Week1_Lecture1.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from everything import __future__ as PyConAPAC",
      "# click the logo for more infomation!"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<a href=\"http://tw.pycon.org/2014apac/en/\" target=\"_blank\" class=\"svg\"><svg enable-background=\"new 4784.332 2788.145 461.619 152.118\" height=\"152.118px\" id=\"Layer_1\" version=\"1.1\" viewBox=\"4784.332 2788.145 461.619 152.118\" width=\"461.619px\" x=\"0px\" xml:space=\"preserve\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" y=\"0px\">\n",
        "<g>\n",
        "\t<path d=\"M4826.781,2936.36l-6.527-25.453l3.43-8.292c0.43-1.207,0.076-2.661-0.799-3.284l-15.896-11.305   c-0.303-0.215-0.639-0.303-0.97-0.272l-0.156-0.001l-0.157,0.001c-0.331-0.03-0.666,0.057-0.969,0.272l-15.896,11.305   c-0.876,0.623-1.229,2.077-0.799,3.284l3.43,8.292l-6.526,25.453c-0.11,0.732,0.029,1.492,0.377,2.071   c0.349,0.577,0.87,0.913,1.42,0.91l18.912-0.04l0.15-0.021l0.058,0.021l0.057-0.021l0.149,0.021l18.913,0.04   c0.551,0.002,1.072-0.333,1.42-0.91C4826.751,2937.852,4826.891,2937.092,4826.781,2936.36\" fill=\"#04556A\"/>\n",
        "\t<path d=\"M4791.88,2890.831c0.217,0.605,0.604,1.067,1.075,1.278c0.186,0.086,0.382,0.126,0.576,0.126   c0.293,0,0.585-0.096,0.85-0.284l11.513-8.186l11.532,8.137c0.265,0.187,0.556,0.282,0.847,0.282   c0.195-0.001,0.39-0.043,0.577-0.129c0.472-0.214,0.858-0.677,1.073-1.282l3.674-10.404c0.428-1.209,0.07-2.66-0.807-3.279   l-15.921-11.239c-0.312-0.22-0.659-0.305-0.997-0.268c-0.34-0.036-0.685,0.049-0.998,0.27l-15.896,11.308   c-0.876,0.624-1.229,2.076-0.799,3.284L4791.88,2890.831\" fill=\"#D0272B\"/>\n",
        "\t<path d=\"M4791.854,2869.031c0.216,0.608,0.605,1.069,1.075,1.28c0.188,0.084,0.383,0.125,0.577,0.125   c0.292,0,0.584-0.098,0.848-0.285l11.513-8.188l11.533,8.141c0.265,0.186,0.557,0.28,0.848,0.28c0.194,0,0.389-0.043,0.577-0.128   c0.47-0.214,0.858-0.676,1.071-1.283l3.676-10.401c0.427-1.211,0.071-2.662-0.807-3.281l-15.921-11.239   c-0.313-0.22-0.66-0.306-0.998-0.267c-0.339-0.037-0.685,0.051-0.997,0.271l-15.896,11.307c-0.875,0.622-1.229,2.075-0.798,3.284   L4791.854,2869.031\" fill=\"#04556A\"/>\n",
        "\t<path d=\"M4810.917,2813.852c-1.164,0.227-2.339-0.868-2.631-2.444c-0.291-1.576,0.415-3.038,1.577-3.264   c1.161-0.226,2.34,0.868,2.629,2.444C4812.783,2812.164,4812.076,2813.626,4810.917,2813.852z M4803.672,2811.408   c-0.291,1.576-1.467,2.671-2.63,2.444c-1.161-0.225-1.869-1.688-1.577-3.265c0.29-1.575,1.469-2.67,2.63-2.444   C4803.257,2808.37,4803.963,2809.831,4803.672,2811.408z M4826.303,2831.652c-4.274-3.2-9.096-5.475-13.559-8.159   c1.278-2.67,2.662-5.425,3.708-8.277c2.551-6.958-5.023-11.708-8.367-14.865l-1.135-0.844c-0.124-1.399-0.259-3.256-0.259-4.709   c0-2.68,1.783-6.653,1.783-6.653l-2.586,2.68l-2.585-2.68c0,0,1.781,3.973,1.781,6.653c0,1.452-0.131,3.306-0.252,4.705   l-1.141,0.848c-3.343,3.158-10.918,7.907-8.367,14.865c1.046,2.852,2.43,5.606,3.708,8.277c-4.463,2.684-9.284,4.959-13.56,8.159   c-1.026,0.767-1.431,2.494-0.919,3.925l4.457,12.518c0.26,0.731,0.729,1.287,1.295,1.541c0.226,0.103,0.462,0.152,0.695,0.152   c0.353-0.001,0.705-0.115,1.022-0.342l13.864-9.861l13.864,9.861c0.317,0.226,0.668,0.341,1.022,0.342   c0.232,0,0.469-0.049,0.694-0.152c0.568-0.254,1.037-0.809,1.296-1.541l4.457-12.518   C4827.734,2834.146,4827.329,2832.419,4826.303,2831.652\" fill=\"#D0272B\"/>\n",
        "\t<path d=\"M4882.667,2889.938c5.603,0,9.297-2.892,9.297-13.956c-0.127-10.813-4.84-12.95-9.297-12.95h-20.883v26.906   H4882.667z M4843.956,2847.442h40.112c11.715,0,25.85,3.646,25.85,28.414c0,28.038-15.154,30.049-25.85,29.672   c-5.094-0.251-21.647-2.263-22.284-2.514v36.461h-17.828V2847.442\" fill=\"#04556A\"/>\n",
        "\t<path d=\"M4934.617,2847.442l18.21,44.13l19.993-44.13h19.355l-30.688,63.492v28.541h-17.828v-28.541l-28.397-63.492   H4934.617\" fill=\"#04556A\"/>\n",
        "\t<path d=\"M5031.518,2846.437c12.989,0,22.413,1.257,32.473,4.149v13.83c-0.129,0-15.792-1.76-28.271-1.76   c-13.116,0-18.082,2.892-18.082,30.804c0,20.619,3.438,30.552,18.082,30.552c13.371,0,28.271-1.006,28.271-1.006v13.705   c-8.405,2.64-19.102,3.771-32.473,3.52c-23.557-0.251-31.707-17.853-31.707-47.022   C4999.811,2863.787,5006.178,2846.437,5031.518,2846.437\" fill=\"#D0272B\"/>\n",
        "\t<path d=\"M5114.16,2923.759c15.025,0,19.61-4.904,19.61-29.672c0-28.666-0.418-31.055-14.553-31.055   c-13.753,0-24.668,1.761-24.668,31.055C5094.549,2919.233,5098.242,2923.759,5114.16,2923.759z M5119.217,2846.814   c22.029,0,32.38,4.149,32.38,47.273c0,40.61-14.517,45.89-37.438,45.89c-22.921,0-37.438-4.023-37.438-45.89   C5076.721,2850.962,5097.824,2846.814,5119.217,2846.814\" fill=\"#D0272B\"/>\n",
