{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "import numpy\n",
      "import numpy.linalg as la"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nodes = [0, 1]\n",
      "#nodes = [0, 0.5, 1]\n",
      "#nodes = [3, 3.5, 4]\n",
      "#nodes = [0, 1, 2]\n",
      "#nodes = np.linspace(0, 1, 12)\n",
      "\n",
      "max_degree = len(nodes)-1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nodes = np.array(nodes)\n",
      "powers = np.arange(max_degree+1)\n",
      "\n",
      "Vt = nodes ** powers.reshape(-1, 1)\n",
      "\n",
      "a = nodes[0]\n",
      "b = nodes[-1]\n",
      "rhs = 1/(powers+1) * (b**(powers+1) - a**(powers+1))\n",
      "\n",
      "if len(nodes) <= 4:\n",
      "    print Vt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[1 1]\n",
        " [0 1]]\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "weights = la.solve(Vt, rhs)\n",
      "\n",
      "print weights"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.5  0.5]\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(len(nodes) + 1):\n",
      "    approx = np.dot(weights, nodes**i)\n",
      "    true = 1/(i+1)*(b**(i+1) - a**(i+1))\n",
      "    \n",
      "    print \"Error at degree %d: %g\" % (i, approx-true)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Error at degree 0: 0\n",
        "Error at degree 1: 0\n",
        "Error at degree 2: 0.166667\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    }
   ],
   "metadata": {}
  }
 ]
}