{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy as sp\n",
      "import matplotlib.pyplot as pt\n",
      "\n",
      "import scipy.optimize as opt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def f(x):\n",
      "    return x**3 - x +1\n",
      "\n",
      "def df(x):\n",
      "    return 3*x**2 - 1\n",
      "\n",
      "xmesh = np.linspace(-2, 2, 100)\n",
      "pt.ylim([-3, 10])\n",
      "pt.plot(xmesh, f(xmesh))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "[<matplotlib.lines.Line2D at 0x48d41d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Eiopk7y06Wh5xcfK9kzExwI03alMvue7UKbmb4pIlwIQJcspiq1ZaV6VvDHUfd/GinAKW\nlSWP3bvl1LDeveXRs6d3zSZwOGTIHzggt1n96Sd55OXJH05du8rDbJY/pG67jT0+PTp7FpgzRx6D\nBwP/+If8/48ax1D3QdXVshe+ciXw6ady/Lp/f/nigN69gZYtta5QfdXVsie/e7ccRtq1C9i5U750\nOD5e/ibSvbv8MzKSb8LRyunTwPz58ujTB3jlFTmsRs5jqPuQ3buBjAy5/WhICDBokDyiorSuTDsn\nTsghptxc+RvLjh3Azz/LoO/R4/IREeHbLyV2tyNHZJAvXQqkpACTJ8vhM2o6hrrBVVbKEF+wQIbV\nyJHy8OUgb0xZmXwgt2OHnP+8Y4f8XPful0P+rrvkQ1oO3bhOCGDjRuBf/wK++Ub+u5wwAbj1Vq0r\n824MdYMqKJA9n4wM4Pe/B555Rv46y2EF1/z8M/DDD/L4/nt5OBxX9+a7d5e/ATHoG3b0qNzfPCMD\naNFCbr41YoSc0krKMdQN5scfgfR0+dBzzBhg3DguzHCXkhLZi78U9D/8IAO9e/fL4/Pdusmep68H\nvd0un9+sXCmfZTzyCDBqlHwQ7+ttozaGukHs3g28+CKQnQ2kpgJPP+1ds1aMQAiguFiGe27u5SEc\nh0OO0V86zGY5XtyihdYVu48QwJ49snOxZo38OClJPsNJSjLmw3i9YKh7ufx8GeYbNgBTpgBPPsl5\nvHpjt8ve6c6dMuz37JHDY5GRQJcuci79pSMsDLjBC9drCyGnkV5a37B+vVwpfP/9cmZV375cFOYp\nDHUvVV4OpKUB77wjl01PmCBXb5J3OHdOzqP/8Uc5j/7HH+XfS0vlqtjoaBn6V66UDQ7WxzOR6mrg\n8GH5w+nSbyM7dsjFXZfWN9x7r6yfPI+h7mVqauTquhdfBB58EHjtNbk/ChlDVZWcT79/v1wle2ml\nbGGh3DIhOFiO0V/aByc4WG7P0LGjPC5t0dC6tWtj1ULIFbsnTsjDbr96j5+8PBnowcFydfGVzw5C\nQlRvDnIBQ92L7NwJjB0rxyPnzZP/IZHvOH9eboNw9KjcB+fScSmAT56Us3QqKmRv+qabLm+W1qqV\nHMO/tJkacHmTNYdDruA8c0b+eeONl/fxCQyUP0Qu7fETGSkPDvHpF0PdC5w7B7z8slyYMWMGMHo0\nZwxQwxwOGe6XNkurqpJBf/GiPISQId+ihdzDJyBADt8FBHjnmD5dxneU6tx338lFGd26yRkuQUFa\nV0TeoEULDstR0zDU3ezCBbnvxaJFwJtvAgMHal0RERkZQ92N8vKA4cNlTys3V74ggojInbi1kZt8\n+KFc1j96NPDFFwx0IvIM9tRVdv68fLNLZibw1Vec2UJEnqW4p56VlYXo6GhERkZixowZatTktUpK\ngHvukdPTduxgoBOR5ykK9ZqaGowfPx5ZWVnYu3cv3n//fezbt0+t2rzK998DiYlyD+mPP5YvrCAi\n8jRFob59+3ZEREQgLCwM/v7+GDJkCFatWqVWbV7jvfeAP/5RbpH7t79x7jkRaUfRmPqxY8cQGhpa\n+/eQkBBs27ZNcVHeQgjg1VeBZcvkRlxdumhdERH5OkWh7udklzQtLa32Y4vFAovFouS2ulBdLbfF\nzc2V2+SaTFpXRETezGazwWazKb6OolAPDg5GUVFR7d+LiooQUsduQFeGuhFUVsqXA1RXAzYb3/RC\nRMpd2+F9+eWXXbqOojH1Hj164ODBgygsLITD4cCKFSuQkpKi5JK6V14u95Tu0AH4/HMGOhHpi6Ke\n+g033ID58+fjvvvuQ01NDR577DHExMSoVZvu/Pwz0K8f8Ic/ALNn84EoEekPd2l00vHjsoc+YIDc\