        "\t<path d=\"M5173.112,2847.442h18.083l36.928,59.469v-59.469h17.827v92.033h-17.827l-37.055-58.841v58.841h-17.956   V2847.442\" fill=\"#D0272B\"/>\n",
        "\t<g>\n",
        "\t\t<path d=\"M5205.187,2806.618h-2.106v7.407h2.106c0.554,0,1.025-0.197,1.413-0.591    c0.388-0.394,0.582-0.868,0.582-1.423v-3.381c0-0.603-0.182-1.09-0.545-1.459    C5206.273,2806.803,5205.79,2806.618,5205.187,2806.618z\" fill=\"#6E6F72\"/>\n",
        "\t\t<polygon fill=\"#6E6F72\" points=\"5190.453,2817.48 5193.039,2817.48 5191.746,2808.355   \"/>\n",
        "\t\t<polygon fill=\"#6E6F72\" points=\"5214.736,2817.48 5217.322,2817.48 5216.029,2808.355   \"/>\n",
        "\t\t<path d=\"M5237.851,2791.896h-113.817c-4.294,0-7.775,3.481-7.775,7.774v29.47c0,4.294,3.481,7.774,7.775,7.774    h113.816c4.294,0,7.775-3.481,7.775-7.774v-29.47C5245.625,2795.376,5242.144,2791.896,5237.851,2791.896z M5140.101,2822.764    v3.417h-11.103v-3.203c0-0.074,0.254-0.499,0.762-1.278c0.235-0.356,0.5-0.749,0.798-1.18l0.91-1.309    c0.529-0.726,1.362-1.889,2.496-3.49c1.072-1.502,1.875-2.862,2.405-4.081c0.432-0.997,0.647-1.927,0.647-2.789    c0-0.701-0.197-1.299-0.59-1.791c-0.432-0.517-0.985-0.775-1.663-0.775c-0.973,0-1.663,0.561-2.068,1.681    c-0.136,0.369-0.203,0.813-0.203,1.33v0.887h-3.436v-0.61c0-2.192,0.591-3.867,1.774-5.025c1.021-1.022,2.364-1.533,4.027-1.533    c1.526,0,2.829,0.572,3.907,1.718c1.078,1.145,1.616,2.482,1.616,4.009c0,1.576-0.351,3.098-1.053,4.563    c-0.381,0.813-1.275,2.211-2.679,4.194c-0.381,0.542-0.948,1.385-1.7,2.531l-0.628,0.942c-0.406,0.616-0.714,1.103-0.923,1.46    c-0.099,0.183-0.148,0.293-0.148,0.332h6.853V2822.764z M5152.907,2820.917c0,1.54-0.542,2.845-1.625,3.916    c-1.084,1.071-2.383,1.608-3.898,1.608c-1.54,0-2.848-0.539-3.926-1.616c-1.078-1.077-1.616-2.38-1.616-3.907v-12.636    c0-1.539,0.542-2.847,1.626-3.926c1.083-1.077,2.389-1.616,3.916-1.616c1.54,0,2.845,0.542,3.917,1.626    c1.071,1.084,1.607,2.389,1.607,3.916V2820.917z M5160.891,2826.2h-3.492v-17.827h-2.974v-2.439    c0.836-0.098,1.635-0.415,2.392-0.951c0.758-0.535,1.303-1.185,1.635-1.949h2.438L5160.891,2826.2L5160.891,2826.2z     M5175.006,2821.194h-2.235v4.988h-3.491v-4.988h-6.17v-3.51l6.17-14.668h3.491v14.668h2.235V2821.194z M5194.375,2826.2    l-0.817-5.321h-3.646l-0.848,5.321h-3.635l3.935-23.148h4.802l3.879,23.148H5194.375z M5205.094,2817.48h-2.014v8.719h-3.491    v-23.148h5.505c1.699,0,3.054,0.536,4.064,1.608c0.936,1.022,1.404,2.328,1.404,3.916v3.362c0,1.527-0.533,2.833-1.598,3.916    C5207.899,2816.939,5206.608,2817.48,5205.094,2817.48z M5218.658,2826.2l-0.817-5.321h-3.646l-0.848,5.321h-3.635l3.935-23.148    h4.803l3.879,23.148H5218.658z M5234.392,2810.978h-3.622v-2.715c0-0.554-0.196-1.028-0.591-1.423    c-0.395-0.394-0.868-0.591-1.423-0.591c-0.554,0-1.025,0.197-1.413,0.591c-0.388,0.395-0.582,0.868-0.582,1.423v12.673    c0,0.554,0.194,1.025,0.582,1.413c0.388,0.388,0.859,0.582,1.413,0.582c0.555,0,1.028-0.194,1.423-0.582    c0.395-0.388,0.591-0.859,0.591-1.413v-3.196h3.622v3.233c0,1.54-0.542,2.845-1.625,3.916c-1.084,1.071-2.384,1.608-3.899,1.608    c-1.54,0-2.847-0.539-3.925-1.616c-1.079-1.077-1.616-2.38-1.616-3.907v-12.636c0-1.539,0.542-2.847,1.625-3.926    c1.084-1.077,2.39-1.616,3.916-1.616c1.54,0,2.845,0.542,3.917,1.626c1.07,1.084,1.607,2.389,1.607,3.916V2810.978z\" fill=\"#6E6F72\"/>\n",
        "\t\t<path d=\"M5147.273,2806.193c-0.554,0-1.025,0.197-1.414,0.591c-0.388,0.394-0.583,0.868-0.583,1.423v12.654    c0,0.554,0.195,1.028,0.583,1.423c0.388,0.394,0.859,0.591,1.414,0.591s1.028-0.197,1.423-0.591    c0.394-0.394,0.591-0.868,0.591-1.423v-12.654c0-0.554-0.197-1.028-0.591-1.423    C5148.301,2806.39,5147.827,2806.193,5147.273,2806.193z\" fill=\"#6E6F72\"/>\n",
        "\t\t<polygon fill=\"#6E6F72\" points=\"5169.28,2817.683 5169.28,2810.449 5166.396,2817.683   \"/>\n",
        "\t</g>\n",
        "</g>\n",
        "</svg></a>\n",
        "<style>\n",
        "a.svg:after {\n",
        "  content: \"\";\n",
        "  position: absolute;\n",
        "  top: 0;\n",
        "  right: 0;\n",
        "  bottom: 0;\n",
        "  left: 0;\n",
        "}\n",
        "</style>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 0,
       "text": [
        "<IPython.core.display.HTML at 0x10ab91b50>"
       ]
      }
     ],
     "prompt_number": 0
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Video: W01_L01_P03"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pylab as pl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = 20\n",
      "n = 120"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x2 = np.linspace(-L/2,L/2,n+1)\n",
      "print x2\n",
      "print x2.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-10.          -9.83333333  -9.66666667  -9.5         -9.33333333\n",
