Hhh_optimization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# KERAS and TENSORFLOW\n",
    "TUTORIAL: Using a Multi Layer Perceptron in order to separate resonant di-Higgs decaying into WWbb from TTbar. \n",
    "(%lsmagic for magic commanda and ! for bash instruction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using Theano backend.\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "require(['notebook'],\n",
       "  function() {\n",
       "    IPython.CodeCell.config_defaults.highlight_modes['magic_text/x-c++src'] = {'reg':[/^%%cpp/]};\n",
       "    console.log(\"JupyROOT - %%cpp magic configured\");\n",
       "  }\n",
       ");\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to JupyROOT 6.08/06\n",
      "If you had no error so far, this is great! We can start the tutorial.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Luca2/Library/Python/2.7/lib/python/site-packages/root_numpy/__init__.py:34: RuntimeWarning: ROOT 6.08/06 is currently active but you installed root_numpy against ROOT 6.08/00. Please consider reinstalling root_numpy for this ROOT version.\n",
      "  RuntimeWarning)\n",
      "/Users/Luca2/Library/Python/2.7/lib/python/site-packages/root_numpy/__init__.py:46: RuntimeWarning: numpy 1.12.1 is currently installed but you installed root_numpy against numpy 1.11.0. Please consider reinstalling root_numpy for this numpy version.\n",
      "  RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "# We start by importing all the necessary packages\n",
    "import sys;\n",
    "import os, sys, array, re, math, random, subprocess, glob\n",
    "from math import *\n",
    "import numpy as np\n",
    "import scipy\n",
    "from numpy.lib.recfunctions import stack_arrays\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import cPickle\n",
    "from sklearn.feature_selection import SelectKBest, f_classif\n",
    "from sklearn.model_selection import train_test_split, GridSearchCV\n",
    "from sklearn.preprocessing import StandardScaler, RobustScaler\n",
    "from sklearn.utils import compute_class_weight\n",
    "from keras.models import Sequential, Model\n",
    "from keras.layers import Dense, Activation, Dropout, Highway, MaxoutDense, Masking, GRU, Merge, Input, merge\n",
    "from keras.callbacks import EarlyStopping, ModelCheckpoint\n",
    "from keras.utils.np_utils import to_categorical\n",
    "import deepdish.io as io\n",
    "import ROOT\n",
    "from ROOT import gSystem, gROOT, gApplication, TFile, TTree, TCut, TH1F, TCanvas\n",
    "from root_numpy import root2array \n",
    "from IPython.display import HTML, IFrame\n",
    "import seaborn as sns; sns.set()\n",
    "print \"If you had no error so far, this is great! We can start the tutorial.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here there are few paramters we may want to change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I'm now importing an external file with few function and defining the input/output files location.\n"
     ]
    }
   ],
   "source": [
    "print \"I'm now importing an external file with few function and defining the input/output files location.\"\n",
    "# Check this file out, it contains many functions we will use.\n",
    "execfile(\"Useful_func.py\")\n",
    "# Fix random seed for reproducibility\n",
    "seed = 7; np.random.seed(seed);\n",
    "# Input paramters\n",
    "debug = True #(Verbose output)\n",
    "folder='Plots_hh_tt_MLP/' # Folder with Plots\n",
    "MakePlots=True # Set False if you want to run faster\n",
    "folderCreation  = subprocess.Popen(['mkdir -p ' + folder], stdout=subprocess.PIPE, shell=True); folderCreation.communicate()\n",
    "folderCreation2 = subprocess.Popen(['mkdir -p models/'], stdout=subprocess.PIPE, shell=True); folderCreation2.communicate()\n",
    "# Sample location\n",
    "h_file = \"files/MVA_GluGluToRadionToHHTo2B2VTo2L2Nu_M-500_narrow_13TeV-madgraph-v2.root\"\n",
    "TT_df_list = ['files/tt_dataframe_0.csv','files/tt_dataframe_1.csv','files/tt_dataframe_2.csv','files/tt_dataframe_3.csv','files/tt_dataframe_4.csv','files/tt_dataframe_5.csv']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we manipulate the input ROOT files into a format we can pass to Keras."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Now we manipulate the input ROOT files into a format we can pass to Keras.\n",
      "Assuming a Signal of 1pb and a background of 87pb (B.R. included) you expect, after the preselection, to have: 889.349 S and  57075.852626 B\n",
      "---> hh Displayed as panda dataframe: \n",
      "             MT2  mass_trans  dphi_llmet  dphi_llbb  eta_l1l2     pt_l1l2  \\\n",
      "0     204.876617   58.227169   -0.656254   2.360411 -1.251371  133.172607   \n",
      "1     173.696640   68.748177   -0.735540   2.977401  1.251243  123.683105   \n",
      "2     178.231232   14.852475    0.171652  -3.039625  0.289626   57.809509   \n",
      "3     194.113281   67.502968   -0.730394   2.759843  0.350090   57.006603   \n",
      "4     181.141830   39.649441   -0.392053  -0.138721  2.177732  114.623611   \n",
      "5      94.638977   26.768946    0.671493   1.468435 -1.165310   52.720341   \n",
      "6     266.408600  101.897797   -1.080848   1.870067 -0.059288  194.387604   \n",
      "7     230.762573   14.189651   -0.104791   2.388038 -1.408746  128.767166   \n",
      "8     155.667847   69.072807    0.447384  -2.809182  1.673839  143.117401   \n",
      "9     191.026337   26.472750    0.290987  -2.227521 -0.849107   39.522270   \n",
      "10    218.591721  101.979210    1.037712  -2.052243  2.009086  107.664413   \n",
      "11    218.232437  108.420624    1.430708  -2.420350  1.366055  108.757416   \n",
      "12    155.935745   86.095787   -2.096370   1.282199  2.218262   26.654335   \n",
      "13    171.737411   32.679867   -0.324180  -3.084855  1.039126  112.239471   \n",
      "14     82.502678   50.436195   -1.017292  -1.495375  1.833064   43.668354   \n",
      "15    206.274841  154.961578   -2.463731   1.888270 -0.533481  140.808441   \n",
      "16    160.787094   76.863861   -1.125551   0.070430  0.776785  134.968597   \n",
      "17    174.723175  118.717674   -1.399207   2.706383 -0.383907  111.991447   \n",
      "18    186.592270   55.796970    0.555323  -0.333149  1.722190  119.924469   \n",
      "19    201.342697   43.528446   -0.609672   2.653898 -1.963772   39.268116   \n",
      "20    174.760239   70.868286    0.917689  -2.412076 -1.863463   65.397598   \n",
      "21    219.884537  137.566147    1.678475  -3.107000  0.158365  215.947906   \n",
      "22    164.822388  115.598427    1.976192  -2.218270 -1.237565  186.468826   \n",
      "23    257.602386   11.186421    0.088423  -2.753372  0.178020  140.733627   \n",
      "24    186.320770   14.254823    0.121331  -2.808169 -0.532978   69.528839   \n",
      "25    174.197510  137.995041   -1.434729   2.256102 -0.188686  135.109421   \n",
      "26    203.310822   74.842720   -0.742130   2.589442  0.924444   61.924526   \n",
      "27    201.449203  168.134491    1.486326   1.305446 -0.110999  155.970825   \n",
      "28    175.501602  141.529633   -2.310097  -2.557052 -1.004337  150.022308   \n",
      "29    221.971985  256.039886   -2.748778   2.633971  1.781850  198.588394   \n",
      "...          ...         ...         ...        ...       ...         ...   \n",
      "7693  200.072388  140.721878    2.217213   2.926198 -0.165758  195.003250   \n",
      "7694  196.583130   61.832939   -0.891013   2.822829 -1.435865  101.358055   \n",
      "7695  197.456650   20.129309   -0.249710   2.815999  1.193409   40.311649   \n",
      "7696  235.415161   24.919502   -0.303239  -2.000724  0.225778  197.428299   \n",
      "7697  169.410339   71.721642   -0.720468   2.858706 -1.238876   96.818573   \n",
      "7698  192.090729   46.218784   -0.475346   2.649529 -1.525180   64.198029   \n",
      "7699  194.974426   97.519272   -1.153366  -3.073576  0.377251  176.535156   \n",
      "7700  175.130646   20.551977   -0.199625  -1.212341 -0.837711  187.095215   \n",
      "7701  189.111191   10.048808   -0.139411   2.425931  1.024268  182.810699   \n",
      "7702  196.218430   20.202848   -0.262503  -3.136873 -0.348467   69.336807   \n",
      "7703  171.062027   86.492241   -0.924573  -2.816086  1.967445   92.126038   \n",
      "7704  207.393509   69.976501    1.393513  -2.071962  2.358028   29.158417   \n",
      "7705  187.742767   80.216782   -1.049781   2.822077  0.995517   48.085922   \n",
      "7706  172.074615  107.271889   -1.358487   2.487991 -0.520102   58.639587   \n",
      "7707  157.964020   37.382038    0.313143  -3.126572  0.744720  137.455002   \n",
      "7708  234.918488   67.299988    0.899531  -1.894487  0.056422   36.860741   \n",
      "7709  142.218353  111.079216   -2.244605   3.065428 -1.083478  136.949570   \n",
      "7710  205.749619   26.294548    0.289620  -2.695047  1.333566  105.916916   \n",
      "7711  224.334106  178.637939    2.811847  -2.990774 -1.642985  137.133911   \n",
      "7712  313.913818   77.948868   -0.454745   2.623618  0.681273  146.308243   \n",
      "7713  169.805038   57.198608    0.655012  -2.945300  0.360201  126.521118   \n",
      "7714  221.667480   65.567123    0.417313   2.743998 -0.106522  211.614853   \n",
      "7715  159.707245   98.480476    0.813247   1.323424 -2.003189   56.266758   \n",
