linear_regression_project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 欢迎来到线性回归项目\n",
    "\n",
    "若项目中的题目有困难没完成也没关系，我们鼓励你带着问题提交项目，评审人会给予你诸多帮助。\n",
    "\n",
    "所有选做题都可以不做，不影响项目通过。如果你做了，那么项目评审会帮你批改，也会因为选做部分做错而判定为不通过。\n",
    "\n",
    "其中非代码题可以提交手写后扫描的 pdf 文件，或使用 Latex 在文档中直接回答。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 目录:\n",
    "[1 矩阵运算](#1-矩阵运算)  \n",
    "[2 Gaussian Jordan 消元法](#2-Gaussian-Jordan-消元法)  \n",
    "[3  线性回归](#3-线性回归)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 任意选一个你喜欢的整数，这能帮你得到稳定的结果\n",
    "seed = 9090"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 矩阵运算\n",
    "\n",
    "## 1.1 创建一个 4*4 的单位矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 这个项目设计来帮你熟悉 python list 和线性代数\n",
    "# 你不能调用任何NumPy以及相关的科学计算库来完成作业\n",
    "\n",
    "\n",
    "# 本项目要求矩阵统一使用二维列表表示，如下：\n",
    "A = [[1,2,3], \n",
    "     [2,3,3], \n",
    "     [1,2,5]]\n",
    "\n",
    "B = [[1,2,3,5], \n",
    "     [2,3,3,5], \n",
    "     [1,2,5,1]]\n",
    "\n",
    "# 向量也用二维列表表示\n",
    "C = [[1],\n",
    "     [2],\n",
    "     [3]]\n",
    "\n",
    "# DONE 创建一个 4*4 单位矩阵\n",
    "I = [[1, 0, 0, 0], \n",
    "     [0, 1, 0, 0],\n",
    "     [0, 0, 1, 0],\n",
    "     [0, 0, 0, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 返回矩阵的行数和列数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE 返回矩阵的行数和列数\n",
    "def shape(M):\n",
    "    if M is None:\n",
    "        return (0, 0)\n",
    "    \n",
    "    row = len(M)\n",
    "    col = 0\n",
    "    \n",
    "    if(row > 0):\n",
    "        col = len(M[0])\n",
    "    \n",
    "    return (row, col)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.004s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 shape 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 每个元素四舍五入到特定小数数位"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE 每个元素四舍五入到特定小数数位\n",
    "# 直接修改参数矩阵，无返回值\n",
    "def matxRound(M, decPts=4):\n",
    "    for i in range(len(M)):\n",
    "        for j in range(len(M[i])):\n",
    "            M[i][j] = round(M[i][j], decPts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.026s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 matxRound 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_matxRound"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.4 计算矩阵的转置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE 计算矩阵的转置\n",
    "def transpose(M):\n",
    "    if M is None:\n",
    "        return None\n",
    "    \n",
    "    row, col = shape(M)\n",
    "    \n",
    "    if row > 0:\n",
    "        col = len(M[0])\n",
    "    \n",
    "    MT = list()\n",
    "    \n",
    "    for i in range(col):\n",
    "        MT_ROW = list()\n",
    "        MT.append(MT_ROW)\n",
    "        \n",
    "        for j in range(row):\n",
    "            MT_ROW.append(0)\n",
    "    \n",
    "    for i in range(len(M)):\n",
    "        for j in range(len(M[i])):\n",
    "            MT[j][i] = M[i][j]\n",
    "    \n",
    "    return MT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.025s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 transpose 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_transpose"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.5 计算矩阵乘法 AB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE 计算矩阵乘法 AB，如果无法相乘则raise ValueError\n",
    "def matxMultiply(A, B):\n",
    "    row_a, col_a = shape(A)\n",
    "    row_b, col_b = shape(B)\n",
    "    \n",
    "    if col_a != row_b:\n",
    "        raise ValueError()\n",
    "    \n",
    "    AB = list()\n",
    "    \n",
    "    for i in range(row_a):\n",
    "        R = list()\n",
    "        AB.append(R)\n",
