta0 = 327.008, theta1 = 71.214, 差值 = 4506.1847\n",
      "第72次: theta0 = 329.051, theta1 = 71.659, 差值 = 4327.7398\n",
      "第73次: theta0 = 331.053, theta1 = 72.095, 差值 = 4156.3613\n",
      "第74次: theta0 = 333.015, theta1 = 72.523, 差值 = 3991.7694\n",
      "第75次: theta0 = 334.938, theta1 = 72.942, 差值 = 3833.6953\n",
      "第76次: theta0 = 336.822, theta1 = 73.353, 差值 = 3681.8810\n",
      "第77次: theta0 = 338.669, theta1 = 73.755, 差值 = 3536.0785\n",
      "第78次: theta0 = 340.478, theta1 = 74.150, 差值 = 3396.0498\n",
      "第79次: theta0 = 342.252, theta1 = 74.537, 差值 = 3261.5662\n",
      "第80次: theta0 = 343.990, theta1 = 74.915, 差值 = 3132.4082\n",
      "第81次: theta0 = 345.693, theta1 = 75.287, 差值 = 3008.3648\n",
      "第82次: theta0 = 347.362, theta1 = 75.650, 差值 = 2889.2336\n",
      "第83次: theta0 = 348.998, theta1 = 76.007, 差值 = 2774.8199\n",
      "第84次: theta0 = 350.601, theta1 = 76.356, 差值 = 2664.9370\n",
      "第85次: theta0 = 352.172, theta1 = 76.699, 差值 = 2559.4055\n",
      "第86次: theta0 = 353.711, theta1 = 77.035, 差值 = 2458.0531\n",
      "第87次: theta0 = 355.220, theta1 = 77.363, 差值 = 2360.7142\n",
      "第88次: theta0 = 356.699, theta1 = 77.686, 差值 = 2267.2299\n",
      "第89次: theta0 = 358.148, theta1 = 78.002, 差值 = 2177.4476\n",
      "第90次: theta0 = 359.568, theta1 = 78.311, 差值 = 2091.2207\n",
      "第91次: theta0 = 360.959, theta1 = 78.614, 差值 = 2008.4083\n",
      "第92次: theta0 = 362.323, theta1 = 78.912, 差值 = 1928.8754\n",
      "第93次: theta0 = 363.660, theta1 = 79.203, 差值 = 1852.4919\n",
      "第94次: theta0 = 364.970, theta1 = 79.489, 差值 = 1779.1332\n",
      "第95次: theta0 = 366.253, theta1 = 79.768, 差值 = 1708.6795\n",
      "第96次: theta0 = 367.511, theta1 = 80.043, 差值 = 1641.0158\n",
      "第97次: theta0 = 368.744, theta1 = 80.311, 差值 = 1576.0316\n",
      "第98次: theta0 = 369.952, theta1 = 80.575, 差值 = 1513.6208\n",
      "第99次: theta0 = 371.136, theta1 = 80.833, 差值 = 1453.6814\n",
      "第100次: theta0 = 372.296, theta1 = 81.086, 差值 = 1396.1156\n",
      "第101次: theta0 = 373.433, theta1 = 81.334, 差值 = 1340.8294\n",
      "第102次: theta0 = 374.548, theta1 = 81.576, 差值 = 1287.7326\n",
      "第103次: theta0 = 375.640, theta1 = 81.814, 差值 = 1236.7384\n",
      "第104次: theta0 = 376.710, theta1 = 82.048, 差值 = 1187.7635\n",
      "第105次: theta0 = 377.759, theta1 = 82.276, 差值 = 1140.7281\n",
      "第106次: theta0 = 378.787, theta1 = 82.500, 差值 = 1095.5553\n",
      "第107次: theta0 = 379.794, theta1 = 82.720, 差值 = 1052.1713\n",
      "第108次: theta0 = 380.781, theta1 = 82.935, 差值 = 1010.5053\n",
      "第109次: theta0 = 381.748, theta1 = 83.146, 差值 = 970.4893\n",
      "第110次: theta0 = 382.696, theta1 = 83.353, 差值 = 932.0579\n",
      "第111次: theta0 = 383.625, theta1 = 83.555, 差值 = 895.1484\n",
      "第112次: theta0 = 384.536, theta1 = 83.754, 差值 = 859.7005\n",
      "第113次: theta0 = 385.428, theta1 = 83.948, 差值 = 825.6564\n",
      "第114次: theta0 = 386.303, theta1 = 84.139, 差值 = 792.9604\n",
      "第115次: theta0 = 387.160, theta1 = 84.326, 差值 = 761.5592\n",
      "第116次: theta0 = 387.999, theta1 = 84.509, 差值 = 731.4014\n",
      "第117次: theta0 = 388.822, theta1 = 84.688, 差值 = 702.4379\n",
