{
 "metadata": {
  "name": "main_analysis"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# The Kinematics of the Local Group in a Cosmological Context"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook containts all data analysis for the ApJ Letter *The Kinematics of the Local Group in a Cosmological Context*\n",
      "by Jaime E. Forero-Romero, Yehuda Hoffman, Sebastian Bustamante, Stefan Gottloeber and Gustavo Yepes.\n",
      "\n",
      "Follow through the notebook to generate the figures and numbers used in the paper . You can also generate results that were mentioned but not explicitly reported. For instance, the results for pairs obtained for a Friend-of-Friends halo finder. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "%pylab inline\n",
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "from make2DHistogram import *\n",
      "from generateInfo import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Global paths and constants\n",
      "data_path = \"../data/\"\n",
      "\n",
      "G_GRAV = 4.54E-48 #units of Mpc^3 Msun^-1 s^-2\n",
      "KM_TO_MPC = 3.2E-20\n",
      "HUBBLE = 0.70\n",
      "E_UNITS = 1.0E-36\n",
      "L_UNITS = 1.0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here one can select between two halo finders: \"BDM\" or \"FOF\".\n",
      "\n",
      "The boolean narrow_data is True if we want to produced plots with a narrower selection for distances and total mass closer to the observations. narrow_data = False corresponds to the *full* sample and narrow_data = True corresponds to the *reduced* sample.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "halo_finder=\"BDM\" \n",
      "narrow_data = False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## MonteCarlo for the observed values\n",
      "\n",
      "Here we generate one million points from the observational constraints for the LG (separation, velocities, distances)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The reference is van der Marel et al. ApJ,753:8\n",
      "V_M31 = array([66.1,-76.3,45.1]) #km/s\n",
      "V_M31_sigma = array([26.7, 19.0, 26.5])\n",
      "\n",
      "R_M31 = array([-378.9,612.7,-283.1]) # kpc\n",
      "R_M31_sigma = abs(R_M31/20.0) #This is an approximated value, not the actual observational uncertainty\n",
      "\n",
      "print R_M31_sigma, sqrt(sum(R_M31*R_M31))\n",
      "\n",
      "R_M31 = R_M31 / 1000.0 # in Mpc\n",
      "R_M31_sigma = R_M31_sigma /1000.0\n",
      "\n",
      "M31_Mass = 1.6E12\n",
      "M31_Mass_sigma = 0.5E12\n",
      "MW_Mass = 1.6E12\n",
      "MW_Mass_sigma = 0.5E12\n",
      "\n",
      "Mass_Total = 3.14E12 # in units of Msun\n",
      "Mass_Total_sigma = 0.58E12"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 18.945  30.635  14.155] 774.023326522\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#generate the velocities, positions and masses\n",
      "n_points = 1000000\n",
      "V_M31_MonteCarlo = zeros((n_points,3))\n",
      "R_M31_MonteCarlo = zeros((n_points,3))\n",
      "\n",
      "M31_Mass_MonteCarlo = (random.normal(M31_Mass,M31_Mass_sigma, n_points))\n",
      "MW_Mass_MonteCarlo = (random.normal(MW_Mass,MW_Mass_sigma, n_points))\n",
      "\n",
      "negative_M31 = where(M31_Mass_MonteCarlo < 0.0)\n",
      "negative_MW = where(MW_Mass_MonteCarlo < 0.0)\n",
      "\n",
      "Total_Mass_MonteCarlo = M31_Mass_MonteCarlo + MW_Mass_MonteCarlo\n",
      "Reduced_Mass_MonteCarlo = (M31_Mass_MonteCarlo * MW_Mass_MonteCarlo)/Total_Mass_MonteCarlo\n",
      "\n",
      "for i in range(3):\n",
      "    V_M31_MonteCarlo[:,i] = random.normal(V_M31[i],V_M31_sigma[i],n_points)\n",
      "    R_M31_MonteCarlo[:,i] = random.normal(R_M31[i],R_M31_sigma[i],n_points)\n",
      "\n",
      "#don't use the items with negative values of the mass\n",
      "positive = where((M31_Mass_MonteCarlo > 0.0) & (MW_Mass_MonteCarlo > 0.0))[0]\n",
      "\n",
      "V_M31_MonteCarlo = V_M31_MonteCarlo[positive,:]\n",
      "R_M31_MonteCarlo = R_M31_MonteCarlo[positive,:]\n",
      "M31_Mass_MonteCarlo = M31_Mass_MonteCarlo[positive]\n",
      "MW_Mass_MonteCarlo = MW_Mass_MonteCarlo[positive]\n",
      "\n",
      "Total_Mass_MonteCarlo = M31_Mass_MonteCarlo + MW_Mass_MonteCarlo\n",
      "Reduced_Mass_MonteCarlo = (M31_Mass_MonteCarlo * MW_Mass_MonteCarlo)/Total_Mass_MonteCarlo\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compute the angular momentum, energy and lambda\n",
      "\n",
      "# array of angular momentum (vector) and the norm\n",
      "J = cross(R_M31_MonteCarlo, V_M31_MonteCarlo) \n",
      "J_norm = sqrt(J[:,0]**2 + J[:,1]**2 + J[:,2]**2) \n",
      "\n",
      "# Mechanical energy\n",
      "R_M31_MonteCarlo_norm  = sqrt(R_M31_MonteCarlo[:,0]**2 + R_M31_MonteCarlo[:,1]**2 + R_M31_MonteCarlo[:,2]**2)\n",
      "E_kin = 0.5*(V_M31_MonteCarlo[:,0]**2 + V_M31_MonteCarlo[:,1]**2 + V_M31_MonteCarlo[:,2]**2)\n",
      "E_kin = E_kin * KM_TO_MPC * KM_TO_MPC\n",
      "E_pot = -G_GRAV * Total_Mass_MonteCarlo / R_M31_MonteCarlo_norm\n",
      "\n",
      "E_kin = E_kin/E_UNITS\n",
      "E_pot = E_pot/E_UNITS\n",
      "E = E_kin + E_pot \n",
      "\n",
      "# Lambda\n",
      "lambda_obs = (Reduced_Mass_MonteCarlo**1.5) * (J_norm * L_UNITS * KM_TO_MPC)* sqrt(abs(E * E_UNITS)) / (G_GRAV * (Total_Mass_MonteCarlo)**(5.0/2.0))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Total mass histogram\n",
      "n, bins, patches = hist(Total_Mass_MonteCarlo, 20, normed=0, color = 'silver')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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teL1eAFJSUnjsscfIzc0FYOfOnSQlJV2z/wQREZkuzrh4vuk8FBcXxzxuXy4jLi7uquZW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\n/wOCunsYjjsaNwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1065b0a50>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# M31 mass histogram\n",
      "n, bins, patches = hist(M31_Mass_MonteCarlo, 20, normed=0, color = 'silver')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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sOjo6zPYTJ06QnZ2N2+2mrq7ObB8bG6O8vBy3201eXh5nz56Ndh1FRGQORBUY\nNpuN7373u7z//vu89dZbvPzyy/zyl7+ksbGRwsJCTp8+TUFBAY2NjQB0d3ezb98+uru78fv9bN++\nHcMwANi2bRvNzc0Eg0GCwSB+vx+A5uZm7HY7wWCQHTt2sHPnzjlaZRERiUZUgZGamsqDDz4IwF13\n3cWKFSsIh8O0t7dTXV0NQHV1NQcOHACgra2NiooKbDYb6enpZGRkEAgEGBgYYHR0lNzcXACqqqrM\nPlcuq7S0lKNHj8a2piIiEpOYT6s9c+YM77zzDmvXrmVwcBCHwwGAw+FgcHAQgP7+fvLy8sw+LpeL\ncDiMzWbD5XKZ7U6nk3A4DEA4HCYtLW2qyPh4EhMTGRoaIiUlZdrv37Nnj/k6Pz9fpxSKiFyhs7Mz\npqd8XimmwPj4448pLS3l+eef5wtf+MK0afP1DOorA0NERKa7+ot0fX191MuK+iypixcvUlpaSmVl\nJZs3bwamtirOnTsHwMDAAMuWLQOmthz6+vrMvqFQCJfLhdPpJBQKzWi/3Ke3txeAiYkJRkZGZmxd\niIjI/IkqMAzDoLa2Fo/Hw1NPPWW2l5SU4PV6AfB6vWaQlJSU4PP5GB8fp6enh2AwSG5uLqmpqSQk\nJBAIBDAMg5aWFjZt2jRjWa2trRQUFMS0oiIiEpuodkn97Gc/47XXXuOBBx5g9erVwNRps08//TRl\nZWU0NzeTnp7O/v37AfB4PJSVleHxeIiPj6epqcncXdXU1MSWLVu4cOECxcXFbNiwAYDa2loqKytx\nu93Y7XZ8Pt9crK+IiEQpqsD4yle+wqVLl6457ciRI9ds37VrF7t27ZrRvmbNGk6dOjWj/Y477jAD\nZ7FJTk6edo2JiMjtQDcfjEIkEtGN4UTktqNbg4iIiCUKDBERsUSBISIiligwRETEEgWGyKeMHu8q\nN4vOkhL5lNHjXeVm0RaGiIhYosAQERFLFBgiImKJAkNERCy5bQMjOTk56jNJRERuR7ftWVK6H5SI\nyOzctlsYIiIyOwoMETHpoj+5ntt2l9TN8u677/Lggw8udBnTqCZrFmNNML91Wb3o71o1LfSu2s7O\nzgWv4WqLsaZYLOotDL/fT1ZWFm63m3/6p3+65jy9vb1R/dws77777k1bdrRUkzWLsSZYnHUtxpqi\nPSZ5My3GmmKxaLcwJicn+Yu/+AuOHDmC0+kkJyeHkpISVqxYMW2+nJwcli5dukBVishll3dnRSMp\nKYnh4eEyIzBIAAAHOklEQVQ5rkjm2qINjK6uLjIyMkhPTwfgj//4j2lra5sRGK+88gp2u33Wy/80\nbSaKLAax3MOqoKAgplPWk5KSqKuri7q/WBNnGIax0EVcS2trK4cOHeKHP/whAK+99hqBQIAXX3zR\nnEfXRIiIzF60H/uLdgvDShgs0qwTEflUWrQHvZ1OJ319fea/+/r6cLlcC1iRiMjtbdEGxsMPP0ww\nGOTMmTOMj4+zb98+SkpKFrosEZHb1qLdJRUfH89LL73E+vXrmZycpLa2dsYBbxERmT+LdgsDYOPG\njfzqV7/ipZdewuv1Xvd6jL/6q7/C7XazatUq3nnnnZte242uEens7CQxMZHVq1ezevVq/uEf/uGm\n1lNTU4PD4SA7O/u3zjPfY2SlrvkeJ5javfnoo49y//33s3LlSl544YVrzjef42Wlpvkeq9/85jes\nXbuWBx98EI/Hw7e//e1rzjef42SlpoV4T8HUWWKrV6/mscceu+b0hfj7u1Fdsx4rY5GbmJgwli9f\nbvT09Bjj4+PGqlWrjO7u7mnz/Od//qexceNGwzAM46233jLWrl274DX913/9l/HYY4/d1DqudPz4\ncePkyZPGypUrrzl9vsfIal3zPU6GYRgDAwPGO++8YxiGYYyOjhqZmZkL/p6yUtNCjNX//d//GYZh\nGBcvXjTWrl1r/PSnP502fSHeVzeqaSHGyTAM4zvf+Y7x5JNPXvN3L9Tf343qmu1YLeotDJh+PYbN\nZjOvx7hSe3s71dXVAKxdu5ZIJMLg4OCC1gTzexbXunXrrnsvn/keI6t1wfyf7Zaammre1uKuu+5i\nxYoV9Pf3T5tnvsfLSk0w/2P1uc99DoDx8XEmJydJSUmZNn0h3lc3qgnmf5xCoRAHDx7kG9/4xjV/\n90L9/d2oLpjdWC36wAiHw6SlpZn/drlchMPhG84TCoUWtKa4uDjeeOMNVq1aRXFxMd3d3TetHivm\ne4ysWuhxOnPmDO+88w5r166d1r6Q4/XbalqIsbp06RIPPvggDoeDRx99FI/HM236QozTjWpaiHHa\nsWMHzz33HEuWXPsjdaHeTzeqa7ZjtegDw+rFeVen5M28qM/Ksh966CH6+vp47733+Mu//Es2b958\n0+qxaj7HyKqFHKePP/6YJ554gueff5677rprxvSFGK/r1bQQY7VkyRLeffddQqEQx48fv+aV3PM9\nTjeqab7H6cc//jHLli1j9erV1/22Pt/jZKWu2Y7Vog8MK9djXD1PKBTC6XQuaE1f+MIXzE3njRs3\ncvHiRYaGhm5aTTcy32Nk1UKN08WLFyktLeVP//RPr/lHshDjdaOaFvI9lZiYyB/90R/x85//fFr7\nQr6vfltN8z1Ob7zxBu3t7dx7771UVFTw+uuvU1VVNW2ehRgnK3XNeqxiO5xy8128eNG47777jJ6e\nHmNsbOyGB73ffPPNm35AyUpN586dMy5dumQYhmEEAgHjnnvuuak1GYZh9PT0WDroPR9jZLWuhRin\nS5cuGZWVlcZTTz31W+eZ7/GyUtN8j9Wvf/1rY3h42DAMw/jkk0+MdevWGUeOHJk2z3yPk5WaFuI9\ndVlnZ6fx1a9+dUb7Qv79Xa+u2Y7Vor0O47Lfdj3G97//fQD+7M/+jOLiYg4ePEhGRgaf//zn+dGP\nfrTgNbW2tvLKK68QHx/P5z73OXw+302tqaKigmPHjvHhhx+SlpZGfX09Fy9eNOuZ7zGyWtd8jxPA\nz372M1577TUeeOABVq9eDcCzzz5r3vZ+IcbLSk3zPVYDAwNUV1dz6dIlLl26RGVlJQUFBQv6t2el\npoV4T13p8q6mhRwnq3XNdqwW7c0HRURkcVn0xzBERGRxUGCIiIglCgwRkUXIyu1+Ljt+/DgPPfQQ\nNpuN//iP/zDb3333Xb785S+zcuVKVq1axf79+2OqSYEhIrIIbd26Fb/fb2nee+65B6/Xy5NPPjmt\n/fOf/zwtLS3893//N36/n6eeeoqPPvoo6poUGCIii9C1bqvzwQcfsHHjRh5++GF+//d/n1/96lfA\nVGBkZ2fPuKLb7XazfPlyAO6++26WLVvGr3/966hrWvSn1YqIyJRvfvObfP/73ycjI4NAIMD27ds5\nevSopb5dXV1cvHjRDJBoKDBERG4BH3/8MW+++SZf//rXzbbx8XFLfQcGBqiqquLVV1+NqQYFhojI\nLeDSpUskJSXd8FkaV9+j6qOPPuKrX/0qzz77LLm5uTHVoGMYIiK3gISEBO69915aW1uBqZsZ/uIX\nv5g2j2EY0240OD4+zte+9jWqqqp4/PHHY65BV3qLiCxCV95Wx+FwsHfvXh599FG2bdvGwMAAFy9e\npKKigr//+7/n7bff5vHHH2d4eJg777yTu+++m1OnTvHaa69RU1PD/fffby7X6/XywAMPRFWTAkNE\nRCzRLikREbFEgSEiIpYoMERExBIFhoiIWKLAEBERSxQYIiJiyf8DkZ2FguLUqRwAAAAASUVORK5C\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1065b06d0>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#surface density plots in the E-J space. This defines the 1-sigma surface\n",
      "H, xedges,yedges = histogram2d(J_norm,E, bins=(30,38))\n",
      "X,Y=meshgrid(yedges[0:-1],xedges[0:-1])\n",
      "th=4000 # 4000, corresponds to 1-sigma, 200 to 3-sigma\n",
      "print 'This is the fraction of points included inside the contour:',sum(H[where(H>th)])/sum(H) \n",
      "levels=array([th])\n",
      "C=contour(X,Y,H, levels, colors='k', linewidths=2)\n",
      "ax = axes()\n",
      "ax.set_xlabel(\"Energy\")\n",
      "ax.set_ylabel(\"Angular Momentum\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "This is the fraction of points included inside the contour: 0.653646842527\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.text.Text at 0x1064600d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Fi5g3bx4A4J133mmwrhaRITgnQAapqalBt27dUF1djcLCQvTq1UvuSK3SlClT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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1065d6f90>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# N-body data\n",
      "The next four cells put into a single file the data from the pairs (their IDs) and the halo catalogs. This is done for Bolshoi and the three constrained simulation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate the pair data for Bolshoi\n",
      "FOF_file=data_path+\"Bolshoi_catalog_\"+halo_finder+\".dat\"\n",
      "ID_file=data_path+\"IsoPairs_Bolshoi_\"+halo_finder+\"_ID.dat\"\n",
      "output_file=data_path+\"pair_physical_vweb_Bolshoi\"+halo_finder+\".dat\"\n",
      "generate_info(FOF_file, ID_file, output_file=output_file, hubble=HUBBLE)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1924\n",
        "selected in total"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1923\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate the pair data for CLUES 1\n",
      "FOF_file=data_path+\"IC2710_halos_catalog.dat\"\n",
      "ID_file=data_path+\"index_LG_IC2710\"\n",
      "output_file=data_path+\"pair_physical_vweb_IC2710.dat\"\n",
      "generate_info(FOF_file, ID_file, output_file=output_file, hubble=0.73)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n",
        "selected in total 1\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate the pair data for CLUES 2\n",
      "FOF_file=data_path+\"IC16953_halos_catalog.dat\"\n",
      "ID_file=data_path+\"index_LG_IC16953\"\n",
      "output_file=data_path+\"pair_physical_vweb_IC16953.dat\"\n",
      "generate_info(FOF_file, ID_file, output_file=output_file, hubble=0.73)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n",
        "selected in total 1\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate the pair data for CLUES 3\n",
      "FOF_file=data_path+\"IC10909_halos_catalog.dat\"\n",
      "ID_file=data_path+\"index_LG_IC10909\"\n",
      "output_file=data_path+\"pair_physical_vweb_IC10909.dat\"\n",
      "generate_info(FOF_file, ID_file, output_file=output_file, hubble=0.73)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n",
        "selected in total 1\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "After saving all the data into a single file, that file is reloaded to keep in memory the data we care about (radial velocities, tangential velocities, separations, total_mass, angular momentum, energy, lambda). This is for Bolshoi."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#load the data from Bolshoi and make selections on distances and mass\n",
      "bolshoi_file=data_path+\"pair_physical_vweb_Bolshoi\"+halo_finder+\".dat\"\n",
      "physical_prop=np.loadtxt(bolshoi_file) \n",
      "\n",
      "#define the main quantities we will use later to prepare the plots\n",
      "radial_vel = physical_prop[:,0]\n",
      "tangential_vel = physical_prop[:,1]\n",
      "distance = physical_prop[:,8]\n",
      "total_mass = physical_prop[:,9]/ 1E12\n",
      "\n",
      "energy = physical_prop[:,5] + physical_prop[:,6] \n",
      "angular_momentum = physical_prop[:,7] \n",
      "\n",
      "mu = physical_prop[:,10]\n",
      "\n",
      "lambda_orbit = mu**1.5 * (angular_momentum * L_UNITS * KM_TO_MPC)* sqrt(abs(energy * E_UNITS)) / (G_GRAV * (total_mass *1E12 )**(5.0/2.0))\n",
      "\n",
      "if(narrow_data):\n",
      "    index_good_mass = where((total_mass>1.0) & (total_mass<4.0) & (distance>0.70) & (distance<0.80))\n",
      "    index_good_mass = index_good_mass[0]\n",
      "    physical_prop = physical_prop[index_good_mass,:]\n",
      "\n",
      "    radial_vel = physical_prop[:,0]\n",
      "    tangential_vel = physical_prop[:,1]\n",
      "    distance = physical_prop[:,8]\n",
      "    total_mass = physical_prop[:,9]/1E12\n",
      "\n",
      "    energy = physical_prop[:,5] + physical_prop[:,6] \n",
      "    angular_momentum = physical_prop[:,7] \n",
      "\n",
      "    mu = physical_prop[:,10]\n",
      "\n",
      "    lambda_orbit = mu**1.5 * (angular_momentum * L_UNITS * KM_TO_MPC)* sqrt(abs(energy * E_UNITS)) / (G_GRAV * (total_mass *1E12 )**(5.0/2.0))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Figure with the separation distribution\n",
      "fig = figure(1, figsize=(9.5,6.5))\n",
      "ax = axes()\n",
      "ax.set_xlabel(\"$\\mathrm{Pair\\ Separation\\ [Mpc]}$\",fontsize=25)\n",
      "ax.set_ylabel(\"$\\mathrm{N_{pairs}}$\",fontsize=25)\n",
      "ticklabels_x = ax.get_xticklabels()\n",
      "ticklabels_y = ax.get_yticklabels()\n",
      "\n",
      "for label_x in ticklabels_x:\n",
      "    label_x.set_fontsize(18)\n",
      "    label_x.set_family('serif')\n",
      "for label_y in ticklabels_y:\n",
      "    label_y.set_fontsize(18)\n",
      "    label_y.set_family('serif')\n",
      "n, bins, patches = ax.hist(distance, 20, normed=0, color = 'silver')\n",
      "ax.set_xlim([0.4,1.0])\n",
      "filename='separation_'+halo_finder\n",
      "if(narrow_data):\n",
      "    filename=filename+'_narrow'\n",
      "savefig(filename + '.eps',format = 'eps', transparent=True)\n",
      "savefig(filename + '.pdf',format = 'pdf', transparent=True)\n",
