machinelearning_notebook/4_logistic_regression/1-Least_squares.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 最小二乘（Generalized Least Squares）\n",
    "\n",
    "## 1. 最小二乘的基本原理\n",
    "\n",
    "最小二乘法（generalized least squares）是一种数学优化技术，它通过最小化误差的平方和找到一组数据的最佳函数匹配。 最小二乘法通常用于曲线拟合、求解模型。很多其他的优化问题也可通过最小化能量或最大化熵用最小二乘形式表达。\n",
    "\n",
    "最小二乘原理的一般形式为：\n",
    "$$\n",
    "L = \\sum (V_{obv} - V_{target}(\\theta))^2\n",
    "$$\n",
    "其中$V_{obv}$是我们观测的多组样本值，$V_{target}$是我们假设拟合函数的输出值，$\\theta$为构造模型的参数。$L$是目标函数，如果通过调整模型参数$\\theta$，使得$L$下降到最小则表明，拟合函数与观测最为接近，也就是找到了最优的模型。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 示例\n",
    "\n",
    "假设我们有下面的一些观测数据，我们希望找到他们内在的规律。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import sklearn\n",
    "from sklearn import datasets\n",
    "\n",
    "# load data\n",
    "d = datasets.load_diabetes()\n",
    "\n",
    "X = d.data[:, 2]\n",
    "Y = d.target\n",
    "\n",
    "# draw original data\n",
    "plt.scatter(X, Y)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 数学原理\n",
    "有$N$个观测数据为：\n",
    "$$\n",
    "\\mathbf{X} = \\{x_1, x_2, ..., x_N \\} \\\\\n",
    "\\mathbf{Y} = \\{y_1, y_2, ..., y_N \\}\n",
    "$$\n",
    "其中$\\mathbf{X}$为自变量，$\\mathbf{Y}$为因变量。\n",
    "\n",
    "我们希望找到一个模型能够解释这些数据，假设我们使用最简单的线性模型来拟合数据：\n",
    "$$\n",
    "y = ax + b\n",
    "$$\n",
    "那么问题就变成求解参数$a$, $b$能够使得模型输出尽可能和观测数据有比较小的误差。\n",
    "\n",
    "如何构建函数来评估模型输出与观测数据之间的误差是一个关键问题，这里我们使用观测数据与模型输出的平方和来作为评估函数（也被称为损失函数Loss function):\n",
    "$$\n",
    "L = \\sum_{i=1}^{N} \\{y_i - (a x_i + b)\\}^2 \\\\\n",
    "L = \\sum_{i=1}^{N} (y_i - a x_i - b)^2 \n",
    "$$\n",
    "\n",
    "使误差函数最小，那么我们就可以求出模型的参数:\n",
    "$$\n",
    "\\frac{\\partial L}{\\partial a} = -2 \\sum_{i=1}^{N} (y_i - a x_i - b) x_i \\\\\n",
    "\\frac{\\partial L}{\\partial b} = -2 \\sum_{i=1}^{N} (y_i - a x_i - b)\n",
    "$$\n",
    "既当偏微分为0时，误差函数为最小，因此我们可以得到:\n",
    "$$\n",
    "-2 \\sum_{i=1}^{N} (y_i - a x_i - b) x_i = 0 \\\\\n",
    "-2 \\sum_{i=1}^{N} (y_i - a x_i - b) = 0 \\\\\n",
    "$$\n",
    "\n",
    "将上式调整一下顺序可以得到：\n",
    "$$\n",
    "a \\sum x_i^2 + b \\sum x_i = \\sum y_i x_i \\\\\n",
    "a \\sum x_i + b N = \\sum y_i\n",
    "$$\n",
    "通过求解二元一次方程组，我们即可求出模型的最优参数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 求解程序"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 949.435260, b = 152.133484\n"
     ]
    },
    {
     "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": [
    "N = X.shape[0]\n",
    "\n",
    "S_X2 = np.sum(X*X)\n",
    "S_X  = np.sum(X)\n",
    "S_XY = np.sum(X*Y)\n",
    "S_Y  = np.sum(Y)\n",
    "\n",
    "A1 = np.array([[S_X2, S_X], \n",
    "               [S_X, N]])\n",
    "B1 = np.array([S_XY, S_Y])\n",
    "# numpy.linalg模块包含线性代数的函数。使用这个模块，可以计算逆矩阵、求特征值、解线性方程组以及求解行列式等。\n",
    "coeff = np.linalg.inv(A1).dot(B1)\n",
    "\n",
    "print('a = %f, b = %f' % (coeff[0], coeff[1]))\n",
    "\n",
    "x_min = np.min(X)\n",
    "x_max = np.max(X)\n",
    "y_min = coeff[0] * x_min + coeff[1]\n",
    "y_max = coeff[0] * x_max + coeff[1]\n",
    "\n",
    "plt.scatter(X, Y, label='original data')\n",
    "plt.plot([x_min, x_max], [y_min, y_max], 'r', label='model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 如何使用迭代的方法求出模型参数\n",
    "\n",
    "当数据比较多的时候，或者模型比较复杂，无法直接使用解析的方式求出模型参数。因此更为常用的方式是，通过迭代的方式逐步逼近模型的参数。\n",
    "\n",
    "### 2.1 梯度下降法\n",
    "在机器学习算法中，对于很多监督学习模型，需要对原始的模型构建损失函数，接下来便是通过优化算法对损失函数进行优化，以便寻找到最优的参数。在求解机器学习参数的优化算法中，使用较多的是基于梯度下降的优化算法(Gradient Descent, GD)。\n",
    "\n",
    "梯度下降法有很多优点，其中最主要的优点是，**在梯度下降法的求解过程中只需求解损失函数的一阶导数，计算的代价比较小，这使得梯度下降法能在很多大规模数据集上得到应用。**\n",
    "\n",
    "梯度下降法的含义是通过当前点的梯度方向寻找到新的迭代点。梯度下降法的基本思想可以类比为一个下山的过程。假设这样一个场景：\n",
    "* 一个人被困在山上，需要从山上下来(i.e. 找到山的最低点，也就是山谷)。\n",
    "* 但此时山上的浓雾很大，导致可视度很低。因此，下山的路径就无法确定，他必须利用自己周围的信息去找到下山的路径。\n",
    "* 这个时候，他就可以利用梯度下降算法来帮助自己下山。\n",
    "    - 具体来说就是，以他当前的所处的位置为基准，寻找这个位置最陡峭的地方，然后朝着山的高度下降的地方走\n",
    "    - 同理，如果我们的目标是上山，也就是爬到山顶，那么此时应该是朝着最陡峭的方向往上走。\n",
    "    - 然后每走一段距离，都反复采用同一个方法，最后就能成功的抵达山谷。\n",
    "\n",
    "\n",
    "我们同时可以假设这座山最陡峭的地方是无法通过肉眼立马观察出来的，而是需要一个复杂的工具来测量，同时，这个人此时正好拥有测量出最陡峭方向的能力。所以，此人每走一段距离，都需要一段时间来测量所在位置最陡峭的方向，这是比较耗时的。那么为了在太阳下山之前到达山底，就要尽可能的减少测量方向的次数。这是一个两难的选择，如果测量的频繁，可以保证下山的方向是绝对正确的，但又非常耗时，如果测量的过少，又有偏离轨道的风险。所以需要找到一个合适的测量方向的频率，来确保下山的方向不错误，同时又不至于耗时太多！\n",
    "\n",
    "\n",
    "![gradient_descent](images/gradient_descent.png)\n",
    "\n",
    "如上图所示，得到了局部最优解。x,y表示的是$\\theta_0$和$\\theta_1$，z方向表示的是花费函数，很明显出发点不同，最后到达的收敛点可能不一样。当然如果是碗状的，那么收敛点就应该是一样的。\n",
    "\n",
    "对于某一个损失函数\n",
    "$$\n",
    "L = \\sum_{i=1}^{N} (y_i - a x_i - b)^2\n",
    "$$\n",
    "\n",
    "我们更新的策略是：\n",
    "$$\n",
    "\\theta^1 = \\theta^0 - \\eta \\triangledown L(\\theta)\n",
    "$$\n",
    "其中$\\theta$代表了模型中的参数，例如$a$, $b$\n",
    "\n",
    "此公式的意义是：$L$是关于$\\theta$的一个函数，我们当前所处的位置为$\\theta_0$点，要从这个点走到L的最小值点，也就是山底。首先我们先确定前进的方向，也就是梯度的反向，然后走一段距离的步长，也就是$\\eta$，走完这个段步长，就到达了$\\theta_1$这个点！\n",
    "\n",
    "我们更新的策略是：\n",
    "\n",
    "$$\n",
    "a^1 = a^0 + 2 \\eta [ y - (ax+b)]*x \\\\\n",
    "b^1 = b^0 + 2 \\eta [ y - (ax+b)] \n",
    "$$\n",
    "\n",
    "下面就这个公式的几个常见的疑问：\n",
    "\n",
    "* **$\\eta$是什么含义？**\n",
    "$\\eta$在梯度下降算法中被称作为学习率或者步长，意味着我们可以通过$\\eta$来控制每一步走的距离，以保证不要步子跨的太大，错过了最低点。同时也要保证不要走的太慢，导致太阳下山了，还没有走到山下。所以$\\eta$的选择在梯度下降法中往往是很重要的。\n",
    "![gd_stepsize](images/gd_stepsize.png)\n",
    "\n",
    "* **为什么要梯度要乘以一个负号？**\n",
    "梯度前加一个负号，就意味着朝着梯度相反的方向前进！梯度的方向实际就是函数在此点上升最快的方向，而我们需要朝着下降最快的方向走，自然就是负的梯度的方向，所以此处需要加上负号。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 示例代码"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    0: loss = 2590736.867664, a = 18.689017, b = 148.815329\n",