      "第118次: theta0 = 389.629, theta1 = 84.864, 差值 = 674.6214\n",
      "第119次: theta0 = 390.419, theta1 = 85.036, 差值 = 647.9064\n",
      "第120次: theta0 = 391.194, theta1 = 85.205, 差值 = 622.2493\n",
      "第121次: theta0 = 391.953, theta1 = 85.371, 差值 = 597.6082\n",
      "第122次: theta0 = 392.697, theta1 = 85.533, 差值 = 573.9429\n",
      "第123次: theta0 = 393.426, theta1 = 85.692, 差值 = 551.2148\n",
      "第124次: theta0 = 394.141, theta1 = 85.847, 差值 = 529.3867\n",
      "第125次: theta0 = 394.841, theta1 = 86.000, 差值 = 508.4230\n",
      "第126次: theta0 = 395.527, theta1 = 86.150, 差值 = 488.2894\n",
      "第127次: theta0 = 396.199, theta1 = 86.296, 差值 = 468.9532\n",
      "第128次: theta0 = 396.858, theta1 = 86.440, 差值 = 450.3826\n",
      "第129次: theta0 = 397.504, theta1 = 86.581, 差值 = 432.5475\n",
      "第130次: theta0 = 398.137, theta1 = 86.719, 差值 = 415.4186\n",
      "第131次: theta0 = 398.757, theta1 = 86.854, 差值 = 398.9680\n",
      "第132次: theta0 = 399.365, theta1 = 86.986, 差值 = 383.1689\n",
      "第133次: theta0 = 399.961, theta1 = 87.116, 差值 = 367.9954\n",
      "第134次: theta0 = 400.545, theta1 = 87.243, 差值 = 353.4228\n",
      "第135次: theta0 = 401.117, theta1 = 87.368, 差值 = 339.4272\n",
      "第136次: theta0 = 401.678, theta1 = 87.490, 差值 = 325.9859\n",
      "第137次: theta0 = 402.227, theta1 = 87.610, 差值 = 313.0769\n",
      "第138次: theta0 = 402.765, theta1 = 87.727, 差值 = 300.6790\n",
      "第139次: theta0 = 403.293, theta1 = 87.842, 差值 = 288.7721\n",
      "第140次: theta0 = 403.810, theta1 = 87.955, 差值 = 277.3368\n",
      "第141次: theta0 = 404.317, theta1 = 88.066, 差值 = 266.3542\n",
      "第142次: theta0 = 404.814, theta1 = 88.174, 差值 = 255.8066\n",
      "第143次: theta0 = 405.300, theta1 = 88.280, 差值 = 245.6767\n",
      "第144次: theta0 = 405.777, theta1 = 88.384, 差值 = 235.9479\n",
      "第145次: theta0 = 406.245, theta1 = 88.486, 差值 = 226.6043\n",
      "第146次: theta0 = 406.703, theta1 = 88.586, 差值 = 217.6308\n",
      "第147次: theta0 = 407.152, theta1 = 88.684, 差值 = 209.0126\n",
      "第148次: theta0 = 407.592, theta1 = 88.779, 差值 = 200.7357\n",
      "第149次: theta0 = 408.023, theta1 = 88.873, 差值 = 192.7866\n",
      "第150次: theta0 = 408.446, theta1 = 88.966, 差值 = 185.1522\n",
      "第151次: theta0 = 408.860, theta1 = 89.056, 差值 = 177.8202\n",
      "第152次: theta0 = 409.265, theta1 = 89.144, 差值 = 170.7785\n",
      "第153次: theta0 = 409.663, theta1 = 89.231, 差值 = 164.0157\n",
      "第154次: theta0 = 410.053, theta1 = 89.316, 差值 = 157.5207\n",
      "第155次: theta0 = 410.435, theta1 = 89.399, 差值 = 151.2829\n",
      "第156次: theta0 = 410.809, theta1 = 89.481, 差值 = 145.2921\n",
      "第157次: theta0 = 411.176, theta1 = 89.561, 差值 = 139.5385\n",
      "第158次: theta0 = 411.535, theta1 = 89.639, 差值 = 134.0128\n",
      "第159次: theta0 = 411.888, theta1 = 89.716, 差值 = 128.7059\n",
      "第160次: theta0 = 412.233, theta1 = 89.791, 差值 = 123.6091\n",
      "第161次: theta0 = 412.571, theta1 = 89.865, 差值 = 118.7142\n",
      "第162次: theta0 = 412.903, theta1 = 89.937, 差值 = 114.0131\n",
      "第163次: theta0 = 413.228, theta1 = 90.008, 差值 = 109.4982\n",
      "第164次: theta0 = 413.546, theta1 = 90.077, 差值 = 105.1621\n",
