CanILP + DirILP General case.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-22T00:55:38.492803Z",
     "start_time": "2020-04-22T00:55:25.690897Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# coding: utf-8\n",
    "%pylab inline\n",
    "import random\n",
    "import string\n",
    "import math\n",
    "import time \n",
    "import itertools\n",
    "from math import log as ln\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from gurobipy import *\n",
    "from scipy import spatial\n",
    "from scipy import sparse\n",
    "from sklearn.cluster import DBSCAN\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create a simulated universe with different selection intervals for catalogs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_catalog = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mock(num=10, size=10, seed=None):\n",
    "    \"return dataframe of simulated objects\"\n",
    "    if seed is not None: \n",
    "        np.random.seed(seed)\n",
    "    obj = np.random.random(size=(num,3)) \n",
    "    obj[:,0:2] *= size;  obj[:,1] -= size/2 #The location is scaled to simulate objects on a 10x10 grid. \n",
    "    #objid = np.arange(obj.shape[0]) # object id\n",
    "    df = pd.DataFrame(obj,columns=['x','y','u'])\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cat(mdf):\n",
    "    \"return simulated catalog and selection\"\n",
    "    sigma = 1/100*np.random.randint(4, 10, (mdf.shape[0],1))\n",
    "    det = mdf.values[:,:2] + sigma * np.random.randn(mdf.shape[0],2)\n",
    "    df = pd.DataFrame(det,columns=['x','y'])\n",
    "    df['Sigma'] = sigma\n",
    "    a, b = (0,1)\n",
    "    sel = np.logical_and(mdf.u>=a, mdf.u<b)\n",
    "    #df['selected'] = np.array(sel, dtype=np.bool)\n",
    "    return df.values, sel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_cat(mdf):\n",
    "    \"return simulated catalog with random selection intervals\"\n",
    "    sigma = 1/100*np.random.randint(4, 10, (mdf.shape[0],1))\n",
    "    det = mdf.values[:,:2] + sigma * np.random.randn(mdf.shape[0],2)\n",
    "    df = pd.DataFrame(det,columns=['x','y'])\n",
    "    df['Sigma'] = sigma\n",
    "    num_endpoints = random.randrange(6,10,2) #Random multiple of 2 from 6 to 16 #So the number of intervals = num_endpoints / 2\n",
    "    endpoints_list = sorted([random.random() for x in range(num_endpoints)])\n",
    "    selection_boolean_list = []\n",
    "    for index in range(int(num_endpoints/2)):\n",
    "        a = endpoints_list[2*index]\n",
    "        b = endpoints_list[2*index+1]\n",
    "        sel = np.logical_and(mdf.u>=a, mdf.u<b)\n",
    "        selection_boolean_list.append(sel)\n",
    "    final_sel = selection_boolean_list[0]\n",
    "    for i in range(1,int(num_endpoints/2)):\n",
    "        final_sel = final_sel | selection_boolean_list[i]\n",
    "    df = df[final_sel].values\n",
    "    return df, final_sel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "num=100\n",
    "size=30\n",
    "Qmat=np.empty((1,2))\n",
    "m = mock(num=num,size=size, seed = 20)\n",
    "# generate 3 catalogs with sigma=0.1\" and different selection intevals\n",
    "cmat = []\n",
    "sel_list = []\n",
    "for i in range(num_catalog): #List of catalogs with coordinates and conditions\n",
    "    catalog_i, final_sel = cat(m)\n",
    "    cmat.append(catalog_i)\n",
    "    sel_list.append(final_sel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "true_matching_dict = {}\n",
    "count_list = [0]*num\n",
    "for source_index in range(num):\n",
    "    index_list = []\n",
    "    for catalog_index in range(num_catalog):\n",
    "        if sel_list[catalog_index][source_index] == True:\n",
    "            index_list.append((catalog_index, count_list[catalog_index]))\n",
    "            count_list[catalog_index]+=1\n",
    "    true_matching_dict[source_index] = index_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20,20))\n",
    "for i in range(num_catalog):\n",
    "    x, y = cmat[i][:,:2].T\n",
    "    plt.scatter(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nway matching procedure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### DBSCAN for Clustering "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of clusters: 96\n"
     ]
    },
    {
     "data": {
      "image/png": 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ijCEAAAAgZxzSrWer57otS8f17s8B1F/Q1AuO1ZTzjlb5pt16d8YH+s/fXlMsmmg0z+116egTR2nImL4OpASQyyiGAAAAmlFWuVoPrn9d5ZFKjSzop68POVXDCvo4HQtok4DHq16hfO1oqGs05rEs+T0ehRMJBT1e5Xm9+uNJpzmQsvPxeN3qP6ynXJYlO5FMOaf0pNH62d2XZzgZAFAMAQAApGSbpGbuXKJbVz6laPLjM1b2RFdoUeUa/e3ob2lkYT+HEwJt86dJp+uqGc8ott/tZH63W3+edIaCXp9W7NmlAYXFmjpomPxuvl1oT8eePEbT//aabPvAcsgX8OryG8+Q28NtZAAyj7/pAQAA9rOloUK3rXxKS/eub3QYr5EUScZ139qXdcdR1zoRD/jCJvYbpIfPuEC3LZyltVV7NLCoi35YOlEn9R8sSZo8YIjDCTuvwaP66MyLx+vl6fMUi8QkSb6AT6dPG6fBo1iJCMAZVrOHn2VYaWmpKSsrczoGAADIUbXxBl0491bVJcIyjWqhzwRcXr02+Q8ZTAagM1n23jrNfG6RJGnyeUfrkGOHOpwIQGdnWdYiY0xpqjFWDAEAAHzilfIyxZLxZkshSYom44racfndHMoL4OAdcuxQyiB0WuHEDkmWgp7WH3YPZ1EMAQAAfGJ93Y5PzxNqjkcuza5Ypkk9DpPHxZkgAIDcFLOrta3uFUUSO2WU1IbqJ5RUWJIljxVSvm+IeoUma1DhBfK6C52OiyawlQwAAOATz26Zq3vX/leRVpRDXsstr8ujSwZO0cWDJsuyrAwkBAAgO+yNLNO88muUlK2kiTQ5z5JPfnexTuz3hPzurhlMiP01t5XMlekwAAAA2erU3kcp5PG3am7c2Gqwo3p44xt6ZuucNCcD0N621dboieUf6sXVq1QfizkdB+hQjDFatOtHSpj6ZkshSTKKKWpXaU3VPzKUDgeLrWQAAACfCHkCuu+Y7+r6sru1M7q3Va+JJON6ZONbOr//xDSnA9Be/vrePN1TtkAuy5KRlEgmdd6I0brh2HHqX1TkdDwg6zUktihq72n1fKO4djS8rUP0kzSmQluxYggAAGA/PQPF+vnYaQq4Wn+w9N5YXRoTAWhPi8q36e6yBYratsKJhCKJhBLJpJ5atVxTHvmnnl21wumIQNaz5GrxoobP87oK0pQGXxTFEAAAwOcc0WWIzu8/UT6XR36XV0G3TwG3T939qVcSDAh1z3BCAG1108w3FbPtlGMJY/TD119RZTic4VRAxxLy9lPI00dS687Xc1tBDSm6JL2hPueDqq26du6jmjzjDl0z5xEtqdyS0ffvSNhKBgAAkMJ1w87QWX2O1XuVqxV0+3RC90P0wd4N+uWHjxxwc5nf5dX1I85xMCmA1lhfValb58zSyj0Vzc4z+nir2a9PmpKZYEAHVdrzds3ZfqVsE1HSRJuYZclleTWg4Cvql392xrK9V7FB35g/XRH748/XOyM1WlS5WXcdd6HG9xiasRwdBbeSAQAAHIT3K9fqH+tnaHNDhQaGeuiaoafpiC58kQlks3VVlTr3icfUEI+1avPL2O7d9d8LL0t7LqCjs5MRbax5Uisr75DRgSvxLHnVO2+Kxnb9iQKebhnN9eW37tVHNTsbPR9W0F0vnPztjGbJFs3dSsaKIQAAgINwVMkw3VNyvdMxAByEO+bPUTgRb/WJKP0LOIAaaA23K6ChxZeqMrJIu8Jz9ls5ZMntCjhSCknSmhSlkCStra2QMUaW1botcLmCM4YAAAAAdGqLyrcp2cqdEj6XW5cedmSaEwGdy9E9b9PQosvkcxXLZfnVI3iCTug73ZFSKJyIybJSVx1F3iClUAqsGAIAAADQqfXIy9fO+vomxz2WJZfLJRmj6485TuP7D8hgOqDjc1lejSr5jkaVfMfpKLp/9WypifWBlw09PrNhOgiKIQBZqTa+R7MrntS62vcV8hRqXLcva0zRBKdjAQCADuj60uP0vddeVjiR+PSZ1+XS0b376N4zztUHu3aoJhrVcX37qXsoz8GkAL6o5zYvld3ECsH5Fet13cgT5GpiRVGuohgCkHXq4lW6Z831iiUbZGRUFd+h57f+RbujW3RijwudjgcAADqYqUOH68fjT9Cf5s2RkVEimdQZQ0fo5pNPUcDj1YkDBjkdEUA7Mc2cJrZs73bNr9jAzWSfw61kALJKxK7X3au/qXp7b6Mxj+XVD0Y9rICbn+QBAICDF7UT2lpTo27BkIoCAafjAEiD25a9pn+vnatkE+PDC3so5Pbp8JJ+umLYOPUK5sZh883dSsb6KQBZZUb5/SlLIUlKmLi21q/KcCIAANBZ+N0eDe1SQimUpbJp0QI6rlN6j2qyFJKktTUVWlq1VY+vX6hz37xHG+t2ZyxbtmIrGYCsYYzR8urZzc55YftfdX3+ffK5+IIOuak+Ua8N9ZuU587T+voNmrN7ntyWW5N6nCify6sZ5a+rNlGrw4oP1dl9TleRNzd+CgYA6LiWlW3Qvb95ThtWbVcoP6Bzr5ioi64/RW436xhw8B5et0CWrCa3lO17Hje2Eglbf1r2uu46flomI2YdiiEAWcTINnazM+oT1Vq05xWN6/7lDGUCssdz2/6rF7a9JI/Lo4gdOeALntW1a2T02Rc7u3bu1vw97+nmQ3+jAm+BQ4kBAGje+pXb9YsrHlA0Epck1ddGNP1vb+i5h97V5d8/VWdePJ6CCAflo5qdzZ4ztD8j6b3dG9OapyPg3zAAWcOyXAq68pudY5TU8pp3M5QIyB7vVy3Rf7e/rLiJK2yHG33Bk5Q54JltbNUnGvTqjjcyHRUAgFb7zz1vKhZLNHreUBvRP//4km7/8RMOpEJHNrKwp1yyWj0/3+tPY5qOgWIIQFbxuYMtz3G1PAfobGaUv6FoMnZQr0mYhJZVr0hTIgAA2iZcH9Uz/5ql/73071o0+yOZZOrVHbFIQnNmfKDyzXsynBAd2TdGnih5SbhQAAAgAElEQVS/+8DNUQG3V4Pyusrnch/wPOj26tIhx2UyXlaiGAKQVfoGRzQ77rUCOqbkjAylAbJHbaK2Ta/r6itp5yQAALRdfW1E3zn3L3r4jhlaOm+dGuqizc73eNxau2xrhtKhMxhR1FMPjL9UY4t6y5KlQm9AVw+foCcmXaPjug2W3+VRgccvn8uts/ofpsuHjXM6suM4YwhAVjmxx9e0pnah4ubALxJc8siyLB1dcqpGFfKXN3LPkV0O147ITiVM4+X2TfG5fDq999Q0pgIA4OC8NH2uKsqrFYvGWzU/aYy69S5Ocyp0Nkd1HaAnJ1/X6Pl94y/R1voqbWvYqyEF3dQ9wDmMEsUQgCzTIzBQlw3+g17b8Q9tD69V0JWvUYXj1D9vtAaExqjI193piIAjzug9VXN3z1dNvFZx0/IX017Lo6sGXaphBUMzkA4AgNaZ8+qyVpdCbo9LPft10agjBqQ5FXJJv7wu6pfXxekYWYViCEDW6RsariuH3Op0DCCr5Hvy9ftDf623dr2tt3a+oz2xypQ3bnjlUZGvSL895CYVeJs/zB0AgEwrKslr9dwxRw/WT++8WJbV+oOEARw8zhgCAKCDyPOEdHafM3TzYb9V32Af+Vw+SZLrk/8MyxuiywZfrFsP/x2lEAAgK517+UT5g94W5wXz/PradZPVpRtbfYB0Y8UQAAAdTMDt128O+YXm7V6gpXs/VBdfF53c8yT1CfZ2OhoAAM06+oSRuuj6L+nRO19TPGY3O9fr49tVIBMsY1JfDeiE0tJSU1ZW5nQMAAAAAEAa1VY36P7fv6i3X1ysRLxxQVTYJaTp834pt8ed4tUADpZlWYuMMaWpxthKBgAAAADIqIKikH74x6/pf++8WF17FkqW5HZbCgR9ChUE9JsHvk4pBGQIa/MAAAAAAI6YMPVQTZh6qHZsqdSSuWuUVxjUsZNHyx9o+RwiAO2DYggAAAAA4Khe/Ut02teOczoGkJPYSgYAAAAAAJCjKIYAAAAAoB2FE3EtrNikFXt3KJsu+wGAVNhKBgAAAADt5OmNS/TbxTPktlyyTVI9ggX6x8RpGphf4nQ0AEiJFUMAAAAA0A6WV5XrN4tfUdiOqy4RVdiOa3Ndpa6Y9aiSrBwCkKUohgAAAACgHTy6bqFitn3AMyNpbyysxXu2OhMKAFpAMQQAAAAA7WB3pF5JNV4ZZMnS3liDA4kAoGUUQwAAAADQDk7uPUJBt7fR85id0PDCHoon7RSvAgBncfg0AAAAALSD8wYdpkfWLdSW+ipF7IQkyfrkv06dcbfcLpdGFPXQqX1H69yBh6pXsNDRvAAgsWIIAAAAANpFwO3Vk1Ou0qRew+X6uBKSkRRL2rJlFEvaWlZVrjuWvaWpM+7WjK0rnA0MAKIYAgAAAIB29c6OtSnPGtrHSIrYCf144fOqi0czFwwAUqAYAgAAAIB2srxqh9xW677Nclsuzd21Ic2JAKB5FEMAAAAA0E6KfQHZJtmquZYkl2WlNxAAtIBiCAAAAADaybDC7uqXV/zpGUPNSRqj8T0GZyAVADSNYggAAAAA2ollWXpg4jT1DBY0PUdSwO3Rn48/XyGPL3PhACAFiiEAAAAAaEd9QkV6aspV8qQ4a8htuTSlzwi9fcYNmtx7uAPpAOBAFEMAAAAA0M66Bwt06bBjFXR7P33mtVzq6g/pltJzVOLPczAdAHzG43QAAAAAAOiM/vewL2lMcU89tGaBqmMRndxnhL4xaqKKfEGnowHApyiGAAAAACANLMvSuQMP07kDD3M6CgA0ia1kAAAAAAAAOYpiCAAAAAAAIEdRDAEAOqz6SEw7qmplJ5NORwEAAAA6JM4YAgB0OOFYXL974