{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "import numpy as np\n",
      "import numpy.linalg as la\n",
      "import matplotlib.pyplot as pt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(-1, 1, 100)\n",
      "\n",
      "pt.xlim([-1.2, 1.2])\n",
      "pt.ylim([-1.2, 1.2])\n",
      "\n",
      "for k in range(2): # crank up\n",
      "    pt.plot(x, np.cos(k*np.arccos(x)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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15Xu6opq6NqUDPQf0wgcvqLelV682vaqV5SudXhYA5C3v4V5XV6dz587pN7/5TdZjZmdn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\nHQB86H8Byc1tnytXS/AAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x49f7c50>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Does any of this matter?\n",
      "\n",
      "What if we interpolate random data?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 10 # crank up\n",
      "\n",
      "i = np.arange(n, dtype=np.float64)\n",
      "\n",
      "# Chebyshev nodes:\n",
      "nodes = np.cos((2*(i+1)-1)/(2*n)*np.pi)\n",
      "\n",
      "# Equispace nodes:\n",
      "# nodes = np.linspace(-1, 1, n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pt.plot(nodes, 0*nodes, \"o\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "[<matplotlib.lines.Line2D at 0x589b090>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ki4u1fv16DQ0NjVkXjUZVUlIiv9+vxsbGtO3333+/5s2bp8HBwWxbAQBMkaxDoaGhQeFw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\nCgAAi1AAAFj/D6uy2ocT//dLAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x539ad90>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "V = np.cos(i*np.arccos(nodes.reshape(-1, 1)))\n",
      "data = np.random.randn(n)\n",
      "coeffs = la.solve(V, data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(-1, 1, 1000)\n",
      "Vfull = np.cos(i*np.arccos(x.reshape(-1, 1)))\n",
      "pt.plot(x, np.dot(Vfull, coeffs))\n",
      "pt.plot(nodes, data, \"o\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[<matplotlib.lines.Line2D at 0x5563f10>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TjUbT7F6AMwQHAyUltEuOUj36KDByJH2MZ8wWr7wCXL1KG7S7q9JSYOxY5W9k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\nizHmXuLjOfEryu9+Z3+pZ9U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       "text": [
        "<matplotlib.figure.Figure at 0x5563ed0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 75
    }
   ],
   "metadata": {}
  }
 ]
}