{
 "metadata": {
  "name": "",
  "signature": "sha256:82bc14c3cf36e5ea55087ac44c67ccb199af57823353d8fdd0285400fa289cbf"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph import generators\n",
      "\n",
      "HG = generators.generic_hypergraph(6, ((3, 4), (4, 3), (5, 1)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "from functools import partial\n",
      "from matplotlib import pyplot as plt\n",
      "\n",
      "from numpy import linalg as LA\n",
      "\n",
      "from hypergraph import generators\n",
      "from hypergraph.analytical import prediction\n",
      "from hypergraph.diffusion_engine import DiffusionEngine\n",
      "from hypergraph import utils\n",
      "from hypergraph.markov_diffusion import create_markov_matrix_model_nodes\n",
      "from hypergraph.markov_diffusion import create_markov_matrix_model_hyper_edges\n",
      "\n",
      "def hypergraph_analytical_edges(HG):\n",
      "    phis = []\n",
      "    number_of_nodes = len(HG.nodes())\n",
      "    all_phis = 0\n",
      "    for edge in HG.hyper_edges():\n",
      "        phis.append(len(edge))\n",
      "        all_phis += len(edge)\n",
      "    \n",
      "    pis = [phi / all_phis for phi in phis]\n",
      "    return pis\n",
      "\n",
      "\n",
      "\n",
      "def show_models(HG):\n",
      "    all_models={\"node\": {\"analytical\": partial(prediction, model='hypergraph'),\n",
      "                    \"numerical\": create_markov_matrix_model_nodes,\n",
      "                    \"name\": \"node\",\n",
      "                   },\n",
      "            \"hyperedges\": {\"analytical\": hypergraph_analytical_edges,\n",
      "                           \"numerical\": create_markov_matrix_model_hyper_edges,\n",
      "                           \"name\": \"hyperedges\",\n",
      "                           }\n",
      "    }\n",
      "    t_max = 100000\n",
      "    number_of_walkers = 1\n",
      "    \n",
      "    \n",
      "    model = all_models['node']\n",
      "    \n",
      "    def show_model(model):\n",
      "        markov_matrix = model[\"numerical\"](HG)\n",
      "        \n",
      "        \n",
      "        t_per_walker = int(t_max / number_of_walkers)\n",
      "\n",
      "        engine = DiffusionEngine(markov_matrix, t_per_walker=t_per_walker)\n",
      "\n",
      "        freqs_matrix = LA.matrix_power(markov_matrix, 40)[0]\n",
      "        frequencies, states = engine.simulate(t_max)\n",
      "\n",
      "        connected_elements = [freq[0] + 1 for freq in frequencies]\n",
      "\n",
      "        if model['name'] == \"node\":\n",
      "            missing_nodes = set(HG.nodes()) - set(connected_elements)\n",
      "            for missing_node in missing_nodes:\n",
      "                frequencies.append((missing_node, 0))\n",
      "                \n",
      "        frequencies = [(node, frequency) for node, frequency in frequencies]\n",
      "        frequencies.sort(key=lambda x: x[0])\n",
      "        xs, ys = zip(*frequencies)\n",
      "\n",
      "        ys = np.array(ys, dtype='float')\n",
      "        ys /= sum(ys)\n",
      "        width = 0.2  \n",
      "\n",
      "        ys_prediction = model[\"analytical\"](HG)\n",
      "\n",
      "        plt.figure(figsize=(10, 8))\n",
      "        plt.bar(xs, ys, width=width, color='crimson', label='Simulated')\n",
      "\n",
      "        plt.bar(np.array(xs) + width, freqs_matrix, width=width, label='Traversal matrix to N')\n",
      "\n",
      "        plt.bar(np.array(xs) + 2 * width, ys_prediction, width=width, color='#dcccdd', label='Analytical')\n",
      "        plt.legend(loc=0)\n",
      "        plt.title(\"Comparison after %s iterations with %s walkers\" % (t_max, number_of_walkers))\n",
      "        \n",
      "    show_model(all_models[\"node\"])\n",
      "    show_model(all_models[\"hyperedges\"])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "show_models(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000\n",
        "100000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAHsCAYAAADhF7gcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAAAAAAAAAAAAAAAAAECj/X96sY17KRtt7wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff9ad703860>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAloAAAHsCAYAAAAKIAMfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIkSZIkSZL+//4NudaYU90dRnMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff9ac4f7390>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HG = generators.uniform_hypergraph(15, 14, 4)\n",
      "show_models(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000\n",
        "100000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAl0AAAHsCAYAAADo/BhmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff9ac53a080>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAl0AAAHsCAYAAADo/BhmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff9ac5e29b0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}