n+5yBTkTu5Gp2cpsAJxw7JhcVDR8OTJ3KQCci/eI2AY2w24E+feRLLSZN0roaIqKGsafegJMnZaCP\nGMFAJyLvwFCvR1mZHEMfOBD4+9+1roaIyDl8UFqHykoZ6L//PTBzJsfQicjz+I5SlVy4ADz4oFwh\nunQpA52ItMHZLyq4eBEYMwZo3ly+fo6BTkTehrNfrjBpElBQAKxdyzexE5F3YnT9z3/+A6xZA2zd\nCrRurXU1RESu4Zg6gKws4NFHgW+/BcLDta6GiMj17PT5nvqePcDIkcCnnzLQicj7+fSD0hMngORk\nYM4cOX2RiMjb+ezwy4ULcrXoPffItxcREekJ56k30fjxwJEjwKpVQDOf/n2FiPSIY+pNsHQpsH49\nsG0bA52IjMXneurbtslx9G++AaKjta6GiKhuXFHqhFOngIcflqtFGehEZEQ+01O/eFH20GNigFmz\ntK6GiKhh7Kk3YuZM4PRpYPp0rSshInIfn3hQunkz8M9/Aj/8APj7a10NEZH7GL6nfuoUMGwYsGwZ\nEBqqdTVERO5l6DF1IYBBg4CwMNlTJyLyFpynXoclS4D8fOC997SuhIjIMwzbU8/Lk/u5bNoExMZ6\n/PZERIpw9ssVHA45jv7yywx0IvItLof6xIkTERMTA7PZjIEDB6KiokLNuhR57TX5jtGnn9a6EiIi\nz3I51Pv164effvoJu3btQlRUFKbrZAL4Dz8ACxcCixfzHaNE5HtcDnWr1Ypm/9sNKzExEcXFxaoV\n5arz54FRo4DZs4FOnbSuhojI81QZU1+6dCmSkpLUuJQiL70E3HknMHSo1pUQEWmjwSmNVqsVdrv9\nus9PmzYNycnJAICpU6eiRYsWGDZsmHsqdFJ2NrB8ObB7N4ddiMh3NRjq69ata/Cbly9fjszMTGzY\nsKHB89LS0mo/tlgssFgsThfojPPngTFjgHnzgMBAVS9NROQRNpsNNptN8XVcnqeelZWFF154AZs2\nbUKHDh3qv4EH5qmnpQG5ucBnn7GXTkTG4PHX2UVGRsLhcKB9+/YAgF69euHNN99UrTBn7d0r3zOa\nmwuEhLjtNkREHuWT7yi9eBHo3RsYPhwYN84ttyAi0oRPrihduFD++dRT2tZBRKQXXttTP34c6NqV\ne7sQkTH53PDLsGFyS91p01S/NBGR5nxq692vvwa2bpUvkCYiosu8bkzd4QCeeQaYMwe48UatqyEi\n0hevC/XZs4E77gAefFDrSoiI9MerxtSPHgW6dQO2bQPCw1W5JBGRLvnElMaJE+XQCwOdiKhuXtNT\n37xZLjLavx9o3VqFwoiIdMzQPfWLF4HUVCA93X2BrsZGOp7gDXV6Q40A61Qb69QHrwj15cuB3/zG\nvfuke8v/0d5QpzfUCLBOtbFOfdD9PPVffgH+/ndg1SruwEhE1Bjd99SnTQOsVuCuu7SuhIhI/9z+\noDQ+Ph67du1y5y2IiAzHbDZj586dTf4+t4c6ERF5ju6HX4iIyHkMdSIiA1E91CdOnIiYmBiYzWYM\nHDgQFRUVdZ6XlZWF6OhoREZGYsaMGWqX0aCPPvoIcXFxaN68OXJycuo9LywsDF27dkVCQgJ69uzp\nwQolZ+vUsi0BoKysDFarFVFRUejXrx/Ky8vrPE+r9nSmfZ577jlERkbCbDYjNzfXY7VdqbE6bTYb\n2rZti4SEBCQkJOC1117zeI1jxoyByWRCly5d6j1HD23ZWJ16aMuioiLce++9iIuLQ+fOnTFv3rw6\nz2tyewqVrV27VtTU1AghhJg8ebKYPHnydedUV1eL8PBwUVBQIBwOhzCbzWLv3r1ql1Kvffv2iQMH\nDgiLxSJ27NhR73lhYWHi1KlTHqvrWs7UqXVbCiHExIkTxYwZM4QQQqSnp9f5/7kQ2rSnM+3zxRdf\niP79+wshhMjOzhaJiYkerdHZOjdu3CiSk5M9XtuVvvnmG5GTkyM6d+5c59f10JZCNF6nHtry+PHj\nIjc3VwghxJkzZ0RUVJQq/zZV76lbrVY0ayYvm5iYiOLi4uvO2b59OyIiIhAWFgZ/f38MGTIEq1at\nUruUekVHRyMqKsqpc4WGz5GdqVPrtgSA1atXY9SoUQCAUaNG4bPPPqv3XE+3pzPtc2X9iYmJKC8v\nR2lpqe7qBLT99wgAvXv3xs0331zv1/XQlkDjdQLat2VQUBDi4+MBAAEBAYiJiUFJSclV57jSnm4d\nU1+6dCmSkpKu+/yxY8cQGhpa+/eQkBAcO3bMnaW4xM/PD3379kWPHj2wSKdv5NBDW5aWlsJkMgEA\nTCZTvf/otGhPZ9qnrnPq6oy4kzN1+vn5YevWrTCbzUhKSsLevXs9WqMz9NCWztBbWxYWFiI3NxeJ\niYlXfd6V9nRpRanVaoXdbr/u89OmTUNycjIAYOrUqWjRogWGDRt23Xl+Hlga6kyNjdmyZQs6deqE\nkydPwmq1Ijo6Gr1799ZVnZ5oS6D+