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 },
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Quiz 3 (Batch 2)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. Write a *function* which reads a matrix and *returns* the matrix in the form list of lists.\n",
      "1. Write another *function* which takes, as an argument, a matrix $A$ in the form of list of lists; and *returns* $(A + A^t)/2$ where $A^t$ denotes the *transpose* of $A$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create the file we'll be using to test the following.\n",
      "wfl = open(\"test.txt\", \"w\")\n",
      "wfl.write(\"0 1 2\\n\")\n",
      "wfl.write(\"1 0 4\\n\")\n",
      "wfl.write(\"0 0 1\\n\")\n",
      "wfl.close()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def read_matrix(filename) :\n",
      "    \"\"\"Read a matrix from a file called filename. This returns a list of lists.\"\"\"\n",
      "    fl = open(filename, \"r\")\n",
      "    mat = []\n",
      "    for line in fl :\n",
      "        row = []\n",
      "        words = line.split()\n",
      "        for w in words :\n",
      "            row.append(float(w))\n",
      "        mat.append(row)\n",
      "    fl.close()\n",
      "    return mat\n",
      "        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print read_matrix(\"test.txt\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[0.0, 1.0, 2.0], [1.0, 0.0, 4.0], [0.0, 0.0, 1.0]]\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def symmetric(matrix) :\n",
      "    \"\"\"It computes (A + A^t)/2 of the matrix A.\"\"\"\n",
      "    no_rows = len(matrix)\n",
      "    if no_rows == 0 :\n",
      "        retval = matrix\n",
      "    else :\n",
      "        no_cols = len(matrix[0])\n",
      "        if no_rows != no_cols :\n",
      "            print \"Expected a square matrix.\"\n",
      "            retval = None\n",
      "        else :\n",
      "            sym = []\n",
      "            for i in range(no_rows) :\n",
      "                symrow = []\n",
      "                for j in range(no_rows) :\n",
      "                    symentry = (float(matrix[i][j] + matrix[j][i]))/2.0\n",
      "                    symrow.append(symentry)\n",
      "                sym.append(symrow)\n",
      "            retval = sym\n",
      "    return retval"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print symmetric(read_matrix(\"test.txt\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[0.0, 1.0, 1.0], [1.0, 0.0, 2.0], [1.0, 2.0, 1.0]]\n"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}