PROJECT_Group11_CalibrationRun.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PROJECT: PARTICLE DETECTOR DATA ANALYSIS\n",
    "### Dataset: Run260, Calibration Run\n",
    "\n",
    "<a id =6></a><br>\n",
    "The project is outlined as following:\n",
    " \n",
    " - [INTRODUCTION: THE DATA](#1)\n",
    " \n",
    " - [ADDING NEW COLUMNS](#2)\n",
    " \n",
    " - [GATHERING EVENTS](#3)\n",
    " \n",
    " - [FINDING TRAJECTORIES](#4)\n",
    " \n",
    " - [VISUALIZING THE EVENTS](#5)\n",
    " \n",
    " - [DETECTOR MATRIX](#7)\n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Important imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "from os import listdir\n",
    "from os.path import isfile, join, getsize\n",
    "from IPython.display import Markdown, display\n",
    "def printmd(string):\n",
    "    display(Markdown(string)) # for markdown purposes\n",
    "from numba import vectorize, int64, int32, jit, njit, cuda, float64"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "# <a id =1></a><br> I. INTRODUCTION: THE DATA\n",
    "[Content Outline](#6)\n",
    "\n",
    "In this project, we analyze the data obtained through a set of particle detectors. The detectors consist on four layers of cells fulls of a gas. Each of the cells is traversed by an anodic cable in its middle. When a particle traverses the gas, it ionizes it, with the ions being then attracted towards the cable. The cell then emmits a signal when the ions reach the cable. \\\n",
    "The ions can be considered to travel at a constat drift velocity $v_d$ towards the cable. The impact possition in a cell $x$ can be expressed as\n",
    "    \n",
    "    \n",
    "$$\n",
    "x = v_d (t_R - t_0),\n",
    "$$\n",
    "    \n",
    "being $t_0$ as the pedestal time and $t_R$ the time recorded by the detector. As the maximum drift time  $T_{Max} = \\frac{L}{2 v_d} = 390$ ns ($L=42$ mm is the lenght of the cell) is a known country, $t_0$ can be calculated, which will be explained later.    \n",
    "\\\n",
    "The data obtained are encoded in a CSV file. The way we can interpret its content is exlained as it is needed. It is the goal of this project to analyze these data so that we can track the trajectories of the particles through them. More specifically, the tasks to do are:\n",
    "    \n",
    "    - grouping the data into events corresponding to a particle hitting the detector,\n",
    "    - obtain and plot the drift times, and\n",
    "    - plot the trajectory of the particle with left - right ambiguity.\n",
    "    \n",
    "This was done for both a calibration run and for the data obtained in a real experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "## DESCRIPTION OF THE DATA"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Files concatenated: \n",
      " ['data/Run000260/data_000000.txt', 'data/Run000260/data_000001.txt', 'data/Run000260/data_000002.txt', 'data/Run000260/data_000003.txt', 'data/Run000260/data_000004.txt', 'data/Run000260/data_000005.txt', 'data/Run000260/data_000006.txt', 'data/Run000260/data_000007.txt'] \n",
      "\n",
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 9879056 entries, 0 to 9879055\n",
      "Data columns (total 5 columns):\n",
      " #   Column       Dtype  \n",
      "---  ------       -----  \n",
      " 0   FPGA         int64  \n",
      " 1   TDC_CHANNEL  int64  \n",
      " 2   ORBIT_CNT    int64  \n",
      " 3   BX_COUNTER   float64\n",
      " 4   TDC_MEAS     float64\n",
      "dtypes: float64(2), int64(3)\n",
      "memory usage: 376.9 MB\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "# Set as FALSE for Calibration run, and TRUE for Physics Run\n",
    "REAL_DATA = False\n",
    "\n",
    "# Limit the amount of data we are accepting \n",
    "if REAL_DATA == True:\n",
    "    mypath = 'data/Run000333/'\n",
    "else:\n",
    "    mypath = 'data/Run000260/'\n",
    "\n",
    "max_mb = 256 # maximum size of data in mb to read\n",
    "files = [join(mypath, f) for f in listdir(mypath) if isfile(join(mypath, f))]\n",
    "mb = 0\n",
    "for i in range(len(files)):\n",
    "    mb += getsize(files[i])/1024**2 # getsize returns size in bytes\n",
    "    if mb >= max_mb:\n",
    "        files = files[:(i-1)]\n",
    "        break\n",
    "\n",
    "# Concatenate the files and load the data\n",
    "data = pd.concat([pd.read_csv(file) for file in files], axis = 0)\n",
    "data.reset_index(inplace=True, drop=True) #This resets the index from 0 to onwards\n",
    "# data = pd.read_csv(files[0])\n",
    "\n",
    "# Drop the 'HEAD' column\n",
    "data.drop('HEAD', inplace=True, axis=1) # We remove the 'HEAD', inplace = True because we return nothing\n",
    "\n",
    "# Print the description of the data\n",
    "printmd('## DESCRIPTION OF THE DATA')\n",
    "print('Files concatenated:', '\\n', files, '\\n') # To check which files are read\n",
    "print(data.info())\n",
    "# display(data.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "## THE DATAFRAME"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "The dataframe below presents the first 10 hits as presented in the raw data."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>116</td>\n",
       "      <td>1897414884</td>\n",
       "      <td>1533.0</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>71</td>\n",
       "      <td>1897414887</td>\n",
       "      <td>1650.0</td>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>67</td>\n",
       "      <td>1897414914</td>\n",
       "      <td>980.0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>70</td>\n",
       "      <td>1897414922</td>\n",
       "      <td>1287.0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>57</td>\n",
       "      <td>1897414922</td>\n",
       "      <td>2162.0</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>24</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2026.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>139</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2028.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2026.0</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   FPGA  TDC_CHANNEL   ORBIT_CNT  BX_COUNTER  TDC_MEAS\n",
       "0     1          116  1897414884      1533.0      24.0\n",
       "1     1           71  1897414887      1650.0      21.0\n",
       "2     1           67  1897414914       980.0       8.0\n",
       "3     1           70  1897414922      1287.0       8.0\n",
       "4     0           57  1897414922      2162.0      22.0\n",
       "5     0           24  1897414934      2014.0      13.0\n",
       "6     0           26  1897414934      2014.0      20.0\n",
       "7     0           26  1897414934      2026.0      13.0\n",
       "8     0          139  1897414934      2028.0       0.0\n",
       "9     0           33  1897414934      2026.0      14.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualize the first 10 entries of the file\n",
    "printmd('## THE DATAFRAME')\n",
    "printmd('The dataframe below presents the first 10 hits as presented in the raw data.')\n",
    "display(data.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "## HISTOGRAM OF HITS PER TDC CHANNEL"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "Remark: There are a lot of hits falling under the mean time trigger channel: 139."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot histogram\n",
    "fig, (ax1,ax2) = plt.subplots(1,2,figsize=(10,4))\n",
    "\n",
    "df_0 = data[data['FPGA']==0]\n",
    "df_1 = data[data['FPGA']==1]\n",
    "\n",
    "max_channel = data['TDC_CHANNEL'].max()\n",
    "df_0.hist('TDC_CHANNEL', ax=ax1, bins=max_channel)#, range=(137,138))\n",
    "df_1.hist('TDC_CHANNEL', ax=ax2, bins=max_channel)#, range=(137,138))\n",
    "ax1.set_title('FPGA 0')\n",
    "ax2.set_title('FPGA 1')\n",
    "\n",
    "printmd('## HISTOGRAM OF HITS PER TDC CHANNEL')\n",
    "printmd('Remark: There are a lot of hits falling under the mean time trigger channel: 139.')\n",
    "plt.show()\n",
    "\n",
    "# The difference between the channel distributions reflect the difference between the beams used in \n",
    "# the calibration run and the physics run. \n",
    "# Discontinuity and lesser amplitudes: shift in chamber"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# <a id =2></a><br> II. ADDING NEW COLUMNS: TIME, DETECTOR, LAYER, AND CELL\n",
    " [Content Outline](#6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CONSTANTS: TRIGGER CHANNELS AND TMAX, L, Vd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "st1 = 137  # Scintillator trigger channel 1\n",
    "st2 = 138  # Scintillator trigger channel 2\n",
    "mtt = 139  # Mean-time trigger channel\n",
    "T_M = 390  #(maximum drift time in ns)\n",
    "L = 42  # (lenght of the cell in mm)\n",
    "v_d = L/(2*T_M)  # (constant drift velocity in mm/ns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## TIME COLUMN\n",
    " \n",
    " Let's add a column to the existing data.\n",
    "\n",
    "This new column will be the time measurements(ns). The time measurement in nanoseconds is given by:\n",
    "\n",
    "```python\n",
    " data['time']=data['ORBIT_CNT']*2564*25+data['BX_COUNTER']*25+data['TDC_MEAS']*25/30\n",
    "```\n",
    " \n",
    "Now, the rate of passage of particles through the detector was rather limited, i.e. the chance to get two particle within the same orbit is extremely small. Therefore we can drop the orbit part of the formula yields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>116</td>\n",
       "      <td>1897414884</td>\n",
       "      <td>1533.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>38345.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>71</td>\n",
       "      <td>1897414887</td>\n",
       "      <td>1650.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>41267.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>67</td>\n",
       "      <td>1897414914</td>\n",
       "      <td>980.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>24506.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>70</td>\n",
       "      <td>1897414922</td>\n",
       "      <td>1287.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>32181.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>57</td>\n",
       "      <td>1897414922</td>\n",
       "      <td>2162.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>54068.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   FPGA  TDC_CHANNEL   ORBIT_CNT  BX_COUNTER  TDC_MEAS          time\n",
       "0     1          116  1897414884      1533.0      24.0  38345.000000\n",
       "1     1           71  1897414887      1650.0      21.0  41267.500000\n",
       "2     1           67  1897414914       980.0       8.0  24506.666667\n",
       "3     1           70  1897414922      1287.0       8.0  32181.666667\n",
       "4     0           57  1897414922      2162.0      22.0  54068.333333"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['time'] = data['BX_COUNTER']*25 + data['TDC_MEAS']*25/30\n",
    "\n",
    "# We have added a new time column to the data. The first 5 rows are\n",
    "data.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As stated earlier, the actual time taken by the ionization to reach the anodic wire (drift time) is proportional to the distance:\n",
    "\n",
    "$$\n",
    "x = v_d t_i= v_d(t_R-t_0)\n",
    "$$\n",
    "\n",
    "where $v_d$ is the constant drift velocity, $t_R$ is the time recorded by the electronics and $t_0$ is a time pedestal which needs to be determined for every particles crossing the detector (the drift time is $t_R-t_0$). This is possible thanks to the geometry of the layers, more precisely by the fact that they are staggered by exactly half a cell. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DETECTOR, LAYER, AND CELL COLUMNS\n",
    "\n",
    "Before processing the dataset, we have to create some missing columns, in fact the DataFrame with the events must contain the following information:\n",
    "* CHAMBER, which is the Detector number. The data to be analyzed have been gathered by a series of (4) particle detectors: [1-4]\n",
    "* LAYER.  Such detectors were composed by four layers of cells: [1-4];\n",
    "* CELL, which is in the number of the cell.  The actual detector has 16 cells per layer: [1-16]\n",
    "* POSTION, which is the position where a particle traverses the cell [0-21] (in mm. The maximum 21 mm value corresponds to the position of the anodic wire to where the particles travel. In this case the left-right ambiguity is NOT resolved). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![(Picture of detector configuration)](./detector.png)\n",
    "\n",
    "The channels are mapped to the four detectors in the following ways:\n",
    "\n",
    "* Detector 1 $\\rightarrow$ FPGA 0, TDC_CHANNEL in [1-64]\n",
    "* Detector 2 $\\rightarrow$ FPGA 0, TDC_CHANNEL in [65-128]\n",
    "* Detector 3 $\\rightarrow$ FPGA 1, TDC_CHANNEL in [1-64]\n",
    "* Detector 4 $\\rightarrow$ FPGA 1, TDC_CHANNEL in [65-128]\n",
    "\n",
    "Notice that since we have 4 layers with 16 cells per layes, each detector will have 64 cells. Therefore, we can assume that the TDC_CHANNEL is a label for all the cells in the chamber.\n",
    "\n",
    "Even though not used as such, an external trigger was present anyway. When it fired a special 64 bit word (a row in the csv file) were produced enconding the trigger information, i.e. the timing at which it occurred and which of the kind of trigger fired. More precisely:\n",
    "\n",
    "* Mean-time trigger: TDC_CHANNEL=139\n",
    "* Scintillator trigger: TDC_CHANNEL=137 or 138"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(Detectory, Layer, Cell) example: \n",
      " [(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5), (2, 3, 6), (2, 3, 7), (2, 3, 8), (2, 3, 9), (2, 3, 10), (2, 3, 11), (2, 3, 12), (2, 3, 13), (2, 3, 14), (2, 3, 15), (2, 3, 16)]\n"
     ]
    }
   ],
   "source": [
    "# Define function to add the detector, layer and cell columns \n",
    "\n",
    "@vectorize([int64(int64, int64)])\n",
    "def giveDetector(fpga, channel):\n",
    "    if channel > 128:\n",
    "        return -1\n",
    "\n",
    "    channel -= 1\n",
    "    return fpga*2 + 1 + channel // 64\n",
    "\n",
    "@vectorize([int64(int64)])\n",
    "def giveLayer(channel):\n",
    "    if channel > 128:\n",
    "        return -1\n",
    "\n",
    "    layer_map = {0 : 1,\n",
    "                 1 : 4,\n",
    "                 2 : 2,\n",
    "                 3 : 3}\n",
    "\n",
    "    cell_index = channel % 64\n",
    "    layer = layer_map[cell_index % 4]\n",
    "    \n",
    "    return layer\n",
    "\n",
    "@vectorize([int64(int64)])\n",
    "def giveCell(channel):\n",
    "    if channel > 128:\n",
    "        return -1\n",
    "\n",
    "    channel -= 1\n",
    "    cell_index = channel % 64\n",
    "    cell = cell_index // 4 + 1\n",
    "\n",
    "    return cell\n",
    "\n",
    "# Test of functions(one particular layer and detector arrangement)\n",
    "if __name__ == '__main__':\n",
    "    first_cell_of_layer = 67\n",
    "    a = np.arange(first_cell_of_layer,first_cell_of_layer+16*4,4)\n",
    "    print('(Detectory, Layer, Cell) example: \\n',list(zip(giveDetector(0,a), giveLayer(a), giveCell(a))))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "Dataframe now has new columns: time, detector, layer, and cell."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "      <th>detector</th>\n",
       "      <th>layer</th>\n",
       "      <th>cell</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>116</td>\n",
       "      <td>1897414884</td>\n",
       "      <td>1533.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>38345.000000</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>71</td>\n",
       "      <td>1897414887</td>\n",
       "      <td>1650.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>41267.500000</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>67</td>\n",
       "      <td>1897414914</td>\n",
       "      <td>980.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>24506.666667</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>70</td>\n",
       "      <td>1897414922</td>\n",
       "      <td>1287.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>32181.666667</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>57</td>\n",
       "      <td>1897414922</td>\n",
       "      <td>2162.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>54068.333333</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   FPGA  TDC_CHANNEL   ORBIT_CNT  BX_COUNTER  TDC_MEAS          time  \\\n",
       "0     1          116  1897414884      1533.0      24.0  38345.000000   \n",
       "1     1           71  1897414887      1650.0      21.0  41267.500000   \n",
       "2     1           67  1897414914       980.0       8.0  24506.666667   \n",
       "3     1           70  1897414922      1287.0       8.0  32181.666667   \n",
       "4     0           57  1897414922      2162.0      22.0  54068.333333   \n",
       "\n",
       "   detector  layer  cell  \n",
       "0         4      1    13  \n",
       "1         4      3     2  \n",
       "2         4      3     1  \n",
       "3         4      2     2  \n",
       "4         1      4    15  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the detector, layer & cell columns according to the previous functions\n",
    "data['detector'] = giveDetector(data['FPGA'], data['TDC_CHANNEL'])\n",
    "data['layer'] = giveLayer(data['TDC_CHANNEL'])\n",
    "data['cell'] = giveCell(data['TDC_CHANNEL'])\n",
    "\n",
    "printmd(\"Dataframe now has new columns: time, detector, layer, and cell.\")\n",
    "display(data.head(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# <a id =3></a><br>III. FINDING EVENTS \n",
    " [Content Outline](#6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A trigger dataset is formed by applying a mask to the original data in order to isolate the hits that correspond to the TDC_CHANNEL 139. Similar lines of code are presented for the two other trigger channels, scintillator 1 and 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1897414934</td>\n",
       "      <td>50700.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>1897415301</td>\n",
       "      <td>70300.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>1897415425</td>\n",
       "      <td>33375.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>1897415544</td>\n",
       "      <td>30850.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>1897415674</td>\n",
       "      <td>29950.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      ORBIT_CNT     time\n",
       "8    1897414934  50700.0\n",
       "72   1897415301  70300.0\n",
       "87   1897415425  33375.0\n",
       "115  1897415544  30850.0\n",
       "140  1897415674  29950.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>24235</th>\n",
       "      <td>1897537507</td>\n",
       "      <td>26853.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24238</th>\n",
       "      <td>1897537507</td>\n",
       "      <td>26857.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24239</th>\n",
       "      <td>1897537507</td>\n",
       "      <td>26850.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24241</th>\n",
       "      <td>1897537507</td>\n",
       "      <td>26860.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244487</th>\n",
       "      <td>1918505505</td>\n",
       "      <td>1525.833333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         ORBIT_CNT          time\n",
       "24235   1897537507  26853.333333\n",
       "24238   1897537507  26857.500000\n",
       "24239   1897537507  26850.833333\n",
       "24241   1897537507  26860.000000\n",
       "244487  1918505505   1525.833333"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trigger_mtt = data.loc[data['TDC_CHANNEL']==mtt, ['ORBIT_CNT','time']]\n",
    "trigger_st = data.loc[(data['TDC_CHANNEL']==st1) | (data['TDC_CHANNEL']==st2), ['ORBIT_CNT','time']]\n",
    "\n",
    "display(trigger_mtt.head())\n",
    "if not trigger_st.empty:\n",
    "    display(trigger_st.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `.isin()`  function, the orbits found in trigger_mtt data is isolated from the original dataset to produce the 'events' dataset because, supposedly, **one event corresponds to one common orbit.** The next lines of code sorts the hits by orbits and reindexed to present the data for each event."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "## Events in the Mean time Trigger"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "      <th>detector</th>\n",
       "      <th>layer</th>\n",
       "      <th>cell</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event</th>\n",
       "      <th>index</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">1</th>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>24</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>50360.833333</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>50366.666667</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2026.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>50660.833333</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0</td>\n",
       "      <td>27</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2024.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>50609.166667</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>29</td>\n",
       "      <td>1897414934</td>\n",
       "      <td>2026.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>50657.500000</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             FPGA  TDC_CHANNEL   ORBIT_CNT  BX_COUNTER  TDC_MEAS  \\\n",
       "event index                                                        \n",
       "1     5         0           24  1897414934      2014.0      13.0   \n",
       "      6         0           26  1897414934      2014.0      20.0   \n",
       "      7         0           26  1897414934      2026.0      13.0   \n",
       "      10        0           27  1897414934      2024.0      11.0   \n",
       "      11        0           29  1897414934      2026.0       9.0   \n",
       "\n",
       "                     time  detector  layer  cell  \n",
       "event index                                       \n",
       "1     5      50360.833333         1      1     6  \n",
       "      6      50366.666667         1      2     7  \n",
       "      7      50660.833333         1      2     7  \n",
       "      10     50609.166667         1      3     7  \n",
       "      11     50657.500000         1      4     8  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "## Events in the Scintillator Trigger"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "      <th>detector</th>\n",
       "      <th>layer</th>\n",
       "      <th>cell</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event</th>\n",
       "      <th>index</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>24242</th>\n",
       "      <td>1</td>\n",
       "      <td>80</td>\n",
       "      <td>1897537507</td>\n",
       "      <td>1857.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>46434.166667</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">2</th>\n",
       "      <th>244481</th>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>1918505505</td>\n",
       "      <td>26.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>664.166667</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244485</th>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>1918505505</td>\n",
       "      <td>34.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>860.000000</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244483</th>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>1918505505</td>\n",
       "      <td>27.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>685.000000</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244482</th>\n",
       "      <td>1</td>\n",
       "      <td>68</td>\n",
       "      <td>1918505505</td>\n",
       "      <td>34.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>870.833333</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              FPGA  TDC_CHANNEL   ORBIT_CNT  BX_COUNTER  TDC_MEAS  \\\n",
       "event index                                                         \n",
       "1     24242      1           80  1897537507      1857.0      11.0   \n",
       "2     244481     0           16  1918505505        26.0      17.0   \n",
       "      244485     0           11  1918505505        34.0      12.0   \n",
       "      244483     0            9  1918505505        27.0      12.0   \n",
       "      244482     1           68  1918505505        34.0      25.0   \n",
       "\n",
       "                      time  detector  layer  cell  \n",
       "event index                                        \n",
       "1     24242   46434.166667         4      1     4  \n",
       "2     244481    664.166667         1      1     4  \n",
       "      244485    860.000000         1      3     3  \n",
       "      244483    685.000000         1      4     3  \n",
       "      244482    870.833333         4      1     1  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#.isin function compares the two arrays and takes only the orbits that are found in the trigger\n",
    "events_mtt = data.loc[data['ORBIT_CNT'].isin(trigger_mtt['ORBIT_CNT'])]\n",
    "events_st = data.loc[data['ORBIT_CNT'].isin(trigger_st['ORBIT_CNT'])]\n",
    "\n",
    "def create_events(df):\n",
    "    events = df.copy(deep=False)\n",
    "    # We remove the events that are in channels above 128\n",
    "    events = events[events['TDC_CHANNEL'] <= 128]\n",
    "\n",
    "    # We now group by orbit\n",
    "    events['event'] = events.groupby('ORBIT_CNT').ngroup()+1\n",
    "\n",
    "    # Common orbits correspond to a single event\n",
    "    events.set_index(['event', events.index], inplace=True) # We make the events column an index\n",
    "    events.rename_axis(('event','index'), inplace=True)\n",
    "    events.sort_values(['ORBIT_CNT','detector','layer','cell'], inplace=True) # We sort according to these categories\n",
    "    \n",
    "    return events\n",
    "\n",
    "printmd('## Events in the Mean time Trigger')\n",
    "events_mtt = create_events(events_mtt)\n",
    "display(events_mtt.head(5))\n",
    "if not trigger_st.empty:\n",
    "    printmd('## Events in the Scintillator Trigger')\n",
    "    events_st = create_events(events_st)\n",
    "    display(events_st.head(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# <a id =4></a><br> IV. FINDING THE TRAJECTORIES\n",
    " [Content Outline](#6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Computing $t_0$\n",
    "\n",
    "To compute the constant $t_0$, which is different for every event, we can use the following relation:\n",
    "\n",
    "$$T_{MAX}=\\frac{t_{1}+t_{3}}{2}+t_{2}$$\n",
    "\n",
    "where $t_1 = t_{1'}-t_0$, $t_2 = t_{2'}-t_0$ and $t_3 = t_{3'}-t_0$, are the drift times of those three cells and $t_{i'}$ is the time measurement of the respective cell. The drift times can be calculated in this way because $t_0$ is essentially the same for each cell in one event, because the particle velocity of the muons is much higher than the drift velocity of the electrons. Then the relation becomes:\n",
    "\n",
    "$$T_{MAX}=\\frac{t_{1'}-t_0+t_{3'}-t_0}{2}+t_{2'}-t_0$$\n",
    "\n",
    "from which we get:\n",
    "\n",
    "$$t_0=\\frac{t_{1'}+t_{3'}+2t_{2'}-2T_{MAX}}{4}$$\n",
    "\n",
    "Finally we notice that $t_{1'}$, $t_{2'}$, $t_{3'}$ are the times recorded by each cell, which are already available in our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findTrajectories(df):\n",
    "    data = df.copy(deep=False)\n",
    "    data['t0_123'] = 0\n",
    "    data['t0_234'] = 0\n",
    "    for i in data.index.get_level_values(0).unique():\n",
    "        present_detectors = data.loc[i,'detector'].unique()\n",
    "        ev = data.loc[i].copy(deep=False)\n",
    "        \n",
    "        for det in present_detectors:\n",
    "            sub_ev = ev.loc[ev['detector'] == det].copy(deep=False)\n",
    "            for l in range(1,4):\n",
    "                fst_layer = sub_ev.loc[sub_ev['layer'] == l, 'cell']\n",
    "                sec_layer = sub_ev.loc[sub_ev['layer'] == l+1, 'cell']\n",
    "\n",
    "                # Find successor for each cell in layer\n",
    "                if l % 2 == 0:\n",
    "                    successor_mask = fst_layer.isin(sec_layer) | fst_layer.isin(sec_layer+1)\n",
    "                else:\n",
    "                    successor_mask = fst_layer.isin(sec_layer) | fst_layer.isin(sec_layer-1)\n",
    "                \n",
    "                # Drop whole sub_event if the current layer is completely empty\n",
    "                if successor_mask.sum() == 0:\n",
    "                    sub_ev['t0_123'] = np.nan\n",
    "                    sub_ev['t0_234'] = np.nan\n",
    "                    break\n",
    "\n",
    "                else:\n",
    "                    # Drop rows where no successor was found\n",
    "                    sub_ev.loc[(successor_mask==False).index, 't0_123'] = np.nan\n",
    "                    sub_ev.loc[(successor_mask==False).index, 't0_234'] = np.nan\n",
    "\n",
    "            na_mask = sub_ev['t0_1'].notna()\n",
    "            if na_mask.sum() > 0:\n",
    "                t_1 = sub_ev.loc[(sub_ev.loc[na_mask, 'layer']==1).index, 't0_1'].iloc[0]\n",
    "                t_2 = sub_ev.loc[(sub_ev.loc[na_mask, 'layer']==2).index, 't0_1'].iloc[0]\n",
    "                t_3 = sub_ev.loc[(sub_ev.loc[na_mask, 'layer']==3).index, 't0_1'].iloc[0]\n",
    "                t_4 = sub_ev.loc[(sub_ev.loc[na_mask, 'layer']==4).index, 't0_1'].iloc[0]\n",
    "                sub_ev.loc[na_mask,'t0_123'] = 0.5*(0.5*(t_1 + t_3) + t_2)\n",
    "                sub_ev.loc[na_mask, 't0_234'] = 0.5*(0.5*(t_2 + t_4) + t_3)\n",
    "\n",
    "    return data\n",
    "\n",
    "\n",
    "# np.isin or in function of numpy/python is not supported by numba\n",
    "# That's why we make a new .isin function to be able to use the @njit decorator\n",
    "@njit\n",
    "def myIsin(array_a, array_b):\n",
    "    result = np.zeros(len(array_a), dtype=np.bool_)\n",
    "    for i,a in enumerate(array_a):\n",
    "        for j,b in enumerate(array_b):\n",
    "            if a == b:\n",
    "                result[i] = True\n",
    "                break\n",
    "    return result\n",
    "\n",
    "\n",
    "@njit\n",
    "def findTrajectories_np(data, inds, columns):\n",
    "    det_ind, lay_ind, cel_ind, time_ind, t0_1_ind, t0_2_ind = columns #detector, layer, cel, time, 1t0, 2t0 are the columns\n",
    "    #np.roll (array, shift, axis)  #elements of the input array are being shifted\n",
    "    ev_locs = np.where(inds - np.roll(inds,1)!=0)[0]  #np.where(condition,[x,y]) return elements chosen from x or y depending on condition.\n",
    "    ev_locs = np.append(ev_locs, [len(inds)])\n",
    "\n",
    "    for i in range(len(ev_locs)-1):\n",
    "    \n",
    "        ev = data[ev_locs[i]:ev_locs[i+1]]\n",
    "\n",
    "        # Every row registered in same detector?\n",
    "        if np.unique(ev[:,det_ind]).size != 1:\n",
    "            sub_ev_locs = np.where(ev[:,det_ind]-np.roll(ev[:,det_ind],1)!=0)[0]\n",
    "            sub_ev_locs = np.append(sub_ev_locs, [len(ev[:,det_ind])])\n",
    "\n",
    "        else:\n",
    "            sub_ev_locs = np.array([0,len(ev[:,det_ind])])\n",
    "\n",
    "        for j in range(len(sub_ev_locs)-1):\n",
    "            sub_ev = ev[sub_ev_locs[j]:sub_ev_locs[j+1]]\n",
    "\n",
    "            for l in range(1,4):\n",
    "                fst_layer = sub_ev[sub_ev[:,lay_ind]==l,cel_ind]\n",
    "                sec_layer = sub_ev[sub_ev[:,lay_ind]==l+1,cel_ind]\n",
    "\n",
    "                # Find successor for each cell in layer\n",
    "                if l % 2 == 0:\n",
    "                    successor_mask = myIsin(fst_layer, sec_layer) | myIsin(fst_layer, sec_layer+1)\n",
    "                else:\n",
    "                    successor_mask = myIsin(fst_layer, sec_layer) | myIsin(fst_layer, sec_layer-1)\n",
    "\n",
    "                # Drop whole sub_event if the current layer is completely empty\n",
    "                if np.any(successor_mask) == False:\n",
    "                    sub_ev[:,t0_1_ind] = np.nan\n",
    "                    sub_ev[:,t0_2_ind] = np.nan\n",
    "                    break\n",
    "\n",
    "                # Else mark rows where no predecessor was found\n",
    "                # if one cell was found with no predecessor\n",
    "                elif np.all(successor_mask) == False: # False has to be np.array([False]) so that numba broadcasts\n",
    "                    idx = np.nonzero(successor_mask==np.array([False]))[0] + np.nonzero(sub_ev[:,lay_ind]==l)[0][0]\n",
    "                    sub_ev[idx,t0_1_ind] = np.nan\n",
    "                    sub_ev[idx,t0_2_ind] = np.nan\n",
    "\n",
    "            # Compute t0 if a trajectory was found\n",
    "            mask = ~np.isnan(sub_ev[:,t0_1_ind]) # mask where values are numbers and not NaN\n",
    "            if np.any(mask) == True:\n",
    "                t_1 = sub_ev[sub_ev[mask,lay_ind]==1,time_ind][0]\n",
    "                t_2 = sub_ev[sub_ev[mask,lay_ind]==2,time_ind][0]\n",
    "                t_3 = sub_ev[sub_ev[mask,lay_ind]==3,time_ind][0]\n",
    "                t_4 = sub_ev[sub_ev[mask,lay_ind]==4,time_ind][0]\n",
    "                sub_ev[mask,t0_1_ind] = 0.5*(0.5*(t_1 + t_3) + t_2 - T_M)\n",
    "                sub_ev[mask,t0_2_ind] = 0.5*(0.5*(t_2 + t_4) + t_3 - T_M)\n",
    "\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "      <th>detector</th>\n",
       "      <th>layer</th>\n",
       "      <th>cell</th>\n",
       "      <th>t0_123</th>\n",
       "      <th>t0_234</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event</th>\n",
       "      <th>index</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">1</th>\n",
       "      <th>5</th>\n",
       "      <td>0.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1.897415e+09</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>50360.833333</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>50230.833333</td>\n",
       "      <td>50365.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>1.897415e+09</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>50366.666667</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>50230.833333</td>\n",
       "      <td>50365.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>1.897415e+09</td>\n",
       "      <td>2026.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>50660.833333</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>50230.833333</td>\n",
       "      <td>50365.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>1.897415e+09</td>\n",
       "      <td>2024.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>50609.166667</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>50230.833333</td>\n",
       "      <td>50365.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>1.897415e+09</td>\n",
       "      <td>2026.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>50657.500000</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>50230.833333</td>\n",
       "      <td>50365.625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             FPGA  TDC_CHANNEL     ORBIT_CNT  BX_COUNTER  TDC_MEAS  \\\n",
       "event index                                                          \n",
       "1     5       0.0         24.0  1.897415e+09      2014.0      13.0   \n",
       "      6       0.0         26.0  1.897415e+09      2014.0      20.0   \n",
       "      7       0.0         26.0  1.897415e+09      2026.0      13.0   \n",
       "      10      0.0         27.0  1.897415e+09      2024.0      11.0   \n",
       "      11      0.0         29.0  1.897415e+09      2026.0       9.0   \n",
       "\n",
       "                     time  detector  layer  cell        t0_123     t0_234  \n",
       "event index                                                                \n",
       "1     5      50360.833333         1      1     6  50230.833333  50365.625  \n",
       "      6      50366.666667         1      2     7  50230.833333  50365.625  \n",
       "      7      50660.833333         1      2     7  50230.833333  50365.625  \n",
       "      10     50609.166667         1      3     7  50230.833333  50365.625  \n",
       "      11     50657.500000         1      4     8  50230.833333  50365.625  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "      <th>detector</th>\n",
       "      <th>layer</th>\n",
       "      <th>cell</th>\n",
       "      <th>t0_123</th>\n",
       "      <th>t0_234</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event</th>\n",
       "      <th>index</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <th>24242</th>\n",
       "      <td>1.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>1.897538e+09</td>\n",
       "      <td>1857.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>46434.166667</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">2</th>\n",
       "      <th>244481</th>\n",
       "      <td>0.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.918506e+09</td>\n",
       "      <td>26.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>664.166667</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244485</th>\n",
       "      <td>0.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>1.918506e+09</td>\n",
       "      <td>34.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>860.000000</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244483</th>\n",
       "      <td>0.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.918506e+09</td>\n",
       "      <td>27.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>685.000000</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244482</th>\n",
       "      <td>1.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>1.918506e+09</td>\n",
       "      <td>34.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>870.833333</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              FPGA  TDC_CHANNEL     ORBIT_CNT  BX_COUNTER  TDC_MEAS  \\\n",
       "event index                                                           \n",
       "1     24242    1.0         80.0  1.897538e+09      1857.0      11.0   \n",
       "2     244481   0.0         16.0  1.918506e+09        26.0      17.0   \n",
       "      244485   0.0         11.0  1.918506e+09        34.0      12.0   \n",
       "      244483   0.0          9.0  1.918506e+09        27.0      12.0   \n",
       "      244482   1.0         68.0  1.918506e+09        34.0      25.0   \n",
       "\n",
       "                      time  detector  layer  cell  t0_123  t0_234  \n",
       "event index                                                        \n",
       "1     24242   46434.166667         4      1     4     NaN     NaN  \n",
       "2     244481    664.166667         1      1     4     NaN     NaN  \n",
       "      244485    860.000000         1      3     3     NaN     NaN  \n",
       "      244483    685.000000         1      4     3     NaN     NaN  \n",
       "      244482    870.833333         4      1     1     NaN     NaN  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def calculate_t0(df, numba_optimized=True):\n",
    "    events = df.copy(deep=False)\n",
    "\n",
    "    if not numba_optimized:\n",
    "        events = findTrajectories(events)\n",
    "\n",
    "    else:\n",
    "        events['t0_123'] = 0\n",
    "        events['t0_234'] = 0\n",
    "        level0_inds = events.index.get_level_values(0).to_numpy()\n",
    "        c_names = ['detector', 'layer', 'cell', 'time', 't0_123', 't0_234']\n",
    "        columns = np.array([events.columns.get_loc(column) for column in c_names])\n",
    "\n",
    "        data = findTrajectories_np(events.to_numpy(), level0_inds, columns)\n",
    "        events = pd.DataFrame(data=data, index=events.index, columns=events.columns)\n",
    "\n",
    "        events['detector'] = events['detector'].astype(np.int32)\n",
    "        events['layer'] = events['layer'].astype(np.int32)\n",
    "        events['cell'] = events['cell'].astype(np.int32)\n",
    "\n",
    "    return events\n",
    "\n",
    "events_mtt = calculate_t0(events_mtt)\n",
    "display(events_mtt.head(5))\n",
    "if not trigger_st.empty:\n",
    "    events_st = calculate_t0(events_st)\n",
    "    display(events_st.head(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# <a id =5></a><br> V. CHARACTERIZING THE EVENTS\n",
    " [Content Outline](#6)\n",
    "## CALCULATION OF DRIFT TIMES "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "#### For the Mean time Trigger"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAEWCAYAAACjYXoKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3debwcVZ338c+XEPYlEJaBhBAiqEQdIV4BJyMiYTBAZHvAQVl9MUQRGFnmYRNlU4RxkBFRGAQegiAxMiIRwbAGFIUQwhoCEmOUK5GACWGRIEl+zx91Lulc+vat2327q/v29/169aurTp+u+nXdpH9d55w6pYjAzMysFqsVHYCZmbU+JxMzM6uZk4mZmdXMycTMzGrmZGJmZjVzMjEzs5o5mVhhJF0h6av9tK0Rkl6XNCitT5f0b/2x7bS92yUd2V/b68N+vy7pZUl/6eftvi5pVFpeW9LPJS2R9JN+2Pahku6oPUprJU4mVheS5kt6U9Jrkl6R9BtJX5T0zr+5iPhiRJyfc1t7VKoTEX+KiPUiYnk/xH6OpOu7bX+viJhU67b7GMdWwCnA6Ij4hzKv7yZpRUoMr0vqlDRF0kd723Y6VvPS6kHA5sDQiDhY0lGSfl0hrtkl+1wuaWnJ+pkRcUNE7Fnlx7YW5WRi9fTpiFgf2Bq4EDgNuLq/dyJp9f7eZpPYGvhrRCysUOeFiFgPWB/YBXgG+JWkceUq93CstgZ+FxHL8gQVER9IyWg94FfA8V3rEXFBnm3YABQRfvjR7w9gPrBHt7KdgBXAB9P6tcDX0/ImwK3AK8Aisi+p1YAfpve8CbwOnAqMBAI4GvgTcH9J2eppe9OBbwIzgCXALcDG6bXdgM5y8QLjgb8Db6f9PV6yvX9Ly6sBZwF/BBYC1wEbpte64jgyxfYy8JUKx2nD9P6X0vbOStvfI33mFSmOa8u8912fI5VfBswsWQ/gOOA54A8lZdsC53b7vMcBS4Hlaf2VXv7O7xyXkrKjgF932/+X0v5fA84H3gP8FngVmAKsUVJ/AvBY+rfwG+AfS147Dfhz2s6zwLii/637kT0G6i86a0IRMUNSJ/Bx4KluL58CdAKbpvVdsrfE4ZI+TvaFdReApJGpzieA7cm+cDcvs8sjgE8BfyD7wr4UOKyXGH8p6QJg24joqe5R6fFJViaTy4DDS+r8M/A+4L3ADEk/jYg5Zbb1XbKEMgoYCtwBLIiIqyXtBVwfEcMrxVzGT4EvSVo3It5IZfsDO5MlqNLPe7akKP28kt4gO97/3Mf9VjIe+AiwFTAL+CfgUOCvZEnls8AkSWOAa4BPAzPJ/l5TJb2PLFEfD3w0Il5I/w4G9WOMVgM3c1mjvQBsXKb8bWALYOuIeDsifhXpp2gF50TEGxHxZg+v/zAinkpfqF8FPtPVQV+jQ4FvR8S8iHgdOAM4pFsT0rkR8WZEPA48Dny4+0ZSLP8KnBERr0XEfOBiVk1K1XgBEDCkpOybEbGowrGqt4si4tWImE32Q+KOdPyWALcDO6Z6xwD/ExEPRcTyyPqp3iL7cbEcWBMYLWlwRMyPiN8X8FmsDCcTa7RhZM1Y3X0LmAvcIWmepNNzbOv5Prz+R2AwWXNarbZM2yvd9uqsenZUOvrqb8B6ZbazCbBGmW0NqzG+YWRNS6+UlPV2rOrtxZLlN8usdx2frYFT0qCNVyS9QnY2s2VEzAVOBM4BFkqaLGnL+odueTiZWMOkUUbDgHeNFEq/zE+JiFFkTRwnl3Qi93SG0tuZy1YlyyPIzn5eBt4A1imJaxArm9fybPcFsi+90m0vY9UvyDxeTjF139af+7id7g4AZpU0cUHvn6lUkVOJPw98IyKGlDzWiYgbASLiR6n5besU50UFxmolnEys7iRtIGkCMJmsD+DJMnUmSNpWksg6ZZenB2Rf0qOq2PVhkkZLWgc4D7gpsqHDvwPWkrSPpMFknd5rlrzvRWBk6TDmbm4ETpK0jaT1gAuAH0fO0VBdUixTgG9IWl/S1sDJwPWV3/luygyTdDbwb8CZfd1GiReB4ZLWqGEb1foB8EVJO6fPtG76O60v6X2Sdpe0JtkggTdZ+W/ECuZkYvX0c0mvkf3a/ArwbeDzPdTdDriLbATRb4HvR8T09No3gbNSs8d/9GH/PyQbMfYXYC3g3wFSO/2XgKvIzgLeIOv879J14d5fJc0qs91r0rbvJ+vcXwqc0Ie4Sp2Q9j+P7IztR2n7eW0p6XWy4/Yw8CFgt4io5aLBe4DZwF8kvVzDdvosImaS9ZtcBiwma/o8Kr28JtkQ85fJ/qabUVvStH6k3vs4zczMKvOZiZmZ1czJxMzMauZkYmZmNXMyMTOzmtV1OhVJ88nm0FkOLIuIDkkbAz8mmxphPvCZiFichoR+B9ib7CKvoyJiVtrOkWTDNyGby2lSKv8I2WidtYHbgC/3dtX0JptsEiNHjuy/D2nWX559Nnt+3/uKjcOsm0ceeeTliNi0Up1GzM31yYgoHV54OnB3RFyYrnI+nWzytr3IhoduRzaH0OXAzin5nA10kF2k9IikqRGxONWZCDxIlkzGk03N0KORI0cyc+bM/vx8Zv1jt92y5+nTi4zC7F0k/bG3OkU0c+0HdN0XYhLZBHRd5ddF5kFgiKQtyCbquzPNK7QYuBMYn17bICJ+m85GrivZlpmZNVC9z0yCbK6lIJu87Upg84hYABARCyRtluoOY9X5gzpTWaXyzjLl7yJpItkZDCNGjKj1M5nVx1ln9V7HrEnVO5mMTVNFbwbcKemZCnVVpiyqKH93YZbErgTo6OjwVZrWnPaoeDNJs6ZW12auiHghPS8Ebia7OdKLqYmK9Nx1F7lOVp2YbzjZhHqVyoeXKTdrTY89lj3MWlDdkkmaoG39rmVgT7L7GEwluwsd6fmWtDwVOCJN7rYLsCQ1h00D9pS0kaSN0nampddek7RLGgl2RMm2zFrPiSdmD7MWVM9mrs2Bm7PveVYHfpTuYvcwMEVS1y1XD071byMbFjyXbGjw5wEiYpGk88kmsQM4LyK67odxLCuHBt9OLyO5zMysPuqWTCJiHmXuLhcRfwXGlSnvuk91uW1dQ5mZVNMMox+sOVgzM6uJr4A3M7OaOZmYmVnNnEzMmsSBwydw4PAJjDz9F0WHYtZnjZhOxcxymDV8+6JDMKuaz0zMmsSYzjmM6ZxTdBhmVXEyMWsSp94/iVPvn9R7RbMm5GYuswYo7QeZf+E+BUZiVh9OJmYFKk0ykwuMw6xWbuYyM7Oa+czErJs8TVI91XFzlrUrJxOzBuvpOpLzxk1scCRm/cfJxNpSM55BPL35qKJDMKuak4lZkxg7P7uXyQMjd+jx7KVZEp9Zd04mZk3ihN9k47keGLlDwZGY9Z2TiVlOnjPLrGdOJmYV1JJAnHysnTiZ2IDWiI52Jw0zX7RoZmb9wGcm1jZ6OoNoljOLMz91fJ/qN+PwZmtfTiZmTWLe0OFFh2BWNScTGxAGwq/0cXMfAuDubXcuOBKzvnMyMWsSx8y4GXAysdbkZDLA5f3FPhB+2Xdplj4Qs3biZGLWQvIkyoH0w8Bah5OJNT1/OfY/H1Prb04mbaT7r9o8XyL+0jGzPJxMBohGf+nXsj8nqPJOmnBK0SH4b2NVczJpY83WUd3uX2QLNti06vc24m/Z7n8fq8zJZACq9Yul2ZJMT1olzrwmzLkfgFu337XgSMz6zsnE6qYev2QHWgIpddijtwFOJtaanExazEBrahjIyaEZ9HUoca37aMX+szwxVBq80gyfoRk4mZhZWUUm+nqf1Tb7IJVW5GTSwhr9nz3PrLt5f9lVuy9rTY1MDu32Jd4snEysXzkJmLWnuicTSYOAmcCfI2KCpG2AycDGwCzg8Ij4u6Q1geuAjwB/Bf41IuanbZwBHA0sB/49Iqal8vHAd4BBwFURcWG9P49ZvRy7/xlFh5BbO/xoaIfP2J8acWbyZWAOsEFavwi4JCImS7qCLElcnp4XR8S2kg5J9f5V0mjgEOADwJbAXZLem7b1PeBfgE7gYUlTI+LpBnwms363eJ0Niw6h7eVNIM1+o7Ui1DWZSBoO7AN8AzhZkoDdgc+lKpOAc8iSyX5pGeAm4LJUfz9gckS8BfxB0lxgp1RvbkTMS/uanOo6mVhLOujJuwC46UN7FBxJ9YoaDu4+ueLV+8zkv4FTgfXT+lDglYhYltY7gWFpeRjwPEBELJO0JNUfBjxYss3S9zzfrbzsjSAkTQQmAowYMaKGj2NWPwMhmZTq6693f8G3trolE0kTgIUR8Yik3bqKy1SNXl7rqXy1CttatTDiSuBKgI6OjrJ1zGzgcYJqnHqemYwF9pW0N7AWWZ/JfwNDJK2ezk6GAy+k+p3AVkCnpNWBDYFFJeVdSt/TU7mZWdPoKakNpKHL5X7d94uIOCMihkfESLIO9Hsi4lDgXuCgVO1I4Ja0PDWtk16/JyIilR8iac00Emw7YAbwMLCdpG0krZH2MbVen8fMzHpWxHUmpwGTJX0deBS4OpVfDfwwdbAvIksORMRsSVPIOtaXAcdFxHIASccD08iGBl8TEbMb+knqyKfnZtZKlP34z1lZWg1YLyJerV9I9dXR0REzZ84sOoxeOZm0n7XeXgrA0sFrFRyJNUqrNHNJeiQiOirV6bWZS9KPJG0gaV2ys4NnJf3f/grSzDJLB6/lRGItK0+fyeh0JrI/cBswAji8rlGZtaHDZv2Cw2b5jNRaU54+k8GSBpMlk8si4m1JHl5r1s8mPPMrAK4f0xpNH1a7gTQpZZ4zk/8B5gPrAvdL2hpo2T4TMzPrf72emUTEpcClJUV/lPTJ+oVkZmatJk8H/OaSrpZ0e1ofzcrrQczMzHI1c11Ldi3Hlmn9d8CJ9QrIzMxaT54O+E0iYkq6p0jXJIzL6xyXWds55HO+HY+1rjxnJm9IGkqaRFHSLsCSukZlZmYtJc+Zyclkc169R9IDwKasnFvLzPrJMQ/9FIAf7HxgwZGY9V2e0VyzJH0CeB/ZdPDPRsTbdY/MrM2M+/0MwMmkXbX6NSe9JhNJxwE3dE2iKGkjSZ+NiO/XPbo24/m4zKxV5ekzOSYiXulaiYjFwDH1C8nMzFpNnmSyWroXOwCSBgFr1C8kMzNrNXk64KcBUyRdQTai64vAL+salVkbWrr6mkWHYFa1PMnkNOALwLFkHfB3AFfVMyizdnTUZ84tOgSzquUZzbUCuDw9zMzM3iXPaK6xwDnA1qm+gIiIUfUNzay9nPDAjQB8d+xnC47ErO/yNHNdDZwEPAJ4GhWzOhn7x8cBJxNrTXmSyZKIuL3ukZiZWcvKk0zulfQt4KfAW12FETGrblG1EV+oaGYDQZ5ksnN67igpC2D3/g/HzMxacWqVPKO5fFdFswZYvPYGRYdgVrU8o7k2By4AtoyIvdKdFj8WEVfXPTqzNnLsAWcWHYJZ1XynRTMzq1meZLJJREwBVkB2p0U8RNis351637Wcet+1RYdhVpU8HfC+06JZA4z58zNFh2BWNd9p0czMalYxmUhaDVgL8J0WzcysRxWTSUSskHRxRHwMmN2gmMzMrMXk6YC/Q9L/Kb1Blpn1vwXrb8KC9TcpOgyzquTtM1kXWCZpKStnDfYVVmb96KRP/0fRIZhVrbc+EwEfiIg/NSgeMzNrQb31mYSkm4GPNCietuDJHa2cr911JQDn7TGx4EjM+i5Pn8mDkj7a1w1LWkvSDEmPS5ot6dxUvo2khyQ9J+nHktZI5Wum9bnp9ZEl2zojlT8r6VMl5eNT2VxJp/c1RrNmMnrhPEYvnFd0GGZVyZNMPgn8VtLvJT0h6UlJT+R431vA7hHxYWAHYHy64PEi4JKI2A5YDByd6h8NLI6IbYFLUj3SXGCHAB8AxgPflzRI0iDge8BewGjgs6mumZk1WJ4O+L2q2XBEBPB6Wh2cHl1T138ulU8iuyXw5cB+aRngJuCy1GezHzA5It4C/iBpLrBTqjc3IuYBSJqc6j5dTbxmZla9PGcm0cOjV+kM4jFgIXAn8HvglTS/F0AnMCwtDwOeh3fm/1oCDC0t7/aensrLxTFR0kxJM1966aU8oZuZWR/kOTP5BVnyENnV8NsAz5I1O1UUEcuBHSQNAW4Gti9XLT2Xu44lKpSXS4Rlk1xEXAlcCdDR0ZErEZo12ryNy/4WMmsJeW6O9aHSdUljgC/0ZScR8Yqk6cAuwBBJq6ezj+HAC6laJ7AV0ClpdWBDYFFJeZfS9/RUbtZyzhx/QtEhmFUtTzPXKtK933sd3SVp03RGgqS1gT2AOcC9rJwo8kjglrQ8Na2TXr8n9btMBQ5Jo722AbYDZgAPA9ul0WFrkHXST+3r5zEzs9rludPiySWrqwFjgDwdD1sAk9Koq9WAKRFxq6SngcmSvg48CnTdsfFq4Iepg30RWXIgImZLmkLWsb4MOC41nyHpeLIbdw0CrokIzx9mLeuCX34X8BmKtaY8fSbrlywvI+tD+d/e3hQRTwA7limfx8rRWKXlS4GDe9jWN4BvlCm/Dbitt1jMWsGoRX8uOgSzquXpMzm3EYGYmVnr6rXPRNKdXX0faX0jSdPqG5aZmbWSPB3wm0bEK10rEbEY2Kx+IZmZWavJ02eyXNKIrpmDJW1NzosWzSy/pzcbVXQIZlXLk0y+Avxa0n1pfVfA05qa9TPPFmytLE8H/C/ThYq7kF2NflJEvFz3yMzMrGXkuc7kALILCG9N60Mk7R8RP6t7dGZt5JKf/xfgOy7aqkrvfzT/wn0KjKSyPB3wZ0fEkq6V1Bl/dv1CMmtPW7z2Mlu85pN+a015kkm5Onn6WszMrE3kSSYzJX1b0nskjZJ0CfBIvQMzM7PWkSeZnAD8Hfgx8BNgKXBcPYMyM7PWkmc01xtpUsbzI+KNBsRk1pZmDXt/0SGYVa1iMpH0JeB0YN20/jpwUUR8vwGxmbWV//zEUUWHYFa1Hpu5JJ0FTAB2i4ihETEU+CSwV3rNzMwMqHxmcjjw4TQ1PJBNHy/pM8DjwNfrHdxAUjpW3Kycy2++AIBjDziz4EjM+q5iM1dpIikpe1PSivqFZNaeNnrz1aJDMKtapdFcnZLGdS+UtDuwoH4hmZlZq6l0ZvLvwC2Sfk12XUmQ3ft9LLBfA2IzM7MW0eOZSbqf+geB+4GRwKi0/EHfa93MzErl6TO5pkGxmLW1B7b+cNEhmFXNc2yZNYnvjv1s0SGYVS3PdCpmZmYVVbpo8e70fFHjwjFrX9dOOZtrp/juDtaaKjVzbSHpE8C+kiaT3WXxHRExq66RmbWZtZa9VXQIZlWrlEy+RjYv13Dg291eC2D3egVlZmatpcdkEhE3ATdJ+mpEnN/AmMzMrMXkmYL+fEn7Arumould94M3MzODHMlE0jeBnYAbUtGXJY2NiDPqGplZm7n7PTsVHYJZ1fJcZ7IPsENErACQNAl4FHAyMetHP9j5wKJDMKta3utMhpQsb1iPQMzMrHXlOTP5JvCopHvJhgfvis9KzPrd5B+dDsAhn7uw4EjM+i5PB/yNkqaTzRgs4LSI+Eu9AzMzs1WV3mRv/oX7FBjJu+WamysiFgBT6xyLmZm1KM/NZWZmNatbMpG0laR7Jc2RNFvSl1P5xpLulPRcet4olUvSpZLmSnpC0piSbR2Z6j8n6ciS8o9IejK951JJenckZmZWbxWTiaTVJD1V5baXAadExPbALsBxkkaTTdFyd0RsB9yd1gH2ArZLj4nA5SmGjYGzgZ3Jrnc5uysBpToTS943vspYzQp36/s/zq3v/3jRYZhVpbebY62Q9LikERHxp75sOPWzLEjLr0maAwwju+XvbqnaJGA6cFoqvy4iAnhQ0hBJW6S6d0bEIgBJdwLj06CADSLit6n8OmB/4Pa+xFlPpZ1lZr25fkxzdaia9UWeDvgtgNmSZgBvdBVGxL55dyJpJLAj8BCweUo0RMQCSZulasOA50ve1pnKKpV3likvt/+JZGcwjBgxIm/YZg211ttLAVg6eK2CIzHruzzJ5NxadiBpPeB/gRMj4tUK3RrlXogqyt9dGHElcCVAR0dH2TpmRbv2J+cAvs7EWlOvHfARcR8wHxiclh8Gct3LRNJgskRyQ0T8NBW/mJqvSM8LU3knsFXJ24cDL/RSPrxMuZmZNVivyUTSMcBNwP+komHAz3K8T8DVwJyIKL0fylSga0TWkcAtJeVHpFFduwBLUnPYNGBPSRuljvc9gWnptdck7ZL2dUTJtszMrIHyNHMdRzaK6iGAiHiupJ+jkrHA4cCTkh5LZWcCFwJTJB0N/Ak4OL12G7A3MBf4G/D5tL9Fks4nOyMCOK+rMx44FrgWWJus471pOt/NzNpJnmTyVkT8vauvQ9Lq9NA3USoifk35fg2AcWXqB1niKreta4BrypTPBD7YWyxmZlZfeZLJfZLOBNaW9C/Al4Cf1zcss/Zz04f2KDoEs6rlSSanA0cDTwJfIGuOuqqeQZm1IycTa2V5Zg1ekW6I9RBZ89azqUnKzPrRRn9bAsDidXzLIGs9eW7buw9wBfB7sj6QbSR9ISLc2W3Wjy7/2TcBX2dirSlPM9fFwCcjYi6ApPcAv8Ajp8zMLMkza/DCrkSSzGPlhYZmZmY9n5lIOjAtzpZ0GzCFrM/kYFZe82FmZlaxmevTJcsvAp9Iyy8BG727upmZtasek0lEfL6RgZi1u+t33LvoEMyqlmc01zbACcDI0vp9mYLezHp36/a7Fh2CWdXyjOb6GdmEjT8HVtQ3HLP2tcWrLwGwYINNC47ErO/yJJOlEXFp3SMxa3OX3Hox4OtMrDXlSSbfkXQ2cAfwVldhROS6p4mZmQ18eZLJh8imkt+dlc1ckdbNzMxyJZMDgFER8fd6B2NmZvmMPP0X7yzPv3CfAiPJ5LkC/nFgSL0DMTOz1pXnzGRz4BlJD7Nqn4mHBpv1ox/sdEDRIZhVLU8yObvuUZgZd2+7c9EhmFUtz/1M7mtEIANFaTumWV+M+msnAPOGDi84ErO+y3MF/GusvOf7GsBg4I2I2KCegZm1mwumXQb4OhNrTXnOTNYvXZe0P7BT3SIyM7OWk2c01yoi4mf4GhMzMyuRp5nrwJLV1YAOVjZ7mZmZ5RrNVXpfk2XAfGC/ukRjZmYtKU+fie9rYtYA3/2nQ4oOwaxqlW7b+7UK74uIOL8O8Zi1rQdG7lB0CGZVq3Rm8kaZsnWBo4GhgJOJWT8a/eI8AJ7efFTBkZj1XaXb9l7ctSxpfeDLwOeBycDFPb3PzKrztbuvBHydibWmin0mkjYGTgYOBSYBYyJicSMCMzOzfJphBuFKfSbfAg4ErgQ+FBGvNywqMzNrKZUuWjwF2BI4C3hB0qvp8ZqkVxsTnpmZtYJKfSZ9vjrezMzaU56LFs2sAf5z1yOLDsGsak4mZk1i1vDtiw7BrGp1a8qSdI2khZKeKinbWNKdkp5Lzxulckm6VNJcSU9IGlPyniNT/eckHVlS/hFJT6b3XCpJ9fosZo0wpnMOYzrnFB2GWVXq2S9yLTC+W9npwN0RsR1wd1oH2AvYLj0mApfDO0OTzwZ2Jpv2/uyuBJTqTCx5X/d9mbWUU++fxKn3Tyo6DLOq1K2ZKyLulzSyW/F+wG5peRIwHTgtlV8XEQE8KGmIpC1S3TsjYhGApDuB8ZKmAxtExG9T+XXA/sDt9fo8lfjuimbW7ho9YmvziFgAkJ43S+XDgOdL6nWmskrlnWXKy5I0UdJMSTNfeumlmj+EmZmtqlk64Mv1d0QV5WVFxJVkF1/S0dHhe7GY2YBV1NXwjT4zeTE1X5GeF6byTmCrknrDgRd6KR9eptzMzArQ6GQyFegakXUkcEtJ+RFpVNcuwJLUDDYN2FPSRqnjfU9gWnrtNUm7pFFcR5Rsy6wlnTduIueNm1h0GGZVqVszl6QbyTrQN5HUSTYq60JgiqSjgT8BB6fqtwF7A3OBv5HNTkxELJJ0PvBwqndeV2c8cCzZiLG1yTreC+l8N+svnnreWpmyAVTto6OjI2bOnNmv2/RoLusPY+c/BvgmWVYftfSfSHokIjoq1WmWDniztnfCbyYDTibWmjyZo5mZ1czJxMzMauZkYmZmNXMyMTOzmrkD3qxJnPmp44sOwaxqTiZmTWLe0OG9VzJrUm7mMmsS4+Y+xLi5DxUdhllVfGZi1iSOmXEzAHdvu3PBkZj1nZNJlXzVu5nZSm7mMjOzmjmZmJlZzZxMzMysZu4zMWsSJ004pegQzKrmZGLWJBZssGnRIZhVzc1cZk1iwpz7mTDn/qLDMKuKz0zMmsRhj94GwK3b71pwJGZ952TSB762xMysPDdzmZlZzZxMzMysZk4mZmZWM/eZmDWJY/c/o+gQzKrmZGLWJBavs2HRIZhVzc1cZk3ioCfv4qAn7yo6DLOqOJmYNQknE2tlTiZmZlYzJxMzM6uZk4mZmdXMycTMzGrmocFmTeKog88pOgSzqjmZmDWJpYPXKjoEs6q5mcusSRw26xccNsszU1trcjIxaxITnvkVE575VdFhmFXFycTMzGrW8slE0nhJz0qaK+n0ouMxM2tHLZ1MJA0CvgfsBYwGPitpdLFRmZm1n5ZOJsBOwNyImBcRfwcmA/sVHJOZWdtp9aHBw4DnS9Y7gZ27V5I0EZiYVl+X9GyV+9sEeLnK99abY6tO08T2sa6FiyZ0LTVNbGU4tuoUFpsu6rVKpdi27u3NrZ5MVKYs3lUQcSVwZc07k2ZGREet26kHx1Ydx1Ydx1adgRxbqzdzdQJblawPB14oKBYzs7bV6snkYWA7SdtIWgM4BJhacExmZm2npZu5ImKZpOOBacAg4JqImF3HXdbcVFZHjq06jq06jq06AzY2Rbyri8HMzKxPWr2Zy8zMmoCTiZmZ1czJJIdmm7JF0nxJT0p6TNLMVLaxpDslPZeeN2pgPNdIWijpqZKysvEoc2k6lk9IGtPguM6R9Od07B6TtHfJa2ekuJ6V9Kl6xZX2tZWkeyXNkTRb0pdTeTMct55iK/zYSVpL0gxJj6fYzk3l20h6KB23H6cBOUhaM63PTa+PLCC2ayX9oeS47ZDKG/Y3LYlxkKRHJd2a1vvvuEWEHxUeZBor4roAAAa6SURBVB37vwdGAWsAjwOjC45pPrBJt7L/BE5Py6cDFzUwnl2BMcBTvcUD7A3cTnaN0C7AQw2O6xzgP8rUHZ3+tmsC26S/+aA6xrYFMCYtrw/8LsXQDMetp9gKP3bp86+XlgcDD6XjMQU4JJVfARyblr8EXJGWDwF+XMfj1lNs1wIHlanfsL9pyT5PBn4E3JrW++24+cykd60yZct+wKS0PAnYv1E7joj7gUU549kPuC4yDwJDJG3RwLh6sh8wOSLeiog/AHPJ/vZ1ERELImJWWn4NmEM2o0MzHLeeYutJw45d+vyvp9XB6RHA7sBNqbz7ces6njcB4ySVu9i5nrH1pGF/UwBJw4F9gKvSuujH4+Zk0rtyU7ZU+o/VCAHcIekRZVPFAGweEQsg+zIANissusrxNMPxPD41K1xT0hxYWFypCWFHsl+yTXXcusUGTXDsUlPNY8BC4E6yM6FXImJZmf2/E1t6fQkwtFGxRUTXcftGOm6XSFqze2xl4q6H/wZOBVak9aH043FzMuldrilbGmxsRIwhmy35OEm7FhxPXxR9PC8H3gPsACwALk7lhcQlaT3gf4ETI+LVSlXLlNU1vjKxNcWxi4jlEbED2YwXOwHbV9h/obFJ+iBwBvB+4KPAxsBpjY5N0gRgYUQ8UlpcYf99js3JpHdNN2VLRLyQnhcCN5P9h3qx6xQ5PS8sLkKoEE+hxzMiXkz/4VcAP2Blc0zD45I0mOzL+oaI+GkqborjVi62Zjp2KZ5XgOlk/Q1DJHVdhF26/3diS69vSP6mz/6IbXxqNoyIeAv4fxRz3MYC+0qaT9ZUvzvZmUq/HTcnk9411ZQtktaVtH7XMrAn8FSK6chU7UjglmIifEdP8UwFjkgjWXYBlnQ16zRCtzbpA8iOXVdch6RRLNsA2wEz6hiHgKuBORHx7ZKXCj9uPcXWDMdO0qaShqTltYE9yPp07gUOStW6H7eu43kQcE+kXuUGxfZMyY8DkfVJlB63hvxNI+KMiBgeESPJvsPuiYhD6c/jVu/RAwPhQTbq4ndkbbNfKTiWUWQjZx4HZnfFQ9aeeTfwXHreuIEx3UjW7PE22S+ao3uKh+z0+XvpWD4JdDQ4rh+m/T6R/sNsUVL/KymuZ4G96nzM/pms2eAJ4LH02LtJjltPsRV+7IB/BB5NMTwFfK3k/8UMss7/nwBrpvK10vrc9PqoAmK7Jx23p4DrWTniq2F/025x7sbK0Vz9dtw8nYqZmdXMzVxmZlYzJxMzM6uZk4mZmdXMycTMzGrmZGJmZjVzMrG2J2l5ms11dprx9WRJZf9vSNpS0k0l6zemaTJOknSUpC17eN8qr0m6StLoOnyWtSXdJ2lQFe89XtLn+zsmaw8eGmxtT9LrEbFeWt6MbFbVByLi7G71Vo+V8xgh6R/IZnrdOq1PJ5tVd2aZffT4Wn+SdBywekR8p4r3rkP2uXfs/8hsoPOZiVmJyKaomUg2oaHSGcVPJP2cbHLNkVp5f5Q7gM3SWc1XgQ7ghrS+dtc2JR3U/TVJ0yV1pNdfl3RRmrjzLkk7pdfnSdo31Rkk6VuSHk5nQl/o4SMcSrqKWdJuaTs3SXpG0g3pKmwkXSjp6bSt/0qf/W/AfEl1my3ZBq7Ve69i1l4iYl5q5uqasfdjwD9GxCKtepOgfcmuJO662dE4ypx9RMRNko4vfU2rzua9LjA9Ik6TdDPwdeBfyO4TMonsavOjyabb+KiyWWcfkHRHZFO+k7a5BtmVyvNLtr0j8AGyOZceAMZKeppsOpT3R0R0TQGSzAQ+Th2nkrGByWcmZuWVftvfGRH1nBzw78Av0/KTwH0R8XZaHpnK9ySbx+kxsungh5LNgVVqE+CVbmUzIqIzsskZH0vbexVYClwl6UDgbyX1FwJl+33MKvGZiVk3kkYBy1k5Y+8bdd7l27Gy83IF8BZARKzQyhldBZwQEdMqbOdNsjmVSr1VsrycrD9lWWrKGkc26d/xZLPIkt7/ZtWfxNqWz0zMSkjalOz2pZeVfMHn9RrZbW77+loe04BjlU0Nj6T3plmj3xERi4FBkronlFUou0/JhhFxG3Ai2f1JuryXlbPamuXmMxMzWDs1Hw0GlpHNjvvtym8p61rgCklvAh+LiDd7eq2KbV9F1kQ1K3Wiv0T5WzPfQTbr710VtrU+cEtKOgJOKnltLHBuFfFZm/PQYLMBRNKOwMkRcXgj32vmZi6zASQiHgXureaiRbIO/K/2c0jWJnxmYmZmNfOZiZmZ1czJxMzMauZkYmZmNXMyMTOzmjmZmJlZzf4/aPFyq0+felAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "#### For the Scintillator Trigger"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEWCAYAAACNJFuYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3debwcVZ338c+XEAhL2EJgQgIJEUbBZSQTFp+MiIQZBSOLD4w4oOCLAWUbWeaBsCigDoIOMoPOwCAwiaJEZEBWZQ9RHIMhgCwBiTFKJBKQNUiQJL/njzqXNLfv7Vv3dldXL9/369WvrjpVXfXrurf71+ecqlOKCMzMzCqtVXYAZmbWepwczMysipODmZlVcXIwM7MqTg5mZlbFycHMzKo4OVhDSLpE0ucbtK1tJC2XNCzNz5b0j43YdtrejyQd1qjtDWK/X5b0nKQ/NHi7yyVNTNPrSbpR0kuSftCAbR8i6bb6o7R24+RgA5K0WNJrkl6R9KKkn0n6rKQ3/38i4rMR8aWc29qr1joR8buI2DAiVjUg9rMlXdlr+3tHxMx6tz3IOLYGTgZ2jIi/6GP5HpJWpy/65ZKWSLpa0s4DbTsdq0Vp9kBgS2BURBwk6XBJP60R16MV+1wlaUXF/OkR8d2I+Lshvm1rY04OltdHI2IkMB44DzgVuLzRO5G0dqO32SLGA3+MiGU11nk6IjYERgK7AY8DP5E0ta+V+zlW44FfRcTKPEFFxDtTctkQ+AlwXM98RJybZxvWoSLCDz9qPoDFwF69ynYBVgPvSvMzgC+n6c2Bm4AXgefJvnTWAr6TXvMasBw4BZgABHAE8DtgTkXZ2ml7s4GvAPcBLwHXA5ulZXsAS/qKF/gw8GfgjbS/hyq2949pei3gTOC3wDLg28DGaVlPHIel2J4DzqhxnDZOr382be/MtP290nteneKY0cdrq95HKv8mMK9iPoBjgSeB31SUbQec0+v9HgusAFal+RcH+Du/eVwqyg4Hftpr/8ek/b8CfAl4G/C/wMvA1cA6FetPAx5M/ws/A95TsexU4PdpO08AU8v+X/djzaNTf6VZwSLiPklLgPcDj/RafDKwBBid5nfLXhKflPR+si+gOwAkTUjrfADYgewLdMs+dvkp4EPAb8i+gC8CDh0gxh9LOhfYLiL6W/fw9Pgga5LDN4FPVqzzN8Dbgb8E7pN0bUQs6GNb3yBLEBOBUcBtwNKIuFzS3sCVETGuVsx9uBY4RtIGEfFqKtsf2JUs4VS+37MkReX7lfQq2fH+m0Hut5YPA38NbA3MB/4PcAjwR7Ik8QlgpqRJwBXAR4F5ZH+vGyS9nSzxHgfsHBFPp/+DYQ2M0erkZiWrx9PAZn2UvwGMAcZHxBsR8ZNIPxVrODsiXo2I1/pZ/p2IeCR9QX4e+PueDus6HQJ8PSIWRcRy4DTg4F5NNudExGsR8RDwEPBXvTeSYvk4cFpEvBIRi4ELeGuSGYqnAQGbVJR9JSKer3GsinZ+RLwcEY+S/TC4LR2/l4AfATul9Y4E/isi5kbEqsj6eV4n+7GwClgX2FHS8IhYHBG/LuG9WD+cHKweY8majXr7GrAQuE3SIknTc2zrqUEs/y0wnKz5ql5bpe1Vbntt3lp7qTy76E/Ahn1sZ3NgnT62NbbO+MaSNeW8WFE20LEq2jMV06/1Md9zfMYDJ6eTGF6U9CJZbWOriFgInACcDSyTNEvSVsWHbnk5OdiQpLNoxgJVZ8KkX84nR8REsiaFkyo6VfurQQxUs9i6YnobstrJc8CrwPoVcQ1jTXNWnu0+TfYlVrntlbz1Cy+P51JMvbf1+0Fup7cDgPkVTUow8HuqVOawy08B/xIRm1Q81o+IqwAi4nupuWt8ivP8EmO1XpwcbFAkbSRpGjCLrA394T7WmSZpO0ki66RclR6QfelOHMKuD5W0o6T1gS8C10R2quuvgBGSPiJpOFkn8LoVr3sGmFB52m0vVwEnStpW0obAucD3I+fZPj1SLFcD/yJppKTxwEnAlbVfWU2ZsZLOAv4ROH2w26jwDDBO0jp1bGOovgV8VtKu6T1tkP5OIyW9XdKektYl6zR/jTX/I9YCnBwsrxslvUL2a/AM4OvAp/tZd3vgDrIzZP4X+M+ImJ2WfQU4MzUz/PMg9v8dsjOi/gCMAP4JILVzHwNcRvYr/VWyzvAePReC/VHS/D62e0Xa9hyyzu4VwPGDiKvS8Wn/i8hqVN9L289rK0nLyY7bL4B3A3tERD0Xod0FPAr8QdJzdWxn0CJiHlm/wzeBF8iaGg9Pi9clOyX6ObK/6RbUlwStwTRwP6GZmXUb1xzMzKyKk4OZmVVxcjAzsypODmZmVqWth8/YfPPNY8KECWWHYd3uiSey57e/vdw4zHK6//77n4uI0bXWaevkMGHCBObNm1d2GNbt9tgje549u8wozHKT9NuB1nGzkpmZVWnrmoNZSzjzzLIjMGs4Jwezeu1V88Z2Zm3JzUpm9Xrwwexh1kFcczCr1wknZM/ukLYO4pqDmZlVcXIwM7MqTg5mZlbFycHMzKq4Q9qsDhOm38ykcdMAuLbkWMwaycnButKE6Te/Ob34vI/Uta3543aoNxyzluPkYF2jMiE00qQlC9JUfUnGrJU4OZjV6ZQ5M9PUYG6Jbdba3CFtZmZVnBzMzKyKm5XMcqi3A7uRHeBmzeCag5mZVXHNwaxOX5x6FAC3lByHWSM5OZjV6bEtJ5YdglnDOTmY1WnK4p57ObgvwTqHk4NZnY7/2aw0dUapcZg1kjukzcysipODmZlVcbOSvYXPxzczcM3BzMz64JqDdZxm135O/9BxACxyrcs6iJODWZ0WjRpXVVbU8OBmzeJmJbM6TV04l6kL55YdhllDueZgVmEoTVJH3ncdAHdut2shMZmVwcnB2pbPrDIrjpODdb1W7x9wErQyuM/BzMyqFF5zkDQMmAf8PiKmSdoWmAVsBswHPhkRf5a0LvBt4K+BPwIfj4jFRcdn1q5co7AiNaNZ6XPAAmCjNH8+cGFEzJJ0CXAEcHF6fiEitpN0cFrv402Iz+rQu0mmG7+kTpx2ctkhOFFYwxXarCRpHNk4xpeleQF7AtekVWYC+6fp/dI8afnUtH7XmzD95jcf1nqWbjSapRuNLjsMs4Yqus/h34BTgNVpfhTwYkSsTPNLgLFpeizwFEBa/lJa/y0kHSVpnqR5zz77bJGxm+UybcEcpi2YU3YYZg1VWLOSpGnAsoi4X9IePcV9rBo5lq0piLgUuBRg8uTJVcuts/VXeyqzVnXoA9kNQm/aYffSYjBrtCL7HKYA+0raBxhB1ufwb8AmktZOtYNxwNNp/SXA1sASSWsDGwPPFxif2ZC4ec+6QWHNShFxWkSMi4gJwMHAXRFxCHA3cGBa7TDg+jR9Q5onLb8rIlwzsI7m/iRrVWVcBHcqMEvSl4EHgMtT+eXAdyQtJKsxHFxCbB2tGWe0dNJZM934hd1Jfz+rT1OSQ0TMBman6UXALn2sswI4qBnxdAp/kAfWjV/wlfw/YkPl4TPM6nT0/qeVHYJZwzk5dCD/WmyuF9bfuOwQrEH82VnDycFaUjt9SA98+A4Arnn3XnVtp53es3U+Jwdrik7+4mtUcrDm6eT/x0ZxcugQ9XS85nntUD5M3d4ZbNbOnBxs0PylXzwfYyubk4OVytV7s9bk5NCi/MvRzMo0qOQgaS1gw4h4uaB4upoTQns6/KCzyw7BrOEGHFtJ0vckbSRpA+Ax4AlJ/6/40Mzaw4rhI1gxfETZYZg1VJ6aw44R8bKkQ4BbyMZGuh/4WqGRWddp15rTofOzuK+c5D4T6xx5ksNwScPJ7tj2zYh4Q5JHSy1Ju36BdrJpj/8EyJ8cWuFv6BMBbCB5ksN/AYuBh4A5ksYD7nMw6xCtkKyaYbDvs9sT6IDJISIuAi6qKPqtpA8WF5J1um75MiqLj681woDJQdKWwLnAVhGxt6Qdgfex5j4MZmZN1+2/7IuWp1lpBvDfwBlp/lfA93FyaAj/yhuYj1H5+vsb+Eu5c+VJDptHxNWSTgOIiJWSVhUcl7UAfynnc/A/nFd2CFbBNYrGyJMcXpU0CggASbsBLxUalZk1XD0dst2uG2tOeZLDScANwNsk3QuMBg4sNCqzNnLk3GsB+NauHys5knKV+Yu96FGJu1Ges5XmS/oA8HZAwBMR8UbhkVlD+B+/eFN/fR/g5JBH7//HTv7l3e7yDJ9xLNl4So9GxCPAhpKOKT40MzMrS55mpSMj4j96ZiLiBUlHAv9ZXFhm1inqrb3W01zlmvPQ5UkOa0lSRPR0SA8D1ik2LDPri7/sWlennSWVJzncClwt6RKyM5Y+C/y40KjM2siKtdctO4SW4yTW/vIkh1OBzwBHk3VI3wZcVmRQZu3k8L8/p+wQzBouz9lKq4GL08PMrHCueZQvz9hKU4CzgfFpfQEREROLDc2sPRx/71UAfGPKJ0qOpP10Wjt9J8nTrHQ5cCLZDX48bMYQ+UPQuab89iHAyaEZXKNonjzJ4aWI+FHhkVhT+UNmrcb/k60lT3K4W9LXgGuB13sKI2J+YVGZmVmp8iSHXdPz5IqyAPZsfDhmZu2jk2s7ec5W8l3fzGp4Yb2Nyg6hNJ385djthnwnuIjwzX7MgKMPOL3sEMwabsCB98juBHcrsFWa/xVwQlEBmZlZ+fIkh80j4mpgNWR3gsOntJq96ZR7ZnDKPTPKDsOsoXwnOLM6Tfr942WHYNZweWoOve8E923g+IFeJGmEpPskPSTpUUnnpPJtJc2V9KSk70taJ5Wvm+YXpuUThvyuzMysLjVrDpLWAkYAQ7kT3OvAnhGxXNJw4KeSfkSWbC6MiFlppNcjyMZtOgJ4ISK2k3QwcD7w8aG+MTOzsnTCiAg1aw5p0L0LImJlz53g8t4iNDLL0+zw9Oi5PuKaVD4T2D9N75fmScunSlL+t2JmZo2Sp1npNkn/dyhf1JKGSXoQWAbcDvwaeDF1agMsAcam6bHAU/Bmp/dLwKg+tnmUpHmS5j377LODDcms4ZaO3JylIzcvOwyzhsrTIX0SsAGwUtIK1ozKOuCVPxGxCnivpE2A64Ad+lotPfeVfKKqIOJS4FKAyZMnVy03a7YTP/rPZYdg1nA1aw6ptvDOiFgrItaJiI0iYmSexFApIl4EZgO7AZtI6klK44Cn0/QSYOu037WBjYHnB7MfMzNrjJo1h4gISdcBfz3YDUsaDbwRES9KWg/Yi6yT+W7gQGAWcBhwfXrJDWn+f9Pyu3ruW91pPORAZ/nCHZcC8MW9jio5ErPGydOs9HNJO0fELwa57THATEnDyGooV0fETZIeA2ZJ+jLwANn9IkjP35G0kKzGcPAg92dWih2XLSo7BLOGy5McPgh8RtJvgVdZ0+fwnloviohfAjv1Ub4I2KWP8hXAQXmCNjOzYuVJDnsXHoWZmbWUPMmhI9v9zcysf3mSw81kCUJkV0tvCzwBvLPAuMzaxqLNxg68klmbyXOzn3dXzkuaBHymsIjM2szpHx5wqDGztpOn5vAWETFf0s5FBNNpfMqqmbWrPHeCO6lidi1gEuBxK8ySc3/8DcA1COsseWoOIyumV5L1QfxPMeGYtZ+Jz/++7BDMGi5Pn8M5zQjEzMxax4Cjskq6PQ2c1zO/qaRbiw3LzMzKlKdZaXQaOA+AiHhB0hYFxmRm1jHa9cY/eZLDKknbRMTvACSNxxfGmb3psS0mlh2CWcPlSQ5nkN3i8540vzvg4SfNEo/Gap0oT4f0j9OFb7uRXSV9YkQ8V3hkZmZWmjwd0geQ3Zfhpoi4keyOcPsP9DqzbnHhjf/KhTf+a9lhmDVUnmalsyLiup6ZdPOes4AfFhdW+/JV0d1nzCuuSFvnGbDm0M86gx52w8zM2kee5DBP0tclvU3SREkXAvcXHZiZmZUnTw3geODzwPfJOqRvA44tMigzs07UTtc85Dlb6dV0v+cvRcSrTYjJrK3MH/uOskMwa7iayUHSMcB0YIM0vxw4PyL+swmxmbWFr37g8LJDMGu4fvscJJ0JTAP2iIhRETEK+CCwd1pmZmYdqlbN4ZPAX0XEip6CiFgk6e+Bh4AvFx1cu/Dpq93t4uvOBeDoA04vORKzxqnZrFSZGCrKXpO0uriQzNrLpq+9XHYIZg1X61TWJZKm9i6UtCewtLiQzMysbLVqDv8EXC/pp2TXNQSwMzAF2K8JsZmZWUn6rTlExKPAu4A5wARgYpp+V1pmZmYdKk+fwxVNisWsLd07/q/KDsHaUKtfEOcxkszq9I0pnyg7BLOGyzO2kpmZdZlaF8HdmZ7Pb144Zu1nxtVnMePqs8oOw6yhajUrjZH0AWBfSbPIBt17U0TMLzQyszYxYuXrZYdg1nC1ksMXyMZVGgd8vdeyAPYsKigzMytXv8khIq4BrpH0+Yj4UhNjMjOzkuUZsvtLkvYFdk9FsyPipmLDMjOzMg2YHCR9BdgF+G4q+pykKRFxWqGRmbWJO9+2S9khmDVcnuscPgK8NyJWA0iaCTwAODmYAd/a9WNlh2DWcHmvc9ikYnrjPC+QtLWkuyUtkPSopM+l8s0k3S7pyfS8aSqXpIskLZT0S0mTBvdWzMysUfIkh68AD0iakWoN9wPn5njdSuDkiNgB2A04VtKOZGdA3RkR2wN3pnmAvYHt0+Mo4OJBvROzksz63nRmfW/6wCuatZE8HdJXSZpNNiKrgFMj4g85XreUNLR3RLwiaQEwlmxE1z3SajOB2cCpqfzbERHAzyVtImlM2o6ZmTVRrrGV0hf0DUPdiaQJwE7AXGDLni/8iFgqaYu02ljgqYqXLUllb0kOko4iq1mwzTbbDDUkMzOrofCxlSRtCPwPcEJE1Lpllvooi6qCiEsjYnJETB49enSjwjQzswqFJgdJw8kSw3cj4tpU/IykMWn5GGBZKl8CbF3x8nHA00XGZ2ZmfauZHCStJemRoWxYkoDLgQURUTn8xg3AYWn6MOD6ivJPpbOWdgNecn+DtYOb3vF+bnrH+8sOw6yhBrrZz2pJD0naJiJ+N8htTwE+CTws6cFUdjpwHnC1pCOA3wEHpWW3APsAC4E/AZ8e5P7MSnHlpNa7UYtZvfJ0SI8BHpV0H/BqT2FE7FvrRRHxU/ruRwCY2sf6ARybIx6zljLijRUArBg+ouRIzBonT3I4p/AozNrYjB+cDcDB/3BeuYGYNVCe6xzukTQe2D4i7pC0PjCs+NDMzKwsA56tJOlI4Brgv1LRWOCHRQZlZmblytOsdCzZqKxzASLiyYoL17rWhOk3lx2CmVlh8lzn8HpE/LlnRtLa9HFxmpmZdY48NYd7JJ0OrCfpb4FjgBuLDcusfVzz7r3KDsGs4fIkh+nAEcDDwGfIrke4rMigzNqJk4N1ojxnK61OQ3XPJWtOeiJdk9BV3Mdg/dn0Ty8B8ML6uW51YtYW8twm9CPAJcCvyS5q21bSZyLiR0UHZ9YOLv7hVwBf52CdJU+z0gXAByNiIYCktwE3A04OZmYdKs/ZSst6EkOyiDUjqZqZWQfqt+Ygqeeu6Y9KugW4mqzP4SDgF02IzczMSlKrWemjFdPPAB9I088CmxYWkZlZl+l9wsvi88of6bff5BARHjLbLIcrd9qn7BDMGi7P2UrbAscDEyrXH2jIbrNucdMOu5cdglnD5Tlb6Ydkd3S7EVhdbDhm7WfMy88CsHQj39PcOkee5LAiIi4qPBKzNnXhTRcAvs7BOkue5PDvks4CbgNe7ymMiPmFRWVmZqXKkxzeTXYv6D1Z06wUad7MzDpQnuRwADCxcthuMzPrbHmukH4I2KToQMzMrHXkqTlsCTwu6Re8tc/Bp7KaAd/a5YCyQzBruDzJ4azCozBrY3dut2vZIViHqbxiuqyrpfPcz+GeZgTSinwPB8tj4h+XALBo1LiSIzFrnDxXSL/CmntGrwMMB16NiI2KDMysXZx76zcBX+dgnSVPzWFk5byk/YFdCovIzMxKl+dspbeIiB/iaxzMzDpanmalj1XMrgVMZk0zk5mZdaA8ZytV3tdhJbAY2K+QaMzMrCXk6XPwfR3MavjG/zm47BCsg5V1Wmut24R+ocbrIiK+VEA8Zm3n3gnvLTsEs4arVXN4tY+yDYAjgFGAk4MZsOMziwB4bMuJJUdina6ZtYhatwm9oGda0kjgc8CngVnABf29zqzbfOHOSwFf52CdpWafg6TNgJOAQ4CZwKSIeKEZgZmZWXlq9Tl8DfgYcCnw7ohY3rSoSuQhM8zMal8EdzKwFXAm8LSkl9PjFUkvNyc8MzMrQ7/JISLWioj1ImJkRGxU8RiZZ1wlSVdIWibpkYqyzSTdLunJ9LxpKpekiyQtlPRLSZMa8/bMzGwoBj18xiDMAD7cq2w6cGdEbA/cmeYB9ga2T4+jgIsLjMusob66+2F8dffDyg7DrKHyXCE9JBExR9KEXsX7AXuk6ZnAbODUVP7tiAjg55I2kTQmIpYWFZ9Zo8wft0PZIZg1XJE1h75s2fOFn563SOVjgacq1luSysxa3qQlC5i0ZEHZYZg1VLOTQ3/UR1mfg/tJOkrSPEnznn322YLDMhvYKXNmcsqcmWWHYdZQzU4Oz0gaA5Cel6XyJcDWFeuNA57uawMRcWlETI6IyaNHjy40WDOzbtXs5HAD0NNzdxhwfUX5p9JZS7sBL7m/wcysPIV1SEu6iqzzeXNJS4CzgPOAqyUdAfwOOCitfguwD7AQ+BPZMB1mZlaSIs9W+kQ/i6b2sW4AxxYVi5mZDU5hycGsW3xx6lFlh2DWcE4OZnXyUN3WiVrlVFaztjVl8YNMWfxg2WGYNZRrDngkVqvP8T+bBfiOcNZZXHMwM7MqTg5mZlbFycHMzKo4OZiZWRV3SJvV6fQPHVd2CGYN5+RgVqdFo8aVHYJZw7lZyaxOUxfOZerCuWWHYdZQrjmY1enI+64D4M7tdi05ErPGcc3BzMyqODmYmVkVJwczM6vStX0OHk/JzKx/XZsczBrlxGknlx2CWcM5OZjVaelGo8sOwazh3OdgVqdpC+YwbcGcssMwayjXHMzqdOgDtwBw0w67lxyJWeO45mBmZlWcHMzMrIqTg5mZVXFyMDOzKu6QNqvT0fufVnYIZg3n5GBWpxfW37jsEMwazs1KZnU68OE7OPDhO8oOw6yhnBzM6uTkYJ3IycHMzKo4OZiZWRUnBzMzq+LkYGZmVXwqq1mdDj/o7LJDMGs4JwezOq0YPqLsEMwazs1KZnU6dP7NHDrft521zuLkYFanaY//hGmP/6TsMMwaysnBzMyqtFRykPRhSU9IWihpetnxmJl1q5ZJDpKGAf8B7A3sCHxC0o7lRmVm1p1aJjkAuwALI2JRRPwZmAXsV3JMZmZdqZVOZR0LPFUxvwTYtfdKko4CjkqzyyU9McT9bQ48N8TXFs2xDU0psb2vZ+L8abVW83EbGsfWD51fc/FAsY0faPutlBzUR1lUFURcClxa986keRExud7tFMGxDY1jGxrHNjSdHlsrNSstAbaumB8HPF1SLGZmXa2VksMvgO0lbStpHeBg4IaSYzIz60ot06wUESslHQfcCgwDroiIRwvcZd1NUwVybEPj2IbGsQ1NR8emiKpmfTMz63Kt1KxkZmYtwsnBzMyqdGVyaLVhOiQtlvSwpAclzUtlm0m6XdKT6XnTJsVyhaRlkh6pKOszFmUuSsfxl5ImlRDb2ZJ+n47dg5L2qVh2WortCUkfKji2rSXdLWmBpEclfS6Vl37sasRW+rGTNELSfZIeSrGdk8q3lTQ3Hbfvp5NUkLRuml+Ylk8oIbYZkn5Tcdzem8qb+nlI+xwm6QFJN6X5xh23iOiqB1ln96+BicA6wEPAjiXHtBjYvFfZV4HpaXo6cH6TYtkdmAQ8MlAswD7Aj8iuUdkNmFtCbGcD/9zHujumv+26wLbpbz6swNjGAJPS9EjgVymG0o9djdhKP3bp/W+YpocDc9PxuBo4OJVfAhydpo8BLknTBwPfL/C49RfbDODAPtZv6uch7fMk4HvATWm+YcetG2sO7TJMx37AzDQ9E9i/GTuNiDnA8zlj2Q/4dmR+DmwiaUyTY+vPfsCsiHg9In4DLCT72xcV29KImJ+mXwEWkF31X/qxqxFbf5p27NL7X55mh6dHAHsC16Ty3set53heA0yV1NcFtEXG1p+mfh4kjQM+AlyW5kUDj1s3Joe+humo9UFphgBuk3S/suFBALaMiKWQfbiBLUqLrv9YWuVYHpeq8VdUNL+VFluqsu9E9kuzpY5dr9igBY5dahp5EFgG3E5WU3kxIlb2sf83Y0vLXwJGNSu2iOg5bv+SjtuFktbtHVsfcRfh34BTgNVpfhQNPG7dmBxyDdPRZFMiYhLZiLTHStq95HjyaoVjeTHwNuC9wFLgglReSmySNgT+BzghIl6utWofZYXG10dsLXHsImJVRLyXbFSEXYAdauy/1NgkvQs4DXgHsDOwGXBqs2OTNA1YFhH3VxbX2P+gY+vG5NByw3RExNPpeRlwHdkH5JmeKml6XlZehP3GUvqxjIhn0gd4NfAt1jR/ND02ScPJvny/GxHXpuKWOHZ9xdZKxy7F8yIwm6y9fhNJPRfpVu7/zdjS8o3J39TYiNg+nJrpIiJeB/6bco7bFGBfSYvJmsb3JKtJNOy4dWNyaKlhOiRtIGlkzzTwd8AjKabD0mqHAdeXEyHUiOUG4FPpLI3dgJd6mlCapVeb7gFkx64ntoPTWRrbAtsD9xUYh4DLgQUR8fWKRaUfu/5ia4VjJ2m0pE3S9HrAXmR9IncDB6bVeh+3nuN5IHBXpF7WJsX2eEWyF1mbfuVxa8rfNCJOi4hxETGB7Dvsrog4hEYet6J701vxQXZWwa/I2jbPKDmWiWRnhjwEPNoTD1l74J3Ak+l5sybFcxVZE8MbZL82jugvFrKq6n+k4/gwMLmE2L6T9v3L9AEYU7H+GSm2J4C9C47tb8iq6b8EHkyPfVrh2NWIrfRjB7wHeCDF8AjwhYrPxX1kneE/ANZN5SPS/MK0fGIJsd2VjtsjwJWsOaOpqZ+Hijj3YM3ZSg07bh4+w8zMqnRjs5KZmQ3AyUokqtQAAAMNSURBVMHMzKo4OZiZWRUnBzMzq+LkYGZmVZwcrKNIWpVGynw0jaZ5kqQ+/88lbSXpmor5q9KQCCdKOlzSVv287i3LJF0maccC3st6ku6RNGwIrz1O0qcbHZN1D5/Kah1F0vKI2DBNb0E2YuW9EXFWr/XWjjVj0CDpL8hG0Ryf5meTjVg6r4999LuskSQdC6wdEf8+hNeuT/a+d2p8ZNYNXHOwjhXZcCRHkQ0up/SL/weSbiQb6HCC1twb4jZgi1Tr+DwwGfhuml+vZ5uSDuy9TNJsSZPT8uWSzk+DKN4haZe0fJGkfdM6wyR9TdIvUk3lM/28hUNIV7hK2iNt5xpJj0v6brpCF0nnSXosbetf03v/E7BYUmEj0VpnW3vgVczaV0QsSs1KPaOhvg94T0Q8r7fe8GRfsqtMe27cMpU+agcRcY2k4yqX6a0jH28AzI6IUyVdB3wZ+FuyeyTMJLsS+QiyoRV2Vjai572SbotseGzSNtchu4p1ccW2dwLeSTZezr3AFEmPkQ198Y6IiJ7hHpJ5wPspcNgQ61yuOVg3qPz2vj0iihyo7c/Aj9P0w8A9EfFGmp6Qyv+ObAyeB8mGzh5FNn5Rpc2BF3uV3RcRSyIbKO/BtL2XgRXAZZI+BvypYv1lQJ/9JmYDcc3BOpqkicAq1oyG+mrBu3wj1nTkrQZeB4iI1VozWqaA4yPi1hrbeY1sPJxKr1dMryLrj1iZmo6mkg3AdhzZCJ2k17825HdiXc01B+tYkkaT3SrxmxVf2Hm9QnZLzcEuy+NW4Ghlw2gj6S/TiLxviogXgGGSeieIt1B2j4aNI+IW4ASyezP0+EvWjBhqNiiuOVinWS811wwHVpKNPPr12i/p0wzgEkmvAe+LiNf6WzaEbV9G1iQ0P3UqP0vft4G9jWxE1TtqbGskcH1KIgJOrFg2BThnCPGZ+VRWs1YlaSfgpIj4ZDNfawZuVjJrWRHxAHD3UC6CI+vQ/nyDQ7Iu4pqDmZlVcc3BzMyqODmYmVkVJwczM6vi5GBmZlWcHMzMrMr/B8llp6/C6wVVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def make_hist(df):\n",
    "    events = df.copy(deep=False)\n",
    "    \n",
    "    #  Check if t0_123 & t0_234 are \"reasonably close\" to each other, and if they are compute average\n",
    "    mask = np.abs(events['t0_123'] - events['t0_234']) < T_M/4\n",
    "    events.loc[mask, 't0'] = (events['t0_123'] + events['t0_234'])/2\n",
    "    events.loc[~mask, 't0'] = np.nan\n",
    "\n",
    "    #  Optionally drop t0_123 and t0_234\n",
    "    events.drop(['t0_123', 't0_234'], inplace=True, axis=1)\n",
    "\n",
    "    #  Compute drift time and position\n",
    "    events['drift_time'] = events['time'] - events['t0']\n",
    "    events['x'] = v_d*events['drift_time']\n",
    "\n",
    "    #  Clean up data for events which have a negative drift time or a position over 21mm\n",
    "    events.loc[(events['drift_time']<0) | (events['x']>L/2), 't0'] = np.nan\n",
    "\n",
    "    hist, edges,_ = plt.hist(events.loc[events['t0'].notna(), 'drift_time'], bins=100)\n",
    "    mid_edges = (edges[:-1] + edges[1:])/2\n",
    "\n",
    "    plt.title('Distribution of Drift Times')\n",
    "    plt.axvline(mid_edges[np.argmax(hist)], c='r', ls='--')\n",
    "    plt.xlabel('Drift time (ns)')\n",
    "    plt.ylabel('Number of Occurrences')\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "    return events\n",
    "\n",
    "\n",
    "printmd('#### For the Mean time Trigger')    \n",
    "events_mtt = make_hist(events_mtt)\n",
    "if not trigger_st.empty:\n",
    "    printmd('#### For the Scintillator Trigger')    \n",
    "    events_st = make_hist(events_st)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  FILTERING THE DATA "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "### Useful Events"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Time Trigger:\n",
      "\"useful rows\" / \"all rows\":  0.7248652838992968\n",
      "\"useful events\" / \"all events\" 0.9690319274265875\n",
      "\n",
      " Scintillator Trigger\n",
      "\"useful rows\" / \"all rows\":  0.6337090354499126\n",
      "\"useful events\" / \"all events\" 0.9809257375381485\n"
     ]
    }
   ],
   "source": [
    "def print_useful_events(df):\n",
    "    events = df.copy(deep=False)\n",
    "\n",
    "    # Ratio of \"useful rows\" to all rows\n",
    "    try:\n",
    "        print('\"useful rows\" / \"all rows\": ', 1 - len(events[events['t0'].isna()])/events.shape[0]) \n",
    "    except ZeroDivisionError:\n",
    "        print('Error: Dataframe is empty')\n",
    "\n",
    "    #  Event is counted as useful if 4 or more times are available\n",
    "    event_groups = events.loc[events['t0'].notna(),'time'].groupby('event').count() \n",
    "    # print(event_groups) \n",
    "    try:\n",
    "        print('\"useful events\" / \"all events\"', (event_groups>3).sum()/len(event_groups))  # some events only have 3 (or below) hits\n",
    "    except ZeroDivisionError:\n",
    "        print('Error: Dataframe is empty')\n",
    "\n",
    "printmd('### Useful Events')\n",
    "print('Mean Time Trigger:')\n",
    "print_useful_events(events_mtt)\n",
    "if not trigger_st.empty:\n",
    "    print('\\n','Scintillator Trigger')\n",
    "    print_useful_events(events_st)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now we filter the data according to the following criteria\n",
    "1. Drop hits that do not align\n",
    "2. Obtain events that have at least one hit per layer (i.e. 4 layer representation)\n",
    "3. Sort out events that have only one detector representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "### Event 1 for the Mean time Trigger"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "      <th>detector</th>\n",
       "      <th>layer</th>\n",
       "      <th>cell</th>\n",
       "      <th>t0</th>\n",
       "      <th>drift_time</th>\n",
       "      <th>x</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event</th>\n",
       "      <th>index</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1</th>\n",
       "      <th>415</th>\n",
       "      <td>1.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>452.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>11314.166667</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>11130.520833</td>\n",
       "      <td>183.645833</td>\n",
       "      <td>9.888622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>411</th>\n",
       "      <td>1.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>450.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>11257.500000</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>11130.520833</td>\n",
       "      <td>126.979167</td>\n",
       "      <td>6.837340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>417</th>\n",
       "      <td>1.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>458.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>11457.500000</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>11130.520833</td>\n",
       "      <td>326.979167</td>\n",
       "      <td>17.606571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>409</th>\n",
       "      <td>1.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>445.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>11145.000000</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>11130.520833</td>\n",
       "      <td>14.479167</td>\n",
       "      <td>0.779647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>414</th>\n",
       "      <td>1.0</td>\n",
       "      <td>104.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>459.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>11495.000000</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>11123.229167</td>\n",
       "      <td>371.770833</td>\n",
       "      <td>20.018429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>410</th>\n",
       "      <td>1.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>447.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>11181.666667</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "      <td>11123.229167</td>\n",
       "      <td>58.437500</td>\n",
       "      <td>3.146635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>412</th>\n",
       "      <td>1.0</td>\n",
       "      <td>99.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>455.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>11397.500000</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>11123.229167</td>\n",
       "      <td>274.270833</td>\n",
       "      <td>14.768429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>416</th>\n",
       "      <td>1.0</td>\n",
       "      <td>101.0</td>\n",
       "      <td>1.897417e+09</td>\n",
       "      <td>452.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>11313.333333</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>11123.229167</td>\n",
       "      <td>190.104167</td>\n",
       "      <td>10.236378</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             FPGA  TDC_CHANNEL     ORBIT_CNT  BX_COUNTER  TDC_MEAS  \\\n",
       "event index                                                          \n",
       "1     415     1.0         16.0  1.897417e+09       452.0      17.0   \n",
       "      411     1.0         14.0  1.897417e+09       450.0       9.0   \n",
       "      417     1.0         15.0  1.897417e+09       458.0       9.0   \n",
       "      409     1.0         13.0  1.897417e+09       445.0      24.0   \n",
       "      414     1.0        104.0  1.897417e+09       459.0      24.0   \n",
       "      410     1.0        102.0  1.897417e+09       447.0       8.0   \n",
       "      412     1.0         99.0  1.897417e+09       455.0      27.0   \n",
       "      416     1.0        101.0  1.897417e+09       452.0      16.0   \n",
       "\n",
       "                     time  detector  layer  cell            t0  drift_time  \\\n",
       "event index                                                                  \n",
       "1     415    11314.166667         3      1     4  11130.520833  183.645833   \n",
       "      411    11257.500000         3      2     4  11130.520833  126.979167   \n",
       "      417    11457.500000         3      3     4  11130.520833  326.979167   \n",
       "      409    11145.000000         3      4     4  11130.520833   14.479167   \n",
       "      414    11495.000000         4      1    10  11123.229167  371.770833   \n",
       "      410    11181.666667         4      2    10  11123.229167   58.437500   \n",
       "      412    11397.500000         4      3     9  11123.229167  274.270833   \n",
       "      416    11313.333333         4      4    10  11123.229167  190.104167   \n",
       "\n",
       "                     x  \n",
       "event index             \n",
       "1     415     9.888622  \n",
       "      411     6.837340  \n",
       "      417    17.606571  \n",
       "      409     0.779647  \n",
       "      414    20.018429  \n",
       "      410     3.146635  \n",
       "      412    14.768429  \n",
       "      416    10.236378  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "### Event 1 for the Scintillator Trigger"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>FPGA</th>\n",
       "      <th>TDC_CHANNEL</th>\n",
       "      <th>ORBIT_CNT</th>\n",
       "      <th>BX_COUNTER</th>\n",
       "      <th>TDC_MEAS</th>\n",
       "      <th>time</th>\n",
       "      <th>detector</th>\n",
       "      <th>layer</th>\n",
       "      <th>cell</th>\n",
       "      <th>t0</th>\n",
       "      <th>drift_time</th>\n",
       "      <th>x</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event</th>\n",
       "      <th>index</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1</th>\n",
       "      <th>246685</th>\n",
       "      <td>1.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2112.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>52821.666667</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>52672.812500</td>\n",
       "      <td>148.854167</td>\n",
       "      <td>8.015224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246690</th>\n",
       "      <td>1.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2118.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>52966.666667</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>52672.812500</td>\n",
       "      <td>293.854167</td>\n",
       "      <td>15.822917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246681</th>\n",
       "      <td>1.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2109.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>52725.833333</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>52672.812500</td>\n",
       "      <td>53.020833</td>\n",
       "      <td>2.854968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246687</th>\n",
       "      <td>1.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2121.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>53043.333333</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>52672.812500</td>\n",
       "      <td>370.520833</td>\n",
       "      <td>19.951122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246686</th>\n",
       "      <td>1.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2112.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>52808.333333</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>52548.229167</td>\n",
       "      <td>260.104167</td>\n",
       "      <td>14.005609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246688</th>\n",
       "      <td>1.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2109.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>52730.000000</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>52548.229167</td>\n",
       "      <td>181.770833</td>\n",
       "      <td>9.787660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246680</th>\n",
       "      <td>1.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2108.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>52710.833333</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>52548.229167</td>\n",
       "      <td>162.604167</td>\n",
       "      <td>8.755609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246684</th>\n",
       "      <td>1.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>1.918507e+09</td>\n",
       "      <td>2112.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>52815.000000</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>52548.229167</td>\n",
       "      <td>266.770833</td>\n",
       "      <td>14.364583</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              FPGA  TDC_CHANNEL     ORBIT_CNT  BX_COUNTER  TDC_MEAS  \\\n",
       "event index                                                           \n",
       "1     246685   1.0         16.0  1.918507e+09      2112.0      26.0   \n",
       "      246690   1.0         14.0  1.918507e+09      2118.0      20.0   \n",
       "      246681   1.0         15.0  1.918507e+09      2109.0       1.0   \n",
       "      246687   1.0         13.0  1.918507e+09      2121.0      22.0   \n",
       "      246686   1.0         68.0  1.918507e+09      2112.0      10.0   \n",
       "      246688   1.0         66.0  1.918507e+09      2109.0       6.0   \n",
       "      246680   1.0         67.0  1.918507e+09      2108.0      13.0   \n",
       "      246684   1.0         65.0  1.918507e+09      2112.0      18.0   \n",
       "\n",
       "                      time  detector  layer  cell            t0  drift_time  \\\n",
       "event index                                                                   \n",
       "1     246685  52821.666667         3      1     4  52672.812500  148.854167   \n",
       "      246690  52966.666667         3      2     4  52672.812500  293.854167   \n",
       "      246681  52725.833333         3      3     4  52672.812500   53.020833   \n",
       "      246687  53043.333333         3      4     4  52672.812500  370.520833   \n",
       "      246686  52808.333333         4      1     1  52548.229167  260.104167   \n",
       "      246688  52730.000000         4      2     1  52548.229167  181.770833   \n",
       "      246680  52710.833333         4      3     1  52548.229167  162.604167   \n",
       "      246684  52815.000000         4      4     1  52548.229167  266.770833   \n",
       "\n",
       "                      x  \n",
       "event index              \n",
       "1     246685   8.015224  \n",
       "      246690  15.822917  \n",
       "      246681   2.854968  \n",
       "      246687  19.951122  \n",
       "      246686  14.005609  \n",
       "      246688   9.787660  \n",
       "      246680   8.755609  \n",
       "      246684  14.364583  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def prepare_for_vis(df):\n",
    "    # Drop all not aligning hits\n",
    "    visual_evs = df.dropna(subset = ['t0']).copy()\n",
    "\n",
    "    \n",
    "    #  Sort out events which do not go through each layer for each present detector\n",
    "    go_through_each_lay = (visual_evs.loc[:,['layer','detector']].groupby(['event','detector']).nunique() == 4).loc[:,'layer']\n",
    "    go_through_each_lay = go_through_each_lay.groupby('event').all()\n",
    "    \n",
    "    #  Sort out events which are only registered in one detector\n",
    "    multiple_detectors = visual_evs.loc[:,'detector'].groupby('event').nunique() > 1\n",
    "    \n",
    "    #  Combine the two masks\n",
    "    index_mask = go_through_each_lay & multiple_detectors\n",
    "\n",
    "    #  Apply mask to the dataframe\n",
    "    visual_evs = visual_evs.loc[visual_evs.index.get_level_values(0).map(index_mask),:]\n",
    "\n",
    "    #  Reindex the event index level starting from 1\n",
    "    visual_evs.reset_index(level='event', inplace=True)\n",
    "    visual_evs.loc[:,'event'] = (visual_evs.loc[:,'event'].diff()!=0).cumsum()\n",
    "    visual_evs.set_index(['event', visual_evs.index], inplace=True)\n",
    "    \n",
    "    return visual_evs\n",
    "\n",
    "events_mtt_vis = prepare_for_vis(events_mtt)\n",
    "printmd('### Event 1 for the Mean time Trigger')\n",
    "display(events_mtt_vis.head(8))\n",
    "if not trigger_st.empty:\n",
    "    events_st_vis = prepare_for_vis(events_st)\n",
    "    printmd('### Event 1 for the Scintillator Trigger')\n",
    "    display(events_st_vis.head(8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# <a id =7></a><br> VI. THE DETECTOR MATRIX \n",
    " [Content Outline](#6)\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "The following paths represent some of the event trajectories found in the data. <span style='color:blue'> Blue </span> dots indicate paths at the right of the anodic wire, while <span style='color:green'> green </span> dots indicate paths at the left as in the project description"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "#### Event Path 1"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "This event follows a trajectory of a particle through detectors 3 and 4."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "#### Event Path 2"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "This event follows a trajectory of a particle through detectors 1 and 2."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArkAAADMCAYAAAB3LrvvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3de7BddX338feHJEiAIBdJzA2oYni0TBt4lKIoHi5PixGiWNsqXqBSsB1UQCyXJzMI0+IAXoLjWBg0Gh8JOFRBLlNqQDnx0gITQgIJQYOVkJCQcClyLbd8nz/WL3Ebc85ee621T/b+nc9rZk/2OWftz/6ufVa+57fXXmv9FBGYmZmZmeVkh+1dgJmZmZlZ0zzINTMzM7PseJBrZmZmZtnxINfMzMzMsuNBrpmZmZllx4NcMzMzM8uOB7lmZmZmlh0Pcq0SSQ9JekHSM5KekvQfkv5eUqltStKApLUN1TJf0j83kdWS+SVJq9L6PSDp403mm5mNpNx7dkv2npIek/TzbuRbf/Eg1+o4LiImAPsCFwPnAPO2b0mdkzRmG99+DjgOeC1wIvBVSe8Y0cLMzJqVc8/e7BJg5UjVYr3Ng1yrLSJ+GxE3An8DnCjpQABJr0l7RB+WtEHSFZLGS9oFuAWYIunZdJsiaQdJ50r6taQnJF0rac/NzyPpnWnvw1OS1kg6SdKpwEeAs1POTWnZN0saTMuukDS7JWe+pMsl/Zuk54AjtrFOn4+IByJiU0TcCfwMeHsXX0YzsxGRY89Oy70dOBD4dpdeOuszHuRaYyLiLmAt8K70rUuAGcBMYH9gKnB+RDwHvAdYFxG7pts64DPA+4F3A1OA/wa+DiBpH4om+zVg75S5NCKuBBYAl6ac4ySNA24CFgITgU8DCyQd0FLuCcBFwARg2I+1JI0H3gasqPramJn1mpx6dtq7+3XgU0A08PJYBjzItaatA/aUJOAU4MyIeDIingG+AHxomMd+EpgTEWsj4kXgAuCDksZSvPO/LSKuiYiXI+KJiFg6RM6hwK7AxRHxUkT8BLgZ+HDLMjdExC/Sntr/abNOVwDLgB+1Wc7MrN/k0rM/A9wZEXeXX3XL3djtXYBlZyrwJMU7952Bu4veCYCA4Y6l2he4XtKmlu+9CkwCpgO/LlnDFGBNRLTmrE61bbamTJCkL1J8/HVERHjvgJnlpu97tqQpFIPc/13y+WyU8CDXGiPpbRRN6efA48ALwB9HxCPbWHxbA8Y1wCci4hfbyF4DHDLEU2+dtQ6YLmmHlqa5D/CrNs+/9XNeSPER3bsj4ul2y5uZ9ZOMevYhwGTg/jRAHw+Ml/QoMDUiXh3msZYxH65gtUnaTdKxwPeAqyLivtSovgHMlTQxLTdV0l+kh20A9pL02paoK4CLJO2blt9b0vvSzxYAR0v6a0ljJe0laWZL1htacu6kuDrC2ZLGSRqguFLC9zpYp/MojgH7PxHxRNnHmZn1ugx79i3AfhTH/c4EzgfuAWZ6gDu6eZBrddwk6RmKd/NzgK8Af9vy83OAB4E7JD0N3AYcABARDwDXAP+VzqadAnwVuBFYmHLvAP4sLf8wMAs4i+KjtaXAn6bnmQe8JeX8MCJeAmZT7IV9HPgX4OPpOcv6AsWehFUtZxP/3w4eb2bWa7Ls2RHxYkQ8uvkG/BZ4Od23UUw+zNDMzMzMcuM9uWZmZmaWHQ9yzczMzCw7HuSamZmZWXY8yDUzMzOz7HiQa2ZmZmbZ8SDXzMzMzLLT6Ixnko4DjpswYcIpM2bMaDLazGxErLj/AV54/lm1X7L/uWebWb8brmd35Tq5kmqH3n777QAcccQRjeQMDAzULQmAwcHBxmqqm9NklmvqzxzX1HnWDbctHXa5q+d9mQ3r14yKQe5mvdSzm8zKuaac1801uabWnDo9u/ThCpLGSLpH0s2dFGlmZiPPPdvMRrtOjsk9HVjZrUK2l4H5AwzMH/jd1wPFzcysz2XZs83Myio1yJU0DXgv8M3uljOyBuYPsGj1IhatXlQMdgdg0aLi5oGumfWrXHu2mVknyu7JvQw4G9g01AKSTpW0WNLiRiozM7Oq3LPNbNRre3UFSccCGyPibkkDQy0XEVcCV6bHNH82WxcMnjS45VCFwZMG4aTf7cEdHNw+NZmZ1ZFzzzYz60SZS4gdBsyWNAvYCdhN0lUR8dHuljYyBk8a/P2vB7e5mJlZv8i6Z5uZldX2cIWIOC8ipkXEfsCHgJ+4WZqZ9Sb3bDOzQqOTQWw28fXTOOHks4b8+ftnvZt77lrEmWeeWet55s6dC8AZZ5xRK2ezyy67bNiaNl+zrUxNddetyaxey3FNrml75lx2Uf3XIDcj3bNz3A5dU//WlPO65VBTnZ7d6GQQm2fP2X///U9ZtWpVY7lmZiNFEhExKiaDcM82s343XM9uO8iVtBPwU+A1FHt+vx8Rnx/uMZMmT4/h9gqcdvIHWbv6Qc9mNkJZvZbjmlxTL+a06udBbj/07By3Q9fUvzXlvG6517TZUD27zOEKLwJHRsSzksYBP5d0S0Tc0UhlDfm9qySUfUzxEJ9sZmY56YuebWbWbWVOPIuIeDZ9OS7deupyM1tP6lDqMQOe+MHM8tMPPdvMbCSUnfFsjKSlwEbg1oi4cxvLbLmw+AvPP9d0nWZmVpJ7tplZyasrRMSrwExJuwPXSzowIpZvtcyWC4tPmjx9RPca/MGkDmUeM+jDFcwsT73es83MRkJHlxCLiKckDQLHAMvbLD6iOjkWd8tjOn+ImVnf6OWebWbWbW0PV5C0d9obgKTxwNHAA90uzMzMOueebWZWKLMndzLwHUljKAbF10bEzd0tq9mLDjel3y+o7Jp6p6ac1y33mvpA3/fsnLefXstxTa4p55o8GYSZWYtJk6ezYf2avr1Obifcs82s3w3Xs9vuyZU0Hfh/wOuBTcCVEfHVbS0bETcBN0k6Rar3N6Lpixd7wgjX1Es15bxuvV7TDbctrZ3Vy/q9ZzeZlXNNOa+ba3JNrTl1enaZwxVeAc6KiCWSJgB3S7o1Iu6v/KzbWZkrMfjKC2bWp7Lr2WZmVZSZDGJ9RCxJ958BVgJTu11Yt5SZOMITRZhZv8qtZ5uZVdXRJcQk7QccBGzzwuLAqY1UZWZmtblnm9loVnqQK2lX4AfAGRHx9NY/b72wuKSevbB4mYkjPFGEmfW7XHq2mVlVpQa5ksZRNMsFEXFdd0vqvjITR3hwa2b9KreebWZWRZnJIATMA1ZGxFe6X5KZmVXlnm1mVmg7yAUOAz4GHClpabrNqvOkc+fO3XKR317IaVKTNfXa65TzujWZ5Zr6Mycjo6Jnu6aRzcq5ppzXrcmsXqypHU8GYWbWQhIR4ckgzMz6wHA9u+0gV9K3gGOBjRFxYJknnDR5epxw8llD/vy0kz/I2tUPeqKHEcrqtRzX5Jp6MadVvw9yO+3bI92zc9wOXVP/1pTzuuVe02ZD9ewyhyvMB45ppAozMxsJ83HfNrNRrsxkED8FnhyBWho1MH/gDyZ7GBjw5A5mlr9+7dtmZk0qsye372xrVjPPYmZmZmY2ejQ2yJV0qqTFkha/8PxzTcWamVkXuGebWe46mtZ3OK2z50yaPH27zp6zrVnNPIuZmdnv9FLPNjPrhsYGub1mW7OaeXBrZmZmNjqUmfHsGuA/gQMkrZV0cvfLMjOzqty3zcwangxiS6j0GLC6gajXAY/3UE6TWa5pZHOazOq1nCazXBPsGxF7N/R8faEHe3aTWTnXlPO6NZnlmkY2p8msWj27K4PcpkhaHBFv7ZUc1+SaejHHNW2fLPtDvfi7yrmmnNfNNbmmJnKyvISYmZmZmY1uHuSamZmZWXZ6fZB7ZY/lNJnlmkY2p8msXstpMss1WR29+LvKuaac163JLNc0sjlNZtXK6eljcs3MzMzMquj1PblmZmZmZh3zINfMzMzMstOTg1xJ35K0UdLymjnTJd0uaaWkFZJOr5G1k6S7JC1LWRfWrG2MpHsk3Vwj4yFJ90laKmlxzXp2l/R9SQ+k1+vtFTIOSLVsvj0t6YwaNZ2ZXuvlkq6RtFPFnNNTxopO69nWtihpT0m3SlqV/t2jYs5fpZo2SSp9iZQhsr6Yfnf3Srpe0u4Vc/4pZSyVtFDSlKo1tfzsc5JC0usq1nSBpEdatqtZVeuR9GlJv0yv+6Vl1s3ac8/uKKeRvt1Ez045jfVt9+yOstyzS9ZUq29HRM/dgMOBg4HlNXMmAwen+xOAXwFvqZglYNd0fxxwJ3Bojdo+C1wN3Fwj4yHgdQ295t8B/i7d3xHYvWbeGOBRios0V3n8VOA3wPj09bXASRVyDgSWAztTTGN9G/CmOtsicClwbrp/LnBJxZw3AwcAg8Bba9b058DYdP+SGjXt1nL/M8AVVWtK358O/IhiooG22+oQNV0AfK7D3/u2co5Iv//XpK8n1tnGfWv/+6+Qk3XPTjmN9O2me3bKqdy33bM7znLPLpdVq2/35J7ciPgp8GQDOesjYkm6/wywkuI/YpWsiIhn05fj0q3SWXuSpgHvBb5Z5fFNk7QbxcY1DyAiXoqIp2rGHgX8OiLqzKI0FhgvaSxFw1tXIePNwB0R8XxEvAIsAo4v++AhtsX3UfyBIf37/io5EbEyIn5ZtpY2WQvT+gHcAUyrmPN0y5e7UHIbH+b/7Fzg7AZyOjJEzj8AF0fEi2mZjXWfxwru2SOrSz0b6vdt9+zyWe7Z5bJq9e2eHOR2g6T9gIMo3s1XzRgjaSmwEbg1IqpmXUaxEW2qWksSwEJJd0s6tUbOG4DHgG+nj+O+KWmXmrV9CLim6oMj4hHgS8DDwHrgtxGxsELUcuBwSXtJ2hmYRfFOtY5JEbE+1bkemFgzr2mfAG6p+mBJF0laA3wEOL9GzmzgkYhYVjWjxafSR3LfKvNR4xBmAO+SdKekRZLe1kBd1iWZ9mxopm93o2dDjb7tnl2Le/bQavXtUTHIlbQr8APgjK3e9XQkIl6NiJkU77gOkXRghVqOBTZGxN1V62hxWEQcDLwHOE3S4RVzxlJ8RHB5RBwEPEfxkU4lknYEZgP/WiNjD4p3338ETAF2kfTRTnMiYiXFR0G3Av8OLANeGfZBfUzSHIr1W1A1IyLmRMT0lPGpinXsDMyhRsNtcTnwRmAmxR/PL1fMGQvsARwK/CNwrSQ1UJ81LOOeDc307UZ7NtTv2+7Z1bhnt1Wrb2c/yJU0jqJZLoiI65rITB8LDQLHVHj4YcBsSQ8B3wOOlHRVxTrWpX83AtcDh1TJAdYCa1v2cnyfooFW9R5gSURsqJFxNPCbiHgsIl4GrgPeUSUoIuZFxMERcTjFRyGratQFsEHSZID0b0987C3pROBY4CORDl6q6WrgLys+9o0Uf+yWpW19GrBE0us7DYqIDWmwsgn4BvW28+vSx9h3UeyVa3tihY2snHt2qqWJvt10z4b6fds9u0Pu2aXU6ttZD3LTaH8esDIivlIza+/NZz9KGk/xH/qBTnMi4ryImBYR+1F8NPSTiOj43a6kXSRN2Hyf4iD2Smc2R8SjwBpJB6RvHQXcXyUr+TA1DlVIHgYOlbRz+j0eRXF8XsckTUz/7gN8oIHabgROTPdPBG6omVebpGOAc4DZEfF8jZw3tXw5mwrbOEBE3BcREyNiv7Str6U4oejRCjVNbvnyeCpu58APgSNT5gyKk3Uer5hlXZBzz051NNK3u9CzoX7fds/ugHt2afX6dnR49ttI3Cg26PXAyxQv9MkVc95JcfzTvcDSdJtVMetPgHtS1nLg/AbWc4CKZ+pSHJO1LN1WAHNq1jITWJzW74fAHhVzdgaeAF7bwOtzIcV/2OXAd0lnV1bI+RnFH4BlwFF1t0VgL+DHFHsXfgzsWTHn+HT/RWAD8KMaNT0IrGnZztueYTtEzg/S630vcBMwtWpNW/38Icqdqbutmr4L3JdquhGYXDFnR+CqtH5LgCPrbqO+lfv9d5CTbc9Oj2+sbzfVs1NWI33bPbujLPfsclm1+ran9TUzMzOz7GR9uIKZmZmZjU4e5JqZmZlZdjzINTMzM7PseJBrZmZmZtnxINfMzMzMsuNBrpmZmZllx4NcMzMzM8uOB7lmZmZmlh0Pcs3MzMwsOx7kmpmZmVl2PMg1MzMzs+x4kGtmZmZm2fEg18zMzMyy40GumZmZmWXHg1wzMzMzy44HuWZmZmaWHQ9yzczMzCw7HuSamZmZWXY8yDUzMzOz7HiQa2ZmZmbZ8SDXzMzMzLLjQa6ZmZmZZceDXDMzMzPLjge5ZmZmZpYdD3LNzMzMLDse5JqZmZlZdjzINTMzM7PseJBrZmZmZtnxINfMzMzMsuNBrpmZmZllx4NcMzMzM8uOB7lmZmZmlh0Pcs3MzMwsOx7kmpmZmVl2PMg1MzMzs+x4kGtmZmZm2fEg18zMzMyy40GumZmZmWXHg1wzMzMzy44HuWZmZmaWHQ9yzczMzCw7HuSamZmZWXY8yDUzMzOz7HiQa2ZmZmbZ8SDXzMzMzLLjQa6ZmZmZZceDXDMzMzPLjge5ZmZmZpYdD3LNzMzMLDse5Folkh6S9IKkZyQ9Jek/JP29pFLblKQBSWsbqmW+pH9uIqsl86/TOj0vabDJbDOzkTYKevalktZIelrSaklzmsy3/uRBrtVxXERMAPYFLgbOAeZt35I6J2nMNr79JHAZxXqZmeUg5549D/hfEbEb8A7gBEkfGNnKrNd4kGu1RcRvI+JG4G+AEyUdCCDpNZK+JOlhSRskXSFpvKRdgFuAKZKeTbcpknaQdK6kX0t6QtK1kvbc/DyS3pn2PjyV3rGfJOlU4CPA2SnnprTsmyUNpmVXSJrdkjNf0uWS/k3Sc8AR21in2yLiWmBdN187M7ORlmnP/mVEPNfyrU3A/l14+ayPeJBrjYmIu4C1wLvSty4BZgAzKZrNVOD81IjeA6yLiF3TbR3wGeD9wLuBKcB/A18HkLQPRZP9GrB3ylwaEVcCC4BLU85xksYBNwELgYnAp4EFkg5oKfcE4CJgAvDzbrweZma9LLeenQbcz6Z12gW4uuZLZH3Og1xr2jpgT0kCTgHOjIgnI+IZ4AvAh4Z57CeBORGxNiJeBC4APihpLMU7/9si4pqIeDkinoiIpUPkHArsClwcES9FxE+Am4EPtyxzQ0T8IiI2RcT/1FlhM7M+lk3PjoiLKQbBBwPfBX5b7iWwXI3d3gVYdqZSHM+6N7AzcHfROwEQsK1jqTbbF7he0qaW770KTAKmA78uWcMUYE1EtOasTrVttqZklplZzrLq2RERwD2S/gK4EPhsyRosQx7kWmMkvY2iKf0ceBx4AfjjiHhkG4vHNr63BvhERPxiG9lrgEOGeOqts9YB0yXt0NI09wF+1eb5zcxGjcx79ljgjR0+xjLjwxWsNkm7SToW+B5wVUTclxrVN4C5kiam5aamd9cAG4C9JL22JeoK4CJJ+6bl95b0vvSzBcDR6dJeYyXtJWlmS9YbWnLuBJ6jOLFhnKQB4LhUX9l1GiNpJ4pGuYOkndJxY2ZmfS23np1OgPukpD1UOAQ4DfhxJ6+L5ceDXKvjJknPULybnwN8Bfjblp+fAzwI3CHpaeA24ACAiHgAuAb4r3Q27RTgq8CNwMKUewfwZ2n5h4FZwFkUH60tBf40Pc884C0p54cR8RIwm+JEiceBfwE+np6zrI9R7NW4nOKkjBco/gCYmfWrnHv28RSHRzwDXEVxwtvXOni8ZUjF4StmZmZmZvnwnlwzMzMzy44HuWZmZmaWHQ9yzczMzCw7HuSamZmZWXY8yDUzMzOz7HiQa2ZmZmbZaXTGM0nHAcdNmDDhlBkzZjQZbWY2Ilbc/wAvPP+s2i/Z/9yzzazfDdezS18nV9IYYDHwSEQc22bZ2hffvf322wE44ogjeiKnl2saGBionbNZy5zllfXq69RLNeW8br1e0w23LR12uavnfZkN69f0/SC3X3t2k1k515Tzurkm19SaU6dnd3K4wunAyg6WNzOz7cc928xGtVKDXEnTgPcC3+xuOVbHwPwBBuYPlF9+oLiZWV7cs83Myu/JvQw4G9jUxVqshoH5AyxavYhFqxeVGugODMCiRcXNA12z7Lhnm9mo13aQK+lYYGNE3N1muVMlLZa0uLHqzMysI+7ZZmaFMldXOAyYLWkWsBOwm6SrIuKjrQtFxJXAldDMSQzWmcGTBrfswR08abD98oO/24M72H5xM+sf7tlmZpQY5EbEecB5AJIGgM9t3SytN5QZ3P7e8p0tbmZ9wD3bzKywXSaDmDt3LnPnzu2ZnCazerGmpvTiurmmkc1pMqvXcmxovfi7ck0jm5VzTTmvW5NZvVhTO6Wvk1sqLF1YfP/99z9l1apVjeWamY0USURE318ntwz3bDPrd8P17LaDXEk7AT8FXkNxeMP3I+Lzwz1m0uTpccLJZw3589NO/iBrVz+Y9cWLe7GmpiaN8IQRrqmXampy3Tbr50Gue7Zrck3bJ8c1bZ8sGLpnlznx7EXgyIh4VtI44OeSbomIOxqpzMzMmuSebWZGuRPPAng2fTku3Xwmbp9rdyUGX3nBrD+5Z5uZFcrOeDZG0lJgI3BrRNzZ3bKsm9pNHOGJIsz6m3u2mVnJQW5EvBoRM4FpwCGSDtx6mdYLi7/w/HNN12lmZiW5Z5uZlTsmd4uIeErSIHAMsHyrn225sPikydP90VgPazdxhCeKMMuDe7aZjWZtB7mS9gZeTs1yPHA0cEnXK7OuajdxhAe3Zv3JPdvMrFBmT+5k4DuSxlAc3nBtRNzc3bLYcpHgM888sydycq+pSTm/Tr2W45q2T1aP6+ue3WRWzjXlvG6uyTU1lePJIMzMWngyCDOz/jFcz+7omNx2IuIm4CZJp9SdMCDnixc3XVNTkzyAJ3rotxzX1HnWDbctHXa5ia+fVvu5+kUv9uwms3KuKed1c02uqTWnTs9ue3UFSdMl3S5ppaQVkk7vsE4zMxsh7tlmZoUye3JfAc6KiCWSJgB3S7o1Iu7vcm1WQbtJHrYsVyzmE8zM8uOebWZGiT25EbE+Ipak+88AK4Gp3S7MOtdukoctyw14sgezXLlnm5kVOjomV9J+wEHAH8yeI+lU4NRGqjIzs9rcs81sNCs9yJW0K/AD4IyIeHrrn7deWFySLyy+HbSb5GHLcoM+XMEsd+7ZZjbalRrkShpH0SwXRMR13S3J6mh3LO6W5cotZmZ9yD3bzKzc1RUEzANWRsRXul+SmZlV5Z5tZlZoO8gFDgM+BhwpaWm6zarzpHPnzt0yk0Uv5DSZ1Ys1NaUX1801jWxOk1m9lpMR9+ztkNNklmvqz5wms1xTMzzjmZlZC894ZmbWP4br2W0HuZK+BRwLbIyIA8s84aTJ0+OEk88a8uennfxB1q5+MOsZOnqxpqZmRvOsaK6pl2pqct026/dBbqd92z3bNY3mmnJet9xr2myonl3mcIX5wDGNVGE9YWD+wLDX0f29ZQd8LV2zPjQf920zG+XKTAbxU+DJEajFRkDZCSPAk0aY9Sv3bTOzcntyS5F0qqTFkha/8PxzTcWamVkXuGebWe46mvFsOK0XFp80ebovLN6jyk4YAZ40wixn7tlmlrvGBrnWP8pOGAEe3JqZmVl/auxwBTMzMzOzXlFmxrNrgP8EDpC0VtLJ3S/LzMyqct82M2t4MogtodJjwOoGol4HPN5DOU1muaaRzWkyq9dymsxyTbBvROzd0PP1hR7s2U1m5VxTzuvWZJZrGtmcJrNq9eyuDHKbImlxRLy1V3Jck2vqxRzXtH2y7A/14u8q55pyXjfX5JqayPExuWZmZmaWHQ9yzczMzCw7vT7IvbLHcprMck0jm9NkVq/lNJnlmqyOXvxd5VxTzuvWZJZrGtmcJrNq5fT0MblmZmZmZlX0+p5cMzMzM7OOeZBrZmZmZtnpyUGupG9J2ihpec2c6ZJul7RS0gpJp9fI2knSXZKWpawLa9Y2RtI9km6ukfGQpPskLZW0uGY9u0v6vqQH0uv19goZB6RaNt+elnRGjZrOTK/1cknXSNqpYs7pKWNFp/Vsa1uUtKekWyWtSv/uUTHnr1JNmySVvkTKEFlfTL+7eyVdL2n3ijn/lDKWSlooaUrVmlp+9jlJIel1FWu6QNIjLdvVrKr1SPq0pF+m1/3SMutm7blnd5TTSN9uomennMb6tnt2R1nu2SVrqtW3I6LnbsDhwMHA8po5k4GD0/0JwK+At1TMErBruj8OuBM4tEZtnwWuBm6ukfEQ8LqGXvPvAH+X7u8I7F4zbwzwKMVFmqs8firwG2B8+vpa4KQKOQcCy4GdgbHAbcCb6myLwKXAuen+ucAlFXPeDBwADAJvrVnTnwNj0/1LatS0W8v9zwBXVK0pfX868COKiQbabqtD1HQB8LkOf+/byjki/f5fk76eWGcb9639779CTtY9O+U00reb7tkpp3Lfds/uOMs9u1xWrb7dk3tyI+KnwJMN5KyPiCXp/jPASor/iFWyIiKeTV+OS7dKZ+1Jmga8F/hmlcc3TdJuFBvXPICIeCkinqoZexTw64ioM4vSWGC8pLEUDW9dhYw3A3dExPMR8QqwCDi+7IOH2BbfR/EHhvTv+6vkRMTKiPhl2VraZC1M6wdwBzCtYs7TLV/uQsltfJj/s3OBsxvI6cgQOf8AXBwRL6ZlNtZ9Hiu4Z4+sLvVsqN+33bPLZ7lnl8uq1bd7cpDbDZL2Aw6ieDdfNWOMpKXARuDWiKiadRnFRrSpai1JAAsl3S3p1Bo5bwAeA76dPo77pqRdatb2IeCaqg+OiEeALwEPA+uB30bEwgpRy4HDJe0laWdgFsU71TomRcT6VOd6YGLNvKZ9Aril6oMlXSRpDfAR4PwaObOBRyJiWdWMFp9KH8l9q8xHjUOYAbxL0p2SFkl6WwN1WZdk2rOhmb7djZ4NNfq2e3Yt7tlDq9W3R8UgV9KuwA+AM7Z619ORiHg1ImZSvOM6RNKBFWo5FtgYEXdXraPFYRFxMPAe4DRJh1fMGUvxEcHlEXEQ8BzFRzqVSNoRmA38a42MPSjeff8RMAXYRdJHO82JiJUUHwXdCvw7sAx4ZdgH9TFJcx/5POcAAALqSURBVCjWb0HVjIiYExHTU8anKtaxMzCHGg23xeXAG4GZFH88v1wxZyywB3Ao8I/AtZLUQH3WsIx7NjTTtxvt2VC/b7tnV+Oe3Vatvp39IFfSOIpmuSAirmsiM30sNAgcU+HhhwGzJT0EfA84UtJVFetYl/7dCFwPHFIlB1gLrG3Zy/F9igZa1XuAJRGxoUbG0cBvIuKxiHgZuA54R5WgiJgXEQdHxOEUH4WsqlEXwAZJkwHSvz3xsbekE4FjgY9EOnippquBv6z42DdS/LFblrb1acASSa/vNCgiNqTByibgG9Tbzq9LH2PfRbFXru2JFTaycu7ZqZYm+nbTPRvq92337A65Z5dSq29nPchNo/15wMqI+ErNrL03n/0oaTzFf+gHOs2JiPMiYlpE7Efx0dBPIqLjd7uSdpE0YfN9ioPYK53ZHBGPAmskHZC+dRRwf5Ws5MPUOFQheRg4VNLO6fd4FMXxeR2TNDH9uw/wgQZquxE4Md0/EbihZl5tko4BzgFmR8TzNXLe1PLlbCps4wARcV9ETIyI/dK2vpbihKJHK9Q0ueXL46m4nQM/BI5MmTMoTtZ5vGKWdUHOPTvV0Ujf7kLPhvp92z27A+7ZpdXr29Hh2W8jcaPYoNcDL1O80CdXzHknxfFP9wJL021Wxaw/Ae5JWcuB8xtYzwEqnqlLcUzWsnRbAcypWctMYHFavx8Ce1TM2Rl4AnhtA6/PhRT/YZcD3yWdXVkh52cUfwCWAUfV3RaBvYAfU+xd+DGwZ8Wc49P9F4ENwI9q1PQgsKZlO297hu0QOT9Ir/e9wE3A1Ko1bfXzhyh3pu62avoucF+q6UZgcsWcHYGr0votAY6su436Vu7330FOtj07Pb6xvt1Uz05ZjfRt9+yOstyzy2XV6tue1tfMzMzMspP14QpmZmZmNjp5kGtmZmZm2fEg18zMzMyy40GumZmZmWXHg1wzMzMzy44HuWZmZmaWHQ9yzczMzCw7/x8cANEDRDaf7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "#### Event Path 3"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "This trajectory presents a particle that MAY have excited electrons in the cells, therefore a detection of multiple hits is present. Further filtration would be needed to avoid these kinds of path from showing up, nevertheless, we can use this to characterize the behavior of the particle as it traverses the detectors."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "#### Event Path 4"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "Trajectory of event detected by scintillator trigger."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotDetector(ax, event, is_empty):\n",
    "    detector = np.zeros((4,16*2+1))\n",
    "\n",
    "    even_layers = event['layer']%2 == 0\n",
    "    odd_layers = even_layers == False\n",
    "\n",
    "    def fillDetectorMatrix(matrix, i, j, s=0):\n",
    "        matrix[i,j*2+s] = 1\n",
    "        matrix[i,j*2+1+s] = 1\n",
    "\n",
    "    def plotLeftRight(ax, cell, position, layer, odd, left):\n",
    "        if left == True:\n",
    "            ax.scatter((cell-1-position/L)*2+0.5+odd, layer-1, s=10, c='g', marker='+')\n",
    "        else:\n",
    "            ax.scatter((cell-1+position/L)*2+0.5+odd, layer-1, s=10, c='b', marker='+')\n",
    "    \n",
    "    if is_empty == False:\n",
    "        fillDetectorMatrix(detector, event.loc[even_layers,'layer']-1,\n",
    "                    event.loc[even_layers,'cell']-1, s=0)\n",
    "        fillDetectorMatrix(detector, event.loc[odd_layers,'layer']-1,\n",
    "                    event.loc[odd_layers,'cell']-1, s=1)\n",
    "\n",
    "        for odd,left in [[odd, left] for odd in [True, False] for left in [True,False]]:\n",
    "            if odd == True:\n",
    "                layers = odd_layers\n",
    "            else:\n",
    "                layers = even_layers\n",
    "\n",
    "            plotLeftRight(ax, event.loc[layers, 'cell'], event.loc[layers, 'x'],\n",
    "                     event.loc[layers, 'layer'], odd, left)\n",
    "\n",
    "    detector[(0,1,2,3),(0,32,0,32)] = 0.5 # Mark \"cell offset\"\n",
    "    ax.matshow(detector, origin='lower', cmap='bone', vmin=0, vmax=1)\n",
    "\n",
    "    # Major ticks\n",
    "    ax.set_xticks(np.arange(1.5, 32, 2));\n",
    "    ax.set_yticks(np.arange(0, 4, 1));\n",
    "\n",
    "    # # Labels for major ticks\n",
    "    ax.set_xticklabels(np.arange(1, 17, 1));\n",
    "    ax.set_yticklabels(np.arange(1, 5, 1));\n",
    "\n",
    "    # # Minor ticks\n",
    "    # # ax.set_xticks(np.arange(-.5, 32, 2), minor=True);\n",
    "    ax.set_yticks(np.arange(0.5, 4, 1), minor=True);\n",
    "\n",
    "    ax.grid(which='minor', axis='y', color='w', linewidth=1)\n",
    "    ax.xaxis.set_ticks_position('bottom')\n",
    "    \n",
    "    vert_line = np.array([0,1])\n",
    "    for l in range(4):\n",
    "        for c in range(16):\n",
    "            if l%2 == 0:\n",
    "                ax.plot([c*2+0.5,c*2+0.5], vert_line+l-0.5, c='w')\n",
    "            else:\n",
    "                ax.plot([c*2+1.5,c*2+1.5], vert_line+l-0.5, c='w')\n",
    "\n",
    "def plotEvent(event):\n",
    "    fig, axes = plt.subplots(2, 2, figsize=(12,4))\n",
    "\n",
    "    for i in range(0,4):\n",
    "        sub_ev = event.loc[event['detector']==i+1, :]\n",
    "        plotDetector(axes[1-i%2,i//2], sub_ev, sub_ev.empty)\n",
    "        axes[1-i%2,i//2].set_title('Detector {}'.format(i+1))\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "printmd(\"The following paths represent some of the event trajectories found in the data. <span style='color:blue'> Blue </span> dots indicate paths at the right of the anodic wire, while <span style='color:green'> green </span> dots indicate paths at the left as in the project description\")\n",
    "printmd(\"#### Event Path 1\")\n",
    "printmd(\"This event follows a trajectory of a particle through detectors 3 and 4.\")\n",
    "plotEvent(events_mtt_vis.loc[47])\n",
    "\n",
    "printmd(\"#### Event Path 2\")\n",
    "printmd(\"This event follows a trajectory of a particle through detectors 1 and 2.\")\n",
    "plotEvent(events_mtt_vis.loc[5])\n",
    "\n",
    "printmd(\"#### Event Path 3\")\n",
    "printmd(\"This trajectory presents a particle that MAY have excited electrons in the cells, therefore a detection of multiple hits is present. Further filtration would be needed to avoid these kinds of path from showing up, nevertheless, we can use this to characterize the behavior of the particle as it traverses the detectors.\")\n",
    "plotEvent(events_mtt_vis.loc[57])\n",
    "\n",
    "if not trigger_st.empty: \n",
    "    printmd(\"#### Event Path 4\")\n",
    "    printmd(\"Trajectory of event detected by scintillator trigger.\")\n",
    "    plotEvent(events_st_vis.loc[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "### Final Remarks: \n",
    "We have fulfilled the project goals through the previous code. In the end, valid trajectories were found through the sorting and filtering of the data using the trigger channels, mean time and scintillator. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.1"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}