      "第165次: theta0 = 413.858, theta1 = 90.145, 差值 = 100.9976\n",
      "第166次: theta0 = 414.164, theta1 = 90.212, 差值 = 96.9981\n",
      "第167次: theta0 = 414.464, theta1 = 90.277, 差值 = 93.1570\n",
      "第168次: theta0 = 414.758, theta1 = 90.341, 差值 = 89.4680\n",
      "第169次: theta0 = 415.045, theta1 = 90.404, 差值 = 85.9251\n",
      "第170次: theta0 = 415.328, theta1 = 90.466, 差值 = 82.5224\n",
      "第171次: theta0 = 415.604, theta1 = 90.526, 差值 = 79.2545\n",
      "第172次: theta0 = 415.875, theta1 = 90.585, 差值 = 76.1161\n",
      "第173次: theta0 = 416.140, theta1 = 90.643, 差值 = 73.1019\n",
      "第174次: theta0 = 416.401, theta1 = 90.700, 差值 = 70.2070\n",
      "第175次: theta0 = 416.656, theta1 = 90.755, 差值 = 67.4268\n",
      "第176次: theta0 = 416.906, theta1 = 90.810, 差值 = 64.7567\n",
      "第177次: theta0 = 417.150, theta1 = 90.863, 差值 = 62.1924\n",
      "第178次: theta0 = 417.390, theta1 = 90.915, 差值 = 59.7295\n",
      "第179次: theta0 = 417.626, theta1 = 90.967, 差值 = 57.3643\n",
      "第180次: theta0 = 417.856, theta1 = 91.017, 差值 = 55.0926\n",
      "第181次: theta0 = 418.082, theta1 = 91.066, 差值 = 52.9110\n",
      "第182次: theta0 = 418.303, theta1 = 91.114, 差值 = 50.8157\n",
      "第183次: theta0 = 418.520, theta1 = 91.162, 差值 = 48.8034\n",
      "第184次: theta0 = 418.733, theta1 = 91.208, 差值 = 46.8708\n",
      "第185次: theta0 = 418.941, theta1 = 91.253, 差值 = 45.0147\n",
      "第186次: theta0 = 419.145, theta1 = 91.298, 差值 = 43.2321\n",
      "第187次: theta0 = 419.345, theta1 = 91.342, 差值 = 41.5201\n",
      "第188次: theta0 = 419.542, theta1 = 91.384, 差值 = 39.8759\n",
      "第189次: theta0 = 419.734, theta1 = 91.426, 差值 = 38.2968\n",
      "第190次: theta0 = 419.922, theta1 = 91.467, 差值 = 36.7803\n",
      "第191次: theta0 = 420.107, theta1 = 91.507, 差值 = 35.3238\n",
      "第192次: theta0 = 420.287, theta1 = 91.547, 差值 = 33.9250\n",
      "第193次: theta0 = 420.465, theta1 = 91.586, 差值 = 32.5815\n",
      "第194次: theta0 = 420.638, theta1 = 91.623, 差值 = 31.2913\n",
      "第195次: theta0 = 420.809, theta1 = 91.661, 差值 = 30.0522\n",
      "第196次: theta0 = 420.975, theta1 = 91.697, 差值 = 28.8621\n",
      "第197次: theta0 = 421.139, theta1 = 91.733, 差值 = 27.7192\n",
      "第198次: theta0 = 421.299, theta1 = 91.767, 差值 = 26.6215\n",
      "第199次: theta0 = 421.456, theta1 = 91.802, 差值 = 25.5673\n",
      "第200次: theta0 = 421.610, theta1 = 91.835, 差值 = 24.5548\n",
      "第201次: theta0 = 421.761, theta1 = 91.868, 差值 = 23.5824\n",
      "第202次: theta0 = 421.909, theta1 = 91.900, 差值 = 22.6486\n",
      "第203次: theta0 = 422.053, theta1 = 91.932, 差值 = 21.7517\n",
      "第204次: theta0 = 422.195, theta1 = 91.963, 差值 = 20.8903\n",
      "第205次: theta0 = 422.335, theta1 = 91.993, 差值 = 20.0631\n",
      "第206次: theta0 = 422.471, theta1 = 92.023, 差值 = 19.2686\n",
      "第207次: theta0 = 422.604, theta1 = 92.052, 差值 = 18.5055\n",
      "第208次: theta0 = 422.735, theta1 = 92.080, 差值 = 17.7727\n",
      "第209次: theta0 = 422.864, theta1 = 92.108, 差值 = 17.0689\n",
      "第210次: theta0 = 422.989, theta1 = 92.136, 差值 = 16.3930\n",
      "第211次: theta0 = 423.113, theta1 = 92.163, 差值 = 15.7438\n",
      "第212次: theta0 = 423.233, theta1 = 92.189, 差值 = 15.1204\n",
