Markov-PageRank.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Processos Estocásticos: o algoritmo PageRank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Francisco Aparecido Rodrigues, francisco@icmc.usp.br.<br>\n",
    "Universidade de São Paulo, São Carlos, Brasil.<br>\n",
    "https://sites.icmc.usp.br/francisco <br>\n",
    "Copyright: Creative Commons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nessa aula vamos aprender sobre o algoritmo PageRank proposto por Sergey Brin e Larry Page para ordenar páginas na web. Esse algoritmo é conhecido como o \"coração\" do Google, pois o processo de busca na web se baseia nesse algoritmo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inicialmente, vamos definir o grafo que represente as páginas da web."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "g = nx.DiGraph()\n",
    "g.add_nodes_from([1,2,3,4,5,6])\n",
    "g.add_edge(1,2)\n",
    "g.add_edge(1,3)\n",
    "g.add_edge(3,1)\n",
    "g.add_edge(3,2)\n",
    "g.add_edge(3,5)\n",
    "g.add_edge(5,4)\n",
    "g.add_edge(5,6)\n",
    "g.add_edge(4,5)\n",
    "g.add_edge(4,6)\n",
    "g.add_edge(6,4)\n",
    "\n",
    "options = {\n",
    "    'node_color': 'blue',\n",
    "    'node_size': 1000,\n",
    "    'width': 1,\n",
    "    'arrowstyle': '-|>',\n",
    "    'arrowsize': 20,\n",
    "}\n",
    "\n",
    "npos=nx.circular_layout(g,scale=1)\n",
    "\n",
    "nx.draw(g,pos = npos, with_labels=True, **options, arrows=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 1. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0.]\n",
      " [1. 1. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 1. 1.]\n",
      " [0. 0. 0. 1. 0. 1.]\n",
      " [0. 0. 0. 1. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "A = nx.to_numpy_matrix(g)\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos transformar a matriz em uma matriz de probabilidade de transição."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         0.5        0.5        0.         0.         0.        ]\n",
      " [0.16666667 0.16666667 0.16666667 0.16666667 0.16666667 0.16666667]\n",
      " [0.33333333 0.33333333 0.         0.         0.33333333 0.        ]\n",
      " [0.         0.         0.         0.         0.5        0.5       ]\n",
      " [0.         0.         0.         0.5        0.         0.5       ]\n",
      " [0.         0.         0.         1.         0.         0.        ]]\n"
     ]
    }
   ],
   "source": [
    "N = A.shape[0]\n",
    "P = np.zeros((N,N))\n",
    "for i in range(0,N):\n",
    "    for j in range(0,N):\n",
    "        if(np.sum(A[i,:]) > 0):\n",
    "            P[i,j] = A[i,j]/np.sum(A[i,:])\n",
    "        else:\n",
    "            P[i,j] = 1/N\n",
    "print(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A seguir, obtemos a matriz Google:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.025      0.45       0.45       0.025      0.025      0.025     ]\n",
      " [0.16666667 0.16666667 0.16666667 0.16666667 0.16666667 0.16666667]\n",
      " [0.30833333 0.30833333 0.025      0.025      0.30833333 0.025     ]\n",
      " [0.025      0.025      0.025      0.025      0.45       0.45      ]\n",
      " [0.025      0.025      0.025      0.45       0.025      0.45      ]\n",
      " [0.025      0.025      0.025      0.875      0.025      0.025     ]]\n"
     ]
    }
   ],
   "source": [
    "G = np.zeros((N,N))\n",
    "alpha = 0.85\n",
    "for i in range(0,N):\n",
    "    for j in range(0,N):\n",
    "        G[i,j] = alpha*P[i,j] + (1-alpha)/N\n",
    "print(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A distribuição estacinária é igual ao PageRank:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 0.03721196507800219\n",
      "2 : 0.05395734936310332\n",
      "3 : 0.041505653356233116\n",
      "4 : 0.375080815109834\n",
      "5 : 0.20599833187742747\n",
      "6 : 0.2862458852154\n"
     ]
    }
   ],
   "source": [
    "eigvals, eigvecs = np.linalg.eig(G.T)\n",
    "eigvec1 = eigvecs[:,np.isclose(eigvals, 1)]\n",
    "eigvec1 = eigvec1[:,0]\n",
    "\n",
    "stationary = eigvec1 / eigvec1.sum()\n",
    "\n",
    "stationary = stationary.real\n",
    "for i in range(0,N):\n",