g29vmSNXJaloM+rH39lks4oHeV0NAAAAKBDoRgCAHQ4Nz32qmYtW69YwpYkReIJ/frx19SjOF+lw/o5nC5zFq7bqunvLlZVXViTDxmqC44/VCG/z+lYAAAA6EAohgAAHUplXYPe2a8U2ieasHXt3U+pdFg/HTO8v849bqx6FOU7lDL9Hpn1vv76yhxF4glJ0vKtO/XU/A/1xPcuohwCHJRI2Hr6mTK99PISJRJJTZ48WhddOE55eX6nowEAkBLFUDuLJ+u1au9T2lL3tiy5VegboCLfIA3In6RC3wCn4wFAh7e7ul5et7tRMSRJdtJoweotWrB6i+5/db5+feFUnXnMaAdSpldtOKq/vDRbMfuzs5Ui8YR27K3V0wuW6dITj3IwHZDbbvrV01qydLOi0Y9L26eeXqi589boJzeeoZWrytXQEFOfPl00Yfxw+Xx8KQ4AcB6fjdpRPNmgFzddqvpEuSQjSdodXSZJ+qDynzqs5Os6pOQyBxMCQMfXv3txqw6bjiWS+vXjr2n86EHqkh/MQLLMqG6I6JbnZh5QCu0TiSf01vJ1FEOAQ1av3qGlS7d8WgpJUjxua9OmPfr2DY/ImM/mut0uXXvNJH31K8fIsiwH0gIA8DFuJWtHC3fdofrEdu0rhfZnm6g+qPynqmObMh8MADqRoM+r6047vlVzbWP0zrL1aU6UOdsqq3X2rQ/ppcWrmpzTLT+UwUQA9rdy1XYlTeOvAyXp849tO6m/3zdTf79/ZgaSAQDQNIqhdhJPNmhd7cvNzkmahLbUvZOhRADQeV31pWM0rHfXFufZSSOToqzvqG574R1VN0QafYO5v17FBZkLBOAA3bsXyONu/ZfXxhg9+1yZKqvq05gKAIDmUQy1k/KGhbJa+L/TqOWtDwCA1vnjFWcqL+BTSzswThgzODOBMmDOR5uaXI2wz+NzlmhjRVWGErVOMhlRNLFVSRN1OgqQVsceM0ShPJ9crtZvDfP5PFqzZkcaUwEA0DyKoXZiyZLbaunIJqMB+ZMzkgcAOruhvbrq2Z9erktOOkquJtqhvl0L1a0wL8PJ0sfvbfloQDuZ1HPvLc9AmpYZk9Tmqj9q0dYj9cH2U1S2+TCt3HmZ6qLZkQ9obx6PW3fecYlGDO8lr9ctr9fd4muStlG3bqz0AwA4h2KonfQKHdPiZoVi7zAV+vpnJA8A5IKexfm68csnafoPpyng8WjfD+ktSwp4PbrtijOdDdjOzjtmjPye5r/RTCSNHp+7RJfe9YRmrXD2fKXtNfdqZ+1DSpqIkiYio5hqIrO1fMd5Wrf7xzItrH4COqLevYt1z12X6/FHv6lHHrpOZ515RLPz+/btoqFDemQoHQAAjVnZ9EVZaWmpKSsrczpGm22pm63ZO34h28T0+QOoXfLp9AH/UIl/hDPhAKCT27J7r/79ZplWbavQyL7ddfmUUg3oXux0rHYViSf0nX89ryUbt8uypHAs0ez8gNejH5x1gqZNaP4b03QwxmjRliNkm5qU45b8GtrtTnXNOzXDyYDMMsbookvu1c5djf9dcLtdemL6t1RSku9AMgBALrEsa5ExpjTlGMVQ+wonKrWx9g1trZ+l3ZHlSpiwuviG65geP1DP4JFOxwMAdAIfba/Qmh27NX/1Zr22dLXC8aYLojy/V7N+8w35PC1vQ2tPxiT03uYRSnVT5z5uq0CH931bXndJ5oK10QcV5Xr8ow9UE4vqjMEjdOrAEfK4WHiN1lnw3jr9+rfPHnCNvc/n1re+cbLOOfsoB5MBAHIFxZCDjDGyWjoZFQCANlqwZrOeeW+Z3lq2TpEUBVHI79X070zT0F4t3+LW3pZsm6RoYlMzMywVBydrZI9/ZixTWzy4fJFuXfiOoratpIxCHq+O7N5bD5/2P5RDaLW589bovvtnatv2KnXrWqArLp+o0049zOlYAIAc0VwxlNkfH+YgSiEAQDodN3yAjhs+QFfe8/9Utn5bo/GEnVRJQciBZNLALjdpdcXVzcwwqg7Plp2sk9uVnVtpqiJh3bzwbUVt+9NnDYm4FleUa8bG1TpryCgH06EjGT9uuMaPG+50DAAAGuHHXAAAdAJXn3ysAp+7tcznceuEUYPVJS/oSKaAd6AkbwuzLCVNJBNx2mRe+WZ5XY0P/G5IxPXyxo8cSAQAANC+KIYAAOgEJowcpB+fc5LyAz6FfF75PG6dNGaI/jDtNMcyua1CSc0fkO339JXHlfltbq2V5/WlfO6SpUKfP8NpAAAA2h9byQAA6CQuGHeYzjtmrLZWVqskP6SiUMDRPD5PD1nyySiactxlBTSk6x+zetv1+D4D5E1xjpDf49aFIw93IBEAAED7YsUQAACdiNfj1uAeJY6XQvt0DZ3dxIhPh/aeoYJAyjMQs4bX5dbDp16gYn9A+V6f8r0++d1u/fCoE3RE995OxwMAAPjCWDEEAADSpn+XG7U3MlOJZLX2bStzWUENLrn1kzOIspcxRi+uX6XHVi3RwIJiHdqtl0p79tNJ/QapJODMgd4AAADtjWIIAACkjc/TU4f1maHymn+qJjJXPndf9S66RgX+I52O1qKfvDtDL6xfpXAiLklaXbVbKyp36WxuIgMAAJ0IxRAAAEgrr7ubBnT5idMxDsq6vXv0/LqVitifHZ4dthNasWeX3ti8VqcNGuFgOgAAgPbDGUMAAACfM798sxLJZKPnETuhx1YtcSARAABAelAMAQAAfM6c7ZuVMI2LIUkq27lNxpgMJwIAAEgPiiEAANBpNMRjWlpRru11NW3+GHujYb2+ZW2T41E7oVVVFW3++AAAANmEM4YAAECncO/SBfrL4jnyuFyKJ20d27Of7jn5PBX6/Af1cVbs2SW/y62Ybacct43ROc8/oivGHKWfHTtJlmW1R3wAAABHsGIIAAB0eK9uXKM7l8xVxE6oLh5T1LY1f8dWffftFw/6Y/UM5Sue4nyh/cWSth5ZtUSvbFzd1sgAAABZgWIIAAB0ePd+MP/Ta+X3iSdtvbttk/aEG2SMUXl9rXaH61v8WEOLu2pM1x7yupr/MimciOvB5Yu+UG4AAACnsZUMAAB0eLvDDSmfe1wuzSvfrNsWzVJ5fZ2MMRrbtafumny2+hUUNfnx/nXK+bp+5gt6b8dWWZal6H7X1u+vJhZtl/wAAABOYcUQAADo8E7oO0geq/GXNS7L0o9nv6KNNXsVtROKJW19sLtcF7w0XXYz28W6BIJ67PSvae6F39AL51yiQq+v0Ry/260zB49s198HAABAplEMAQCADi2ciGtwURe5LEufPwbaa7lU/7ktZrYxqo5FNXv7xhY/dvdgnkaV9NAfTzhdAbdH7k8Omg66PeqbV6grxx7dTr8LAAAAZ7CVDAAAdFg7G+p07vOPqDoWUSzZ+Baxqlgk5euSyaTK62pb/T6nDx6pIUUlenjlYpXX12pSv8H66vBDFEqxkggAAKAjoRgCAAAd1v8tmKld4TrZxhz0aw/r3uug5o8s6a7fT5h60O8DAACQzSiGAACtVrO3QbPeWK76uoiOOm6oho/u43Qk5Lg3Nq896FLI43JpfJ+BGtu1Z5pSAQAAdBwUQwCAZm3bskeLF6xXxY5qPfufBTImqUTc1oN3v6WiLiFd8a0pOuWsI+TxuJ2OihzkaeFK+c+zJJ0zZJT+eMLp6QkEAADQwVAMAQBSMsbo/r+8pv8+uVCyjGLRz5/fYrS3sl533fKSZs74UDfffZncbu40QGZ9edhYPb5qacrzhT7PbVnqHszTrRNPl9dFkQkAACBxKxkAoAmL5q/Ty8+UKRZLpCiFPpNIJLXyw21aOHdNBtMBH/tJ6Yka07WHQh6vAm6P/G6PPC6XLEl5Hq8GFBTJbbnktj7ePvbs2Zf8f/buPDzK6mD/+H2eZ2Yy2UMIYYewC4iCRFDcqGJdarW1ttVal6q1tWrfbm9/3a3dX7u3drPVaq1b6161WndFEQ2CiohsguwkIXtmf87vD4UKZGOZeWYy3891cV3Nc07IfWEhmXvOopBLKQQAALADK4YAAF165L7FikYSvU+UFI8lVPf8Sh1xzKQ0pwJ2VRwM6d4PflJ1Wzfqje31Gls+QHOGjVbKegoYR8YYxVJJSVKBy489AAAAu+MnJABAlxLx5F7Nj/WxRAIONGOMDh8yQocPGbHzmWP+uyqIQggAAKB7bCUDAHRp7snTFC4M9nl+sIAX3wAAAECuoRgCAHTpmBOm6NDaMTvLoUDAlTHdzw+FKIYAAACAXMNP8QCALrmuo6t/cY5eXrhGL85foZKysIpLwrrul4/I2t3mBhzVjBvsT1AAALqwsaVV33/kSc1fs04B19HpUw/SV084ViUFIb+jAUBWoRgCAHTLGKOZR4zTzCPGSZLi8aTuuHG+mrd37DKvqKhAx5441Y+IAADsoT0W05nX36LmSFRWUjyV0t2vLtMbW+v1jwvPlulpCSwA5Bm2kgEA+iwUCujXf71EUw4dqUDAUSDoasLkYfrF9RepqLjA73gAAKg9Fte5N/9TTe+WQjvEUymtrG/Uko2bfcsGANmIFUMAgL0yZPgA/fL6i9XeFpG1UmlZod+RAADY6Qv3PKg3tzV0OWZltbK+UTNGDMtwKgDIXhRDAIB9UlJKIQQAyC6bW9u0cN16ebsfhreDlcZWVWY2FABkObaSAQAAAOgXNre2KeS63Y6HgwHNZLUQAOyCYggAAABAvzC+qlLxVKrb8c5EMoNpACA3UAwBAAAA6BfKwmF9atZh3Y7Hk0mluttmBgB5imIIAAAAQL8xefAgdXcZ/ZiBAxRweAkEAO/F4dMAAAAAcpq179w29uqmLfreI0+quzVBm1vatLWtXYNLSzKaDwCyGcUQAAAAgJy1ubVNl9x+jzY0tyiR8pT0vG7nRpJJffPB/+j3Hz2jx0OqASCfsI4SAAAAQE6y1uri2+7R6obtiiSSPZZCOzyzep3OuuFWxZIcRA0AEsUQAAAAgBz15rYGbWxplbeXB0qvrG/UHYtfS1Mq7I9EMqVFazbolbWblOpD0Qdg/7GVDAAAAEBOaolG5TrdHTXdvZS1emjZmzr/8BlpSIV9Nf+NtfrqzQ/KWslaTwE3oP877xQddVCN39GAfo0VQwAAAABy0tQhg5VM7duqkuJQ6ACnwf7Y1tKuL934L7VH4+qIxdUZT6o1EtVl192jq27/zz7/dwbQO4ohAAAAADmppCCkL7/vKBUG/7sRwjW9ryAKuY4+MfPQdEbDXnqg7o1utwQ+sOgN/fE/L2Q4EZA/KIYAAAAA5KwLZh2m6z7+IZ04aZxmDB+qS46s3aUo2p1rjD5ZO13HTxibwZToTXNnRPFkqsuxRMrTrc8uznAiIH9wxhAAAACAnDZ79EjNHj1y58fHjR+j/73vYTV2dMqzVuMGDtAJE8dreHmZ5owdpaFlpT6mRVeOnDhadzz3qiLxRJfj7dG4rLUyfVgRBmDvUAwBAAAA6FdqRw7XE5dfpE2tbSpwXVWVFPsdCb2YPWGUZowZpuffXNftnI3bWzRiYEUGUwH5ga1kAAAAAPodY4yGl5dRCuUIxzG69pIPaXB5SbdzHqhbnsFEQP6gGAIAAAAA+C7gOqodN6Lb8RdXvZ3BNED+oBgCAAAAAGSFeYdM6HYswZX1QFpQDAEAAAAAssLRk2sU7uJWuZDr6KRDJ/qQCOj/KIYAAAAAAFmhIBjQ9895vwoC7i7Pk55V0mPFEJAOFEMAAAAAgKxx0vRJOvHQiXKd/15N71mr3z+yQA8vftPHZED/RDEEAAAAAMgaiWRKj726UinP7vI8Gk/qT48u9CkV0H9RDAEAAAAAskZbNCbP2i7H6lvaM5wG6P8ohgAAAAAAWaOiqFAl4VCXY1NHDs5wGqD/oxgCAAAAAGQNxzH6yunH7XI7mZEUDgX0P6cd7V8woJ/a8x5AAAAAAAB8dFrtZFUUF+pPj76gjdtbNXVEtS4/ZY4OGl7tdzSg36EYAgAAAABknaMn1+joyTV+xwD6PbaSAQAAAAAA5CmKIQAAAAAAgDxFMQQAAAAAAJCnKIYAAAAAAADyFMUQAAAAAABAnqIYAgAAAAAAyFMUQwAAAAAAAHmKYggAAAAAACBPUQwBAAAAAADkKYohAAAAAACAPEUxBAAAAAAAkKcohgAAAAAAAPIUxRAAAAAAAECeohgCAAAAAADIUxRDAAAAAAAAeYpiCAAAAAAAIE9RDAEAAAAAAOQpiiEAAAAAAIA8RTEEAAAAAACQpyiGAAAAAAAA8hTFEAAAAAAAQJ6iGAIAAAAAAMhTFEMAAAAAAAB5imIIAAAAAAAgT1EMAQAAAAAA5CmKIQAAAAAAgDyVtmLIGPNdY8xGY8ySd3+dmq6vBQAAAAAAgL0XSPPv/0tr7c/S/DUAAAAAAACwD9hKBgAAAAAAkKfSXQxdYYx51RhzgzFmQFcTjDGXGmPqjDF19fX1aY4DAAAAAACAHYy1dt8/2ZjHJA3pYuibkl6Q1CDJSvq+pKHW2ot6+v1qa2ttXV3dPucBAAAAAADArowxi6y1tV2N7dcZQ9baeX0M8GdJD+zP1wIAAAAAAMCBlc5byYa+58MPS1qarq8FAAAAAACAvZfOW8muMcZM1ztbydZK+kwavxYAAAAAAAD2UtqKIWvteen6vQEAAAAAALD/uK4eAAAAAAAgT1EMAQAAAAAA5CmKIQAAAAAAgDxFMQQAAAAAAJCnKIYAAAAAAADyFMUQAAAAAABAnkrbdfUAAADYd9tjnVqwbY3CblBHDx6nApcf2wAAwIHHTxgAAABZ5uZVC/XTpY8r4DgykiSjP805W7VVo31OBgAA+hu2kgEAAGSRN5q36GevP66Yl1RHMq72ZFztyZg+8/ztiqYSfscDAAD9DMUQAABAFrlr3RLFU6k9nkdTCd25drEPiQAAQH9GMQQAAJBFmqId8mT3eJ60nn7y6qO67+1XfUgFAAD6K4ohAACALGGt1XP1a7odT9iUvrP4AXUk4xlMBQAA+jOKIQAAgCyxsGGtmuKRHucEjKu6hnUZSgQAey/hJbWkaaVebnpTcY+z0YBsx61kAAAAWWJRw/o+zQu7wTQnAYB980rzSn3v9Rvk2Xe2xFpZfX3y+Zo9cKrPyQB0hxVDAAAAWWJQuEQ7LqjvTtBxNXPgqAwlAoC+a0926juv/VntyYg6U1F1pqKKpGL64bIb1Rhr8TsegG5QDAEA4JOEF9Gy5gc1f+u1Wt7ysBJe1O9I8NkpI6Yo5Lrdjjsyum7OOQo4/AgHIPvMr+/6cHzPenpq28sZTgOgr9hKBgCAD9a0zdd/Nn1fVilZpRQwYS1suF5njf6DigNVfseDT0qDYf3xyLN14fy/7zFmJM0bNkmHVA7PfDAA6IP2ZESxLs4UStiUGuOtPiQC0Be83QQAQIY9vOEqPbzp2/IUl1VKkpS0UXUkG/Xs1t/4nA5+O7J6rM6uOUwhZ9f37wrcoC6ffJxPqQCgdzXFQ2Vluxx7atsiLWx8XdZ2PQ7APxRDAABk0JLt/9Cajme6GbV6q/25jOZBdvrOjFN16cQ5KguGZSRNLh+s6486VweVD/Y7GgB0K5qKye3mJWZjvFVXLf2LfrfqrgynAtAbtpIBAJBmnk1pbfvz2hZdrlebev6B2MpTJNmswkBFhtIhG7nG0ZVT5urKKXNlrZUxPR9IDQDZoDo8QAHjKmW9LsetrB7Y9Jw+NvIEVYcHZDgdgO5QDAEAkEbxVIfufvtKtSW2KGEjvc53FFBrYgvFEHaiFEK2entzk2649wUtXbVZI4dU6MIzZuvQiZyBlc8mlIzU4HCl3o5s7XaOldVzDa/qwyPYGgtkC4ohAADS6KXGm9Sc2CDP7nkYZ9eMykPD0poJAPbXmg0Nuvi7tykWT8rzrDZsbdbLb2zQ1ZedormHT/A7HnxijFHA6f5mxR1cw4kmQDbhbyQAAGm0qu2JPpdCrkKaXHGqwm5ZmlMBwP659vZnFY0m5Hn/PUg4Fk/qZ397gsOF89jGznptjNT3Ou/EwbMykAZAX7FiCACANDI9vAdj5MjIkSdPhW6ZDhlwlmZUnp3BdACwb15buanLu6da2qJqaY+qorQw45ngv9Zkh1zjSur+DZELa05VYaAgc6EA9IpiCACANJpYdpJeafqHUja+85mRUXV4sj4y+nc+JgOAfTegtEhtHbE9nhsjFYWDPiRCNhhbPExeNwdPDy6o1P+bfJ6mlo/JcCoAvWErGQAAaTRz4LmqKpigoCmUI1dBU6hCd4DmDf2m39EAYJ+deOSkLp+PHT5QoSDvPeerAjekS8edoQLnv+VgyAQ0qKBC1878MqUQkKX4VxsAgDQKOmGdOeq32hRZom3RN1UaHKIxxXPkOiG/owHAPrHW6taHFnU5tnztNr2+arOmjh+a4VTIFh8YdpRGFQ3RPRueVmO8WbMqp+r04ceoNFjkdzQA3aAYAgAgzYwxGl40Q8OLZvgdBQD225MvrVQk1v0ZMp/9wR36zdfO0oyDRmQwFbLJtIpxmlYxzu8YQJ+1xBv0QuPD2hZdr2GFYxRywlrX8YbKQ4M0e+DJqg7373/PKIYAAAAA9NlTdat6HE8kPf3gukd0588vkjEmQ6kAYN9s7Fytv6z5tlI2qZRNannbSzvHHDlatP1xfXzUFzW5vP/epscZQwAAAAD6rDDU+3vL9U3t2t7SmYE0ALB/7tnwe8W9qFI2uceYJ08JG9NdG65VyqZ8SJcZFEMAAAAA+uz42ZMUCro9zrHWKtyHAgkA/BT3YtoSXdfrvIQX17bo2xlI5A+KIQAAAAB9NuvgUZp7+IRui5+A6+jwg0eruKggw8kAYO+4xpVjeq9FkjaujZ2rM5DIH9T4AAD0wPOsbr17of5xX53a2qIaP3awPv/p4zVt8nC/owGAL4wxuvqyU1T3+no98dIKLVm+Ueu3NqkgGFDKsxo9dICu+szJfscEgF65JqCpZUfo1Zb5vc59tuFe1Q6cl4FUmWestX5n2Km2ttbW1dX5HQMAALW1R/XX257X/Q8vUTyx557yMaOq9KlPzNHcOZN8SAcA2WVTfYtWrN2mIb9IrRYAACAASURBVFVlmlRTzaHTAHJGNNWhH7x+vqx660aMfjDtzpz9980Ys8haW9vVGCuGAADYTSKR0mX/e4vWb9qu7t4/eevtBv3ol//Whk3N+uRZszMbEACyzLBB5Ro2qNzvGACw18JusYaEa7Q5+laP84rdspwthXrDGUMAAOzmmRdWamtDa7el0A7RWEI33fG8OiPxzAQDAADAATe94tgex4OmQMdVn5mhNJlHMQQAwG6WLd+kWGzPK0u7EnAdrdvQmOZEAAAASJcpFUfINV1vqHLkam71RzSn6rQMp8octpIBALCb4UMrFHAdJVNer3MTiZQGDijJQCoAAACkQ2VosGqKp2ptxzKlbGLn84CCunT8jzS8aJyP6dKPFUMAAOzmxLlTVFDQ+3snwaCr6dNGqbqqNAOpAAAAkC7njv6qppTNkmsCCpigyoNV+uSYr/X7UkjiVjIAALq0Zl29vnr1XdrW0NbtnKNmj9e3vniqiosKMpgMAAAA6RL3ooqnoioOlPerw6Z7upWMFUMAAHRh7OhBuvOGzyoQ6P5b5dVf/SClEAAAQD8ScsIqCVb0q1KoNxRDAAD0oKwk3OXzglBAAdfNcBoAAADgwKIYAgCgB2d9cOYe5w0VhAI67f2HyHHy550kAAAA9E8UQwAA9OCcM2fpxOMmKxR0VVxUoFDQ1ZG1Y3XZp47zOxr6yFqrSCKhbDpXEQAAIFtw+DQAAH3Q1Nyhtzc2adiQcg0ayC1kueLm15boly8+r5ZYVGUFBfrC4XN0/rTpeXVuAAAAQE+HT/d+Fy8AANCAimINqCj2Owb2wh3LXtOPnn9akWRSktQUjeonC55RyHV1ztRDfE4HAACQHdhKBgAA+p14KqVfLHxuZym0QySZ1E8XzvcpFQAAQPZhxRAAAOg3/rVyuX70/DPa0t6m7jbLb49EFE0mFA4EM5oNAAAgG7FiCAAA9AuPvrVK//vEI9rcQym0w4OrVmQkEwAAQLajGAIAAP3Czxc+p+huW8e68/35T6klFk1zIgAAgOxHMQSgz9qaOvTgDU/q9p8/oDfr1vgdBwB2sb61pc9zOxMJ3fzakjSmAQAAyA2cMQSgT16dv1zf+eiv5Hme4tGEbjJ3q3JIhb7yx0s0cUaNFjy4WNHOmGrnTdOQmkF+xwWQh8YNGKhXt23p09y4l9Lja9foitoj0pwKAAAguxlre9uFnzm1tbW2rq7O7xgAdtO6vU2fnPxlxSOJPcbcgCtJChYE5HlWslYfufJkXfDtMzMdE0Cem79+nS556N4+byd7/5jxuu7UM9KcCgAAwH/GmEXW2tquxthKBqBHjVuadclh3+iyFJKkVDKlVDKlaEdM8Uhc8WhCd//uEb3+wsoMJwWQ744eOVrXnXKGDhpYpaDjyDVGBa7b5dzCQEAXHXpYhhMCAABkH7aSAejRTd+7S+0tnXv1OfFIQo/eMl9Tj5iQplQA0LVjR9Xo2FE1kqREKqUn1q3R8oYG3btimbZ0tCvgOEp6nr4+51gdMXykv2EBAACyAMUQgB4tfPgVeSlvrz7HWqtEvG9bOQAgXYKuq5PGTtBJYyfof2YdqVXbG9UUjWjqoMEqCgb9jgcAAJAVKIYA9ChcFFLf7/l593OKCzT3I7PTkgcA9tX4yoF+RwAAAMg6nDEEoEcfuPh9CgS7PqNDkorKChUsCMgNujJGChcV6IhTp6v2xGkZTAkAAAAA2BesGALQo49cebIe+uvT2rK2fo+xQEFAF333LB32vql6/I4FirRHdcSp0zXtqEkyxviQFgAAAACwNyiGAPTIDbj6yBUn6bpv3aFEdNebyYJBVyMnDtWwcYN13jc+5FNCAADgB5vaKuu1ygTGyBheVgBArmIrGYBeHf/xI1VYXCDj/HcVUCDoqnpklQ455iAfkwEAgEyzqQbFGz+u+La5SjR+WPGts5SKPOx3LADAPqIYAtCr4vIi/eqxb+nQYyfLcYzcoKujTp+pnz70NbaMAQCQZxLbL5KNvywpJtlOyTYr2fxFeYnX/Y4GANgHxlrrd4adamtrbV1dnd8xAPQglfJkjOQ49MoAAOQbL7FciYYzJCX2HAxMV6DkAjkFx8k4FRnPBgDonjFmkbW2tqsxNgMD2CuuSyEEAEC+sqlN6rIUkqTkEiVbVko2Kbf8xwoUcf4gAOQCXuEBAAAA6BtT1vO47ZAUU6rl67KpjRmJBADYP6wYAgAAANAnTqBG77y37PUy01Mq8qACJZemP1See2DZm/rdcy9oa1u7hpSVqjgUVEc8oalDqnXR4TM1efAgvyMCyHIUQwAAAAD6xLhVUnC2lFjQy8yUZKMZyZTPbnzpZf3imecUSSQlSW0NjTvHVjY06t9vrNCvzviA5k0c51dEADmArWQAAAAA+swtuqAPs0JywsenPUu+Snmebnl5iX78xDM7S6GuxFIpffPfjyrl9bbCC0A+Y8UQgLwR6YjqX399Rs/+62UVlxbqgxcdpzmnHCpjjN/RAADIGY5brpRCkuLdzCiUU/RROcGDMxkrr1x574N6ds1aeX24YTqSTOjt5haNqRyQgWQAchHFEIC8EO2M6fJ5P1bDpmYl4u+8s/bm4rU67cJjdfG3P+xzOgAAcocJHSaZIsnuXgw5MqGjFCi5XCZ0uC/Z8sFrm7do/ltrFU12v1LovVKeVWlBKM2pAOQytpIB6PdWvbZeF876jjavbdhZCklStDOu+65/So1bmn1MBwBAbjEmqGDlH98ph1QkKSgpLKfwowpW3iinYBarcdOobsOmvdoaNnPEMFUVF6cxEYBcx4ohAP1aZ3tUXzvr1+pojXQ5HgwGtKxujY457bAMJwMAIHc5oVkKVS+QF31E1muRU3CUnOBBfsfKC4OKixV0XMVTvZdDRtI3Tjgu/aEA5DSKIQD9Tktju+Y/sFiRzpji0fguq4R253meKgaWZjAdAAD9g3FK5Rad5XeMvDNvwjh99z+PS4ne5xaFQlrTuF0HVXNlPYDuUQwB6FdefGypfnTpXyQZpZIpeZ6V18M7asYxmjqbK1wBAEBuCAcD+vsnPqrL7/6X6js6ZGRkZRVLpro4jNpqYFGRLzkB5A6KIQD9RrQzph9/5nrFIn14C20HKzkOx60BAIDccVD1ID32mU9pzfamnecNfeSm23Y5kNpIKguHdfioET6lBJAreDUEoN9Y/Mxymb0seXraZgYAAJCtjDEaN7BSEwdVaeKgKv30tJNUWhBSSSikwmBAYyoH6OZzzpLDQeAAesGKIQD9huftvny6F0aafsyk9IQBAADIoJMPmqjjJ4zTG1vrVRQKavzASm6HA9AnFEMA+o0Zxx4kL5Xa43kg6EpWSib/O2aMUXFZWJ/9/kczGREAACBtQq6rQ4cN8TsGgBxDMQSg3ygqCesrv71AP73iJlnPKplMKVQQ1NwPzdTpF8/V/Tc8pRVL1ilYENSseQfrA+cfo4oqbiQDAAAAkL+M3ePkev/U1tbauro6v2MAyHENm5v1zH2LFOmIqfaEqZo0fbTfkQAAAADAN8aYRdba2q7GWDEEoN+pGlqhMz97gt8xAAAAACDrcSsZAAAAAABAnqIYAgAAAAAAyFMUQwAAAAAAAHmKYggAAAAAACBPUQwBAAAAAADkKYohAAAAAACAPEUxBAAAAAAAkKcohgAAAAAAAPIUxRAAAAAAAECeohgCAAAAAADIUxRDAAAAAAAAeSrgdwAAAAAAAA60WDKpp9a+pTcbGrWlvVUpa3X8mLGaN3acXIc1EsAOFEMAAAAAgH5leUO9zr3zn+pMJBRLpXY+f3DFCh1cXa2/nXmWQq7rY0Ige1AMAQAAAAD6DWutLr3/PjVFo3uMdSYSem3rVv342ae1vTOigOPoI1Onas7IUT4kBbIDxRAAAAAAoN9Y3tCg7ZFIt+ORZFJ/W7JE9t2PH161Uucecqi+cexxmQkIZBk2VgIAAAAA+o14KiUj0+Mc+57/HUkmddOSxVrT1JTeYECWohgCAAAAAPQbU6urFXT37qVuwvN0zfxn05QIyG4UQwAAAACAfiPgOPrVyacqHAgoYP67cqjnNUTSM2vfUtLz0hsOyEKcMQQAAAAA6FeOranRYxd8Sne+vlRb2tpUUViohs5O3f/mcsXfc0vZe1lJjZ2dGlxSktmwgM8ohgAAAAAA/c6w0lJ9/ogjd368tb1d97+5vNv5jnFUEQ5nIhqQVSiGAAAAAAD93uCSEl05+wj99oUFiu+2ZawwENCF06erIMBL5P1hrdWiplf12NZnFffiOrpqto4dNFsBhz/XbMZ/HQAAAABAXrh81mwdOWKkfvb8fC3ZskXxVEqFgaAuPuywXVYXYe+kbEobOjfrgU2P6YXGRYrbhCRpRdsaPVP/gr4z9YtyDEccZyuKIQAAAABA3jhs2DDdetbHZK1VZyKhwmBQjuntaGp0Z2HjYv1p9c1K2qRiXnyXsYRN6s221arb/opmDZzhU0L0hsoOAAAAAJB3jDEqDoUohfbD250bde2qv6oj1blHKbSDJ08Pb3kyw8mwNyiGAAAAAADAXnt481NKesle522LNmQgDfYVxRAAAAAAANhrjfHt8uT1Oq88VJaBNNhXFEMAAAAAAGCvHVoxRSEn1OOcgAno/YOPy1Ai7AuKIQAAAAAAsNeOrz5KFcEyGXV9TlPIBDWt/CAdPWhWhpNhb3ArGQAA6Na69iVa0/6SNnS+rqb4RpUFq3VU9XmaUHqE39EAAIDPwm5YHxp2kq5765Y9xlzj6pSh79M5oz4swwHfWY1iCAAA7CLpxfX01uu1qOlfkuwuY9FYu/614Sc6cejlmlZxoj8BAQBA1rhr47+7fJ6yKbUlOiiFcgDFEAAAkCTFvYhWti7Q8/W3qimxsdt5SRvT01uv18HlJ8gYdqUDAJCvYqm4tsebuh0fWlidwTTYVxRDAABAGzqX6s63vyPPekraWK/zo16HYl6Hwm5pBtIBAIBs5BpHRkZ2txXGOxxXfWSGE2Ff8DYfAAB5LmUTuvvtqxX3In0qhSTJVUAhpyjNyQAAQDYLOAHNGjhdbhfVwtxBc1Qe5Jr6XMCKIQAAutEZq1ND668VS6xWOHSIBpV/UeHgJL9jHXDrO5bKk9fn+QFToJkDz5Bj3DSmAgAAueDTY8/VtmiDNka2SDLybEoHlx+kS8ae43c09BHFEAAAXWiLPK4NjZ+RtRFJUiKyXu3Rx1VTfY8KQwf7nO7A8myyz3NdhTSz8gwdPei8NCYCAAC5oiRQrB9N+7pWd6zT1mi9RhcN14iiYX7Hwl6gGAIAQFIiuVENrb9TZ/xFBd0aReMv7yyF3uHJ2k5tbf6eaqr/4VvOdBhRPE3WpnqcUxWq0YlDL9ewoklyTTBDyQAAQC4wxmh8SY3Gl9T4HQX7gGIIAJD3Yok1WrP1ZFnbKckqlnij27mR+OLMBcuQkBPWKcO+rIc2/Uye9eQpqaAJa0TRVJ0y7EsqCVb6HREAAABpQjEEAMhb8eQG1bf8VC2d90rq23aqgDMwvaF8clD5MRpSOEGvtzyuaKpd40tmaVTxdBlj/I4GAACANKIYAgDkpURqq9ZsPUme1yr18eBlYwo1sPTy9AbzUUVoiI4adK7fMQAAAJBBXFcPAMhL21v/LM/rUF9LISmggSWXakDJJ9MZCwAAAMgoVgwBAPJSR2yBpEQfZxeouuJrqiq9NJ2RAAAAgIxjxRAAIC+FgjXq67dBY1xVFJ2V1jwAAACAHyiGAAB5aWDpZTKmoIuRHYcth+SYErnOAI2qukkBl5u5AAAA0P+wlQwAkJcKQwdrxMA/aPP2/6eUbZGsp8LQYRpQcr6KCo5QIrVeklVhaIaM4dslAAAA+id+0gUA5K3SwhNVMuwEJVNb5Dilcp3SnWPBwGAfkwEAAACZQTEEAMhrxjgKBob5HQMAAADwBWcMAQAAAAAA5CmKIQAAAAAAgDxFMQQAAAAAAJCnKIYAAAAAAADyFMUQAAAAAABAnqIYAgAAAAAAyFMUQwAAAAAAAHmKYggAAAAAACBPUQwBAAAAAADkKYohAAAAAACAPEUxBAAAAAAAkKcohgD0STT2st7efLTWbBiuNRvGqL7pm/JsxO9YAAAAAID9QDEEoFcdkce0qf4DSqZWS/IkRdXWcYM2b/uY39EAAAAAAPuBYghAjzzP09bGC7sciyXqFIsvzWwgAAAAAMABQzEEoEeR6KOSUt2OR2OLMhcGAAAAAHBAUQwB6FE8sbzHcdetyFASAAAAAMCBRjEEoEfB4Lgex4vCJ2UoCQAA2SPlReXZuN8xAADYbwG/AwDIbsWF75dRhaya9xgrL/mCHCfsQyoAAPzRHl+p1+u/pbb465KMqoqO05Sq7ynkVvodDQCAfcKKIQA9MiakEUMekmNG7jbiso0MAJBX4qkmvbjpE2qNvyqrlKySauh8Wi9tOk+xZIOstX5HBABgr1EMAehVwB0mqWW3pyk1tf6fYvElfkQCACBjPJtUyotqTdMflLLtu4xZJdWZXKNn179P89efoIbO+T6lBABg37CVDECvOqPPyMrb47m1MbV23KZBoek+pAIAIL2SXrveaLhaWzsekVVK6uJ74Q5WSUVTm/XKtis1a9gdKg1NzFxQAAD2AyuGAPTK2s5uRjx5Xns3YwAA5LbFWz6rrR3/kVVCPZVC7+XZuNa13JDeYAAAHEAUQwB6VVhwtGQTezw3pkglRaf5kAgAgPRqi7+p1vjrstrbm8c8dSbWpiMSAABpQTEEoFeuO1CV5d+UMYXa8c+GMUUKh45UUfj9/oYDACANOhPrZPbh1AWjoCoKZqYhEQAA6cEZQwD6pLz00woXzFZbx23ybLuKCz+govCJMsb1OxoAAAdcSWjiu1vI9oYj1ynUqPIL0pIJAIB0oBgC0GcFoUNUEDrE7xgAAKRdcbBGVYXHqiHyjDwb22XMKChJsrKqLpqn9vgbSnitqiw8UhMGfFHhQLUfkQEA2CcUQwAAAEAXplX/TGua/qSNbXcoZSMaWHiUaso/rbbEcsl6qiqaq3BgsN8xAQDYLxRDAAAAQBccE9L4yis1vvLKXZ6Xh6f5lAgAgAOPw6cBAAAAAADyFMUQAAAAAABAnmIrGQAgIxLJlJ6sW6mFS9epurJEpx87TUOryvyOBQAAAOS1/SqGjDEflfRdSZMlzbLW1r1n7OuSLpaUkvR5a+0j+/O1AAC5KxpL6JIf3K71W5sViSUUDLi65d+LdM3nT9cR02r8jgcAAADkrf3dSrZU0pmSnnnvQ2PMFElnS5oq6WRJvzfGuPv5tQAAOaixpUPf+eNDWr2hQZFYQtI7q4ei8aS+86d/K+V5PicEAAAA8td+rRiy1r4hScaY3YfOkHS7tTYm6S1jzCpJsyQt2J+vBwDILXc9/op+9vcnlPJsl+OxeFKrNzRq4qhBGU4GAAAAQErfGUPDJb3wno83vPsMAJAn1m1p6rEUkqRILKG1myiGgP7I86weuLtO99yxUB0dMc06crwu+Mz7NKias8UAAMgmvW4lM8Y8ZoxZ2sWvM3r6tC6edfnKwBhzqTGmzhhTV19f39fcAIAsd/eTr/RYCu3whzufk7W9zwOQW35zzYP687WPaeP67Wre3qHHH35Vnzv/OrU0d/odDQAAvEevxZC1dp619uAuft3Xw6dtkDTyPR+PkLSpm9//OmttrbW2dtAg3jEGgP5i/ZamPs2rb25XQ3NHmtMAyKTG+jY9+tArikUTO5+lUlaRzrjuv+slH5MBAIDd7e/h0925X9LZxpgCY8wYSRMkvZimrwUAyEIzJ4/q0zxrpVCQ+wmA/mT1yi0KBfc8sSAeT+r+f76ka753r5YueduHZAAAYHf7VQwZYz5sjNkg6UhJDxpjHpEka+3rkv4haZmkhyVdbq1N7W9YAEDu+Ni86QoFei58XMfokAnDVF5SmKFUADKheki54vFkl2MtzZ167KFX9eXLbtTlF16n15asYzspkOM8z+rFBav0x98+qttufk4N9a1+RwKwF0w2fSOura21dXV1fscAABwgy9du1RXX3Kn2SFzeu+cNOUYKh4KSkQYNKNEfvvZRVVWU+JwUwIEUjyd1+twf7/x735Ng0NUpZxymK75ySgaSATjQksmUvnLFzVq1YotisaSCIVeO4+iqH52lw2eP8zsegHcZYxZZa2u7HKMYAgCkU8rz9NqqzYrGEjp04nBtbWzT8rVbNXhgqaZPHC5jurqvAEAuW/baen39f25RpDPep/kFBQH9/E8XauJBw9KcDMCBtH5do/73ypvV2Ni+x1hJaVj/fOCLCvSyehhAZvRUDKXrunoAACRJruNo+sThOz+uGVapmmGVPiYCkG6FRQWyfVgttEMsltSCZ1ZQDAE5pKW5U1/83E3d3jTopTwtX7ZJBx8ysstxANmDYggAAAAHVM3YQaqqLtPG9Y3qy+J01zUqKODHUiAXtLZG9NMf3K8XF6yW53ndzrN6Z6sogOyXrlvJAAAAkKeMMfr+z85W1aAyFRaFVFgU6nG+G3B13IlTM5QOwP74+pduVd3CnkshSQqHg5owaWiGUgHYH7w1AwAAgANu+KiBuvne/9Fri9eppaVT4yYM0Y+/fZdWr9qqVPKdF5TGSIGAqyu+coqGDhvgc2IAvVm1YovefqtByWTPpZAktbVG9ND9i3Xahw7LQDIA+4NiCAAAAGnhOEaHzqzZ+fFv/3qJXlvytpYv3aiW5g6NHlut2UdNUHlFkX8hAfTZ1i0tcty+bTpJJj394df/0czDx2jocIpfIJtRDAEAACAjjDE6ZMZoHTJjtN9RAOyD8RMHK5lI9Xm+53l6+ollOvu8o9KYCsD+4owhAAAAAECvBg+p0LHHT1Yo1Lf1BZ5nldiLIgmAPyiGAAAAAAB98pVvfFAfOGOGjOl9bjDoas4xk9IfCsB+oRgCAAAAAPSJ6zq66LPHK1QQ7HaOMVJBOKjTz6zVuAmDM5gOwL7gjCEAAAAAQJ+Fw0FdevkJuu53jysWTUiSgiFXxcUFmjtvqoIBV8edMEWTJg/zOSmAvqAYAgAAAADsldPPrNXI0QN11+0L1djQrtlzxuvMj81SWTm3DAK5hmIIAAAAALDXZswcoxkzx/gdA8B+4owhAAAAAACAPEUxBAAAAAAAkKcohgAAAAAAAPIUxRAAAAAAAECeohgCAAAAAADIUxRDAAAAAAAAeYpiCAAAAAAAIE9RDAEAAAAAAOQpiiEAAAAAAIA8FfA7AAAAAAAA6P864wnd/dJSPb5slSqLi/SJIw/VzDEj/I6V9yiGAAAAgAywNqlUcrWMUybXHep3HADIqOaOiM787d/V0NqhlLWSpMeXrdKXTj5a5x890+d0+Y1iCAAAAEizaOcDam/5f5ISsjapQPBQlZR/T26gRo5T6nc8AEirt+q362PX3qrOeGKX54mUp2sefEanz5isiuIiPfvmWt3y/GI1d0Y0b+oEnXPkoSouCPmUOn9QDAEAAABplEgsVVvLFyQb2fksmXhRzQ0nS3IUDB2jsso/ynHK/AsJAGn05Vsf3KMU2sFK+tOTL6miKKw/P/WiIomkJGnFlgbds+h1/fPKc1UUCmYwbf7h8GkAAAAgjTrbfrlLKbQrT4n402pp/ERGMwFApmxrbddbDU09znlh1Tr96cmFO0shSYolU9rS0qa7Xlqa7oh5j2IIAAAASJNkcrXi0f/0Pi/xilLJdRlIBACZlfKs9O6ZQt1xHEdB193jeTSR1NPL16QrGt5FMQQAAACkSUfrzyR5fZjpKZXalO44AJBxQ8pLVF5U2O24a4xOmjZRXhflkWOMBpUWpzMeRDEEAAAApE0y/mKf5waCk9KYBAD8YYzRuXOmdzs+cmCFLjmuVoNKi+UYs8tYKOD2+Lk4MCiGAAAAgDRx3MF9mhcIzZHjVKY5DQD442OzD1FBYM+tYgXBgK768AlyHEd/vvhMjRk0QIXBgEoKQioKBfWtM47XwSOG+JA4v3ArGQAAAJAmRSWfV2vTpZJS3c4JBI9SeeVtmQsFABlWXhjW1WeeqKvuflSetUp6ngoCAZ1x2BQdPmaEJGn4gHLd94XztXpbo1ojMU0ZPljhIJVFJvCnDAAAAKRJQeHJCnYer0Ts0S5GC1U64FcKF56W8VwAkGkfnDFZM8cM18OvrlAkltDcKWM1dfiuqyqNMRo/uMqnhPmLYggAAABIo7KKn6tx6xxJ7e956spxB6sgfKpfsQAg44ZVlOmiY2v9joHdcMYQAAAAkEaOO1AVg+6SG5gsKSgpqGBojiqq7pYx/DgOAPAXK4YAAACANAsGD1Zl9WPyvCZJQTlOid+RAACQRDEEAAAAZIzjDPA7AgAAu2DtKgAAAAAAQJ5ixVAO6WiL6Om7X9LGNds0cXqNaiYPU0tjm8ZMGaHSAcV+xwMAAAAAADmGYihHrF+5RV8+9RrFYgnFI4mdzwMhV8YYffizJ+jCb35IxhgfUwIAAAAAgFzCVrIc8fMrblR7S+cupZAkJeMpJWJJ3fOHx/XU3S/5lA4AAAAAAOQiiqEc0NEW0arX1sva7uck4kld951/Zi4UAAAAACCndCabtbptgTZ1vi5rPb/jIEuwlSwHOMaoLxvEmre1qX7jdg0aXpn2TAAAAACA3LGg/m96qfEfck1AVlaFbpk+Mur/VBEa5nc0+IwVQzmgsCSsqbPHyzg910NuwNGSZ9/MUCoAAAAAQC54q/1F1TXeqZSNK+51KuFF1JbYpnvXf0u2p60pyAsUQzniy9deoMrB5T0eLh0sCKq4rDCDqQAAAAAA2aghtlaLt9+jZc2P6uXGu5W00V3Graya4hv0xxVn6aWG29lalsfYSpYjBg2v1I2LfqjH7ligv/3ofjXVt+4xJxBwVXv8VB/SAQAAAACygbVWj2/5jd5oeVTeu6uBPCW6nR/12vRCwy1qT27X+4Z8LlMxyMsZWAAAG5lJREFUkUVYMZQD3nhpja657AZdde7vZD2rG1/+oS79wVkKhYMqKg2rsCSs8oEl+sE/P69QOOh3XAAAAACAT9a0v6DlLY8raePylOixFNohaWN6rfkhRVPtGUiIbMOKoSz3r+uf0vVX3614NCFrrV5/YZUe+OvT+sVDX9XJ5x6t1xeuVigc1NTZ4+QGXL/jAjiAOiJxWVmVFBaosaVDT768SvFEUkcfOlajBg/wOx4AAACy0NLmh5XYbdtYX7gmoNbEFoXd8WlIhWxGMZTFOloj+st371I8+t+GNxaJa+OabXr8Hy/o1AuOVe0JbB0D+pstja266i8P69VVmyRJ1QNKtK2pXY5jJCv9/q7ndN4ptfrMh+b4nBQAAADZxrPJHseNXFml9niesgmVBavTFQtZjK1kWeyNl9YoENxzFVCsM67nHljsQyIA6ZZIpnTRj27XkpUblUx5SqY8bWpoVTLlKZ5IKZ5MKZZI6u8P12nZW1v8jgsAAIAsM7l8nnp6qV/olitgCnZ5FjAFmlx+osJuWZrTIRtRDGWx4rJCWW/PqwONkUoHFPuQCEC6PbtktToiMXld/N1/r1giqUcWLs9QKgAAAOSKiWXHanBB99vBJpQdrQ+P/KEGFtRIkkJOkQ6rPFMnDLkyQwmRbdhKlsUmzaxR6YBiRTtjsu95jRgKh3TaRXP9igUgjTY2tCqe2HNp7x6slEpxpSgAAAB25RhXZ9f8Rn9dfaFak7uuMA+asI6sOk+FgXKdP/Y6WevJGNaL5Dv+H5DFHMfRD//5eVUNr1RhSYGKSsMKhYO64Jtn6OAjOBAM6I8OGl2tYB8OkreSnlq8Whu2Nac/FAAAAHKK4zi6aPyNmj3wXBW6FQo5xZpYOlcXjf+bCgPlO+dRCkGSjLU9b1fIpNraWltXV+d3jKzjeZ6W172l9pZOTZk1TiXlRX5HApAm1lpd+INbtWp9g+LJnlcOGWM0rKpM9/zkIhljMpQQAAAAQK4xxiyy1tZ2NUY9mAMcx9GUWeM068RplEJAP2eM0R+/+jF9fN4MlRSGepxrrVVTW6deX8Mh1AAAAAD2DcUQAGSZwoKgPv+xY/Xory/TgNLCHucaGTW3RzKUDAAAAEB/QzEEAFkqEHB13dc+rpHVFQq6Xf9znUildPC4oRlOBgAAAKC/oBgCgCxWM7RSd/34U7r+G2drWFWZQu85mDocCuiSDx6hipKeVxUBAAAAQHe4rh4AspwxRpPHDNFt3ztf9zz9qp5YtErlxWF9fN4MzZ462u94AAAAAHIYt5IBAAAAAAD0Y9xKBgAAAAAAgD1QDAEAAAAAAOQpiiEAAAAAAIA8RTEEAAAAAACQpyiGAAAAAAAA8hTFEAAAAAAAQJ6iGAIAAAAAAMhTFEMAAAAAAAB5imIIAAAAAAAgT1EMAQAAAAAA5CmKIQAAAAAAgDxFMQQAAAAAAJCnAn4HAADgQLHW6sW3NmjF1gaNqqzQ0RNGy3V4DwQAAADoDsUQACDnrWts1rJNW/WHJ1/QxqY2JVIpuY7RoNJi3fqZs1VVUux3RAAAACArUQwBAHJWLJHUF277lxasfluetUp6dudY0pM2NLXqczffp39c9gkfUwIAAADZi/X1AICcdcUt9+vpFWsVT3m7lELvtXTjVm1rbctwMgAAACA3UAwBAHLSgtVv67lV6/o097Flq9OcBgAAAMhNFEMAgJx03VML+zTPSEp6XnrDAAAAADmKYggAkJM2NLf2aZ7rGB07cUya0wAAAAC5iWIIAJCTZowaJseYXueVF4ZVUzUgA4kAAACA3EMxBADISZ973xEqDAbUWzfU1BlVNJHMTCgAAAAgx1AMAQByUk3VAN1x2Sc0b8p4VZUUyXW6bohcx1HA4dsdAAAA0JWA3wEAANhXYwdV6tfnfFCS9LsnFuj6Z+t2WR0Ucl2dMm2iAi7FEAAAANAVflIGAPQLlx43S3MnjVVBwFVJQUjhYEDTRw3Vtz54vN/RAAAAgKzFiiEAQL8QdF394uwPaMP2Fq3c1qBRlRUaVz3Q71gA+gnPelrR9obakq0aXzJJA0KVfkcCAOCAoBgCAPQrIyrLNaKy3O8YAPqRrdHN+uWKHyuaikiSkjal91XP05nDz5Hpw+2IAABkM7aSAQAAAN2w1uraVT9XS6JZUS+qqBdV0ib0dP0TeqXlZb/jAQCw3yiGAAAAgG5sim5QS6JZVnaX53Evpqe3PeZTKgAADhyKIQAAAKAbsVRMjrreLtYYb1Ak1ZnhRAAAHFicMQQAAAB0Y2TRaKmbYmhbbIu+8srndGj5TAVMQMWBYh1VdZxGFI3ObEgAAPYDK4YAAACAbgSdoM4bfYncbt5PTdmUXm5+US82Pa+n6h/TNcu/p2fqH89wSgAA9h3FEAAAANCDmZWzNL3isF7nWVnFbVz/XH+LOpIdGUgGAMD+oxhKs/ZERFsi2+VZz+8oAAAA2EcFbrjPc13jakXbG2lMAwDAgcMZQ2nSnozoJ8tu04uNy+UYR4Vugb406SwdUz3N72gAAADYS4dXHqm67S8obuN9mh9yQmlOBADAgUExlCZXvXajXmt+SwmbkmxKMS+hq5fepPJQqZJeUpPLR+nisadoQukIv6MCAACgFweVTlVt5RFa0DhfVj2vBHeNq4PKpmQoGQAA+4etZGmwOdKopS3r3imF3iMlq+3xVrUmO7Wwcbk+v+harWjb4FNKAAAA9JUxRueNvkQnDTlVpptbylwTUJFbpCsmfEWu4f1XAEBuoBhKg/pYiwJ9+KONegn9ZfVDGUgEAACA/WWM0bzBpypggnuMuXJ11ohP6P8OuVZjisf7kA4AgH1DMZQGY4qHKOr1bf/58tb1aU4DAACAA6UkUKoLaj6toAkq5IQUNMH/396dB1laFuYCf95zuk/3LCyzsiPbACMiIC1qALcAAZcIRkm8V+NWV03ikqi3koreG7VibsoymlSpiFdN9KrRqGxRc1UUUYgCA4obAuIWYBx2h2GYXt/7xxxyB6Z7Bpjp83XP+f2qqDn9fd/peah6661znvne98tgGcyZ+52dZ6w8NYOtrUsjAJjL3OM6C3YbXJi9hpdk7aa7tnvtiuE9epAIAICdZWTpk3PEbo/Ntb+5JpN1IkfvcVyWdpY1HQsAHhXF0CwZWXJ4vrD2itTUGa9ppeQPDzqth6kAANgZdhvcPSctf3rTMaDn1t5/W7609tLcuun2HLX7YTlt75OyeGBh07GAHaAYmiVnHXBSvrLu6oxOjc94zZOWrc7TVj6+h6kAAAAeuRvv/WUuvf3KfOXXl2WyTmYqNdfe85NceMvX8t7j/jJLO1ZCwHxlj6FZcvDiffLWo16cxQMLpj0/1BrMKw45o8epAAAAHr7xqYm840fvz1t/8N58ce03Ml4nMtVdFTFZJ7N+YkNes+Z/5sJbvpbxqYmG0wKPhmJoFp204nG54OR35LS9j89QGUxJUpIMtzo5Y58Tcthu+zYdEQAAYEZfuPWS/Gj9jRmrM6+EGK8T+cQvL8zfXPfB1DrzVhrA3GQp2Sxrl1b+YvWL8qx9npSL112TWmtO2fv4HLPnIU1HAwAA2KaL1/17xraxPcYDJupkrlt/U66/9+c5cnffdWA+UQz1QCklxyw5NMcsObTpKAAAAA/bRJ182NdO1snccO8vFEMwz1hKBgAAwLROXjGSgbQf1rUDZSDLhmxCDfONYggAAIBp/d5+p2WvBcsf1rWd1mCeuNRTl2G+UQwBAAAwrQUDw/n7Y9+Sk5cfn/Y0Xx/baWUgAzlw4T5559F/lk5rsIGUwI6wxxAAAAAzGmi188YjXpETll6dz9/85dwzvj5H7bEqLzrgORlotdMqrawYWtp0TOBRUgwBAACwXSetOD4nrTi+6RjATmYpGQAAAECfUgwBAAAA9CnFEAAAAECfUgwBAAAA9CnFEAAAAECf8lQyoHFTE7dkfPTSlLIogwt+J6UMNx0JAACgLyiGgJ6otWb8/vMztuGc1Km70u48JcO7vzmjG/4x4xv/KUlNkmy6p5XhJe9PZ8GzU+tYRjeck/GNn07qWAaGz8jQ7m9Kq7Wk0f8XAACAXYViCOiJ0Xvfm7H7zk3q/UmSiU1fyIbRi5O68SFXTmXT3X+cgc61uf+e12dy9DtJNiVJxjf+cyZGL8nilV9zVxEAAMBOoBgCZl2dujdjG85JMrrF0alpSqH/fEc2/eavMjl2RR4ohTYbT526M+P3X5TOwrNnLS9Aktx9z335wLlfz2X/fmNarZJnPm11Xv3fnpHFi4aajgYAsNPYfBqYdVMTNyWl84jeMzlxwwOryx6sbszk2FU7JxjADMbGJvJHr/94vv6N67Jp03g2bhzLF/7t2rzkFR/KnXdtaDoeAMBOoxgCZl1p753UsUf0noHObyVluilqOK32wTsnGMAMvnnZDbnzzg2ZmnpwQ33PPRvz+y/+QC7/9o0NJQMA2LkUQ8Csa7X3zsDQSUkeuvyiPc2xpLSWZWj3N6e0lnev2fLkQAYtIwNm2fU33JqJialpz01O1rz1beflr//XRRkfn+xxMoDeun/Dplx2wZW57Pwrs/He+5uOA8wCxRDQEwuWvD8Dw6clKVsc3fyFqrQPSdJJ0snA8OlZtOJrabUWZNHyz6bdeXKSwSSdtAYOz6Jln0mrvbzn+YH+MjE53VrWB/vW5TfkIx/7Zg/SADTj8guvytn7vTrvfuU5efcrz8nv7/fqfOu8K5qOBexkpdbtf/DplZGRkbpmzZqmYwCzZPz+L+b+u9+Y5KH/2jSUxXtdnlZ75bTvq1PrU+t4Wu1ls54R6G+11nzoI5fmc+dfNeMdQ1tasKCTL13wZz1IBtBbd6+7Jy8+9HUZHx1/0PH2YDsf/eF7ss8hezWUDHg0SilX11pHpjvnjiGgZ8Y3fTlbl0JJykAmR7894/tKa3elENATl3/7xlzwr9c8rFIoSTZtGstc+kc2gJ3lvH/40lalUJJMjk/mVcf999x+850NpAJmg2II6JlS9sj0005JWrv1Og7AVs6/8Jps2rT1F6GZrDps75RStn8hwDzzzW0sGRvdOJZ3vez9PUwDzCbFENAznUX/JZv3Enqoge7m1ADN2nDf6LTHBwZaabdbaXVLoFarZHh4MG947am9jAfQM3etvXub57//zesyNfXw7q4E5jbFENAz7cHVGd7j7UmGk7JbUhantJZm0bJPppTpCiOA3nr6U49IpzOw1fGhzkA+fM7L8+wzjsnhq/bOGacdnXPf99I89sh9G0gJMPuW7r2k6QhAj2z9yQdgFnUWvSiDC56TibErUsrCtDsnpBRTETA3nPncJ+TLX/1h1q1bn02j42m1SgYH23nTn56egx6zPG98w+80HRGgJ/7gz5+Xf/iTD2dqhj3XDnn8gWm13GcAuwLfxoCeK63dMjh8StMxALayYEEn577vpbn46z/Od668KcuWLc7znnNcDj5oRdPRAHrq9Jc/I59514W59aZ1054/83Wn9zgRMFsUQwAAWxgaGsyzzzgmzz7jmKajADSmlJKjTjwya39+W+rUg5++OLxoKAceuX9DyYCdzb1/AAAAbOV5f3RaOkODDzpWWiVL9tozR55wWEOpgJ1NMQQAAMBWDh85NK97/yszvHg4C3dfkOGFQzngiH3zt//3LSndpzQC85+lZAAAAEzrtJc8LU97wVPy02t+noV7LMxBR+2vFIJdjGIIAACAGQ0t6OSoE49oOgYwSywlAwAAAOhTiiEAAACAPqUYAgAAAOhTiiEAAACAPqUYAgAAAOhTiiEAAACAPqUYAgAAAOhTiiEAAACAPqUYAgAAAOhTiiEAAACAPqUYAgAAAOhTiiEAAACAJOOTk1l//6bUWpuO0jMDTQcAAACA6dz8m9/k3CuuzFU335rH7LlHXv2kE/KE/fZtOha7mJ/dfld+8uvb84nvfC/fv2Vtak2WL16Y//GcZ+aU1Yc1HW/WlbnUgo2MjNQ1a9Y0HQMAAICG/eLuu3PW//lkNo6NZ7L7vXVooJ2/e9YZOf2IwxtOx65g49h4Xvupi3LNr27J6MTkVuc7A+18+A+fnycetH8D6XauUsrVtdaR6c65YwgAAIA55z3fujwbRsey5a0MoxOTedOX/i1fv+lnWbpwQV5w9ONy2LJljWVkfnvnFy/J1b+8JWOTW5dCSTI2MZkPXnrFLlEMbYtiCAAAgDnllt+sz+W//FWmW98yOjGZ837047RLySe+e23++rRTcuZRj+15Rua3yampfOH7P5mxFHrAz++4u0eJmqMYAgAAYE64df36/PEFF+XGO++cdmnPliZrzeTERN76lYtz6qrDsqjT6VFKdgWTU1OZmJra7nVH7buyB2ma5alkAAAANG6q1vzXT382P1p323ZLoS0NtFpZc8sts5iMXVFnYCCrVm57GWKrlLz+t3+rR4maoxgCAACgcVfdfHPu2HjftMvHtmd4wGIYHrlnHX3EjOdaSc59yZlZtXJ57wI1RDEEAABA427fcF/Gt7Pfy3Q67XZG9ttvFhKxq9t3z92zYHD6UnHhUCcrd1vc40TNUAwBAADQuGP33SeTU9PfL9QuJb996CH53ccemU67nYWDg1nU6WT3oaF85AVnpd3y1ZZH7sTDHpOpOv2Y2zA6lpd+9LMZHZ/ocarec78dAAAAjdt/jz1yyNKluemuu7Y6N9Bu5S3PfHoO3HPPvPnke3PFr/4ji4c6eerBB2XIMjIepSULF+Qtz3pG3v6vX8vkNAXR+ORkLrn+Zzn9cYc3kK531KoAAADMCR8487kZbLcfdKzTbudJBxyQA/fcM0my7+675azHPTanrjpMKcQOe+HI0XnusaunPTc+NZU7NtzX40S9pxgCAABgTjh02bJ8/Ozfy6FLl6ZdSjrtdp67+oi873ef23Q0dmGnrj4sCzuDWx1vlZLjH7Pr71+1Q/VqKeWFSd6WZHWSE2qta7rHD0pyXZLru5d+p9b6mh35uwAAANj1PXH//fPlV74s942NpdNub3UHEexsTzv84KxauSzX//qObJrYvKfQgsGBnLzqoKzeZ2XD6Wbfjt5398Mkz09y7jTnbqq1HruDvx8AAIA+tKjTaToCfaLdauVjL39hPnXl93LRtT/JQLuVs0eOzvOPO6rpaD2xQ8VQrfW6JCml7Jw0AAAAAD02NDiQl584kpefONJ0lJ6bzT2GDi6lfLeUcmkp5eSZLiqlvKqUsqaUsub222+fxTgAAAAAbGm7dwyVUi5Osvc0p95Sa71whretTXJgrfXOUsrxSS4opRxVa13/0AtrrR9K8qEkGRkZ2fr5cAAAAADMiu0WQ7XWUx7pL621jiYZ7b6+upRyU5LDk6x5xAkBAAAAmBWzspSslLKilNLuvj4kyaokP5uNvwsAAACAR2eHiqFSylmllJuTPCXJF0spX+6eemqS75dSrk3yuSSvqbXetWNRAQAAANiZdvSpZOcnOX+a459P8vkd+d0AAAAAzK7ZfCoZAAAAAHOYYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPqUYggAAACgTymGAAAAAPpUqbU2neE/lVJuT/LLpnNMY3mSO5oOAQ+Dscp8YawyXxirzBfGKvOFscp8sauN1cfUWldMd2JOFUNzVSllTa11pOkcsD3GKvOFscp8YawyXxirzBfGKvNFP41VS8kAAAAA+pRiCAAAAKBPKYYeng81HQAeJmOV+cJYZb4wVpkvjFXmC2OV+aJvxqo9hgAAAAD6lDuGAAAAAPqUYmgbSimnl1KuL6X8tJTyF03ngW0ppfyilPKDUsr3Silrms4DDyilfLSUclsp5YdbHFtaSvlqKeXG7p9LmswIyYxj9W2llFu6c+v3SinPajIjJEkp5YBSyiWllOtKKT8qpbyhe9zcypyyjbFqbmVOKaUMl1KuLKVc2x2rb+8eP7iUckV3Xv1MKaXTdNbZYCnZDEop7SQ3JDk1yc1JrkryolrrjxsNBjMopfwiyUit9Y6ms8CWSilPTbIhycdrrY/rHntXkrtqrX/bLd6X1Fr/vMmcMMNYfVuSDbXWdzeZDbZUStknyT611mtKKbsluTrJmUleFnMrc8g2xurZMbcyh5RSSpJFtdYNpZTBJJcleUOSNyY5r9b66VLKB5NcW2s9p8mss8EdQzM7IclPa60/q7WOJfl0kuc1nAlg3qm1fjPJXQ85/LwkH+u+/lg2f0iERs0wVmHOqbWurbVe0319b5LrkuwXcytzzDbGKswpdbMN3R8Hu//VJM9M8rnu8V12XlUMzWy/JP+xxc83xyTG3FaTfKWUcnUp5VVNh4Ht2KvWujbZ/KExycqG88C2vLaU8v3uUjNLc5hTSikHJTkuyRUxtzKHPWSsJuZW5phSSruU8r0ktyX5apKbktxTa53oXrLLdgKKoZmVaY5Zd8dcdmKt9QlJzkjyJ90lEQDsmHOSHJrk2CRrk/xds3Hg/yulLE7y+SR/Wmtd33QemMk0Y9XcypxTa52stR6bZP9sXkG0errLepuqNxRDM7s5yQFb/Lx/klsbygLbVWu9tfvnbUnOz+bJDOaqdd19Bx7Yf+C2hvPAtGqt67ofFKeS/O+YW5kjuntgfD7JJ2ut53UPm1uZc6Ybq+ZW5rJa6z1JvpHkyUn2LKUMdE/tsp2AYmhmVyVZ1d2FvJPkD5Jc1HAmmFYpZVF3Q7+UUhYlOS3JD7f9LmjURUle2n390iQXNpgFZvTAl+yus2JuZQ7obpL6kSTX1Vrfs8Upcytzykxj1dzKXFNKWVFK2bP7ekGSU7J5T6xLkryge9kuO696Ktk2dB+b+PdJ2kk+Wmt9Z8ORYFqllEOy+S6hJBlI8injlbmilPLPSZ6eZHmSdUn+KskFSf4lyYFJfpXkhbVWm/7SqBnG6tOzealDTfKLJK9+YA8XaEop5aQk30rygyRT3cN/mc17t5hbmTO2MVZfFHMrc0gp5fHZvLl0O5tvoPmXWus7ut+zPp1kaZLvJnlxrXW0uaSzQzEEAAAA0KcsJQMAAADoU4ohAAAAgD6lGAIAAADoU4ohAAAAgD6lGAIAAADoU4ohAAAAgD6lGAIAAADoU4ohAAAAgD71/wD24uRKrJaLRwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "label = []\n",
    "X = []\n",
    "for i in range(num_catalog):\n",
    "    label += [i]*len(cmat[i])\n",
    "    first_coord, second_coord = cmat[i][:,:2].T\n",
    "    X += [(i, j) for i, j in zip(first_coord, second_coord)]\n",
    "label = np.array(label)\n",
    "X = np.array(X)\n",
    "sigma_max = 0.1\n",
    "result = DBSCAN(eps=5*sigma_max, min_samples=2).fit(X)\n",
    "y_pred = DBSCAN(eps=5*sigma_max, min_samples=2).fit_predict(X)\n",
    "fig = plt.figure(figsize=(20,20))\n",
    "plt.scatter(X[:,0], X[:,1], c=y_pred)\n",
    "print('Number of clusters: {}'.format(len(set(y_pred[np.where(y_pred != -1)]))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### DirILP General Case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_candidate_list(clustering_result, catalog_label, clustering_label):\n",
    "    candidate_dict = {}\n",
    "    list_of_label = catalog_label[np.where(clustering_result.labels_==clustering_label)] #The catalog id of all sources found in the island\n",
    "    for j in np.unique(list_of_label):\n",
    "        list_of_indices = []\n",
    "        for k in range(sum(list_of_label==j)):\n",
    "            list_of_indices.append(((np.where(cmat[j][:,:2]==clustering_result.components_[np.where(clustering_result.labels_==clustering_label)][list_of_label==j][k])[0][0]), j))\n",
    "        candidate_dict[j] = list_of_indices # catalog id: (source id, catalog id)\n",
    "\n",
    "    # Get all the (catalog_id, source_id) pairs\n",
    "    candidate_list = []\n",
    "    for key in candidate_dict.keys():\n",
    "        list_of_value = candidate_dict[key]\n",
    "        for pair in list_of_value:\n",
    "            candidate_list.append(pair)\n",
    "\n",
    "    catalog_list = []\n",
    "    source_list = []\n",
    "    coord_1_list = []\n",
    "    coord_2_list = []\n",
    "    Sigma_list = []\n",
    "    for catalog_source_pair in candidate_list:\n",
    "        catalog_list.append(catalog_source_pair[1])\n",
    "        source_list.append(catalog_source_pair[0])\n",
    "        coord_1_list.append(cmat[catalog_source_pair[1]][catalog_source_pair[0]][0])\n",
    "        coord_2_list.append(cmat[catalog_source_pair[1]][catalog_source_pair[0]][1])\n",
    "        Sigma_list.append(cmat[catalog_source_pair[1]][catalog_source_pair[0]][2])\n",
    "    df = pd.DataFrame({'Catalog_id': catalog_list, 'Source_id': source_list, 'Coordinate_1': coord_1_list, 'Coordinate_2': coord_2_list}) #Make a dataframe from the information provided\n",
    "    return(candidate_list, df, catalog_list, Sigma_list)\n",
    "\n",
    "def get_distance(list_of_indexes, df):\n",
    "    '''\n",
    "    Given 2 pairs of (source_index, catalog_index), return the square distance between them\n",
    "    df has the columns ('Catalog id', 'Source id', Coord 1, Coord 2, Sigma)\n",
    "    '''\n",
    "    coord_list = []\n",
    "    for i in range(2):\n",
    "        coord_list+=[np.array(df[(df['Catalog_id'] == list_of_indexes[i][1]) & (df['Source_id'] == list_of_indexes[i][0])].iloc[:,-2:])[0]]\n",
    "    array_matrix = np.array(coord_list)\n",
    "    return(np.linalg.norm(array_matrix[1]-array_matrix[0])**2)\n",
    "\n",
    "def sum_of_distance(list_of_objects, df):\n",
    "    '''\n",
    "    Given n pairs of (catalog_index, source_index), return the sum of all pairwise square distance.\n",
    "    '''\n",
    "    num_of_objects = len(list_of_objects)\n",
    "    coord_list = []\n",
    "    for i in range(num_of_objects):\n",
    "        coord_list+=[np.array(df[(df['Catalog_id'] == list_of_objects[i][1]) & (df['Source_id'] == list_of_objects[i][0])].iloc[:,-2:])[0]]\n",
    "    array_matrix = np.array(coord_list)\n",
    "    pairwise_dist = spatial.distance.pdist(np.array(array_matrix))**2\n",
    "    sum_of_square_dist = sum(pairwise_dist)\n",
    "    return sum_of_square_dist\n",
    "\n",
    "def Bayes_factor(list_of_objects, df):\n",
    "    '''\n",
    "    Compute -ln B_o\n",
    "    '''\n",
    "    sum_ln_kappa_rad = 0\n",
    "    kappa_rad_sum = 0\n",
    "    kappa_sum = 0\n",
    "    neg_ln_Bayes = 0\n",
    "    num_of_objects = len(list_of_objects)\n",
    "    for object in list_of_objects:\n",
    "        sum_ln_kappa_rad += ln(kappa_rad_dict[object])\n",
    "        kappa_rad_sum += kappa_rad_dict[object]\n",
    "        kappa_sum += kappa_dict[object]\n",
    "    for index_1 in range(num_of_objects):\n",
    "        for index_2 in range(index_1+1,num_of_objects):\n",
    "            neg_ln_Bayes+=(1/(4*kappa_sum))*kappa_dict[list_of_objects[index_1]]*kappa_dict[list_of_objects[index_2]]*get_distance([list_of_objects[index_1],list_of_objects[index_2]],df)\n",
    "    neg_ln_Bayes = neg_ln_Bayes + (1 - num_of_objects)*ln(2) - sum_ln_kappa_rad + ln(kappa_rad_sum)\n",
    "    return(neg_ln_Bayes)\n",
    "\n",
    "def compute_distance_dictionary(list_of_indices, df):\n",
    "    '''\n",
    "    Return a dictionary with the form: dict[('Source_id_1', 'Catalog_id_1'), ('Source_id_2', 'Catalog_id_2')] = square distance between them. \n",
    "    '''\n",
    "    distance_dict = {}\n",
    "    for current_pair_index in range(len(list_of_indices)):\n",
    "        for next_pair_index in range(current_pair_index + 1, len(list_of_indices)):\n",
    "            if list_of_indices[next_pair_index][1]!= list_of_indices[current_pair_index][1]: # Only find distances for sources from different catalogs\n",
    "                distance_dict[(list_of_indices[current_pair_index],list_of_indices[next_pair_index])] = get_distance([list_of_indices[current_pair_index],list_of_indices[next_pair_index]], df)\n",
    "    return distance_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-22T00:56:07.311872Z",
     "start_time": "2020-04-22T00:56:07.204429Z"
    }
   },
   "outputs": [],
   "source": [
    "def mycallback(model, where):\n",
    "    start_time = [0]\n",
    "    if where == GRB.Callback.POLLING:\n",
    "        # Ignore polling callback\n",
    "        pass\n",
    "    elif where == GRB.Callback.PRESOLVE:\n",
    "        # Presolve callback\n",
    "        cdels = model.cbGet(GRB.Callback.PRE_COLDEL) #number of cols removed by presolve to this point\n",
    "        rdels = model.cbGet(GRB.Callback.PRE_ROWDEL) #number of rows removed by presolve to this point\n",
    "    elif where == GRB.Callback.SIMPLEX: #Currently in simplex\n",
    "        # Simplex callback\n",
    "        itcnt = model.cbGet(GRB.Callback.SPX_ITRCNT) #Current simplex iteration count\n",
    "        #if itcnt - model._lastiter >= 100:\n",
    "        model._lastiter = itcnt\n",
    "        obj = model.cbGet(GRB.Callback.SPX_OBJVAL) # Current simplex objective value\n",
    "        ispert = model.cbGet(GRB.Callback.SPX_ISPERT) \n",
    "        pinf = model.cbGet(GRB.Callback.SPX_PRIMINF) # Current primal infeasibility\n",
    "        dinf = model.cbGet(GRB.Callback.SPX_DUALINF) # Current dual infeasibility\n",
    "        if ispert == 0:\n",
    "            ch = ' '\n",
    "        elif ispert == 1:\n",
    "            ch = 'S'\n",
    "        else:\n",
    "            ch = 'P'\n",
    "    elif where == GRB.Callback.MIP: #Currently in MIP\n",
    "        # General MIP callback\n",
    "        nodecnt = model.cbGet(GRB.Callback.MIP_NODCNT) #Current explored node count\n",
    "        objbst = model.cbGet(GRB.Callback.MIP_OBJBST) #Current best objective\n",
    "        objbnd = model.cbGet(GRB.Callback.MIP_OBJBND) #Current best objective bound\n",
    "        solcnt = model.cbGet(GRB.Callback.MIP_SOLCNT) #Current count of feasible solutions found\n",
    "        #if nodecnt - model._lastnode >= 100:\n",
    "        model._lastnode = nodecnt\n",
    "        actnodes = model.cbGet(GRB.Callback.MIP_NODLFT) #Current unexplored node count\n",
