{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>Decay Times in Microseconds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1257.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.421448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.931721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.319997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.960001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.880002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.120004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>20.319996</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Decay Times in Microseconds\n",
       "count                  1257.000000\n",
       "mean                      3.421448\n",
       "std                       3.931721\n",
       "min                       0.319997\n",
       "25%                       0.960001\n",
       "50%                       1.880002\n",
       "75%                       4.120004\n",
       "max                      20.319996"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas\n",
    "\n",
    "data = pandas.read_csv('20250212_EC_decays.txt')\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>Decay Times in Microseconds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1255.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.394741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.877424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.319997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.960000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.879998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.120002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>19.880012</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Decay Times in Microseconds\n",
       "count                  1255.000000\n",
       "mean                      3.394741\n",
       "std                       3.877424\n",
       "min                       0.319997\n",
       "25%                       0.960000\n",
       "50%                       1.879998\n",
       "75%                       4.120002\n",
       "max                      19.880012"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cropped_data = data[data['Decay Times in Microseconds'] >= 0.3]\n",
    "cropped_data = cropped_data[cropped_data['Decay Times in Microseconds'] <= 20]\n",
    "cropped_data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([242, 195, 167, 101,  81,  68,  53,  52,  41,  33,  25,  19,  18,\n",
       "        14,  17,   6,   5,   5,   9,   9,   8,   9,   3,   6,   3,   5,\n",
       "         9,   9,   2,   2,   4,   6,   4,   5,   2,   1,   5,   8,   2,\n",
       "         2,   0])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_range = (0.3, max(data['Decay Times in Microseconds']))\n",
    "bins = np.arange(0.3, max(data['Decay Times in Microseconds']) + 0.5, 0.5)\n",
    "hist = cropped_data.hist(range=data_range, bins=bins)\n",
    "\n",
    "values = np.histogram(cropped_data[\"Decay Times in Microseconds\"], range=data_range, bins=bins)[0]\n",
    "bincenters = 0.5*(bins[1:]+bins[:-1])\n",
    "\n",
    "hist[0][0].errorbar(bincenters, values, yerr=np.sqrt(values), fmt='none', color='red')\n",
    "hist[0][0].set_xlabel('Time (μs)')\n",
    "hist[0][0].set_ylabel('Counts')\n",
    "\n",
    "#hist[0][0].set_yscale('log')\n",
    "values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cropped_data_2 = cropped_data[cropped_data['Decay Times in Microseconds'] <= 7]\n",
    "data_range = (0.3, max(cropped_data_2['Decay Times in Microseconds']))\n",
    "bins = np.arange(0.3, max(cropped_data_2['Decay Times in Microseconds']) + 0.5, 0.5)\n",
    "hist = cropped_data_2.hist(range=data_range, bins=bins)\n",
    "hist[0][0].set_yscale('log')\n",
    "\n",
    "times, bins = np.histogram(cropped_data_2, bins=bins, range=data_range)\n",
    "times = np.log(times)\n",
    "bins = bins[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'unumpy' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mNameError\u001b[39m                                 Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[5]\u001b[39m\u001b[32m, line 3\u001b[39m\n\u001b[32m      1\u001b[39m line, cov = np.polyfit(bins, times, deg=\u001b[32m1\u001b[39m, cov=\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[32m----> \u001b[39m\u001b[32m3\u001b[39m coeff = \u001b[43munumpy\u001b[49m.uarray(line, np.sqrt(np.diag(cov)))\n\u001b[32m      4\u001b[39m coeff\n",
      "\u001b[31mNameError\u001b[39m: name 'unumpy' is not defined"
     ]
    }
   ],
   "source": [
    "line, cov = np.polyfit(bins, times, deg=1, cov=True)\n",
    "\n",
    "coeff = unumpy.uarray(line, np.sqrt(np.diag(cov)))\n",
    "coeff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1137124579584188+/-0.10976894836916962"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma = coeff[0]\n",
    "tau = -1 / gamma\n",
    "tau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Decay Times in Microseconds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1102.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.161488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.617221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.319997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.879998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.640000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.040010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>6.960006</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Decay Times in Microseconds\n",
       "count                  1102.000000\n",
       "mean                      2.161488\n",
       "std                       1.617221\n",
       "min                       0.319997\n",
       "25%                       0.879998\n",
       "50%                       1.640000\n",
       "75%                       3.040010\n",
       "max                       6.960006"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cropped_data_2.describe()"
   ]
  }
 ],
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