      "第213次: theta0 = 423.352, theta1 = 92.215, 差值 = 14.5216\n",
      "第214次: theta0 = 423.468, theta1 = 92.240, 差值 = 13.9465\n",
      "第215次: theta0 = 423.581, theta1 = 92.265, 差值 = 13.3943\n",
      "第216次: theta0 = 423.693, theta1 = 92.289, 差值 = 12.8638\n",
      "第217次: theta0 = 423.802, theta1 = 92.313, 差值 = 12.3544\n",
      "第218次: theta0 = 423.909, theta1 = 92.336, 差值 = 11.8652\n",
      "第219次: theta0 = 424.014, theta1 = 92.359, 差值 = 11.3953\n",
      "第220次: theta0 = 424.116, theta1 = 92.382, 差值 = 10.9441\n",
      "第221次: theta0 = 424.217, theta1 = 92.403, 差值 = 10.5107\n",
      "第222次: theta0 = 424.316, theta1 = 92.425, 差值 = 10.0945\n",
      "第223次: theta0 = 424.412, theta1 = 92.446, 差值 = 9.6947\n",
      "第224次: theta0 = 424.507, theta1 = 92.467, 差值 = 9.3108\n",
      "第225次: theta0 = 424.600, theta1 = 92.487, 差值 = 8.9421\n",
      "第226次: theta0 = 424.691, theta1 = 92.507, 差值 = 8.5880\n",
      "第227次: theta0 = 424.780, theta1 = 92.526, 差值 = 8.2479\n",
      "第228次: theta0 = 424.868, theta1 = 92.545, 差值 = 7.9213\n",
      "第229次: theta0 = 424.953, theta1 = 92.564, 差值 = 7.6076\n",
      "第230次: theta0 = 425.037, theta1 = 92.582, 差值 = 7.3064\n",
      "第231次: theta0 = 425.119, theta1 = 92.600, 差值 = 7.0170\n",
      "第232次: theta0 = 425.200, theta1 = 92.618, 差值 = 6.7392\n",
      "第233次: theta0 = 425.279, theta1 = 92.635, 差值 = 6.4723\n",
      "第234次: theta0 = 425.356, theta1 = 92.652, 差值 = 6.2160\n",
      "第235次: theta0 = 425.432, theta1 = 92.668, 差值 = 5.9698\n",
      "第236次: theta0 = 425.507, theta1 = 92.685, 差值 = 5.7334\n",
      "第237次: theta0 = 425.579, theta1 = 92.700, 差值 = 5.5064\n",
      "第238次: theta0 = 425.651, theta1 = 92.716, 差值 = 5.2883\n",
      "第239次: theta0 = 425.721, theta1 = 92.731, 差值 = 5.0789\n",
      "第240次: theta0 = 425.789, theta1 = 92.746, 差值 = 4.8778\n",
      "第241次: theta0 = 425.857, theta1 = 92.761, 差值 = 4.6846\n",
      "第242次: theta0 = 425.923, theta1 = 92.775, 差值 = 4.4991\n",
      "第243次: theta0 = 425.987, theta1 = 92.789, 差值 = 4.3209\n",
      "第244次: theta0 = 426.050, theta1 = 92.803, 差值 = 4.1498\n",
      "第245次: theta0 = 426.112, theta1 = 92.817, 差值 = 3.9855\n",
      "第246次: theta0 = 426.173, theta1 = 92.830, 差值 = 3.8277\n",
      "第247次: theta0 = 426.233, theta1 = 92.843, 差值 = 3.6761\n",
      "第248次: theta0 = 426.291, theta1 = 92.856, 差值 = 3.5305\n",
      "第249次: theta0 = 426.348, theta1 = 92.868, 差值 = 3.3907\n",
      "第250次: theta0 = 426.404, theta1 = 92.880, 差值 = 3.2564\n",
      "第251次: theta0 = 426.459, theta1 = 92.892, 差值 = 3.1275\n",
      "第252次: theta0 = 426.513, theta1 = 92.904, 差值 = 3.0036\n",
      "第253次: theta0 = 426.566, theta1 = 92.915, 差值 = 2.8847\n",
      "第254次: theta0 = 426.617, theta1 = 92.927, 差值 = 2.7705\n",
      "第255次: theta0 = 426.668, theta1 = 92.938, 差值 = 2.6608\n",
      "第256次: theta0 = 426.718, theta1 = 92.949, 差值 = 2.5554\n",
      "第257次: theta0 = 426.766, theta1 = 92.959, 差值 = 2.4542\n",
      "第258次: theta0 = 426.814, theta1 = 92.970, 差值 = 2.3570\n",
      "第259次: theta0 = 426.861, theta1 = 92.980, 差值 = 2.2637\n",
      "第260次: theta0 = 426.906, theta1 = 92.990, 差值 = 2.1740\n",
      "第261次: theta0 = 426.951, theta1 = 93.000, 差值 = 2.0879\n",