    "        itcnt = model.cbGet(GRB.Callback.MIP_ITRCNT) #Current simplex iteration count\n",
    "        cutcnt = model.cbGet(GRB.Callback.MIP_CUTCNT) #Current count of cutting planes applied\n",
    "    elif where == GRB.Callback.MIPSOL: #Found a new MIP incumbent\n",
    "        # MIP solution callback\n",
    "        start_time.append(model.cbGet(GRB.Callback.RUNTIME)) \n",
    "        nodecnt = model.cbGet(GRB.Callback.MIPSOL_NODCNT) #Current explored node count\n",
    "        obj = model.cbGet(GRB.Callback.MIPSOL_OBJ) #Objective value for new solution\n",
    "        objbst = model.cbGet(GRB.Callback.MIPSOL_OBJBST)\n",
    "        objbnd = model.cbGet(GRB.Callback.MIPSOL_OBJBND)\n",
    "        solcnt = model.cbGet(GRB.Callback.MIPSOL_SOLCNT) #Curent count of feasible solutions found\n",
    "        best_gap = abs(100*(objbnd - objbst)/objbst)\n",
    "        current_gap = abs(100*(objbnd - obj)/obj) #Gap of the new solution found\n",
    "        x_MIP = model.cbGetSolution(model._vars)\n",
    "        x_MIP = np.array(x_MIP)\n",
    "        index_list = np.where(x_MIP > 0.1)\n",
    "        res_list = [model._vars[i] for i in index_list[0]]\n",
    "        nonzero_x = []\n",
    "        for solution in res_list:\n",
    "            if solution.Varname[1:4] == \"'x'\":\n",
    "                nonzero_x.append(solution.VarName)\n",
    "        for i in range(len(nonzero_x)):\n",
    "            print('\\n x = %s' %nonzero_x[i])\n",
    "        model._logfile.write('\\n**** New solution # %d, Obj %g, Current Gap %g%%, Best Obj %g, Best Gap %g%%, Elapsed time %g,'\n",
    "               % (solcnt, obj, current_gap, objbst, best_gap, model.cbGet(GRB.Callback.RUNTIME)))\n",
    "        for i in range(len(nonzero_x)):\n",
    "            model._logfile.write('\\n x = %s' %nonzero_x[i])\n",
    "\n",
    "    elif where == GRB.Callback.MIPNODE: #Currently exploring a MIP node\n",
    "        # MIP node callback\n",
    "        if model.cbGet(GRB.Callback.MIPNODE_STATUS) == GRB.OPTIMAL:\n",
    "            x = model.cbGetNodeRel(model._vars) #Values from the node relaxation solution at the current node\n",
    "            model.cbSetSolution(model.getVars(), x)\n",
    "    elif where == GRB.Callback.BARRIER:\n",
    "        # Barrier callback\n",
    "        itcnt = model.cbGet(GRB.Callback.BARRIER_ITRCNT)\n",
    "        primobj = model.cbGet(GRB.Callback.BARRIER_PRIMOBJ)\n",
    "        dualobj = model.cbGet(GRB.Callback.BARRIER_DUALOBJ)\n",
    "        priminf = model.cbGet(GRB.Callback.BARRIER_PRIMINF)\n",
    "        dualinf = model.cbGet(GRB.Callback.BARRIER_DUALINF)\n",
    "        cmpl = model.cbGet(GRB.Callback.BARRIER_COMPL)\n",
    "\n",
    "    elif where == GRB.Callback.MESSAGE:\n",
    "        # Message callback\n",
    "        msg = model.cbGet(GRB.Callback.MSG_STRING)\n",
    "        model._logfile.write(msg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get a particular island to run the matching procedure\n",
    "candidate_list, df, catalog_list, Sigma_list = get_candidate_list(result, label, 43)\n",
    "\n",
    "detection_total = len(candidate_list) #Total number of sources across different catalogs\n",
    "\n",
    "kappa_dict = {} \n",
    "kappa_rad_dict = {}\n",
    "ln_kappa_rad_dict = {}\n",
    "\n",
    "for i in range(len(candidate_list)):\n",
    "    kappa_dict[(candidate_list[i][0], candidate_list[i][1])] = 1/(Sigma_list[i])**2 #in arcsecond \n",
    "    kappa_rad_dict[(candidate_list[i][0], candidate_list[i][1])] = 1/((Sigma_list[i]*np.pi/180/3600)**2) #in radian\n",
    "    ln_kappa_rad_dict[(candidate_list[i][0], candidate_list[i][1])] = ln(1/((Sigma_list[i]*np.pi/180/3600)**2))\n",
    "    \n",
    "sigma_min = min(Sigma_list)\n",
    "sigma_max = max(Sigma_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using license file /home/idies/gurobi.lic\n",
      "Set parameter ServerPassword\n",
      "Set parameter TokenServer to value zinc30.sdss.pha.jhu.edu\n",
      "Set parameter TSPort to value 61000\n"
     ]
    }
   ],
   "source": [
    "######################### ILP Formulation ###########################\n",
    "\n",
    "mo = Model(\"likelihood\")\n",
    "\n",
    "M = np.ceil(1/sigma_min**4*sum_of_distance(candidate_list, df)/(4*1/sigma_max**2))\n",
    "M_2 = num_catalog * max(kappa_dict.values())\n",
    "rounding_index = -2 #round number to nearest 10 if rounding_index = -1. to round to nearest 100, change to -2\n",
    "error_threshold = 1/100 * min(ln_kappa_rad_dict.values())\n",
    "\n",
    "var_x_dict = {}\n",
    "var_y_dict = {}\n",
    "var_z_dict = {}\n",
    "var_u_dict = {}\n",
    "var_chi_dict = {}\n",
    "t_list = []\n",
    "p_list = []\n",
    "b_list = [ln(1/(sigma_max*np.pi/180/3600)**2)]\n",
    "c_list = [0, round(min(kappa_dict.values()),rounding_index)]\n",
    "########################### SET VARIABLES ###########################\n",
    "\n",
    "# Compute b_list\n",
    "while b_list[-1] < ln(num_catalog/(sigma_min*np.pi/180/3600)**2): \n",
    "    b_list.append(b_list[-1]+error_threshold)\n",
    "\n",
    "num_breakpoints = len(b_list) # = P in the paper\n",
    "\n",
    "# Compute c_list\n",
    "while c_list[-1] < round(num_catalog*max(kappa_dict.values()),rounding_index):\n",
    "    c_list.append(c_list[-1]+10**(-rounding_index))\n",
    "    \n",
    "# Variables for x\n",
    "for subset_index in range(detection_total):\n",
    "    for catalog_source_pair in candidate_list:\n",
    "        var_x_dict[('x', subset_index, catalog_source_pair)] = mo.addVar(vtype=GRB.BINARY, name=str(('x', subset_index, catalog_source_pair)))\n",
    "\n",
    "# Variables for y\n",
    "for subset_index in range(detection_total):\n",
    "    for product_of_catalog_source_pairs in list(itertools.combinations(candidate_list, r = 2)):\n",
    "        if product_of_catalog_source_pairs[0][1] != product_of_catalog_source_pairs[1][1]:\n",
    "            var_y_dict[('y', subset_index, product_of_catalog_source_pairs[0], product_of_catalog_source_pairs[1])] = mo.addVar(vtype=GRB.BINARY, name=str(('y', subset_index, product_of_catalog_source_pairs[0],product_of_catalog_source_pairs[1])))\n",
    "\n",
    "# Variables for z\n",
    "for subset_index in range(detection_total):\n",
    "    for catalog_index in range(num_catalog + 1):\n",
    "        var_z_dict[('z', subset_index, catalog_index)] = mo.addVar(vtype=GRB.BINARY, name=str(('z', subset_index, catalog_index)))\n",
    "\n",
    "# Variables for t\n",
    "for subset_index in range(detection_total):  \n",
    "    t_list.append(mo.addVar(lb = 0, vtype=GRB.CONTINUOUS, name=str(('t', subset_index))))\n",
    "\n",
    "# Variables for u\n",
    "for subset_index in range(detection_total):\n",
    "    for gridpoint_index in range(len(c_list)):\n",
    "        var_u_dict[('u', subset_index, gridpoint_index)] = mo.addVar(vtype=GRB.BINARY, name=str(('u', subset_index, gridpoint_index)))\n",
    "    \n",
    "# Variables for p\n",
    "for subset_index in range(detection_total):  \n",
    "    p_list.append(mo.addVar(lb = -GRB.INFINITY, vtype=GRB.CONTINUOUS, name=str(('p', subset_index))))\n",
    "    \n",
    "# Variables for chi\n",
    "for subset_index in range(detection_total):\n",
    "    for breakpoint_index in range(num_breakpoints):\n",
    "        var_chi_dict[('chi', subset_index, breakpoint_index)] = mo.addVar(vtype=GRB.BINARY, name=str(('chi', subset_index, breakpoint_index)))\n",
    "\n",
    "########################### SET OBJECTIVES ###########################\n",
    "\n",
    "# Set objective\n",
    "mo.setObjective(quicksum(p_list[subset_index] - quicksum(var_x_dict['x',subset_index,catalog_source_pair]*ln_kappa_rad_dict[catalog_source_pair] for catalog_source_pair in candidate_list) \n",
    "                         + b_list[0]*var_chi_dict[('chi', subset_index, 0)] + error_threshold*quicksum(var_chi_dict[('chi', subset_index, breakpoint_index)] for breakpoint_index in range(1,num_breakpoints))\n",
    "                         + t_list[subset_index] for subset_index in range(detection_total)), GRB.MINIMIZE)\n",
    "\n",
    "########################### SET CONSTRAINTS ###########################\n",
    "\n",
    "# All detections (i,c) needs to belong to some subset (S_j)\n",
    "# Equation B14\n",
    "for catalog_source_pair in candidate_list:    \n",
    "    x_constraint = []\n",
    "    for variable in var_x_dict.keys():\n",
    "        if variable[-1] == catalog_source_pair:\n",
    "            x_constraint.append(var_x_dict[variable])\n",
    "    mo.addConstr(lhs = quicksum(variable for variable in x_constraint), sense=GRB.EQUAL, rhs = 1)\n",
    "\n",
    "# Every subset takes no more than 1 detection from each catalog\n",
    "# Equation B15\n",
    "for subset_index in range(detection_total):\n",
    "    for catalog_index in catalog_list:\n",
    "        x_constraint = []\n",
    "        for variable in var_x_dict.keys():\n",
    "            if (variable[1] == subset_index) & (variable[-1][1] == catalog_index):\n",
    "                x_constraint.append(var_x_dict[variable])\n",
    "        mo.addConstr(lhs = quicksum(variable for variable in x_constraint), sense=GRB.LESS_EQUAL, rhs = 1)\n",