      "savefig(filename + '.png',format = 'png', transparent=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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NEeYAAABsjDAHAABgY4Q5AAAAG7PNfeYAAKjtfH19uaE9XBDmAACwiaKiIm3atKm6y3AR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\nVBXl2k5l5re4uNi8+eabpmvXrqZhw4a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ZKC4ujkaPHk1SqZRkMhnFxMSQ0WikiooKio2N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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1064ce5d0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Figure with the total mass distribution\n",
      "print amin(total_mass), amax(total_mass)\n",
      "\n",
      "fig = figure(1, figsize=(9.5,6.5))\n",
      "ax = axes()\n",
      "ax.set_xlabel(\"$\\mathrm{Total\\ Mass\\ [10^{12}\\ M_{\\odot}]}$\",fontsize=25)\n",
      "ax.set_ylabel(\"$\\mathrm{N_{pairs}}$\",fontsize=25)\n",
      "ticklabels_x = ax.get_xticklabels()\n",
      "ticklabels_y = ax.get_yticklabels()\n",
      "\n",
      "for label_x in ticklabels_x:\n",
      "    label_x.set_fontsize(18)\n",
      "    label_x.set_family('serif')\n",
      "for label_y in ticklabels_y:\n",
      "    label_y.set_fontsize(18)\n",
      "    label_y.set_family('serif')\n",
      "\n",
      "ax.set_xlim([1.0,12.0])\n",
      "n, bins, patches = ax.hist(total_mass, 20, normed=0, color = 'silver')\n",
      "\n",
      "filename='total_mass_'+halo_finder\n",
      "if(narrow_data):\n",
      "    filename=filename+'_narrow'\n",
      "savefig(filename + '.eps',format = 'eps', transparent=True)\n",
      "savefig(filename + '.pdf',format = 'pdf', transparent=True)\n",
      "savefig(filename + '.png',format = 'png', transparent=True)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.4431 13.3105714286\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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4e3vLMAy3fkr//gMAag4fTxdwufbs2SNfX1/FxMRIktLT0yVJQUFBTn2Dg4MlnQ96pdLT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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106515f90>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#observational data\n",
      "mean_point = [-110.0, 0.0]\n",
      "sigma_point = [4.4, 34.3]\n",
      "delta_radial = 4.5\n",
      "delta_tangential = 17.5\n",
      "\n",
      "#load the data from the CLUES pairs\n",
      "n_clues = 3\n",
      "clues1=data_path+\"pair_physical_vweb_IC10909.dat\"\n",
      "clues2=data_path+\"pair_physical_vweb_IC16953.dat\"\n",
      "clues3=data_path+\"pair_physical_vweb_IC2710.dat\"\n",
      "clues=chararray([n_clues], itemsize=1024)\n",
      "clues[0]=clues1;clues[1]=clues2; clues[2]=clues3\n",
      "clues_data = np.zeros([n_clues,4])\n",
      "if(narrow_data):\n",
      "    n_clues = 1\n",
      "for i in range(n_clues):\n",
      "    tmp_dat = np.loadtxt(clues[i])\n",
      "    clues_data[i,0] = tmp_dat[0]# radial \n",
      "    clues_data[i,1] = tmp_dat[1]# tangential\n",
      "    clues_data[i,2] = tmp_dat[8]# separation\n",
      "    clues_data[i,3] = tmp_dat[9]/1E12 #total mass\n",
      "    \n",
      "filename='test_rt_'+halo_finder\n",
      "\n",
      "if(narrow_data):\n",
      "    filename=filename+'_narrow'\n",
      "\n",
      "n=MakeSimple2DPlot(radial_vel,tangential_vel,filename=filename, \n",
      "                      clues=clues_data,clues_label='$\\mathrm{Constrained\\ Sim.}$',\n",
      "                      contours=0,xlims=[-240.0,0.0], ylims=[0.0,240.0],\n",
      "                      nbins=13,nxbins=13,nybins=13,bw=1, \n",
      "                      xlabel='$\\mathrm{Radial\\ Velocity\\ [km\\ s^{-1}]}$', \n",
      "                      ylabel='$\\mathrm{Tangential\\ Velocity\\ [km\\ s^{-1}]}$', \n",
      "                      mean_obs=mean_point, sigma_obs=sigma_point)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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5cuSI0RHsVKtWzegIdjZs2GB0hEzVqlXL6Ah20u9/AO6VSxZOi8UiHx8fffnl\nl3rggQfu6T14ljoAAIBzuOxd6nPmzLnnsilJEREROZgGAAAAt+NyhTP9GejNmze/r/epW7dulu8P\nAACAnOFyhXPixIku/f4AAADuxuUKJwAAAFyLy900FB0dLQ8Px/Xkhx56yGHvDQAA4I5crnCeOHHC\n6AgAAAC4C5xSBwAAgENROAEAAOBQFE4AAAA4FIUTAAAADkXhzAFz585V0aJF1a1bt0z3z549W4UK\nFVKJEiXsfk2aNCnT1yxZskQhISEKCAhQmTJlNHjwYCUlJTnyMAAAABzC5e5Sz03Onz+vV199VZGR\nkUpISJDFYsl0nMVi0ZAhQzRy5Mhsve/MmTPVq1cvzZ8/Xx07dtSJEyfUtGlT/fbbb1q7dq1Dl4UC\nAADIaTSX+9C1a1dVrVpVP/744x3HWq3WbL3npUuX9NZbb6lt27bq2LGjJCkoKEgRERHasGGD5s6d\ne1+ZAQAAnI3CeR9mzJihMWPGKE+enJsoXrx4sRISEhQaGpphe7NmzVSgQAFNnz49xz4LAADAGUxX\nOAcOHOi0zypevHiOv+fmzZslSY8++miG7Xnz5lWVKlW0fft23bhxI8c/FwAAwFFMVzinTp2qs2fP\nGh3Dzq5du9S8eXMFBQWpRIkSatq0qVauXGk37vDhw7JYLCpRooTdvsDAQKWmpur48ePOiAwAAJAj\nTHfTUHJysurXr68PP/xQL730kjw9PY2OJOnmIzlnzpyp6tWrKzY2VmPGjNGLL76o8PBwDR061DYu\nPj5eklSwYEG790jfFhcXZ7fvyy+/tP0+JCREISEhOX0IAAA43datW7Vt2zajY+A+ma5w5suXT8OG\nDVN0dLQaNGigOnXqqFevXgoKCjIsU7t27dS+fXvlz59fkuTv76/Jkyfr119/1bvvvqsOHTrooYce\nuq/P6N27d05EBQAgV3n22Wf17LPP2r4eN26cgWlwr0x3Sn3WrFnq1q2bBg8erE2bNqlhw4YaPny4\nnn/+eS1btkypqalOz1SgQAFb2bzV888/r5SUFP3www+2bd7e3pKkxMREu/Hp29LHAAAAuALTFc70\npYSkm+tfNmrUSAsXLtT06dN1+PBhPfroo3r33Xd16tQpA1Pe5O/vL+nmep7pKlasKKvVmul1qGfO\nnJGnp6fKlSvntIwAAAD3y3SFMzNXr17V8uXL9fXXXysqKkoffvihateurRdeeEHfffedwz9/1KhR\nSklJsdvlmZOMAAAgAElEQVR+7tw5SZKfn59tW7169SRJkZGRGcbeuHFDUVFRqlmzpvLly+fAtAAA\nADnLdIVzwIABtt///vvvCgsLU4kSJfTaa69p3759evHFF7VmzRqdOHFCU6dO1W+//aYGDRpo3bp1\nDss0evRo7du3z2776tWr5enpqaZNm9q2tW3bVkWKFNGyZcsyjF2zZo2SkpLUo0cPh+UEAABwBNPd\nNDRjxgyVKVNGixYt0s6dOyVJpUqV0qBBg9SzZ08FBgbaxpYsWVKjRo3S5cuX1bNnT8XHx6t169b3\n/NlZPU0oLCxM8+bNU8WKFZWQkKDRo0dr586dGj58eIZT5D4+Pho/frx69+6tBQsWqFOnTjpx4oQG\nDRqkhg0bqkuXLvecDwAAwAgWa3afuegi0p8z7uHhoeeee05hYWH617/+dcfnjycnJ6tRo0baunVr\ntj9r9uzZeu2112S1WnXjxg1ZLBblzZtXJUqUyLBW5oYNGzRv3jxt27ZNcXFxSkpK0qOPPqo+ffpk\nuOb0VkuWLFF4eLj+/PNP5cuXTx06dNCYMWMyvfnIYrFo165d2c7tLLnx5qbdu3cbHcFO+lJYuLPc\n+Gcq/Vrs3OTIkSNGR7BToUIFoyPY2b9/v9ERMlWrVi2jI9gpU6aM0RFs/P39s/24aOQeppvhlKT+\n/furf//+2foBSUxM1JAhQ/Tss8/e9SMqu3btqq5du95xXIMGDdSgQYO7eu82bdqoTZs2d/UaAACA\n3Mh013BWrlxZ48ePz/b/jf3yyy+aMmWKunfvrqeeesrB6QAAANyP6WY4hwwZclfjGzRooClTpsjP\nz48ZRQAAAAcwXeHMzinuW3l4eCgsLMwxYQAAAGC+wnk7O3bs0LVr11SyZEkWTgcAAHAi013D2b17\n90y3b9++XevXr1d4eLiaN2+uP/74w8nJAAAA3JPpZjijo6Mz3f7GG2/Yfh8XF6cOHTpkeIY5AAAA\nHMN0M5zZ4e3trZiYGKNjAAAAuAWXnuGMjIzUnj17ZLFYJN180k9MTIzmzp2b6Xir1arY2FgtX75c\nvr6+zowKAADgtly6cKakpOjEiRPasmWLfv75Z9uTB+50p7qfn5/Wrl3rhIQAAABw6cIZEhKikJAQ\nSVJUVJRat26tpKQkde3aNdPHXnl4eCgoKEgtW7ZkhhMAAMBJXLpw3qpKlSqaOXOmhg8frvfee8/o\nOE7n5eVldAQ7p0+fNjqCndz43wnZlxufEZ6cnGx0BDu58WcvNypSpIjRETLF9w9mZKqbhqpXr66X\nXnrJ6BgAAAC4hakKp6enp/r165etsTt37nRwGgAAAEgmK5x3g8dZAgAAOIfLXsO5bds2ffPNNwoL\nC1OlSpUk3VzQfeLEibZlkm4nISFBkZGRzogJAADg9ly2cIaGhio2Nla//fabNm3aJOnmMknvv/9+\ntl5/p1IKAACAnOGyhbNOnTpaunSpateubdvm4+Mji8WiwYMHq0mTJvL09Mz0tfHx8erUqZOzogIA\nALg1ly2c33zzjS5evKhixYrZtnl6esrb21sjRoxQ4cKFs3x9tWrVHB0RAAAAcvGbhm4tm+mOHTt2\nx7IpSQsWLHBEJAAAAPyDSxfOzPj4+Cg1NVVxcXF2+44dO6Zjx45JkoKDg50dDQAAwC2ZrnCePn1a\n5cuXl5+fn5YtW5ZhX/78+RUeHq4RI0YYlA4AAMD9mK5wjhs3TmXKlFFaWpr+/vvvDPtKliyp6dOn\ny8/PT3PnzjUoIQAAgHsxXeGMiorS2rVrtXv3bvXo0SPTMW+++aYWL17s5GQAAADuyXSFMzU1Vfny\n5dMTTzxx2zEeHh5KTEx0YioAAAD3ZbrCeeXKlTuOSU5O1rlz55yQBgAAAKYrnMHBwfr444+zHDNw\n4EBVrVrVSYkAAADcm8su/H47w4YNU40aNbRlyxZ169ZNjz/+uHx8fHTp0iVt375dU6ZM0Y4dO7Rt\n2zajowIAALgF0xXOxx57TNOmTVPPnj21evXqDM9Mt1qt8vT01NSpU/XUU08ZmBIAAMB9mO6UuiR1\n7txZv/76q1588UXlyZNHVqtVFotFTZs21ebNm9WzZ0+jIwIAALgN081wpnviiSe0bNkypaWl6fz5\n8ypWrJjy5DHt4QIAAORapm9gHh4eCggIMDoGAACA2zJt4UxNTdW3336rpUuX6s8//9SDDz6oZs2a\nqUuXLsqfP7/R8QAAANyGKQvn6dOn1bZtW+3YsSPD9hUrVmjixIlasWKFKlSoYFA6AAAA92K6wnn1\n6lW1aNFCaWlpGjZsmEqXLq28efPq/PnzOnbsmFauXKkWLVrot99+U+HChY2OCwAAYHqmK5yTJ0/W\no48+qvnz52dYEildamqqhgwZogkTJujdd981ICEAAIB7Md2ySMuXL9dnn32WadmUJE9PT33yySda\nv369k5MBAAC4J9MVzvz588vHxyfLMXny5GGJJAAAACcxXeFMSkrK1rhr1645OAkAAAAkExbO0qVL\na/Xq1VmOWbdunUqUKOGkRAAAAO7NdIVzyJAhevnll/XFF1/o4sWLGfZFR0dr7Nixat26td566y2D\nEgIAALgX013I+PTTT2v06NHq06eP+vTpIy8vL+XLl0+JiYlKSUmRJH344YeqWbOmwUkBAADcg+lm\nOCXpjTfe0KpVq/Too48qOTlZCQkJSklJUfny5bVgwQINHz7c6IgAAABuw3QznOmaNWumZs2a6fTp\n0/rzzz/l7++v4OBg2/6lS5eqdevWBiYEAABwD6ac4bxV6dKl9cwzz2Qom5L0wQcfGJQIAADAvbjk\nDOeVK1cUERFx28Xd7yQ+Pl779u3L4VQAAADIjEsWTqvVqvfff/++3uNeyyoAAADujksWzsKFCytv\n3rzq37+/mjVrdtflMSEhQZ06dXJQOgAAANzKJQunJPn