      "第262次: theta0 = 426.995, theta1 = 93.009, 差值 = 2.0053\n",
      "第263次: theta0 = 427.038, theta1 = 93.018, 差值 = 1.9258\n",
      "第264次: theta0 = 427.081, theta1 = 93.028, 差值 = 1.8496\n",
      "第265次: theta0 = 427.122, theta1 = 93.037, 差值 = 1.7763\n",
      "第266次: theta0 = 427.163, theta1 = 93.046, 差值 = 1.7060\n",
      "第267次: theta0 = 427.202, theta1 = 93.054, 差值 = 1.6384\n",
      "第268次: theta0 = 427.241, theta1 = 93.063, 差值 = 1.5736\n",
      "第269次: theta0 = 427.279, theta1 = 93.071, 差值 = 1.5112\n",
      "第270次: theta0 = 427.317, theta1 = 93.079, 差值 = 1.4514\n",
      "第271次: theta0 = 427.354, theta1 = 93.087, 差值 = 1.3939\n",
      "第272次: theta0 = 427.389, theta1 = 93.095, 差值 = 1.3387\n",
      "第273次: theta0 = 427.425, theta1 = 93.103, 差值 = 1.2857\n",
      "第274次: theta0 = 427.459, theta1 = 93.110, 差值 = 1.2348\n",
      "第275次: theta0 = 427.493, theta1 = 93.118, 差值 = 1.1859\n",
      "第276次: theta0 = 427.526, theta1 = 93.125, 差值 = 1.1389\n",
      "第277次: theta0 = 427.559, theta1 = 93.132, 差值 = 1.0938\n",
      "第278次: theta0 = 427.590, theta1 = 93.139, 差值 = 1.0505\n",
      "第279次: theta0 = 427.622, theta1 = 93.146, 差值 = 1.0089\n",
      "第280次: theta0 = 427.652, theta1 = 93.152, 差值 = 0.9690\n",
      "第281次: theta0 = 427.682, theta1 = 93.159, 差值 = 0.9306\n",
      "第282次: theta0 = 427.712, theta1 = 93.165, 差值 = 0.8937\n",
      "第283次: theta0 = 427.740, theta1 = 93.171, 差值 = 0.8584\n",
      "第284次: theta0 = 427.768, theta1 = 93.178, 差值 = 0.8244\n",
      "第285次: theta0 = 427.796, theta1 = 93.184, 差值 = 0.7917\n",
      "第286次: theta0 = 427.823, theta1 = 93.190, 差值 = 0.7604\n",
      "第287次: theta0 = 427.850, theta1 = 93.195, 差值 = 0.7303\n",
      "第288次: theta0 = 427.876, theta1 = 93.201, 差值 = 0.7013\n",
      "第289次: theta0 = 427.901, theta1 = 93.207, 差值 = 0.6736\n",
      "第290次: theta0 = 427.926, theta1 = 93.212, 差值 = 0.6469\n",
      "第291次: theta0 = 427.951, theta1 = 93.217, 差值 = 0.6213\n",
      "第292次: theta0 = 427.975, theta1 = 93.223, 差值 = 0.5967\n",
      "第293次: theta0 = 427.998, theta1 = 93.228, 差值 = 0.5730\n",
      "第294次: theta0 = 428.021, theta1 = 93.233, 差值 = 0.5503\n",
      "第295次: theta0 = 428.044, theta1 = 93.238, 差值 = 0.5286\n",
      "第296次: theta0 = 428.066, theta1 = 93.242, 差值 = 0.5076\n",
      "第297次: theta0 = 428.088, theta1 = 93.247, 差值 = 0.4875\n",
      "第298次: theta0 = 428.109, theta1 = 93.252, 差值 = 0.4682\n",
      "第299次: theta0 = 428.130, theta1 = 93.256, 差值 = 0.4497\n",
      "第300次: theta0 = 428.150, theta1 = 93.261, 差值 = 0.4319\n",
      "第301次: theta0 = 428.170, theta1 = 93.265, 差值 = 0.4148\n",
      "第302次: theta0 = 428.190, theta1 = 93.269, 差值 = 0.3983\n",
      "第303次: theta0 = 428.209, theta1 = 93.274, 差值 = 0.3826\n",
      "第304次: theta0 = 428.228, theta1 = 93.278, 差值 = 0.3674\n",
      "第305次: theta0 = 428.246, theta1 = 93.282, 差值 = 0.3529\n",
      "第306次: theta0 = 428.264, theta1 = 93.286, 差值 = 0.3389\n",
      "第307次: theta0 = 428.282, theta1 = 93.290, 差值 = 0.3255\n",
      "第308次: theta0 = 428.299, theta1 = 93.293, 差值 = 0.3126\n",
      "第309次: theta0 = 428.316, theta1 = 93.297, 差值 = 0.3002\n",