    "\n",
    "# Definition of variables y\n",
    "# Equation B16\n",
    "for subset_index in range(detection_total):\n",
    "    for product_of_catalog_source_pairs in list(itertools.combinations(candidate_list, r = 2)): \n",
    "        if product_of_catalog_source_pairs[0][1] != product_of_catalog_source_pairs[1][1]:\n",
    "            mo.addConstr(var_y_dict[('y', subset_index, product_of_catalog_source_pairs[0], product_of_catalog_source_pairs[1])] >= var_x_dict[('x', subset_index, product_of_catalog_source_pairs[0])] \n",
    "                         + var_x_dict[('x', subset_index, product_of_catalog_source_pairs[1])] - 1)\n",
    "            mo.addConstr(var_y_dict[('y', subset_index, product_of_catalog_source_pairs[0], product_of_catalog_source_pairs[1])] <= var_x_dict[('x', subset_index, product_of_catalog_source_pairs[0])])\n",
    "            mo.addConstr(var_y_dict[('y', subset_index, product_of_catalog_source_pairs[0], product_of_catalog_source_pairs[1])] <= var_x_dict[('x', subset_index, product_of_catalog_source_pairs[1])])\n",
    "\n",
    "# The cardinality of any subset from a partition P is from 0 to K\n",
    "# Equation B17\n",
    "for subset_index in range(detection_total):\n",
    "    z_constraint = []\n",
    "    for catalog_index in range(num_catalog + 1):\n",
    "        z_constraint.append(var_z_dict[('z', subset_index, catalog_index)])\n",
    "    mo.addConstr(lhs = quicksum(variable for variable in z_constraint), sense=GRB.EQUAL, rhs = 1)\n",
    "    \n",
    "# Only 1 of u^o_k is 1\n",
    "# Equation B18\n",
    "for subset_index in range(detection_total):\n",
    "    u_constraint = []\n",
    "    for gridpoint_index in range(len(c_list)):\n",
    "        u_constraint.append(var_u_dict[('u', subset_index, gridpoint_index)])\n",
    "    mo.addConstr(lhs = quicksum(variable for variable in u_constraint), sense=GRB.EQUAL, rhs = 1)\n",
    "    \n",
    "# Definition of variables chi\n",
    "# Equation B19\n",
    "for subset_index in range(detection_total):\n",
    "    chi_constraint_with_b = []\n",
    "    chi_constraint = []\n",
    "    x_constraint = []\n",
    "    for breakpoint_index in range(1, num_breakpoints):\n",
    "        chi_constraint_with_b.append(var_chi_dict[('chi', subset_index, breakpoint_index)]*(exp(b_list[breakpoint_index])-exp(b_list[breakpoint_index-1]))/10**10) #Divide by 10**10 to scale the coefficient so that the matrix range is not so large across all the constraints\n",
    "    for catalog_source_pair in candidate_list:    \n",
    "        x_constraint.append(var_x_dict[('x', subset_index, catalog_source_pair)]*kappa_rad_dict[catalog_source_pair]/10**10) #Divide by 10**10 to scale the coefficient so that the matrix range is not so large across all the constraints\n",
    "    mo.addConstr(lhs = exp(b_list[0])* var_chi_dict[('chi', subset_index, 0)] + quicksum(variable for variable in chi_constraint_with_b), sense=GRB.GREATER_EQUAL, rhs = quicksum(variable for variable in x_constraint))\n",
    "    \n",
    "    for breakpoint_index in range(num_breakpoints):\n",
    "        chi_constraint.append(var_chi_dict[('chi', subset_index, breakpoint_index)])\n",
    "    for chi_index in range(len(chi_constraint) - 1):\n",
    "        mo.addConstr(chi_constraint[chi_index] >= chi_constraint[chi_index + 1])\n",
    "        \n",
    "# Definition of variables t\n",
    "# Equation B20\n",
    "for subset_index in range(detection_total):\n",
    "    for gridpoint_index in range(1,len(c_list)):\n",
    "        mo.addConstr(lhs = t_list[subset_index], sense=GRB.GREATER_EQUAL, \n",
    "                     rhs = -M * (1 - var_u_dict[('u', subset_index, gridpoint_index)]) \n",
    "                     + quicksum(1/(4*c_list[gridpoint_index])\n",
    "                                *kappa_dict[product_of_catalog_source_pairs[0]]*kappa_dict[product_of_catalog_source_pairs[1]]\n",
    "                                *var_y_dict[('y', subset_index, product_of_catalog_source_pairs[0], product_of_catalog_source_pairs[1])]\n",
    "                                *get_distance(product_of_catalog_source_pairs, df) for product_of_catalog_source_pairs in list(itertools.combinations(candidate_list, r = 2)) if product_of_catalog_source_pairs[0][1] != product_of_catalog_source_pairs[1][1]))\n",
    "\n",
    "# Definition of variables z\n",
    "# Equation B21\n",
    "for subset_index in range(detection_total):\n",
    "    x_constraint = []\n",
    "    for catalog_source_pair in candidate_list:\n",
    "        x_constraint.append(var_x_dict[('x', subset_index, catalog_source_pair)])\n",
    "    for catalog_index in range(num_catalog + 1):\n",
    "        mo.addConstr(lhs = quicksum(variable for variable in x_constraint), sense=GRB.LESS_EQUAL,\n",
    "                     rhs = catalog_index * var_z_dict[('z', subset_index, catalog_index)] + num_catalog * (1 - var_z_dict[('z', subset_index, catalog_index)]))\n",
    "        mo.addConstr(lhs = quicksum(variable for variable in x_constraint), sense=GRB.GREATER_EQUAL,\n",
    "                     rhs = catalog_index * var_z_dict[('z', subset_index, catalog_index)])\n",
    "\n",
    "# Definition of variables u\n",
    "# Equation B222\n",
    "for subset_index in range(detection_total):\n",
    "    x_constraint = []\n",
    "    for catalog_source_pair in candidate_list:\n",
    "        x_constraint.append(var_x_dict[('x', subset_index, catalog_source_pair)]*round(kappa_dict[catalog_source_pair],rounding_index))\n",
    "    for gridpoint_index in range(len(c_list)):\n",
    "        mo.addConstr(lhs = quicksum(variable for variable in x_constraint), sense=GRB.LESS_EQUAL,\n",
    "                     rhs = c_list[gridpoint_index] * var_u_dict[('u', subset_index, gridpoint_index)] + M_2 * (1 - var_u_dict[('u', subset_index, gridpoint_index)]))\n",
    "        mo.addConstr(lhs = quicksum(variable for variable in x_constraint), sense=GRB.GREATER_EQUAL,\n",
    "                     rhs = c_list[gridpoint_index] * var_u_dict[('u', subset_index, gridpoint_index)])\n",
    "    \n",
    "# Definition of variables p\n",
    "# Equation B23\n",
    "for subset_index in range(detection_total):\n",
    "    x_constraint = []\n",
    "    for catalog_source_pair in candidate_list:    \n",
    "        x_constraint.append(var_x_dict[('x', subset_index, catalog_source_pair)])\n",
    "    mo.addConstr(lhs = p_list[subset_index], sense=GRB.GREATER_EQUAL, \n",
    "                     rhs = ln(2)*(1 - quicksum(variable for variable in x_constraint) - ln(2)*var_z_dict[('z', subset_index, 0)]))\n",
    "\n",
    "# Heuristic constraints:\n",
    "# When 2 sources are more than 5*sigma_max away, they should not be from the same object. Hence, set the y variable corresponding to these 2 sources to 0.\n",
    "distance_dict = compute_distance_dictionary(candidate_list, df)\n",
    "dist_constraint_var=[]\n",
    "for pair,distance in distance_dict.items():\n",
    "    for j in range(detection_total):\n",
    "        if distance > 5*sigma_max:\n",
    "            dist_constraint_var.append(var_y_dict[tuple(['y']+[j]+list(pair))])\n",
    "for variable in dist_constraint_var:\n",
    "    variable.ub = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (linux64)\n",
      "Optimize a model with 2190 rows, 900 columns and 18210 nonzeros\n",
      "Model fingerprint: 0x4ebb65f4\n",
      "Variable types: 20 continuous, 880 integer (880 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [2e-13, 5e+12]\n",
      "  Objective range  [3e-01, 3e+01]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [7e-01, 2e+03]\n",
      "Warning: Model contains large matrix coefficient range\n",
      "         Consider reformulating model or setting NumericFocus parameter\n",
      "         to avoid numerical issues.\n",
      "\n",
      " x = ('x', 0, (44, 2))\n",
      "\n",
      " x = ('x', 1, (44, 1))\n",
      "\n",
      " x = ('x', 2, (92, 0))\n",
      "\n",
      " x = ('x', 3, (92, 3))\n",
      "\n",
      " x = ('x', 4, (44, 4))\n",
      "\n",
      " x = ('x', 5, (92, 2))\n",
      "\n",
      " x = ('x', 6, (44, 3))\n",
      "\n",
      " x = ('x', 7, (92, 1))\n",
      "\n",
      " x = ('x', 8, (92, 4))\n",
      "\n",
      " x = ('x', 9, (44, 0))\n",
      "Found heuristic solution: objective -63.9312634\n",
      "Presolve removed 350 rows and 160 columns\n",
      "Presolve time: 0.15s\n",
      "Presolved: 1840 rows, 740 columns, 13770 nonzeros\n",
      "\n",
      " x = ('x', 0, (44, 2))\n",
      "\n",
      " x = ('x', 1, (44, 1))\n",
      "\n",
      " x = ('x', 2, (92, 0))\n",
      "\n",
      " x = ('x', 3, (92, 3))\n",
      "\n",
      " x = ('x', 4, (44, 4))\n",
      "\n",
      " x = ('x', 5, (92, 2))\n",
      "\n",
      " x = ('x', 6, (44, 3))\n",
      "\n",
      " x = ('x', 7, (92, 1))\n",
      "\n",
      " x = ('x', 8, (92, 4))\n",
      "\n",
      " x = ('x', 9, (44, 0))\n",
      "Found heuristic solution: objective -5.3518166\n",
      "Variable types: 10 continuous, 730 integer (730 binary)\n",
      "\n",
      "Root relaxation: objective -2.562708e+02, 267 iterations, 0.02 seconds\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 -256.27082    0   31  -63.93126 -256.27082   301%     -    0s\n",