        "  -9.16666667  -9.          -8.83333333  -8.66666667  -8.5         -8.33333333\n",
        "  -8.16666667  -8.          -7.83333333  -7.66666667  -7.5         -7.33333333\n",
        "  -7.16666667  -7.          -6.83333333  -6.66666667  -6.5         -6.33333333\n",
        "  -6.16666667  -6.          -5.83333333  -5.66666667  -5.5         -5.33333333\n",
        "  -5.16666667  -5.          -4.83333333  -4.66666667  -4.5         -4.33333333\n",
        "  -4.16666667  -4.          -3.83333333  -3.66666667  -3.5         -3.33333333\n",
        "  -3.16666667  -3.          -2.83333333  -2.66666667  -2.5         -2.33333333\n",
        "  -2.16666667  -2.          -1.83333333  -1.66666667  -1.5         -1.33333333\n",
        "  -1.16666667  -1.          -0.83333333  -0.66666667  -0.5         -0.33333333\n",
        "  -0.16666667   0.           0.16666667   0.33333333   0.5          0.66666667\n",
        "   0.83333333   1.           1.16666667   1.33333333   1.5          1.66666667\n",
        "   1.83333333   2.           2.16666667   2.33333333   2.5          2.66666667\n",
        "   2.83333333   3.           3.16666667   3.33333333   3.5          3.66666667\n",
        "   3.83333333   4.           4.16666667   4.33333333   4.5          4.66666667\n",
        "   4.83333333   5.           5.16666667   5.33333333   5.5          5.66666667\n",
        "   5.83333333   6.           6.16666667   6.33333333   6.5          6.66666667\n",
        "   6.83333333   7.           7.16666667   7.33333333   7.5          7.66666667\n",
        "   7.83333333   8.           8.16666667   8.33333333   8.5          8.66666667\n",
        "   8.83333333   9.           9.16666667   9.33333333   9.5          9.66666667\n",
        "   9.83333333  10.        ]\n",
        "(121,)\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = x2[:-1]\n",
      "print x.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(120,)\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u = np.exp(-x**2)\n",
      "print u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  3.72007598e-44   1.01422975e-42   2.61573301e-41   6.38150345e-40\n",
        "   1.47273678e-38   3.21513923e-37   6.63967720e-36   1.29707974e-34\n",
        "   2.39694967e-33   4.19009319e-32   6.92884712e-31   1.08385405e-29\n",
        "   1.60381089e-28   2.24495707e-27   2.97259301e-26   3.72336312e-25\n",
        "   4.41171920e-24   4.94484702e-23   5.24288566e-22   5.25848261e-21\n",
        "   4.98910939e-20   4.47773244e-19   3.80159442e-18   3.05313461e-17\n",
        "   2.31952283e-16   1.66695501e-15   1.13323932e-14   7.28772410e-14\n",
        "   4.43337775e-13   2.55123274e-12   1.38879439e-11   7.15151993e-11\n",
        "   3.48362407e-10   1.60522806e-09   6.99704599e-09   2.88512906e-08\n",
        "   1.12535175e-07   4.15225353e-07   1.44927889e-06   4.78511739e-06\n",
        "   1.49453385e-05   4.41561749e-05   1.23409804e-04   3.26272454e-04\n",
        "   8.15987835e-04   1.93045414e-03   4.32023947e-03   9.14594704e-03\n",
        "   1.83156389e-02   3.46966856e-02   6.21765240e-02   1.05399225e-01\n",
        "   1.69013315e-01   2.56375757e-01   3.67879441e-01   4.99351789e-01\n",
        "   6.41180388e-01   7.78800783e-01   8.94839317e-01   9.72604477e-01\n",
        "   1.00000000e+00   9.72604477e-01   8.94839317e-01   7.78800783e-01\n",
        "   6.41180388e-01   4.99351789e-01   3.67879441e-01   2.56375757e-01\n",
        "   1.69013315e-01   1.05399225e-01   6.21765240e-02   3.46966856e-02\n",
        "   1.83156389e-02   9.14594704e-03   4.32023947e-03   1.93045414e-03\n",
        "   8.15987835e-04   3.26272454e-04   1.23409804e-04   4.41561749e-05\n",
        "   1.49453385e-05   4.78511739e-06   1.44927889e-06   4.15225353e-07\n",
        "   1.12535175e-07   2.88512906e-08   6.99704599e-09   1.60522806e-09\n",
        "   3.48362407e-10   7.15151993e-11   1.38879439e-11   2.55123274e-12\n",
        "   4.43337775e-13   7.28772410e-14   1.13323932e-14   1.66695501e-15\n",
        "   2.31952283e-16   3.05313461e-17   3.80159442e-18   4.47773244e-19\n",
        "   4.98910939e-20   5.25848261e-21   5.24288566e-22   4.94484702e-23\n",
        "   4.41171920e-24   3.72336312e-25   2.97259301e-26   2.24495707e-27\n",
        "   1.60381089e-28   1.08385405e-29   6.92884712e-31   4.19009319e-32\n",
        "   2.39694967e-33   1.29707974e-34   6.63967720e-36   3.21513923e-37\n",