      "第310次: theta0 = 428.333, theta1 = 93.301, 差值 = 0.2883\n",
      "第311次: theta0 = 428.349, theta1 = 93.304, 差值 = 0.2769\n",
      "第312次: theta0 = 428.365, theta1 = 93.308, 差值 = 0.2659\n",
      "第313次: theta0 = 428.381, theta1 = 93.311, 差值 = 0.2554\n",
      "第314次: theta0 = 428.396, theta1 = 93.314, 差值 = 0.2453\n",
      "第315次: theta0 = 428.411, theta1 = 93.318, 差值 = 0.2356\n",
      "第316次: theta0 = 428.426, theta1 = 93.321, 差值 = 0.2262\n",
      "第317次: theta0 = 428.441, theta1 = 93.324, 差值 = 0.2173\n",
      "第318次: theta0 = 428.455, theta1 = 93.327, 差值 = 0.2087\n",
      "第319次: theta0 = 428.469, theta1 = 93.330, 差值 = 0.2004\n",
      "第320次: theta0 = 428.482, theta1 = 93.333, 差值 = 0.1925\n",
      "第321次: theta0 = 428.496, theta1 = 93.336, 差值 = 0.1849\n",
      "第322次: theta0 = 428.509, theta1 = 93.339, 差值 = 0.1775\n",
      "第323次: theta0 = 428.522, theta1 = 93.342, 差值 = 0.1705\n",
      "第324次: theta0 = 428.534, theta1 = 93.345, 差值 = 0.1638\n",
      "第325次: theta0 = 428.547, theta1 = 93.347, 差值 = 0.1573\n",
      "第326次: theta0 = 428.559, theta1 = 93.350, 差值 = 0.1510\n",
      "第327次: theta0 = 428.570, theta1 = 93.352, 差值 = 0.1451\n",
      "第328次: theta0 = 428.582, theta1 = 93.355, 差值 = 0.1393\n",
      "第329次: theta0 = 428.593, theta1 = 93.357, 差值 = 0.1338\n",
      "第330次: theta0 = 428.605, theta1 = 93.360, 差值 = 0.1285\n",
      "第331次: theta0 = 428.615, theta1 = 93.362, 差值 = 0.1234\n",
      "第332次: theta0 = 428.626, theta1 = 93.365, 差值 = 0.1185\n",
      "第333次: theta0 = 428.637, theta1 = 93.367, 差值 = 0.1138\n",
      "第334次: theta0 = 428.647, theta1 = 93.369, 差值 = 0.1093\n",
      "第335次: theta0 = 428.657, theta1 = 93.371, 差值 = 0.1050\n",
      "第336次: theta0 = 428.667, theta1 = 93.373, 差值 = 0.1008\n",
      "第337次: theta0 = 428.676, theta1 = 93.376, 差值 = 0.0968\n",
      "第338次: theta0 = 428.686, theta1 = 93.378, 差值 = 0.0930\n",
      "第339次: theta0 = 428.695, theta1 = 93.380, 差值 = 0.0893\n",
      "第340次: theta0 = 428.704, theta1 = 93.382, 差值 = 0.0858\n",
      "第341次: theta0 = 428.713, theta1 = 93.384, 差值 = 0.0824\n",
      "第342次: theta0 = 428.722, theta1 = 93.385, 差值 = 0.0791\n",
      "第343次: theta0 = 428.731, theta1 = 93.387, 差值 = 0.0760\n",
      "第344次: theta0 = 428.739, theta1 = 93.389, 差值 = 0.0730\n",
      "第345次: theta0 = 428.747, theta1 = 93.391, 差值 = 0.0701\n",
      "第346次: theta0 = 428.755, theta1 = 93.393, 差值 = 0.0673\n",
      "第347次: theta0 = 428.763, theta1 = 93.394, 差值 = 0.0647\n",
      "第348次: theta0 = 428.771, theta1 = 93.396, 差值 = 0.0621\n",
      "第349次: theta0 = 428.778, theta1 = 93.398, 差值 = 0.0596\n",
      "第350次: theta0 = 428.786, theta1 = 93.399, 差值 = 0.0573\n",
      "第351次: theta0 = 428.793, theta1 = 93.401, 差值 = 0.0550\n",
      "第352次: theta0 = 428.800, theta1 = 93.403, 差值 = 0.0528\n",
      "第353次: theta0 = 428.807, theta1 = 93.404, 差值 = 0.0507\n",
      "第354次: theta0 = 428.814, theta1 = 93.406, 差值 = 0.0487\n",
      "第355次: theta0 = 428.821, theta1 = 93.407, 差值 = 0.0468\n",
      "第356次: theta0 = 428.827, theta1 = 93.408, 差值 = 0.0449\n",
      "第357次: theta0 = 428.834, theta1 = 93.410, 差值 = 0.0432\n",
      "第358次: theta0 = 428.840, theta1 = 93.411, 差值 = 0.0415\n",
