{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy.linalg as la"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/lib/pymodules/python2.7/numpy/oldnumeric/__init__.py:11: ModuleDeprecationWarning: The oldnumeric module will be dropped in Numpy 1.9\n",
        "  warnings.warn(_msg, ModuleDeprecationWarning)\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 6\n",
      "\n",
      "np.random.seed(0)\n",
      "A = (\n",
      "     +         np.diag(np.random.randn(n))\n",
      "     + np.roll(np.diag(np.random.randn(n)), 1)\n",
      "     + np.roll(np.diag(np.random.randn(n)), -1)\n",
      "     )\n",
      "\n",
      "np.set_printoptions(precision=2)\n",
      "A"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "array([[ 3.22,  0.95,  0.  ,  0.  ,  0.  ,  0.  ],\n",
        "       [ 0.12,  0.4 , -0.15,  0.  ,  0.  ,  0.  ],\n",
        "       [ 0.  ,  0.44,  0.98, -0.1 ,  0.  ,  0.  ],\n",
        "       [ 0.  ,  0.  ,  0.33,  2.24,  0.41,  0.  ],\n",
        "       [ 0.  ,  0.  ,  0.  ,  1.49,  1.87,  0.14],\n",
        "       [ 0.  ,  0.  ,  0.  ,  0.  , -0.21, -0.22]])"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P, L, U = la.lu(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array([[ 1.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],\n",
        "       [ 0.  ,  1.  ,  0.  ,  0.  ,  0.  ,  0.  ],\n",
        "       [ 0.04,  0.82,  1.  ,  0.  ,  0.  ,  0.  ],\n",
        "       [ 0.  ,  0.  , -0.35,  1.  ,  0.  ,  0.  ],\n",
        "       [ 0.  ,  0.  , -0.  ,  0.66,  1.  ,  0.  ],\n",
        "       [ 0.  ,  0.  , -0.  ,  0.  , -0.13,  1.  ]])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([[ 3.22,  0.95,  0.  ,  0.  ,  0.  ,  0.  ],\n",
        "       [ 0.  ,  0.44,  0.98, -0.1 ,  0.  ,  0.  ],\n",
        "       [ 0.  ,  0.  , -0.95,  0.08,  0.  ,  0.  ],\n",
        "       [ 0.  ,  0.  ,  0.  ,  2.27,  0.41,  0.  ],\n",
        "       [ 0.  ,  0.  ,  0.  ,  0.  ,  1.6 ,  0.14],\n",
        "       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  , -0.2 ]])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* Observe bandwidth growth.\n",
      "* Asymptotic cost of operating on banded matrices? (Mat-vec? Factorization?)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}