6+mr06NHy8vK6p9dXq1YthxMBAAAgMy5b\nONeuXXvPZVOS5s6dm4NpjJeQkGB0BJdQunRpoyPY2b9/v9ERMhUbG2t0BDve3t5GR7Czbds2oyPY\nyY3fu927dxsdwWW0atXK6Ah2eBw07pfL3qV+vzOUFStWzKEkAAAAyIrLFs47SU5O1oYNG7RmzRrb\ntsjISF26dMnAVAAAAO7HlIVz1qxZKlmypBo1aqTXX3/dtj05OVndunXTnDlzDEwHAADgXkxXOFet\nWqVevXqpdu3aGj9+vIoVK2bbV6NGDS1fvlyRkZFav369gSkBAADch+kK59ixYzVv3jytWLFC/fv3\nV6FChezGhIeH67PPPjMgHQAAgPsxXeFMTExUx44dsxzj5eWlpKQkJyUCAABwb6YrnNldNuXixYsO\nTgIAAADJhIXTarXqyJEjWY6ZOnWqgoKCnBMIAADAzZmucL7++utq2LChFi5cqMTERNv2ixcvatWq\nVWrdurX69eunQYMGGZgSAADAfbjsk4ZuJzQ0VJs2bdLLL78sDw8PWSwWFSxYUNeuXZPVapXFYlFE\nRIRq1KhhdFQAAAC3YLoZTkmaOHGiZs+erXLlyik1NVXJycmyWq167LHHtHLlSvXv39/oiAAAAG7D\nZWc4Dx8+nOXjKV955RW98sorio6O1rlz51SqVCmVKlXKiQkBAAAguXDhbN26tfbt23fHcWXLllXZ\nsmWdkAgAAACZcdlT6gcOHNDevXuNjgEAAIA7cNnCKUnPPfecJk+erEuXLhkdBQAAALfh0oWzY8eO\nOnPmjKpXr662bdtq9erVSktLMzoWAAAAbuGyhTM4OFjjx49XeHi4Dh8+rF69emn+/PmqUKGChg4d\nqj/++MPoiAAAAJALF841a9bYfu/h4aGmTZtqwYIF+u2331SuXDn16NFDNWvW1BdffKGEhAQDkwIA\nALg3ly2c5cuXz3S7t7e3Xn31VW3dulVz5szRiRMnFBISok6dOumnn36S1Wp1clIAAAD35rKFMzsq\nVaqk8PBwHTp0SK+88opmzZqlihUrasSIEXd83joAAAByhqkLZ7rr16/r/PnzOnfunI4fP67w8HBV\nrlxZX3zxhdHRAAAATM9lF37Pji1btmjWrFlasmSJLl++bNtesmRJde7cWc8//7yB6QAAANyDyxbO\nX3/9VTVr1rTbfvr0ac2ZM0dz5szR8ePHbddsenl56aWXXlLXrl3VpEkTWSwWZ0cGAABwSy5bON94\n4w3t3LlTkpScnKylS5dq9uzZ2rhxo1JTU23jatSooa5du6pDhw7y9vY2Ki4AAIDbctnCefDgQa1Y\nsUKrVq3S4sWLMyx9FBgYqM6dO6tr166qVKmSgSkBAADgsoUzKSlJoaGhGU6Zt2rVynbK3MPDLe6H\nAgAAyPVctnBKktVq1dNPP62uXbuqY8eOnDIHAADIhVy2cHp6eup///tfpjcOAQAAIPdw2fPOVatW\npWwCAAC4AJctnN26dTM6gs3cuXNVtGjRLDNduHBBPXr0UGBgoAICAlS3bl1t2rTptuOXLFmikJAQ\nBQQEqEyZMho8eLCSkpIcER8AAMChXLZwvvnmm0ZH0Pnz5xUaGqr3339fCQkJt13b8/Lly6pXr54O\nHz6s/fv3KyYmRi1atFDjxo21bt06u/EzZ85U+/btNWjQIJ07d06bN2/WihUr1LJlS6WlpTn6sAAA\nAHKUyxbO3KBr166qWrWqfvzxxyzHjRs3TlFRUZo2bZp8fX1lsVg0bNgwPfbYYwoLC8uwbuilS5f0\n1ltvqW3bturYsaMkKSgoSBEREdqwYYPmzp3r0GMCAADIaRTO+zBjxgyNGTNGefLc/t4rq9WqGTNm\nqHLlyqpcuXKGfaGhoTp+/Lg2bNhg25a+pmhoaGiGsc2aNVOBAgU0ffr0nD0IAAAAB6Nw3ofixYvf\ncczRo0d19uxZPfroo3b70rfdei3n5s2bM+xLlzdvXlWpUkXbt2/XjRs37ic2AACAU1E4Hezw4cOS\npBIlStjtCwwMlHSzlN463mKx3HZ8amqqjh8/7qC0AAAAOc9l1+F0FfHx8ZKkggUL2u1L3xYXF3fP\n49PNmDHD9vsnnnhCTz755H2kBgAgdzh48KAOHjxodAzcJ7ctnEuXLlXr1q2NjpFjhg8fbnQEO6dP\nnzY6gp39+/cbHcHOtWvXjI6Qqfz58xsdwU5u/P7xhLPsCQkJMTqCndKlSxsdwWX4+/sb+tn169e3\nfb1kyRLDsuDeue0p9Q8++MApn5P+j1FiYqLdvvRtt/6DdbfjAQAAcjuXnOG8cuWKIiIibrvu5Z3E\nx8dr3759OZwqc5UqVZIknT171m7fmTNnJEkVKlSwbatYsaJ2796ts2fP2hXLM2fOyNPTU+XKlXNg\nYgAAgJzlkoXTarXq/fffv6/3uNeyerfKly+vwMBARUZG2u3bu3evJGU4VVCvXj0tXLhQkZGRGZZR\nunHjhqKiolSzZk3ly5fP4bkBAAByiksWzsKFCytv3rzq37+/mjVrdtflMSEhQZ06dXJQOnvdu3fX\nBx98oKioKFWpUsW2fenSpQoODlaDBg1s29q2bashQ4Zo2bJlat++vW37mjVrlJSUpB49ejgtNwAA\nQE5wycIpSb6+vho9erS8vLzu6fXVqlXL4UQ3Z14zM2TIEC1dulS9e/fW8uXL5ePjo08++UT79u3T\n6tWr5eHxf5fS+vj4aPz48erdu7cWLFigTp066cSJExo0aJAaNmyoLl265HhuAAAAR3LZm4bWrl17\nz2VTkubMmXPfGWbPnq0CBQqocuXKslgsmjdvngoUKGB3jWWhQoW0efNmVapUSY888ohKlCihNWvW\naO3atWrcuLHd+3bv3l2LFi1SRESEAgICVKdOHb344ov6/vvvnXYpAAAAQE6xWG83LWdCa9eu1dmz\nZ1WhQgU988wzRsfJMRaLRUeOHDE6hp3cuCzSqVOnjI5g59aF/3OT3LhcU278c54bV41IX883N3HE\nWaX7xbJI2Xfrza1Ga9iw4W3PKCL3ctkZznthtVqVlpamNWvWaNKkSUbHAQAAcAsuew3nvWjatKkk\n6cSJE3r++efVr18/gxMBAACYnylnOHfs2KGaNWvKy8tLnp6edr/KlSunAgUKGB0TAADALZhuhjM6\nOlpNmjTRtWvXVLx4ccXGxiogIECSdP36dcXExKhly5b673//a3BSAAAA92C6Gc6PPvpITZs2VUxM\njE6ePKmnn35aJ06c0IkTJ3TmzBkdOnRIV69eVVxcnNFRAQAA3ILpCueOHTs0d+5cFS1aVJKUJ08e\nXbp0yba/QoUKmjdvnkaOHGlURAAAALdiusLp5+eX4frMhx9+WD/88EOGMYGBgcxwAgAAOInpCmfR\nokWVkpKipKQkSVKjRo00duxYpaSk2MZYrVb9+eefRkUEAABwK6YrnEFBQapevbqCg4OVmJioZs2a\n6a+//lLr1q115MgRxcfHa+DAgSpSpIjRUQEAANyC6e5S79ixo6ZMmSKLxaLr16+raNGiioiIUJcu\nXfT9999LujnD+dlnnxmcFAAAwD2YrnA+9dRTOnbsmJKTk203DnXu3FmXLl3S2LFjlZCQoH//+996\n7bXXDE4KAADgHkxXOKWbNwX9U79+/XiyEAAAgAFMdw1ndu3cudPoCAAAAG7BbQtnWFiY0REAAADc\ngsueUt+2bZu++eYbhYWFqVKlSpKkuLg4TZw4URaLJcvXJiQkKDIy0hkxAQAA3J7LFs7Q0FDFxsbq\nt99+06ZNmyRJKSkpev/997P1+juVUgAAAOQMly2cderU0dKlS1W7dm3bNh8fH1ksFg0ePFhNmjSR\np6dnpq+Nj49Xp06dnBUVAADArbls4fzmm2908eJFFStWzLbN09NT3t7eGjFihAoXLpzl66tVq+bo\niAAAAJCL3zR0a9lMd+zYsTuWTUlasGCBIyIBAADgH1y6cGbGx8cnW+OCg4MdnAQAAACSC59Sv1s7\nduzQtWvXVLJkSZUrV87oOAAAAG7DdDOc3bt3z3T79u3btX79eoWHh6t58+b6448/nJwMAADAPZlu\nhjM6OjrT7W+88Ybt93FxcerQoYN++OEHZ8UCAABwW6ab4cwOb29vxcTEGB0DAADALbj0DGdkZKT2\n7NljW8TdarUqJiZGc+fOzXS81WpVbGysli9fLl9fX2dGBQAAcFsuXThTUlJ04sQJbdmyRT///LOs\nVqskqWvXrlm+zs/PT2vXrnVCQgAAALh04QwJCVFISIgkKSoqSq1bt1ZSUpK6du1qK5+38vDwUFBQ\nkFq2bMkMJwAAgJO4dOG8VZUqVTRz5kwNHz5c7733ntFxAAAA8P+Z6qah6tWr66WXXsrW2MWLFzs4\nDQAAACQTzXBKN5+l3q9fv2yNDQ8PV7t27RycyHni4+ONjmDnyJEjRkewc/ToUaMj2ClSpIjRETKV\nG3N5eXkZHcFObvzZO3z4sNER7Pj7+xsdwWXExsYaHcFObvzZg2sxVeFMFxsbq59++kmnTp1SSkqK\n3f74+Hjt27fPgGQAAADux3SFc/v27WrevLni4uKyHJe+lBIAAAAcy3SFc9iwYSpfvrxCQ0P14IMP\nytPT025MQkKChgwZYkA6AAAA92O6wnn+/Hnt2bNHefJkfWjz5893UiIAAAD3Zqq71CWpbNmydyyb\nkvT55587IQ0AAABMVziDg4N18uTJO47bu3evE9IAAADAdIVz1KhRGjFihHbv3p3luAkTJjgpEQAA\ngHsz3TWc06dPV/ny5dWyZUuVLl1aFStWVL58+TKMSUhI0IEDBwxKCAAA4F5MVzjHjRun8+fPS5LO\nnTunXbt2ZTqOZZEAAACcw3SF08/PT7Vq1VLfvn0zXRJJujnD2alTJycnAwAAcE+mK5z+/v7q06eP\nGjVqlOW4atWqOSkRAACAezNd4Zw+fboCAgLuOG7u3LlOSAMAAADTFc7g4OBsjatYsaKDkwAAAEAy\n4bJI6ZKTk7VhwwatWbPGti0yMlKXLl0yMBUAAID7MWXhnDVrlkqWLKlGjRrp9ddft21PTk5Wt27d\nNGfOHAPTAQAAuBfTFc5Vq1apV69eql27tsaPH69ixYrZ9tWoUUPLly9XZGSk1q9fb2BKAAAA92G6\nwjl27FjNmzdPK1asUP/+/VWoUCG7MeHh4frss88MSAcAAOB+TFc4ExMT1bFjxyzHeHl5KSkpyUmJ\nAAAA3JvpCqe3t3e2xl28eNHBSQAAACCZsHBarVYdOXIkyzFTp05VUFCQcwIBAAC4OdMVztdff10N\nGzbUwoULlZiYaNt+8eJFrVq1Sq1bt1a/fv00aNAgA1MCAAC4D9Mt/B4aGqpNmzbp5ZdfloeHhywW\niwoWLKhr167JarXKYrEoIiJCNWrUMDoqAACAWzDdDKckTZw4UbNnz1a5cuWUmpqq5ORkWa1WPfbY\nY1q5cqX69+9vdEQAAAC3YboZzhs3bshiseiVV17RK6+8oujoaJ07d06lSpVSqVKljI4HAADgdkw3\nw1mrVi11797d9nXZsmVVs2ZNu7J59uxZ9ejRQ48//rhatWqlkydPOjsqAACAWzBd4UxJSdHQoUOz\nHJOYmKgGDRpo4cKFevbZZ+Xh4aGmTZvq+vXrTkoJAADgPkxXOCtVqqTixYvrnXfeUcuWLTVy5Egl\nJCRkGLNgwQIdPnxYI0eO1Oeff65vv/1W9erV07x58wxKDQAAYF6mu4azb9++qlChguLi4iRJq1ev\n1nfffadff/1V+fPnlyT9/PPPkqQmTZrYXjd8+HC98cYb6tGjh/NDAwAAmJjpZjh//PFHValSRXPm\nzNGaNWv0xRdf6MaNG5o8ebJtzPHjx2WxWFShQgXbtrJly9pKKgAAAHKO6WY4f/75Z61fv942mylJ\nLVu2VIcOHTR48GBJ0uXLlyVJhQsXzvDavHnzOi8oAACAmzDdDKfFYslQNiWpRIkS8vT0tH2dmppq\nG3ur9O0AAADIOaYrnMnJyTp16lSGbXv37pWvr6/t67S0NLvXJSUlUTgBAAAcwHSn1Dt37qwnn3xS\nrVq1UkBAgE6ePKnvv/9eS5YskST9/vvvio6OltVq1cGDB/Xwww9Lkr766ivVqlXLyOgAAACmZLrC\nGRYWpqVLl2rmzJm2bT179tS0adM0YsQI/f7776pZs6Zat26t9u3ba8aMGTp37pzeeecdbdiwwcDk\nAAAA5mS6wunl5aWff/5ZS5cuVXR0tOrWrWububx69aqSk5NVrFgxSdKePXtUs2ZNWSwWjRs3TlWq\nVDEyOgAAgCmZrnBKUp48edS+fXu77Q888IAeeOAB29ezZ8/WkCFDVKRIEZ6zDgAA4CAWq9VqNTqE\nERYvXqx27doZHSNHWCwWuxulcoP4+HijI9j551OncoPly5cbHSFTR44cMTqCHW9vb6Mj2MmNP3v+\n/v5GR7Dz9ddfGx3BzrJly4yOkKndu3cbHcGOl5eX0RFs3n33XblpdXFpprtLPbvCw8ONjgAAAOAW\nTHlKPTY2Vj/99JNOnTqllJQUu/3x8fHat2+fAckAAADcj+kK5/bt29W8efM7Pqbyn4u+AwAAwDFM\nVziHDRum8uXLKzQ0VA8++GCGJwylS0hI0JAhQwxIBwAA4H5MVzjPnz+vPXv2KE+erA9t/vz5TkoE\nAADg3kx301DZsmXvWDYl6fPPP3dCGgAAAJiucAYHB+vkyZN3HLd3714npAEAAIDpCueoUaM0YsSI\nO65jNmHCBCclAgAAcG+mu4Zz+vTpKl++vFq2bKnSpUurYsWKypcvX4YxCQkJOnDggEEJAQAA3Ivp\nCue4ceN0/vx5SdK5c+e0a9euTMexLBIAAIBzmK5w+vn5qVatWurbt2+mSyJJN2c4O3Xq5ORkAAAA\n7sl0hdPf3199+vRRo0aNshxXtWpVJyX6P0FBQbp27Zrd9rx589o9j/nChQsaOnSo1qxZo9TUVFWq\nVEljxoxRvXr1nBUXAAAgR5iucE6fPl0BAQGZ7lu7dq3Onj2rChUqaN68eU5OdvM0/tmzZ+847vLl\ny6pXr558fX21f/9++fj46JNPPlHjxo21Zs0aNW7c2AlpAQAAcobpCmdwcPBt91mtVqWlpWnNmjXy\n8/NTxYoVnZgs+8aNG6eoqCgdPHhQvr6+km4+QWnJkiUKCwvToUOHbnu5AAAAQG5jumWRstK0aVN1\n7dpV3bt317Rp04yOkymr1aoZM2aocuXKqly5coZ9oaGhOn78uDZs2GBQOgAAgLtnysK5Y8cO1axZ\nU15eXvL09LT7Va5cORUoUMDomJk6evSozp49q0cffdRuX/q2zZs3OzsWAADAPTPdKfXo6Gg1adJE\n165dU/HixRUbG2u7pvP69euKiYlRy5Yt9d///teQfCNGjNCKFSt04cIF+fr6qnnz5nr77bdVrFgx\nSdLhw4clSSVKlLB7bWBgoCTpyJEjdvs+/fRT2+9r1qypZ555xhHxAQBwqujoaEVHRxsdA/fJdIXz\no48+UtOmTTVt2jQVLVpU9erV06ZNm2z7jxw5orCwMMXFxdkKnLNYLBYVKFBAv/zyiwoWLKjNmzer\nS5cu+vbbb/Xrr78qICBA8fHxkqSCBQvavT59W1xcnN2+AQMGODY8AAAGKFu2rMqWLWv7msvKXJPp\nTqnv2LFDc+fOVdGiRSVJefLk0aVLl2z70+9QHzlypNOz7dq1S++8844KFy4sT09PNWjQQFOmTNHJ\nkyf1zjvvOD0PAACAM5iucPr5+WW4PvPhhx/WDz/8kGFMYGBgprOEjpZ+x/mtmjdvLk9PT61atUqS\n5O3tLUlKTEy0G5u+LX0MAACAKzBd4SxatKhSUlKUlJQkSWrUqJHGjh2rlJQU2xir1ao///zTqIgZ\neHp6qlixYrbHcaYv1ZTZep1nzpyRdHOWFgAAwFWYrnAGBQWpevXqCg4OVmJiopo1a6