      "epoch    1: loss = 2557255.189453, a = 36.831348, b = 148.828655\n",
      "epoch    2: loss = 2525130.800853, a = 54.614824, b = 148.822534\n",
      "epoch    3: loss = 2494255.916234, a = 72.046438, b = 148.816532\n",
      "epoch    4: loss = 2464581.753419, a = 89.133153, b = 148.810649\n",
      "epoch    5: loss = 2436061.445196, a = 105.881792, b = 148.804882\n",
      "epoch    6: loss = 2408649.957111, a = 122.299046, b = 148.799229\n",
      "epoch    7: loss = 2382304.015732, a = 138.391470, b = 148.793687\n",
      "epoch    8: loss = 2356982.039720, a = 154.165492, b = 148.788256\n",
      "epoch    9: loss = 2332644.073594, a = 169.627411, b = 148.782932\n",
      "epoch   10: loss = 2309251.724102, a = 184.783402, b = 148.777713\n",
      "epoch   11: loss = 2286768.099073, a = 199.639520, b = 148.772598\n",
      "epoch   12: loss = 2265157.748666, a = 214.201696, b = 148.767584\n",
      "epoch   13: loss = 2244386.608923, a = 228.475748, b = 148.762669\n",
      "epoch   14: loss = 2224421.947529, a = 242.467375, b = 148.757851\n",
      "epoch   15: loss = 2205232.311697, a = 256.182166, b = 148.753129\n",
      "epoch   16: loss = 2186787.478095, a = 269.625597, b = 148.748500\n",
      "epoch   17: loss = 2169058.404731, a = 282.803039, b = 148.743962\n",
      "epoch   18: loss = 2152017.184726, a = 295.719754, b = 148.739515\n",
      "epoch   19: loss = 2135637.001889, a = 308.380901, b = 148.735155\n",
      "epoch   20: loss = 2119892.088045, a = 320.791536, b = 148.730882\n",
      "epoch   21: loss = 2104757.682020, a = 332.956616, b = 148.726693\n",
      "epoch   22: loss = 2090209.990240, a = 344.881000, b = 148.722587\n",
      "epoch   23: loss = 2076226.148871, a = 356.569449, b = 148.718562\n",
      "epoch   24: loss = 2062784.187440, a = 368.026633, b = 148.714617\n",
      "epoch   25: loss = 2049862.993883, a = 379.257126, b = 148.710750\n",
      "epoch   26: loss = 2037442.280956, a = 390.265414, b = 148.706960\n",
      "epoch   27: loss = 2025502.553972, a = 401.055894, b = 148.703244\n",
      "epoch   28: loss = 2014025.079785, a = 411.632875, b = 148.699602\n",
      "epoch   29: loss = 2002991.857005, a = 422.000581, b = 148.696032\n",
      "epoch   30: loss = 1992385.587369, a = 432.163154, b = 148.692533\n",
      "epoch   31: loss = 1982189.648231, a = 442.124651, b = 148.689103\n",
      "epoch   32: loss = 1972388.066142, a = 451.889051, b = 148.685741\n",
      "epoch   33: loss = 1962965.491447, a = 461.460255, b = 148.682445\n",
      "epoch   34: loss = 1953907.173892, a = 470.842084, b = 148.679215\n",
      "epoch   35: loss = 1945198.939172, a = 480.038285, b = 148.676048\n",
      "epoch   36: loss = 1936827.166411, a = 489.052532, b = 148.672944\n",
      "epoch   37: loss = 1928778.766513, a = 497.888424, b = 148.669902\n",
      "epoch   38: loss = 1921041.161364, a = 506.549490, b = 148.666919\n",
      "epoch   39: loss = 1913602.263848, a = 515.039190, b = 148.663996\n",
      "epoch   40: loss = 1906450.458648, a = 523.360914, b = 148.661131\n",
      "epoch   41: loss = 1899574.583794, a = 531.517985, b = 148.658322\n",
      "epoch   42: loss = 1892963.912935, a = 539.513662, b = 148.655569\n",
      "epoch   43: loss = 1886608.138306, a = 547.351138, b = 148.652870\n",
      "epoch   44: loss = 1880497.354362, a = 555.033542, b = 148.650225\n",
      "epoch   45: loss = 1874622.042047, a = 562.563943, b = 148.647632\n",
      "epoch   46: loss = 1868973.053689, a = 569.945349, b = 148.645090\n",
      "epoch   47: loss = 1863541.598476, a = 577.180708, b = 148.642599\n",
      "epoch   48: loss = 1858319.228507, a = 584.272908, b = 148.640157\n",
      "epoch   49: loss = 1853297.825385, a = 591.224784, b = 148.637763\n",
      "epoch   50: loss = 1848469.587337, a = 598.039110, b = 148.635417\n",
      "epoch   51: loss = 1843827.016840, a = 604.718609, b = 148.633117\n",
      "epoch   52: loss = 1839362.908723, a = 611.265949, b = 148.630862\n",
      "epoch   53: loss = 1835070.338746, a = 617.683744, b = 148.628653\n",
      "epoch   54: loss = 1830942.652617, a = 623.974558, b = 148.626486\n",
      "epoch   55: loss = 1826973.455442, a = 630.140902, b = 148.624363\n",
      "epoch   56: loss = 1823156.601589, a = 636.185240, b = 148.622282\n",
      "epoch   57: loss = 1819486.184948, a = 642.109985, b = 148.620242\n",
      "epoch   58: loss = 1815956.529568, a = 647.917504, b = 148.618242\n",
      "epoch   59: loss = 1812562.180670, a = 653.610117, b = 148.616282\n",
      "epoch   60: loss = 1809297.895998, a = 659.190096, b = 148.614361\n",
      "epoch   61: loss = 1806158.637522, a = 664.659671, b = 148.612477\n",
      "epoch   62: loss = 1803139.563458, a = 670.021025, b = 148.610631\n",
      "epoch   63: loss = 1800236.020598, a = 675.276301, b = 148.608822\n",
      "epoch   64: loss = 1797443.536950, a = 680.427596, b = 148.607048\n",
      "epoch   65: loss = 1794757.814654, a = 685.476969, b = 148.605309\n",
      "epoch   66: loss = 1792174.723185, a = 690.426435, b = 148.603605\n",
      "epoch   67: loss = 1789690.292815, a = 695.277972, b = 148.601934\n",
      "epoch   68: loss = 1787300.708335, a = 700.033517, b = 148.600297\n",
      "epoch   69: loss = 1785002.303019, a = 704.694970, b = 148.598692\n",
      "epoch   70: loss = 1782791.552830, a = 709.264191, b = 148.597119\n",
      "epoch   71: loss = 1780665.070844, a = 713.743007, b = 148.595576\n",
      "epoch   72: loss = 1778619.601901, a = 718.133206, b = 148.594065\n",
      "epoch   73: loss = 1776652.017457, a = 722.436540, b = 148.592583\n",