    "        \n",
    "        for j in range(col_b):\n",
    "            R.append(0)\n",
    "            \n",
    "    for i in range(row_a):\n",
    "        for j in range(col_b):\n",
    "            for k in range(col_a):\n",
    "                AB[i][j] += A[i][k] * B[k][j]\n",
    "                \n",
    "    return AB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.145s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 matxMultiply 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_matxMultiply"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# 2 Gaussian Jordan 消元法\n",
    "\n",
    "## 2.1 构造增广矩阵\n",
    "\n",
    "$ A = \\begin{bmatrix}\n",
    "    a_{11}    & a_{12} & ... & a_{1n}\\\\\n",
    "    a_{21}    & a_{22} & ... & a_{2n}\\\\\n",
    "    a_{31}    & a_{22} & ... & a_{3n}\\\\\n",
    "    ...    & ... & ... & ...\\\\\n",
    "    a_{n1}    & a_{n2} & ... & a_{nn}\\\\\n",
    "\\end{bmatrix} , b = \\begin{bmatrix}\n",
    "    b_{1}  \\\\\n",
    "    b_{2}  \\\\\n",
    "    b_{3}  \\\\\n",
    "    ...    \\\\\n",
    "    b_{n}  \\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "返回 $ Ab = \\begin{bmatrix}\n",
    "    a_{11}    & a_{12} & ... & a_{1n} & b_{1}\\\\\n",
    "    a_{21}    & a_{22} & ... & a_{2n} & b_{2}\\\\\n",
    "    a_{31}    & a_{22} & ... & a_{3n} & b_{3}\\\\\n",
    "    ...    & ... & ... & ...& ...\\\\\n",
    "    a_{n1}    & a_{n2} & ... & a_{nn} & b_{n} \\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE 构造增广矩阵，假设A，b行数相同\n",
    "def augmentMatrix(A, b):\n",
    "    if A is None or b is None:\n",
    "        return None\n",
    "    \n",
    "    row_len = len(A)\n",
    "    AB = list()\n",
    "    \n",
    "    for i in range(row_len):\n",
    "        row = list()\n",
    "        AB.append(row)\n",
    "        \n",
    "        for j in range(len(A[i])):\n",
    "            row.append(A[i][j])\n",
    "        \n",
    "        if type(b[i]) is list:\n",
    "            row.append(b[i][0])\n",
    "        else:\n",
    "            row.append(b[i])\n",
    "    \n",
    "    return AB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.011s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 augmentMatrix 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_augmentMatrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 初等行变换\n",
    "- 交换两行\n",
    "- 把某行乘以一个非零常数\n",
    "- 把某行加上另一行的若干倍："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE r1 <---> r2\n",
    "# 直接修改参数矩阵，无返回值\n",
    "def swapRows(M, r1, r2):\n",
    "    row_len = len(M)\n",
    "    \n",
    "    if r1 < 0 or r1 >= row_len:\n",
    "        return\n",
    "    \n",
    "    if r2 < 0 or r2 >= row_len:\n",
    "        return\n",
    "    \n",
    "    col_len = len(M[0])\n",
    "    \n",
    "    for i in range(col_len):\n",
    "        tmp = M[r1][i]\n",
    "        M[r1][i] = M[r2][i]\n",
    "        M[r2][i] = tmp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.004s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 swapRows 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_swapRows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE r1 <--- r1 * scale\n",
    "# scale为0是非法输入，要求 raise ValueError\n",
    "# 直接修改参数矩阵，无返回值\n",
    "def scaleRow(M, r, scale):\n",
    "    row_len = len(M)\n",
    "    \n",
    "    if r < 0 or r >= row_len:\n",
    "        return\n",
    "    \n",
    "    if scale == 0:\n",
    "        raise ValueError()\n",
    "        \n",
    "    col_len = len(M[0])\n",
    "        \n",
    "    for i in range(col_len):\n",