a//vpLrVu3\n1pEjRxQfH6+BAweqSJEiTs21ceNGrVu3zm57amqqLl68aLtpqHz58goMDFRkZKTd2L1790qS6tev\n7y/Ehb8AACAASURBVNCsAAAAOcl0hbNjx476448/FBcXp+vXryt//vyKiIjQypUrVblyZfn6+mrC\nhAnq2rWrU3Nt3LhRkydPttv+448/KjU1Vc2aNZN088ai7t2769ChQ4qKisowdunSpQoODlaDBg2c\nkhkAACAnmK5wPvXUUzp27Jj2799vu3Goc+fOmjBhgkqUKKEHHnhAYWFheu2115yay2KxaOXKlfr8\n8891/fp1Wa1W/fLLL3r99ddVvHhxffDBB7axQ4YMUZUqVdS7d29dvHhRaWlpCg8P1759+zR16lR5\neJju2wYAAEzMdMsiScp0uaN+/fqpX79+BqS56fXXX5e3t7cWLVqk8PBwJSYmqnDhwmrRooVGjhyZ\nYd3NQoUKafPmzRo6dKgeeeQRpaamqlKlSlq7dq3q1atn2DEAAADcC1MUztTUVMXGxio1NVWlSpUy\nOk6m/Pz81L9/f/Xv3z9b44sVK6bp06c7OBUAAIDjuWzhrFevns6fP6+4uDiVLl1a5cqVU/PmzfXK\nK68YHQ0AAAC3cNnC+b///U8tW7bU/PnznX7HOQAAALLPZe8+yZMnj2bMmEHZBAAAyOVctnBWrlxZ\n/6+9O4+Lqt7/B/46wy7K4gIKuADukrmA4C4aueaGpnkrc/fmzcyt8mqm6bfy2qKtlluLdl0oNc3S\nEjFzA00zd0VRARVFBQSU5f37wx9zZxyWGeVwZuD1fDx8OHzO53PmPZ8ZDu/5nHM+nxo1ajx0+6FD\nh5ZiNERERERUFJtNOAtbJtISx48fL6VIiIiIiKg4Nptwisgjtb9x40YpRUJERERExbHZm4aOHz+O\nrVu3wtXV1eK2ly9fLnStciIiIiIqfTabcN64cQN9+vR5qLYiAkVRSjkiIiIiIiqMzSacwKOfVici\nIiIi9dlswlm7dm1s374djo6OFrdNTExEp06dVIiKiIiIiB5kswmnv78/GjZs+FBt69WrZ7VLYD6s\nS5cuaR2CCS8vL61DMJGWlqZ1CCZq166tdQiFssa4nJyctA7BhDXGZI3vXZ06dbQOwYQ1HjcBWOX8\n0l27dtU6BL1Zs2ZpHQI9hAp7l7qHh0cpRUJERERExbHZhDMlJeWR2vOUOhEREVHZsNmE8/Tp07h4\n8eJDt//oo49KMRoiIiIiKorNJpz5+fkYMmQITpw4oXUoRERERFQMm71p6B//+AdSUlLw3HPPQVEU\nuLu7o1evXpg8ebLWoRERERGRAZtNOL/55huTspycHA0iISIiIqLi2Owp9cI4ODhoHQIRERERPaBc\nJZxEREREZH1s9pQ6EVF5cO7cORw8eBDZ2dkIDAxEaGgo7O15aCai8oVHNSIijZw7dw6//fab/udj\nx44hPT0d3bt3h6IoGkZGRFS6eEqdiEgDd+/exe7du03KL168iLNnz2oQERGRephwEhFp4NixY7h7\n9y4AoHLlyggMDNRv+/PPPx95+V4iImvChJOIqIyJCE6ePKn/OTg4GB07dtTPtHHr1i1cuXJFq/CI\niEodE04iojJ29epVZGRkAACcnJwQGBgIR0dHNGjQQF+Hp9WJqDxhwklEVMYSEhL0j/39/WFnZwcA\nRqfVL1y4wNPqZUhEkJeXp3UYROUW71InIipjly5d0j+uW7eu/rG3tzecnJxw9+5dZGVlITU1FdWq\nVdMixAohMzMTBw4cQGxsLJKSkgDcH3F+/PHH0a5dO9SpU4ezBRCVEo5wEhGVoezsbKSmpgIAFEWB\nj4+PfptOp4Ovr6/+54IkiErfsWPHMG/ePOh0OqxatQpZWVnIycnBuXPn0K9fP6xZswZffvklMjMz\ntQ6VqFxgwklEVIYMbwaqUaOGyZK8hgkobxxSx19//YXDhw9j//79WLdunf6GLUVRULNmTbz66qu4\ncOECwsPD8dlnnyE7O1vrkIlsHhNOIqIylJKSon/s7e1tst3Ly0v/+Nq1a2USU0Vy7do1xMbGIiYm\nBk2bNi2ynp2dHRYtWoSIiAj88MMPZRghUfnEhJOIqAwZJpGGyWWBqlWr6pe2vHPnDk/plrKjR49i\n8uTJqF+/fol1FUXBwoULcezYMdy+fbsMoiMqv5hwEhGVERHBjRs39D/XqFHDpI5OpzO6UciwPj2a\n7OxsnD59GmPGjDG7jbu7OwYPHox9+/apGBlR+ceEk4iojGRlZemvB3RwcECVKlUKrceEUx1XrlxB\nUFBQoSPLxRk8eLDRVFZEZDkmnEREZaTg7nTg/qnzoqbcqVq1qv7xzZs3VY+rorh37x48PDwsbufh\n4cEbh4geERNOIqIycuvWLf1jT0/PIusZbmPCWXocHByQnp5ucbu0tDQ4OzurEBFRxcGEk4iojBgm\nj8WNtBluu337NlccKiXe3t44cuSI0UizOTZu3Ag/Pz+VoiKqGJhwEpFVunbtGg4cOIBff/0Vf/zx\nB86cOYP8/PwS24kIsrKycO/evTKI0jJpaWn6x+7u7kXWc3Z2hqOjIwAgJycHWVlZqsdWEVSqVAmB\ngYFYvny52W3u3LmDb7/9FmFhYSpGRlT+cWlLIrIq8fHx+OGHH5CTk4OwsDD4+PggMzMTf/zxB779\n9ls8+eST6NKlC3Q64+/Lf//9N1auXIk7d+5ARDB8+HC0bdtWo1dROMOE083Nrch6iqLA3d1dP2fn\n7du3UalSJdXjqwiCgoKwYMECDB061KxRy9mzZ6N+/fpG19Vai+zsbNy+fRv5+fmoVKlSsV9iiLTG\nhJOIrMb27duxefNmPPnkk+jVq5fRTTXBwcG4fPkyPv/8cxw6dAgTJkyAi4uLfntQUBDmz5+Pb7/9\nFrGxsVqEX6y8vDxkZGTofy7qDvUCbm5u+oQzPT0dtWrVUjW+isLHxwfNmjVD586dsWPHDqO17A2J\nCN58802sXr0aL730UhlHWbyLFy8iNjYWx44d069Wde3aNXh5eaFVq1Zo3ry5fi5XImvBU+pEZBV2\n7tyJzZs3o2PHjujdu3ehd3AHBgZiwoQJiI+Px+LFi5GXl2e03cnJCU2aNCmrkC1SMPIKAK6uriUm\nBIYJ6cPc6EJFCwkJQUBAAJo3b45x48bh77//1m+7c+cOli5diubNm2PVqlWYMGECKleurGG0/5OX\nl4cff/wRUVFR6N+/P86fP4/4+HicOnUKKSkpeOedd3D58mV8+umnvNmMrA6/AhGR5pKSkrBx40a4\nubmhX79+xdatV68eOnbsiJiYGGzcuBEDBw4soygfjWHSaE4Cw4RTXS1btkSnTp2wb98+dO7cGdnZ\n2XByckJGRgaCgoLQsWNHNGrUyOTSDa2ICDZt2gR7e3ucOHHC5PS5vb09BgwYgP79+2PhwoVYuHAh\nxo0bV+JIOlFZYcJJRJrbunUr8vPzERISAgcHhxLrd+rUCTExMdixYwe6detmE9euGZ5ONyfhNKxj\n2JZKj4eHB3r06IHu3bsjOzsbubm5cHFxscrT0X///Tdu3LiBgwcPFvv5URQF06ZNQ0pKCn766ScM\nGTKkDKMkKpp1fHUjogorLS0Nf/31FwCgQYMGZrXx9fVFlSpVkJubiz179qgZXqm5c+eO/rE5Caer\nq2uhban0KYoCFxcXVKlSxSqTTQA4ePAg3nzzTbNP78+cOROnT5/mGvBkNazzN4uIKoyTJ0/qH/v6\n+prdzsfHB6dOncLx48fRs2fPQuscPnwYe/bswd27d5GamgofHx/07NkT9erVM6qXk5ODX375BceP\nH4ednR1EBAEBAfqYQkNDLX9hDzBMGg2TyaI8OMIpIkWuTETl27Vr13D16lVERkaa3cbNzQ1Dhw5F\nXFwcunXrpmJ0ROZhwklEmrp69ar+seFd5yUpSNoM2xuKjo5Gy5YtMXbsWNjb2yMvLw+bNm3Cu+++\ni2effRbt27fX112+fDk8PT0xdepU/TV7R48exWeffYbnnnvuYV6WCUsTTgcHB9jb2yM3Nxd5eXm4\nd+8enJycSiUWsi1JSUno0KGDfm5Wc/Xo0QPz5s1TKSoiy/CUOhFpyjARs7OzM7tdQd2iTjf7+/uj\nZ8+e+lOkdnZ2GDBgAIKCgrBq1SpcunQJAJCVlYU///wT7du3N7pB5LHHHivVyb4zMzP1j81JOBVF\nMapn2J4qlpycHLM+Mw9ydXVFTk6OChERWY4JJxFpyvAmoezsbLPb3b17FwCKHPWrXr16oeWhoaHI\nz8/Hzz//DOB+YmdnZ4cff/zR5OYcf39/i5Lg4hgmjOaO5BpO9s7rOCsuZ2dnXL9+3eJ2169f56g4\nWQ2eUi8nzL3ZoixZ44Gudu3aWodgwhpjKksZGRnYtWsXFEVBSEhIsZ/lglFJ4H/Jqb+/P4KCgvTl\nFy9eBADUqlXLqLyAnZ0dli5dipMnT+q3Dx8+HMuXL8fRo0fRsGFDNGjQAKGhoRg3blyJ0+K0a9eu\nxNeYn5+PZcuW6X+eMmWKWb8fFy5cQHJyMoD7d+b37t27xDbA/TXDqWQ7duzQOoRCPfiZevLJJ9G5\nc2fcuHED1apVM3s///3vfzFkyBAMHTr0kWMy/N0jehgc4SQiTXXs2BHA/XkGDx06ZFab3NxcnD9/\nHgDQpk0bi56vYF7CzMxM/enGkSNH4r333kPXrl1x5coVbNq0Cf/+978xevRo3Lhxw6L9F+b27dv6\nSeqrVKli9pcxw+QiNTX1keMg21S1alVEREQYfWkpyYULF/DHH3+UOK8tUVlhwklEmqpbt65+RMfc\nKY5iY2ORk5MDOzs7s0f9ChScNndzczM6nR8aGorZs2frV3IZM2YMzp8/jwULFli0/8IYrvri6elp\ndjvDhLM0El+yXSNGjMDChQtx6tSpEuvm5ORg3LhxePbZZy26EY9ITUw4iUhzb7zxBhwdHbF169Yi\n7zo3tH79egDAM888g5o1a1r0XGfOnAEA/V3q165dw6uvvmpUx9vbG8OHD8fo0aMRFxdn0f4LYzg6\naUnCaVj31q1bjxwH2a7HHnsMr776Krp27VrsZzItLQ0DBgxAfn4+XnnllTKMkKh4TDiJSHNNmjTB\nlClTcPfuXbz++uvF1v3tt9+wf/9+NGjQAKNHjy6yXsEpd0Migi1btqBSpUp4/vnnAdxfn3rfvn24\ncuWKSX1fX194eHgYle3YsQNjx47Frl27zHlpAIyTxapVq5rdzvC5mXDS008/jVmzZqFnz56IiIjA\nhg0bcPnyZVy9ehVxcXF48cUXUbduXVStWhVLliyx2knsqWJiwklEVmH8+PGYMWMGduzYgZkzZ+qv\neTQUExODefPmoWXLlli8eHGRf1AdHR3h4uKC7777Dvn5+QDu39W+aNEinD9/HnPmzIGfn5++fl5e\nHmbNmqW/QQe4fxr8u+++M7nhYsWKFTh+/DhWrFhh9mszXO3FkmU4mXDSg3r37o09e/agT58+WLBg\nAUJCQtCsWTP84x//gLOzM7Zt24b58+ebtUQsUVni1x8ishrjxo1D06ZNMX/+fHTv3h3Dhg1DQEAA\nbt26hY0bN+LAgQN47rnn8Pzzzxc7evPUU09h0qRJ+OWXXzBt2jRkZ2cjMzMTzZo1w4oVK+Dj46Ov\na29vj7CwMIwfPx6LFi1CamoqnJ2dAdw/Zd+lSxejfffu3RvLly9H9+7dzX5dTDipNDk7O2PgwIEY\nOHCg1qEQmU0REdE6CHo0iqLg2rVrWodhwhqnRbLGmKzxvbMGJ06cwOHDh3Hjxg24uLigQYMG8PX1\ntXi1FbW5ubmVWOeDDz7A8uXLAQATJ07EmDFjzNr3lStXEBERAQDw8vLCb7/9ZlY7TotkHluZFska\nWNO0SO3btwdTF9vDEU4iskpNmjRBkyZNjMqs6Y+eJdLS0vSPzUlQC6truA8iIlvDaziJiFSWnp6u\nf1wwD6g5XFxc9JcOZGdn61dXIiKyNUw4iYhUZrhkpiUJp6IoRvUfXHqTiMhWMOEkIlLZw45wAoCr\nq6v+MRNOIrJVTDiJiFR2584d/WPDBNIcHOEkovKACScRkcoeJeHkCCcRlQdMOImIVPYoCWelSpX0\nj7OyskotJiKissSEk4hIRSKCzMxM/c+GCaQ5DOsb7oeIyJYw4SQiUlFOTo5+mU57e3uLlxxkwklE\n5QETTiIiFRmeBrd0dBO4PxdnYfsiIrIlTDiJiFRkmCQWrNFuCcM2nPidiGwVl7YkIlJRdna2/vGj\nJpyG+yKyBikpKYiPj0d2djaqVKmCZs2awcnJSeuwyAox4SQiUpHhqOTD/CE2TDh5Sp2sRVxcHDZs\n2IA///wTLVq0QKVKlZCSkoKzZ8+iR48eGDBgAHx9fbUOk6wIT6kTEanoUUc4DZNUnlInreXn52Px\n4sX48MMP8fTTT+PSpUuIjo7Gli1bcODAAcTFxcHPzw/jx4/HH3/8oXW4ZEU4wklEpKJ79+7pHzs6\nOlrc3rCN4b6ItPDpp5/i4sWLOHToEDw8PEy2BwQEYMGCBYiMjESfPn3wxhtvoHXr1hpEStaGI5xE\nRCoyHJV8mITTcISTCSdp6cSJE9i1axe2bNlSaLJpKDQ0FKtXr8Y777yjnxaMKjYmnEREKsrJydE/\nfpiE03DeTp5SJy1t2LABL730Ejw9Pc2qHxERAR8fH+zdu1flyMgWMOEkIlJRaSachvsiKksZGRnY\ntWsXRo0aZVG7f/3rX9i8ebNKUZEtYcJJRKQiw9Pglq4y9GCb3NzcUomJyFLJycnw8/ND9erVLWrX\nrl07XLhwQZ2gyKYw4SQiUpFhkmhvb/l9moZtmHCSVu7du/fQ03rx2mMCmHASEanK8IaJh0k4eUqd\nrIGHhweuXLkCEbGoXWJiYok3GFHFwISTiEhFhgmnnZ2dxe0N23CEk7Ti4+ODKlWqIDo62qJ2X331\nFTp06KBSVGRLmHBasfXr16N169bw9vZGnTp1MG3aNK40QmRjHvWUuk73v8N0fn5+qcREZClFUdC3\nb18sWrTI7Dbp6en473//i6eeekrFyMhWMOG0UsuXL8eQIUMwdepUXL16Fbt27cLGjRvRp08f/tEh\nsiGGI5yKoljc3nCEk7/7pKUnn3wScXFx+Prrr0usm5eXh+HDh6NTp06oUaNGGURH1o4JpxW6efMm\nJk+ejMGDB+OZZ54BANSrVw/vvfceoqOjzfplJ1O///671iFUOJx/D0bXvD3MKXVLRzhjY2Mtfg56\neMePH9c6hDLj6uqKBQsWYNq0afjggw+KvBkoJSUFkZGRSEpKwiuvvFLGUZK1YsJphdauXYu0tDQM\nHDjQqLxHjx5wcXHB0qVLNYrMtu3evVvrECqcffv2aR2C5gwTzocZ4WTCad0qUsIJAP7+/vj444+x\nevVq1KlTB7NmzUJMTAxiY2OxZcsWDBs2DPXr14eTkxPefffdh5p7lsonrqVuhXbt2gUAaN68uVG5\ng4MDmjRpgv379yMnJ+eh5vQjorJlmCQaJo/mMkxSLb1DmEgNvr6+WLRoEc6fP4+NGzdi69atyM7O\nRuXKlREaGoo1a9bAzc1N6zDJyjDhtEKnT5+GoiioVauWyTYfHx8cOnQI8fHxaNSokQbREZElHnWE\nMy0tTf/4zJkzpRITUWnw9/fHpEmTtA6DbIQi/MpsdRo2bIhz584hOzvbZBRz6NChWLt2Lfbu3YvQ\n0FAAD/dHjIiIyFYxdbE9HOEsB/iLR0RERNaMNw1ZIXd3dwBAZmamybaCsoI6RERERNaOCacVatiw\nIUQEycnJJtuSkpJgZ2eHgIAADSIjIiIishwTTivUuXNnAMCRI0eMynNycnDixAmEhYVxqgkiIiKy\nGUw4rdDgwYPh5uaGH374wah869atyMrKwqhRozSKzLplZ2dj5cqVCA8PR40aNeDp6YlGjRphxowZ\nuHPnTqFtMjMzMWXKFNSpUwfe3t4IDg5GVFRUkc8RHR2Njh07wtvbGz4+PhgzZgxSU1PVekk2Y+vW\nrfD19UV4eHiRdXbu3AkXFxfUqlXL5N+0adMKbcP+Lpo5fQ7wM66WLl26wMvLy+Sz7OPjg6tXr5rU\nt/R9IFNc7tnGCVmlZcuWiZ2dnaxatUpERM6fPy8NGjSQbt26SX5+vsbRWad//vOfotPpZMmSJZKb\nmysiIhs3bpTKlStLcHCw3L1716h+bm6uhIeHS+PGjSUhIUFERL755hvR6XSyfPlyk/3/8ssvYm9v\nLwsWLBARkZSUFGnbtq00a9ZMMjIyVH511ik9PV3GjRsngYGBoiiKhIeHF1l3586dMmLECLP3zf4u\nnCV9zs+4erp06aLv05JY+j6QqWXLlolOp5PVq1eLyP/+Jnbt2lXy8vI0jo7MwYTTiq1bt05atWol\nXl5e4ufnJ1OnTpWsrCytw7Ja48ePl2eeecakfMaMGaIoinz55ZdG5cuWLRNFUWTr1q1G5QMHDhQP\nDw+5efOmviwnJ0cCAgIkLCzMqO5ff/0liqLI7NmzS++F2JCxY8fK2LFjJT09vcTkJzo6Wl544QWz\n9sv+Lpolfc7PuHq6dOkiFy5cMKuuJe8DmUpNTRV3d3cZMmSIUfmmTZtEURRZsWKFNoGRRZhwUrmx\nadMm2bNnT6HliqLIuHHjjMrDwsKkSpUqJiPGq1atMklQf/75Z1EURd59912T/Tdo0ED8/PxK6VXY\nlqSkJP3j0kw42d9Fs6TP+RlXjyUjnJa8D2Tq888/F0VRZM2aNUbl9+7dk0qVKkn79u01iowswWs4\nqdx46qmn0LZtW5Pye/fuAQA8PT31ZdnZ2Thw4ACaNm1qMnF+wZKiBUuMGj5+cLnRgrLExEScO3fu\n0V+EjSlsNayiWLJAAfu7aOb2OT/j6hMz5kC29H0gU+Yu90zWjQknlXtxcXEAgIEDB+rLzp07BxEp\ncvlQwHgZwdOnTwMo/I99Qf2zZ8+WXtDlkIjgzJkzGDRoEAIDA+Ht7Y2OHTti5cqVJnXZ34+On3H1\nLVq0CC1btkStWrVQv359jB07FgkJCUZ1LH0fyFRJyz3n5eUhPj5eg8jIEkw4qVxLT0/HV199hcjI\nSISEhOjLb9++DQCoVKmSSZuCslu3bj10fSpcQkICxo8fj3PnzuHkyZPo2bMnRo0ahX/+859G9djf\nj46fcfXdvXsX27dvR1JSEtasWYO9e/eiVatWOHHihL4O+/XRsQ/LBy5tSVYnMzMT33//vdn1BwwY\nAFdX10K3TZ8+Hc7Ozvj8889LK7xypzT7uzjt2rXDyZMn9W09PT0xY8YMHDp0CEuWLMGzzz6L9u3b\nW7xfW1RWfU7Fe5T3Yf369ahWrZp+W+vWrbF69Wq0aNECEydOxPbt20s9XiJbxoSTrM61a9fw/PPP\nm1VXURS0a9eu0JWXPv74Y6xduxZ//PGH0R8GwPLlQ8vzcqOl1d8lcXR0LHTBgr59++L777/H5s2b\n9Qlnee5voGz6nJ/xkj3K+/DgMQUAHnvsMdSpUwcxMTHIysqCi4tLhezX0mbYhw/2FfvQdjDhJKtT\nt25di06PVKlSxaRs1apVmDVrFrZv347GjRubbA8MDISiKEUuHwoADRo00Jc1bNgQAJCcnIzHH3+8\nxPq2pDT6+1F4eXkBAFJSUvRl5bm/gbLpc37GS6bG++Dt7Y2LFy/ixo0b8PPzs/h9IFMNGzbEwYMH\nkZycbJJYcrln28FrOMnqKIoCNzc3s/89eOfnDz/8gAkTJmDz5s0IDg4GAGRkZOhvigAAZ2dnhIaG\n4tixYyZ3mv71118A7q8kUqCo5UYL6hf8YbFFj9rf5vrwww9x/fp1k/KCVVmqV6+uLyvP/Q2UTZ/z\nM16yh30fjhw5gvXr1xe6z6tXr0Kn06Fq1aoALH8fyBSXey4fmHBSufLzzz9jxIgRiIqKMroeMC4u\nDuPGjTOqO3r0aNy5cwe//PKLUfn69evh4eGBQYMG6cu6desGf39/k+VG//rrL5w9exYjR45U4dWU\nLx9++CF+//13k/ItW7YAAHr06KEvY3+XDn7G1fHnn39i3rx5JuXHjh1DQkIC2rdvb3SDiyXvA5ni\ncs/lhHZTgBKVrp07d4qLi4t06tRJZs+ebfRv+PDh0qVLF6P6eXl5Eh4eLo0aNdKvGFKw3FxhK1ds\n27ZN7O3t5d1335X8/Hz9sn9BQUFc9k/uT0L+YB8bqlevntSvX1/i4uJERCQzM1MWLlwoOp1Ohg0b\nZlKf/V2ykvqcn3F1rFy5UhRFkRkzZsidO3dEROTYsWPSokULqVKlivz5559G9S19H8gUl3u2fUw4\nqdzo37+/6HQ60el0oiiKyb/CVmTJzMyUKVOmiJ+fn3h5eUnr1q0lKiqqyOeIjo6WDh06iJeXl9Sq\nVUtGjx4tqampar4sq7Zjxw5xdnYWZ2dn0el0YmdnJ87OzuLi4iL37t0zqhsbGyv/+te/pFmzZlKz\nZk2pUqWKBAcHy8cff1zk/tnfpizpcxF+xtWQlpYmX375pTzxxBNSu3ZtqVq1qtSqVUueffZZOXny\nZKFtLH0fyBSXe7ZtiogZSyUQERERET0kXsNJRERERKpiwklEREREqmLCSURERESqYsJJRERERKpi\nwklEREREqmLCSURERESqYsJJREQE4ODBg2jTpg0uX76sdShE5Y691gEQERFpKSoqCps3b4aiKIiL\ni0N+fr7WIRGVO5z4nYiICEBMTAzCw8Nx4cIF1KlTR+twiMoVnlInIqpA6tWrh/DwcISHh2PDhg1a\nh2NVzB1/2bBhg74P/f39VY6KqHzgCCdROSIiSEtLg6OjI1xcXFR/vvT0dCiKgsqVK6v+XI/KlmJV\nk06nK/SUcVl/dqzRzp070bVrV4tGOIvqTyIyxhFOIgudPn0abdu2Rc2aNaHT6aDT6eDo6Ih27doh\nPDwcnTt3RocOHdClSxfMmTMHiYmJqse0YcMGeHl5wdHREZ6enli7dq1JncGDB6NmzZrYs2fPIz3X\n33//jVq1asHJyQnu7u547733SmyzaNEitGjRAg4ODvo+c3V1RUhICPbt22dS/+zZs2jQoIG+wGnK\npgAAIABJREFUrk6nw2OPPYbTp0+rHmtpKq0+V9PWrVtL/OwQET0qJpxEFmrYsCH27t2L5ORkdO/e\nHQAwYsQI7NmzB9HR0YiJicHu3buxdu1aXLx4Ef7+/njrrbdUjal///6Ij4/H008/DQBQFMVo+40b\nNxAVFYVr165h3bp1j/RcQUFBuHDhAiZNmlTocxXm5ZdfxuHDh/H777/r26xevRqxsbEICwszqV+/\nfn2cOXMGkyZNgre3Nw4fPoyjR4+iYcOGqsdaWszp84MHD+LIkSNlFlNhevbsifPnzxf52SEiKg1M\nOIkekqIo8Pb2BgC4urqabPfy8sKyZcsQEhKC2bNnY/LkyarGU7lyZTzxxBOFbqtWrRpef/11dOzY\nEePHj3/k53JyckKPHj0sbhcWFoY2bdpARLBlyxaznmfGjBlo3rz5w4Sp38fDxPqozOnzzZs34/Dh\nw2UcmSlXV9ciPzu2JCoqChERESX+69WrF+7cuaN1uEQVCqdFIlJZ3759sXfvXixevBivv/46atSo\nodpzFTc6NX/+/DJ7ruK88MILOHDgANauXYvFixfD2dm50Hr5+flYt24dYmNjHyVMANqN2pXU57t3\n77aam07Kw8hmZGQkIiMjtQ6DiArBEU4ilVWtWhXA/ZsyLly4oG0wVuCZZ56Bk5MT0tLSEBUVVWS9\nX3/9FS1btoSnp2cZRld2Tpw4gR07dmgdBhFRmWDCSaSypKQkAICjoyPq16+vWRx5eXm4fv06bt26\npVkMAODu7o7+/fsDAFauXFlkvZUrV2LEiBFlFJU6CuvzvLw87Nu3D5GRkRARs6fiIfUV3G2el5en\ncSRE5Q8TTiIV5eTkYO3atVAUBTNnzix0tC4uLg5TpkxBZGQkunXrhscffxxjxozB+fPni9zvyZMn\nMWbMGAQHB6NTp07o1KkTvvjii0KTl5s3b6Jq1apwdHSEl5cXFi1aVCoxPIoXXngBwP1paC5dumSy\n/fbt29i/f3+J115+//336NatG5544gmEhISgc+fOZl0b+qADBw5g0KBBCA0NRZcuXRAWFoZ33nmn\nyOv8jhw5gmeeeQZt2rRB165dERERgYkTJ+pfS3F9/sknn+D1119HVlYWAOCdd97Rz+k4cuRIfb2V\nK1eiadOm+rv03dzc8Morr+i3f/fdd3B2doZOp0OlSpUwZcoUi193Sb766iujmQKaNGmCY8eO4dy5\ncwgPD0ezZs3g7e2NhQsX4tatW3j55ZfRp08fNGvWDF27dsWBAwcA3P/SNXbsWPTq1QsNGzZEp06d\nsHv3brPjuHv3LubOnauf/aFz58547bXX8Nprr2HVqlWP/Dq3b9+OwYMH44UXXoCiKOjRoweGDh2K\nP//885H3TUT/nxDRQxs+fLgoiiKTJk0yKr93757s3LlTOnXqJG5ubrJo0aJC2ycmJoqzs7O0aNFC\ncnJyREQkMzNTBg0aJG5ubrJ//36TNqtXrxYXFxeZNWuW5ObmiohIbm6uvP322xIYGCiKoshXX31l\n1CYtLU1effVVURRF5syZ88gxiIhER0cXuj9z5OXlia+vryiKIm+99ZbJ9s8//1ymT59e7D4mTpwo\nfn5+cvr0aX3Z6tWrxc7OTpYvX252rIsXLxYPDw/ZsmWLviw1NVWGDRsmQUFBcvHiRaP6X3/9tTg5\nOcnbb7+tL7t796506tRJ6tWrp39PiutzEZE333yz0PfqQa+88oooiiLvv/++ybbly5dLw4YNJSkp\nqdh9GFIUpdDyFStWFBpP48aNpUOHDvLXX3/py9LT02Xbtm3Sv39/URRFZs+eLf/4xz/kwoULIiKS\nk5MjISEh4uHhIcePH5enn35akpOTReT+70ZwcLBUrlxZEhMTzYo5MjJSJk2apO9bEZEtW7aIg4ND\nif2ntqL6k4iMMeEkegQFCaefn5906dJFunTpIm3atBEHBwdRFEVGjhwpN2/eLLL9uXPnxMXFRWrV\nqiWZmZn68ps3b4qTk5OEhoYa1T9w4IA4OjpKz549C93fqFGjikxifv3110KTH0tjKPAoCaeIyGuv\nvSaKokj9+vVNtrVr105OnDhRZNuvvvpKFEWR1atXm2zr27evVK1aVbKyskqMdevWraLT6eTzzz83\n2U9+fr40bdpUQkND9YnOoUOHxNHRUXr37m1U99ChQ6IoitjZ2Rm930X1uYjI7NmzzUo4ExISxM7O\nTtq0aWOybcGCBbJu3bpi2z/IkoTz7bfflpEjRxoleoYKXl/NmjUlLi7OaNvbb78tiqJIvXr19Ilo\ngf/7v/8TRVHkiy++KDHe27dvi6IoRglvgZEjR8rKlStL3IeamHASmYen1IlKweDBgxEdHY3o6Gjs\n378fN27cwIQJE7BixQrMmjWryOv0AgICkJSUhLNnzxqt7uLh4QFvb2+TU3pz5sxBTk4ORo8eXej+\n/Pz8iozRzs6uVGIoLQWn1ePj441Or546dQp5eXlo3LhxkW3nzZsHnU6Hfv36mWwLDw/HzZs3sXfv\n3hJjeP311wEAgwYNMtmmKAr69euHAwcO4PvvvwcAzJ07Fzk5OSbXlrZs2RJffvkl1q1bBw8PD315\nUX1uiTp16qB79+6IjY01ei9EBD/++CMGDBjwyM9RmOnTp+PWrVtYtmxZka+joLx27dpo3bq10baC\n2RiCg4NRt25do21eXl4AgGvXrpUYh06ng4ODA2bPno3r168bbQsNDYWDg4N5L4iINMVpkYhUUKVK\nFXz00Uc4d+4cPvnkE9SuXRvTp08vtK6Hhweys7OxYcMG/Pbbbzh+/Dhyc3Nx7do15Obm6uvl5eXh\nl19+gaIoaNmyZanGa24MpalRo0YIDQ3F/v37sWLFCnTo0AFAyTcLnT9/HmfPnoWdnR169+5tsj0j\nIwP16tVDdnZ2sc9/6dIlHDlyBM7OzqhWrVqhdWrXrg3g/rWigwYNwk8//QRFUdCiRQuTuqNGjSr2\n+R7F+PHjsXXrVixZsgSff/45AGDHjh3o2LFjqSS1hnJzczFixAh89dVX+OCDD8xqU9iE/AVxNWrU\nqMht5tycU7lyZcyYMQNz5szB5s2b0bJlS7Ro0QI9evTA6NGjodNx3ITIFvA3lUhFBaNPn3zySZF1\nvvnmG9SpUwdz5sxBu3btsH79esTExOgnlS+QkpKi/wNd2lMFmRtDaSsY5Vy/fj2ys7ORn5+P9evX\n45lnnimyzdWrVwEADg4O+lFlw3+xsbGIj49Hz549i33uy5cvA7g/e0BRCkbPLl26hJSUFOTk5AAo\n/f4vSe/eveHn54fVq1frb2RaunQpxowZU+rP9cYbbyA4OBiBgYGYMWMGzp49W2Kb4vqwuG3mmj17\nNrZu3YrBgwcjISEBX375JSIjIxESEoIrV6488v6JSH1MOIlUVJCYXL582eR0IAAsXrwYw4cPR9u2\nbREbG4tnnnmmyGSmevXq+pGhu3fvllqMlsRQ2oYOHQonJyekp6dj3bp12LZtG0JCQuDm5lZkm4LL\nBu7evYsbN2489HMXJNOZmZlF1klJSQFw//RwtWrV9KNpN2/efOjnLc5HH32kv7PbkE6nw+jRo5GR\nkYFvv/0WV69e1Y/klrYZM2boLwfJzs7GCy+8YBVTN3Xv3h2rVq3ClStXkJCQgLfeegvHjh3D2LFj\ntQ6NiMzAhJOojJw8edKkbMGCBVAUBQsXLoS9vfEVLvfu3dM/3r59O6Kjo/Hkk09CRPD333+XWlzm\nxrBt2zZs37691J4XuD8nZ8Eo8IoVK/DVV1/pRz2L4ufnh8cffxwign379hVaZ//+/SWuUR4QEID6\n9esjNze3yOmfzp07BwDo0aMH7Ozs8MQTT0BEsH///kLrJyYm6tuUpCB5NUzmbty4UeSXidGjR8PO\nzg5LlizBypUrjaZQKk0FSWyHDh0wceJE7Nmzx+xT62q4fPky+vbta1RWu3Zt/Pvf/8Zbb72F3377\nTaPIiMgSTDiJVFQwUiciRgnQ7t27kZSUhLS0NAD/u4miwJkzZ4xOFSYmJiI5ORkzZ86EnZ0dvvnm\nm0Kf7+DBgwBg0XWX5saQlJSE5ORks/drroIEMyYmBnFxcYiIiCixzfz586EoCpYvX17o9rfffht1\n6tQpcT9z584FAKxbt85kW15eHn788Uc0btwYw4cPB3D/1K6dnR0+/fTTQvc3e/bsEp+zQEFiZ3jj\nTGJiInx9fQut7+Pjgz59+uDw4cP4+uuvTZIwNbz99tuoX78+Zs6ciVOnTqn+fIXJzc3Fzz//jISE\nBJNtAQEBqi4VS0Slhwkn0UPKz8/XJ2RFJWLt2rXTn542vBP7s88+Q2ZmJp599lmICObMmaMf6UpK\nSsL48ePRp08f/XKY8fHxaNCgAdq2bYtPPvkEq1evxkcffaRvk5GRgUmTJumvS/z6668RExOD9PR0\n/XPevn0bwP8SzAKWxlCgYD8F+31YERER8PX1hYjg6aefNmtN7169euG9997Dpk2b8Nlnn+nL7969\ni8mTJ2PAgAFGlwUUFevQoUMxf/58zJ8/H7/++qu+PDc3F9OnT4ebmxs2btyoX++9bdu2+Oyzz3Dg\nwAFMmDBBf2NSfn4+PvjgA3h7eyMwMFC/n6L6HAD69OmD6tWrY8OGDRAR3Lp1C5cvX0ZAQECRr3v8\n+PEAgIEDB5b6zUIFMaampurLnJ2dMXnyZGRnZ2PIkCEmq1QVtCns9RX3+bD0s5Obm4unn37aaGnY\na9eu4b333sPkyZPN2gcRaazMJ2IisnGnTp2SsLAw8fb2FkVRRKfTiU6nEx8fH2nXrp2cPXvWqH5M\nTIwEBgaKi4uLLF26VD7++GN57rnnROT+XI+