        "   1.47273678e-38   6.38150345e-40   2.61573301e-41   1.01422975e-42]\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(x,u)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[<matplotlib.lines.Line2D at 0x3df7f50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD9CAYAAABDaefJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAGsFJREFUeJzt3X9s1PX9B/DnwZ3ACEKFtpS7aqV3cO0oLVpE3DA3hZR1\n4xQ3k7LMEKysITbM6Yxz2WZrIqMjbov0n2pEcW5YtqAlSzkGczczHC0CYmY7dvxovJa22AJSQCwc\n7+8fn28LBXrt/fjc+/P+fJ6P5JJe79PP55WmPnn5+nw+749NCCFARESmMEZ2AURElDwMdSIiE2Go\nExGZCEOdiMhEGOpERCbCUCciMpGoof74448jMzMTBQUFw26zdu1aeDweFBYW4uDBg0kvkIiIRi9q\nqK9atQqBQGDYzxsbG3HkyBGEQiG8+uqrWLNmTdILJCKi0Ysa6osWLUJaWtqwn2/fvh0rV64EACxY\nsABnzpxBd3d3ciskIqJRsyfywx0dHcjOzh5873K50N7ejszMzCHb2Wy2RA5DRGRZsd70n/CJ0usP\nOFyACyH4StLrhRdekF6DWV7z5r2AsWMF3ntPfi1mePFvM7mveCQU6k6nE+FwePB9e3s7nE5nIrsk\nSpnOTqC1Fdi4EdiwQXY1RMmRUKj7/X689dZbAIC9e/diypQpN4xeiIzqlVeAggJg9WrgxAng3/+W\nXRFR4qLO1FesWIF//vOf6OnpQXZ2Nqqrq3Hp0iUAQEVFBUpLS9HY2Ai3242JEyfijTfeSEnRVufz\n+WSXoLy+PuC114BXXvHBbgeeflrr1rdtk12Z2vi3KZ9NxDu4ieUgNlvc8yEiPfz+98CHHwJbt2rv\nz58HcnK073k8UksjGhRPdjLUyZJmzgTeeQe4556r3/vFL4Bz57TAJzKCeLKTywSQ5fT0AL29wPz5\nQ7+/ZAmwb5+cmoiShaFOltPaCuTnA9dffZufD7S0APyfSlIZQ50sp7UVyMu78fvp6cDYsQBviiaV\nMdTJcoYLdUD7fmtraushSiaGOlkOQ53MjKFOlsNQJzNjqJOlnDsHfP65dk36zTDUSXUMdbKU//4X\nmDVLOyF6MwNXwBCpiqFOlhJt9AIA2dnA2bPAF1+kriaiZGKok6WMFOo2G+D1cgRD6mKok6WMFOoA\n5+qkNoY6WQpDncyOoU6W0d8PtLWNvAojQ51UxlAnywiFgNtvB8aNi75dXh6vgCF1MdTJMgYW8hpJ\nbq72JKQvv9S/JqJkY6iTZYxmng4ADoe23vr//qd/TUTJxlAnyxhtqAOcq5O6GOpkGceOAW736LZ1\nu4GjR/Wth0gPDHWyjPZ2wOUa3bYuF9DRoW89RHpgqJMlXL4MnDwJZGWNbnunU/tHgEg1DHWyhO5u\nYOpU7SToaLBTJ1Ux1MkSYhm9ANq27NRJRQx1soSODm2kMloZGcDp09pdqEQqYaiTJcTaqY8dC0yf\nrt2ERKQShjpZQqydOsCTpaQmhjpZQqydOsCTpaQmhjpZQkdHfKHOTp1Uw1AnS2hvj2/8wk6dVMNQ\nJ9MTIr6ZOjt1UhFDnUzv1Clg/Hhg4sTYfo6dOqmIoU6mF89JUoCdOqmJoU6mF89JUgCYMQPo7ASu\nXEl+TUR6YaiT6cVzkhTQHns3ZYq2EBiRKhjqZHrxduoARzCknhFDPRAIwOv1wuPxoKam5obPe3p6\nsHTpUhQVFWHOnDl488039aiTKG7xduoAT5aSeqKGeiQSQWVlJQKBAFpaWrBlyxa0XveMr9raWsyb\nNw8ff/wxgsEgnnnmGVy+fFnXooliwU6drCRqqDc3N8PtdiMnJwcOhwNlZWVoaGgYsk1WVhbOnj0L\nADh79iymTp0Ku92uX8VEMUq0U2eok0qipm9HRweys7MH37tcLjQ1NQ3ZZvXq1XjggQcwY8YM9PX1\nYevWrTfdV1VV1eDXPp8PPp8v/qqJYpBop/7++8mth2g4wWAQwWAwoX1EDXWbzTbiDtatW4eioiIE\ng0EcPXoUS5YswaFDhzBp0qQh210b6kSpcv488NVXQFpafD/P8Qul0vUNb3V1dcz7iDp+cTqdCIfD\ng+/D4TBc17U8H374IR599FEAQG5uLu68804cPnw45kKI9DCwPMAo+pOb4olSUk3UUC8uLkYoFEJb\nWxv6+/tRX18Pv98/ZBuv14vdu3cDALq7u3H48GHMnDlTv4qJYhDv3aQDBjp1IZJXE5Geoo5f7HY7\namtrUVJSgkgkgvLycuTl5aGurg4AUFFRgZ///OdYtWoVCgsLceXKFfzmN7/BbbfdlpLiiUaSyElS\nAJg0SXsK0hdfaDciERmdTQj9exCbzYYUHIboBr/+tRbI69fHv4/8fKC+HigoSF5dRKMRT3byjlIy\ntc5OICsrsX1kZQFdXcmph0hvDHUyta4u7QHSiZg+naFO6mCok6l1dwOZmYntIzNT2w+RChjqZGoM\ndbIahjqZGkOdrIahTqZ18SJw4UL8d5MO4EydVMJQJ9M6eRLIyIj/btIB7NRJJQx1Mq1kjF4Ahjqp\nhaFOppWsUE9PB3p7gUgk8X0R6Y2hTqaVjGvUAcDh0JYI6O1NfF9EemOok2klq1MHtP3wZCmpgKFO\nppXsUOdcnVTAUCfT6upiqJP1MNTJtNipkxUx1Mm0uruTc6IU4A1IpA6GOpkWO3WyIoY6mdLFi9pD\npxNdImAAQ51UwVAnU0rWEgEDGOqkCoY6mVIy5+kAZ+qkDoY6mVIy5+kAlwogdTDUyZSSeY06oC0V\nMHkylwog42Ookyklu1MHOFcnNTDUyZSSPVMHOFcnNTDUyZSSPX4B2KmTGhjqZEocv5BVMdTJlBjq\nZFUMdTIlztTJqhjqZDrJXiJgADt1UgFDnUwn2UsEDGCokwoY6mQ6eszTAYY6qYGhTqajV6hnZAA9\nPVwqgIyNoU6mo1eoOxzArbcCp04lf99EycJQJ9PRK9QBjmDI+BjqZDonT+ob6idP6rNvomRgqJPp\ndHdr8289ZGSwUydjY6iT6bBTJysbMdQDgQC8Xi88Hg9qampuuk0wGMS8efMwZ84c+Hy+ZNdIFBN2\n6mRl9mgfRiIRVFZWYvfu3XA6nZg/fz78fj/y8vIGtzlz5gyefPJJ7Ny5Ey6XCz09PboXTRSN3p16\nU5M++yZKhqidenNzM9xuN3JycuBwOFBWVoaGhoYh2/zpT3/C9773PbhcLgDAtGnT9KuWaASXLwOn\nTwNTp+qzf3bqZHRRO/WOjg5kZ2cPvne5XGi6rk0JhUK4dOkSvvWtb6Gvrw8//vGP8dhjj92wr6qq\nqsGvfT4fxzSki54ebc0Xe9S/7PjxkkbSUzAYRDAYTGgfUf/0baNYPOPSpUs4cOAA/v73v+PChQtY\nuHAh7r33Xng8niHbXRvqRHoZWPdFLxkZPFFK+rm+4a2uro55H1FD3el0IhwOD74Ph8ODY5YB2dnZ\nmDZtGiZMmIAJEybg/vvvx6FDh24IdaJU0PPGI+Bqpy5E8hcMI0qGqDP14uJihEIhtLW1ob+/H/X1\n9fD7/UO2eeihh/Cvf/0LkUgEFy5cQFNTE/Lz83Utmmg4ep4kBYCJE4GxY4Fz5/Q7BlEionbqdrsd\ntbW1KCkpQSQSQXl5OfLy8lBXVwcAqKiogNfrxdKlSzF37lyMGTMGq1evZqiTNHpezjhg4GTppEn6\nHocoHjYhhND9IDYbUnAYIvzsZ8DkycDzz+t3jIULgZdfBu67T79jEAHxZSfvKCVTSWWnTmREDHUy\nFb1n6gCXCiBjY6iTqbBTJ6tjqJOp6H1JI8AbkMjYGOpkGkLof/MRwBuQyNgY6mQaX3wBjBsHTJig\n73HYqZORMdTJNFJxkhTgiVIyNoY6mUYqTpICPFFKxsZQJ9NIVaeelqYtE9Dfr/+xiGLFUCfTSFWn\nPmYMkJ7OEQwZE0OdTCNVnTrAuToZF0OdTCNVnTrAuToZF0OdTIOdOhFDnUyEnToRQ51MJBVLBAzg\nDUhkVAx1Mg2OX4gY6mQSFy9qr8mTU3M8jl/IqBjqZAoD8/RUPQya4xcyKoY6mUJXFzB9euqON326\ndkwio2Gokyl0dQFZWak7XkYGcOoUcPly6o5JNBoMdTKFzs7UdupjxwJTp/JkKRkPQ51MIdXjF4Aj\nGDImhjqZQqrHL4B2PIY6GQ1DnUwh1eMXQDteZ2dqj0k0EoY6mQI7dSINQ51MgTN1Ig1DnZQnhLxQ\n5/iFjIahTso7fRr42teA8eNTe1yOX8iIGOqkPBldOsDxCxkTQ52UJ+PKF+Dq+EWI1B+baDgMdVKe\njCtfAGDSJG0BsXPnUn9souEw1El5ssYvAEcwZDwMdVKerPELwCtgyHgY6qQ8WeMXgFfAkPEw1El5\nHL8QXcVQJ+Vx/EJ01YihHggE4PV64fF4UFNTM+x2+/btg91ux7Zt25JaINFIOH4huipqqEciEVRW\nViIQCKClpQVbtmxBa2vrTbd77rnnsHTpUghetEsp9NVXQF8fcNttco7P8QsZTdRQb25uhtvtRk5O\nDhwOB8rKytDQ0HDDdhs3bsT3v/99pKen61Yo0c10d2sPgR4jaZCYlcXxCxmLPdqHHR0dyM7OHnzv\ncrnQ1NR0wzYNDQ14//33sW/fPtiGeZx7VVXV4Nc+nw8+ny/+qon+n8yTpAA7dUquYDCIYDCY0D6i\nhvpwAX2tp556CuvXr4fNZoMQYtjxy7WhTpQsskM9PR3o7QUiEe25pUSJuL7hra6ujnkfUUPd6XQi\nHA4Pvg+Hw3C5XEO22b9/P8rKygAAPT092LFjBxwOB/x+f8zFEMWqs1PeSVIAsNuvPoBaZh1EA6KG\nenFxMUKhENra2jBjxgzU19djy5YtQ7Y5duzY4NerVq3CsmXLGOiUMrI7deDqCIahTkYQNdTtdjtq\na2tRUlKCSCSC8vJy5OXloa6uDgBQUVGRkiKJhtPVBRQUyK2Bc3UyEptIwTWIA/N2omR7+GFg5Upg\n+XJ5NaxaBSxaBDz+uLwayJziyU7eUUpKM9L4hcgIGOqkNJlLBAzgUgFkJAx1UlYkonXIM2bIrcPl\nAtrb5dZANIChTso6eRJISwPGjZNbR3Y2Q52Mg6FOygqHtS5ZNpdLq4XICBjqpKxwWOuSZcvMBE6f\n1hYXI5KNoU7Kam83RqiPHavdeHTihOxKiBjqpDCjjF8AjmDIOBjqpCyjjF8ArQ6GOhkBQ52UxVAn\nuhFDnZTV3m6s8QsvayQjYKiTkgZuPHI6ZVeiYadORsFQJyV1dgLTpgEOh+xKNAx1MgqGOinJSKMX\ngOMXMg6GOinJSCdJASAjAzh7Frh4UXYlZHUMdVKS0UJ9zBhtYTF26yQbQ52UZLTxC8ARDBkDQ52U\nZLROHeDJUjIGhjopiaFOdHMMdVKSkdZ9GcD1X8gIGOqknEuXgM8/l//Eo+vxYRlkBAx1Uk5np3YJ\nod0uu5KhOH4hI2Cok3KMOHoBOH4hY2Cok3KM8nCM66WnA+fPAxcuyK6ErIyhTsox4pUvAGCz8Vp1\nko+hTsox6vgF4AiG5GOok3KM2qkDwO23A599JrsKsjKGOinnyBHA7ZZdxc3l5gJHj8qugqyMoU5K\nuXJFC02jhrrbDYRCsqsgK2Ook1I6O4FJk7SXEXk82v9JEMnCUCelhEJacBqVx6PVKITsSsiqGOqk\nlFDIuKMXAEhL0x6xd/Kk7ErIqhjqpJQjR4zdqQMcwZBcDHVSitE7dYAnS0kuhjopxegzdeDqXJ1I\nhhFDPRAIwOv1wuPxoKam5obP//jHP6KwsBBz587FN77xDXzyySe6FEpk9MsZB3D8QjJFXbw0Eomg\nsrISu3fvhtPpxPz58+H3+5GXlze4zcyZM/HBBx9g8uTJCAQC+NGPfoS9e/fqXjhZz4kTwK23Gvdy\nxgEcv5BMUTv15uZmuN1u5OTkwOFwoKysDA0NDUO2WbhwISZPngwAWLBgAdq5mhHpRIXRC8DLGkmu\nqJ16R0cHsq9ZZMPlcqGpqWnY7V9//XWUlpbe9LOqqqrBr30+H3w+X2yVkuWpcOULoF3WOG6cdllj\nZqbsakglwWAQwWAwoX1EDXWbzTbqHf3jH//Apk2bsGfPnpt+fm2oE8VDhStfBgyMYBjqFIvrG97q\n6uqY9xF1/OJ0OhG+Zh3RcDgM103WPP3kk0+wevVqbN++HWlpaTEXQTQaqoxfAF4BQ/JEDfXi4mKE\nQiG0tbWhv78f9fX18Pv9Q7b57LPP8Mgjj+Dtt9+GW5U2ipRk5NUZr+d28woYkiPq+MVut6O2thYl\nJSWIRCIoLy9HXl4e6urqAAAVFRV48cUXcfr0aaxZswYA4HA40NzcrH/lZCmqXM44wOMB3ntPdhVk\nRTYh9D9Hb7PZkILDkIm1twPz52urNKpg3z6gogI4cEB2JaSyeLKTd5SSElQ6SQpcPVHKXoZSjaFO\nSlDpJClw9bLG7m7ZlZDVMNRJCZ9+ClxzI7MS8vO1uolSiaFOSjhwALj7btlVxOauuzhTp9RjqJPh\nRSLAxx8D8+bJriQ2d90F7N8vuwqyGoY6GV4oBKSna3NqlbBTJxkY6mR4Ko5eAMDrBTo6gLNnZVdC\nVsJQJ8Pbv1/relVjtwNz5wIHD8quhKyEoU6Gd+CAmqEOcARDqcdQJ0O7ckXrdFUN9bvvZqhTajHU\nydCOH9eedpSeLruS+LBTp1RjqJOhqTpPH5Cfr/3DdP687ErIKhjqZGgqz9MB4JZbtGA/dEh2JWQV\nDHUyNFUvZ7wW5+qUSgx1Miwh1O/UAc7VKbUY6mRYn30GOBxAVpbsShLD5QIolRjqZFh79gD33CO7\nisQVFADHjgFnzsiuhKyAoU6GtWMH8O1vy64icePHA4sWAbt2ya6ErIChToYUiQCBgDlCHQBKS4HG\nRtlVkBUw1MmQPvoIyMwE7rhDdiXJUVqq/Z/HlSuyKyGzY6iTITU2At/5juwqkmfmTG3pYC7uRXpj\nqJMhNTZq3a2ZcARDqcBQJ8Pp7gaOHAHuu092JcnFUKdUYKiT4QQCwOLF2jXqZvLNbwItLUBPj+xK\nyMwY6mQ4Zhy9AMC4ccADDwA7d8quhMyMoU6G0t+vXc+9dKnsSvRRWgr89a+yqyAzY6iTodTXA/Pm\nqb80wHCWL9fGS11dsishs2Kok2EIAWzYADz7rOxK9DNtGrBiBVBbK7sSMiuGOhnGrl1asJeUyK5E\nX08/DdTV8cEZpA+GOhnGhg3AT38K2GyyK9GX2w3cfz+waZPsSsiMbEIIoftBbDak4DCksIMHgWXL\ntNUMb7lFdjX627tXG8OEQoDdLrsaMqp4spOdOhnChg3A2rXWCHQAuPdewOkE/vIX2ZWQ2bBTJ+ne\nfRf4yU+053hOniy7mtQJBoEf/EBbvGzGDNnVkBHFk50MdZLq6FFg4ULt2m0zPBAjVi++COzeDbz/\nPscwdCOGOinlyy+19V3Ky4HKStnVyHHlinZDUmEhUFMjuxoyGs7ULSIYDMouIWF9fcAPfwjMmgU8\n+aS8OmT/LseMAd5+G9iyBXjlFe2STpXJ/n3SKEI9EAjA6/XC4/GgZphWYu3atfB4PCgsLMRBLhit\nO9X/w9m/X3sY87RpwJtvyr2E0Qi/y2nTtPHL5s3AI48Ap07Jrih+Rvh9Wl3UUI9EIqisrEQgEEBL\nSwu2bNmC1tbWIds0NjbiyJEjCIVCePXVV7FmzRpdCyZ1/ec/wFNPaY+oW7dOuwFnwgTZVRmD2w18\n+CFw551AURHwu99xNUeKT9RQb25uhtvtRk5ODhwOB8rKytDQ0DBkm+3bt2PlypUAgAULFuDMmTPo\n7u7Wr2JSwrlzwOHDwNatwPPPaydBS0qAiRO1Tv3RR2VXaDzjxgG//a02ijlwQAv6hx8G1q/XVnYM\nh7UFz4iiElH8+c9/Fk888cTg+z/84Q+isrJyyDbf/e53xZ49ewbfP/jgg+Kjjz4asg0Avvjiiy++\n4njFKupFVLZRDjuvPzt7/c/xyhciotSIOn5xOp0Ih8OD78PhMFwuV9Rt2tvb4XQ6k1wmERGNRtRQ\nLy4uRigUQltbG/r7+1FfXw+/3z9kG7/fj7feegsAsHfvXkyZMgWZmZn6VUxERMOKOn6x2+2ora1F\nSUkJIpEIysvLkZeXh7q6OgBARUUFSktL0djYCLfbjYkTJ+KNN95ISeFERHQTMU/hY7B161aRn58v\nxowZI/bv3z/ks3Xr1gm32y1mz54tdu7cqWcZpvTCCy8Ip9MpioqKRFFRkdixY4fskpSzY8cOMXv2\nbOF2u8X69etll6O8O+64QxQUFIiioiIxf/582eUoZ9WqVSIjI0PMmTNn8Hu9vb1i8eLFwuPxiCVL\nlojTp0+PuB9dQ721tVUcPnxY+Hy+IaH+6aefisLCQtHf3y+OHz8ucnNzRSQS0bMU06mqqhIvv/yy\n7DKUdfnyZZGbmyuOHz8u+vv7RWFhoWhpaZFdltJycnJEb2+v7DKU9cEHH4gDBw4MCfVnn31W1NTU\nCCGEWL9+vXjuuedG3I+uywR4vV7MmjXrhu83NDRgxYoVcDgcyMnJgdvtRnNzs56lmJLgVUVxG809\nGBQ7/k3Gb9GiRUhLSxvyvWvvA1q5ciXee++9EfcjZe2XEydODLmKxuVyoaOjQ0YpStu4cSMKCwtR\nXl6OM2fOyC5HKR0dHcjOzh58z7/BxNlsNixevBjFxcV47bXXZJdjCt3d3YMXnmRmZo7qxs6EF/tc\nsmQJum7yaPR169Zh2bJlo97PaK+Jt5LhfrcvvfQS1qxZg1/96lcAgF/+8pd45pln8Prrr6e6RGXx\n7y359uzZg6ysLHz++edYsmQJvF4vFi1aJLss07DZbKP6u0041Hft2hXzz/Da9tEZ7e/2iSeeiOkf\nUBrdPRgUm6ysLABAeno6li9fjubmZoZ6gjIzM9HV1YXp06ejs7MTGRkZI/5MysYv187a/H4/3nnn\nHfT39+P48eMIhUK4x4pPSEhAZ2fn4NfvvvsuCgoKJFajntHcg0Gjd+HCBfT19QEAzp8/j7/97W/8\nm0wCv9+PzZs3AwA2b96Mhx9+eOQf0uc8rmbbtm3C5XKJ8ePHi8zMTLF06dLBz1566SWRm5srZs+e\nLQKBgJ5lmNJjjz0mCgoKxNy5c8VDDz0kurq6ZJeknMbGRjFr1iyRm5sr1q1bJ7scpR07dkwUFhaK\nwsJC8fWvf52/zziUlZWJrKws4XA4hMvlEps2bRK9vb3iwQcfjOmSxpQ8+YiIiFKDTz4iIjIRhjoR\nkYkw1ImITIShTkRkIgx1IiITYagTEZnI/wGn1GMS033R8AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2d25590>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ut = np.fft.fft(u)\n",
