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 "metadata": {
  "name": "",
  "signature": "sha256:25d5e2f06395ff6dda482f8e546b880517bb26be941ce99e5ac3ece7976bf49b"
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Purpose of the notebook\n",
      "explore pykov\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import pykov\n",
      "\n",
      "T = pykov.Chain({('A','B'): .3, ('A','A'): .7, ('B','A'): 1.})\n",
      "T.steady()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "{'B': 0.23076923076923075, 'A': 0.76923076923076938}"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "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 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",
      "\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",
      "all_models = {\n",
      "    \"node\": {\n",
      "        \"analytical\": partial(prediction, model='hypergraph_nodes'),\n",
      "        \"numerical\": create_markov_matrix_model_nodes,\n",
      "        \"name\": \"node\",\n",
      "    },\n",
      "    \"hyperedges\": {\n",
      "        \"analytical\": partial(prediction, model='hypergraph_edges'),\n",
      "        \"numerical\": create_markov_matrix_model_hyper_edges,\n",
      "        \"name\": \"hyperedges\",\n",
      "    }\n",
      "}\n",
      "\n",
      "\n",
      "def show_models(HG):\n",
      "    model = all_models['node']\n",
      "\n",
      "    def show_model(model):\n",
      "        markov_matrix = model[\"numerical\"](HG)\n",
      "        print(markov_matrix)\n",
      "    show_model(model)\n",
      "\n",
      "\n",
      "def transition_matrix_to_pykov_chain(matrix):\n",
      "    chain = pykov.Chain()\n",
      "    \n",
      "    for i, row in enumerate(matrix):\n",
      "        for j, column in enumerate(row):\n",
      "            chain[(i, j)] = column\n",
      "    return chain\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HG = generators.generic_hypergraph(9, ((3, 5), (3, 3)))\n",
      "show_models(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.33333333  0.11111111  0.11111111  0.22222222  0.          0.\n",
        "   0.11111111  0.          0.11111111]\n",
        " [ 0.11111111  0.33333333  0.22222222  0.11111111  0.          0.\n",
        "   0.11111111  0.11111111  0.        ]\n",
        " [ 0.08333333  0.16666667  0.33333333  0.25        0.          0.08333333\n",
        "   0.          0.08333333  0.        ]\n",
        " [ 0.16666667  0.08333333  0.25        0.33333333  0.          0.08333333\n",
        "   0.          0.          0.08333333]\n",
        " [ 0.          0.          0.          0.          0.33333333  0.16666667\n",
        "   0.16666667  0.16666667  0.16666667]\n",
        " [ 0.          0.          0.16666667  0.16666667  0.16666667  0.33333333\n",
        "   0.          0.          0.16666667]\n",
        " [ 0.16666667  0.16666667  0.          0.          0.16666667  0.\n",
        "   0.33333333  0.16666667  0.        ]\n",
        " [ 0.          0.16666667  0.16666667  0.          0.16666667  0.\n",
        "   0.16666667  0.33333333  0.        ]\n",
        " [ 0.16666667  0.          0.          0.16666667  0.16666667  0.16666667\n",
        "   0.          0.          0.33333333]]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_stuff(xs, ys, ys_prediction, freqs_matrix):\n",
      "    width = 0.2\n",
      "    plt.figure(figsize=(10, 8))\n",
      "    plt.bar(xs, ys, width=width, color='crimson', label='Steady state for chains')\n",
      "\n",
      "    print('prediction', ys_prediction)\n",
      "    plt.bar(np.array(xs) + 1 * width, ys_prediction, width=width, color='#dcccdd', label='Analytical')\n",
      "    plt.bar(np.array(xs) + 2 *  width, freqs_matrix, width=width, label='Traversal matrix to N')\n",
      "    plt.legend(loc=0)\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mm = create_markov_matrix_model_nodes(HG)\n",
      "print('Matrix from model nodes')\n",
      "print(mm)\n",
      "\n",
      "chain = transition_matrix_to_pykov_chain(mm)\n",
      "print('\\nChain')\n",
      "print(chain)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Matrix from model nodes\n",
        "[[ 0.33333333  0.11111111  0.11111111  0.22222222  0.          0.\n",
        "   0.11111111  0.          0.11111111]\n",
