{
 "metadata": {
  "name": "",
  "signature": "sha256:d514892e91439011b3eb3230f11ce497bb0b91c5eabfb8ddf0c282d8ebf07dd4"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "\n",
      "import ndl\n",
      "\n",
      "%matplotlib inline\n",
      "\n",
      "%precision 3\n",
      "pd.set_option('display.precision', 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First we'll try a strictly agglutinative morphemic alignment, with a one-to-one mapping between forms and meanings:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "morphemes = pd.DataFrame()\n",
      "morphemes['Cues'] = [('stem','a','c'),('stem','a','d'),('stem','b','c'),('stem','b','d')]\n",
      "morphemes['Outcomes'] = [('nom','sg'),('nom','pl'),('acc','sg'),('acc','pl')]\n",
      "morphemes['Frequency'] = [1,1,1,1]\n",
      "morphemes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Cues</th>\n",
        "      <th>Outcomes</th>\n",
        "      <th>Frequency</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> (stem, a, c)</td>\n",
        "      <td> (nom, sg)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> (stem, a, d)</td>\n",
        "      <td> (nom, pl)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> (stem, b, c)</td>\n",
        "      <td> (acc, sg)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> (stem, b, d)</td>\n",
        "      <td> (acc, pl)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 50,
       "text": [
        "           Cues   Outcomes  Frequency\n",
        "0  (stem, a, c)  (nom, sg)          1\n",
        "1  (stem, a, d)  (nom, pl)          1\n",
        "2  (stem, b, c)  (acc, sg)          1\n",
        "3  (stem, b, d)  (acc, pl)          1"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "After 1,000 learning iterations, we check the associations between the cues and the outcomes:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W1 = ndl.rw(morphemes,M=1000)\n",
      "W1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>acc</th>\n",
        "      <th>nom</th>\n",
        "      <th>pl</th>\n",
        "      <th>sg</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>a</th>\n",
        "      <td>-0.37</td>\n",
        "      <td> 0.62</td>\n",
        "      <td> 0.13</td>\n",
        "      <td> 0.12</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>b</th>\n",
        "      <td> 0.62</td>\n",
        "      <td>-0.37</td>\n",
        "      <td> 0.12</td>\n",
        "      <td> 0.13</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>c</th>\n",
        "      <td> 0.13</td>\n",
        "      <td> 0.12</td>\n",
        "      <td>-0.37</td>\n",
        "      <td> 0.62</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>d</th>\n",
        "      <td> 0.12</td>\n",
        "      <td> 0.13</td>\n",
        "      <td> 0.62</td>\n",
        "      <td>-0.37</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>stem</th>\n",
        "      <td> 0.25</td>\n",
        "      <td> 0.25</td>\n",
        "      <td> 0.25</td>\n",
        "      <td> 0.25</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "       acc   nom    pl    sg\n",
        "a    -0.37  0.62  0.13  0.12\n",
        "b     0.62 -0.37  0.12  0.13\n",
        "c     0.13  0.12 -0.37  0.62\n",
        "d     0.12  0.13  0.62 -0.37\n",
        "stem  0.25  0.25  0.25  0.25"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And, the complete forms get the right interpretation:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pd.DataFrame([ndl.activation(c,W1) for c in morphemes.Cues],index=morphemes.Cues)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>acc</th>\n",
        "      <th>nom</th>\n",
        "      <th>pl</th>\n",
        "      <th>sg</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>Cues</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>(stem, a, c)</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, a, d)</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, b, c)</th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, b, d)</th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "              acc  nom  pl  sg\n",
        "Cues                          \n",
        "(stem, a, c)    0    1   0   1\n",
        "(stem, a, d)    0    1   1   0\n",
        "(stem, b, c)    1    0   0   1\n",
        "(stem, b, d)    1    0   1   0"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we'll try a paradigm with the same cues and the same outcomes, but this time they're not arrange with a one-to-one correspondence:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gestalt = morphemes.copy()\n",
      "gestalt['Cues'] = [('stem','a','c'),('stem','b','c'),('stem','b','d'),('stem','a','d')]\n",
      "gestalt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Cues</th>\n",
        "      <th>Outcomes</th>\n",
        "      <th>Frequency</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> (stem, a, c)</td>\n",
        "      <td> (nom, sg)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> (stem, b, c)</td>\n",