      "print ut"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  1.06347231e+01 +0.00000000e+00j  -1.03755326e+01 +1.05646184e-14j\n",
        "   9.63525115e+00 -9.10743616e-15j  -8.51695015e+00 +1.60188898e-14j\n",
        "   7.16594710e+00 -1.11610729e-14j  -5.73893778e+00 +1.42870572e-14j\n",
        "   4.37479655e+00 -6.71684930e-15j  -3.17433408e+00 +7.39007447e-15j\n",
        "   2.19237999e+00 -3.82693790e-15j  -1.44127699e+00 +2.71606957e-15j\n",
        "   9.01877400e-01 -9.05387747e-16j  -5.37175233e-01 -2.70742243e-16j\n",
        "   3.04545989e-01 -7.84095011e-16j  -1.64345650e-01 -4.78631213e-16j\n",
        "   8.44173994e-02 +1.12049346e-15j  -4.12737711e-02 -1.96672320e-15j\n",
        "   1.92081155e-02 +2.05058106e-15j  -8.50871142e-03 -3.14344432e-15j\n",
        "   3.58765981e-03 +1.22124533e-15j  -1.43988280e-03 -2.82397735e-15j\n",
        "   5.50061763e-04 +3.05644486e-15j  -2.00015751e-04 -4.22282433e-15j\n",
        "   6.92285704e-05 +4.44449945e-15j  -2.28073568e-05 -5.37776816e-15j\n",
        "   7.15209008e-06 -6.21762416e-16j  -2.13481095e-06 -4.39261238e-16j\n",
        "   6.06532803e-07 +8.41039477e-16j  -1.64027852e-07 -1.82161092e-15j\n",
        "   4.22230231e-08 +8.91912292e-16j  -1.03454532e-08 -1.59906775e-15j\n",
        "   2.41278197e-09 -6.36965597e-16j  -5.35618365e-10 -1.18385208e-16j\n",
        "   1.13177663e-10 -3.84030602e-16j  -2.27636902e-11 +2.71302702e-16j\n",
        "   4.35730618e-12 -1.68676281e-15j  -7.94170285e-13 +8.14832094e-16j\n",
        "   1.36335387e-13 -2.72139164e-15j  -2.20379270e-14 +1.16534965e-15j\n",
        "   2.72004641e-15 -4.92430301e-16j  -6.66133815e-16 -1.27637962e-15j\n",
        "   0.00000000e+00 +1.21552840e-15j  -1.11022302e-15 -3.57960494e-15j\n",
        "  -4.44089210e-16 +3.14412867e-15j  -4.44089210e-16 -5.09848479e-15j\n",
        "   0.00000000e+00 +5.06943293e-15j   0.00000000e+00 -6.24487423e-15j\n",
        "   8.88178420e-16 +6.05410277e-15j   0.00000000e+00 -6.73916852e-15j\n",
        "   1.11022302e-15 +1.95044484e-15j  -1.24024851e-15 -2.51108270e-15j\n",
        "   3.65386297e-16 +1.66862022e-15j  -4.24803964e-16 -2.33887490e-15j\n",
        "   3.53477013e-16 +1.81258807e-15j  -5.58364119e-17 -2.27731351e-15j\n",
        "   3.29597460e-16 +5.12921782e-16j   1.04950770e-16 -1.09999546e-15j\n",
        "   5.20417043e-18 +1.17306068e-15j   9.36750677e-17 -1.82525610e-15j\n",
        "   2.08166817e-17 +1.66115137e-15j   1.45716772e-16 -2.01674761e-15j\n",
        "  -1.42247325e-16 +1.25107518e-16j  -2.77555756e-17 -8.44002958e-16j\n",
        "  -1.11022302e-16 +8.55193704e-16j  -2.22044605e-16 -1.69577019e-15j\n",
        "   1.94289029e-16 +1.93336758e-15j  -6.10622664e-16 -2.67028854e-15j\n",
        "   1.33226763e-15 +1.00906031e-15j  -1.55431223e-15 -1.80809928e-15j\n",
        "   1.88737914e-15 +2.62752538e-15j  -1.77635684e-15 -3.60835893e-15j\n",
        "   1.66533454e-15 +2.96141185e-15j  -2.88657986e-15 -3.91205894e-15j\n",
        "   1.11022302e-15 -1.95044484e-15j  -1.86837596e-15 +1.38980697e-15j\n",
        "   9.66881333e-16 -1.90961975e-15j  -1.35155288e-15 +1.23936507e-15j\n",
        "   5.34701406e-16 -1.76565190e-15j   2.77881017e-16 +3.56514352e-16j\n",
        "   5.58580959e-16 -1.59884790e-15j   1.17093835e-16 -9.39627400e-17j\n",
        "  -4.49293380e-16 +1.82433108e-16j   7.94503352e-16 -2.08040094e-15j\n",
        "   1.56125113e-15 +2.38556015e-15j  -1.96440086e-14 -4.07676486e-15j\n",
        "   1.36248651e-13 +2.97445380e-15j  -7.91755550e-13 -3.70601665e-15j\n",
        "   4.35562697e-12 +2.92165710e-15j  -2.27602381e-11 -3.72505912e-15j\n",
        "   1.13174775e-10 +2.93758197e-15j  -5.35614386e-10 -3.76147884e-15j\n",
        "   2.41277975e-09 +2.14197091e-15j  -1.03454492e-08 -2.99172050e-15j\n",
        "   4.22230190e-08 +2.86309783e-15j  -1.64027845e-07 -4.27891230e-15j\n",
        "   6.06532798e-07 +3.76247976e-15j  -2.13481094e-06 -5.27498566e-15j\n",
        "   7.15209008e-06 +6.21762416e-16j  -2.28073568e-05 -1.68278607e-15j\n",
        "   6.92285704e-05 +7.17798259e-16j  -2.00015751e-04 -1.69836970e-15j\n",
        "   5.50061763e-04 +7.68671074e-16j  -1.43988280e-03 -2.05950532e-15j\n",
        "   3.58765981e-03 +6.68179845e-16j  -8.50871142e-03 -1.32382641e-15j\n",
        "   1.92081155e-02 +3.74130603e-16j  -4.12737711e-02 -1.32204547e-15j\n",
        "   8.44173994e-02 +7.83921866e-16j  -1.64345650e-01 -1.63295948e-15j\n",
        "   3.04545989e-01 +4.05925338e-16j  -5.37175233e-01 -7.50300948e-16j\n",
        "   9.01877400e-01 +1.79413658e-17j  -1.44127699e+00 +6.34428546e-16j\n",
