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     "cell_type": "heading",
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     "metadata": {},
     "source": [
      "Linear Fitting using Gradient Descent Algorithm"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# y = mx + b\n",
      "# m is slope, b is y-intercept\n",
      "def computeErrorForLineGivenPoints(b, m, points):\n",
      "    totalError = 0\n",
      "    for i in range(0, len(points)):\n",
      "        x = points[i, 0]\n",
      "        y = points[i, 1]\n",
      "        totalError += (y - (m * x + b)) ** 2\n",
      "    return totalError / float(len(points))\n",
      "\n",
      "def stepGradient(b_current, m_current, points, learningRate):\n",
      "    b_gradient = 0\n",
      "    m_gradient = 0\n",
      "    N = float(len(points))\n",
      "    for i in range(0, len(points)):\n",
      "        x = points[i, 0]\n",
      "        y = points[i, 1]\n",
      "        b_gradient += -(2/N) * (y - ((m_current * x) + b_current))\n",
      "        m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))\n",
      "    new_b = b_current - (learningRate * b_gradient)\n",
      "    new_m = m_current - (learningRate * m_gradient)\n",
      "    return [new_b, new_m]\n",
      "\n",
      "import random\n",
      "from numpy.random import randn\n",
      "from numpy import *\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "random.seed(100)\n",
      "\n",
      "n = 100\n",
      "x = randn(n) * 10 + 50\n",
      "y = x * 1.5 + randn(n) * 10\n",
      "points = array([x, y]).transpose()\n",
      "\n",
      "b = 0\n",
      "m = 0\n",
      "for i in range(100):\n",
      "    b, m = stepGradient(b, m, array(points), 0.02)\n",
      "    if i % 10 == 0:\n",
      "        print b, m, computeErrorForLineGivenPoints(b, m, points)\n",
      "# plt.scatter(x, y)\n",
      "# plt.plot(arange(0,100), m*arange(0,100)+b)\n",
      "# plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2.90940202215 147.414059472 53091441.0482\n",
        "2.51063478e+20 1.27737150853e+22 4.06758732977e+47\n",
        "2.19755719833e+40 1.1180825566e+42 3.11637835829e+87\n",
        "1.92352056874e+60 9.7865702736e+61 2.38761046405e+127\n",
        "1.68365646235e+80 8.56617940729e+81 1.8292656002e+167\n",
        "1.47370354614e+100 7.4979719745e+101 1.40149018714e+207\n",
        "1.28993187772e+120 6.56297061471e+121 1.07375044086e+247\n",
        "1.12907664062e+140 5.74456445504e+141 8.22652930299e+286\n",
        "9.88280142863e+159 5.02821400786e+161 inf\n",
        "8.65041048269e+179 4.40119286792e+181 inf\n"
       ]
      }
     ],
     "prompt_number": 55
    },
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     "cell_type": "code",
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     "input": [],
     "language": "python",
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