ffPKJhISESKNGjaRbt24SGRkpx44dk8TERAkJCZGg\noCCTieP3798vAwYMkNatW0t4eLgMGDBAfv/9d3nrrbekRo0aEhQUJOHh4XLs2DE5e/astGnTRipV\nqiQ6nU7s7OykVatWcuDAgYeK4eTJkxIaGiqurq76/bVo0ULWr1//0H36+uuvi06nM5rE3Rz79u2T\nQYMGSXBwsHTv3l369+8vv/76q377qVOnzIp17969MnjwYOnQoYN069ZNOnfuLHPnzpW0tLRCnzc2\nNlYGDx4sTZs2lfDwcOndu7fR/JUl9XmBw4cPS3h4uDz++OPSvXv3YuceFbk/YX7t2rUlISHBon4y\n9OC8kTExMRIcHCxOTk6i0+nEyclJgoOD5dChQ5KQkCBeXl76z7i7u7sMHz5cTp06JW3atNH3q6Io\nEhQUJEuXLpUDBw5ISEiIfn8Ffb5mzRqT5zLcVpTExETp1auXHDlyRPr16ydhYWHStWtX6dq1q0RF\nRT10P5QWzsNJZB5FxAquBicq5/Lz8/Hbb7/h5MmTcHZ2xvPPPw8nJyetw7IaSUlJ+PHHHzFu3Dit\nQ7FqiYmJ+Oc//4lNmzY99D50Op1+zXB6dOxPIvMw4SQiskL5+fmIjo5G27ZtUalSJQDAm2++iVat\nWj3S9ZtMkEoX+5PIPLyGk4jICn3xxReIiIjQLxiQnp6OmJiYMrlZiIiotDHhJCKyQtWrV4eTkxPa\nt2+P7OxsjB49Gv/+97+1DouI6KHwlDoRkZWaMmUK4uLikJubi8mTJyMyMvKR98lTwKWL/UlkHiac\nREQViL+/v34O0Jdffhn9+/fXNiAbtGHDBixatAgAkJCQgPj4eI0jIrJ+TDiJiIiISFW8hpOIiIiI\nVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhU\nxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTF\nhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWE\nk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhUxYST\niIiIiFTFhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOI\niIiIVMWEk4iIiIhUxYSTiIiIiFTFhJOIiIiIVGVvSeUqVaogIyNDrViIiIiIyEZ5enoiNTW10G2K\niIi5O1IUBQXVH/z/YcpKaz/WFsP777+PV155pcL3Q0lly5Ytw6hRoyp8P5gTw/r16xEZGalpDGVd\n9jBttm3bhoiICE1jsIZ+KKls3759CA0NrfD9UFLZyZMn0bhx4wrfD+bEkJSUhFq1amkaQ1mXPUyb\njIwMuLq6ahqDmv3w4GNDPKVORERERKpiwklEREREqmLCqYKwsDCtQ7AJLVu21DoEm9G0aVOtQ7AJ\nAQEBWodgE3x9fbUOwSZUr15d6xBsRpUqVbQOwSY4ODhoHYJmmHCqoG3btlqHYBNatWqldQg2gwmn\neQIDA7UOwSb4+flpHYJNYMJpPiac5nF0dNQ6BM0w4SQiIiIiVTHhJCIiIiJVMeEkIiIiIlUx4SQi\nIiIiVTHhJCIiIiJVMeEkIiIiIlUx4SQiIiIiVTHhJCIiIiJVMeEkIiIiIlUx4SQiIiIiVTHhJCIi\nIiJVMeEkIiIiIlUx4SQiIiIiVTHhJCIiIiJVMeEkIiIiIlUx4SQiIiIiVTHhJCIiIiJVMeEkIiIi\nIlUx4SQiIiIiVTHhJCIiIiJVMeEkIiIiIlUx4SQiIiIiVTHhJCIiIiJVMeFUwd69e7UOwSYcOnRI\n6xBsxvHjx7UOwSacO3dO6xBswuXLl7UOwSZcv35d6xBsRnp6utYh2IR79+5pHYJmmHCqYN++fVqH\nYBP+/PNPrUOwGUw4zRMfH691CDYhMTFR6xBsAhNO8zHhNE9OTo7WIWiGCScRERERqYoJJxERERGp\nShERMbuyoqgZCxERERHZKE9PT6Smpha6zd6SHVmQmxIRERERAeApdSIiIiJSGRNOIiIiIlIVE04i\nIiIiUpVZCef69evRunVreHt7o06dOpg2bRqysrLUjs2mJSYmwt3dHTodc3pD9+7dw6JFi9CiRQvU\nrFkTtWvXRq9evThZPoCvv/4aHh4eGDFiRKHb9+3bh+HDh6NOnTqoXr06vLy8EBkZicOHD5dxpNoq\nqZ8KbN++Hd27d0edOnVQtWpVNGzYECNGjMCNGzfKKNKyd/v2bSxevBht27ZF9erV4eHhgcceewz/\n+c9/kJuba1L/+vXrGDVqFHx8fODt7Y1OnTohJiZGg8jLlqX9ZGjy5MnQ6XSYM2dOGUWrLUv76u+/\n/8agQYNQt25deHt7o1mzZpg7dy4yMzM1iL7sZGRk4IsvvsBTTz2F+vXro2bNmggICMDzzz+Ps2fP\nGtWtsMdyKcGyZctEp9PJ6tWrRUTk/Pnz0qBBA+natavk5eWV1LzC6tu3ryiKIjqdTutQrMrQoUPF\n3t5e1q9fLyIiGRkZMmzYMLG3t5dt27ZpHJ02rl27JgMGDJCAgABRFEVGjBhhUmf//v2iKIr069dP\nrl69KiIiCQkJ0q5dO3F2dpY//vijrMMuc+b0U4HFixdLtWrV5KeffhIRkby8PJk3b54oiiLHjh0r\nq5DLXM+ePcXFxUU2bNggIiK5ubmybNkysbOzk6eeesqoblpamjRt2lQ6dOggN27ckPz8fHn77bfF\n3t5etm/frkX4ZcaSfjIUGxsrdnZ2oiiKzJkzp6zC1ZQlfXX48GFxcXGRJ554QlJSUkREZOfOneLm\n5iadOnUq89jLUnR0tCiKIhMmTJCMjAwRETl9+rQ0b95cPDw8JD4+XkQq9rG82IQzNTVV3N3dZciQ\nIUblmzZtEkVRZMWKFWrGZrPWrl0rAQEB0qZNGyacBi5evCiKosjgwYONym/fvi12dnbyxBNPaBSZ\ntnr16iUzZ86UM2fOFJlI7d27V1xcXCQtLc2o/PTp06IoirRv376swtWMOf0kInL06FGxt7fXf0k2\n1K1bN/2Bvzzq0aOHvP766yblw4YNE0VRjBLJWbNmiaIocuLECaO6rVu3lsDAQMnNzVU9Xq1Y0k8F\ncnJy5PHHH5chQ4ZUqITTkr4aOXJkoV/qpk6dKoqiyO7du1WPVyvR0dHi6+trUv7zzz+Loigyc+ZM\nEanYx/Jiz/euXbsWaWlpGDhwoFF5jx494OLigqVLl6o6+mqLbt26hZdffhlLliyBi4uL1uFYlYLl\n9OrXr29U7ubmhmrVqiEpKUmLsDS3bNkyvPXWW7C3L3qWstq1a2PhwoWoUqWKUXmDBg3g6emJuLg4\ntcPUnDn9BAALFy5EpUqV8PTTT5ts+/XXX+Hv769WiJobNmwYnn/+eZPysLAwANB/TkQEy5YtQ+PG\njdG4cWOjugMHDkR8fDyio6PVD1gj5vaToYULF8LNzQ3jx49XPT5rYklfJSYmQlEUk2N8QEAAAJTr\nY3yrVq2wbds2k3I/Pz8AQFpaGoCKfSwvNuHctWsXAKB58+ZG5Q4ODmjSpAn2799fodcFLczUqVMR\nERGBJ554QutQrE6DBg3g6OiIkydPGpWnpqbi+vXraNasmUaRaatmzZol1vH19cWLL75Y6LacnBx4\nenqWdlhWx5x+AoAff/wRzZs3h52dncoRWZ/nnnvOJIEE7l87DUD/OTl79iySk5NNju3A/473Bcf/\n8sjcfipw9uxZvPvuu/jiiy/KJD5rYklfPfbYYxARk2P86dOnAaBcH+Pd3NzQtGlTk/JDhw4BADp2\n7AigYh/Li004T58+DUVRUKtWLZNtPj4+yMvLQ3x8vGrB2ZqdO3fixx9/xAcffKB1KFapWrVqWLBg\nATZv3oxvvvkG9+7dQ0pKCsaOHQsfHx/MmzdP6xBtzqlTp5CRkWFyFqKiunTpEm7evIlatWphw4YN\naN++Pby9vVG/fn3861//wvXr17UOURNxcXFwcHBA3759AfwvASjq2A4AZ86cKbsArcSD/VRg7Nix\neOWVVwpNvCqqwvpq+vTpaNKkCV566SVcvHgReXl5+Omnn7B06VJMmTKl0ISsvLpz5w42btyI6dOn\nY/To0Rg0aFCx9SvCsbzYc1O3b98GAFSqVMlkW0HZrVu3VAjL9mRnZ2Ps2LF47733ULVqVa3DsVoT\nJ06Eq6srJk2ahDFjxuDevXsIDQ3F9u3b0bBhQ63Dszkff/wxPDw8MGPGDK1DsQpXr14FcP/L39Gj\nR7FmzRoEBQVh9+7dGDJkCLZt24bY2Fi4u7trHGnZuXTpEjZu3IiJEyfqE0we200V1k/A/Us5rl69\nyt8xA0X1VY0aNbBt2zaMGTMG9erVg6OjI3Q6HWbPno1XX31Vw4jL1rPPPos1a9ZAURRMmzYNM2fO\nLLFNRTiWc86eUjJ37lz4+/vj2Wef1ToUq5WXl4ehQ4di2rRp+Prrr5GRkYHk5GQEBAQgLCys0Otf\nqGh79uzBkiVL8MUXX8DX11frcKxCdnY2gPvT/Xz88cdo3rw5dDodOnXqhLfeegtnz57Fhx9+qHGU\nZUdEMH78eAQFBWH+/Plah2O1iuqnq1ev4tVXX8UXX3xR4rXDFUVxn6ldu3bh8ccfh7u7O5KTk3Hn\nzh2sX78e//nPf9C3b98Sp5wqL7799ltkZWVh165d+Omnn9CyZUucO3euyPoV5VhebMJZMApQ2PxZ\nBWUVaaSgKH/99Rc+/fRTfP7551qHYtWWL1+OtWvX4o033kDv3r1hb28Pb29vLF++HK6urhg5cqT+\nuiAqXnx8PAYOHIh58+aVeKqmIikYndPpdOjcubPRtoiICAD35+esKKZNm4aTJ09i8+bNcHR01Jfz\n2G6sqH6aOHEiBg8ejPbt25u0EZGyDNFqFNVXOTk5eP755+Hg4ICVK1fC29sbdnZ26NWrF9544w1s\n3rwZS5Ys0TDysmVvb4+wsDBERUUhPj4eY8aMKbReRTqWF5twNmzYECKC5ORkk21JSUmws7PT331W\nkf30008AgHbt2qFWrVr6f3v37oWI6H9+//33NY5UWwV/6Asuni7g5OSE1q1bIykpSX9tGRUtKSkJ\nERERGDlyJKZPn651OFalbt26AIDKlSubjEhVr14dAJCSklLmcWnhnXfewZo1a/Drr7/Cy8vLaFuj\nRo0AoMhjO3D/Jr+KoLh+2rp1K6KiooyO65GRkQDu37Veq1Yt/TWvFUFxfXXmzBlcvHgRwcHBcHJy\nMtrWoUMHACjXMx8UJSAgAAEBAdi1a5f+DEyBinYsLzbhLBghOHLkiFF5Tk4OTpw4gbCwMKNvOBXV\na6+9hlu3biE5OdnoX9u2baEoiv7nyZMnax2qpjIyMgCg0NWXCsru3LlTpjHZmpSUFHTr1g1PPfUU\n/u///k9ffvToUc4Ygfs3pgUEBCA9PR1379412lZww9CDfyjLo48++giLFi0ymgYqNTUVCQkJAIDA\nwED4+PiYHNuB+2dsAKBLly5lFq9WSuqntLQ0XLt2zei4/v333wO4P9KXnJxcrqf6MVRSX1X04/v3\n33+PAwcOFLrNxcUFImJ0XXRFPJYXm3AOHjwYbm5u+OGHH4zKt27diqysLIwaNUrV4Kh8CQkJAXD/\nehVDOTk5OHjwIJydnREUFKRFaDbh5s2biIiIQKdOnUyuQ+zbt2+ho1UV0QsvvAARMbkmuGB0pXfv\n3lqEVWaWL1+OuXPnYtu2bfqRTADYtGkT3nzzTQCAoigYOXIkTp06hRMnThi1j4qKQmBgIMLDw8sy\n7DJnTj8VpiKeSjenr5o1awYXFxccPHjQJGEqWLo4ODi4zGIua5s2bcLXX39tUn716lWcPHkSNWvW\n1E/tVlGP5cVeBe3p6Yn3338fY8eOxerVqzFs2DBcuHABU6dORdeuXTF8+PCyitNmVcSDU1Feeukl\nrFixAnPnzsVjjz2Gjh07IiMjA1OnTkViYiLmzZsHV1dXrcPUXGGfmYyMDPTs2RMJCQnaDQQdAAAC\nOklEQVTo16+fyR/EinZHMVD079bkyZOxbt06TJkyBQ0aNEDjxo1x8OBBzJo1Cy1atMDLL79cxpGW\nnf/+978YM2YM+vTpg6ioKERFRem3HT582GiOv+nTpyMqKgpjx47Fhg0b4OnpiXfffRdHjx7FTz/9\nVOhIVXlhST8VpaIc283tK1dXV8yaNQszZszAiy++iPfffx+VK1fG7t27MWfOHPj6+mLixIlavQzV\nKYqCL7/8EsHBwRg2bBgcHR1x9uxZjBo1Cjk5OfjPf/4DoIIfy81ZjmjdunXSqlUr8fLyEj8/P5k6\ndapkZWWV+rJH5UXTpk3F2dlZdDqd6HQ6cXZ2FhcXF0lKStI6NM0lJyfL+PHjpW7duuLh4SHu7u7S\nvn37QpchrChWrFghzs7O4uTkJDqdTuzs7MTZ2Vn8/f31dX744QdRFEV0Op0oimLyT6fTSUJCgoav\nQn3m9FOB1NRUmTBhgvj4+IiHh4f4+/vLtGnTJD09XYPIy06LFi2K/Yw8uBzo9evXZdSoUVKrVi3x\n8vKSjh07ys6dOzWKvuxY2k8iIqtXrxZnZ2dxdHQUnU4n9vb24uzsLC+++KIGr6DsWNpX3333nXTs\n2FHc3d3Fw8ND6tSpI2PHji33f/8uXrwo8+bNk9DQUPHx8ZGqVauKt7e39OvXz+h3qiIfyxWRCvI1\njYiIiIg0UX7PmRARERGRVWDCSURERESqYsJJRERERKpiwklEREREqmLCSURERESqYsJJRERERKr6\nf/vrpaJNq7QMAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1102d4b50>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#find the highest density peak\n",
      "H2d, r_edges, t_edges = histogram2d(radial_vel, tangential_vel, bins=(12,12), range=[[-240.0,0.0],[0.0,240.0]])\n",
      "max_radial_id = argmax(H2d, axis=0)\n",
      "max_tangential_id = argmax(H2d, axis=1)\n",
      "max_r_id = argmax(H2d[arange(12), max_tangential_id])\n",
      "max_t_id = argmax(H2d[max_radial_id, arange(12)])\n",
      "\n",
      "theory_point = array([r_edges[max_r_id]+10.0, t_edges[max_t_id]+10.0])\n",
      "print 'total number of pairs', size(radial_vel)\n",
      "print 'location of the highest density peak in Bolshoi', theory_point\n",
      "\n",
      "#selection of the number of galaxies around the observational constraints\n",
      "index_obs = where((radial_vel>(mean_point[0]-sigma_point[0])) & (radial_vel<(mean_point[0]+sigma_point[0])) \n",
      "    & (tangential_vel<sigma_point[1]))\n",
      "print 'number of points in observations', size(index_obs)\n",
      "\n",
      "#selection of the number of galaxies around the Bolshoi point\n",