      "7716  232.754318  167.295685   -1.602644  -2.349111 -0.188925  144.920792   \n",
      "7717  156.957596   77.083702   -1.103534   2.108479 -1.182097   55.341530   \n",
      "7718  240.729431   68.202286    1.641393  -1.470088  0.512723   14.974986   \n",
      "7719  228.480042   63.059704   -0.710751   2.853086 -0.433621  145.453323   \n",
      "7720  235.229492   74.294647    0.724408  -3.064028  0.543919  135.940582   \n",
      "7721  135.068344   13.145462    0.169250  -3.091506 -0.443745   60.669617   \n",
      "7722  213.869614   44.378094   -0.673089   2.672721 -0.197871  112.548134   \n",
      "\n",
      "      mass_l1l2  eta_b1b2     pt_b1b2   mass_b1b2  dR_minbl  dR_l1l2b1b2  \\\n",
      "0     33.535763 -0.203640  175.310455  114.476646  1.648723     2.582495   \n",
      "1     13.597803  0.856266  192.094803  127.114464  1.823612     3.003485   \n",
      "2     22.098766 -0.486168  175.281631  129.323196  2.422570     3.137065   \n",
      "3     36.555000 -0.034895  208.853546  114.682022  1.713738     2.786565   \n",
      "4     23.970858  0.364718  317.503357  114.779549  1.612752     1.818314   \n",
      "5     37.480194 -1.236115  431.146729   90.074013  0.473781     1.470141   \n",
      "6     21.377642  0.633884  302.644379  127.112778  1.626286     1.994402   \n",
      "7     25.701395 -0.575552  180.849884  120.977737  1.840357     2.529217   \n",
      "8     47.800468  1.170069  108.576263   93.602692  1.094040     2.853995   \n",
      "9     30.245331 -0.452823  162.772476  100.345016  1.683525     2.262497   \n",
      "10    39.122860  1.149880  238.986435  120.760910  1.590568     2.224846   \n",
      "11    17.030104  0.251907  252.248138  100.974930  2.164213     2.664474   \n",
      "12    46.941059 -1.110957   44.280666  122.310265  1.746957     3.567594   \n",
      "13    21.594934  0.734449  190.527496  101.811172  2.242527     3.099864   \n",
      "14    44.065350 -0.475987   22.078348   62.106483  1.523724     2.750976   \n",
      "15    43.320606  2.002678   78.013252  113.693748  1.930553     3.161909   \n",
      "16    39.759941 -1.827504   57.200008  103.411469  1.912357     2.605241   \n",
      "17    32.828754  1.774189   97.663399  131.822189  2.162296     3.461486   \n",
      "18    84.788490  0.066997  240.166275  106.096077  0.935649     1.688388   \n",
      "19    54.634304  0.339492  225.933929  107.435532  2.667988     3.514001   \n",
      "20    12.551134 -1.610677  256.240295  125.553253  2.091437     2.425286   \n",
      "21    23.607716  0.346161  191.874390  103.111122  2.850149     3.112671   \n",
      "22    30.160105 -0.658779  109.007828   72.123009  1.614177     2.292534   \n",
      "23    25.692345  0.459546  331.082977  170.664413  1.980513     2.767727   \n",
      "24    36.475147 -1.265156  179.152283   99.837303  2.305837     2.902050   \n",
      "25    29.469501 -0.282255  155.275955   71.007874  1.936332     2.258042   \n",
      "26    13.155174  0.870476  210.054108  119.208618  2.242718     2.590004   \n",
      "27    26.981125  1.237813  192.078171   85.869255  1.402951     1.877094   \n",
      "28    30.536329 -0.594323  189.090820   88.997498  2.414320     2.589715   \n",
      "29    36.987511  1.997746  176.178986  102.316223  2.122601     2.642804   \n",
      "...         ...       ...         ...         ...       ...          ...   \n",
      "7693  43.870773 -1.398598  135.519836  110.148880  2.645509     3.175300   \n",
      "7694  25.238024  0.358378  131.345154  103.471664  2.722090     3.344797   \n",
      "7695  21.788443  0.136047  216.314072  129.061996  2.776723     3.007967   \n",
      "7696  27.333620 -0.058995  252.458939  101.304131  1.956738     2.020889   \n",
      "7697  30.434336 -0.955995  141.107422  106.946907  1.829208     2.872668   \n",
      "7698  33.333164 -1.288531  192.983444  118.868690  2.667814     2.660077   \n",
      "7699  18.663280  1.379426  164.843765  111.995483  2.204203     3.232835   \n",
      "7700  90.470924  5.088473    1.663574  116.886826  1.671171     6.048920   \n",
      "7701  27.527634  1.146023  241.441605  108.116043  1.872663     2.428984   \n",
      "7702  19.138161  1.203499  175.831680  118.765617  2.706258     3.499796   \n",
      "7703  47.831017  0.777609  135.365524  104.739906  2.404203     3.057131   \n",
      "7704  45.969669 -0.364219  178.758011  116.492409  1.567213     3.421061   \n",
      "7705  20.075317 -0.751698  163.417587  123.043564  2.180343     3.319168   \n",
      "7706  38.936325  0.368952  145.093079   90.442543  1.699983     2.642066   \n",
      "7707  48.414871  0.387493  172.291367   45.296051  2.075141     3.146914   \n",
      "7708  28.916496  0.478818  289.157013  129.432831  1.424103     1.941005   \n",
      "7709  23.962372  0.768244   99.813911   98.636810  1.625290     3.581302   \n",
      "7710  26.784706 -0.172788  148.553513   90.108170  2.488092     3.087456   \n",
      "7711  48.095142 -1.948768  282.976105  119.198494  2.717286     3.006366   \n",
      "7712  28.142521  1.623700  245.693314  230.778259  2.001661     2.787749   \n",
      "7713  12.859926 -0.950743  114.003120  100.445763  1.607930     3.223874   \n",
      "7714  44.102940 -0.363714  122.486526  121.125031  1.570092     2.756025   \n",
      "7715  15.871268 -0.723637  293.642944  126.360336  1.606757     1.840843   \n",
      "7716  26.895376  0.472169  237.312805  102.342567  1.356063     2.440362   \n",
      "7717  47.991428  1.106019   79.990074  129.447433  2.034688     3.111456   \n",
      "7718  39.772011 -0.245780  403.762543  132.761688  1.119696     1.654232   \n",
      "7719  20.991318 -0.834043  242.841873  133.534576  2.412044     2.881048   \n",
      "7720  48.699245  0.640928  292.845245  135.458282  2.564692     3.065564   \n",
      "7721  27.420731  1.278618  128.492554   40.735790  2.895336     3.538919   \n",
      "7722  16.857504  0.527841  213.173950  135.106964  2.221031     2.769494   \n",
      "\n",
      "               HT      met_pt  muon1_pogSF  muon2_pogSF  XsecBr  fin_weight  \n",
      "0      612.819214   61.282345     0.987282     0.947035  0.1214    0.113508  \n",
      "1      409.239655   73.904106     0.987237     0.933848  0.1214    0.111922  \n",
      "2      479.570862  129.828049     0.970192     0.978472  0.1214    0.115246  \n",
      "3      406.660095  156.674927     0.969978     0.959581  0.1214    0.112996  \n",
      "4     1193.651123   90.381561     0.905864     0.978227  0.1214    0.107577  \n",
      "5     1103.774414   31.302710     0.967670     0.995512  0.1214    0.116948  \n",
      "6      823.074524   50.446449     0.968703     0.968464  0.1214    0.113892  \n",
      "7      609.990417  142.523987     0.987607     0.983341  0.1214    0.117898  \n",
      "8      688.912537  169.362030     0.986139     0.982258  0.1214    0.117593  \n",
      "9      471.846100  210.899902     0.969209     0.996801  0.1214    0.117286  \n",
      "10     642.031128   98.203156     0.985588     0.980037  0.1214    0.117262  \n",
      "11     701.432312   62.813049     0.986331     0.934054  0.1214    0.111844  \n",
      "12     286.978546   92.593437     0.979215     0.998484  0.1214    0.118696  \n",
      "13     458.534485   91.337288     0.946711     0.968291  0.1214    0.111286  \n",
      "14     749.500854   61.405735     0.947857     0.948096  0.1214    0.109097  \n",
      "15     455.674286   47.932934     0.977361     0.969237  0.1214    0.115002  \n",
      "16     479.706390   38.443676     0.947520     0.978375  0.1214    0.112542  \n",
      "17     440.118164   75.880432     0.977361     0.979284  0.1214    0.116194  \n",
      "18     928.257690   86.379646     0.986063     0.948392  0.1214    0.113530  \n",
      "19    1254.840698  133.908234     0.986722     0.992028  0.1214    0.118833  \n",
      "20     590.754150   97.869293     0.980351     0.961491  0.1214    0.114431  \n",
      "21     466.097076   39.565063     0.969085     0.977425  0.1214    0.114991  \n",
      "22     838.026489   25.697195     0.946644     0.987772  0.1214    0.113517  \n",
      "23     789.987610  113.798332     0.977843     0.965839  0.1214    0.114655  \n",
      "24     495.317688  198.770233     0.967702     0.969250  0.1214    0.113867  \n",
      "25     533.621826   81.530617     0.976711     0.965890  0.1214    0.114528  \n",
      "26     459.405426  171.989136     0.947779     0.960352  0.1214    0.110498  \n",
      "27     856.802002   98.973785     0.968534     0.959839  0.1214    0.112858  \n",
      "28     585.753662   39.885292     0.977171     0.981927  0.1214    0.116485  \n",
      "29     524.710754   85.795311     0.999913     0.986272  0.1214    0.119723  \n",
      "...           ...         ...          ...          ...     ...         ...  \n",
      "7693   547.774841   31.688334     0.968492     0.985106  0.1214    0.115824  \n",
      "7694   396.080750   50.785320     0.983589     0.986090  0.1214    0.117747  \n",
      "7695   323.394348  162.036865     0.980127     0.978036  0.1214    0.116374  \n",
      "7696   853.706482   34.469147     0.969173     0.968687  0.1214    0.113973  \n",
      "7697   586.812195  106.900612     0.946988     0.981449  0.1214    0.112832  \n",
      "7698   358.228302  150.068100     0.982444     0.997551  0.1214    0.118977  \n",
      "7699   662.596313   45.300636     0.969839     0.968702  0.1214    0.114054  \n",