      "第359次: theta0 = 428.846, theta1 = 93.413, 差值 = 0.0398\n",
      "第360次: theta0 = 428.852, theta1 = 93.414, 差值 = 0.0382\n",
      "第361次: theta0 = 428.858, theta1 = 93.415, 差值 = 0.0367\n",
      "第362次: theta0 = 428.864, theta1 = 93.416, 差值 = 0.0353\n",
      "第363次: theta0 = 428.870, theta1 = 93.418, 差值 = 0.0339\n",
      "第364次: theta0 = 428.876, theta1 = 93.419, 差值 = 0.0325\n",
      "第365次: theta0 = 428.881, theta1 = 93.420, 差值 = 0.0312\n",
      "第366次: theta0 = 428.886, theta1 = 93.421, 差值 = 0.0300\n",
      "第367次: theta0 = 428.892, theta1 = 93.422, 差值 = 0.0288\n",
      "第368次: theta0 = 428.897, theta1 = 93.424, 差值 = 0.0277\n",
      "第369次: theta0 = 428.902, theta1 = 93.425, 差值 = 0.0266\n",
      "第370次: theta0 = 428.907, theta1 = 93.426, 差值 = 0.0255\n",
      "第371次: theta0 = 428.912, theta1 = 93.427, 差值 = 0.0245\n",
      "第372次: theta0 = 428.917, theta1 = 93.428, 差值 = 0.0235\n",
      "第373次: theta0 = 428.921, theta1 = 93.429, 差值 = 0.0226\n",
      "第374次: theta0 = 428.926, theta1 = 93.430, 差值 = 0.0217\n",
      "第375次: theta0 = 428.930, theta1 = 93.431, 差值 = 0.0209\n",
      "第376次: theta0 = 428.935, theta1 = 93.432, 差值 = 0.0200\n",
      "第377次: theta0 = 428.939, theta1 = 93.433, 差值 = 0.0192\n",
      "第378次: theta0 = 428.943, theta1 = 93.434, 差值 = 0.0185\n",
      "第379次: theta0 = 428.947, theta1 = 93.435, 差值 = 0.0177\n",
      "第380次: theta0 = 428.951, theta1 = 93.435, 差值 = 0.0170\n",
      "第381次: theta0 = 428.955, theta1 = 93.436, 差值 = 0.0164\n",
      "第382次: theta0 = 428.959, theta1 = 93.437, 差值 = 0.0157\n",
      "第383次: theta0 = 428.963, theta1 = 93.438, 差值 = 0.0151\n",
      "第384次: theta0 = 428.967, theta1 = 93.439, 差值 = 0.0145\n",
      "第385次: theta0 = 428.970, theta1 = 93.440, 差值 = 0.0139\n",
      "第386次: theta0 = 428.974, theta1 = 93.440, 差值 = 0.0134\n",
      "第387次: theta0 = 428.978, theta1 = 93.441, 差值 = 0.0128\n",
      "第388次: theta0 = 428.981, theta1 = 93.442, 差值 = 0.0123\n",
      "第389次: theta0 = 428.984, theta1 = 93.443, 差值 = 0.0118\n",
      "第390次: theta0 = 428.988, theta1 = 93.443, 差值 = 0.0114\n",
      "第391次: theta0 = 428.991, theta1 = 93.444, 差值 = 0.0109\n",
      "第392次: theta0 = 428.994, theta1 = 93.445, 差值 = 0.0105\n",
      "第393次: theta0 = 428.997, theta1 = 93.445, 差值 = 0.0101\n",
      "第394次: theta0 = 429.000, theta1 = 93.446, 差值 = 0.0097\n"
     ]
    }
   ],
   "source": [
    "# 学习率\n",
    "ETA = 1e-3\n",
    "\n",
    "# 误差的差值\n",
    "diff = 1\n",
    "\n",
    "# 更新次数\n",
    "count = 0\n",
    "\n",
    "# 直到误差的差值小于0.01为止，重复参数更新\n",
    "error = E(train_z, train_y)\n",
    "while diff > 1e-2:\n",
    "    # 更新结果保存到临时变量\n",
    "    tmp_theta0 = theta0 - ETA * np.sum((f(train_z) - train_y))\n",
    "    tmp_theta1 = theta1 - ETA * np.sum((f(train_z) - train_y) * train_z)\n",
    "\n",
    "    # 更新参数\n",
    "    theta0 = tmp_theta0\n",
    "    theta1 = tmp_theta1\n",
    "\n",
    "    # 计算与上一次误差的差值\n",
    "    current_error = E(train_z, train_y)\n",
    "    diff = error - current_error\n",
    "    error = current_error\n",
    "\n",
    "    # 输出日志\n",
    "    count += 1\n",
    "    log = '第{}次: theta0 = {:.3f}, theta1 = {:.3f}, 差值 = {:.4f}'\n",