    "    print(i+1, ':', stationary[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos visualizar o grafo onde o tamanho dos vértices é proporcional ao PageRank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAEuCAYAAADx63eqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOzdd3hUdd7+8fecmUkvpBJCSIAISBGRIoLAUmWRIh0JIGBFkWJ8ZGVRfywIiBQBKYJ0kCqwKoqIAiIdBKSFltBCCCE9mUmdmd8fPvCsLkJIZnKmfF7X5XUt2ZlzbkycO+f7OUVjsVgsCCGEEC5CUTuAEEIIUZ6k+IQQQrgUKT4hhBAuRYpPCCGES5HiE0II4VKk+IQQQrgUKT4hhBAuRYpPCCGES5HiE0II4VKk+IQQQrgUKT4hhBAuRYpPCCGES5HiE0II4VKk+IQQQrgUKT4hhBAuRYpPCCGES5HiE0II4VKk+IQQQrgUndoBhPqKTWYOX0nnt+uZHL6STlpuIRoNVPTz4MlqgTxRJYCGkRXQaDRqRxXivpKz8tkfn8qxaxmcS86hoNiMh17hsXB/GkQG8HR0EEE+7mrHFCrTWCwWi9ohhDpyC4pZsvcyy/ZfpthkoaDYRJHpjz8O7joFnaLB10PPqy2rM+CpSNx1WpUSC3FvR6+kM/unixy+ko5O0WAoNP3h/9dowMtNS5HJQuuaIYxsV4N64f4qpRVqk+JzUXsvpTJy3XEMBcUUFJtL9B5PvUKwjzvzYhpSP6KCjRMK8WCGgmLGf3OGrSeTyCsq2c+xRgPuWoWBT0XxTsda8oucC5Lic0Hzdl9i7s6LJf6g+DMPvcLk7o/Rs2GElZMJUXLJWfn0+mw/qbkFJf7l7T956BUiA73Y8GozKni52SChsFdSfC5m4Z54Zv14kbwi04NffB8eeoVpvR6n6+PhVkomRMml5RbQ+dO93M4twGQu/UeYXqshKtCbfw9/Gh93OeXBVchZnS7k2LUMPvnxQplLDyC/yMyYTb9xLd1ohWRClJzFYmHU+hOklbH0AIpMFq5nGPngq9NWSiccgRSfi8gvMvHmmmPkl3J5814Kiy0MX3MMWTQQ5emrEzf49WoGRWUsvTsKis18d/omv1y8bZXtCfsnxecivjmZRGZekVW3abJYiL+dy4GENKtuV4i/YjZbmPTdOausWvyn/CIzH3571qrbFPZLFrVdxGc/x2MsfPCHReo308m/8hvmony03gH4PdUL38c7/uXrjYUmFv4cT/PoYGvGFeKefrmUirGw+IGvsxQXkfbDfPKvnMCcn4uuQiUC/vYCntGN//I9V9ONnEnKoq5c5uD0pPhcQGKGkcSMvBK91u+pPgR1GoVGp6co7TrJa8biVjEa97BH/vI9++LTyC8y4aGX08KFbW06lvhf1+jdi8VsQucbTFjMR2j9Q8iLP8rtr6YS/uJcdBUq3vM9hcVmvv4tSYrPBchSpws4dSMLvbZk32q3kCg0Ov3//kmDBg3FGTfv+x4PvZbzyTllTCnEgx2/llGi1yluHlRoOQBdhYpoNApejzyJzr8iBcmX/vI9ZgscupxurajCjskRnws4k5SNoeDBy0N3pG2fj+HUT1iKC3CrGH3f5SH4fe4Sl5zN41XkonZhOyazhaTM/NK915BBUfoN3EIi7/u6+JTcUm1fOBYpPheQaSzkYc5/C+r4BoEdXqPgxjnyr51Co9Xf9/VFZjO5+SUvViFKI7/IhEYDD/XDDFhMxaR+PR2fx9qhD6py/30UW/ekGWGfZKnTBehKuMz5nzSKFo8qdTHlpJJz/Lv7vxYNWkVuYC1sS6toMD/kpTMWi5nUrTNAqyOww7AHvl6RG7G7BCk+FxAV6IW7rpTfarP5gTM+N51CeAXP0m1fiBJy1ykPdQKVxWIh7bs5mAyZhPT4Jxrtgxe4grzl1mWuQIrPBTxW2R+3Ehz1mQyZGM7+jLkwD4vZRF7CrxjifsYj6vH7vq/YZOaxynImnLAtjUZDrYq+JX59+vZ5FKVdJ7T3Byj6kj2KSObUrkFmfC6gbrg/haYS3LFFoyHn+DbSts8HixmdfygB7V7Bq+ZT932bp5uWSv4eVkorxF/7W80QztzMpvABN6Uuzkoh98T3oNWT+Omgu18P/PtwfOq2ued7vPRa/lYzxKp5hX2Sm1S7iNgNJ/jqRBImK3+7LcWFBNw8TB3zVerUqUNWVhaZmZlERkby/vvvW3VfQiRn5dNq+q4HFl9peOgVjo7rIDerdgHyHXYRr7Ssznenb2Iqsm7xeXh4EJx5nrXfbvnD19u3b2/V/QgBEObvQYtHgtlz4TbFVrpXJ4CbVqFHg8pSei5CZnwuonYlP3o1jMCjtCe53IOnXktsh5r8uHUzw4YNQ6f7vw+NgoICbty4YbV9CXHHpO71cLPizzH8vlz/bqfaVt2msF9SfC7kvWfrEODthjWuPNBrNUSHePNyi+oAzJ07l+bNm6PVaqlYsSKXL1+mSpUqNG7cmH379pV9h0L8r0r+nkzoVhdPK90iz0OvMKtvA/w973+9qnAeUnwuxNNNy4bXmhHg5Ya2DNcr6bUawv09Wf1S07vX72m1Wr7++muqV6/OnDlzuH79Or/88gsALVu2JDIykiVLlljl7yFE70ZVeKlFtTKXn4deYVyn2rR5NNRKyYQjkJNbXFBSZh6Dlx0mMSPvoR/v4qnXUi/cj8WDm9zzN2SLxYLmT6WamJjIiBEj2Lp1Kx4eHrzyyitMnjwZDw85E1SUzZK9l5n2wzkKi808zMhPq2hw0yq8/LgXb/dqZbuAwi5J8bmoYpOZz/bE8+nOSygazQML0Mvt99+s3+9ch+ebVPmvciuJwsJCxo0bx8KFCzEajXTp0oW5c+cSERFRqr+DEACXUnIZue44l1MNFBSb7luAWkWDXqvhscr+vPVUIE83qM0TTzzB/Pnzeeqp+1+2I5yHFJ+Ly84vYtOviaw6eJVr6UY89Fry8/NQFAW93o1Ck5lHQnwY+nQ1utYPx9PNOnOVZcuWMX78eK5fv84TTzzB7NmzadGihVW2LVyPxWLhxPVMFu+9zJ6LtykoNv/hbkX5RSZ83HW0e7QiL7WoRu1KflgsFtzd3SkqKsLT05OGDRsye/ZsGjVqpOLfRJQHKT5xV0GxiYspuXw0Yw4hISG8NiSGR0J8SnWvz5I6cOAAo0aN4ujRo4SHh/PBBx/w6quv2mx/wjWkZOeTkGqgyGTGXaclOsSbIJ//vnvL448/zsmTJ4Hf59Q9evRg48aN5R1XlDM5uUXc5a7TUi/cn1BLBlXcjDwa5mfT0gNo1qwZhw8fJjExkaeeeorhw4fj4+PDW2+9RX5+6R5BI0SonwdPVQ+iZY0QnqwWeM/SA2jSpAnw++3Q2rZty9q1a8szplCJFJ+wC+Hh4Xz55ZcYDAbefPNNli5dio+PD127duXatWtqxxNOqkWLFvj6+rJw4UKOHz/OmTNn1I4kyoEUn7Arbm5ufPTRR2RlZbF06VJOnTpF1apVeeKJJ9i9e7fa8YSTGTRoEElJSbzyyivMnj2bPn36kJOTo3YsYWNSfMJuvfDCC1y5coVDhw7h7u5O27ZtqVy5MgsWLMBstv69GoXr0Wq1+Pj4ABATE0ObNm149dVXkVMfnJsUn7B7TZo04eDBgyQlJdG8eXNGjRqFn58fI0aMwGg0qh1POJFZs2Zx9uxZFi1apHYUYUNSfMJhhIWFsXHjRnJzcxk5ciSrVq3Cz8+Pzp07c/XqVbXjCSfg6enJxo0bee+99zhx4oTacYSNSPEJh+Pm5sbkyZPJzMxkxYoVxMXFUa1aNR5//HF27typdjzh4GrWrMmcOXPo06cP2dnZascRNiDFJxzagAEDSEhI4PDhw3h5edG+fXvCw8OZO3euzAFFqfXv35927drJvM9JSfEJp9C4cWMOHDhAcnIyrVq1IjY2Fl9fX4YPHy5zQFEqn3zyCefOnWPhwoVqRxFWJsUnnEpoaCjr1q3DaDQSGxvLmjVr8PX1pVOnTly+fFnteMKB3Jn3ffDBBxw/flztOMKKpPiEU9LpdEycOJGMjAxWr17NhQsXiI6Opn79+uzYsUPteMJB1KhRQ+Z9TkiKTzi9/v37Ex8fz9GjR/H19aVjx45UqlSJ2bNnyxxQPNDzzz9Phw4dePnll2Xe5ySk+ITLaNiwIfv27SMlJYU2bdrwzjvv4OPjw+uvv05ubq7a8YQd++STT7h48SILFixQO4qwAik+4XKCg4NZs2YNRqORMWPGsH79evz9/enYsSPx8fFqxxN2yMPDg40bNzJ+/HiOHTumdhxRRlJ8wmXpdDrGjx9Peno6a9euJSEhgRo1alCvXj22b9+udjxhZx555BHmzp1L3759ycrKUjuOKAMpPiGAvn37cvHiRY4dO0ZAQACdOnWiYsWKzJw5U+aA4q6+ffvSsWNHmfc5OCk+If5DgwYN+OWXX0hNTaVDhw6MHTsWHx8fXn31VZkDCgBmzJhBfHw88+fPVzuKKCUpPiHuITAwkNWrV2MwGHj33XfZtGkT/v7+dOjQgQsXLqgdT6jozrzvX//6F7/++qvacUQpSPEJcR86nY4PPviAtLQ0NmzYwNWrV3n00UepU6cO3333ndrxhEqio6OZN28effv2JTMzU+044iFJ8QlRQr169eLChQucPHmSkJAQunTpQmhoKNOmTZM5oAvq06cPnTp1knmfA5LiE+Ih1atXj59//pnU1FQ6derE+++/j7e3Ny+//LLc3cPFzJgxg8uXLzN37ly1o4iHIMUnRCkFBgayYsUKjEYj7733Hv/+978JCAigXbt2xMXFqR1PlAN3d3c2bNjAxIkTOXr0qNpxRAlJ8QlRRoqiMG7cOFJTU/nyyy9JTEykbt261K5dm6+//lrteMLGoqOjWbBggcz7HIgUnxBW1KNHD86fP8+pU6cICwujR48ehISE8NFHH8kc0In16tWLLl268OKLL8q8zwFI8QlhA3Xr1mXXrl2kpaXRpUsXxo8fj5eXF0OHDpWjAic1bdo0rl27xqeffqp2FPEAUnxC2FCFChVYtmwZRqOR8ePHs3XrVoKCgmjTpg1nzpxRO56wojvzvg8//JAjR46oHUfchxSfEOVAURTeffddbt++zZYtW0hOTuaxxx6jVq1afPXVV2rHE1ZSvXp1PvvsM/r160dGRobaccRfkOITopx169aNuLg4zpw5Q0REBD179iQ4OJhJkybJHNAJ9OzZk65du8q8z45J8Qmhktq1a/PTTz+RkZFB9+7d+fDDD/Hy8mLw4MEyB3RwH3/8MTdu3GD27NlqRxH3IMUnhMr8/PxYvHgxBoOBiRMnsm3bNgIDA2ndujWnT59WO54oBXd3d9avX8/kyZM5fPiw2nHEn0jxCWEnFEXhnXfeISUlha1bt5KSkkL9+vWpWbMmmzdvVjueeEjVqlVj4cKFMu+zQ1J8QtihZ599lrNnzxIXF0dUVBR9+vQhKCiICRMmUFxcrHY8UUI9evSge/fuDB06VOZ9dkSKTwg7VqtWLXbs2EFGRga9evViypQpeHt7M3DgQNLT09WOJ0pg6tSpJCUlMWvWLLWjiP8lxSeEA/Dz82PRokUYDAamTJnCjh07CA4OpmXLlpw8eVLteOI+3Nzc2LBhAx999BGHDh1SO45Aik8Ih6IoCrGxsdy6dYtvv/2WjIwMGjRowCOPPMKGDRvUjif+QtWqVVm0aBH9+vWTI3U7IMUnhIPq1KkTp0+f5vz580RHR9O/f38CAwMZP368zAHt0HPPPUfPnj0ZMmSIzPtUJsUnhIOrUaMG27dvJysri379+vHxxx/j7e1NTEwMqampascT/+Gjjz7i1q1bfPLJJ2pHcWlSfEI4CR8fHxYsWEBubi5Tp05l165dhIaG0qJFC06cOKF2PMH/zfumTp3KwYMH1Y7jsqT4hHAyiqIwevRobt68yfbt28nOzqZhw4ZER0ezfv16teO5vKioKD7//HOZ96lIik8IJ9ahQwdOnjzJxYsXqVmzJjExMQQEBPD+++/LHFBF3bp1o3fv3gwePFjmfSqQ4hPCBURHR7Nt2zZycnKIiYlh5syZeHl50b9/f1JSUtSO55I++ugjUlNTmTFjhtpRXI4UnxAuxMvLi3nz5pGTk8PMmTP5+eefCQsLo3nz5hw9elTteC5Fr9ezbt06pk2bxv79+9WO41Kk+IRwQYqi8Oabb5KUlMSOHTswGAw8+eSTVK9enS+++ELteC4jKiqKxYsX079/f9LS0tSO4zKk+IRwce3ateO3334jPj6e2rVrM3jwYCpUqMC4ceMoKipSO57T69q1K3379mXw4MHyPMZyIsUnhAB+f5rAt99+S3Z2Ni+88AKzZs3C29ubPn36kJycrHY8pzZ58mTS0tJk3ldOpPiEEH/g5eXFnDlzyMnJYdasWezfv5/w8HCeeuopjhw5onY8p6TX61m/fj0zZsxg3759asdxelJ8Qoh7UhSFN954gxs3brBz504KCgpo2rQpVatWZeXKlWrHczqRkZF3531yxx3bkuITQjxQ69atOX78OJcvX6ZevXq8+OKL+Pv7849//IPCwkK14zmNLl268Pzzz8u8z8ak+IQQJRYVFcXWrVvJzc1lyJAhzJs3D29vb3r37i1zQCuZNGkSmZmZTJs2Te0oTkuKTwjx0Dw8PJg9ezY5OTnMnTuXgwcPEh4ezpNPPinPnCujO9f3ffLJJ+zdu1ftOE5Jik8IUWoajYbXXnuNxMREdu/ejclkolmzZkRFRbFs2TK14zmsKlWqsHTpUmJiYrh9+7bacZyOFJ8QwipatWrFr7/+yrVr13jiiSd45ZVX8PPzY8yYMTIHLIVnn32WmJgYXnjhBZn3WZkUnxDCqiIiIvj3v/9Nbm4ur7zyCgsWLMDb25uePXuSlJSkdjyHMnHiRHJycvj444/VjuJUpPiEEDbh4eHBjBkzyMnJYcGCBRw9epSIiAgaN24s16qV0J1536xZs/jll1/UjuM0pPiEEDb38ssvc+3atbsf3i1btiQyMpIlS5aonMz+RUREsGzZMpn3WZEUnxCi3Dz99NMcPXqUa9eu0ahRI4YNG4avry9vv/02+fn5asezW506dWLgwIEMGjRI5n1WIMUnhCh3ERERbNmyBYPBwLBhw/j888/x8fGhe/fuJCYmqh3PLk2cOBGDwcBHH32kdhSHJ8UnhFCNm5sb06ZNIzs7m88//5zjx48TGRlJo0aN5Bq2P9HpdKxdu5Y5c+awZ88eteM4NCk+IYRdGDp0KFevXmXfvn0oikKrVq2IiIhg0aJFakezGxERESxfvpyYmBhSUlLUjuOwpPiEEHalWbNmHDlyhMTERJo2bcrw4cPx8fHhrbfekjkg8Pe//50XXnhB5n1lIMUnhLBL4eHhbNq0CYPBwPDhw1m6dCk+Pj507dqVa9euqR1PVRMmTCAvL48pU6aoHcUhSfEJIeyam5sbU6dOJSsriyVLlnDq1CmqVq3KE088we7du9WOp4o78765c+fy888/qx3H4UjxCSEcxuDBg7ly5QoHDx7E3d2dtm3bUrlyZRYsWOByy36VK1dmxYoVDBgwgFu3bqkdx6FI8QkhHM6TTz7JwYMHSUpKonnz5owaNQo/Pz9GjhyJ0WhUO165eeaZZxgyZAgDBw7EZDKpHcdhSPEJIRxWWFgYGzduJDc3l5EjR7Jy5Ur8/Pzo3LkzV69eVTteuRg/fjxFRUVMnjxZ7SgOQ4pPCOHw3NzcmDx5MpmZmaxYsYK4uDiqVavG448/zs6dO9WOZ1M6nY41a9Ywf/58du3apXYchyDFJ4RwKgMGDCAhIYHDhw/j5eVF+/btCQ8PZ+7cuU47BwwPD2fFihUMHDhQ5n0lIMUnhHBKjRs35sCBAyQnJ9OqVStiY2Px9fVl+PDhTjkHfOaZZ3jxxRcZMGCAzPseQIpPCOHUQkNDWbduHUajkdjYWNasWYOfnx+dOnXi8uXLasezqvHjx2MymZg0aZLaUeyaFJ8QwiXodDomTpxIRkYGq1at4sKFC0RHR1O/fn127Nihdjyr0Gq1rFmzhs8++8zpZ5tlIcUnhHA5/fv3Jz4+nqNHj+Lr60vHjh2pVKkSs2fPdvg5YKVKlVi5ciWDBg0iOTlZ7Th2SYpPCOGyGjZsyL59+0hJSaFNmza88847+Pj48Prrr5Obm6t2vFJr3749L7/8ssz7/oIUnxDC5QUHB7NmzRqMRiNjxoxh/fr1+Pv707FjR+Lj49WOVyoffPABZrOZiRMnqh3F7kjxCSHE/9LpdIwfP5709HTWrl1LfHw8NWrUoF69emzfvl3teA/lzrxv0aJF/PTTT2rHsStSfEIIcQ99+/bl0qVLHDt2jICAADp16kTFihWZOXOmw8wBK1WqxKpVq2Te9ycai8ViUTvEX8kvMnEuOYczSVlk5hWRX2gir8iEXqvg5abFU68lOtSHxyr7E+zjrnZcpxEbG0tERASxsbFqRxHCbqSlpTFq1Cg2btyIVqtl4MCBzJw5Ex8fH7WjPdD48ePZs2cPO3bsQKvVqh1HdXZVfNczjOw+f5sjV9I5fi2Dm1n5eOi1mMwWCopNmP8jqQbQaTV46LUUFJnxdNNSp5IfT1UP4slqgTStGoiiaFT7uzgyKT4h/lpxcTGTJ09m9uzZZGZm0rZtW+bPn0+NGjXUjvaXTCYTzzzzDC1atOBf//qX2nFUp3rxmcwW9ly4zWd74jlxPRONBvKLSr+MoFM0uOsUvN11vNKyOn0bV8HfU2/FxM5Pik+Iktm0aRNjx47l0qVLPProo0yfPp1nn31W7Vj3lJycTKNGjVixYgXt27dXO46qVJvxpRsKmb/7Ek9O/pE31x3j0OV0CorNZSo9gGKzBUOhiZScAmbuOM+Tk39kxNpjnEzMtFJyIYT4Xa9evbhw4QInT54kJCSELl26ULFiRaZNm2Z3c8CwsDBWrVrFCy+8wM2bN9WOo6pyLz6LxcK6w9do8fFO5vx0kTRDIYYC21xnkldkpqDYzLenbtJv0UFe/+JXsvKKbLIvIYTrqlevHj///DOpqan8/e9/5/3338fb25uXX36Z7OxstePd1bZtW4YNG0b//v0pLi5WO45qyrX4bmbl0W/RASZ8exZjoYn84vL5jchsgbwiEz/FpdBq2k5+jJO7lwshrC8wMJAVK1ZgNBp57733+Pe//01AQADt2rXj3LlzascDYNy4ceh0Opee9ZVL8d05yms382eOXcvEWKjOnQQKTWay8ooZsfa4HP0JIWxGURTGjRtHamoqX375JYmJidSpU4fatWvzzTffqJpNq9XyxRdfsHTpUn744QdVs6jF5sVXUGzixRVH7h7lFZvVP4n0ztHf36bv4lyy/SxDCCGcT48ePTh//jynTp0iLCyM7t27ExISwkcffaTaHLBixYqsXr2awYMHk5SUpEoGNdm0+AwFxfT//CAH4tNUO8r7K4UmM5nGInot2M+xaxlqxxFCOLm6deuya9cu0tLS6NKlC+PHj8fLy4uhQ4eSmVn+J9+1adOGN954wyXnfTYrPmNhMX0WHuBMUna5zfJKw1BoYsDiQxy9kq52FCGEC6hQoQLLli3DaDQyfvx4tm7dSlBQEG3atOHMmTPlmuWf//wnbm5ujB8/vlz3qzabFF9BsYlBSw8TfzuXAjsuvTvyiky8sOwwZ5Ky1I4ihHARiqLw7rvvcvv2bbZs2UJycjKPPfYYtWrV4quvviqXDHfmfcuXL3e4e5GWhdWLz2KxMGLtcc4kZTlE6d1hLDTR//OD3MzKUzuKEMLFdOvWjbi4OM6cOUNERAQ9e/YkODiYSZMm2XwOGBoayurVqxkyZAg3btyw6b7shdWLb+upm/xyMbXMF6KrwVhoYvT6E9jRXdyEEC6kdu3a/PTTT2RkZNC9e3c+/PBDvLy8GDx4sE3ngK1bt2b48OEuM++zavHdzilg7OZT5BXZ14ksJVVstnDqRhYbjl5XO4oQwoX5+fmxePFiDAYDEyZMYNu2bQQGBtK6dWtOnz5tk33+85//xMPDgw8++MAm27cnVis+i8XC/3z5GwXFjll6dxgLTfxr61lZ8hRCqE5RFMaMGUNKSgrffPMNKSkp1K9fn5o1a7Jlyxar72v16tWsXLmS77//3qrbtjdWK76tp25y+HI6RSbHXyYsLDbLkqcQwq507tyZs2fPEhcXR1RUFL179yYoKIgJEyZYbXkyNDSUNWvWMGTIEBITE62yTXtkleLLKzQ59BLnn91Z8tx2Wh7cKISwL7Vq1WLHjh1kZGTQq1cvpkyZgre3N4MGDSI9veyXZbVq1YqRI0c69bzPKsX3zckkzE52dGQsNDF31yW1YwghxD35+fmxaNEiDAYDU6ZM4YcffiA4OJiWLVty8uTJMm373Xffxdvbm/fff99Kae2LrqwbsFgszN99ye7uzGINCam5nE/OoVaYr9pRhBDinhRFITY2ltjYWLZt28Y777xDgwYNqF69OlOmTKFPnz6l2uaqVato2LAhLVu2/MMzBk8mZrL15E0OXU4j4baBgmIzigIhPu48ERnA32qG0PmxSnjo7fdJ72U+4vstMYtb2QXWyGJ3iorNLNmboHYMIYQokU6dOnH69GnOnz9PdHQ0zz//PIGBgYwfP/6hly1DQkJYs2YNL774ItevX2fnuVu0m7mbfosOsnhvAr8lZpFTUEyh6ffnqF7PyOPr35J4/6vTNJy4g4lbz2IosM+l0jIX3+e/JDj8mZx/xWSBr08mkWun3zwhhLiXGjVqsH37drKysujXrx8ff/wx3t7eDBgwgNTU1BJvp2XLlgwb+RYd/rWON9YcI/62gbwiE/d71oCx0ISxyMTqQ1f52/RdHExIs8LfyLrKVHyZxkJ+jLt1338Jjk6Dhi3HnPfsJiGE8/Lx8WHBggXk5uYydepUdu7cSWhoKC1atODEiRN3Xzdv3rx7PqLodk4BO/VNKAiq+dA3JSkoNpOaW8iQ5YfZcty+PkPLVHxHr2ag15b7Q9zLVV6RiR/OyoNrhRCOS1EURo8ezc2bN9m+fTvZ2dk0bNiQ6Oholi1bxjvvvEPPnkyEpAoAACAASURBVD3/cJNsQ0ExfRbuJykzH4tS+tNB8ovMjN1yip/s6AHgZWqt365nYix0/mXAMzflmX1CCOfQoUMHTp48ycWLF6lZsyYvvvgieXl5GAwG2rdvT1ra70uTE7ae5WZWvlWeoZpfZGbU+hOk5drH+SBlKr5Dl9Ocepnzjpz8IjIMhWrHEEIIq4mOjuabb74hKCjo7teSk5OpWbMmO09d5avfblj1QQMFxSbe3XzKatsrizIVX1xyjrVyPJSi9BtcndaD1G+ml8v+PHRaTt2QRxYJIZzL1atXMZlMBAUFERERQWhoKAaDgRemrX/gTC/712+4uXw0V6d1J3XrJw/cV5HJwp6Lt7mebrRW/FIrdfHdys6nUKXHDqX/8BnulWqU2/7yikycvFH+T0gWQghbio6OJiMjg9TUVK5fv86tW7e4dDMdz8h6D3yvzicI/+b98KnfocT7M1ssLN9/pQyJraPUxXf2ZrYqJ7YYzv6M4uGNR9Tj5bbPYrOFo1cyym1/Qgihlj0XU9Epmge+zqtWc7xqNkPx9CvxtotMFr4/o/6tIEvdXDn5xVgo3wGfucBI5i9fEND2pXLdL0BWXlG571MIIcrbkSvp5Nnweaq3svPJV/m+zqUuvvwiE5ZyXunM3LMKn8efQecXUr47BvKd9CJ9IYT4T3E2PovdQ6/lcqrBpvt4kFIXX6HJjLkcj/gKbyWQf/U3/Jo8V277/MP+VZpnCiFEebL10ZimHPbxIKW+KtFNq6BoHrwObC35105RnHWLxPlDAbAU5oPFzM3UUVQaOtvm+3f2C/WFEALATWfbzzoLoLfxPh6k1MXnrlMov9oDnwYd8a7d6u6fsw9vpjjrFoEdh5fL/u35TuNCCGEtNUN9uXAr94Gvs5hNcOcfixlLcSEoWjTK/T8r84tMVA3ytlbcUil18fm468r1iE/Re4De4+6fNXoPNDo3tF7+5bJ/X/cyP8FJCCHs3pPVAtkRd+uBF69n7VtH1r61d/9sOLML/6f7U6HlgPu+L8jHDR+VP09LvfdaYb4UmdWbez3oX641aTXwRGSFctufEEKo5elHginJMU2FlgMe+nNYq0CbWqGlTGY9pV5orVzBs1yP+NTk6abj8QgpPiGE84sO8aFmqG0evq1XFF56uppNtv0wSl18Go2GmhVd48nkhcVmHqtcPkuqQgihtrfa18TTyuc1aBUN9SMqUMMOeqNMp9Y8WTWwXE9wUYuHXiHUz+PBLxRCCCfQ5tFQWtYIxk1rvU94N63CzL7ld8et+ylT8TWMrIC3C5z0UbtSyW/JI4QQzmBqz/r4eeopwd3LHshTr/CvbnWJCPAq+8asoEzF1ygqkCKTc1/Y7aFXaPeo+sNYIYQoTwHebmwa1pwKXm5oy9B+HnqFUe1q0LdxFSumK5syFV+IrzvNqgc9+IUOzGKBPo3s5xsmhBDlJSrIm29HtKB+Zf+HnvnpFQ3e7lqm9arPsL89YqOEpVPmy+dfbVUdbzfnvLhbo4H2tSsS4O2mdhQhhFBFJX9PNr/enHHP1qaCl/6Bn/fuOgV3nUK72qHsers1XR+vXE5JS67MA7pm1YPw9dRjKHS+mzibC/PZveA9/r7STJUqVcjMzCQ7O5tnn32WUaNGqR1PCCHKhUajYeBTUTzfpAq7zt9m8/FEfrueSXJ2PlpFg9n8+5Lmo5X8aFMzhL5NqhDqa78nBJa5+DQaDa+1rM7H28+Tp/KNR62tasUAcoy32L732N2v6XQ6WrVqdZ93CSGEc9JpFTrUqUiHOhUBKDKZyS8yoVMUPPQKGge5ttsqdwrt1SjCGpuxK556LcPb1ODXo0fp3LkzWu3vh/fFxcXs27ePxMRElRMKIYS69FoFXw89nm5ahyk9sFLx+XnoGdvpUbyc5EbOigaigrzo1TACjUbDhg0bqFGjBoqi0KJFC06fPk1kZCSNGzdm7969ascVQgjxEKz2bIiBTaOoUdGnTKe92gs3ncK8mIZ3/y5eXl7s2LGDRx99lGXLlnHt2jX27duHRqOhVatWVKlShUWLFqmcWgghRElYrfgURcPc/g1xc/Dn1nnqtYxqV5PoEJ8/fD0iIoIzZ87wyCO/n5bbrFkzjhw5QmJiIk2aNGH48OH4+voSGxtLfn6+GtGFEEKUgFVbqkqgl0Mved5Z4ny1ZfUSvyc8PJzNmzdjMBh44403WLJkCT4+Pjz33HNcu3bNhmmFEEKUhtUPzwY2jaJOuJ9DHvm567R/WOJ8GG5ubkydOpWsrCyWLFnCb7/9RtWqVWnYsCF79uyxQVohhBClYfV2UhQNy4Y0oUqgJ3oHmvd56BWWDG78X0ucpTF48GCuXLnCgQMH0Ov1tG7dmoiICD777DPMKj7DUAghhA2KD8DXQ8/G15oT6ueBzgHKz0OvMLd/Q5pHB1t1u02bNuXQoUMkJSXRrFkzRowYgZ+fH6NGjSIvL8+q+xJCCFEyNluPDPR246vhT1Ml0Muulz099QrzYxrSvnZFm+0jLCyMjRs3YjAYGDFiBCtWrMDX15cuXbpw9epVm+1XCCHEf7NpIwX7uPPV8KepFeZj9YcalpXGYsbLTcuyIU/S9lHbld5/cnNzY8qUKWRmZrJ8+XLOnDlDtWrVaNCgAbt27SqXDEII4epsfijm56Fn8+tP80rLanjoFLt4cK2nXsF0+zJPZ+2iabVAVTIMHDiQy5cvc+jQITw9PWnXrh3h4eHMnTtX5oBCCGFD5bIGqdcqxHaoxZY3nqZqsLdqR39aRYOnXss/n61Dv6BEFs/+mEceeYQffvgBi8WiSqYmTZpw4MABkpKSaNGiBbGxsfj6+jJixAiMRqMqmYQQwpmV6/CtdiU/fhjd6u7RX3me+OLlpuXxCH92vNWKQU9F8ebw4SiKQkJCAj179qR+/fr8+uuv5Zbnz8LCwtiwYQNGo5HRo0ezevVq/Pz8ePbZZ7l8+bJquYQQwtmU+1knd47+to1qRb8mVfDUa/Gy0fP89IoGd51Co8gAZvd7gk3DmhMR4AVAZGQk7u7uABgMBs6dO8fZs2dtkuNh6HQ6Jk2aREZGBitWrODcuXNER0dTv359fvrpJ7XjCSGEw1PtdMtqwd5M6v4Yv77Xnvc61yYy0AsvNy3WOAj0dtPipdcS0zSS7aNasen15nSoU/EPdw/XaDTUrFnz7lMX+vXrx6BBg8q+cysaMGAACQkJHD58GB8fHzp06EClSpX49NNPZQ4ohBClpLGoNdz6E4vFwrFrmfwUd4tDl9M5l5xNsdmCXqtgLCzG/BcpPfVaFAUKi8xEBHrROCqAp6OD+Xu9MDweMEv8xz/+wdGjR3nuuecYPXo0u3fvtutn7d2+fZuRI0eyadMmdDodQ4YM4eOPP8bHp+wX3f+n2NhYIiIiiI2Ntep2hRDCHthN8f2ZxWLhZlY+p25kcTIxk9u5hRgLi8kvNKHXKXjptfh46KhTyY96lf2pWdEXfRmuF+zevTs//vgjycnJVi8SaysuLmbChAnMnTuXrKwsOnTowLx584iOjrbK9qX4hBDOzG6Lr7yZzWYqV65MWFgYx48fVztOia1fv55x48aRkJBA3bp1mT59Oh07dizTNqX4hBDOzH5vqVLOFEVh//79nD59mjFjxqgdp8T69evHpUuXOHbsGBUqVKBTp06EhYXxySefyBxQCCHuQYrvP1SrVo1FixYxffp0du/erXach9KgQQN++eUXUlJSaNeuHe+++y4+Pj4MGzaM3NxcteMJIYTdkOL7k6FDh9K9e3c6d+5Mdna22nEeWnBwMF988QUGg4F//OMfbNy4EX9/f5555hkuXryodjwhhFCdFN89fPnll/j7+9OyZUu1o5SaTqfj//2//0daWhrr16/n8uXL1KpVi7p167Jt2za14wkhhGqk+O5BURQOHDjA2bNn+Z//+R+145RZ7969uXjxIidOnCAoKIjOnTtTsWJFZsyYIXNAIYTLkeL7C1FRUSxevJiZM2eyc+dOteNYRf369dmzZw+pqal07NiRf/7zn3h7e/PKK6845LKuEEKUhhTffQwePJiePXvSpUsXpyqGwMBAVq5cicFgYNy4cWzevJmAgADat2/P+fPn1Y4nhBA2JdfxPYDZbKZKlSoEBQVx8uRJtePYzKZNmxg7diyXLl0iICCAHj16sHjxYrVjCSGE1ckR3wPcub4vLi7OqS/o7tWrFxcuXODkyZN4enqydOlSQkNDmTp1qswBhRBORY74SmjVqlUMHjyYHTt20K5dO7Xj2FRsbCyBgYFcunSJdevWodFo6N+/P5988gn+/v5qxxNCiDKRI74SGjRoEL169aJr165kZmaqHcfmvLy8WL58OUajkQ8++IBvvvmGwMBA2rZtS1xcnNrxhBCi1KT4HsL69esJDAx06Ov7HpaiKIwdO5bbt2+zefNmkpKSqFu3Lo8++ihff/212vGEEOKhSfE9hDvzvnPnzjF69Gi145S75557jnPnznHq1CnCw8Pp0aMHwcHBTJkyReaAQgiHIcX3kCIjI1m+fDlz5szhxx9/VDuOKurWrcvOnTtJS0ujW7duTJgwAS8vL4YMGeISy8BCCMcmxVcKAwYMoE+fPnTr1s2lP+grVKjA0qVLMRgMTJgwge+++47AwEBat27N6dOn1Y4nhBD3JMVXSmvXriUoKIinn35a7SiqUxSFMWPGkJKSwtdff82tW7eoX78+NWvWZMuWLWrHE0KIP5DiKyVFUdi3bx8XLlxg1KhRasexG126dCEuLo64uDgiIyPp3bs3QUFBfPjhhzIHFELYBSm+MoiMjGTFihV8+umn7NixQ+04dqVWrVr8+OOPZGRk0LNnTyZNmoSnpycvvPAC6enpascTQrgwKb4yiomJoV+/fnTr1o2MjAy149gdPz8/Pv/8cwwGA5MnT2b79u0EBwfTqlUrp74FnBDCfknxWcEXX3xBSEiIzPvuQ1EU3n77bW7dusW3335LWloaDRo0oEaNGnz55ZdqxxNCuBApPiu4c33fpUuXGDFihNpx7F6nTp04c+YM58+fp1q1avTr14+goCD+9a9/UVxcrHY8IYSTk+KzkoiICFauXMm8efP4/vvv1Y7jEGrUqMEPP/xAVlYWffr0YerUqXh7ezNgwABSU1PVjieEcFJSfFb0/PPP079/f3r06CEncDwEHx8fPvvsM3Jzc5k6dSo//fQToaGhtGjRghMnTqgdTwjhZKT4rGzVqlWEhobKvK8UFEVh9OjRJCcns23bNrKysmjYsCHR0dGsX79e7XhCCCchxWdld67vi4+PZ/jw4WrHcVgdO3bk1KlTXLx4kRo1ahATE0NAQAAffPCBzAGFEGUixWcDERERrFq1igULFrBt2za14zi06Ohovv/+e7Kysujfvz/Tp0/Hy8uL/v37k5KSonY8IYQDkuKzkX79+hETE0PPnj1JS0tTO47D8/HxYf78+eTm5jJjxgx2795NWFgYzZs359ixY2rHE0I4ECk+G1q5ciUVK1aUeZ8VKYrCiBEjuHnzJjt27CA3N5fGjRtTvXp1vvjiC7XjCSEcgBSfDd25vi8hIYHXX39d7ThOp127dpw8eZL4+HgeffRRBg8eTIUKFRg3bpzMAYUQf0mKz8bCw8NZs2YNCxcu5LvvvlM7jlOqVq0a3333HdnZ2QwaNIhZs2bh5eVF3759ZQ4ohPgvUnzloHfv3gwcOJCePXvKhdk25OXlxaeffkpOTg6zZs1i7969hIWF8dRTT3HkyBG14wkh7IQUXzlZvnw5lSpVknlfOVAUhTfeeIOkpCR+/PFH8vPzadq0KdWqVWPVqlVqxxNCqEyKr5woisKBAwe4cuUKw4YNUzuOy2jbti0nTpzg8uXL1K1bl6FDh+Lv78/YsWMpLCxUO54QQgVSfOUoLCyMNWvWsGjRIrZu3ap2HJcSFRXF1q1byc7OZsiQIXz66ad4e3vTu3dvkpOT1Y4nhChHUnzlrFevXgwaNIjevXtz+/ZtteO4HC8vL2bPnk12djaffvopBw8eJDw8nCeffJJDhw6pHU8IUQ6k+FSwbNkywsPDZd6nIkVRGDZsGImJiezevZvi4mKaNWtGVFQUK1asUDueEMKGpPhUcOf6vqtXr/Lqq6+qHcfltWrVimPHjnHlyhUaNGjASy+9hL+/P2PGjJE5oBBOSIpPJWFhYaxbt47Fixfz9ddfqx1HAJGRkXz11Vfk5uby0ksvsWDBAry9venZsydJSUlqxxNCWIkUn4p69OjB4MGD5UJrO+Ph4cHMmTPJyclh3rx5HDlyhIiICBo3bsz+/fvVjieEKCMpPpUtWbKEypUr07x5c7WjiHt49dVXuX79Onv27AGgRYsWREZGsmTJEpWTCSFKS4pPZXeu77t+/Tovv/yy2nHEX2jRogVHjx7l2rVrNGrUiGHDhuHn58fbb79Nfn6+2vGEEA9Bis8OhIaGsm7dOpYuXcpXX32ldhxxHxEREWzZsoWcnBxeffVVPv/8c3x8fOjevTuJiYlqxxNClIAUn53o0aMHQ4cOlXmfg/Dw8GD69OlkZ2ezcOFCjh07RmRkJI0aNWLv3r1qxxNC3IcUnx1ZsmQJVapUoXnz5lgsFrXjiBJ66aWXuHbtGvv27UNRFFq1akWVKlVYtGiR2tGEEPcgxWdn9u/fz/Xr13nppZfUjiIeUrNmzThy5AiJiYk0adKE4cOH4+vry1tvvSVzQCHsiBSfnQkNDWXjxo0sX76cLVu2qB1HlEJ4eDibN2/GYDDwxhtvsHTpUnx8fOjatSvXrl1TO54QLk+Kzw5169aNl156ieeff15uoOzA3NzcmDp1KllZWSxevJiTJ09StWpVnnjiibuXRwghyp8Un536/PPPiYyMpHnz5pjNZrXjiDIaMmQIV69e5cCBA7i5udG6dWsiIiJYsGCBfH+FKGdSfHbswIEDJCUlybzPiTRt2pRDhw6RlJREs2bNGDlyJH5+fowcORKj0ah2PCFcghSfHQsODmbDhg2sWLGCTZs2qR1HWFFYWBgbN27EYDAwYsQIVq5ciZ+fH507d+bq1atqxxPCqUnx2blu3brx8ssvExMTI/M+J+Tm5saUKVPIzMxk+fLlnD17lmrVqtGgQQN27typdjwhnJIUnwNYtGgRUVFRNGvWTOZBTmzgwIFcvnyZQ4cO4enpSfv27QkPD2fu3LnyfRfCiqT4HMT+/fu5efMmQ4cOVTuKsLEmTZpw4MABbt68ScuWLYmNjcXX15c333xT5oBCWIEUn4MIDg5m06ZNrFq1ii+//FLtOKIcVKxYkfXr12M0Gnnrrbf44osv8PPz49lnn+Xy5ctqxxPCYUnxOZDOnTvz2muvERMTIw9GdSE6nY4PP/yQjIwMVq5cyblz54iOjqZ+/fr8+OOPascTwuFI8TmYBQsWUK1aNbm+z0XFxMSQkJDAkSNH8PX15ZlnnqFSpUrMnj1bfh6EKCEpPgd04MABbt26xZAhQ9SOIlTSqFEj9u3bx61bt2jdujXvvPMOPj4+vP766+Tm5qodTwi7JsXngAIDA9m0aROrV69mw4YNascRKgoJCWHt2rUYjUb+53/+h3Xr1uHv70/Hjh2Jj49XO54QdkmKz0E9++yzDBs2jIEDB1pt3mexWP7rH+EYdDodEyZMICMjgzVr1hAfH0+NGjWoV68e27dvVzueEHZFY5FPN4dWu3Zt8vLySEhIQFHK9nvMnDlzGDVq1B++tmXLFrp3716m7Qp1nDhxgjfffJP9+/cTGhrKmDFjGD16dJl/ToRwdFJ8Di49PZ3KlSvTq1cvVq9eXaZtJSQkULdu3bvPjvP29iYxMZEKFSpYI6pQSWpqKqNGjeLLL79Eq9UyaNAgZsyYgY+Pj9rRbKLIZCY3v5j8YhNFJgtuWgUPvYKvhx6tolE7nrADUnxOYNu2bXTu3Jm1a9fSr1+/Mm0rJiaGdevWodVqGTNmDJMmTbJSSqG24uJiJk2axJw5c8jMzKRt27bMnz+fGjVqqB2t1IpMZs7fyuH0jSyOXsng12sZXE83olU0KBoNGg1YLGAyW7BgoWqQN42iAmgUFcBjlf2pEeorZeiCpPicxIgRI1i4cCEJCQlERESUejsJCQnUrFkTrVbLrVu35GjPSX355ZeMHTuW+Ph4ateuzfTp0+nUqZPasUosMcPIigNXWHv4OhYsmM2QV2Qq8fu93LQAuGkVBjevyoCmkYT6etgorbA3UnxOpHbt2hgMBi5dusTs2bPp3bs31apVe+jtPPnkk0RGRsodYlzAyZMnefPNN9m7dy8hISG88847xMbG2uUc0Gy2sOfibRbuSeDYtQzMFgtFprJ/fLnrFCxAi+hgXm1VnabVAtFo5CjQmUnxOZH09HTCw8Px8vIiKyuL6dOn89Zbb/3l6wuLzVxI+b9lohPXM8jOL6bQZEYDuOkUArzcaBj5f0tD0SE+sjTkhNLT0xk9ejTr169HURQGDBjAzJkz8fPzUzsaANfTjby59hgXU3IxFpb8yO5haABPNy0NIwOY2fdxOQJ0YlJ8TmTHjh1079797o2M+/bty/r16//wGovFwq9XM1j0SwK7zqfgplNKtEx0Z2nIZLbQ+bFKvNyyOnUq2ceHorAek8nElClTmDVrFhkZGbRp04Z58+ZRq1YtVfKYzRZWHrzC1O/PU1hsxlQOH1c6RYO7TuHD7vXo3qCyHP05ISk+J9K9e3e+//57CgoKAIiKiuLKlSsA5BeZ2PRrIp/tiSfNUEhekYnSfue1Gg16nYaoQG9e/1s0XR8Pl6NAJ7R582bGjh3LxYsXqVWrFtOmTaNLly7ltv/EDCPD1xzj4q1cjA8xv7MWT72WRlEBfNK3ASG+7uW+f2E7UnxOxGKxsGPHDt5++23OnDmDxWKhoKCAs7eMvLHmVzIMRQ91AkBJeLlpqRLgxbyYhjwS6pynx7u606dP8+abb7Jnzx6Cg4OJjY1lzJgxNp0DnkvOpt+ig+TmF5fLUd5f0SsaArzd2DSsOVUCvVTLIaxLis8JWSwWtmzZwvMDBtHp3QWcN4WQX2S7Gxgrmt/PjhvVrgavtoqWoz8nlZmZyejRo1m3bh0ajYb+/fszc+ZMq5/5+9v1TGIWH8Rgo1new1I04OepZ9Ow5kSHyC93zkCKz0klZhjpNf8XkjMMaPTls0zjqddSPcSb1S82JcDbrVz2Kcqf2Wxm6tSpzJw5k/T0dFq1asW8efOoU6dOmbd9PjmHXp/tJ7eg2ApJrUcDVPDS882bLYgIkCM/R2d/5yyLMruUkkvXuXtJNZjKrfTg9xNkLtzKoeu8vdzKzi+3/YrypSgKY8eO5fbt22zevJmbN29Sr149atWqxVdffVXq7SZn5dN30QG7Kz0AC5CdV0yvz/aTlVekdhxRRlJ8TuZqmoFen+0n01ikymykyGThZlY+PebvIy23oNz3L8rXc889x7lz5zh16hSVK1emZ8+eBAcHM3ny5Id6PqDFYmHU+uPkFthvqZgsFjKMRbz371NqRxFlJMXnRNJyC+j12X5y8otQc/3aZLZwO6eAvosOkK/C2Xii/NWtW5edO3eSlpZGt27dmDBhAl5eXgwePJjMzMy7r9u0aRMnT578r/dv/DWRk4lZmOz8WbqFxWZ2xN1i17kUtaOIMpDicyJjNp0kK68Isx1MbYvMFm5k5vHRtji1o4hyVKFCBZYuXYrRaGTChAls27aNwMBAWrduzeHDhxk8eDBt2rTh5s2bd9+TnJXP+G/OWP2MY1vJLzLz1oYTsuTpwKT4nMR3p26yPz7NKrdwspb8IjPrjl7n16sZakcR5UxRFMaMGUNKSgpff/01KSkpNG3aFKPRSGZmJh06dCA/P//uEmdhsZ0f6v1JXpFJljwdmJzV6QTScgtoPX03OXZ4UgBAJX8Pdr3dGg+9Vu0oQiVms5mwsDBu375992t16tRh1Xd7GLDkiMMc7f0nd53Cjrf+RqRc3+dw5IjPCYzfeob8Yvv94MgwFvLpzotqxxAqiouLu1t6er0evV5PXFwcvcYtIL/IPn9hexCzxcLy/ZfVjiFKQYrPwaUbCvnhzC27WuL8s/wiMysOXHW45SxhPXXr1sVoNGIymSgsLKSwsJDUnDx0UU9gwTFveFBksrD+yHU5gcsBSfE5uHVHrjnEx4bFYuH7M8lqxxAq8vT0/MNtzjYcvY5W6/gfQd+duvngFwm74vg/dS7MZLawZO9l8h3gSMpQaOKzn+PVjiHsyNJ9V2x6K73yYCg0seiXBLVjiIckxefA9sen2vVs788SUnO5lJKrdgxhB1Ky88l0kssBLqXkUuBA/x0KKT6HduhyOnl2ciPfktCg4ejVdLVjCDtw6kYW7k6wzAngoddyPjlH7RjiIejUDiBK79DlNKtfrJ78xbsUJJ1Ho/x+6YHWN4jKry60yrbzikwcvZLB800irbI94bh+S8zEWGj7szkNZ38mc99aTNm30XoHENR5NB5V6ll1HyazhVM3sqgfYd2nVAjbkeJzUBaLhbibtvktM/CZYfg+3tEm2/71mlzMLn5frbD1ich5l4+TsXs5Ic/9A7fwmphybbPakFdk4vCVdAY0jbLJ9oX1Ocdagwu6lV1Akb3f2PAerqcbHTK3KL3/vFfnHefKYWkwa+8X+D/dH/fKj6LRKOh8g9H5BttkX79d/++/o7BfUnwO6kamETedbb59mbtXcH12DMmr3iH/6n/fULgs9FqF2zny1AZXcf36dQIDA3nuuec4e/bs3a8bbHyXIYvZRMHNS5iNWdz47BUS5w0m/YcFmIts87OXleeYF+G7KlnqdFC2Og08oM1Q9EFV0Gj1GOL2kLJpIpWGzkEfUMk6O7CYOXv+Ill+eutsT9i1q1ev4u7uztatW9m+fTvNmzdn4sSJFNv4TuomQyaYizGe30fFgVPRKFpub/qQrP3rCfjbC1bfn6xiDOLFJwAABohJREFUOBYpPgdlq//Q3MNr3f3fPo+1w3D2Z/Lij6Jv3NUq28/Ly2P4iJEoObessj1h3woLCykoKMBisVBQUMCuXbsYMHAQmuc/temjs+48gNm3UVd0PoG//+8m3W1WfCZ7eCSKKDEpPgflXl43fNZowIofUV7e3nz//XdyY18XcenSJerWrYteryckJISPP/6YXr16Ef3eNmv+WP0XrYcPWhvN8+5Fr3WE+yeJO2TG56C83bRY+7ka5vxc8hJ+xVJciMVsIvfMLgqun8azWkOr7cNktuApT2lwGUFBQTRt2pRly5YRHx9Pnz59UBQFvWL7jx6fx9qT8+tWTIZMTPm55Bz9Cq9HmthkX3onuSbRVcgRn4OKDvGx+s1xLWYTmXtWU5SeCBoFfVAEIT3fQx8UYbV9KBoNwT5uVtuesG8BAQHs2bPnv74e5OPGzax8m+7b/+nnMeVlc2PRa2h0erwfbYl/83422Vd4BQ+bbFfYhhSfg/J21xHk48atbOudpab18qfSkE+str17qVnRF41GloVc3eMRFbiZZdublmu0OoI6vkFQxzdsux8NNKkaZNN9COuS43MHVr+yY90pQgM8WS1A7RjCDjStFoi7jS7HKW9eblqeiHSs/xZdnXP85LmoptUDcXOg2YK3u46GkVJ8Ah6r7O80czGzGR4L91c7hngIzvGT56Ja1wylHM4RsJoik5mnqsmSkIA64X5O8wBXs8VCVJCcpexIHOhjU/zZI6E+1Kzoq3aMElE00KF2RQK85cQWAV5uOuqG+6kdo8w0GmhVI0Tm1g5Gis/Bvf63aLzd7P/yAHedlldaVlc7hrAjjvKzez+eei2vtZKfa0cjxefg2teuiFax/982w/w9eLyKnAAg/k/72hXROficL8jbjUZRMrd2NI79UyfQaxVGtK1h1xeFe+q1/KNjrQe/ULgUnVbhhWZRDnt2p5dey7BW0bLM6YAc8ydO/MGLT1ejarAX9njgp9dqaB4dxN/rWekm18KpDHLgZ9hZgO5PVFY7higFKT4noFU0zOvf0GaPKSqL/9/evf3GEMVxAP/OnJmdHbtWddkGrdALaevSVUVcQ4lEIoRUREkQwoPrqxfhQUIE8dAQEpe4xB8gLvEiEbe4JAh1jTYaNGha1m53ZnY9IGnEdW07Mzvfzz+wJ9mT33fOb+ac41cEdi0cZfcwyKEiIT9WTyl2dMfiZ3RVYMuccgQ0ngHiRs6rlJSR4v5BbJ45zFEFRFcFdi4chXBQs3so5GAba8tQENLgwIbFTwlZQvmA3lg6frDdQ6EMMfhyyKrJxZhUGoZftf9v1VWBurGFmDOSLU76PVXIaKivds27Pp+QsX9xlO/2XMwdM43+ipAlNCypRrQoz9bw01WB2ZUF2Da30rYxkLtUDAh9a3k6uyR9b3EW9uWGdTdz9iyjf+ZTZBxdMQ4ThoZtKSK6KjA/Ogh76qr4REz/ZENtGUYX5jl25aerMqYP788WZw6Q0uls3+pGTmBaKew49winbjQjYXbPbe1dSRKgKTI21ZZhDT/xpgzFkxbqDl7Fk7cfkbScU5r8ioyaIfk4srzG9XsPicGX8+40t2HdqTv48DmJhNE9AairAkX5OhqWjEFpxB1HqJFzfeo0UX/4Oh6/+dgjD21/oqsCNUPzcWhZNTTFOR+PUeYYfB6QMCzsPN+IkzebIQHozFIx8asy0mlg/YxSrJ1awidhypqEYWHV8Vu43dSGuI2HWeuqwMzyCPYuquL8ziEMPg9p7UjgxI0mHLvWBDOVQqwzs4IS8AkENAWrpxSjrroQeb148DRlXyqVxtFrL7HrQiMMMw2rB0uVIkvQFBnb543Aguggtu5zDIPPg0wrhUuNrThzsxn3WtrRkTDgVwQSpgXjh/cqPiFDU2TEDQvhoA/Ror6oHz8Yk0r6QXbiUTGUc5rex7Du9F08a/3UI6s/Xf16sey+RVWIhPzd/nvU8xh8hPa4gQct7Xj4ugNtsSRiSRMSJAQ0BeGgDyMG9kHFwBCCPKWCbPJ99bf74mNIAGLJ7AdgwCcgZAlb51ZylZfjGHxE5BoJw8LZ+69x4PJzvGqLo9O0kPqPCibkrxvoh0V6Y+20EsyqKMiZm+Hp1xh8RORK91vacfjKC1x5+u637fquurbu8wM+1JYXYOXEIShzyYXOlB0MPiIi8hSu6YmIyFMYfERE5CkMPiIi8hQGHxEReQqDj4iIPIXBR0REnvIF6y/SXgHCKW8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "npos=nx.circular_layout(g,scale=1)\n",
    "\n",
    "s = stationary*10000\n",
    "nx.draw(g,pos = npos, with_labels=True, node_size = s, arrows=True)\n",
    "plt.draw()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos considerar outro exemplo, onde verificaremos que ser o mais conectado não é o mais importante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "N = 10\n",
    "g = nx.DiGraph()\n",
    "g.add_nodes_from(np.arange(1,N+1))\n",
    "g.add_edge(1,2)\n",
    "g.add_edge(3,2)\n",
    "g.add_edge(4,2)\n",
    "g.add_edge(5,2)\n",
    "g.add_edge(2,10)\n",
    "g.add_edge(10,9)\n",
    "g.add_edge(9,8)\n",
    "g.add_edge(8,7)\n",
    "g.add_edge(7,6)\n",
    "g.add_edge(6,9)\n",
    "g.add_edge(9,7)\n",
    "g.add_edge(9,6)\n",
    "g.add_edge(8,6)\n",
    "\n",
    "options = {\n",
    "    'node_color': 'blue',\n",
    "    'node_size': 1000,\n",
    "    'width': 1,\n",
    "    'arrowstyle': '-|>',\n",
    "    'arrowsize': 20,\n",
    "}\n",
    "\n",
    "\n",
    "npos=nx.circular_layout(g,scale=1)\n",