      "7700   748.596741   56.840313     0.969194     0.969188  0.1214    0.114035  \n",
      "7701   719.531616   28.466713     0.938317     0.947378  0.1214    0.107918  \n",
      "7702   385.390472   85.918633     0.967391     0.978498  0.1214    0.114916  \n",
      "7703   578.524658  102.058815     0.986135     0.894611  0.1214    0.107100  \n",
      "7704   454.530884  101.946220     0.956799     0.977399  0.1214    0.113530  \n",
      "7705   452.955963  133.220886     0.968170     0.997085  0.1214    0.117193  \n",
      "7706   314.414062  124.313698     0.968508     0.969211  0.1214    0.113957  \n",
      "7707   447.827423  104.527733     0.978028     0.968668  0.1214    0.115012  \n",
      "7708   725.649414  162.524338     0.980076     0.997424  0.1214    0.118675  \n",
      "7709   383.043884   27.739447     0.946727     0.959556  0.1214    0.110284  \n",
      "7710   386.947693   78.369316     0.987494     0.980594  0.1214    0.117555  \n",
      "7711   791.639954   59.786327     0.987100     0.986449  0.1214    0.118210  \n",
      "7712   606.775269  204.320679     0.978284     0.966922  0.1214    0.114835  \n",
      "7713   347.274109   62.473137     0.978310     0.967830  0.1214    0.114946  \n",
      "7714   953.479919  118.362251     0.976721     0.976708  0.1214    0.115812  \n",
      "7715  1051.094116  275.468628     0.980369     1.072719  0.1214    0.127672  \n",
      "7716   776.372131   93.582672     0.976655     0.976606  0.1214    0.115792  \n",
      "7717   244.060928   97.685898     0.969111     0.947098  0.1214    0.111426  \n",
      "7718   777.270691  145.077225     0.959979     0.996996  0.1214    0.116191  \n",
      "7719   535.098083   56.455437     0.976743     0.977349  0.1214    0.115891  \n",
      "7720   651.727661   80.849159     0.978129     0.977488  0.1214    0.116072  \n",
      "7721   274.465332   99.669472     0.966929     0.997242  0.1214    0.117061  \n",
      "7722   542.500610   40.115543     0.976637     0.996804  0.1214    0.118185  \n",
      "\n",
      "[7723 rows x 18 columns]\n",
      "The shape for hh is (samples, features): \n",
      "(7723, 18)\n",
      "The shape for tt is (samples, features): \n",
      "(1937550, 18)\n",
      "Index([u'MT2', u'mass_trans', u'dphi_llmet', u'dphi_llbb', u'eta_l1l2',\n",
      "       u'pt_l1l2', u'mass_l1l2', u'eta_b1b2', u'pt_b1b2', u'mass_b1b2',\n",
      "       u'dR_minbl', u'dR_l1l2b1b2', u'HT', u'met_pt', u'muon1_pogSF',\n",
      "       u'muon2_pogSF', u'XsecBr', u'fin_weight'],\n",
      "      dtype='object')\n",
      "Index([u'MT2', u'mass_trans', u'dphi_llmet', u'dphi_llbb', u'eta_l1l2',\n",
      "       u'pt_l1l2', u'mass_l1l2', u'eta_b1b2', u'pt_b1b2', u'mass_b1b2',\n",
      "       u'dR_minbl', u'dR_l1l2b1b2', u'HT', u'met_pt', u'muon1_pogSF',\n",
      "       u'muon2_pogSF', u'XsecBr', u'fin_weight'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "print \"Now we manipulate the input ROOT files into a format we can pass to Keras.\"\n",
    "# Our goal is to separate Signal from Background. We need to select only \"good events\".\n",
    "# 1) We apply a preselection to our Signal and Background events\n",
    "my_selec = 'met_pt>20 && met_pt<500 && muon1_pt>20 && fabs(muon1_eta)<2.4 && muon2_pt>10 && fabs(muon2_eta)<2.4 && pt_l1l2<500 && pt_b1b2<500 && mass_l1l2>12 && mass_l1l2<500 && mass_b1b2<500 && b1jet_pt>20 && fabs(b1jet_eta)<2.4 && b2jet_pt>20 && fabs(b2jet_eta)<2.4 && mass_trans>10 && mass_trans<500 && HT<4000'\n",
    "# 2) We select the TTree branches that contains the information we want to keep\n",
    "my_branches = [\"MT2\",\"mass_trans\",\"dphi_llmet\",\"dphi_llbb\",\"eta_l1l2\",\"pt_l1l2\",\"mass_l1l2\",\"eta_b1b2\",\"pt_b1b2\",\"mass_b1b2\",\"dR_minbl\",\"dR_l1l2b1b2\",\"HT\",\"met_pt\",\"muon1_pogSF\",\"muon2_pogSF\",\"XsecBr\"]\n",
    "# 3) We select the TTree branches that contains the information we want to use in the training (FEATURES)\n",
    "my_branches_training = [\"MT2\",\"mass_trans\",\"dphi_llmet\",\"dphi_llbb\",\"eta_l1l2\",\"pt_l1l2\",\"mass_l1l2\",\"eta_b1b2\",\"pt_b1b2\",\"mass_b1b2\",\"dR_minbl\",\"dR_l1l2b1b2\",\"HT\",\"met_pt\"]\n",
    "    \n",
    "# Converting Root files into a DATAFRAME (Very useful, checnl root2panda in Useful_func.py)\n",
    "hh    = root2panda(h_file, 'DiHiggsWWBBAna/evtree', branches=my_branches, selection=my_selec)\n",
    "## TT is so heavy that I already saved the final dataframe (and I splitted it if 5 so that each df is smaller than 100 Mb).\n",
    "ttbar_df_list = (pd.read_csv(f_df) for f_df in TT_df_list)\n",
    "ttbar = pd.concat(ttbar_df_list, ignore_index=True)\n",
    "ttbar = ttbar.drop(ttbar.columns[[0]], 1) #Remove 2 extra columns we have in this df, so it match with Signal\n",
    "\n",
    "# These processes have a different cross-sextion. You need to know how to weight each event such that yuo can estimate the real number of events expected in a given Luminosity.\n",
    "# The weight is (Xsec*Br)*Lumi/N_totalEvent_genrated.\n",
    "# First you need to knwow the Total number of MC events generated\n",
    "MyFile_hh =  ROOT.TFile.Open(h_file,\"read\");\n",
    "h_prehlt_hh = ROOT.TH1F(MyFile_hh.Get(\"TriggerResults/hevent_filter\"))\n",
    "nTOT_prehlt_hh = h_prehlt_hh.GetBinContent(2) # Here is stored the number of total event generated\n",
    "nTOT_prehlt_ttbar = 102114184 #Harcoded\n",
    "Lumi = 36.42 * 1000 #1000 is for passing from fb-1 to pb-1 (in which the xsec is expressed). \n",
    "hh['XsecBr'] = hh['XsecBr']*Lumi/nTOT_prehlt_hh\n",
    "ttbar['XsecBr'] = ttbar['XsecBr']*Lumi/nTOT_prehlt_ttbar\n",
    "# Add all weights in the df (you are adding the Data/MC scale factors too)\n",
    "hh['fin_weight']    = hh['XsecBr'] * hh['muon1_pogSF'] * hh['muon2_pogSF'] #1pb is S Xsec.\n",
    "ttbar['fin_weight'] = ttbar['XsecBr'] * ttbar['muon1_pogSF'] * ttbar['muon2_pogSF'] #87pb is TT Xsec.\n",
    "print \"Assuming a Signal of 1pb and a background of 87pb (B.R. included) you expect, after the preselection, to have:\",hh['fin_weight'].sum(),\"S and \",ttbar['fin_weight'].sum(),\"B\"\n",
    "\n",
    "## Alternatively you can save a df as a h5 file (for quick loading in the future)\n",
    "#  Ex: io.save(open('models/ttbar.h5', 'wb'), ttbar); ttbar = io.load(open('models/ttbar.h5', 'rb'));\n",
    "if debug:\n",
    "    print(\"---> hh Displayed as panda dataframe: \"); print(hh)\n",
    "    print(\"The shape for hh is (samples, features): \"); print(hh.shape)\n",
    "    print(\"The shape for tt is (samples, features): \"); print(ttbar.shape)\n",
    "    print hh.keys()\n",
    "    print ttbar.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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L8qkkNybZWmv9WL9tR3rPT0+tdW96j1h7Rb//RUkurbUOcwHxP0vvMWyX9be59Ofszo4E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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x138eb2b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OT2jJ+GScGZ+MM+OTcbZWxudKJz1HGbz3J3lqKWV6Sfjdlt4iakfOsO+2Zdu2JTm4gvbn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\nnjv8d0Q0Vk0FFjUdvhh45QjrpZZUT76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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113888550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dSd6W5E1JUhTF7Ume2lqe/dj2c7dmns+VZfn5/a0aAGAyDbZxajK4nuwezx0L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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1393c8fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0AjW9MB71AFu/38vx4wfzidAu9cIkfD+3anvEeaeeleTstmNnk8zu5iaPPbba+RHnhYWj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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x135fb6a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qF/3qF/3qHz3rF/3qF/3a3bq8cP+BJM8rpWwO8zdm7TFYpzfvWGtd3RSiN3w8yZHtLREA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\nJEmSJKkHFtKSJEmSJPXgb8eNo8s9a/VcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13ae9b790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OJNcluSpJSinbknyn1no8yUeTvDPJe0opH0jyhiRTST4y4Nu9P8lvl1K+0X/9ziQ3Du1k\noJHJzmQunt456mEAAACrMOrl4d6S5PNJPp1kT5LdtdaP9fcdSO/53am1HknysiQv6be/NMkVtdZB\nb3x9d5J/l+TPkvxpkn+d5F8O6RwAAADgtCa63fG/b3kc3Hvv0bH+Rk1OdrJly1QOHZpd8/c/nJw/\nuepLo/fPHsxFUxeaLU7y9SP3JMnj/r1YTzXJ+qAmGTdqknGjJhk3a6EmL7jgvIFW4B71jDc8yr6Z\nA9k/e/DMDR/DRVMXZsfm7WduCAAA0NgoVzWH0zJbDQAArBdmvAEAAKAhwRsAAAAaErwBAACgIcEb\nAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoS\nvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACg\nIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAA\nABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwB\nAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHB\nGwAAABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAa\nErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAA\noCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsA\nAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKChyVEPAGhv/+zBVfexY/P2THb8ygAA\ngOXyVzSsczs2b191HwvB/eLpnavuCwAAzjaCN6xzk51JgRkAAEbIPd4AAADQkOANAAAADQneAAAA\n0NBI7/EupZyTZE+Slyc5nuSGWuuNp2n7/CQ3JXlukjuTvLHW+vlF+1+d5B1Jtif5VJLX1Vrv6+/b\nkuR3klzRf58PJXlbrXW+0akBAABAktHPeL87yQuSvDTJm5LsLqW8YmmjUspUkk8m+WySH05yW5JP\n9LenlPIjST6Y5PoklybZkuTmRV38qyQXJXlJkl9IcmWSa1qcEAAAACw2suDdD82vTXJNrfULtdY/\nS/KuJFefovmr0pupfmut9ctJrk1yNMkr+/uvTvKRWuuHaq1fSvKLSa4opTytv/+KJP9XrfXOWuun\nk/xJkh9vdW4AAACwYJQz3s9L8oT0Zq8X3JrkhaWUpeO6NMmttdZukvQ/703yokX7P7PQuNZ6T5K7\n+9uT5NtJfqGU8sRSykVJfjrJXw/3dAAAAODRRnmP9/Yk99VaH1y07WCSc5I8Ocm9S9reueT4g0me\ns2j//lPsf2r/6zcl+dfpzZJ3kvw/6V2WPrBOZyKdzsRyDnlcbdjQecTntWzDht73eXJy7Z/LerGS\nn8l6qknWBzXJuFGTjBs1ybhZTzU5yuD9xCQnlmxbeL1pwLabBtxfkvxVemF7e3r3fP9qkn8x6GC3\nbp3KxMT4Bu8F09PnjnoIq/bt+d45bNkyNeKRsGA1P5P1UJOsL2qScaMmGTdqknGzHmpylMH7gTw6\nYC+8PjZg22Nn2l9KeWaSG5PsrLUeSJJSyhOTvL+U8tu11pODDPb++2fHfsZ7evrcHDlyPHNza3ux\n9qNHjydJDnVmRzwSFqzkZ7KeapL1QU0ybtQk40ZNMm7WQk0OOjE1yuC9L8lTSimTi8LvtvQWUTt8\nirbblmzbluTAAPufn94l7QcW7fvrJOcl2ZrkW4MMdn6+m/n57iBNR2pubj4nT45nUQ5qbq73fV7r\n57GerOZnsh5qkvVFTTJu1CTjRk0ybtZDTY7yYvkvJnko310ALUkuT3LHKZ6v/bkkLy6lTCRJ//Nl\n/e0L+y9faFxK2ZlkZ3/7/vQC/vcs6u/7kszkkfeRAwAAwNCNbMa71nqslHJLkptKKVcl2ZHkuiRX\nJUkpZVuS79Rajyf5aJJ3JnlPKeUDSd6QZCrJR/rdvT/JX5RSbk9yR5L3Jvl4rfVvSyn3JPlvST5U\nStmV5CnpPT/8dxdWSQcAAIBWRr083FuSfD7Jp5PsSbK71vqx/r4D6T2/O7XWI0leluQl/faXJrmi\n1jrb3397emF8d3qPJzuUfoDvX8Z+RZLZJJ9Nb3XzDyf59fanBwAAwNluots16TuIe+89OtbfqMnJ\nTrZsmcqhQ7Nr/v6Hrx+5J0ly8fTOEY+EBSv5maynmmR9UJOMGzXJuFGTjJu1UJMXXHDeQCtwj3rG\nGwAAANY1wRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACg\nIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAA\nABoSvAEAAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwB\nAACgIcEbAAAAGhK8AQAAoKHJUQ8AGH+///H/ltnjD6XzwN3LOq7Tmcj8fPfh19NTG7P7ykuGPTwA\nABhrgjdwRrPHH8qRYw+lO3ti1EMBAIA1R/AGBjYxkZy/edPA7RdmvA/PnEi3e+b2AACwHgnesM5d\nf/MdOTL74Kr6ONp9KEkvdN/45ssGOmZyspMtW6Zy6NBsrnnvZ3PoqNlyAADOToI3rHNHZh9cdeid\nmBrSYAAA4CwkeMNZYrmXiS82f84TkiTTGzYOc0gAAHBWELzhLLGcy8SX+vqRe5IkF0/vHOaQAADg\nrOA53gAAANCQGW+G6uT8yeybObCqPvbPHsxFUxcOaUQAAACjZcabodo3cyD7Zw+uqo+Lpi7Mjs3b\nhzQiAACA0TLjzdBdNHWhe4EBAAD6zHgDAABAQ2a84RSuv/mOHJl9cCh9TU9tzO4rLxlKXwAAwNoj\neMMpHJl9MIeOnhj1MAAAgHVA8IbHMDHRe/71ShyeOZFud8gDAgAA1hzBGx7D+Zs35cY3X7aiY3ft\n2WvWHAAAsLgaAAAAtCR4AwAAQEOCNwAAADQkeAMAAEBDgjcAAAA0JHgDAABAQx4nBmPs+pvvyJHZ\nB1fVx+EZjzQDAIBRErxhjB2ZfdCzwAEAYI0TvGENmJhIzt+8aVV9TE9tHNJoAACA5RC8YQ04f/Om\n3Pjmy0Y9DAAAYAUsrgYAAAANmfGGxg7PnMiuPXtXfCwAALC2Cd7QWLcbC6QBAMBZbMXBu5Tyc0k+\nU2v9Rinl15L8L0n2Jrmm1vrAsAYIa9UwFzOzMBoAAKxdKwre/aD9tiQ/Xkq5OMnbk/xBkh9L8s4k\n1w5rgLBW7b7yklEPAQAAGAMrXVztl5P8Uq31tiSvSPK5Wuvrk/zTJK8c1uAAAABgrVtp8L4oye39\nr/+HJJ/qf31Pki2rHRQAAACsFyu9x/sbSZ5VSjknyQ8k+fP+9pekF74BAACArDx435TkT5M8kORL\ntdbbSylvSnJDkl8f1uCA9WU1j1ZbMD210f3zAACsKSsK3rXWG0opNcnTk/xxf/PhJFfXWv9wWIMD\n1hePVgMA4Gy04seJ1Vr/Y5KUUjb1X//JsAYFrC/DeBza4ZkT6XaHMBgAAHicreY53m9M8qtJdpZS\nnpXkrUn21VrfMazBAevDMC4N37Vnr9lyAADWpBWtal5K+bn0ntd9S5IH+5u/nORtpZRdQxobAAAA\nrHkrfZzYdUmuqbX+RpK5JKm1vi/Jm5O8YThDAwAAgLVvpcG7JPnMKbZ/OsnOlQ8HAAAA1peVBu9v\nphe+l3pxkv0rHw4AAACsLysN3h9IsqeU8j8lmUhS+outvTfJHw1rcAAAALDWrfQ53u8qpZyf5MNJ\nzknyiSQnk9yU5DeHNzwAAABY21bzHO//s5TyjiQ/kN7M+X+vtR4Z2siAsbJ/9uCy2m/YMJFvz5+b\no0ePZ26umx2bt2eys+JfOQAAsGYN/FdwKeVHk9xWaz3Z/3qpf1BK77bvWuupFl4D1qgdm7ev6viF\n0H7xtLUXAQA4+yxn+ukvkmxL8q3+19307u9eqptkw2oHBoyPyc7kskPz5GQnW7ZM5VBnNnNz3UYj\nAwCA8bec4P20JPf2v/7eJPPDHw4AAACsLwMH71rr1xe9/HdJXltr/dLwhwQAAADrx0ofJ/b0JLPD\nHAgAAACsRytdYvhdST5YSnl3kq8mOb54Z6317tUODOBUDs+cyK49e1fVx/TUxuy+8pIhjQgAAB7b\nSoP3v0hvAbUfTW8xtQUTsbga0FC3mxw6emLUwwAAgIGtNHj/xFBHAXAG01MbV93H4ZkT6VpgHQCA\nx9lKg/c/THJDrfXY4o2llOkkb0/yX1Y7MIDFhnFp+K49e82WAwDwuBs4eJdSvi/J9/Rf7k7yX0sp\nh5Y0e26S1ye5djjDAwAAgLVtOTPe35vkP+a793T/2Wna/eGqRgRDcP3Nd+TI7IMrPv7wjFlRAABg\nOJbzHO9PlFL+fnqPIPv/kvxIknsXNekmmam13j/UEcIKHJl90CXFAADAWFjWPd4LjwkrpTwtyd21\nVssUMdYmJpLzN29a8fHDWNALAAA4u610cbV7kvx8KeWyJBvTe4zYw2qtvzxIJ6WUc5LsSfLy9J4F\nfkOt9cbTtH1+kpvSu4/8ziRvrLV+ftH+Vyd5R5LtST6V5HW11vv6+yaS/EaSNyZ5QpKPJvnfaq0P\nDHi+rFHnb96UG9982aiHAQAAnMU6KzzuXya5JckLkzw9ydOWfAzq3UlekOSlSd6UZHcp5RVLG5VS\nppJ8Mslnk/xwktuSfKK/PaWUH0nywSTXJ7k0yZYkNy/q4lf7/b86yU/332/3MsYJAAAAK7LSGe+f\nT/LLtdZbVvrG/dD82iQ/U2v9QpIvlFKeneTq9GakF3tVejPib621dksp1ya5Iskr0wvYVyf5SK31\nQ/2+fzHJ1xcuiU/yliTX1Vr/3/7+3Ules9KxAwAAwKBWOuO9Kat/Vvfz0rvs+7ZF225N8sJSytJx\nXZrk1oV7yvuf9yZ50aL9n1loXGu9J73AfWmSZyd5SpJ/v2j/v6m1/uQqxw8AAABntNIZ708l+R/T\nuz97pbYnua/WuviZTweTnJPkyXnkiunb07uvO0vaPmfR/v2n2P/U9GbK70/y4lLKb6YXwv/vJL9a\nax142etOZyKdzsSZG47Ihg2dR3we3Th636PJydGOY7FxGsvZZHFNqgvGwbj8noQFapJxoyYZN+up\nJlcavG9P8q5Syo8n+XKSRwTYWuvbB+jjiUuPW/R66TLUp2u7aYD9m/v735nkV5JsSG+Rtg1J/tcB\nxpkk2bp1KhMT4xu8F0xPnzvS9//2fO/9t2yZGuk4Fv6TpNOZGPlYznbT0+fmvIfUBeNj1L8nYSk1\nybhRk4yb9VCTKw3eVyf5VpLn9z8W6yYZJHg/kEcH7IXXxwZse2yA/SeTnJveKub/JUlKKbuS/NtS\nyjW11vkBxpr7758d+xnv6elzc+TI8czNDXRKTRw9ejxJcqgzO7IxJMn8fPfhz4cOjXYsZ6vFNaku\nGAfj8nsSFqhJxo2aZNyshZocdDJn4OBdStlaa70/SWqtp1y5vJSyMcnLBuxyX5KnlFIma60n+9u2\npXdp+OFTtN22ZNu2JAcG2L/Q5r8v2lfTu6T9gvQuST+j+fnuw3+0j7O5ufmcPDm6opyb632PRjmG\npcZpLGejubl5dcFYGfXvSVhKTTJu1CTjZj3U5HIulr+3lPI9izeUUm5Zsm1Lkj8dsL8vJnkovQXQ\nFlye5I5TzEJ/Lr17tCf67zuR5LL+9oX9ly8a184kO/vb/zrJg+kt5rbg+5McTfLtAccKAAAAK7Kc\nS81PdZ31/5zes7O/dYZ2j1JrPVZKuSXJTaWUq5LsSHJdkquSpJSyLcl3aq3H03u82DuTvKeU8oEk\nb0gyleSulQ12AAAgAElEQVQj/e7en+QvSim3J7kjyXuTfLzW+rf9vn4/ye+UUl7TH99vJ/mDRTPt\nAAAA0MRK7/F+LMu5Hvst6YXmTyf5TpLdtdaP9fcdSC+E31xrPVJKeVl6i6K9PsmXklxRa51Nklrr\n7aWUN6R3b/nWJH+e5HVL3uddST6ZXvD+4yT/x8pOD1jrDs+cyK49e1fVx/TUxuy+8pIhjQgAgPWs\nRfAeWK31WJLX9D+W7ptY8vovk/zQY/R1c5KbT7PvwSTX9j+As1y3mxw6OvDTBAEAYFVGGrwBHk/T\nUxtX3cfhmRPpjv86iwAAjJHlBu9T/bnpT1BgTRjGpeG79uw1Ww4AwLIsN3i/r5RyfNHrTUneVUo5\n2n+99p9sDgAAAEO0nOD9mTz6Wdl7kzyl/7G4HQAAAJBlBO9a6481HAcAAACsS51RDwAAAADWM8Eb\nAAAAGvI4MYAVODxzIrv27F1VH9NTG4ey0joAAONN8AZYgW43HisGAMBABG+AZZie2rjqPg7PnEi3\nO4TBAACwJgjeAMswjEvDd+3Za7YcAOAsYnE1AAAAaEjwBgAAgIYEbwAAAGhI8AYAAICGBG8AAABo\nSPAGAACAhgRvAAAAaEjwBgAAgIYEbwAAAGhI8AYAAICGBG8AAABoSPAGAACAhgRvAAAAaEjwBgAA\ngIYEbwAAAGhI8AYAAICGBG8AAABoSPAGAACAhgRvAAAAaEjwBgAAgIYEbwAAAGhI8AYAAICGBG8A\nAABoSPAGAACAhgRvAAAAaEjwBgAAgIYEbwAAAGhI8AYAAICGBG8AAABoSPAGAACAhgRvAAAAaEjw\nBgAAgIYEbwAAAGhI8AYAAICGBG8AAABoSPAGAACAhgRvAAAAaEjwBgAAgIYEbwAAAGhI8AYAAICG\nBG8AAABoSPAGAACAhgRvAAAAaEjwBgAAgIYEbwAAAGhoctQDAM4O+2cPrrqPHZu3Z7Lj1xYAAGuL\nv2CB5nZs3r7qPhaC+8XTO1fdFwAAPJ4Eb6C5yc6kwAwAwFnLPd4AAADQkOANAAAADbnUHGBEDs+c\nyK49e1d8/PTUxuy+8pIhjggAgBYEb4AR6XaTQ0dPjHoYAAA0JngDPM6mpzau6vjDMyfS7Q5pMAAA\nNCd4AzzOVnt5+K49e82UAwCsIRZXAwAAgIYEbwAAAGhI8AYAAICGBG8AAABoSPAGAACAhgRvAAAA\naMjjxHjYyfmT2TdzYFV97J89mIumLhzSiAAAANY+M948bN/MgeyfPbiqPi6aujA7Nm8f0ogAAADW\nPjPePMJFUxfm4umdox4GMIDDMyeya8/eVfUxPbUxu6+8ZEgjAgDgVARvgDWq200OHT0x6mEAAHAG\ngjfAGjM9tXHVfRyeOZFudwiDAQDgjARvgDVmGJeG79qz12w5AMDjxOJqAAAA0JDgDQAAAA0J3gAA\nANCQe7wZO9fffEeOzD64qj4Oz7h3FQAAGA+CN2PnyOyDFn0CAADWDcGbsTUxkZy/edOq+hjGY5cA\nAABWQ/BmbJ2/eVNufPNlox4GAADAqlhcDQAAABoSvAEAAKAhwRsAAAAaErwBAACgoZEurlZKOSfJ\nniQvT3I8yQ211htP0/b5SW5K8twkdyZ5Y63184v2vzrJO5JsT/KpJK+rtd53in72JHl2rfXHhns2\nAAAA8GijnvF+d5IXJHlpkjcl2V1KecXSRqWUqSSfTPLZJD+c5LYkn+hvTynlR5J8MMn1SS5NsiXJ\nzafo58VJ/lmLEwEAAIBTGVnw7ofm1ya5ptb6hVrrnyV5V5KrT9H8VenNiL+11vrlJNcmOZrklf39\nVyf5SK31Q7XWLyX5xSRXlFKetuj9Nib5vSS3tzonAAAAWGqUl5o/L8kT0pu9XnBrkreVUjq11vlF\n2y9NcmuttZsktdZuKWVvkhelN7N9aZJ3LjSutd5TSrm7v/1v+5v/eZIvJflKkh9b7mA7nYl0OhPL\nPexxs2FD5xGfV9ZH7/wmJ0d9IcR3jdNYWJ5h1OQj+xu/+lwvzpbv6bBrElZLTTJu1CTjZj3V5CiD\n9/Yk99VaH1y07WCSc5I8Ocm9S9reueT4g0mes2j//lPsf2qSlFK+L71L2Z+XFV5qvnXrVCYmxjd4\nL5iePnfFx357vnfsli1TwxrOiiz8B0enMzHysbB6q6nJxcalPteLs/nf2bBqEoZFTTJu1CTjZj3U\n5CiD9xOTnFiybeH1pgHbbjrT/lLKRHqXmO+utR4spaxosPffPzv2M97T0+fmyJHjmZubP/MBp3D0\n6PEkyaHO7DCHtmzz892HPx86NNqxsHLDqMnFxqU+14uz8d/ZsGsSVktNMm7UJONmLdTkoBMYowze\nD+TRAXvh9bEB2x4bYP/rk2xIL3yv2Px89+E/VMfZ3Nx8Tp5cWVHOzfXOb6XHtzBOY2FlVlOTj+xn\n/OpzvTjbvqfDqkkYFjXJuFGTjJv1UJOjDN77kjyllDJZaz3Z37YtvUXUDp+i7bYl27YlOTDA/ten\nt3L60f5s98YkG0opM0l+oNZ69xDOBQAAAE5plHepfzHJQ+ktgLbg8iR3LFlYLUk+l+TF/cvG0/98\nWX/7wv7LFxqXUnYm2dnf/gtJnp3kH/Q/bkryV/2vl94XDgAAAEM1shnvWuuxUsotSW4qpVyVZEeS\n65JclSSllG1JvlNrPZ7ko+mtWv6eUsoHkrwhyVSSj/S7e3+Svyil3J7kjiTvTfLxWuvfZolSyv1J\njtdav9r0BAEAACCjnfFOkrck+XySTyfZk94CaB/r7zuQ3vO7U2s9kuRlSV7Sb39pkitqrbP9/ben\nF8Z3p/d4skPpB3gAAAAYpVHe451a67Ekr+l/LN03seT1Xyb5ocfo6+b0nul9pvf8jWUOEwAAAFZs\n1DPeAAAAsK4J3gAAANCQ4A0AAAANCd4AAADQkOANAAAADQneAAAA0JDgDQAAAA0J3gAAANCQ4A0A\nAAANCd4AAADQkOANAAAADQneAAAA0JDgDQAAAA0J3gAAANCQ4A0AAAANCd4AAADQkOANAAAADQne\nAAAA0JDgDQAAAA0J3gAAANCQ4A0AAAANTY56AACMzuGZE9m1Z++q+pie2pjdV14ypBEBAKw/gjew\nZuyfPbjqPnZs3p7Jjl99C7rd5NDRE6MeBgDAuuavT2BN2LF5+6r7WAjuF0/vXHVfa9301MZV93F4\n5kS63SEMBgBgnRO8gTVhsjMpMA/RMC4N37Vnr9lyAIABWFwNAAAAGhK8AQAAoCHBGwAAABoSvAEA\nAKAhwRsAAAAaErwBAACgIcEbAAAAGhK8AQAAoKHJUQ8AgLXt8MyJ7Nqzd1V9TE9tzO4rLxnSiAAA\nxovgDcCqdLvJoaMnRj0MAICxJXgDsCLTUxtX3cfhmRPpdocwGACAMSZ4A7Aiw7g0fNeevWbLAYB1\nz+JqAAAA0JDgDQAAAA0J3gAAANCQ4A0AAAANCd4AAADQkOANAAAADQneAAAA0JDgDQAAAA0J3gAA\nANCQ4A0AAAANCd4AAADQkOANAAAADQneAAAA0JDgDQAAAA0J3gAAANCQ4A0AAAANCd4AAADQkOAN\nAAAADQneAAAA0JDgDQAAAA0J3gAAANCQ4A0AAAANCd4AAADQkOANAAAADQneAAAA0JDgDQAAAA0J\n3gAAANCQ4A0AAAANCd4AAADQkOANAAAADQneAAAA0JDgDQAAAA0J3gAAANCQ4A0AAAANCd4AAADQ\n0OSoBwAAh2dOZNeevavqY3pqY3ZfecmQRgQAMDyCN3BW2T97cNV97Ni8PZMdvz6HqdtNDh09Meph\nAAA04S9H4KyxY/P2VfexENwvnt656r7ozVKv1uGZE+l2hzAYAIBGBG/grDHZmRSYx8wwLg3ftWev\n2XIAYKxZXA0AAAAaErwBAACgIcEbAAAAGhK8AQAAoCHBGwAAABoSvAEAAKAhwRsAAAAaErwBAACg\nIcEbAAAAGhK8AQAAoCHBGwAAABqaHOWbl1LOSbInycuTHE9yQ631xtO0fX6Sm5I8N8mdSd5Ya/38\nov2vTvKOJNuTfCrJ62qt9/X3nZ/khiT/KL3/bPhEkmtrrYcbnRoAAAAkGf2M97uTvCDJS5O8Kcnu\nUsorljYqpUwl+WSSzyb54SS3JflEf3tKKT+S5INJrk9yaZItSW5e1MVNSZ6X5IokP5Xk+5P8fpMz\nAgAAgEVGNuPdD82vTfIztdYvJPlCKeXZSa5O8tElzV+V3oz4W2ut3VLKtemF6FemF7CvTvKRWuuH\n+n3/YpKvl1KeluRbSV6R5LKFGfL+8Z8tpZxTa32g8akCAABwFhvlpebPS/KE9GavF9ya5G2llE6t\ndX7R9kuT3Fpr7SZJP3zvTfKi9IL3pUneudC41npPKeXu/vZ/n+RlSb645P03JNmcZKDg3elMpNOZ\nGPzsHmcbNnQe8XllffTOb3Jy1BdCfNc4jYXlGUZNjqNx/HfCdz3Wz2W91iRrl5pk3KhJxs16qslR\nBu/tSe6rtT64aNvBJOckeXKSe5e0vXPJ8QeTPGfR/v2n2P/UWuvxJP95yb5rknxp4R7wQWzdOpWJ\nifEN3gump89