        " [ 0.11111111  0.33333333  0.22222222  0.11111111  0.          0.\n",
        "   0.11111111  0.11111111  0.        ]\n",
        " [ 0.08333333  0.16666667  0.33333333  0.25        0.          0.08333333\n",
        "   0.          0.08333333  0.        ]\n",
        " [ 0.16666667  0.08333333  0.25        0.33333333  0.          0.08333333\n",
        "   0.          0.          0.08333333]\n",
        " [ 0.          0.          0.          0.          0.33333333  0.16666667\n",
        "   0.16666667  0.16666667  0.16666667]\n",
        " [ 0.          0.          0.16666667  0.16666667  0.16666667  0.33333333\n",
        "   0.          0.          0.16666667]\n",
        " [ 0.16666667  0.16666667  0.          0.          0.16666667  0.\n",
        "   0.33333333  0.16666667  0.        ]\n",
        " [ 0.          0.16666667  0.16666667  0.          0.16666667  0.\n",
        "   0.16666667  0.33333333  0.        ]\n",
        " [ 0.16666667  0.          0.          0.16666667  0.16666667  0.16666667\n",
        "   0.          0.          0.33333333]]\n",
        "\n",
        "Chain\n",
        "{(4, 7): 0.16666666666666666, (1, 3): 0.1111111111111111, (6, 6): 0.33333333333333331, (3, 0): 0.16666666666666666, (8, 0): 0.16666666666666666, (5, 4): 0.16666666666666666, (2, 1): 0.16666666666666666, (1, 6): 0.1111111111111111, (2, 5): 0.083333333333333329, (8, 5): 0.16666666666666666, (0, 3): 0.22222222222222221, (5, 8): 0.16666666666666666, (1, 2): 0.22222222222222221, (3, 8): 0.083333333333333329, (6, 7): 0.16666666666666666, (5, 5): 0.33333333333333331, (2, 0): 0.083333333333333329, (7, 6): 0.16666666666666666, (4, 8): 0.16666666666666666, (4, 4): 0.33333333333333331, (3, 3): 0.33333333333333331, (7, 2): 0.16666666666666666, (2, 2): 0.33333333333333331, (6, 4): 0.16666666666666666, (5, 3): 0.16666666666666666, (1, 1): 0.33333333333333331, (0, 1): 0.1111111111111111, (3, 2): 0.25, (0, 0): 0.33333333333333331, (7, 1): 0.16666666666666666, (4, 5): 0.16666666666666666, (6, 0): 0.16666666666666666, (7, 7): 0.33333333333333331, (2, 3): 0.25, (1, 0): 0.1111111111111111, (0, 8): 0.1111111111111111, (3, 5): 0.083333333333333329, (2, 7): 0.083333333333333329, (8, 3): 0.16666666666666666, (4, 6): 0.16666666666666666, (6, 1): 0.16666666666666666, (3, 1): 0.083333333333333329, (7, 4): 0.16666666666666666, (0, 6): 0.1111111111111111, (8, 8): 0.33333333333333331, (1, 7): 0.1111111111111111, (5, 2): 0.16666666666666666, (0, 2): 0.1111111111111111, (8, 4): 0.16666666666666666}\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chain_transposed = pykov.Chain(chain)\n",
      "xs, ys = zip(*chain_transposed.steady().items())\n",
      "print(xs, ys)\n",
      "print(chain_transposed.succ(1))\n",
      "print('steady pykov', chain_transposed.steady())\n",
      "\n",
      "freqs_matrix = LA.matrix_power(mm, 40)[0]\n",
      "model = all_models['node']     \n",
      "        \n",
      "xs = list(map(int, xs))\n",
      "ys_prediction = model[\"analytical\"](HG)\n",
      "\n",
      "plot_stuff(xs, ys, ys_prediction, freqs_matrix)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(0, 1, 2, 3, 4, 5, 6, 7, 8) (0.12499999999999994, 0.12499999999999993, 0.16666666666666657, 0.16666666666666666, 0.083333333333333356, 0.08333333333333337, 0.083333333333333287, 0.083333333333333287, 0.083333333333333523)\n",
        "{0: 0.1111111111111111, 1: 0.33333333333333331, 2: 0.22222222222222221, 3: 0.1111111111111111, 6: 0.1111111111111111, 7: 0.1111111111111111}\n",
        "steady pykov {0: 0.12499999999999994, 1: 0.12499999999999993, 2: 0.16666666666666657, 3: 0.16666666666666666, 4: 0.083333333333333356, 5: 0.08333333333333337, 6: 0.083333333333333287, 7: 0.083333333333333287, 8: 0.083333333333333523}\n",
        "prediction"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " [0.125, 0.125, 0.16666666666666666, 0.16666666666666666, 0.08333333333333333, 0.08333333333333333, 0.08333333333333333, 0.08333333333333333, 0.08333333333333333]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XDvter7zyChs3bqSkpISmTZsSi8Vo0KABe/bsISkpqbzB/KmnnmL9+pr7BruK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\n3LZYzR2UCi0RERGRkKjQipjVtW3ltkW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       "text": [
        "<matplotlib.figure.Figure at 0x7fad64002400>"
       ]
      }
     ],
     "prompt_number": 21
    }
   ],
   "metadata": {}
  }
 ]
}