        "   2.19237999e+00 -9.37267038e-16j  -3.17433408e+00 +4.09893319e-15j\n",
        "   4.37479655e+00 +2.55155963e-16j  -5.73893778e+00 +5.26373331e-15j\n",
        "   7.16594710e+00 -7.77117243e-15j  -8.51695015e+00 +1.72248626e-14j\n",
        "   9.63525115e+00 -1.72044571e-14j  -1.03755326e+01 +2.88320543e-14j]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(x,ut)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/lib/python2.7/dist-packages/numpy/core/numeric.py:460: ComplexWarning: Casting complex values to real discards the imaginary part\n",
        "  return array(a, dtype, copy=False, order=order)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[<matplotlib.lines.Line2D at 0x3f6c210>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAD9CAYAAABZVQdHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCmPIExEpjCFPRKQwhjwRkcIY8kRECvt/clHppqOEnhYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3ddaa10>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(x,np.fft.fftshift(ut))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "[<matplotlib.lines.Line2D at 0x41e8350>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAD9CAYAAABZVQdHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3f5fb10>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(np.abs(np.fft.fftshift(ut)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "[<matplotlib.lines.Line2D at 0x4717f50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD9CAYAAACsq4z3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x45a6310>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.pi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "3.141592653589793"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.fft.fftfreq(n,1.0/n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([  0.,   1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,\n",
        "        11.,  12.,  13.,  14.,  15.,  16.,  17.,  18.,  19.,  20.,  21.,\n",
        "        22.,  23.,  24.,  25.,  26.,  27.,  28.,  29.,  30.,  31.,  32.,\n",
        "        33.,  34.,  35.,  36.,  37.,  38.,  39.,  40.,  41.,  42.,  43.,\n",
        "        44.,  45.,  46.,  47.,  48.,  49.,  50.,  51.,  52.,  53.,  54.,\n",
        "        55.,  56.,  57.,  58.,  59., -60., -59., -58., -57., -56., -55.,\n",
        "       -54., -53., -52., -51., -50., -49., -48., -47., -46., -45., -44.,\n",
        "       -43., -42., -41., -40., -39., -38., -37., -36., -35., -34., -33.,\n",
        "       -32., -31., -30., -29., -28., -27., -26., -25., -24., -23., -22.,\n",
        "       -21., -20., -19., -18., -17., -16., -15., -14., -13., -12., -11.,\n",
        "       -10.,  -9.,  -8.,  -7.,  -6.,  -5.,  -4.,  -3.,  -2.,  -1.])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = (2*np.pi/L)*np.fft.fftfreq(n,1.0/n)\n",
      "print k\n",
      "print np.fft.fftshift(k)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  0.           0.31415927   0.62831853   0.9424778    1.25663706\n",
        "   1.57079633   1.88495559   2.19911486   2.51327412   2.82743339\n",
        "   3.14159265   3.45575192   3.76991118   4.08407045   4.39822972\n",
        "   4.71238898   5.02654825   5.34070751   5.65486678   5.96902604\n",
        "   6.28318531   6.59734457   6.91150384   7.2256631    7.53982237\n",
        "   7.85398163   8.1681409    8.48230016   8.79645943   9.1106187\n",
        "   9.42477796   9.73893723  10.05309649  10.36725576  10.68141502\n",
        "  10.99557429  11.30973355  11.62389282  11.93805208  12.25221135\n",
        "  12.56637061  12.88052988  13.19468915  13.50884841  13.82300768\n",
        "  14.13716694  14.45132621  14.76548547  15.07964474  15.393804\n",
        "  15.70796327  16.02212253  16.3362818   16.65044106  16.96460033\n",
        "  17.27875959  17.59291886  17.90707813  18.22123739  18.53539666\n",
        " -18.84955592 -18.53539666 -18.22123739 -17.90707813 -17.59291886\n",
        " -17.27875959 -16.96460033 -16.65044106 -16.3362818  -16.02212253\n",
        " -15.70796327 -15.393804   -15.07964474 -14.76548547 -14.45132621\n",
        " -14.13716694 -13.82300768 -13.50884841 -13.19468915 -12.88052988\n",
        " -12.56637061 -12.25221135 -11.93805208 -11.62389282 -11.30973355\n",
        " -10.99557429 -10.68141502 -10.36725576 -10.05309649  -9.73893723\n",
        "  -9.42477796  -9.1106187   -8.79645943  -8.48230016  -8.1681409\n",
        "  -7.85398163  -7.53982237  -7.2256631   -6.91150384  -6.59734457\n",
        "  -6.28318531  -5.96902604  -5.65486678  -5.34070751  -5.02654825\n",
        "  -4.71238898  -4.39822972  -4.08407045  -3.76991118  -3.45575192\n",
        "  -3.14159265  -2.82743339  -2.51327412  -2.19911486  -1.88495559\n",