d8bHfnu8du2XL1LCGsyIL/8HR6UyMfCys3mpqchyNy78Tvmu5vzPWW02y9qlJxo2a\nZNysh5ocZfB+YpITS7YtvN40YNtNA+5/WCnl6iT/JMlPL2ew998/O/Yz3tPT5+bIkeOZm5s/8wGn\ncPTo8STJoc7sMIe2bPPz3Yc/Hzo02rGwcsOoyXE0Lv9O+K5Bf2es15pk7VKTjBs1ybhZCzU56GTM\nKIP3A3l0MF54fWzAtscG3J8kKaW8Kcn7kvxKrfXPlzPY+fnuw3/cjbO5ufmcPLmyopyb653fSo9v\nYZzGwsqspibH0Tj+O+G7Bvm5rLeaZO1Tk4wbNcm4WQ81OcqL5fcleUopZXH435beImpLH/O1r78v\nS9oeGHB/SinXpffosv+91vre1Q0dAAAABjPK4P3FJA+ltwDagsuT3LFkYbUk+VySF5dSJpKk//my\n/vaF/ZcvNC6l7Eyyc2F/KeU16T267FdqrTcM/1QAAADg1EZ2qXmt9Vgp5ZYkN5VSrkqyI8l1Sa5K\nklLKtiTf6S+O9tH0Vi1/TynlA0nekGQqyUf63b0/yV+UUm5PckeS9yb5eK31b0spW5P8bpJbkny4\n3++Ce2utc63P9Wxy/c135Mjsg2du+BgOzyy9XR8AAGDtGuU93knylvRC86eTfCfJ7lrrx/r7DqQX\nwm+utR4ppbwsyU1JXp/kS0muqLXOJkmt9fZSyhuSvD3J1iR/nuR1/X5+Mr3Hhr2m/7HY05L8XZtT\nOzsdmX0wh44KzgAAAAtGGrxrrcdy6kCcWuvEktd/meSHHqOvm9N7pvfS7R9O8uFVDpVlmphIzt/8\nqEXll2V6auOQRgMAADA6o57xZp06f/Om3Pjmy0Y9DAAAgJEb5eJqAAAAsO4J3gAAANCQ4A0AAAAN\nCd4AAADQkOANAAAADQneAAAA0JDHiQGwLhyeOZFde/Y+ZptOZyLz893T7p+e2pjdV14y7KEBAGc5\nwRuAdaHbTQ4dPTHqYQAAPIrgDcCaNj21ceC2p5vxPjxzIt3TT4QDAKyK4A3AmjbopeGTk51s2TKV\nQ4dmc/Lk/CP27dqz12w5ANCM4A2wTPtnD666jx2bt2ey41cwAMDZwF99AMuwY/P2VfexENwvnt65\n6r4AABh/gjfAMkx2JgVmAACWxXO8AQAAoCHBGwAAABoSvP//9u4+yK66POD4dzdLAtmwBCMlMSCi\ntk8RraCi4a0q05GWwVe0IKM2VBRUqmhqZdQhZXQKCoz4kjFYaaNirSJCKeDgtAOjROgEGHxBeapT\nASUQeUnM7iaEvNz+cc6Fy5Ilm7337Ll79/uZ2bl7z+/c3/3tzjP3nuf83iRJkiRJqpCJtyRJkiRJ\nFTLxliRJkiSpQibekiRJkiRVyMRbkiRJkqQKmXhLkiRJklShgboboM7YtmMbv37kHoaHN7N9e2NS\ndawdXcdzBvfvcMskSZIkaWYz8e4Rvxteyx8aG9inb/6k63jO4P4snreog62SJEmSJJl495ADhhax\noH8/tm3bUXdTJEmSJEkl53hLkiRJklQhe7wlSSptGNnCshWrJ/36ocHZLF96RAdbJEmSeoGJtyRJ\npUYD1g9vqbsZkiSpx5h4S5JmvKHB2W29fsPIFhqT21BCkiTNACbekqQZr93h4ctWrLanXJIkjcvF\n1SRJkiRJqpCJtyRJkiRJFTLxliRJkiSpQibekiRJkiRVyMRbkiRJkqQKmXhLkiRJklQhtxOTpBqs\nHV3X1usXz1vEQL8f4ZIkSdOBV22SNMUWz1vU1uubSftBQwd2ojmSJEmqmIm3JE2xgf4Bk2ZJkqQZ\nxDnekiRJkiRVyMRbkiRJkqQKOdRckqQO2TCyhWUrVrdVx9DgbJYvPaJDLZIkSd3AxFuSpA5pNGD9\n8Ja6myFJkrqMibckSW0aGpzddh0bRrbQaHSgMZIkqeuYeEuS1KZODA1ftmK1veWSJPUoF1eTJEmS\nJKlCJt6SJEmSJFXIxFuSJEmSpAqZeEuSJEmSVCETb0mSJEmSKmTiLUmSJElShUy8JUmSJEmqkPt4\nS9I0tHZ0Xdt1LJ63iIF+vwYkSZKq5hWXnnDeqjVsHH28rTo2jGzpUGskjWfxvEVt19FM3A8aOrDt\nuiRJkvTMTLz1hI2jj7N+2MRZ6nYD/QMmzD1sw8gWlq1Y3VYdQ4OzWb70iA61SJIktcvEW0/T1wfz\n581pq46hwdkdao0kzSyNBt4ElSSpx5h462nmz5vDxR84uu5mSNKM0okblhtGttBodKAxkiSpo0y8\nJUnqAp0YGr5sxWp7yyVJ6kJuJyZJkiRJUoVMvCVJkiRJqpCJtyRJkiRJFTLxliRJkiSpQi6uJklS\nj+nEXuCd4H7ikiQVTLwlSeox7gUuSVJ3MfGWpBlq7ei6tutYPG8RA/1+lXSLTuwF3gnuJy5J0lN5\ntSRJM9DieYvarqOZuB80dGDbdakzumVYt/uJS5L0VCbekjQDDfQPmDBLkiRNEVc1lyRJkiSpQibe\nkiRJkiRVyMRbkiRJkqQKmXhLkiRJklQhE29JkiRJkirkquaSpElzL3BJkqRd80pHkjQp7gUuSZI0\nMSbekqRJcS9wSZKkiXGOtyRJkiRJFbLHW5IkVWLDyBaWrVhdaxuGBmezfOkRtbZBkiQTb0lSrVyg\nrXc1GrB+eEvdzZAkqXZepUiSauMCbb1paHB23U1gw8gWGo26WyFJUsHEW5JUGxdo603dMLR72YrV\nbfe2n7dqDRtHH+9IexzyLkkzm4m3JEnSTmwcfdyh8pKkjjDx7hGXXnMXo49to2/T/EnXsWHEiwtJ\n09NE5onPmtXHIzv2Ynh4M9u3P30MsvPENZ6+Ppg/b86kXuuQd0kSmHj3jJFNW9m4aSuNUZNnSTOL\n88RVtfnz5nDxB46e1Gs7MeRdkjT9mXj3mHbuyjd1w6I4kjRRE50nPjDQz777DrK+f5Rt23Y8rbzd\n1dXtMZckSePxCqHHtHNXXpJmqnZ7ze0x717t7CXeySlY47Wjv7+PHTsmNhbdBdokafoy8ZYkzXid\nWF3d/ci7U7fsJd4t7ZAk1cNvd0mS2tSpeeZrR9fxnMH9226LyXtnp021U9euXjuRHu92F2jr5LZo\nnWDPvaSZqK9R41KbEbEnsAI4CdgMXJSZF49z7uHASuAlwF3AmZl5e0v524FPA4uAG4D3ZObDZVkf\ncD7wbmAW8FXgnMx8+iS/cTz00HBXr0n64cuuZeOmrczv/yOHmqsrPDGfdv3O59NKU63bY3Lbjm3c\nP/JAW3U0e91N3qeHicZkc4G2ya7j0o097fvu3f56NJNN3jt1I6IXbyB0++ekZp7pEJP77bd330TO\nq/tb9ULgFcBxwEHA1yLi3sz8butJETEIXA98E1gKnAlcFxEvyMzRiHglcFl5/E7gC8Aq4MSyio8A\npwJvBvYALgd+D1xU5R8nSdJEdWK4++J5izqSvNvz3p06MVy93YS3Ha1tr/NmQDfsz97JUQi9eANA\n6kW1fSOWyfTpwF9l5h3AHRFxKHAW8N0xp59M0SP+0cxsRMTZwAnA2ygS7LOA72Tm18u63wncGxEH\nZ+ZvgA8B52bmzWX5xyh6x028JUk9o9eS927QDTcQOjVsvu4ErRPJZnPYfScWzZvsCIJOtKGTif/6\n4cm3Y2d2Z8G/VpONL6dCdB9vDFWjzm+Sl1L0Pv+45djNwCcion/MMPAlwM2Z2QAok+/VwJEUifcS\n4ILmyZn524i4D1gSEVuAA4EfjnmfgyJiUWa2d3UhSVIP6ZbkvRtUfQNh1qw+HtmxF8PDm9m+ffxE\nZ+lbFnbsPe/d+NuO1bW7OvF3XHLFT9i4aSsAGyY76nQu9AFDc/fgg2/741ra0Df45O9Dc/eYVB3N\nNrTTjp2aZF07tu8xqfjasH0dG3ds3fWJu9DYtDc0+tuup9M3MqajbrsxtGCfPTm3B5L3OhPvRcDD\nmdl6O2UdsCewAHhozLl3jXn9OuDFLeVrd1J+QFnGmPLm0rMHABO6Mujv76O/f0LD92s3MND+h47U\nrlmz+p/yKNXNmJw6A8zmBc86qO5mtO2g+Yv53fDYy4vO6e/vb3nszrmL3WbeJJPU8eqaNWv3r+06\n3YYz3nDopF576TV3MbKp/YR1rL7+Phq70eM9vHkrjUbxeMkVP9nt9xveXPwNfX2w916T+9/umDMM\n+z5G/5a9J/V6qPBGxjTUTTeGGqP70N/f1xPf3XUm3nOBsbdTms/HjvsZ79w5EyifO6buZ3qfcS1Y\nMK+rs+7Lz3l73U2QdmpoaK+6myA9hTGp3bHfgn2qf5MF1b9Fr1j5wUPqbkJXtAG6px2SJqbOWweP\n8fTEt/l80wTP3TSB8sfG1P1M7yNJkiRJUkfVmXjfDzw7Ilp73RdSLKK2YSfnjp0YtJAnh4k/U/n9\nLc8Z8/v0n4AmSZIkSepqdSbedwJbKRZGazoGWLOT/bVvBY4q9+Nu7st9dHm8WX5M8+SIOJBiQbVb\nM3MtcF9refn7fS6sJkmSJEmqWm1zvDNzU0R8DVgZEacBi4G/B04DiIiFwB8yczPF9mIXAJdExKXA\nGcAg8J2yui8DN0XELcAa4PPAteVWYs3yz0TE78rnFwAXV/03SpIkSZJU9/JwHwFuB24EVgDLM/N7\nZdkDFPt3k5kbgROBY8vzlwAnZOZoWX4LRTK+nGJ7svWUCXzpQuDbwFXAFcA3gM9V+YdJkiRJkgTQ\n12hMfLsASZIkSZK0e+ru8ZYkSZIkqaeZeEuSJEmSVCETb0mSJEmSKlTbqubqnIjYk2JxupMo9kG/\nKDNdtV2Vi4g5FAsenpWZN5XHDgb+GTgSuBc4OzN/0PKavwAuAZ5PsRXg6Zn5f1PcdPWYiFhMsaPF\ncRSfg98GPp6ZjxmTqkNEvJDiu/lo4FHgi5l5YVlmTKpWEXEd8FBmLi2fHw6sBF4C3AWcmZm3t5z/\nduDTwCLgBuA9mfnwVLdbvSUi3gx8b8zhKzPzrb0Yk/Z494YLgVdQXHC+H1geEW+tt0nqdeUNn28B\nh7Yc6wOuBh6kiMlvAFdFxHPL8ueW5f8KHAE8BFxdvk6alDJ+vgvMpdj94hTg9cCnjEnVISL6geso\n4ulw4EzgkxFxqjGpukXEKcAJLc8HgeuBHwEvp9gh6LryOBHxSuAy4DyKnYX2BVZNbavVo14E/CdF\n8tz8Ob1XY9LEe5orA/B04EOZeUdmXgV8Fjir3papl0XEiyh6YV4wpui15bEzMvOXmXk+cAvwt2X5\n6cBtmXlxZt5Fse3f84BXT0nD1auC4ov3tMy8KzN/BJwLnIoxqXrsD9wJvC8zf5WZ1wP/DRyDMaka\nRcSzKDps1rQcPplipNBHM/OXwNnAMPC2svws4DuZ+fXM/CnwTuCEcuSG1I5DgJ9n5oMtPxvo0Zg0\n8Z7+XgrsQXEnqOlm4FXlHXepCq8GbqQYJtlqCXBHZo62HLu55bwlwA+bBZm5CbhjJ/VIu+NB4C8z\nc92Y4/tgTKoGmflAZp6cmcMR0RcRRwN/DtyEMal6XUQxyuIXLceWADdnZgOgfFzN+DH5W+C+8rjU\njhcB/7uT4z0Zk87xnv4WAQ9n5uMtx9YBewILKIaoSR2VmV9u/h4RrUWLgLVjTl8HHDDBcmm3lXfH\nb2g+L286nkXRw2hMqm73AM8FrgWupJi7bUxqykXEcRQ3gF4CfLmlaBHFHNpW64AXt5Qbk+qocvpM\nAMdHxMeBWcAVFCPWejImTbynv7nAljHHms/nTHFbpPHicc4Ey6VO+CzwMor5sR/GmFS9TgIWUiQ6\nn8PPSdWgXJflUuADmbl5zE1zY1J1eC5PxtZfAwcDXwD2okdj0sR7+nuMpwdZ8/mmKW6L9BjFSItW\nc3gyFseL1w0Vt0szRER8hmIu2MmZ+fOIMCZVq8y8DZ5IfL4J/AswOOY0Y1JVW06xdsANOykbL+Z2\nFZNeZ2rSMvPeiFgArC+Hkt9Zjli7nGJaTs/FpIn39Hc/8OyIGMjMbeWxhRQLEvglral2Py2rnJcW\nAg+0lC/cSfmdFbdLM0BEfBF4H/COzLyyPGxMaspFxP7AkZl5dcvhXwCzKWLvkDEvMSZVtVOAhREx\nUj6fA1DugvNv7DzmdhWTDyC1ITMfHXPolxTTZR+kB2PSxbemvzuBrTx1MYFjgDWZuaOeJmkGuxV4\nWUTs1XLsmPJ4s/yYZkFEzKXYaudWpDZExHKKLZtOycx/bykyJlWHg4HvlfvLN72cYt2VmzEmNfVe\nQzG3+7Dy55ry5zCK2DqquWVd+Xg048fkgcCBGJNqQ0QcHxGPlJ9xTYcBj1BsI9ZzMdnXaDTqboPa\nFBErKYLvNGAx8DWKbXXGbkgvdVxENIDXZuZNETEL+CnwM+BTFHspfwI4NDPvi4jnUdzNPI9i38Zz\ngRYefgEAAAPiSURBVD8FDmuuXCntrog4hCLmzgdWjCl+CGNSU6z8LLwVeJRinYHnUQwxPx/4Esak\nahYRqwAyc2lEDAG/Br5FMQ/8DIo5ty/MzNGIOJJi6O/7KbYh+zwwnJlvqKHp6hERsTfFZ90PKT7v\nng98lSK+VtKDMWmPd2/4CHA7xfZOK4DlJt2qQ2ZuB95Isdrk7cA7gDdn5n1l+T3AWyhuEq2hmHv7\nJi8m1aY3UqyG+kmKYWZP/BiTqkNL3I1S7NH9VYpFg75gTKrbZOZG4ETgWIqYXAKc0NzyLjNvoUh8\nllNsX7ueIj6lScvMYeB4YD/gNuAy4CvAhb0ak/Z4S5IkSZJUIXu8JUmSJEmqkIm3JEmSJEkVMvGW\nJEmSJKlCJt6SJEmSJFXIxFuSJEmSpAqZeEuSJEmSVCETb0mSJEmSKmTiLUmSJElShQbqboAkSapP\nRPQB7wK+n5m/n+Br7gFWZeY/jjm+J/A/wOcyc9V450fEUcA/AYcDI8D3gX/IzEfb+VskSepW9nhL\nkjSz/TmwCpjbTiURsQ9wNfBnuzjvT4AfAD8FXgWcUj5e0c77S5LUzUy8JUma2frarSAiXk+RSD97\nAqe/C7gf+FBm3p2ZPwLeDxwXEc9vty2SJHUjh5pLktTDIqIBnAW8EzgM+BXwicy8JiJeA9xYnvqb\niDitdYj4bngTsBK4GNiyi3MvB67NzEbLsR3l476TeG9JkrqeibckSb3vAuAc4G+A04CrIuJY4MfA\nScCVwCuBn0+m8sx8d/P3iNjVuXfv5PDHgAcoes0lSeo5DjWXJKn3rcrMFVk4B1gD/F1mPg40FzR7\nKDM3T3XDIuIi4ETgfZm5darfX5KkqWCPtyRJve/GMc9/DLyujoY0RcQewFco5ny/NzP/o872SJJU\nJRNvSZJ639ie5FnA9joaAhARewNXAccCp2SmK5pLknqaQ80lSep9R4x5fhRwR/l7gykUEbOB6yjm\nlB9v0i1Jmgns8ZYkqfedHRF3A7cB7wVeCjQXRBspHw+LiIczc2RnFXTQx4FjgFOBuyNiYUvZo+W8\nc0mSeoo93pIk9b6VwIcpVg0/FnhdZjZXEP8ZcD3wbeCMKWjLqRR7h3+LYiXz1p+jpuD9JUmacn2N\nxpSOMJMkSVOo3Md7svtzS5KkDrDHW5IkSZKkCjnHW5IkARARXwKW7uK0N2Xmf01BcyRJ6hkONZck\nSQBExH7APrs4bW1mbpqK9kiS1CtMvCVJkiRJqpBzvCVJkiRJqpCJtyRJkiRJFTLxliRJkiSpQibe\nkiRJkiRVyMRbkiRJkqQKmXhLkiRJklQhE29JkiRJkir0/8wHxkwZPsYYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13b2cbad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Jrktyba313lLKMxa1fazjHNUDD8wMfMZ7evrM7Nt3MEeOrHyNt9nZuUe/79kzs+L2hmmc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x135f72710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ADYIzAAAANAjOAAAA0CA4AwAAQIPgDAAAAA3DrguA7XZ2fjHHT54aa46n3XhDfvjO2ydU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\nLhlqQ9er14yIWFAff75MItUepRpZdn1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111923450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ANCR4AwAAQEPu4w3Altxz7IGcXTo/kL7mZnbmyJ23DKQvAIBRI3gDsCVnl87nzMLysMsA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\nibckSZIkST1k4i1JkiRJUg/9P8olzDAV+h5eAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13b7a3950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAPrU+v7x5ya5PsmX07kj+vm11k91t61L5/nkqbVuSvLidD4Tfn06q+tn1Frnczenw5Js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\nE5NySZIkSZJqYlIuSZIkSVJN/hVrqlJ9dk6oxAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13b89f450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kkxeFYADYKwRnAOiR8dF9fdUPANAbgjMA9MiJO25tuwQAYBtYVRsAAAAaCM4AAADQwKHa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13b955990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GZ7m7nJmFk31t48TiqUx3pgY0EQAAXF5j4VzX9Zmqqu5OcmdVVW9MciTJO5O8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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13b718e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6WutckvSD+Q1JXpReKD8nyQcGg2utd5VS7uy3/99JXpHk6wuef1WSNUkGofz25ZzM+PhY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\nyiVJkiRJKolJuSRJkiRJJfl/ROHsecfEFTUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13cec9710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XtR9apf2p/a/fkORfpbdK3kny/6R3WvqadToT6XQmzti+bVvnMZ9H2bZtveObnBz9YxkX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\nF8AnjFXVTUQMAldQxNqLgdOBj0XEica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      "text/plain": [