      "epoch   74: loss = 1774759.310646, a = 726.654730, b = 148.591130\n",
      "epoch   75: loss = 1772938.591527, a = 730.789459, b = 148.589707\n",
      "epoch   76: loss = 1771187.082519, a = 734.842379, b = 148.588311\n",
      "epoch   77: loss = 1769502.114022, a = 738.815108, b = 148.586943\n",
      "epoch   78: loss = 1767881.120197, a = 742.709234, b = 148.585602\n",
      "epoch   79: loss = 1766321.634920, a = 746.526311, b = 148.584288\n",
      "epoch   80: loss = 1764821.287889, a = 750.267864, b = 148.583000\n",
      "epoch   81: loss = 1763377.800890, a = 753.935387, b = 148.581737\n",
      "epoch   82: loss = 1761988.984199, a = 757.530345, b = 148.580499\n",
      "epoch   83: loss = 1760652.733134, a = 761.054173, b = 148.579286\n",
      "epoch   84: loss = 1759367.024737, a = 764.508280, b = 148.578096\n",
      "epoch   85: loss = 1758129.914584, a = 767.894044, b = 148.576931\n",
      "epoch   86: loss = 1756939.533728, a = 771.212818, b = 148.575788\n",
      "epoch   87: loss = 1755794.085750, a = 774.465927, b = 148.574668\n",
      "epoch   88: loss = 1754691.843935, a = 777.654671, b = 148.573570\n",
      "epoch   89: loss = 1753631.148552, a = 780.780322, b = 148.572493\n",
      "epoch   90: loss = 1752610.404243, a = 783.844130, b = 148.571438\n",
      "epoch   91: loss = 1751628.077518, a = 786.847318, b = 148.570404\n",
      "epoch   92: loss = 1750682.694337, a = 789.791085, b = 148.569391\n",
      "epoch   93: loss = 1749772.837797, a = 792.676607, b = 148.568397\n",
      "epoch   94: loss = 1748897.145906, a = 795.505037, b = 148.567423\n",
      "epoch   95: loss = 1748054.309442, a = 798.277504, b = 148.566469\n",
      "epoch   96: loss = 1747243.069899, a = 800.995115, b = 148.565533\n",
      "epoch   97: loss = 1746462.217508, a = 803.658956, b = 148.564616\n",
      "epoch   98: loss = 1745710.589343, a = 806.270090, b = 148.563716\n",
      "epoch   99: loss = 1744987.067493, a = 808.829561, b = 148.562835\n",
      "epoch  100: loss = 1744290.577312, a = 811.338391, b = 148.561971\n",
      "epoch  101: loss = 1743620.085732, a = 813.797581, b = 148.561125\n",
      "epoch  102: loss = 1742974.599648, a = 816.208114, b = 148.560295\n",
      "epoch  103: loss = 1742353.164357, a = 818.570953, b = 148.559481\n",
      "epoch  104: loss = 1741754.862068, a = 820.887041, b = 148.558683\n",
      "epoch  105: loss = 1741178.810465, a = 823.157303, b = 148.557902\n",
      "epoch  106: loss = 1740624.161324, a = 825.382646, b = 148.557135\n",
      "epoch  107: loss = 1740090.099189, a = 827.563959, b = 148.556384\n",
      "epoch  108: loss = 1739575.840097, a = 829.702112, b = 148.555648\n",
      "epoch  109: loss = 1739080.630352, a = 831.797961, b = 148.554926\n",
      "epoch  110: loss = 1738603.745351, a = 833.852341, b = 148.554219\n",
      "epoch  111: loss = 1738144.488447, a = 835.866073, b = 148.553526\n",
      "epoch  112: loss = 1737702.189871, a = 837.839962, b = 148.552846\n",
      "epoch  113: loss = 1737276.205677, a = 839.774796, b = 148.552180\n",
      "epoch  114: loss = 1736865.916748, a = 841.671348, b = 148.551527\n",
      "epoch  115: loss = 1736470.727823, a = 843.530375, b = 148.550887\n",
      "epoch  116: loss = 1736090.066576, a = 845.352619, b = 148.550259\n",
      "epoch  117: loss = 1735723.382723, a = 847.138809, b = 148.549644\n",
      "epoch  118: loss = 1735370.147167, a = 848.889657, b = 148.549041\n",
      "epoch  119: loss = 1735029.851171, a = 850.605863, b = 148.548450\n",
      "epoch  120: loss = 1734702.005574, a = 852.288113, b = 148.547871\n",
      "epoch  121: loss = 1734386.140028, a = 853.937078, b = 148.547303\n",
      "epoch  122: loss = 1734081.802266, a = 855.553417, b = 148.546747\n",
      "epoch  123: loss = 1733788.557403, a = 857.137775, b = 148.546201\n",
      "epoch  124: loss = 1733505.987262, a = 858.690785, b = 148.545666\n",
      "epoch  125: loss = 1733233.689723, a = 860.213068, b = 148.545142\n",
      "epoch  126: loss = 1732971.278103, a = 861.705231, b = 148.544628\n",
      "epoch  127: loss = 1732718.380559, a = 863.167870, b = 148.544125\n",
      "epoch  128: loss = 1732474.639507, a = 864.601570, b = 148.543631\n",
      "epoch  129: loss = 1732239.711074, a = 866.006902, b = 148.543147\n",
      "epoch  130: loss = 1732013.264567, a = 867.384429, b = 148.542673\n",
      "epoch  131: loss = 1731794.981959, a = 868.734701, b = 148.542208\n",
      "epoch  132: loss = 1731584.557401, a = 870.058256, b = 148.541752\n",
      "epoch  133: loss = 1731381.696752, a = 871.355623, b = 148.541306\n",
      "epoch  134: loss = 1731186.117121, a = 872.627321, b = 148.540868\n",
      "epoch  135: loss = 1730997.546436, a = 873.873858, b = 148.540438\n",
      "epoch  136: loss = 1730815.723022, a = 875.095730, b = 148.540018\n",
      "epoch  137: loss = 1730640.395202, a = 876.293427, b = 148.539605\n",
      "epoch  138: loss = 1730471.320908, a = 877.467426, b = 148.539201\n",
      "epoch  139: loss = 1730308.267311, a = 878.618197, b = 148.538805\n",
      "epoch  140: loss = 1730151.010464, a = 879.746199, b = 148.538416\n",
      "epoch  141: loss = 1729999.334955, a = 880.851882, b = 148.538036\n",
      "epoch  142: loss = 1729853.033583, a = 881.935688, b = 148.537663\n",
      "epoch  143: loss = 1729711.907037, a = 882.998050, b = 148.537297\n",
      "epoch  144: loss = 1729575.763593, a = 884.039393, b = 148.536938\n",
      "epoch  145: loss = 1729444.418820, a = 885.060132, b = 148.536587\n",
      "epoch  146: loss = 1729317.695300, a = 886.060674, b = 148.536242\n",