    "    print(log.format(count, theta0, theta1, diff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# 绘图确认\n",
    "x = np.linspace(-3, 3, 100)\n",
    "plt.plot(train_z, train_y, 'o')\n",
    "plt.plot(x, f(x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-7 验证数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "370.96734094547423"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(standardize(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "510.46964366017573"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(standardize(200))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "649.9719463748772"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(standardize(300))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 初始化参数\n",
    "theta = np.random.rand(3)\n",
    "\n",
    "# 创建学习数据的矩阵\n",
    "def to_matrix(x):\n",
    "    return np.vstack([np.ones(x.shape[0]), x, x ** 2]).T\n",
    "\n",
    "X = to_matrix(train_z)\n",
    "\n",
    "# 预测函数\n",
    "def f(x):\n",
    "    return np.dot(x, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 误差的差值\n",
    "diff = 1\n",
    "\n",
    "# 重复学习\n",
    "error = E(X, train_y)\n",
    "while diff > 1e-2:\n",
    "    # 更新参数\n",
    "    theta = theta - ETA * np.dot(f(X) - train_y, X)\n",
    "    # 计算与上一次误差的差值\n",
    "    current_error = E(X, train_y)\n",
    "    diff = error - current_error\n",
    "    error = current_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x = np.linspace(-3, 3, 100)\n",
    "\n",
    "plt.plot(train_z, train_y, 'o')\n",
    "plt.plot(x, f(to_matrix(x)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# 均方误差\n",
    "def MSE(x, y):\n",
    "    return (1 / x.shape[0]) * np.sum((y - f(x)) ** 2)\n",
    "\n",
    "# 用随机值初始化参数\n",
    "theta = np.random.rand(3)\n",
    "\n",
    "# 均方误差的历史记录\n",
    "errors = []\n",
    "\n",
    "# 誤差の差分\n",
    "diff = 1\n",
    "\n",
    "# 重复学习\n",
    "errors.append(MSE(X, train_y))\n",
    "while diff > 1e-2:\n",
    "    theta = theta - ETA * np.dot(f(X) - train_y, X)\n",
    "    errors.append(MSE(X, train_y))\n",
    "    diff = errors[-2] - errors[-1]\n",
    "\n",
    "# 绘制误差变化图\n",
    "x = np.arange(len(errors))\n",
    "\n",
    "plt.plot(x, errors)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 用随机数对参数初始化\n",
    "theta = np.random.rand(3)\n",
    "\n",
    "# 均方误差的历史记录\n",
    "errors = []\n",
    "\n",
    "# 误差的差值\n",
    "diff = 1\n",
    "\n",
    "# 重复学习\n",
    "errors.append(MSE(X, train_y))\n",
    "while diff > 1e-2:\n",
    "    # 为了调整学习数据的顺序，准备随机的序列\n",
    "    p = np.random.permutation(X.shape[0])\n",
    "    # 随机取出学习数据，使用随机梯度下降法更新参数\n",
    "    for x, y in zip(X[p,:], train_y[p]):\n",
    "        theta = theta - ETA * (f(x) - y) * x\n",
    "    # 计算与前一次的误差的差值\n",
    "    errors.append(MSE(X, train_y))\n",
    "    diff = errors[-2] - errors[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-2-13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x = np.linspace(-3, 3, 100)\n",
    "\n",
    "plt.plot(train_z, train_y, 'o')\n",
    "plt.plot(x, f(to_matrix(x)))\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}