    "        M[r][i] = scale * M[r][i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.003s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 scaleRow 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_scaleRow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE r1 <--- r1 + r2*scale\n",
    "# 直接修改参数矩阵，无返回值\n",
    "def addScaledRow(M, r1, r2, scale):\n",
    "    row_len = len(M)\n",
    "    \n",
    "    if r1 < 0 or r1 >= row_len:\n",
    "        return\n",
    "    \n",
    "    if r2 < 0 or r2 >= row_len:\n",
    "        return\n",
    "    \n",
    "    col_len = len(M[0])\n",
    "    \n",
    "    for i in range(col_len):\n",
    "        M[r1][i] = M[r1][i] + M[r2][i] * scale "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 0.003s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 addScaledRow 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_addScaledRow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3  Gaussian Jordan 消元法求解 Ax = b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3.1 算法\n",
    "\n",
    "步骤1 检查A，b是否行数相同\n",
    "\n",
    "步骤2 构造增广矩阵Ab\n",
    "\n",
    "步骤3 逐列转换Ab为化简行阶梯形矩阵 [中文维基链接](https://zh.wikipedia.org/wiki/%E9%98%B6%E6%A2%AF%E5%BD%A2%E7%9F%A9%E9%98%B5#.E5.8C.96.E7.AE.80.E5.90.8E.E7.9A.84-.7Bzh-hans:.E8.A1.8C.3B_zh-hant:.E5.88.97.3B.7D-.E9.98.B6.E6.A2.AF.E5.BD.A2.E7.9F.A9.E9.98.B5)\n",
    "    \n",
    "    对于Ab的每一列（最后一列除外）\n",
    "        当前列为列c\n",
    "        寻找列c中 对角线以及对角线以下所有元素（行 c~N）的绝对值的最大值\n",
    "        如果绝对值最大值为0\n",
    "            那么A为奇异矩阵，返回None (你可以在选做问题2.4中证明为什么这里A一定是奇异矩阵)\n",
    "        否则\n",
    "            使用第一个行变换，将绝对值最大值所在行交换到对角线元素所在行（行c） \n",
    "            使用第二个行变换，将列c的对角线元素缩放为1\n",
    "            多次使用第三个行变换，将列c的其他元素消为0\n",
    "            \n",
    "步骤4 返回Ab的最后一列\n",
    "\n",
    "**注：** 我们并没有按照常规方法先把矩阵转化为行阶梯形矩阵，再转换为化简行阶梯形矩阵，而是一步到位。如果你熟悉常规方法的话，可以思考一下两者的等价性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3.2 算法推演\n",
    "\n",
    "为了充分了解Gaussian Jordan消元法的计算流程，请根据Gaussian Jordan消元法，分别手动推演矩阵A为***可逆矩阵***，矩阵A为***奇异矩阵***两种情况。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 推演示例 \n",
    "\n",
    "\n",
    "$Ab = \\begin{bmatrix}\n",
    "    -7 & 5 & -1 & 1\\\\\n",
    "    1 & -3 & -8 & 1\\\\\n",
    "    -10 & -2 & 9 & 1\\end{bmatrix}$\n",
    "\n",
    "$ --> $\n",
    "$\\begin{bmatrix}\n",
    "    1 & \\frac{1}{5} & -\\frac{9}{10} & -\\frac{1}{10}\\\\\n",
    "    0 & -\\frac{16}{5} & -\\frac{71}{10} & \\frac{11}{10}\\\\\n",
    "    0 & \\frac{32}{5} & -\\frac{73}{10} & \\frac{3}{10}\\end{bmatrix}$\n",
    "\n",
    "$ --> $\n",
    "$\\begin{bmatrix}\n",
    "    1 & 0 & -\\frac{43}{64} & -\\frac{7}{64}\\\\\n",
    "    0 & 1 & -\\frac{73}{64} & \\frac{3}{64}\\\\\n",
    "    0 & 0 & -\\frac{43}{4} & \\frac{5}{4}\\end{bmatrix}$\n",
    "\n",
    "$ --> $\n",
    "$\\begin{bmatrix}\n",
    "    1 & 0 & 0 & -\\frac{3}{16}\\\\\n",
    "    0 & 1 & 0 & -\\frac{59}{688}\\\\\n",
    "    0 & 0 & 1 & -\\frac{5}{43}\\end{bmatrix}$\n",
    "    \n",
    "\n",
    "#### 推演有以下要求:\n",
    "1. 展示每一列的消元结果, 比如3*3的矩阵, 需要写三步\n",
    "2. 用分数来表示\n",
    "3. 分数不能再约分\n",
    "4. 我们已经给出了latex的语法,你只要把零改成你要的数字(或分数)即可\n",
    "5. 可以用[这个页面](http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=sys)检查你的答案(注意只是答案, 推演步骤两者算法不一致)\n",
    "\n",
    "_你可以用python的 [fractions](https://docs.python.org/2/library/fractions.html) 模块辅助你的约分_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 分数的输入方法\n",
    "(双击这个区域就能看到语法啦)  \n",
    "  \n",
    "示例一: $\\frac{n}{m}$  \n",
    "\n",
    "示例二: $-\\frac{a}{b}$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 以下开始你的尝试吧!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " -3, -2,-10 ||  1 \n",
      "  1, -1,  8 ||  1 \n",
      "  1,  2, -4 ||  1 \n"
     ]
    }
   ],
   "source": [
    "# 不要修改这里！\n",
    "from helper import *\n",
    "A = generateMatrix(3,seed,singular=False)\n",
    "b = np.ones(shape=(3,1),dtype=int) # it doesn't matter\n",
    "Ab = augmentMatrix(A.tolist(),b.tolist()) # 请确保你的增广矩阵已经写好了\n",
    "printInMatrixFormat(Ab,padding=3,truncating=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "请按照算法的步骤3，逐步推演***可逆矩阵***的变换。\n",
    "\n",
    "在下面列出每一次循环体执行之后的增广矩阵(注意使用[分数语法](#分数的输入方法))\n",
    "\n",
    "$ Ab = \\begin{bmatrix}\n",
    "    1 & \\frac{2}{3} & \\frac{10}{3} & -\\frac{1}{3} \\\\\n",
    "    0 & -\\frac{5}{3} & -\\frac{14}{3} & \\frac{4}{3} \\\\\n",
    "    0 & \\frac{2}{3} & -\\frac{11}{3} & \\frac{2}{3} \\end{bmatrix}$\n",
    "\n",
    "$ --> \\begin{bmatrix}\n",
    "    1 & 0 & 7 & -1 \\\\\n",
    "    0 & 1 & -\\frac{14}{5} & -\\frac{4}{5} \\\\\n",
    "    0 & 0 & -\\frac{9}{5} & \\frac{6}{5} \\end{bmatrix}$\n",
    "    \n",
    "$ --> \\begin{bmatrix}\n",
    "    1 & 0 & 0 & \\frac{11}{3} \\\\\n",
    "    0 & 1 & 0 & -\\frac{8}{3} \\\\\n",
    "    0 & 0 & 1 & -\\frac{2}{3} \\end{bmatrix}$\n",
    "    \n",
    "$...$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  4,  7,  3 ||  1 \n",
      "  5, -1, -9 ||  1 \n",
      " -2,  3,  7 ||  1 \n"
     ]
    }
   ],
   "source": [
    "# 不要修改这里！\n",
    "A = generateMatrix(3,seed,singular=True)\n",
    "b = np.ones(shape=(3,1),dtype=int)\n",
    "Ab = augmentMatrix(A.tolist(),b.tolist()) # 请确保你的增广矩阵已经写好了\n",
    "printInMatrixFormat(Ab,padding=3,truncating=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "请按照算法的步骤3，逐步推演***奇异矩阵***的变换。\n",
    "\n",
    "在下面列出每一次循环体执行之后的增广矩阵(注意使用[分数语法](#分数的输入方法))\n",
    "\n",
    "$ Ab = \\begin{bmatrix}\n",
    "    1 & \\frac{7}{4} & \\frac{3}{4} & \\frac{1}{4} \\\\\n",
    "    0 & 39 & 51 & 1 \\\\\n",
    "    0 & 13 & 17 & 3 \\end{bmatrix}$\n",
    "\n",
    "$ --> \\begin{bmatrix}\n",
    "    1 & 0 & -\\frac{20}{13} & \\frac{8}{39} \\\\\n",
    "    0 & 1 & \\frac{17}{13} & \\frac{1}{39} \\\\\n",
    "    0 & 0 & 0 & \\frac{4}{3} \\end{bmatrix}$\n",
    "    \n",
    "$ --> \\begin{bmatrix}\n",
    "    0 & 0 & 0 & 0 \\\\\n",
    "    0 & 0 & 0 & 0 \\\\\n",
    "    0 & 0 & 0 & 0 \\end{bmatrix}$\n",
    "    \n",
    "$...$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3.3 实现 Gaussian Jordan 消元法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE 实现 Gaussain Jordan 方法求解 Ax = b\n",
    "\n",
    "\"\"\" Gaussian Jordan 方法求解 Ax = b.\n",
    "    参数\n",
    "        A: 方阵 \n",
    "        b: 列向量\n",
    "        decPts: 四舍五入位数，默认为4\n",
    "        epsilon: 判读是否为0的阈值，默认 1.0e-16\n",
    "        \n",
    "    返回列向量 x 使得 Ax = b \n",
    "    返回None，如果 A，b 高度不同\n",
    "    返回None，如果 A 为奇异矩阵\n",
    "\"\"\"\n",
    "from fractions import Fraction as F\n",
    "\n",
    "def print_matrix(AB):\n",
    "    print(\"*\" * 80)\n",
    "    for r in range(len(AB)):\n",
    "        print(AB[r])\n",
    "    print(\"*\" * 80)\n",
    "\n",
    "def gj_Solve(A, b, decPts=4, epsilon=1.0e-16):\n",
    "    if A is None or b is None or len(A) != len(b):\n",
    "        return None\n",
    "    \n",
    "    AB = list()\n",
    "    \n",
    "    for r in range(len(A)):\n",
    "        AB.append(list())\n",
    "        \n",
    "        for c in range(len(A[r])):\n",
    "            AB[r].append(F(A[r][c]))\n",
    "        \n",
    "        if type(b[r]) is list:\n",
    "            AB[r].append(F(b[r][0]))\n",
    "        else:\n",
    "            AB[r].append(F(b[r]))\n",
    "    \n",
    "    for i in range(len(AB)):\n",
    "        # If abs(AB[i][i] is zero, the swap rows\n",
    "        if abs(AB[i][i]) <= epsilon:\n",
    "            n = i\n",
    "            \n",
    "            for j in range(i + 1, len(AB)):\n",
    "                if abs(AB[j][i]) > epsilon:\n",
    "                    n = j\n",
    "                    \n",
    "            if n == i:\n",
    "                return None\n",
    "                    \n",
    "            for j in range(len(AB[0])):\n",
    "                tmp = AB[n][j]\n",
    "                AB[n][j] = AB[i][j]\n",
    "                AB[i][j] = tmp\n",
    "        \n",
    "        # Convert AB[i][i] to 1\n",
    "        scale_0 = 1 / AB[i][i]\n",
    "        \n",
    "        for n in range(len(AB[i])):\n",
    "            AB[i][n] = AB[i][n] * scale_0\n",
    "        \n",
    "        # Convert AB[n][i] to 0\n",
    "        for j in range(len(AB)):\n",
    "            if i == j:\n",
    "                continue\n",
    "            \n",
    "            if abs(AB[j][i]) <= epsilon:\n",
    "                continue\n",
    "            \n",
    "            scale_1 = -1 * AB[j][i]\n",
    "            \n",
    "            for k in range(len(AB[j])):\n",
    "                AB[j][k] = AB[i][k] * scale_1 + AB[j][k]\n",
    "    \n",
    "    result = list()\n",
    "    \n",
    "    for i in range(len(AB)):\n",
    "        row = list()\n",
    "        row.append(round(float(AB[i][-1]), decPts))\n",
    "        result.append(row)\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ".\n",
      "----------------------------------------------------------------------\n",
      "Ran 1 test in 72.732s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "# 运行以下代码测试你的 gj_Solve 函数\n",
    "%run -i -e test.py LinearRegressionTestCase.test_gj_Solve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (选做) 2.4 算法正确判断了奇异矩阵：\n",
    "\n",
    "在算法的步骤3 中，如果发现某一列对角线和对角线以下所有元素都为0，那么则断定这个矩阵为奇异矩阵。\n",
    "\n",
    "我们用正式的语言描述这个命题，并证明为真。\n",
    "\n",
    "证明下面的命题：\n",
    "\n",
    "**如果方阵 A 可以被分为4个部分: ** \n",
    "\n",
    "$ A = \\begin{bmatrix}\n",
    "    I    & X \\\\\n",
    "    Z    & Y \\\\\n",
    "\\end{bmatrix} , \\text{其中 I 为单位矩阵，Z 为全0矩阵，Y 的第一列全0}$，\n",
    "\n",
    "**那么A为奇异矩阵。**\n",
    "\n",
    "提示：从多种角度都可以完成证明\n",
    "- 考虑矩阵 Y 和 矩阵 A 的秩\n",
    "- 考虑矩阵 Y 和 矩阵 A 的行列式\n",
    "- 考虑矩阵 A 的某一列是其他列的线性组合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "证明：\n",
    "\n",
    "$ \\because \\begin{vmatrix}A\\end{vmatrix}=\n",
    "\\begin{vmatrix}\n",
    "I & X\\\\\n",
    "Z & Y \\\\\n",
    "\\end{vmatrix} \n",
    "= \n",
    "\\begin{vmatrix} I \\end{vmatrix}\\begin{vmatrix} Y \\end{vmatrix} = \\begin{vmatrix}Y\\end{vmatrix} $\n",
    "\n",
    "$ \\because Y 的第一列全0 $\n",
    "\n",
    "$ \\therefore \\begin{vmatrix} Y \\end{vmatrix} = 0A_{11} + 0A_{21} + ... + 0A_{n1} = 0$\n",
    "\n",
    "$ \\therefore \\begin{vmatrix} A \\end{vmatrix} = 0, 即A为奇异矩阵。 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 线性回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 随机生成样本点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 不要修改这里！\n",
    "%matplotlib notebook\n",
    "from helper import *\n",
    "\n",
    "X,Y = generatePoints2D(seed)\n",
    "vs_scatter_2d(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 拟合一条直线\n",
    "\n",
    "### 3.2.1 猜测一条直线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#DONE 请选择最适合的直线 y = mx + b\n",
    "m1 = 0.10\n",
    "b1 = 13.4\n",
    "\n",
    "# 不要修改这里！\n",
    "vs_scatter_2d(X, Y, m1, b1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2.2 计算平均平方误差 (MSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "我们要编程计算所选直线的平均平方误差(MSE), 即数据集中每个点到直线的Y方向距离的平方的平均数，表达式如下：\n",
    "$$\n",
    "MSE = \\frac{1}{n}\\sum_{i=1}^{n}{(y_i - mx_i - b)^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8775399621304406\n"
     ]
    }
   ],
   "source": [
    "# DONE 实现以下函数并输出所选直线的MSE\n",
    "def calculateMSE2D(X,Y,m,b):\n",
    "    n = len(X)\n",
    "    \n",
    "    if n != len(Y):\n",
    "        return 0.\n",
    "    \n",
    "    sum = 0\n",
    "    mse = 0\n",
    "    \n",
    "    for i in range(n):\n",
    "        sum += pow((Y[i] - m * X[i] - b), 2)\n",
    "        \n",
    "    mse = sum / n\n",
    "    \n",
    "    return mse\n",
    "\n",
    "# DONE 检查这里的结果, 如果你上面猜测的直线准确, 这里的输出会在1.5以内\n",
    "print(calculateMSE2D(X,Y,m1,b1))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2.3 调整参数 $m, b$ 来获得最小的平方平均误差\n",
    "\n",
    "你可以调整3.2.1中的参数 $m1,b1$ 让蓝点均匀覆盖在红线周围，然后微调 $m1, b1$ 让MSE最小。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 (选做) 找到参数 $m, b$ 使得平方平均误差最小\n",
    "\n",
    "**这一部分需要简单的微积分知识(  $ (x^2)' = 2x $ )。因为这是一个线性代数项目，所以设为选做。**\n",
    "\n",
    "刚刚我们手动调节参数，尝试找到最小的平方平均误差。下面我们要精确得求解 $m, b$ 使得平方平均误差最小。\n",
    "\n",
    "定义目标函数 $E$ 为\n",
    "$$\n",
    "E = \\frac{1}{2}\\sum_{i=1}^{n}{(y_i - mx_i - b)^2}\n",
    "$$\n",
    "\n",
    "因为 $E = \\frac{n}{2}MSE$, 所以 $E$ 取到最小值时，$MSE$ 也取到最小值。要找到 $E$ 的最小值，即要找到 $m, b$ 使得 $E$ 相对于 $m$, $E$ 相对于 $b$ 的偏导数等于0. \n",
    "\n",
    "因此我们要解下面的方程组。\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "\\displaystyle\n",
    "\\frac{\\partial E}{\\partial m} =0 \\\\\n",
    "\\\\\n",
    "\\displaystyle\n",
    "\\frac{\\partial E}{\\partial b} =0 \\\\\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "### 3.3.1 计算目标函数相对于参数的导数\n",
    "首先我们计算两个式子左边的值\n",
    "\n",
    "证明/计算：\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial m} = \\sum_{i=1}^{n}{-x_i(y_i - mx_i - b)}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial b} = \\sum_{i=1}^{n}{-(y_i - mx_i - b)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "证明:\n",
    "\n",
    "1. 设$ f(m) = (y - mx - b)^2 $, $ \\Delta{m} $ 趋近于0. 则有, \n",
    "\n",
    "$ f(m + \\Delta{m}) - f(m) = (y- (m + \\Delta{m})x - b)^2 - (y - mx - b)^2 = ((y - b) - (m + \\Delta{m})x)^2 - ((y - b) - mx)^2 $\n",
    "\n",
    "$ = (y - b)^2 - 2(y - b)(m + \\Delta{m})x + (m + \\Delta{m})^2x^2 - (y - b)^2 + 2(y - b)mx - m^2x^2 $\n",
    "\n",
    "$ = (y - b)^2 - 2(y - b)mx - 2(y - b)\\Delta{m}x + (m + \\Delta{m})^2x^2 - (y - b)^2 + 2(y - b)mx - m^2x^2 $\n",
    "\n",
    "$ = (m + \\Delta{m})^2x^2 - 2(y - b)\\Delta{m}x - m^2x^2 $\n",
    "\n",
    "$ = m^2x^2 + 2m\\Delta{m}x^2 + {\\Delta{m}}^2x^2 - 2(y - b)\\Delta{m}x - m^2x^2 $\n",
    "\n",
    "$ = 2m\\Delta{m}x^2 + {\\Delta{m}}^2x^2 - 2(y - b)\\Delta mx $\n",
    "\n",
    "则有 $ f'(m) = \\frac{f(m + \\Delta{m}) - f(m)}{\\Delta{m}}  = 2mx^2 + \\Delta{m} x^2 - 2(y - b)x $\n",
    "$ = -2x (y -mx - b) $\n",
    "\n",
    "$ \\because E = \\frac{1}{2}\\sum_{i=1}^n{f(m_i)} $\n",
    "\n",
    "$ \\therefore \\frac{\\partial{E}}{\\partial{m}} = \\frac{1}{2}\\sum_{i=1}^n{f'(m_i)} = \\frac{1}{2}\\sum_{i=1}^n{-2x_i(y_i - mx_i - b)} = \\sum_{i=1}^n{-x_i(y_i - mx_i - b)}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. 设$f(b)=(y - mx -b)^2, \\Delta{b}$趋近于0,则有,\n",
    "\n",
    "$ f(b + \\Delta{b}) - f(b) = (y - mx -(b + \\Delta{b}))^2 - (y - mx - b)^2  = -2 ( y - mx) \\Delta{b} + 2 b \\Delta{b} + {\\Delta{b}}^2 $\n",
    "\n",
    "则有 $ f'(b) = \\frac{f(b + \\Delta{b}) - f(b)}{\\Delta{b}} = -2y + 2mx + 2b = -2 (y - mx - b)$\n",
    "\n",
    "$ \\because E = \\frac{1}{2}\\sum_{i=1}^nf(b_i) $\n",
    "\n",
    "$ \\therefore\\frac{\\partial{E}}{\\partial{b}} = \\frac{1}{2}\\sum_{i=i}^nf'(b) = \\frac{1}{2}\\sum_{i=1}^n-2(y_i - mx_i - b) = \\sum_{i=1}^n-(y_i - mx_i - b) $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.2 实例推演\n",
    "\n",
    "现在我们有了一个二元二次方程组\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "\\displaystyle\n",
    "\\sum_{i=1}^{n}{-x_i(y_i - mx_i - b)} =0 \\\\\n",
    "\\\\\n",
    "\\displaystyle\n",
    "\\sum_{i=1}^{n}{-(y_i - mx_i - b)} =0 \\\\\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "为了加强理解，我们用一个实际例子演练。\n",
    "\n",
    "我们要用三个点 $(1,1), (2,2), (3,2)$ 来拟合一条直线 y = m*x + b, 请写出\n",
    "\n",
    "- 目标函数 $E$, \n",
    "- 二元二次方程组，\n",
    "- 并求解最优参数 $m, b$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "写出目标函数，方程组和最优参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "目标函数E为：$ E = \\frac{1}{3}((1 - m -b)^2 + (2 - 2m - b)^2 + (2 - 3m - b)^2) = \\frac{1}{3}(3b^2 + 12mb + 14m^2 - 22m - 10b + 9)$\n",
    "\n",
    "二元二次方程为： $ \\begin{cases}\n",
    "((1 - m - b) + 2(2 - 2m - b) + 3(2 - 3m - b)) = 0 \\\\\n",
    "- (1 - m - b) - (2 - 2m - b) - (2 - 3m - b) = 0\n",
    "\\end{cases} $\n",
    "$ \\Rightarrow  \n",
    "\\begin{cases}\n",
    "11 - 14m - 6b = 0\\\\\n",
    "-5 + 6m + 3b = 0\n",
    "\\end{cases} \n",
    "$\n",
    "\n",
    "最优解为: $\\begin{cases}\n",
    "m = \\frac{1}{2}\\\\\n",
    "b = \\frac{2}{3}\n",
    "\\end{cases}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3.3 将方程组写成矩阵形式\n",
    "\n",
    "我们的二元二次方程组可以用更简洁的矩阵形式表达，将方程组写成矩阵形式更有利于我们使用 Gaussian Jordan 消元法求解。\n",
    "\n",
    "请证明 \n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    \\frac{\\partial E}{\\partial m} \\\\\n",
    "    \\frac{\\partial E}{\\partial b} \n",
    "\\end{bmatrix} = X^TXh - X^TY\n",
    "$$\n",
    "\n",
    "其中向量 $Y$, 矩阵 $X$ 和 向量 $h$ 分别为 :\n",
    "$$\n",
    "Y =  \\begin{bmatrix}\n",
    "    y_1 \\\\\n",
    "    y_2 \\\\\n",
    "    ... \\\\\n",
    "    y_n\n",
    "\\end{bmatrix}\n",
    ",\n",
    "X =  \\begin{bmatrix}\n",
    "    x_1 & 1 \\\\\n",
    "    x_2 & 1\\\\\n",
    "    ... & ...\\\\\n",
    "    x_n & 1 \\\\\n",
    "\\end{bmatrix},\n",
    "h =  \\begin{bmatrix}\n",
    "    m \\\\\n",
    "    b \\\\\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "证明:\n",
    "\n",
    "$\n",
    "\\because X = \n",
    "\\begin{bmatrix}\n",
    "x_1 & 1 \\\\\n",
    "x_2 & 1 \\\\\n",
    "\\dots & \\dots \\\\\n",
    "x_n & 1\n",
    "\\end{bmatrix}\n",
    "\\therefore \n",
    "X^T =\n",
    "\\begin{bmatrix}\n",
    "x_1 & x_2 & \\dots & x_n \\\\\n",
    "1 & 1 & \\dots & 1\n",
    "\\end{bmatrix}\n",
    "$\n",
    "\n",
    "$\n",
    "\\because X^{T}Xh - X^{T}Y = \n",
    "\\begin{bmatrix}\n",
    "x_1 & x_2 & \\dots & x_n \\\\\n",
    "1 & 1 & \\dots & 1\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "x_1 & 1 \\\\\n",
    "x_2 & 1 \\\\\n",
    "\\dots & \\dots \\\\\n",
    "x_n & 1\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "m \\\\\n",
    "b\n",
    "\\end{bmatrix}\n",
    "- \n",
    "\\begin{bmatrix}\n",
    "x_1 & x_2 & \\dots & x_n \\\\\n",
    "1 & 1 & \\dots & 1\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "y_1 \\\\\n",
    "y_2 \\\\\n",
    "\\dots \\\\\n",
    "y_n\n",
    "\\end{bmatrix}\n",
    "$\n",
    "\n",
    "$\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "\\sum_{i=i}^n{x_i}^2 & \\sum_{i=1}^nx_i\\\\\n",
    "\\sum_{i=1}^nx_i & \\sum_{i=1}^n{1}\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "m \\\\\n",
    "b\n",
    "\\end{bmatrix}\n",
    "-\n",
    "\\begin{bmatrix}\n",
    "\\sum_{i=1}^{n}{x_i}{y_i}\\\\\n",
    "\\sum_{i=1}^{n}{y_i}\n",
    "\\end{bmatrix}\n",
    "$\n",
    "\n",
    "$\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "m\\sum_{i=1}^{n}{x_i}^2 + b\\sum_{i=1}^{n}x_i \\\\\n",
    "m\\sum_{i=1}^{n}x_i + b\\sum_{i=1}^{n}{1}\n",