      "epoch  147: loss = 1729195.422355, a = 887.041420, b = 148.535904\n",
      "epoch  148: loss = 1729077.435792, a = 888.002761, b = 148.535573\n",
      "epoch  149: loss = 1728963.577645, a = 888.945081, b = 148.535249\n",
      "epoch  150: loss = 1728853.695944, a = 889.868757, b = 148.534931\n",
      "epoch  151: loss = 1728747.644477, a = 890.774156, b = 148.534619\n",
      "epoch  152: loss = 1728645.282573, a = 891.661642, b = 148.534314\n",
      "epoch  153: loss = 1728546.474885, a = 892.531568, b = 148.534014\n",
      "epoch  154: loss = 1728451.091187, a = 893.384282, b = 148.533720\n",
      "epoch  155: loss = 1728359.006178, a = 894.220124, b = 148.533433\n",
      "epoch  156: loss = 1728270.099288, a = 895.039428, b = 148.533150\n",
      "epoch  157: loss = 1728184.254503, a = 895.842521, b = 148.532874\n",
      "epoch  158: loss = 1728101.360185, a = 896.629725, b = 148.532603\n",
      "epoch  159: loss = 1728021.308903, a = 897.401353, b = 148.532337\n",
      "epoch  160: loss = 1727943.997275, a = 898.157714, b = 148.532077\n",
      "epoch  161: loss = 1727869.325813, a = 898.899110, b = 148.531821\n",
      "epoch  162: loss = 1727797.198769, a = 899.625836, b = 148.531571\n",
      "epoch  163: loss = 1727727.523995, a = 900.338184, b = 148.531326\n",
      "epoch  164: loss = 1727660.212803, a = 901.036437, b = 148.531086\n",
      "epoch  165: loss = 1727595.179837, a = 901.720875, b = 148.530850\n",
      "epoch  166: loss = 1727532.342938, a = 902.391770, b = 148.530619\n",
      "epoch  167: loss = 1727471.623027, a = 903.049391, b = 148.530392\n",
      "epoch  168: loss = 1727412.943986, a = 903.694001, b = 148.530170\n",
      "epoch  169: loss = 1727356.232544, a = 904.325856, b = 148.529953\n",
      "epoch  170: loss = 1727301.418168, a = 904.945210, b = 148.529740\n",
      "epoch  171: loss = 1727248.432959, a = 905.552309, b = 148.529531\n",
      "epoch  172: loss = 1727197.211551, a = 906.147396, b = 148.529326\n",
      "epoch  173: loss = 1727147.691014, a = 906.730709, b = 148.529125\n",
      "epoch  174: loss = 1727099.810763, a = 907.302481, b = 148.528928\n",
      "epoch  175: loss = 1727053.512464, a = 907.862939, b = 148.528735\n",
      "epoch  176: loss = 1727008.739955, a = 908.412309, b = 148.528546\n",
      "epoch  177: loss = 1726965.439156, a = 908.950808, b = 148.528360\n",
      "epoch  178: loss = 1726923.557995, a = 909.478653, b = 148.528179\n",
      "epoch  179: loss = 1726883.046328, a = 909.996055, b = 148.528000\n",
      "epoch  180: loss = 1726843.855869, a = 910.503219, b = 148.527826\n",
      "epoch  181: loss = 1726805.940116, a = 911.000348, b = 148.527655\n",
      "epoch  182: loss = 1726769.254286, a = 911.487641, b = 148.527487\n",
      "epoch  183: loss = 1726733.755249, a = 911.965292, b = 148.527322\n",
      "epoch  184: loss = 1726699.401462, a = 912.433493, b = 148.527161\n",
      "epoch  185: loss = 1726666.152915, a = 912.892430, b = 148.527003\n",
      "epoch  186: loss = 1726633.971067, a = 913.342287, b = 148.526848\n",
      "epoch  187: loss = 1726602.818794, a = 913.783243, b = 148.526696\n",
      "epoch  188: loss = 1726572.660334, a = 914.215474, b = 148.526548\n",
      "epoch  189: loss = 1726543.461235, a = 914.639153, b = 148.526402\n",
      "epoch  190: loss = 1726515.188306, a = 915.054449, b = 148.526259\n",
      "epoch  191: loss = 1726487.809572, a = 915.461529, b = 148.526119\n",
      "epoch  192: loss = 1726461.294221, a = 915.860553, b = 148.525981\n",
      "epoch  193: loss = 1726435.612569, a = 916.251683, b = 148.525846\n",
      "epoch  194: loss = 1726410.736010, a = 916.635074, b = 148.525714\n",
      "epoch  195: loss = 1726386.636980, a = 917.010879, b = 148.525585\n",
      "epoch  196: loss = 1726363.288915, a = 917.379249, b = 148.525458\n",
      "epoch  197: loss = 1726340.666217, a = 917.740330, b = 148.525334\n",
      "epoch  198: loss = 1726318.744212, a = 918.094267, b = 148.525212\n",
      "epoch  199: loss = 1726297.499121, a = 918.441201, b = 148.525093\n",
      "epoch  200: loss = 1726276.908024, a = 918.781270, b = 148.524975\n",
      "epoch  201: loss = 1726256.948827, a = 919.114611, b = 148.524861\n",
      "epoch  202: loss = 1726237.600231, a = 919.441356, b = 148.524748\n",
      "epoch  203: loss = 1726218.841703, a = 919.761637, b = 148.524638\n",
      "epoch  204: loss = 1726200.653451, a = 920.075580, b = 148.524530\n",
      "epoch  205: loss = 1726183.016388, a = 920.383312, b = 148.524424\n",
      "epoch  206: loss = 1726165.912113, a = 920.684955, b = 148.524320\n",
      "epoch  207: loss = 1726149.322881, a = 920.980630, b = 148.524218\n",
      "epoch  208: loss = 1726133.231583, a = 921.270455, b = 148.524118\n",
      "epoch  209: loss = 1726117.621717, a = 921.554545, b = 148.524021\n",
      "epoch  210: loss = 1726102.477370, a = 921.833014, b = 148.523925\n",
      "epoch  211: loss = 1726087.783192, a = 922.105974, b = 148.523831\n",
      "epoch  212: loss = 1726073.524378, a = 922.373533, b = 148.523739\n",
      "epoch  213: loss = 1726059.686650, a = 922.635798, b = 148.523648\n",
      "epoch  214: loss = 1726046.256229, a = 922.892873, b = 148.523560\n",
      "epoch  215: loss = 1726033.219826, a = 923.144863, b = 148.523473\n",
      "epoch  216: loss = 1726020.564620, a = 923.391866, b = 148.523388\n",
      "epoch  217: loss = 1726008.278237, a = 923.633982, b = 148.523305\n",
      "epoch  218: loss = 1725996.348741, a = 923.871308, b = 148.523223\n",
      "epoch  219: loss = 1725984.764612, a = 924.103938, b = 148.523143\n",
      "epoch  220: loss = 1725973.514733, a = 924.331966, b = 148.523064\n",