        "  -1.57079633  -1.25663706  -0.9424778   -0.62831853  -0.31415927]\n",
        "[-18.84955592 -18.53539666 -18.22123739 -17.90707813 -17.59291886\n",
        " -17.27875959 -16.96460033 -16.65044106 -16.3362818  -16.02212253\n",
        " -15.70796327 -15.393804   -15.07964474 -14.76548547 -14.45132621\n",
        " -14.13716694 -13.82300768 -13.50884841 -13.19468915 -12.88052988\n",
        " -12.56637061 -12.25221135 -11.93805208 -11.62389282 -11.30973355\n",
        " -10.99557429 -10.68141502 -10.36725576 -10.05309649  -9.73893723\n",
        "  -9.42477796  -9.1106187   -8.79645943  -8.48230016  -8.1681409\n",
        "  -7.85398163  -7.53982237  -7.2256631   -6.91150384  -6.59734457\n",
        "  -6.28318531  -5.96902604  -5.65486678  -5.34070751  -5.02654825\n",
        "  -4.71238898  -4.39822972  -4.08407045  -3.76991118  -3.45575192\n",
        "  -3.14159265  -2.82743339  -2.51327412  -2.19911486  -1.88495559\n",
        "  -1.57079633  -1.25663706  -0.9424778   -0.62831853  -0.31415927   0.\n",
        "   0.31415927   0.62831853   0.9424778    1.25663706   1.57079633\n",
        "   1.88495559   2.19911486   2.51327412   2.82743339   3.14159265\n",
        "   3.45575192   3.76991118   4.08407045   4.39822972   4.71238898\n",
        "   5.02654825   5.34070751   5.65486678   5.96902604   6.28318531\n",
        "   6.59734457   6.91150384   7.2256631    7.53982237   7.85398163\n",
        "   8.1681409    8.48230016   8.79645943   9.1106187    9.42477796\n",
        "   9.73893723  10.05309649  10.36725576  10.68141502  10.99557429\n",
        "  11.30973355  11.62389282  11.93805208  12.25221135  12.56637061\n",
        "  12.88052988  13.19468915  13.50884841  13.82300768  14.13716694\n",
        "  14.45132621  14.76548547  15.07964474  15.393804    15.70796327\n",
        "  16.02212253  16.3362818   16.65044106  16.96460033  17.27875959\n",
        "  17.59291886  17.90707813  18.22123739  18.53539666]\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(np.fft.fftshift(k),np.abs(np.fft.fftshift(ut)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "[<matplotlib.lines.Line2D at 0x4c2a590>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAD9CAYAAABKgkezAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSkMIY4EZHCGOJERApjiBMRKez/AddzNtmJ6JVWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4943150>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Video: W01_L01_P04"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u = 1/np.cosh(x)\n",
      "ud = -u*np.tanh(x)\n",
      "u2d = u - 2*u**3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ut = np.fft.fft(u)\n",
      "uds = np.fft.ifft(1j*k*ut)\n",
      "u2ds = np.fft.ifft((1j*k)**2*ut)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ks = np.fft.fftshift(k)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(x,ud,\"r\",x,uds,\"mo\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "[<matplotlib.lines.Line2D at 0x4946310>,\n",
        " <matplotlib.lines.Line2D at 0x49467d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD9CAYAAABQvqc9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x494a610>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = 4\n",
      "n = 120\n",
      "x2 = np.linspace(-L/2,L/2,n+1)\n",
      "x = x2[:-1]\n",
      "\n",
      "k = (2*np.pi/L)*np.fft.fftfreq(n,1.0/n)\n",
      "\n",
      "u = 1/np.cosh(x)\n",
      "ud = -u*np.tanh(x)\n",
      "\n",
      "ut = np.fft.fft(u)\n",
      "uds = np.fft.ifft(1j*k*ut)\n",
      "\n",
      "pl.plot(x,ud,\"r\",x,uds,\"mo\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "[<matplotlib.lines.Line2D at 0x6771990>,\n",
        " <matplotlib.lines.Line2D at 0x6771e50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD9CAYAAABUS3cAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/x+UXvdb0UlMuQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x649f950>"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "help(PyConAPAC.call_for_proposal)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2014,
       "html": [
        "<pre>PyCon APAC 2014 Call for Proposal !!\n",
        "\n",
        "    PyCon APAC 2014 is now accepting all types of proposals.\n",
        "    In addition to regular and lightning talks, you can also \n",
        "    submit proposals for tutorials and for SciPy Track.\n",
        "    Please refer to the detail page below:</pre>",
        "<p style=\"text-indent:4;font-family:monospace\">&nbsp&nbsp&nbsp&nbsp<a href=\"http://tw.pycon.org/2014apac/en/call-for-proposals/\">http://tw.pycon.org/2014apac/en/call-for-proposals/</a></p>"
       ]
      }
     ],
     "prompt_number": 2014
    }
   ],
   "metadata": {}
  }
 ]
}