      "\n",
      " x = ('x', 7, (92, 0))\n",
      "\n",
      " x = ('x', 7, (44, 1))\n",
      "\n",
      " x = ('x', 7, (44, 2))\n",
      "\n",
      " x = ('x', 7, (92, 3))\n",
      "\n",
      " x = ('x', 7, (92, 4))\n",
      "\n",
      " x = ('x', 9, (44, 0))\n",
      "\n",
      " x = ('x', 9, (92, 1))\n",
      "\n",
      " x = ('x', 9, (92, 2))\n",
      "\n",
      " x = ('x', 9, (44, 3))\n",
      "\n",
      " x = ('x', 9, (44, 4))\n",
      "H    0     0                    -234.2217555 -256.27082  9.41%     -    0s\n",
      "\n",
      " x = ('x', 7, (92, 0))\n",
      "\n",
      " x = ('x', 7, (92, 1))\n",
      "\n",
      " x = ('x', 7, (44, 2))\n",
      "\n",
      " x = ('x', 7, (92, 3))\n",
      "\n",
      " x = ('x', 7, (92, 4))\n",
      "\n",
      " x = ('x', 9, (44, 0))\n",
      "\n",
      " x = ('x', 9, (44, 1))\n",
      "\n",
      " x = ('x', 9, (92, 2))\n",
      "\n",
      " x = ('x', 9, (44, 3))\n",
      "\n",
      " x = ('x', 9, (44, 4))\n",
      "H    0     0                    -235.4906870 -256.27082  8.82%     -    0s\n",
      "     0     0 -256.27082    0   73 -235.49069 -256.27082  8.82%     -    0s\n",
      "     0     0 -256.27082    0   73 -235.49069 -256.27082  8.82%     -    0s\n",
      "\n",
      " x = ('x', 5, (92, 0))\n",
      "\n",
      " x = ('x', 5, (92, 1))\n",
      "\n",
      " x = ('x', 5, (92, 2))\n",
      "\n",
      " x = ('x', 5, (92, 3))\n",
      "\n",
      " x = ('x', 5, (92, 4))\n",
      "\n",
      " x = ('x', 7, (44, 0))\n",
      "\n",
      " x = ('x', 7, (44, 1))\n",
      "\n",
      " x = ('x', 7, (44, 2))\n",
      "\n",
      " x = ('x', 7, (44, 3))\n",
      "\n",
      " x = ('x', 7, (44, 4))\n",
      "H    0     0                    -239.4345957 -256.27082  7.03%     -    0s\n",
      "     0     0 -256.27082    0   55 -239.43460 -256.27082  7.03%     -    0s\n",
      "     0     0 -256.03488    0   55 -239.43460 -256.03488  6.93%     -    0s\n",
      "     0     2 -256.03488    0   55 -239.43460 -256.03488  6.93%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 6\n",
      "  Cover: 20\n",
      "  Implied bound: 33\n",
      "  Clique: 63\n",
      "  MIR: 31\n",
      "  StrongCG: 3\n",
      "  GUB cover: 10\n",
      "  Zero half: 3\n",
      "  RLT: 48\n",
      "  BQP: 8\n",
      "\n",
      "Explored 416 nodes (17666 simplex iterations) in 3.27 seconds\n",
      "Thread count was 16 (of 16 available processors)\n",
      "\n",
      "Solution count 5: -239.435 -235.491 -234.222 ... -5.35182\n",
      "No other solutions better than -239.435\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective -2.394345957402e+02, best bound -2.394345957402e+02, gap 0.0000%\n",
      "\n",
      "User-callback calls 2189, time in user-callback 0.96 sec\n"
     ]
    }
   ],
   "source": [
    "# Open log file\n",
    "mo.update()\n",
    "\n",
    "logfile = open('DirILP_'+str(num_catalog)+'_catalogs.log', 'w')\n",
    "logfile.write('Theoretical optimal solution: %s' % (Bayes_factor(candidate_list,df)))\n",
    "\n",
    "# Pass data into my callback function\n",
    "mo._logfile = logfile\n",
    "mo._vars = mo.getVars()\n",
    "\n",
    "# Solve model\n",
    "#mo.Params.MIPGap = 0.01\n",
    "mo.optimize(mycallback)\n",
    "\n",
    "# Close log file\n",
    "\n",
    "logfile.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i in mo.getVars():\n",
    "#     if i.x > 0.5:\n",
    "#         if i.VarName[1:4] == \"'x'\":\n",
    "#             print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CanILP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def source_distance(list_of_indexes):\n",
    "    '''\n",
    "    Assume we have more than 1 objects\n",
    "    '''\n",
    "    num_of_objects = len(list_of_indexes)\n",
    "    if num_of_objects == 1:\n",
    "        return 0 #We want to include all the orphans\n",
    "    coord_list = []\n",
    "    for i in range(num_of_objects):\n",
    "        coord_list+=[cmat[list_of_indexes[i][1]][list_of_indexes[i][0]]][:2]\n",
    "    \n",
    "    array_matrix = np.array(coord_list)\n",
    "    pairwise_dist = spatial.distance.pdist(np.array(array_matrix))\n",
    "    return(max(pairwise_dist))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "catalog_id_list = catalog_list.copy()\n",
    "# Get a list of all \"plausible\" matchings     \n",
    "candidate_dict = {}\n",
    "for catalog_id in set(catalog_id_list):\n",
    "    list_of_indices = []\n",
    "    for catalog_source_pair in candidate_list:\n",
    "        if catalog_source_pair[1] == catalog_id:\n",
    "            list_of_indices.append([catalog_source_pair])\n",
    "    candidate_dict[catalog_id] = list_of_indices\n",
    "\n",
    "cat_dict = {} #Give the index of tuple (catalog #, observation # in catalog) among all these tuples from all catalogs and observations\n",
    "# This will serve as the row id of the constraint matrix in sparse matrix form\n",
    "count_of_source = 0\n",
    "for catalog_id in candidate_dict.keys():\n",
    "    for catalog_source_pair in candidate_dict[catalog_id]:\n",
    "        cat_dict[catalog_source_pair[0]] = count_of_source\n",
    "        count_of_source += 1\n",
    "        \n",
    "threshold = [10 * sigma_max for i in range(len(candidate_list))]\n",
    "candidate_matching_list = [[]]\n",
    "for catalog_id in candidate_dict.keys():\n",
    "    candidate_matching_list += [element_1 + element_2 for element_1 in candidate_matching_list for element_2 in candidate_dict[catalog_id] if source_distance(element_1 + element_2) < threshold[catalog_id]]\n",
    "candidate_matching_list.remove([])\n",
    "for catalog_source_pair in candidate_list:\n",
    "    candidate_matching_list.remove([catalog_source_pair]) #Remove all the orphans    \n",
    "#Create the constraint matrix, where the rows are (catalog #, observation # in catalog) and columns are \"plausible\" matchings\n",
    "col_list = []\n",
    "row_list = []\n",
    "\n",
    "for candidate in candidate_matching_list:\n",
    "    col_index = candidate_matching_list.index(candidate)\n",
    "    for catalog_source_pair in candidate:\n",
    "        row_list.append(cat_dict[catalog_source_pair])\n",
    "        col_list.append(col_index)\n",
    "\n",
    "row_index_array = np.array(row_list)\n",
    "col_index_array = np.array(col_list)\n",
    "\n",
    "sparse_df = sparse.coo_matrix((np.ones(len(row_index_array)), (row_index_array, col_index_array)))\n",
    "sparse_df = sparse_df.tocsr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_dict = {}\n",
    "\n",
    "mo = Model(\"likelihood\")\n",
    "x = []\n",
    "count = 0\n",
    "for candidate in candidate_matching_list:\n",
    "    test_dict[count] = candidate\n",
    "    x.append(mo.addVar(vtype=GRB.BINARY, name=str(count), obj = Bayes_factor(candidate, df)))\n",
    "    count += 1\n",
    "for i in range(len(candidate_list)):\n",
    "    start = sparse_df.indptr[i]\n",
    "    end = sparse_df.indptr[i+1]\n",
    "    variables = [x[j] for j in sparse_df.indices[start:end]]\n",
    "    mo.addConstr(lhs = quicksum(variables[i] for i in range(len(variables))), sense=GRB.LESS_EQUAL, rhs = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (linux64)\n",
      "Optimize a model with 10 rows, 232 columns and 800 nonzeros\n",
      "Model fingerprint: 0x4663760c\n",
      "Variable types: 0 continuous, 232 integer (232 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [3e+01, 1e+02]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e+00, 1e+00]\n",
      "Found heuristic solution: objective -118.0517520\n",
      "Presolve time: 0.01s\n",
      "Presolved: 10 rows, 232 columns, 800 nonzeros\n",
      "Variable types: 0 continuous, 232 integer (232 binary)\n",
      "\n",
      "Root relaxation: objective -2.366087e+02, 29 iterations, 0.00 seconds\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "*    0     0               0    -236.6086905 -236.60869  0.00%     -    0s\n",
      "\n",
      "Explored 0 nodes (29 simplex iterations) in 0.05 seconds\n",
      "Thread count was 16 (of 16 available processors)\n",
      "\n",
      "Solution count 2: -236.609 -118.052 \n",
      "No other solutions better than -236.609\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective -2.366086905186e+02, best bound -2.366086905186e+02, gap 0.0000%\n",
      "\n",
      "User-callback calls 42, time in user-callback 0.00 sec\n",
      "[(44, 0), (44, 1), (44, 2), (44, 3), (44, 4)]\n",
      "[(92, 0), (92, 1), (92, 2), (92, 3), (92, 4)]\n"
     ]
    }
   ],
   "source": [
    "mo.update()\n",
    "\n",
    "logfile = open('CanILP'+str(num_catalog)+'_catalogs.log', 'w')\n",
    "logfile.write('Theoretical optimal solution: %s' % (Bayes_factor(candidate_list,df)))\n",
    "\n",
    "mo._logfile = logfile\n",
    "mo._vars = mo.getVars()\n",
    "\n",
    "mo.optimize(mycallback)\n",
    "\n",
    "for i in mo.getVars():\n",
    "    if i.x > 0.5:\n",
    "        print(str(test_dict[int(i.VarName)]))\n",
    "logfile.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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