      "epoch  221: loss = 1725962.588374, a = 924.555481, b = 148.522987\n",
      "epoch  222: loss = 1725951.975181, a = 924.774575, b = 148.522912\n",
      "epoch  223: loss = 1725941.665156, a = 924.989333, b = 148.522838\n",
      "epoch  224: loss = 1725931.648652, a = 925.199842, b = 148.522765\n",
      "epoch  225: loss = 1725921.916352, a = 925.406186, b = 148.522694\n",
      "epoch  226: loss = 1725912.459264, a = 925.608447, b = 148.522625\n",
      "epoch  227: loss = 1725903.268703, a = 925.806706, b = 148.522556\n",
      "epoch  228: loss = 1725894.336285, a = 926.001043, b = 148.522489\n",
      "epoch  229: loss = 1725885.653913, a = 926.191534, b = 148.522424\n",
      "epoch  230: loss = 1725877.213768, a = 926.378257, b = 148.522360\n",
      "epoch  231: loss = 1725869.008296, a = 926.561285, b = 148.522297\n",
      "epoch  232: loss = 1725861.030202, a = 926.740692, b = 148.522235\n",
      "epoch  233: loss = 1725853.272442, a = 926.916548, b = 148.522174\n",
      "epoch  234: loss = 1725845.728205, a = 927.088926, b = 148.522115\n",
      "epoch  235: loss = 1725838.390917, a = 927.257893, b = 148.522057\n",
      "epoch  236: loss = 1725831.254223, a = 927.423516, b = 148.522000\n",
      "epoch  237: loss = 1725824.311982, a = 927.585863, b = 148.521944\n",
      "epoch  238: loss = 1725817.558260, a = 927.744997, b = 148.521889\n",
      "epoch  239: loss = 1725810.987324, a = 927.900983, b = 148.521835\n",
      "epoch  240: loss = 1725804.593630, a = 928.053883, b = 148.521783\n",
      "epoch  241: loss = 1725798.371821, a = 928.203757, b = 148.521731\n",
      "epoch  242: loss = 1725792.316718, a = 928.350666, b = 148.521680\n",
      "epoch  243: loss = 1725786.423315, a = 928.494668, b = 148.521631\n",
      "epoch  244: loss = 1725780.686770, a = 928.635821, b = 148.521582\n",
      "epoch  245: loss = 1725775.102403, a = 928.774181, b = 148.521535\n",
      "epoch  246: loss = 1725769.665688, a = 928.909804, b = 148.521488\n",
      "epoch  247: loss = 1725764.372248, a = 929.042743, b = 148.521442\n",
      "epoch  248: loss = 1725759.217848, a = 929.173052, b = 148.521397\n",
      "epoch  249: loss = 1725754.198393, a = 929.300783, b = 148.521353\n",
      "epoch  250: loss = 1725749.309922, a = 929.425986, b = 148.521310\n",
      "epoch  251: loss = 1725744.548603, a = 929.548712, b = 148.521268\n",
      "epoch  252: loss = 1725739.910728, a = 929.669010, b = 148.521226\n",
      "epoch  253: loss = 1725735.392708, a = 929.786928, b = 148.521186\n",
      "epoch  254: loss = 1725730.991072, a = 929.902512, b = 148.521146\n",
      "epoch  255: loss = 1725726.702459, a = 930.015810, b = 148.521107\n",
      "epoch  256: loss = 1725722.523617, a = 930.126866, b = 148.521069\n",
      "epoch  257: loss = 1725718.451397, a = 930.235724, b = 148.521031\n",
      "epoch  258: loss = 1725714.482753, a = 930.342429, b = 148.520995\n",
      "epoch  259: loss = 1725710.614734, a = 930.447022, b = 148.520959\n",
      "epoch  260: loss = 1725706.844482, a = 930.549546, b = 148.520923\n",
      "epoch  261: loss = 1725703.169232, a = 930.650042, b = 148.520889\n",
      "epoch  262: loss = 1725699.586303, a = 930.748549, b = 148.520855\n",
      "epoch  263: loss = 1725696.093102, a = 930.845107, b = 148.520822\n",
      "epoch  264: loss = 1725692.687115, a = 930.939754, b = 148.520789\n",
      "epoch  265: loss = 1725689.365908, a = 931.032529, b = 148.520757\n",
      "epoch  266: loss = 1725686.127121, a = 931.123468, b = 148.520726\n",
      "epoch  267: loss = 1725682.968469, a = 931.212608, b = 148.520695\n",
      "epoch  268: loss = 1725679.887739, a = 931.299985, b = 148.520665\n",
      "epoch  269: loss = 1725676.882782, a = 931.385632, b = 148.520635\n",
      "epoch  270: loss = 1725673.951521, a = 931.469585, b = 148.520606\n",
      "epoch  271: loss = 1725671.091938, a = 931.551877, b = 148.520578\n",
      "epoch  272: loss = 1725668.302080, a = 931.632540, b = 148.520550\n",
      "epoch  273: loss = 1725665.580052, a = 931.711608, b = 148.520523\n",
      "epoch  274: loss = 1725662.924017, a = 931.789111, b = 148.520496\n",
      "epoch  275: loss = 1725660.332194, a = 931.865080, b = 148.520470\n",
      "epoch  276: loss = 1725657.802855, a = 931.939547, b = 148.520445\n",
      "epoch  277: loss = 1725655.334325, a = 932.012540, b = 148.520420\n",
      "epoch  278: loss = 1725652.924980, a = 932.084089, b = 148.520395\n",
      "epoch  279: loss = 1725650.573243, a = 932.154222, b = 148.520371\n",
      "epoch  280: loss = 1725648.277584, a = 932.222968, b = 148.520347\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch  281: loss = 1725646.036521, a = 932.290353, b = 148.520324\n",
      "epoch  282: loss = 1725643.848614, a = 932.356405, b = 148.520301\n",
      "epoch  283: loss = 1725641.712465, a = 932.421150, b = 148.520279\n",
      "epoch  284: loss = 1725639.626719, a = 932.484614, b = 148.520257\n",
      "epoch  285: loss = 1725637.590060, a = 932.546823, b = 148.520236\n",
      "epoch  286: loss = 1725635.601209, a = 932.607801, b = 148.520215\n",
      "epoch  287: loss = 1725633.658927, a = 932.667572, b = 148.520194\n",
      "epoch  288: loss = 1725631.762010, a = 932.726160, b = 148.520174\n",
      "epoch  289: loss = 1725629.909289, a = 932.783590, b = 148.520154\n",
      "epoch  290: loss = 1725628.099627, a = 932.839883, b = 148.520135\n",
      "epoch  291: loss = 1725626.331922, a = 932.895062, b = 148.520116\n",
      "epoch  292: loss = 1725624.605102, a = 932.949149, b = 148.520097\n",