      "index_max = where((radial_vel>(theory_point[0]-sigma_point[0])) & (radial_vel<(theory_point[0]+sigma_point[0])) \n",
      "    & (tangential_vel<(theory_point[1]+sigma_point[1]/2.0)) & (tangential_vel>(theory_point[1]-sigma_point[1]/2.0)))\n",
      "print 'number of points around the highest density peak', size(index_max)\n",
      "\n",
      "\n",
      "#find the number of points with radial velocities consistent with observations\n",
      "tang_to_radial = abs(tangential_vel / radial_vel)\n",
      "index = where(tang_to_radial<0.32)\n",
      "print 'number of points with the right radial to tang', size(index), '. In percentage:', 1.0*size(index)/radial_vel.size\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total number of pairs 1923\n",
        "location of the highest density peak in Bolshoi [-70.  50.]\n",
        "number of points in observations 5\n",
        "number of points around the highest density peak"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 23\n",
        "number of points with the right radial to tang 242 . In percentage: 0.125845033801\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Figure in the E-J plane\n",
      "n_clues=3\n",
      "clues1=data_path+\"pair_physical_vweb_IC10909.dat\"\n",
      "clues2=data_path+\"pair_physical_vweb_IC16953.dat\"\n",
      "clues3=data_path+\"pair_physical_vweb_IC2710.dat\"\n",
      "clues=chararray([n_clues], itemsize=1024)\n",
      "clues[0]=clues1;clues[1]=clues2; clues[2]=clues3\n",
      "clues_data = np.zeros([n_clues,2])\n",
      "if(narrow_data):\n",
      "    n_clues = 1\n",
      "for i in range(n_clues):\n",
      "    tmp_dat = np.loadtxt(clues[i])\n",
      "    clues_data[i,0] = tmp_dat[5] + tmp_dat[6] # energy\n",
      "    clues_data[i,1] = tmp_dat[7] #angular momentum\n",
      "\n",
      "filename='test_EJ_'+halo_finder\n",
      "if(narrow_data):\n",
      "    filename=filename+'_narrow'\n",
      "MakeSimple2DPlot(energy,angular_momentum,filename=filename, \n",
      "                      clues=clues_data, clues_label='$\\mathrm{Constrained\\ Sim.}$', xlims=[-25.0,0.0], ylims=[0.0,150.0],\n",
      "                      nbins=13,nxbins=13,nybins=13,bw=1, \n",
      "                      xlabel='$\\mathrm{e_{tot} [10^{-36}} \\mathrm{Mpc^2\\ s^{-2}]}$', \n",
      "                      ylabel='$\\mathrm{l_{orb} [Mpc\\ } \\mathrm{km\\ s^{-1}]}$', \n",
      "                      contours=0, X_field=X, Y_field=Y, Z_field=H, levels=levels)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "HOLA\n",
        "\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "0"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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D9c/zoWVnZys+Pl5t27YtMFE0AOfxyiuvaOLEiUW6CSg9PV2DBg3SqFGj5Onp6YB019e6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\nFIETAAAAQb0AgqrFcrWx6x4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1065dbe10>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "index = where((angular_momentum<40.0) & (energy>-20.0) & (energy<-5.0))\n",
      "print 'approx. number of points inside contour', size(index), 'in percentage', 1.0 * size(index)/energy.size"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "approx. number of points inside contour 298 in percentage 0.154966198648\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Figure with the spin parameter distribution\n",
      "fig = figure(1, figsize=(9.5,6.5))\n",
      "ax = axes()\n",
      "ax.set_xlabel(\"$\\log_{10}\\mathrm{\\lambda}$\",fontsize=25)\n",
      "ax.set_ylabel(\"$\\mathrm{Normalized\\ Histogram}$\",fontsize=25)\n",
      "ticklabels_x = ax.get_xticklabels()\n",
      "ticklabels_y = ax.get_yticklabels()\n",
      "\n",
      "for label_x in ticklabels_x:\n",
      "    label_x.set_fontsize(18)\n",
      "    label_x.set_family('serif')\n",
      "for label_y in ticklabels_y:\n",
      "    label_y.set_fontsize(18)\n",
      "    label_y.set_family('serif')\n",
      "\n",
      "n_clues=3\n",
      "clues1=data_path+\"pair_physical_vweb_IC10909.dat\"\n",
      "clues2=data_path+\"pair_physical_vweb_IC16953.dat\"\n",
      "clues3=data_path+\"pair_physical_vweb_IC2710.dat\"\n",
      "clues=chararray([n_clues], itemsize=1024)\n",
      "clues[0]=clues1;clues[1]=clues2; clues[2]=clues3\n",
      "clues_data = np.zeros([n_clues,4])\n",
      "\n",
      "if(narrow_data):\n",
      "    n_clues = 1\n",
      "for i in range(n_clues):\n",
      "    tmp_dat = np.loadtxt(clues[i])\n",
      "    clues_data[i,0] = tmp_dat[5] + tmp_dat[6] # energy\n",
      "    clues_data[i,1] = tmp_dat[7] #angular momentum\n",
      "    clues_data[i,2] = tmp_dat[9] # total mass\n",
      "    clues_data[i,3] = tmp_dat[10] # reduced_mass\n",
      "    \n",
      "    e_CLUES = clues_data[i,0]\n",
      "    l_CLUES = clues_data[i,1]\n",
      "    total_mass_CLUES = clues_data[i,2]\n",
      "    mu_CLUES = clues_data[i,3]\n",
      "\n",
      "    lambda_CLUES = mu_CLUES**1.5 * (l_CLUES * L_UNITS * KM_TO_MPC) * \\\n",
      "        sqrt(abs(e_CLUES * E_UNITS)) / (G_GRAV * (total_mass_CLUES )**(5.0/2.0))\n",
      "    lambda_CLUES = log10(lambda_CLUES)\n",
      "    y_value=1.9\n",
      "\n",
      "    ax.axvline(x=lambda_CLUES,ymin=0.8,ymax=0.95,c=\"black\",linewidth=2)\n",
      "    if(i==0):\n",
      "        ax.scatter(lambda_CLUES, y_value, color='white', edgecolors='black', s=200, label='$\\mathrm{Constrained\\ Sim.}$')  \n",
      "    else:\n",
      "        ax.scatter(lambda_CLUES, y_value, color='white', edgecolors='black', s=200)  \n",
      "        \n",
      "        \n",
      "\n",
      "hist_A, bin_edges_A = histogram(log10(lambda_obs), bins=arange(-3.0,0.5,0.1), density=True)\n",
      "hist_B, bin_edges_B = histogram(log10(lambda_orbit), bins=arange(-3.0,0.5,0.1), density=True)\n",
      "\n",
      "plot(bin_edges_A[:-1],hist_A,color='black',ms=1,linewidth=3.0, label=\"$\\mathrm{Obs.}$\")\n",
      "plot(bin_edges_B[:-1],hist_B,'r--',color='black',ms=2,linewidth=3.0, label=\"$\\mathrm{Bolshoi}$\")\n",
      "\n",
      "ax.legend(loc=0, scatterpoints=1, prop={'size':20})\n",
      "\n",
      "ax.set_xlim([-3.0,0.5])\n",
      "ax.set_ylim([0.0,2.2])\n",
      "filename='test_lambda_'+halo_finder\n",
      "if(narrow_data):\n",
      "    filename=filename+'_narrow'\n",
      "savefig(filename + '.eps',format = 'eps', transparent=True)\n",
      "savefig(filename + '.pdf',format = 'pdf', transparent=True)\n",
      "savefig(filename + '.png',format = 'png', transparent=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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sk8lkwvz583OMSV6Xq6urEBgYKKxevVrQ0dERgoKCBEEQhB9++EEwNTUVXr16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NgwxMTE1Bp/YmIiunTpgvDwcAwdOpQmHxBCANCkA0KIhqm4hfn69esa93nx4gUAwNraWmp7bm4u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\nDQAAwOe+A83a6HS+KB43AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1102dcd90>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "mean_lambda_obs = mean(log10(lambda_obs))\n",
      "variance_obs = var(log10(lambda_obs))\n",
      "mean_lambda_sim = mean(log10(lambda_orbit))\n",
      "variance_sim = var(log10(lambda_orbit))\n",
      "\n",
      "print 'mean lambda, observations', mean_lambda_obs, variance_obs\n",
      "print 'mean lambda, bolshoi', mean_lambda_sim, variance_sim\n",
      "print 'lambda CLUES', lambda_CLUES\n",
      "\n",
      "# calculate the number of points in the simulation that are consistent with mean value and sigma\n",
      "index_sim = where((log10(lambda_orbit)<(mean_lambda_obs+variance_obs)) & (log10(lambda_orbit) > (mean_lambda_obs-variance_obs)))\n",
      "print 'there are ', size(index_sim), 'pairs consistent with the observations'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean lambda, observations -1.72089246657 0.0802272717075\n",
        "mean lambda, bolshoi -1.470309254 0.137777720569\n",
        "lambda CLUES -1.72803661534\n",
        "there are  257 pairs consistent with the observations\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}