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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "8.2.5 Alternative Gauss Jordon Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this notebook, you will implement the alternative Gauss Jordan algorithm that overwrites $ A $ in one sweep with the identity matrix and $ B $ with the inverse of the original matrix $ A $.\n",
      "\n",
      "<font color=red> Be sure to make a copy!!!! </font>\n",
      "\n",
      "<h2> First, let's create a matrix $ A $ and set $ B $ to the identity. </h2>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import laff\n",
      "import flame\n",
      "\n",
      "L = np.matrix( ' 1, 0, 0. 0;\\\n",
      "                -2, 1, 0, 0;\\\n",
      "                 1,-3, 1, 0;\\\n",
      "                 2, 3,-1, 1' )\n",
      "\n",
      "U = np.matrix( ' 2,-1, 3,-2;\\\n",
      "                 0,-2, 1,-1;\\\n",
      "                 0, 0, 1, 2;\\\n",
      "                 0, 0, 0, 3' )\n",
      "\n",
      "A = L * U\n",
      "Aold = np.matrix( np.copy( A ) ) \n",
      "B = np.matrix( np.eye( 4 ) )\n",
      "\n",
      "print( 'A = ' )\n",
      "print( A )\n",
      "\n",
      "print( 'B = ' )\n",
      "print( B )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h2> Implement the alternative Gauss-Jordan algorithm from 8.2.5 </h2>\n",
      "\n",
      "Here is the algorithm:\n",
      "\n",
      "<img src=\"https://studio.edx.org/c4x/UTAustinX/UT.5.01x/asset/8_2_5_Algorithm.png\" alt=\"Alternative Gauss-Jordan algorithm\" width=100%>\n",
      "    \n",
      "<font color=red> Important: if you make a mistake, rerun ALL cells above the cell in which you were working, and then the one where you are working. </font>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create the routine\n",
      "<code> GJ_Inverse_alt </code>\n",
      "with the <a href=\"https://studio.edx.org/c4x/UTAustinX/UT.5.01x/asset/index.html\"> Spark webpage</a> for the algorithm"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# insert code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3> Test the routine </h3>\n",
      "\n",
      "<font color=red> Important: if you make a mistake, rerun ALL cells above the cell in which you were working, and then the one where you are working. </font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "GJ_Inverse_alt( A, B )\n",
      "\n",
      "print( A )\n",
      "print( B )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Matrix $ A $ should now be an identity matrix and $ B $ should no longer be an identity matrix.\n",
      "\n",
      "Check if $ B $ now equals (approximately) the inverse of the original matrix $ A $:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print( Aold * B )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}