      "epoch  293: loss = 1725622.918128, a = 933.002166, b = 148.520079\n",
      "epoch  294: loss = 1725621.269989, a = 933.054135, b = 148.520061\n",
      "epoch  295: loss = 1725619.659702, a = 933.105075, b = 148.520043\n",
      "epoch  296: loss = 1725618.086312, a = 933.155007, b = 148.520026\n",
      "epoch  297: loss = 1725616.548894, a = 933.203951, b = 148.520009\n",
      "epoch  298: loss = 1725615.046544, a = 933.251927, b = 148.519993\n",
      "epoch  299: loss = 1725613.578388, a = 933.298953, b = 148.519977\n",
      "epoch  300: loss = 1725612.143573, a = 933.345050, b = 148.519961\n",
      "epoch  301: loss = 1725610.741272, a = 933.390234, b = 148.519945\n",
      "epoch  302: loss = 1725609.370679, a = 933.434524, b = 148.519930\n",
      "epoch  303: loss = 1725608.031013, a = 933.477937, b = 148.519915\n",
      "epoch  304: loss = 1725606.721512, a = 933.520492, b = 148.519900\n",
      "epoch  305: loss = 1725605.441435, a = 933.562205, b = 148.519886\n",
      "epoch  306: loss = 1725604.190064, a = 933.603092, b = 148.519872\n",
      "epoch  307: loss = 1725602.966697, a = 933.643171, b = 148.519858\n",
      "epoch  308: loss = 1725601.770653, a = 933.682456, b = 148.519845\n",
      "epoch  309: loss = 1725600.601270, a = 933.720964, b = 148.519831\n",
      "epoch  310: loss = 1725599.457903, a = 933.758711, b = 148.519818\n",
      "epoch  311: loss = 1725598.339923, a = 933.795710, b = 148.519806\n",
      "epoch  312: loss = 1725597.246722, a = 933.831977, b = 148.519793\n",
      "epoch  313: loss = 1725596.177703, a = 933.867527, b = 148.519781\n",
      "epoch  314: loss = 1725595.132289, a = 933.902373, b = 148.519769\n",
      "epoch  315: loss = 1725594.109917, a = 933.936530, b = 148.519757\n",
      "epoch  316: loss = 1725593.110038, a = 933.970011, b = 148.519746\n",
      "epoch  317: loss = 1725592.132118, a = 934.002830, b = 148.519734\n",
      "epoch  318: loss = 1725591.175638, a = 934.034999, b = 148.519723\n",
      "epoch  319: loss = 1725590.240092, a = 934.066532, b = 148.519712\n",
      "epoch  320: loss = 1725589.324986, a = 934.097441, b = 148.519702\n",
      "epoch  321: loss = 1725588.429841, a = 934.127738, b = 148.519691\n",
      "epoch  322: loss = 1725587.554189, a = 934.157436, b = 148.519681\n",
      "epoch  323: loss = 1725586.697574, a = 934.186546, b = 148.519671\n",
      "epoch  324: loss = 1725585.859554, a = 934.215081, b = 148.519661\n",
      "epoch  325: loss = 1725585.039694, a = 934.243051, b = 148.519651\n",
      "epoch  326: loss = 1725584.237575, a = 934.270467, b = 148.519642\n",
      "epoch  327: loss = 1725583.452786, a = 934.297341, b = 148.519633\n",
      "epoch  328: loss = 1725582.684926, a = 934.323683, b = 148.519624\n",
      "epoch  329: loss = 1725581.933606, a = 934.349504, b = 148.519615\n",
      "epoch  330: loss = 1725581.198445, a = 934.374814, b = 148.519606\n",
      "epoch  331: loss = 1725580.479074, a = 934.399623, b = 148.519598\n",
      "epoch  332: loss = 1725579.775131, a = 934.423941, b = 148.519589\n",
      "epoch  333: loss = 1725579.086264, a = 934.447779, b = 148.519581\n",
      "epoch  334: loss = 1725578.412130, a = 934.471144, b = 148.519573\n",
      "epoch  335: loss = 1725577.752394, a = 934.494048, b = 148.519565\n",
      "epoch  336: loss = 1725577.106730, a = 934.516498, b = 148.519557\n",
      "epoch  337: loss = 1725576.474819, a = 934.538504, b = 148.519550\n",
      "epoch  338: loss = 1725575.856351, a = 934.560074, b = 148.519542\n",
      "epoch  339: loss = 1725575.251023, a = 934.581218, b = 148.519535\n",
      "epoch  340: loss = 1725574.658540, a = 934.601943, b = 148.519528\n",
      "epoch  341: loss = 1725574.078613, a = 934.622259, b = 148.519521\n",
      "epoch  342: loss = 1725573.510962, a = 934.642172, b = 148.519514\n",
      "epoch  343: loss = 1725572.955312, a = 934.661691, b = 148.519507\n",
      "epoch  344: loss = 1725572.411396, a = 934.680825, b = 148.519501\n",
      "epoch  345: loss = 1725571.878952, a = 934.699579, b = 148.519494\n",
      "epoch  346: loss = 1725571.357726, a = 934.717963, b = 148.519488\n",
      "epoch  347: loss = 1725570.847468, a = 934.735982, b = 148.519482\n",
      "epoch  348: loss = 1725570.347937, a = 934.753646, b = 148.519476\n",
      "epoch  349: loss = 1725569.858895, a = 934.770959, b = 148.519470\n",
      "epoch  350: loss = 1725569.380112, a = 934.787931, b = 148.519464\n",
      "epoch  351: loss = 1725568.911360, a = 934.804566, b = 148.519458\n",
      "epoch  352: loss = 1725568.452420, a = 934.820872, b = 148.519453\n",
      "epoch  353: loss = 1725568.003077, a = 934.836856, b = 148.519447\n",
      "epoch  354: loss = 1725567.563120, a = 934.852523, b = 148.519442\n",
      "epoch  355: loss = 1725567.132345, a = 934.867881, b = 148.519436\n",
      "epoch  356: loss = 1725566.710551, a = 934.882934, b = 148.519431\n",
      "epoch  357: loss = 1725566.297542, a = 934.897690, b = 148.519426\n",
      "epoch  358: loss = 1725565.893128, a = 934.912154, b = 148.519421\n",
      "epoch  359: loss = 1725565.497121, a = 934.926331, b = 148.519416\n",
      "epoch  360: loss = 1725565.109340, a = 934.940228, b = 148.519411\n",
      "epoch  361: loss = 1725564.729607, a = 934.953850, b = 148.519407\n",
      "epoch  362: loss = 1725564.357747, a = 934.967203, b = 148.519402\n",
      "epoch  363: loss = 1725563.993590, a = 934.980291, b = 148.519398\n",
      "epoch  364: loss = 1725563.636972, a = 934.993120, b = 148.519393\n",
      "epoch  365: loss = 1725563.287729, a = 935.005696, b = 148.519389\n",