OqdOnXpdPfXV5In2vJaz7XNtr81T7dqU+3Xr1g1FRUVo3bo1\nvvzySwwYMAB5eXkeqK5ptG5LZ+ipLc+ePYvBgwdj7ty5CAgIuO7rTW1Pl0J93bp1DX59+fLlyMzM\nxIYNG+r8enBwMIqKimr/XlRUhJCQEFdKcblGZ3Tq1AkA0LFjRzz00EPYvn276iGktE5PtCXQcJ0m\nkwl2ux1BQUE4fvw4AgMD6zzPE+15LWfa59pziouLERwc7Na6ruVMnW3atKn9uH///hg3bhzKysrQ\nvn17j9XZGD20pTP00pYXLlzAoEGDMGLECAwYMOC6r7vSnqoPv2RlZWHmzJlYtWoVWrZsWec5PXr0\nwMGDB1FYWAiHw4EVK1YgJSVF7VKcUt+4WlVVFc6cOQMAqKysxNq1axt84u9u9dWph7ZMSUlBRkYG\nACAjI6POf5xatacz7ZOSkoK33noLAJCdnY127drVDid5ijN1lpaW1v472L59O4QQugp0QB9t6Qw9\ntKUQAo899hhiY2ORmppa5zkutacaT3GvFBERIW699VYRHx8v4uPjxdNPPy2EEOLYsWMiKSmp9rzM\nzEwRFRUlwsPDxbRp09Quo0GffPKJCAkJES1bthQmk0ncf//919WYn58vzGazMJvNIi4uzuM1Olun\nENq2pRBCnDp1SvTp00dERkYKq9UqTp8+fV2dWrZnXe2zYMECsWDBgtpznnnmGREeHi66du3a4Iwo\nLeucP3++iIuLE2azWfTq1Ut89913Hq9xyJAholOnTsLf31+EhISIJUuW6LItG6tTD225efNm4efn\nJ8xmc21eZmZmKm5PbhNARGQgXFFKRGQgDHUiIgNhqBMRGQhDnYjIQBjqREQGwlAnIjIQhjoRkYEw\n1ImIDOT/AVlLd2Gigl9nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x48d4190>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iterates = [2, 1.5]\n",
      "\n",
      "x_exact =  opt.fsolve(f, -1)\n",
      "print \"Exact:\", x_exact\n",
      "\n",
      "e = list(np.abs(iterates-x_exact))\n",
      "print \"Errors:\", e"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exact: [-1.32471796]\n",
        "Errors: [3.3247179572447534, 2.8247179572447534]\n"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Evaluate this cell many times in-place (using Ctrl-Enter)\n",
      "\n",
      "xlast, x = iterates[-2:] # grab last two iterates\n",
      "\n",
      "slope = df(x)                             # Newton's method\n",
      "#slope = ( (f(x)-f(xlast)) / (x-xlast) )   # Secant method\n",
      "\n",
      "pt.plot(xmesh, f(xmesh))\n",
      "pt.plot(xmesh, f(x) + slope*(xmesh-x))\n",
      "pt.plot(x, f(x), \"o\")\n",
      "pt.ylim([-3, 10])\n",
      "pt.axhline(0, color=\"black\")\n",
      "\n",
      "# Compute approximate root\n",
      "xnew = x - f(x) / slope\n",
      "iterates.append(xnew)\n",
      "print xnew\n",
      "\n",
      "e.append(abs(xnew - x_exact))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.0\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ogbNnz+LkyZNwd3dHhJFMAD92DPjqK2D5cj40mszboZxDmBw/GduGbIN9I3u5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\ni1w98NBY9AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4e9da90>"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Evaluate convergence history"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i, x in enumerate(iterates):\n",