        "      <td> (nom, pl)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> (stem, b, d)</td>\n",
        "      <td> (acc, sg)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> (stem, a, d)</td>\n",
        "      <td> (acc, pl)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "           Cues   Outcomes  Frequency\n",
        "0  (stem, a, c)  (nom, sg)          1\n",
        "1  (stem, b, c)  (nom, pl)          1\n",
        "2  (stem, b, d)  (acc, sg)          1\n",
        "3  (stem, a, d)  (acc, pl)          1"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W2 = ndl.rw(gestalt,M=1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This time, the number distincton doesn't get learned:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pd.DataFrame([ndl.activation(c,W2) for c in gestalt.Cues],index=gestalt.Cues)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>acc</th>\n",
        "      <th>nom</th>\n",
        "      <th>pl</th>\n",
        "      <th>sg</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>Cues</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>(stem, a, c)</th>\n",
        "      <td> 0.00</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0.60</td>\n",
        "      <td> 0.40</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, b, c)</th>\n",
        "      <td> 0.00</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0.64</td>\n",
        "      <td> 0.36</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, b, d)</th>\n",
        "      <td> 0.99</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.61</td>\n",
        "      <td> 0.39</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, a, d)</th>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.57</td>\n",
        "      <td> 0.43</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "               acc  nom    pl    sg\n",
        "Cues                               \n",
        "(stem, a, c)  0.00    1  0.60  0.40\n",
        "(stem, b, c)  0.00    1  0.64  0.36\n",
        "(stem, b, d)  0.99    0  0.61  0.39\n",
        "(stem, a, d)  1.00    0  0.57  0.43"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But, if we add compound cues, things work:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gestalt2 = gestalt.copy()\n",
      "gestalt2['Cues'] = [('stem','a','c','a&c'),('stem','b','c','b&c'),('stem','b','d','b&d'),('stem','a','d','a&d')]\n",
      "gestalt2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Cues</th>\n",
        "      <th>Outcomes</th>\n",
        "      <th>Frequency</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> (stem, a, c, a&amp;c)</td>\n",
        "      <td> (nom, sg)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> (stem, b, c, b&amp;c)</td>\n",
        "      <td> (nom, pl)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> (stem, b, d, b&amp;d)</td>\n",
        "      <td> (acc, sg)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> (stem, a, d, a&amp;d)</td>\n",
        "      <td> (acc, pl)</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "                Cues   Outcomes  Frequency\n",
        "0  (stem, a, c, a&c)  (nom, sg)          1\n",
        "1  (stem, b, c, b&c)  (nom, pl)          1\n",
        "2  (stem, b, d, b&d)  (acc, sg)          1\n",
        "3  (stem, a, d, a&d)  (acc, pl)          1"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W3 = ndl.rw(gestalt2,M=1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pd.DataFrame([ndl.activation(c,W3) for c in gestalt2.Cues],index=gestalt2.Cues)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>acc</th>\n",
        "      <th>nom</th>\n",
        "      <th>pl</th>\n",
        "      <th>sg</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>Cues</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>(stem, a, c, a&amp;c)</th>\n",
        "      <td> 8.14e-04</td>\n",
        "      <td> 1.00e+00</td>\n",
        "      <td> 0.04</td>\n",
        "      <td> 0.96</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, b, c, b&amp;c)</th>\n",
        "      <td>-4.13e-04</td>\n",
        "      <td> 1.00e+00</td>\n",
        "      <td> 0.95</td>\n",
        "      <td> 0.05</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, b, d, b&amp;d)</th>\n",
        "      <td> 1.00e+00</td>\n",
        "      <td> 2.06e-04</td>\n",
        "      <td> 0.04</td>\n",
        "      <td> 0.96</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>(stem, a, d, a&amp;d)</th>\n",
        "      <td> 9.99e-01</td>\n",
        "      <td> 3.18e-04</td>\n",
        "      <td> 0.96</td>\n",
        "      <td> 0.04</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "                        acc       nom    pl    sg\n",
        "Cues                                             \n",
        "(stem, a, c, a&c)  8.14e-04  1.00e+00  0.04  0.96\n",
        "(stem, b, c, b&c) -4.13e-04  1.00e+00  0.95  0.05\n",
        "(stem, b, d, b&d)  1.00e+00  2.06e-04  0.04  0.96\n",
        "(stem, a, d, a&d)  9.99e-01  3.18e-04  0.96  0.04"
       ]
      }
     ],
     "prompt_number": 65
    }
   ],
   "metadata": {}
  }
 ]
}