      "epoch  366: loss = 1725562.945702, a = 935.018023, b = 148.519385\n",
      "epoch  367: loss = 1725562.610739, a = 935.030106, b = 148.519380\n",
      "epoch  368: loss = 1725562.282686, a = 935.041949, b = 148.519376\n",
      "epoch  369: loss = 1725561.961396, a = 935.053559, b = 148.519372\n",
      "epoch  370: loss = 1725561.646724, a = 935.064938, b = 148.519368\n",
      "epoch  371: loss = 1725561.338531, a = 935.076093, b = 148.519365\n",
      "epoch  372: loss = 1725561.036676, a = 935.087027, b = 148.519361\n",
      "epoch  373: loss = 1725560.741026, a = 935.097744, b = 148.519357\n",
      "epoch  374: loss = 1725560.451449, a = 935.108250, b = 148.519354\n",
      "epoch  375: loss = 1725560.167816, a = 935.118547, b = 148.519350\n",
      "epoch  376: loss = 1725559.890000, a = 935.128641, b = 148.519347\n",
      "epoch  377: loss = 1725559.617879, a = 935.138535, b = 148.519343\n",
      "epoch  378: loss = 1725559.351332, a = 935.148234, b = 148.519340\n",
      "epoch  379: loss = 1725559.090241, a = 935.157740, b = 148.519337\n",
      "epoch  380: loss = 1725558.834492, a = 935.167059, b = 148.519333\n",
      "epoch  381: loss = 1725558.583972, a = 935.176193, b = 148.519330\n",
      "epoch  382: loss = 1725558.338570, a = 935.185146, b = 148.519327\n",
      "epoch  383: loss = 1725558.098179, a = 935.193922, b = 148.519324\n",
      "epoch  384: loss = 1725557.862695, a = 935.202525, b = 148.519321\n",
      "epoch  385: loss = 1725557.632013, a = 935.210957, b = 148.519318\n",
      "epoch  386: loss = 1725557.406033, a = 935.219223, b = 148.519315\n",
      "epoch  387: loss = 1725557.184657, a = 935.227324, b = 148.519313\n",
      "epoch  388: loss = 1725556.967789, a = 935.235266, b = 148.519310\n",
      "epoch  389: loss = 1725556.755334, a = 935.243051, b = 148.519307\n",
      "epoch  390: loss = 1725556.547200, a = 935.250681, b = 148.519305\n",
      "epoch  391: loss = 1725556.343298, a = 935.258160, b = 148.519302\n",
      "epoch  392: loss = 1725556.143538, a = 935.265492, b = 148.519299\n",
      "epoch  393: loss = 1725555.947836, a = 935.272678, b = 148.519297\n",
      "epoch  394: loss = 1725555.756105, a = 935.279723, b = 148.519295\n",
      "epoch  395: loss = 1725555.568265, a = 935.286628, b = 148.519292\n",
      "epoch  396: loss = 1725555.384233, a = 935.293396, b = 148.519290\n",
      "epoch  397: loss = 1725555.203932, a = 935.300030, b = 148.519288\n",
      "epoch  398: loss = 1725555.027283, a = 935.306533, b = 148.519285\n",
      "epoch  399: loss = 1725554.854212, a = 935.312908, b = 148.519283\n",
      "epoch  400: loss = 1725554.684644, a = 935.319156, b = 148.519281\n",
      "epoch  401: loss = 1725554.518507, a = 935.325281, b = 148.519279\n",
      "epoch  402: loss = 1725554.355730, a = 935.331284, b = 148.519277\n",
      "epoch  403: loss = 1725554.196244, a = 935.337169, b = 148.519275\n",
      "epoch  404: loss = 1725554.039980, a = 935.342937, b = 148.519273\n",
      "epoch  405: loss = 1725553.886873, a = 935.348591, b = 148.519271\n",
      "epoch  406: loss = 1725553.736857, a = 935.354133, b = 148.519269\n",
      "epoch  407: loss = 1725553.589869, a = 935.359566, b = 148.519267\n",
      "epoch  408: loss = 1725553.445846, a = 935.364891, b = 148.519265\n",
      "epoch  409: loss = 1725553.304728, a = 935.370111, b = 148.519263\n",
      "epoch  410: loss = 1725553.166456, a = 935.375227, b = 148.519262\n",
      "epoch  411: loss = 1725553.030969, a = 935.380242, b = 148.519260\n",
      "epoch  412: loss = 1725552.898213, a = 935.385158, b = 148.519258\n",
      "epoch  413: loss = 1725552.768130, a = 935.389977, b = 148.519257\n",
      "epoch  414: loss = 1725552.640666, a = 935.394701, b = 148.519255\n",
      "epoch  415: loss = 1725552.515767, a = 935.399331, b = 148.519253\n",
      "epoch  416: loss = 1725552.393381, a = 935.403869, b = 148.519252\n",
      "epoch  417: loss = 1725552.273456, a = 935.408317, b = 148.519250\n",
      "epoch  418: loss = 1725552.155943, a = 935.412678, b = 148.519249\n",
      "epoch  419: loss = 1725552.040792, a = 935.416952, b = 148.519247\n",
      "epoch  420: loss = 1725551.927954, a = 935.421142, b = 148.519246\n",
      "epoch  421: loss = 1725551.817384, a = 935.425249, b = 148.519244\n",
      "epoch  422: loss = 1725551.709033, a = 935.429274, b = 148.519243\n",
      "epoch  423: loss = 1725551.602858, a = 935.433220, b = 148.519242\n",
      "epoch  424: loss = 1725551.498814, a = 935.437088, b = 148.519240\n",
      "epoch  425: loss = 1725551.396858, a = 935.440879, b = 148.519239\n",
      "epoch  426: loss = 1725551.296947, a = 935.444595, b = 148.519238\n",
      "epoch  427: loss = 1725551.199039, a = 935.448238, b = 148.519237\n",
      "epoch  428: loss = 1725551.103094, a = 935.451809, b = 148.519235\n",
      "epoch  429: loss = 1725551.009073, a = 935.455309, b = 148.519234\n",
      "epoch  430: loss = 1725550.916935, a = 935.458739, b = 148.519233\n",
      "epoch  431: loss = 1725550.826644, a = 935.462102, b = 148.519232\n",
      "epoch  432: loss = 1725550.738161, a = 935.465399, b = 148.519231\n",
      "epoch  433: loss = 1725550.651449, a = 935.468630, b = 148.519229\n",
      "epoch  434: loss = 1725550.566474, a = 935.471797, b = 148.519228\n",
      "epoch  435: loss = 1725550.483199, a = 935.474901, b = 148.519227\n",
      "epoch  436: loss = 1725550.401591, a = 935.477945, b = 148.519226\n",
      "epoch  437: loss = 1725550.321615, a = 935.480927, b = 148.519225\n",
      "epoch  438: loss = 1725550.243239, a = 935.483851, b = 148.519224\n",