      "    if i == 0:\n",
      "        continue\n",
      "    print \"%3d %10g %10g | %10g %10g %10g\"%(\n",
      "                        i, x, e[i], \n",
      "                        e[i]/e[i-1],\n",
      "                        e[i]/e[i-1]**2,\n",
      "                        e[i]/e[i-1]**1.62)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  1        1.5    2.82472 |   0.849611   0.255544   0.403397\n",
        "  2          1    2.32472 |   0.822991   0.291353   0.432305\n",
        "  3        0.5    1.82472 |    0.78492   0.337641   0.465239\n",
        "  4          3    4.32472 |    2.37007    1.29887    1.63238\n",
        "  5    2.03846    3.36318 |   0.777664   0.179819   0.313688\n",
        "  6    1.39028      2.715 |   0.807272   0.240032    0.38057\n",
        "  7   0.911612    2.23633 |   0.823694   0.303386   0.443434\n",
        "  8   0.345028    1.66975 |   0.746646   0.333871   0.453317\n",
        "  9    1.42775    2.75247 |    1.64844   0.987237    1.19958\n",
        " 10   0.942418    2.26714 |   0.823674   0.299249    0.43967\n",
        " 11   0.404949    1.72967 |   0.762931   0.336517   0.459292\n",
        " 12     1.7069    3.03162 |    1.75272    1.01333    1.24789\n",
        " 13    1.15576    2.48047 |     0.8182   0.269889   0.411359\n",
        " 14   0.694192    2.01891 |   0.813921   0.328131   0.463416\n",
        " 15  -0.742494   0.582224 |   0.288385   0.142842   0.186552\n",
        " 16    -2.7813    1.45658 |    2.50175    4.29689    3.49855\n",
        " 17   -1.98273   0.658007 |   0.451749   0.310144   0.357792\n",
        " 18   -1.53693   0.212209 |   0.322503   0.490121   0.418053\n",
        " 19   -1.35726  0.0325445 |    0.15336   0.722684   0.400977\n",
        " 20   -1.32566 0.000945137 |  0.0290414   0.892358   0.242818\n",
        " 21   -1.32472 8.31371e-07 | 0.000879629    0.93069  0.0659923\n",
        " 22   -1.32472 6.37046e-13 | 7.6626e-07   0.921683 0.00450924\n",
        " 23   -1.32472 7.10543e-15 |  0.0111537 1.75085e+10     406288\n",
        " 24   -1.32472 7.10543e-15 |          1 1.40737e+14 5.91581e+08\n",
        " 25   -1.32472 7.10543e-15 |          1 1.40737e+14 5.91581e+08\n",
        " 26   -1.32472 7.10543e-15 |          1 1.40737e+14 5.91581e+08\n",
        " 27   -1.32472 7.10543e-15 |          1 1.40737e+14 5.91581e+08\n"
       ]
      }
     ],
     "prompt_number": 85
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}