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   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Quiz 3 (Batch 4)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. Write a *function* which read a matrix from a file and *returns* a list of lists.\n",
      "1. Write another *function* which, as an argument, takes a matrix $A$ in the form of list of lists, and *returns* a Boolean `True` if the matrix is antisymmetric, and returns a `False` otherwise. Note that antisymmetric means $A^t = -A$."
     ]
    },
    {
     "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 0\\n\")\n",
      "wfl.write(\"-1 0 4\\n\")\n",
      "wfl.write(\"0 -4 0\\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"
     ],
     "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, 0.0], [-1.0, 0.0, 4.0], [0.0, -4.0, 0.0]]\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def is_anti_symmetric(A) :\n",
      "    \"\"\"Checks if a matrix is antisymmetric or not.\"\"\"\n",
      "    # Note an antisymmetric matrix has to be a square matrix.\n",
      "    # We assume that the empty matrix is antisymmetric.\n",
      "    \n",
      "    # Note if A^t[i][j] = -A[i][j], we also have A^t[j][i] = \n",
      "    # - A[j][i].\n",
      "    \n",
      "    rows = len(A)\n",
      "    if rows == 0 :\n",
      "        retval = True\n",
      "    else :\n",
      "        cols = len(A[0])\n",
      "        if rows != cols :\n",
      "            print \"Expected a square matrix.\"\n",
      "            retval = None\n",
      "        else :\n",
      "            retval = True\n",
      "            for i in range(rows) :\n",
      "               for j in range(i+1) :\n",
      "                    if A[i][j] != - A[j][i] :\n",
      "                        retval = False\n",
      "    return retval"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "is_anti_symmetric(read_matrix(\"test.txt\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}