    "#npos = nx.spring_layout(g)\n",
    "nx.draw(g,pos = npos, with_labels=True, **options, arrows=True)\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inicialmente, obtemos a matriz de probabilidade de transição, realizando o ajuste estocástico. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         1.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         1.        ]\n",
      " [0.         1.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         1.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         1.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         1.         0.        ]\n",
      " [0.         0.         0.         0.         0.         1.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.5\n",
      "  0.5        0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.33333333\n",
      "  0.33333333 0.33333333 0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         1.         0.        ]]\n"
     ]
    }
   ],
   "source": [
    "A = nx.to_numpy_matrix(g)\n",
    "\n",
    "N = A.shape[0]\n",
    "P = np.zeros((N,N))\n",
    "for i in range(0,N):\n",
    "    for j in range(0,N):\n",
    "        if(np.sum(A[i,:]) > 0):\n",
    "            P[i,j] = A[i,j]/np.sum(A[i,:])\n",
    "        else:\n",
    "            P[i,j] = 1/N\n",
    "print(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A seguir, fazemos o ajuste ergótico e obtemos a matriz Google."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.015      0.865      0.015      0.015      0.015      0.015\n",
      "  0.015      0.015      0.015      0.015     ]\n",
      " [0.015      0.015      0.015      0.015      0.015      0.015\n",
      "  0.015      0.015      0.015      0.865     ]\n",
      " [0.015      0.865      0.015      0.015      0.015      0.015\n",
      "  0.015      0.015      0.015      0.015     ]\n",
      " [0.015      0.865      0.015      0.015      0.015      0.015\n",
      "  0.015      0.015      0.015      0.015     ]\n",
      " [0.015      0.865      0.015      0.015      0.015      0.015\n",
      "  0.015      0.015      0.015      0.015     ]\n",
      " [0.015      0.015      0.015      0.015      0.015      0.015\n",
      "  0.015      0.015      0.865      0.015     ]\n",
      " [0.015      0.015      0.015      0.015      0.015      0.865\n",
      "  0.015      0.015      0.015      0.015     ]\n",
      " [0.015      0.015      0.015      0.015      0.015      0.44\n",
      "  0.44       0.015      0.015      0.015     ]\n",
      " [0.015      0.015      0.015      0.015      0.015      0.29833333\n",
      "  0.29833333 0.29833333 0.015      0.015     ]\n",
      " [0.015      0.015      0.015      0.015      0.015      0.015\n",
      "  0.015      0.015      0.865      0.015     ]]\n"
     ]
    }
   ],
   "source": [
    "G = np.zeros((N,N))\n",
    "alpha = 0.85\n",
    "for i in range(0,N):\n",
    "    for j in range(0,N):\n",
    "        G[i,j] = alpha*P[i,j] + (1-alpha)/N\n",
    "print(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalmente, calculamos o PageRank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 0.014999999999999994\n",
      "2 : 0.06600000000000009\n",
      "3 : 0.015000000000000008\n",
      "4 : 0.015000000000000008\n",
      "5 : 0.014999999999999989\n",
      "6 : 0.2626353316271941\n",
      "7 : 0.14196504412280775\n",
      "8 : 0.09962459236688254\n",
      "9 : 0.2986750318831152\n",
      "10 : 0.07110000000000025\n"
     ]
    }
   ],
   "source": [
    "eigvals, eigvecs = np.linalg.eig(G.T)\n",
    "eigvec1 = eigvecs[:,np.isclose(eigvals, 1)]\n",
    "eigvec1 = eigvec1[:,0]\n",
    "\n",
    "stationary = eigvec1 / eigvec1.sum()\n",
    "\n",
    "stationary = stationary.real\n",
    "for i in range(0,N):\n",
    "    print(i+1, ':', stationary[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "npos=nx.circular_layout(g,scale=1)\n",
    "\n",
    "s = stationary*10000\n",
    "nx.draw(g,pos = npos, with_labels=True, node_size = s, arrows=True)\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notem que os vértices que recebem mais conexões nem sempre apresentam alto PageRank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}