       "<matplotlib.figure.Figure at 0x13cafb610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Producing plots of the features in S and B.\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Plots of the branches we selected\n",
    "if MakePlots:\n",
    "    print \"Producing plots of the features in S and B.\"\n",
    "    for key in ttbar.keys() :\n",
    "        if(key!=\"muon1_pogSF\" and key!=\"muon2_pogSF\" and key!=\"XsecBr\" and key!=\"fin_weight\") :\n",
    "            matplotlib.rcParams.update({'font.size': 16})\n",
    "            fig = plt.figure(figsize=(11.69, 8.27), dpi=100)\n",
    "            bins = np.linspace(my_max(min(ttbar[key]),0.), max(ttbar[key]), 50)\n",
    "            _ = plt.hist(hh[key],  bins=bins, histtype='step', normed=True, label=r'$hh$', linewidth=2)\n",
    "            _ = plt.hist(ttbar[key], bins=bins, histtype='step', normed=True, label=r'$t\\overline{t}$')\n",
    "            plt.xlabel(key)\n",
    "            plt.ylabel('Entries')\n",
    "            plt.legend(loc='best')\n",
    "            plt.savefig(folder + \"/\" + str(key) + '.pdf')\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting the correlation of the features in S and B.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Info in <TCanvas::Print>: pdf file Plots_hh_tt_MLP//Corr_hh.pdf has been created\n",
      "Info in <TCanvas::Print>: pdf file Plots_hh_tt_MLP//Corr_ttbar.pdf has been created\n"
     ]
    }
   ],
   "source": [
    "# Lets look at the correlations of the features\n",
    "c1 = ROOT.TCanvas(); c1.cd(); ROOT.gStyle.SetOptStat(0)\n",
    "if MakePlots:\n",
    "    print \"Plotting the correlation of the features in S and B.\"\n",
    "    h_Corr_hh    = ROOT.TH2F(\"h_Corr_hh\",\"\", len(my_branches_training), 0, len(my_branches_training), len(my_branches_training), 0, len(my_branches_training))\n",
    "    h_Corr_ttbar = ROOT.TH2F(\"h_Corr_ttbar\",\"\", len(my_branches_training), 0, len(my_branches_training), len(my_branches_training), 0, len(my_branches_training))\n",
    "    for var1 in range(len(my_branches_training)):\n",
    "        h_Corr_hh.GetXaxis().SetBinLabel(var1+1,my_branches_training[var1])\n",
    "        h_Corr_ttbar.GetXaxis().SetBinLabel(var1+1,my_branches_training[var1])\n",
    "        for var2 in range(len(my_branches_training)):\n",
    "            h_Corr_hh.GetYaxis().SetBinLabel(var2+1,my_branches_training[var2])\n",
    "            h_Corr_ttbar.GetYaxis().SetBinLabel(var2+1,my_branches_training[var2])\n",
    "            if(var2>=var1):\n",
    "                array_Var1_hh_var1    = np.array( hh[my_branches_training[var1]] )\n",
    "                array_Var1_hh_var2    = np.array( hh[my_branches_training[var2]] )\n",
    "                array_Var1_ttbar_var1 = np.array( ttbar[my_branches_training[var1]] )\n",
    "                array_Var1_ttbar_var2 = np.array( ttbar[my_branches_training[var2]] )\n",
    "                corr = scipy.stats.pearsonr( array_Var1_hh_var1, array_Var1_hh_var2 )[0]\n",
    "                h_Corr_hh.SetBinContent(var1+1,var2+1,corr)\n",
    "                corr = scipy.stats.pearsonr( array_Var1_ttbar_var1, array_Var1_ttbar_var2 )[0]\n",
    "                h_Corr_ttbar.SetBinContent(var1+1,var2+1,corr)\n",
    "    h_Corr_hh.GetZaxis().SetRangeUser(-1.,1.)\n",
    "    h_Corr_ttbar.GetZaxis().SetRangeUser(-1.,1.)\n",
    "    ROOT.gStyle.SetPaintTextFormat(\".2f\");\n",
    "    h_Corr_hh.Draw(\"colzTEXT\")\n",
    "    c1.SaveAs(folder + '/Corr_hh.pdf')\n",
    "    h_Corr_ttbar.Draw(\"colzTEXT\")\n",
    "    c1.SaveAs(folder + '/Corr_ttbar.pdf')\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You need:\n",
    "1. X : matrix with raw=#Events and column=Variables to discriminate.\"\n",
    "2. w : A vector containig the weights of each event\"\n",
    "3. Y : A vector containing for each event if it is signal (0) or TT (1)\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Now lets start to talk about DNN!\n",
      "y is\n"
     ]
    }
   ],
   "source": [
    "print('Now lets start to talk about DNN!')\n",
    "#You only need a Dataframe for the training. So you merge all the one you have\n",
    "df =  pd.concat((hh[my_branches_training], ttbar[my_branches_training]), ignore_index=True)\n",
    "# Turn the df the desired ndarray \"X\" that can be directly used for ML applications.\n",
    "X = df.as_matrix() # Each row is an object to classify, each column corresponds to a specific variable.\n",
    "# Take the weights\n",
    "w =  pd.concat((hh['fin_weight'], ttbar['fin_weight']), ignore_index=True).values\n",
    "# This is the array with the true values: 0 is signal, 1 if TT.\n",
    "y = []\n",
    "for _df, ID in [(hh, 0), (ttbar, 1)]:\n",
    "    y.extend([ID] * _df.shape[0]) # You give to y the ID value (first 0, then 1) a number of time equal to the raw in hh and ttbar\n",
    "print \"y is\"\n",
    "y = np.array(y) # Simply a conversion tu numpy, but still a vector of 0 and 1 (for S and B)\n",
    "\n",
    "# Randomly shuffle and automatically split all your objects into train and test subsets\n",
    "ix = range(X.shape[0]) # array of indices, just to keep track of them for safety reasons and future checks\n",
    "X_train, X_test, y_train, y_test, w_train, w_test, ix_train, ix_test = train_test_split(X, y, w, ix, train_size=0.7) # Train here is 70% of the total statistic\n",
    "# It is common practice to scale the inputs to Neural Nets such that they have approximately similar ranges (it atually improve the results)\n",
    "scaler = StandardScaler() \n",
    "X_train = scaler.fit_transform(X_train)\n",
    "X_test = scaler.transform(X_test) # You are applying the same transformation done to X_train, to X_test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This takes a while, but it is worth do do it once. It shows the correlations for S and B overimposed.\n",
    "# More variables you add in var_toPlot, more times it takes.\n",
    "if MakePlots:\n",
    "    # Next lines to select the same number of entries\n",
    "    rawS = hh.shape[0]\n",
    "    rawB = ttbar.shape[0]\n",
    "    Nraw = rawS;\n",
    "    if (rawB<rawS): Nraw = rawB;\n",
    "    hh_plot    = hh.iloc[0:Nraw]\n",
    "    ttbar_plot = ttbar.iloc[0:Nraw]\n",
    "    # Add the target, that is missing in hh and ttbar\n",
    "    hh_plot['Target'] = 0\n",
    "    ttbar_plot['Target'] = 1\n",
    "    var_toPlot=[\"Target\",\"dphi_llmet\",\"pt_l1l2\",\"mass_l1l2\",\"pt_b1b2\",\"mass_b1b2\",\"HT\",\"met_pt\"]\n",
    "    df_withY = pd.concat((hh_plot[var_toPlot], ttbar_plot[var_toPlot]), ignore_index=True)\n",
    "    # You can select the variable to plot in sns.pairplot using an argumnet vars=['var1','var2'...]\n",
    "    sns_plot = sns.pairplot(df_withY, hue='Target',palette=[\"#e74c3c\",\"#9b59b6\"],plot_kws={\"s\": 3,\"alpha\":0.3},size=5)\n",
    "    sns_plot.savefig(folder + \"/Variables_pairplot.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Multilayer Perceptron (MLP) definition\n",
    "model = Sequential()\n",
    "model.add(Dense(10, input_dim=X_train.shape[1], activation='relu')) # Linear transformation of the input vector. The first number is output_dim.\n",
    "model.add(Dropout(0.1)) # To avoid overfitting. It masks the outputs of the previous layer such that some of them will randomly become inactive and will not contribute to information propagation.\n",
    "model.add(Dense(20, activation='relu'))\n",
    "model.add(Dropout(0.1))\n",
    "model.add(Dense(20, activation='sigmoid'))\n",
    "model.add(Dropout(0.1))\n",
    "model.add(Dense(10,activation='tanh'))\n",
    "model.add(Dropout(0.1))\n",
    "model.add(Dense(20, activation='sigmoid'))\n",
    "model.add(Dropout(0.1))\n",
    "model.add(Dense(2, activation='softmax')) # Last layer has to have the same dimensionality as the number of classes we want to predict, here 2.\n",
    "model.summary()\n",
    "# Now you need to declare what loss function and optimizer to use (and compile your model).\n",
    "model.compile(loss='sparse_categorical_crossentropy', optimizer='adam', metrics=['accuracy'])\n",
    "# Metrics are evaluated by the model during training (here accuracy)\n",
    "# The loss function, also called the objective function is the evaluation of the model used by the optimizer to navigate the weight space.\n",
    "#‘mse‘: for mean squared error.\n",
    "#‘binary_crossentropy‘: for binary logarithmic loss (logloss).\n",
    "#‘categorical_crossentropy‘: for multi-class logarithmic loss (logloss).\n",
    "# http://keras.io/objectives/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "print('---------------------------Training:---------------------------')\n",
    "try:\n",
    "    history = model.fit(X_train, y_train, batch_size=50, epochs=100, verbose=1,\n",
    "              callbacks = [\n",
    "                  EarlyStopping(verbose=True, patience=6, monitor='val_loss'),\n",
