{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as pt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 64\n",
      "omega = exp(2*pi*1j*1./n)\n",
      "\n",
      "opowers = omega**[1,2,3,4,5]\n",
      "\n",
      "xlim([-1.2, 1.2]); xlabel(\"Real\")\n",
      "ylim([-1.2, 1.2]); ylabel(\"Imaginary\")\n",
      "grid()\n",
      "gca().set_aspect(\"equal\")\n",
      "plot(opowers.real, opowers.imag, \"o\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "[<matplotlib.lines.Line2D at 0x3d13b50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FhYVYtmwZ8vPzPStyo/lk3UQUHQJOi+bMmRPWwYl64LSIyBhh9VxeeeUVdHZ2Iicnx3OC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\n4kJEmmBxISJNsLgQkSb+D1rOl8Q5TEx2AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3d13b10>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "opowers = omega**arange(n)\n",
      "plot(opowers.imag)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[<matplotlib.lines.Line2D at 0x42e71d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iIir6IiIuoqIvIuIiKvoiIi7iddGfM2cOLVq0oGrVqqxbt67M6+rXr0+rVq1I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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3d1a650>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot((opowers**2).imag)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[<matplotlib.lines.Line2D at 0x4478b50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kcmlpsonFwIG6IyF33X239MksWKA7kstt3CjLQD/wgO5IfIs1fcLXXwNvvAFs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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4445bd0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot((opowers**5).imag)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "[<matplotlib.lines.Line2D at 0x477da90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aWuTNodpFYfQokbka+ehRIClJ3vjBIFv0Vfyiky361dXUsXbAAHlzBAp7+r5h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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4594c50>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dot(opowers, opowers**3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "(-1.5210055437364645e-14-3.8691272408186705e-14j)"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dot(opowers**17, opowers**3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(-5.7620574978045624e-14-3.8857805861880479e-15j)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dot(opowers**3, opowers**3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(-2.042810365310288e-14-3.0975222387041867e-14j)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dot((opowers**3).conj(), opowers**3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(64.000000000000668+0j)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vdot(opowers**3, opowers**3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "(64.000000000000668+0j)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Now in matrix form"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat = np.vstack(\n",
      "   [opowers**0, opowers**1, opowers**2,\n",
      "   opowers**3, opowers**4, opowers**5]).T\n",
      "mat.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "(64, 6)"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(np.dot(mat, [0, 1, 0,0, 0.3, 0.7]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/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": 13,
       "text": [
        "[<matplotlib.lines.Line2D at 0x4986090>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Qb//kSeCf/1Q2LrlcukRlnPfea/rowXfeARYsAH78UdnYGqqupvUcISHqxsGU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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4792750>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat = opowers[:, newaxis] ** arange(n)\n",
      "mat.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "(64, 64)"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "weights = zeros(n)\n",
      "weights[1] = 1\n",
      "weights[4] = 0.3\n",
      "weights[5] = 0.7\n",
      "plot(dot(mat, weights))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "[<matplotlib.lines.Line2D at 0x4bce2d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Qb//kSeCf/1Q2LrlcukRlnPfea/rowXfeARYsAH78UdnYGqqupvUcISHqxsGU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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x49cca50>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Inverse of `mat`?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dot(mat[:,3].conj(), mat[3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "(64.000000000000455+9.7574726076743483e-14j)"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}