Overview.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quick Overview of permpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import permpy as pp\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Permutations can be initialized in a variety of ways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4 1 3 2"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.Permutation([4,1,3,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1 4 6 17 10 5 8 7 2 16 14 15 20 19 12 11 9 13 18 3"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.Permutation.random(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2 4 5 3 1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.Permutation([-4,10, 33, 0.3815, -20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3 4 6 9 2 7 8 1 5"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.Permutation(346927815)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## And can be viewed in oneline notation, cycle notation, or plotted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p = pp.Permutation(346927815)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "( 8 1 3 6 7 ) ( 9 5 2 4 )\n",
      "3 4 6 9 2 7 8 1 5\n"
     ]
    }
   ],
   "source": [
    "pp.Permutation.change_repr('cycle'); print(p)\n",
    "pp.Permutation.change_repr('oneline'); print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, uses matplotlib for plotting (arguments are passed to the matplotlib axes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AKpgBIBXMANC0IuKtEXF6ffsPIuJ5PY99LCJeNH+j0+5q85uA6riIuAF4V2bePN9j0dxw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106677748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x106677f98>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.plot(title='plot of a permutation', xlabel='position', ylabel='value')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can plot as ascii art if you don't want to use matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      *          \n",
      "            *    \n",
      "          *      \n",
      "    *            \n",
      "                *\n",
      "  *              \n",
      "*                \n",
      "        *        \n",
      "              *  \n"
     ]
    }
   ],
   "source": [
    "p.plot(use_mpl=False) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supports a variety of permutation operations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1067b8518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10675b2b0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = p.inverse()\n",
    "(p * q).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106990b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNPsC+KInrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106990c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x106a30080>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute the direct sum and skew sum\n",
    "(p + q).plot(); (p - q).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1 2 3 4 5 6 7 8 9"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p ** p.order()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1 2 3 4 5 6 7 8 9"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(p ** 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## A wide variety of permutation statistics are built in, and the object is easily extensible"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A few examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 17, 0, 4, 11, 2]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[p.num_ascents(), p.inversions(), p.fixed_points(), p.longestrun(), p.majorindex(), p.num_cycles()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A few more"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 2, 3, 2, 2, 2]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[p.num_cycles(), p.num_peaks(), p.num_ltrmin(), p.num_bonds(), p.num_bonds(), p.num_valleys()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Much of the functionality is geared towards permutation patterns, particularly in enumerating avoidance classes and counting pattern occurrences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the number of permutations avoiding the pattern 132:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Set of 0 permutations,\n",
       " Set of 1 permutations,\n",
       " Set of 2 permutations,\n",
       " Set of 5 permutations,\n",
       " Set of 14 permutations,\n",
       " Set of 42 permutations,\n",
       " Set of 132 permutations,\n",
       " Set of 429 permutations,\n",
       " Set of 1430 permutations,\n",
       " Set of 4862 permutations,\n",
       " Set of 16796 permutations]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = pp.Permutation(132)\n",
    "C = pp.AvClass([p], length = 10)\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the total number of inversions in length 4 permutations of the class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "47"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C[4].total_statistic(pp.Permutation.inversions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot a random length 10 permutation from the class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAADtCAYAAABTTfKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10412c278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1069a3b38>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C[10].get_random().plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Can also plot a heatmap, which helps to visualize an _average_ permutation within any set of permutations\n",
    "\n",
    "Darker areas indicate areas where entries are more common throughout the class. The bigger the class, the more accurate the visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARMAAAEACAYAAACQ65KNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106a547f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "basis = [pp.Permutation(21)]\n",
    "C = pp.AvClass(basis, length=9)\n",
    "C.heatmap()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HNdhgu7MVDFqAIwtkrN0VaY7IaQBZ0CFEO8CoC8IkIacdFYCUSqVSaarIHh0U9oFjGRr2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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106a20b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9,4))\n",
    "ax = fig.add_subplot(131)\n",
    "basis = [pp.Permutation(132)]\n",
    "C = pp.AvClass(basis, length=9)\n",
    "C.heatmap(ax=ax, title='basis = {}'.format(basis))\n",
    "\n",
    "ax = fig.add_subplot(132)\n",
    "basis = [pp.Permutation(123), pp.Permutation(231)]\n",
    "C = pp.AvClass(basis, length=9)\n",
    "C.heatmap(ax=ax, only_length=9, title='basis = {}'.format(basis))\n",
    "\n",
    "ax = fig.add_subplot(133)\n",
    "basis = [pp.Permutation(1324)]\n",
    "C = pp.AvClass(basis, length=9)\n",
    "C.heatmap(ax=ax, only_length=9, blur=True, title='basis = {}'.format(basis))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}