      "epoch  439: loss = 1725550.166431, a = 935.486717, b = 148.519223\n",
      "epoch  440: loss = 1725550.091158, a = 935.489527, b = 148.519222\n",
      "epoch  441: loss = 1725550.017389, a = 935.492280, b = 148.519221\n",
      "epoch  442: loss = 1725549.945095, a = 935.494980, b = 148.519220\n",
      "epoch  443: loss = 1725549.874246, a = 935.497625, b = 148.519219\n",
      "epoch  444: loss = 1725549.804812, a = 935.500219, b = 148.519219\n",
      "epoch  445: loss = 1725549.736765, a = 935.502761, b = 148.519218\n",
      "epoch  446: loss = 1725549.670077, a = 935.505253, b = 148.519217\n",
      "epoch  447: loss = 1725549.604720, a = 935.507696, b = 148.519216\n",
      "epoch  448: loss = 1725549.540668, a = 935.510090, b = 148.519215\n",
      "epoch  449: loss = 1725549.477894, a = 935.512437, b = 148.519214\n",
      "epoch  450: loss = 1725549.416373, a = 935.514737, b = 148.519214\n",
      "epoch  451: loss = 1725549.356080, a = 935.516992, b = 148.519213\n",
      "epoch  452: loss = 1725549.296990, a = 935.519202, b = 148.519212\n",
      "epoch  453: loss = 1725549.239078, a = 935.521369, b = 148.519211\n",
      "epoch  454: loss = 1725549.182321, a = 935.523493, b = 148.519211\n",
      "epoch  455: loss = 1725549.126696, a = 935.525574, b = 148.519210\n",
      "epoch  456: loss = 1725549.072179, a = 935.527615, b = 148.519209\n",
      "epoch  457: loss = 1725549.018750, a = 935.529615, b = 148.519208\n",
      "epoch  458: loss = 1725548.966385, a = 935.531575, b = 148.519208\n",
      "epoch  459: loss = 1725548.915064, a = 935.533497, b = 148.519207\n",
      "epoch  460: loss = 1725548.864766, a = 935.535381, b = 148.519206\n",
      "epoch  461: loss = 1725548.815470, a = 935.537227, b = 148.519206\n",
      "epoch  462: loss = 1725548.767155, a = 935.539037, b = 148.519205\n",
      "epoch  463: loss = 1725548.719803, a = 935.540811, b = 148.519205\n",
      "epoch  464: loss = 1725548.673394, a = 935.542550, b = 148.519204\n",
      "epoch  465: loss = 1725548.627910, a = 935.544255, b = 148.519203\n",
      "epoch  466: loss = 1725548.583330, a = 935.545926, b = 148.519203\n",
      "epoch  467: loss = 1725548.539638, a = 935.547564, b = 148.519202\n",
      "epoch  468: loss = 1725548.496816, a = 935.549169, b = 148.519202\n",
      "epoch  469: loss = 1725548.454846, a = 935.550743, b = 148.519201\n",
      "epoch  470: loss = 1725548.413712, a = 935.552285, b = 148.519201\n",
      "epoch  471: loss = 1725548.373396, a = 935.553797, b = 148.519200\n",
      "epoch  472: loss = 1725548.333882, a = 935.555279, b = 148.519200\n",
      "epoch  473: loss = 1725548.295154, a = 935.556732, b = 148.519199\n",
      "epoch  474: loss = 1725548.257196, a = 935.558156, b = 148.519199\n",
      "epoch  475: loss = 1725548.219993, a = 935.559552, b = 148.519198\n",
      "epoch  476: loss = 1725548.183531, a = 935.560920, b = 148.519198\n",
      "epoch  477: loss = 1725548.147793, a = 935.562261, b = 148.519197\n",
      "epoch  478: loss = 1725548.112766, a = 935.563576, b = 148.519197\n",
      "epoch  479: loss = 1725548.078435, a = 935.564864, b = 148.519196\n",
      "epoch  480: loss = 1725548.044787, a = 935.566128, b = 148.519196\n",
      "epoch  481: loss = 1725548.011808, a = 935.567366, b = 148.519195\n",
      "epoch  482: loss = 1725547.979484, a = 935.568579, b = 148.519195\n",
      "epoch  483: loss = 1725547.947802, a = 935.569769, b = 148.519195\n",
      "epoch  484: loss = 1725547.916751, a = 935.570935, b = 148.519194\n",
      "epoch  485: loss = 1725547.886316, a = 935.572078, b = 148.519194\n",
      "epoch  486: loss = 1725547.856486, a = 935.573198, b = 148.519193\n",
      "epoch  487: loss = 1725547.827248, a = 935.574296, b = 148.519193\n",
      "epoch  488: loss = 1725547.798592, a = 935.575373, b = 148.519193\n",
      "epoch  489: loss = 1725547.770504, a = 935.576428, b = 148.519192\n",
      "epoch  490: loss = 1725547.742975, a = 935.577462, b = 148.519192\n",
      "epoch  491: loss = 1725547.715992, a = 935.578476, b = 148.519192\n",
      "epoch  492: loss = 1725547.689545, a = 935.579470, b = 148.519191\n",
      "epoch  493: loss = 1725547.663624, a = 935.580444, b = 148.519191\n",
      "epoch  494: loss = 1725547.638217, a = 935.581399, b = 148.519191\n",
      "epoch  495: loss = 1725547.613314, a = 935.582335, b = 148.519190\n",
      "epoch  496: loss = 1725547.588906, a = 935.583252, b = 148.519190\n",
      "epoch  497: loss = 1725547.564983, a = 935.584152, b = 148.519190\n",
      "epoch  498: loss = 1725547.541534, a = 935.585033, b = 148.519189\n",
      "epoch  499: loss = 1725547.518551, a = 935.585897, b = 148.519189\n"
     ]
    },
    {
     "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": [
    "n_epoch = 500          # epoch size\n",
    "a, b = 1, 1             # initial parameters\n",
    "epsilon = 0.01         # learning rate\n",
    "\n",
    "for i in range(n_epoch):\n",
    "    for j in range(N):\n",
    "        a = a + epsilon*2*(Y[j] - a*X[j] - b)*X[j]\n",
    "        b = b + epsilon*2*(Y[j] - a*X[j] - b)\n",
    "\n",
    "    L = 0\n",
    "    for j in range(N):\n",
    "        L = L + (Y[j]-a*X[j]-b)**2\n",
    "    print(\"epoch %4d: loss = %f, a = %f, b = %f\" % (i, L, a, b))\n",
    "    \n",
    "x_min = np.min(X)\n",
    "x_max = np.max(X)\n",
    "y_min = a * x_min + b\n",
    "y_max = a * x_max + b\n",
    "\n",
    "plt.scatter(X, Y, label='original data')\n",
    "plt.plot([x_min, x_max], [y_min, y_max], 'r', label='model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 如何可视化迭代过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [