05-Linear-Regression/04-Vectorization/04-Vectorization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 04 向量化运算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([1., 2., 3., 4., 5.])\n",
    "y = np.array([1., 3., 2., 3., 5.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimpleLinearRegression1()"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from playML.SimpleLinearRegression import SimpleLinearRegression1\n",
    "\n",
    "reg1 = SimpleLinearRegression1()\n",
    "reg1.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_hat1 = reg1.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hH+w33wwnqI8ZE1Y/ikir0B23pGfNGrj/fthnHzjzzHCe48SJny5ZF5FWo+KWDXOHRx+F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\nLLSYywanAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10be81898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_hat1, color='r')\n",
    "plt.axis([0, 6, 0, 6])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 向量化实现SimpleLinearRegression\n",
    "\n",
    "代码参见 [这里](playML/SimpleLinearRegression.py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimpleLinearRegression2()"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from playML.SimpleLinearRegression import SimpleLinearRegression2\n",
    "\n",
    "reg2 = SimpleLinearRegression2()\n",
    "reg2.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.80000000000000004"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg2.a_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39999999999999947"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg2.b_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hH+w33wwnqI8ZE1Y/ikir0B23pGfNGrj/fthnHzjzzHCe48SJny5ZF5FWo+KWDXOHRx+F\n/faDE08My9HHjQvDIhUV2gBKJAHNDpWY2a7APcDOgAPD3f2GbAeTHPDss3DZZfDSS2Ese9SocFxY\nhHuJTJhex7BJtSyqb6B9STGVFWX06dEh6VgiGyWdMe7VwO/cfZqZbQNUm9mT7j4ry9kkKVOmwOWX\nw9NPQ8eOMHw4nHEGFBUlnWyjTJheR/9xNTQ0NgFQV99A/3E1ACpviVKzQyXu/o67T0t9vQx4A9Cf\n9nz06qvhPMeDDgqbQV1/fdhj5Be/iLa0AYZNqv2ktNdqaGxi2KTahBKJbJoWjXGbWWegBzB1Hf+s\nr5lVmVnVkiVLMpNOWkdtbRi/3ndfeOEF+OMfYd68sAnUllsmnW6TLapvaNHrIrku7eI2s3bAg8D5\n7v7hF/+5uw9393J3Ly8tLc1kRsmWN98MM0S6dQtHhF1+OfznP3DppdCuXdLpMqZ9SXGLXhfJdWkV\nt5kVEUr7Xncfl91IknXvvBM2ffrqV2H0aDj//FDYgwZBSUnS6TKusqKM4qLPP1AtLmpDZUVZQolE\nNk06s0oMuAN4w93/nP1IkjVLl8LQoXDzzWEhzc9/Hu6yO+T3I4u1DyA1q0TyRTqzSnoCpwE1ZjYj\n9dql7v6P7MWSjPrgA/jzn8MmUCtWwKmnhkMNdt896WStpk+PDipqyRvNFre7Twa0yiJGH30U7q6H\nDg3brZ5wQliq3q1b0slEZBNo5WQ+WrUqFHaXLnDxxfDNb0J1NTzwgEpbJA9ok6l8sno13H132Fb1\n7bfhkENg7Fjo2TPpZCKSQbrjzgdr1oTZId26hQeOX/4yPPFEWLKu0hbJOyrumLnDww+HhTOnnBIW\nyzz0UFiyfuSR2gBKJE+puGPkDk89Fcaujz8eVq6E++6DGTPCknUVtkheU3HH5l//gsMOC3fU774L\nI0bArFlw8smwmT5OkUKgn/RYTJsGxx4LBx8Ms2fDjTfCnDlw1lnQVs+YRQqJijvXzZoV5l/vt18Y\nux4yJGwA9ZvfwBZbJJ1ORBKgW7VcNX9+WCwzahRstRVceSVccAFst13SyUQkYSruXFNXFzZ7uuOO\nMARywQVhEc2OOyadTERyhIo7VyxZEoZBbrklzMvu2zccG9a+fdLJRCTHqLiTVl8P114bTpv56CP4\n6U/DBlCdOyedTERylIo7KcuXw003wZ/+FMr7xz8OY9pduyadTERynIq7ta1cCbfdBoMHw+LF0Lt3\nGNPed9+kk4lIJDQdsLU0NsJf/wp77gn9+sHee8OLL8Ijj6i0RaRFVNzZ1tQE994Le+0VHjh27AhP\nPx3+OuigpNOJSIRU3NniDuPHQ/fu4cSZdu3C3fWLL8LhhyedTkQipuLONHeYOBH23x9+8IOwR/bf\n/x6WrPfurQ2gRGSTqbgz6YUXwuEFxxwTDua9806YOTPMGNEGUCKSIWqTTKiqgqOPhl69YO7csIhm\nzhw44wxtACUiGafi3hQzZ4bhkP33D+U9bFgo7rPPhs03TzqdiOQp3Q5ujLlzw+rG0aPDQ8cBA+D8\n82HbbZNOJiIFQMXdEgsWhMUyI0eGO+rKSrjoIthhh6STiUgBUXG3xNNPh1PUzz4bLr00HMorItLK\nVNwtceqpYQ52p05JJxGRAqaHky3Rtq1KW0QSp+IWEYlMs8VtZiPNbLGZzWyNQCIismHpjHHfBdwM\n3JPdKLltwvQ6hk2qZVF9A+1LiqmsKKNPjw5JxxKRAtRscbv782bWOftRcteE6XX0H1dDQ2MTAHX1\nDfQfVwOg8haRVqcx7jQMm1T7SWmv1dDYxLBJtQklEpFClrHiNrO+ZlZlZlVLlizJ1G+bExbVN7To\ndRGRbMpYcbv7cHcvd/fy0tLSTP22OaF9SXGLXhcRySYNlaShsqKM4qI2n3utuKgNlRVlCSUSkUKW\nznTA0cBLQJmZLTSzs7IfK7f06dGBwT/Yhw4lxRjQoaSYwT/YRw8mRSQR6cwqObk1guS6Pj06qKhF\nJCdoqEREJDIqbhGRyKi4RUQio+IWEYmMiltEJDIqbhGRyKi4RUQio+IWEYmMiltEJDIqbhGRyKi4\nRUQio+IWEYmMiltEJDIqbhGRyKi4RUQio+IWEYmMiltEJDIqbhGRyKi4RUQio+IWEYmMiltEJDIq\nbhGRyKi4RUQio+IWEYmMiltEJDIqbhGRyKi4RUQio+IWEYlMWsVtZkebWa2ZzTWzS7IdSkRE1q/Z\n4jazNsAtwDFAN+BkM+uW7WAiIrJu6dxxHwDMdff57v4xMAY4PruxRERkfdqmcU0HYMFnvl8IHPjF\ni8ysL9A39e0qM5u56fFy0o7A0qRDZJHeX9z0/uJVlu6F6RR3Wtx9ODAcwMyq3L08U793Lsnn9wZ6\nf7HT+4uXmVWle206QyV1wK6f+b5j6jUREUlAOsX9CrCnme1mZpsDJwEPZzeWiIisT7NDJe6+2szO\nBSYBbYCR7v56M79seCbC5ah8fm+g9xc7vb94pf3ezN2zGURERDJMKydFRCKj4hYRiUxGizufl8ab\n2UgzW5yv89PNbFcze9bMZpnZ62Z2XtKZMsnMtjSzl83s1dT7G5B0pkwzszZmNt3MHk06S6aZ2Ztm\nVmNmM1oybS4WZlZiZmPNbLaZvWFmB23w+kyNcaeWxs8BjiQs0nkFONndZ2XkfyBhZtYLWA7c4+57\nJ50n08xsF2AXd59mZtsA1UCfPPr8DNja3ZebWREwGTjP3ackHC1jzOwCoBzY1t17J50nk8zsTaDc\n3fNy8Y2Z3Q284O4jUrP3tnL3+vVdn8k77rxeGu/uzwPvJ50jW9z9HXeflvp6GfAGYdVsXvBgeerb\notRfefNk3sw6At8FRiSdRVrGzLYDegF3ALj7xxsqbchsca9raXze/OAXEjPrDPQApiabJLNSQwkz\ngMXAk+6eT+/veuAiYE3SQbLEgafMrDq1vUY+2Q1YAtyZGuoaYWZbb+gX6OGkfI6ZtQMeBM539w+T\nzpNJ7t7k7vsSVv8eYGZ5MeRlZr2Bxe5enXSWLDo49dkdA5yTGrrMF22BbwB/cfcewApgg88IM1nc\nWhofudTY74PAve4+Luk82ZL6z9BngaOTzpIhPYHjUuPAY4DDzWxUspEyy93rUn9fDIwnDM3mi4XA\nws/8F+BYQpGvVyaLW0vjI5Z6eHcH8Ia7/znpPJlmZqVmVpL6upjwEH12sqkyw937u3tHd+9M+Ll7\nxt1PTThWxpjZ1qkH5qSGEI4C8mZ2l7u/Cywws7W7Ax4BbHBSQCZ3B9yYpfHRMLPRwKHAjma2ELjK\n3e9INlVG9QROA2pS48AAl7r7PxLMlEm7AHenZj9tBtzv7nk3bS5P7QyMD/cWtAXuc/eJyUbKuN8A\n96ZueucDZ27oYi15FxGJjB5OiohERsUtIhIZFbeISGRU3CIikVFxi4hERsUtIhIZFbeISGT+D6TJ\nLLSYywanAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f23da20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_hat2 = reg2.predict(x)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_hat2, color='r')\n",
    "plt.axis([0, 6, 0, 6])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 向量化实现的性能测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.42 s per loop\n",
      "10 loops, best of 3: 27.2 ms per loop\n"
     ]
    }
   ],
   "source": [
    "m = 1000000\n",
    "big_x = np.random.random(size=m)\n",
    "big_y = big_x * 2 + 3 + np.random.normal(size=m)\n",
    "\n",
    "%timeit reg1.fit(big_x, big_y)\n",
    "%timeit reg2.fit(big_x, big_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0021906106687366"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg1.a_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0000124860598785"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg1.b_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0021906106686957"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg2.a_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0000124860598989"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg2.b_"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}