    "                  ModelCheckpoint('models/tutorial-progress.h5', monitor='val_loss', verbose=1, save_best_only=True)\n",
    "              ],\n",
    "              validation_split=0.2, validation_data=None, shuffle=True,\n",
    "              class_weight={\n",
    "                0 : compute_class_weight(\"balanced\", [0, 1], y)[0], # Function that return \"[1/N_classes * ((float(len(y)) / (y == 0).sum())), 1/N_classes * ((float(len(y)) / (y == 1).sum()))]\"\n",
    "                1 : compute_class_weight(\"balanced\", [0, 1], y)[1]\n",
    "              },\n",
    "              sample_weight=None,initial_epoch=0)\n",
    "    \n",
    "except KeyboardInterrupt:\n",
    "    print 'Training ended early.'\n",
    "\n",
    "# Epochs is the number of times that the model is exposed to the training dataset.\n",
    "# Batch Size is the number of training instances shown to the model before a weight update is performed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's make some plots about the convergence of our model. You can check if:\n",
    "#  1. It’s speed of convergence over epochs (slope).\n",
    "#  2. Whether the model may have already converged (plateau of the line).\n",
    "#  3. Whether the mode may be over-learning the training data (inflection for validation line).\n",
    "\n",
    "if debug:\n",
    "    print \"All data in history are: \",history.history.keys()\n",
    "# Summarize history for accuracy\n",
    "plt.plot(history.history['acc'])\n",
    "plt.plot(history.history['val_acc'])\n",
    "plt.title('model accuracy')\n",
    "plt.ylabel('accuracy')\n",
    "plt.xlabel('epoch')\n",
    "plt.legend(['train', 'test'], loc='upper left')\n",
    "plt.show()\n",
    "plt.savefig(folder + '/Check_accuracy.pdf')\n",
    "# Summarize history for loss\n",
    "plt.plot(history.history['loss'])\n",
    "plt.plot(history.history['val_loss'])\n",
    "plt.title('model loss')\n",
    "plt.ylabel('loss')\n",
    "plt.xlabel('epoch')\n",
    "plt.legend(['train', 'test'], loc='upper left')\n",
    "plt.show()\n",
    "plt.savefig(folder + '/Check_loss.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the best network (by default you return the last one, you if you save every time you have a better one you are fine loading it later)\n",
    "model.load_weights('./models/tutorial-progress.h5')\n",
    "print 'Saving weights...'\n",
    "model.save_weights('./models/tutorial.h5', overwrite=True)\n",
    "json_string = model.to_json()\n",
    "open('./models/tutorial.json', 'w').write(json_string)\n",
    "print 'Testing...'\n",
    "yhat = model.predict(X_test, verbose = True, batch_size = 50) # Return a vector of 2 indexes [probToBe_S,probToBe_B]\n",
    "#Turn them into classes\n",
    "yhat_cls = np.argmax(yhat, axis=1) # Transform [probToBe_S,probToBe_B] in a vector of 0 and 1 depending if probToBe_S>probToBe_B. Practically return the index of the biggest element (0 is is probToBe_S, if is probToBe_B)\n",
    "#model.evaluate(): To calculate the loss values for input data.\n",
    "#model.predict(): To generate network output for input data.\n",
    "#model.predict_classes(): To generate class outputs for input data.\n",
    "#model.predict_proba(): To generate class probabilities for input data.\n",
    "\n",
    "if debug:\n",
    "    print; print \"y_test is an array:\",y_test\n",
    "    print \"yhat is an array of [probToBe_S,probToBe_B]: \",yhat\n",
    "    print \"yhat_cls is an array:\",yhat_cls\n",
    "\n",
    "# A Plot of the tructure of the MLP (to see the details of your DNN)\n",
    "from keras.utils import plot_model\n",
    "plot_model(model, to_file=folder+'/model.png')\n",
    "\n",
    "if MakePlots:\n",
    "    # Check the predicted and true S and B (Normalized to the expected events for the given Lumi)\n",
    "    bins = np.linspace(-0.5,1.5,3)\n",
    "    names = ['','','','hh','','','','tt']\n",
    "    fig = plt.figure(figsize=(7.69, 5.27), dpi=100)\n",
    "    ax = plt.subplot()\n",
    "    ax.set_xticklabels(names, rotation=45)\n",
    "    _ = plt.hist(yhat_cls, bins=bins, histtype='step', color='red', label='Prediction',log=True, weights=w_test)\n",
    "    _ = plt.hist(y_test, bins=bins, histtype='stepfilled', alpha=0.4, color='blue',label='Truth',log=True, weights=w_test)\n",
    "    plt.legend(loc='upper right')\n",
    "    plt.show()\n",
    "    plt.savefig(folder + '/Performance.pdf')\n",
    "    # Check the score (y_test==0 is a vector of bools). Ideally you want a distribution that is all red on left and all blue on right.\n",
    "    fig = plt.figure(figsize=(7.69, 5.27), dpi=100)\n",
    "    plt.hist(yhat_cls[y_test==0], label='Signal', normed=True, histtype='step', color='red', weights=w_test[y_test==0])\n",
    "    plt.hist(yhat_cls[y_test==1], label='Background', normed=True, histtype='step', color='blue', weights=w_test[y_test==1])\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    plt.savefig(folder + '/Performance2.pdf')\n",
    "    # Check it on the training (should be similar to the test)\n",
    "    yhat_train = model.predict(X_train, verbose = True, batch_size = 50)\n",
    "    yhat_cls_train = np.argmax(yhat_train, axis=1)\n",
    "    fig = plt.figure(figsize=(7.69, 5.27), dpi=100)\n",
    "    plt.hist(yhat_cls_train[y_train == 0], label='Signal train', normed=True, histtype='step', color='red', weights=w_train[y_train==0])\n",
    "    plt.hist(yhat_cls_train[y_train == 1], label='Background train', normed=True, histtype='step', color='blue', weights=w_train[y_train==1])\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    plt.savefig(folder + '/Performance2_train.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# With \"(y_test != 0) & (yhat_cls == 0)\" you get an arrate of bool: [False False False ..., False False False]\n",
    "print 'Signal efficiency:',     w_test[(y_test == 0) & (yhat_cls == 0)].sum() / w_test[y_test == 0].sum(),\"(\",w_test[(y_test == 0) & (yhat_cls == 0)].sum(),\"/\",w_test[y_test == 0].sum(),\")\"\n",
    "print 'Background efficiency:', w_test[(y_test != 0) & (yhat_cls == 0)].sum() / w_test[y_test != 0].sum(),\"(\",w_test[(y_test != 0) & (yhat_cls == 0)].sum(),\"/\",w_test[y_test != 0].sum(),\")\"\n",
    "print \"S/sqrt(S+B) = \", (w_test[(y_test == 0) & (yhat_cls == 0)].sum())/sqrt(w_test[(y_test == 0) & (yhat_cls == 0)].sum()+w_test[(y_test != 0) & (yhat_cls == 0)].sum())\n",
    "w_1 = np.ones(len(y_test))\n",
    "print 'Signal efficiency (not weighted):',     w_1[(y_test == 0) & (yhat_cls == 0)].sum() / w_1[y_test == 0].sum()\n",
    "print 'Background efficiency (not weighted):', w_1[(y_test != 0) & (yhat_cls == 0)].sum() / w_1[y_test != 0].sum()\n",
    "print \"Let's compare with the training samples:\"\n",
    "w_1 = np.ones(len(y_train))\n",
    "yhat_tr = model.predict(X_train, verbose = True, batch_size = 50)\n",
    "yhat_trcls = np.argmax(yhat_tr, axis=1)\n",
    "print ''; print 'Signal efficiency (not weighted) for training:',     w_1[(y_train == 0) & (yhat_trcls == 0)].sum() / w_1[y_train == 0].sum()\n",
    "print 'Background efficiency (not weighted) for training:', w_1[(y_train != 0) & (yhat_trcls == 0)].sum() / w_1[y_train != 0].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We Trained the MLP to distinguish a Radion of 500 GeV from TTbar. \n",
    "If we have a Radion of 300 GeV or 900 GeV how this MLP will perform?\n",
    "We can find it out now. \n",
    "The ideal approach is to run a mass-independent training, but you will see this in in the parametric training: \"Hhh_optimization_parametric.ipynb\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Let's start with low mass\n",
    "hh3     = root2panda('files/MVA_GluGluToRadionToHHTo2B2VTo2L2Nu_M-300_narrow_13TeV-madgraph-v2.root', 'DiHiggsWWBBAna/evtree', branches=my_branches, selection=my_selec)\n",
    "hh3['fin_weight']    = hh3['XsecBr'] * hh3['muon1_pogSF'] * hh3['muon2_pogSF'] #1pb\n",
    "df3 =  pd.concat((hh3[my_branches_training], ttbar[my_branches_training]), ignore_index=True)\n",
    "# X, w, Y\n",
    "X3 = df3.as_matrix() # Each row is an object to classify, each column corresponds to a specific variable.\n",
    "w3 =  pd.concat((hh3['fin_weight'], ttbar['fin_weight']), ignore_index=True).values\n",
    "y3 = []\n",
    "for _df, ID in [(hh3, 0), (ttbar, 1)]:\n",
    "    y3.extend([ID] * _df.shape[0])\n",
    "y3 = np.array(y3)\n",
    "# Scaler\n",
    "X3 = scaler.transform(X3)\n",
    "yhat3 = model.predict(X3, verbose = True, batch_size = 50) # Return a vector of 2 indeces [probToBe_S,probToBe_B]\n",
    "#Turn them into classes\n",
    "yhat3_cls = np.argmax(yhat3, axis=1) \n",
    "# And Now the efficiency:\n",
    "print; print 'Signal efficiency:',     w3[(y3 == 0) & (yhat3_cls == 0)].sum() / w3[y3 == 0].sum(), \"(\",w3[(y3 == 0) & (yhat3_cls == 0)].sum(),\"/\",w3[y3 == 0].sum(),\")\"\n",
    "print 'Background efficiency:', w3[(y3 != 0) & (yhat3_cls == 0)].sum() / w3[y3 != 0].sum(), \"(\",w3[(y3 != 0) & (yhat3_cls == 0)].sum(),\"/\",w3[y3 != 0].sum(),\")\"\n",
    "print \"S/sqrt(S+B) = \", w3[(y3 == 0) & (yhat3_cls == 0)].sum()/sqrt(w3[(y3 == 0) & (yhat3_cls == 0)].sum()+w3[(y3 != 0) & (yhat3_cls == 0)].sum())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# And now high mass\n",