    "\\end{bmatrix}\n",
    "-\n",
    "\\begin{bmatrix}\n",
    "\\sum_{i=1}^{n}{x_i}{y_i}\\\\\n",
    "\\sum_{i=1}^{n}{y_i}\n",
    "\\end{bmatrix}\n",
    "$\n",
    "\n",
    "$\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "\\sum_{i=1}^{n}-{x_i}(y_i - m{x_i} - b)\\\\\n",
    "\\sum_{i=1}^{n}-(y_i - mx_i - b)\n",
    "\\end{bmatrix}\n",
    "$\n",
    "\n",
    "$\n",
    "\\therefore\n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial{E}}{\\partial{m}} \\\\\n",
    "\\frac{\\partial{E}}{\\partial{b}}\n",
    "\\end{bmatrix}\n",
    "=\n",
    "X^{T}Xh - X^{T}Y\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "至此我们知道，通过求解方程 $X^TXh = X^TY$ 来找到最优参数。这个方程十分重要，他有一个名字叫做 **Normal Equation**，也有直观的几何意义。你可以在 [子空间投影](http://open.163.com/movie/2010/11/J/U/M6V0BQC4M_M6V2AJLJU.html) 和 [投影矩阵与最小二乘](http://open.163.com/movie/2010/11/P/U/M6V0BQC4M_M6V2AOJPU.html) 看到更多关于这个方程的内容。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 求解 $X^TXh = X^TY$ \n",
    "\n",
    "在3.3 中，我们知道线性回归问题等价于求解 $X^TXh = X^TY$ (如果你选择不做3.3，就勇敢的相信吧，哈哈)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# DONE 实现线性回归\n",
    "'''\n",
    "参数：X, Y 存储着一一对应的横坐标与纵坐标的两个一维数组\n",
    "返回：线性回归的系数(如上面所说的 m, b)\n",
    "'''\n",
    "def linearRegression2D(X,Y):\n",
    "    if len(X) != len(Y) or 0 == len(X):\n",
    "        return 0.0, 0.0\n",
    "    \n",
    "    X = [[X[i]] for i in range(len(X))]\n",
    "    E = [[1] for i in range(len(X))]\n",
    "    X = augmentMatrix(X, E)\n",
    "    Y = [[Y[i]] for i in range(len(Y))]\n",
    "    XT = transpose(X)\n",
    "    XTX = matxMultiply(XT, X)\n",
    "    XTY = matxMultiply(XT, Y)\n",
    "    r = gj_Solve(XTX, XTY)\n",
    "    \n",
    "    if r is None or 2 != len(r):\n",
    "        return 0.0, 0.0\n",
    "    else:\n",
    "        return r[0][0], r[1][0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0581 13.3714\n"
     ]
    }
   ],
   "source": [
    "# 请不要修改下面的代码\n",
    "m2,b2 = linearRegression2D(X,Y)\n",
    "assert isinstance(m2,float),\"m is not a float\"\n",
    "assert isinstance(b2,float),\"b is not a float\"\n",
    "print(m2,b2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "你求得的回归结果是什么？\n",
    "请使用运行以下代码将它画出来。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8629909326286568\n"
     ]
    }
   ],
   "source": [
    "## 请不要修改下面的代码\n",
    "vs_scatter_2d(X, Y, m2, b2)\n",
    "print(calculateMSE2D(X,Y,m2,b2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bonus !!!\n",
    "如果你的高斯约当消元法通过了单元测试, 那么它将能够解决多维的回归问题  \n",
    "你将会在更高维度考验你的线性回归实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 生成三维的数据点\n",
    "X_3d, Y_3d = generatePoints3D(seed)\n",
    "vs_scatter_3d(X_3d, Y_3d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "你的线性回归是否能够对付三维的情况?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linearRegression(X,Y):\n",
    "    if X is None or Y is None:\n",
    "        return\n",
    "    \n",
    "    if len(X) != len(Y):\n",
    "        return\n",
    "    \n",
    "    E = [[1] for i in range(len(X))]\n",
    "    X = augmentMatrix(X, E)\n",
    "    Y = [[Y[i]] for i in range(len(Y))]\n",
    "    XT = transpose(X)\n",
    "    XTX = matxMultiply(XT, X)\n",
    "    XTY = matxMultiply(XT, Y)\n",
    "    r = gj_Solve(XTX, XTY)\n",
    "    \n",
    "    if r is None or 3 != len(r):\n",
    "        return 0.0, 0.0, 0.0\n",
    "    else:\n",
    "        return r[0][0], r[1][0], r[2][0]\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coeff = linearRegression(X_3d, Y_3d)\n",
    "vs_scatter_3d(X_3d, Y_3d, coeff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Raw Cell Format",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}