    "hh13    = root2panda('files/MVA_GluGluToRadionToHHTo2B2VTo2L2Nu_M-900_narrow_13TeV-madgraph-v2.root', 'DiHiggsWWBBAna/evtree', branches=my_branches, selection=my_selec)\n",
    "hh13['fin_weight']    = hh13['XsecBr'] * hh13['muon1_pogSF'] * hh13['muon2_pogSF'] #1pb\n",
    "df13 =  pd.concat((hh13[my_branches_training], ttbar[my_branches_training]), ignore_index=True)\n",
    "# X, w, Y\n",
    "X13 = df13.as_matrix() # Each row is an object to classify, each column corresponds to a specific variable.\n",
    "w13 =  pd.concat((hh13['fin_weight'], ttbar['fin_weight']), ignore_index=True).values\n",
    "y13 = []\n",
    "for _df, ID in [(hh13, 0), (ttbar, 1)]:\n",
    "    y13.extend([ID] * _df.shape[0])\n",
    "y13 = np.array(y13)\n",
    "# Scaler\n",
    "X13 = scaler.transform(X13)\n",
    "yhat13 = model.predict(X13, verbose = True, batch_size = 50) # Return a vector of 2 indeces [probToBe_S,probToBe_B]\n",
    "#Turn them into classes\n",
    "yhat13_cls = np.argmax(yhat13, axis=1) \n",
    "# And Now the efficiency:\n",
    "print; print 'Signal efficiency:',     w13[(y13 == 0) & (yhat13_cls == 0)].sum() / w13[y13 == 0].sum(),\"(\",w13[(y13 == 0) & (yhat13_cls == 0)].sum(),\"/\",w13[y13 == 0].sum(),\")\"\n",
    "print 'Background efficiency:', w13[(y13 != 0) & (yhat13_cls == 0)].sum() / w13[y13 != 0].sum(),\"(\",w13[(y13 != 0) & (yhat13_cls == 0)].sum(),\"/\",w13[y13 != 0].sum(),\")\"\n",
    "print \"S/sqrt(S+B) = \",w13[(y13 == 0) & (yhat13_cls == 0)].sum() /sqrt(w13[(y13 == 0) & (yhat13_cls == 0)].sum() + w13[(y13 != 0) & (yhat13_cls == 0)].sum())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Result is clear: a low mass Signal is more similar to Background.\n",
    "Since we trained the MLP for 500 GeV, a 300 GeV Signal will often be marked as Background.\n",
    "On the opposite, a 900 GeV mass signal it will pass very often the selection.\n",
    "\n",
    "Or question now is: how much we could improve a search for a 300 GeV particle if I use a dedicated MLP?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Let's run a MLP on a low mass Signal\n",
    "# Let's start with low mass\n",
    "hh3N     = root2panda('files/MVA_GluGluToRadionToHHTo2B2VTo2L2Nu_M-300_narrow_13TeV-madgraph-v2.root', 'DiHiggsWWBBAna/evtree', branches=my_branches, selection=my_selec)\n",
    "hh3N['fin_weight'] = hh3N['XsecBr'] * hh3N['muon1_pogSF'] * hh3N['muon2_pogSF'] #1pb\n",
    "df3N =  pd.concat((hh3N[my_branches_training], ttbar[my_branches_training]), ignore_index=True)\n",
    "# X, w, Y\n",
    "X3N = df3N.as_matrix() # Each row is an object to classify, each column corresponds to a specific variable.\n",
    "w3N =  pd.concat((hh3N['fin_weight'], ttbar['fin_weight']), ignore_index=True).values\n",
    "y3N = []\n",
    "for _df, ID in [(hh3N, 0), (ttbar, 1)]:\n",
    "    y3N.extend([ID] * _df.shape[0])\n",
    "y3N = np.array(y3)\n",
    "# Randomly shuffle and automatically split all your objects into train and test subsets\n",
    "ix3N = range(X3N.shape[0]) # array of indices, just to keep track of them for safety reasons and future checks\n",
    "X3N_train, X3N_test, y3N_train, y3N_test, w3N_train, w3N_test, ix3N_train, ix3N_test = train_test_split(X3N, y3N, w3N, ix3N, train_size=0.7) # Train here is 70% of the total statistic\n",
    "# It is common practice to scale the inputs to Neural Nets such that they have approximately similar ranges (it atually improve the results)\n",
    "scaler3N = StandardScaler() \n",
    "X3N_train = scaler3N.fit_transform(X3N_train)\n",
    "X3N_test = scaler3N.transform(X3N_test) # You are applying the same transformation done to X_train, to X_test.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print('---------------------------Training:---------------------------')\n",
    "try:\n",
    "    history3N = model.fit(X3N_train, y3N_train, batch_size=50, epochs=100, verbose=1,\n",
    "              callbacks = [\n",
    "                  EarlyStopping(verbose=True, patience=6, monitor='val_loss'),\n",
    "                  ModelCheckpoint('models/tutorial-progress3N.h5', monitor='val_loss', verbose=1, save_best_only=True)\n",
    "              ],\n",
    "              validation_split=0.2, validation_data=None, shuffle=True,\n",
    "              class_weight={\n",
    "                0 : compute_class_weight(\"balanced\", [0, 1], y3N)[0], # Function that return \"[1/N_classes * ((float(len(y)) / (y == 0).sum())), 1/N_classes * ((float(len(y)) / (y == 1).sum()))]\"\n",
    "                1 : compute_class_weight(\"balanced\", [0, 1], y3N)[1]\n",
    "              },\n",
    "              sample_weight=None,initial_epoch=0)\n",
    "    \n",
    "except KeyboardInterrupt:\n",
    "    print 'Training ended early.'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if debug:\n",
    "    print \"All data in hisotry are: \",history3N.history.keys()\n",
    "# Summarize history for accuracy\n",
    "plt.plot(history3N.history['acc'])\n",
    "plt.plot(history3N.history['val_acc'])\n",
    "plt.title('model accuracy')\n",
    "plt.ylabel('accuracy')\n",
    "plt.xlabel('epoch')\n",
    "plt.legend(['train', 'test'], loc='upper left')\n",
    "plt.show()\n",
    "plt.savefig(folder + '/Check_accuracy_300GeV.pdf')\n",
    "# Summarize history for loss\n",
    "plt.plot(history3N.history['loss'])\n",
    "plt.plot(history3N.history['val_loss'])\n",
    "plt.title('model loss')\n",
    "plt.ylabel('loss')\n",
    "plt.xlabel('epoch')\n",
    "plt.legend(['train', 'test'], loc='upper left')\n",
    "plt.show()\n",
    "plt.savefig(folder + '/Check_loss_300GeV.pdf')\n",
    "\n",
    "# Load the best network (by default you return the last one, you if you save every time you have a better one you are fine loading it later)\n",
    "model.load_weights('./models/tutorial-progress3N.h5')\n",
    "print 'Saving weights...'\n",
    "model.save_weights('./models/tutorial3N.h5', overwrite=True)\n",
    "json_string = model.to_json()\n",
    "open('./models/tutorial3N.json', 'w').write(json_string)\n",
    "print 'Testing...'\n",
    "yhat3N = model.predict(X3N_test, verbose = True, batch_size = 50) # Return a vector of 2 indeces [probToBe_S,probToBe_B]\n",
    "#Turn them into classes\n",
    "yhat3N_cls = np.argmax(yhat3N, axis=1)\n",
    "\n",
    "#Now the efficiency\n",
    "print; print 'Signal efficiency (not weighted):',     w3N[(y3N_test == 0) & (yhat3N_cls == 0)].sum() / w3N[y3N_test == 0].sum(),\"(\",w3N[(y3N_test == 0) & (yhat3N_cls == 0)].sum(),\"/\",w3N[y3N_test == 0].sum(),\")\"\n",
    "print 'Background efficiency (not weighted):', w3N[(y3N_test != 0) & (yhat3N_cls == 0)].sum() / w3N[y3N_test != 0].sum(),\"(\",w3N[(y3N_test != 0) & (yhat3N_cls == 0)].sum(),\"/\",w3N[y3N_test != 0].sum(),\")\"\n",
    "print \"S/sqrt(S+B) = \", w3N[(y3N_test == 0) & (yhat3N_cls == 0)].sum()/sqrt(w3N[(y3N_test == 0) & (yhat3N_cls == 0)].sum()+w3N[(y3N_test != 0) & (yhat3N_cls == 0)].sum())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We just saw that a dedicated training at 300 GeV give much better performances that suing the one for 500 GeV. \n",
    "We know that low mass S, is more similar to B.\n",
    "The final question now is: if I use the MLP for low mass I just trained to our initial 500 GeV signal sample will it give better results than the dedicated 500 GeV training?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's start with low mass\n",
    "hh5     = root2panda('files/MVA_GluGluToRadionToHHTo2B2VTo2L2Nu_M-500_narrow_13TeV-madgraph-v2.root', 'DiHiggsWWBBAna/evtree', branches=my_branches, selection=my_selec)\n",
    "hh5['fin_weight']    = hh5['XsecBr'] * hh5['muon1_pogSF'] * hh5['muon2_pogSF'] #1pb\n",
    "df5 =  pd.concat((hh5[my_branches_training], ttbar[my_branches_training]), ignore_index=True)\n",
    "# X, w, Y\n",
    "X5 = df5.as_matrix() # Each row is an object to classify, each column corresponds to a specific variable.\n",
    "w5 = pd.concat((hh5['fin_weight'], ttbar['fin_weight']), ignore_index=True).values\n",
    "y5 = []\n",
    "for _df, ID in [(hh5, 0), (ttbar, 1)]:\n",
    "    y5.extend([ID] * _df.shape[0])\n",
    "y5 = np.array(y5)\n",
    "# Scaler\n",
    "X5 = scaler3N.transform(X5)\n",
    "yhat5 = model.predict(X5, verbose = True, batch_size = 50) # Return a vector of 2 indeces [probToBe_S,probToBe_B]\n",
    "#Turn them into classes\n",
    "yhat5_cls = np.argmax(yhat5, axis=1) \n",
    "# And Now the efficiency:\n",
    "print; print 'Signal efficiency:',     w5[(y5 == 0) & (yhat5_cls == 0)].sum() / w5[y5 == 0].sum(),\"(\",w5[(y5 == 0) & (yhat5_cls == 0)].sum(),\"/\",w5[y5 == 0].sum(),\")\"\n",
    "print 'Background efficiency:', w5[(y5 != 0) & (yhat5_cls == 0)].sum() / w5[y5 != 0].sum(),\"(\",w5[(y5 != 0) & (yhat5_cls == 0)].sum(),\"/\", w5[y5 != 0].sum(),\")\"\n",
    "print \"S/sqrt(S+B) = \", w5[(y5 == 0) & (yhat5_cls == 0)].sum()/sqrt(w5[(y5 == 0) & (yhat5_cls == 0)].sum() + w5[(y5 != 0) & (yhat5_cls == 0)].sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We just learned that a dedicated training is always better.\n",
    "The real problem is that in real life we have no idea about the mass of an eventual new particle.\n",
    "This is why in the next tutorial we will introduce the concept of a \"parametric training\", i.e. trainign all samples together, giving the mass as external paramter, and given a data event we test his probabilty to be Signal (trying each mass) or background. "
   ]
  }
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