{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Representation Graphs and Histograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data =  fall time (t) vs. the height (x) of which an apple is dropped\n",
    "# Simple dataset (x+/-dx, t+/-dt)\n",
    "\n",
    "data_x= [0.49805377, 0.67623611, 0.80522924, 0.97044345, 1.12945511, \n",
    "    1.28508361, 1.43542144, 1.59138769, 1.72742522, 1.89783378]                                                                                                                      \n",
    "\n",
    "data_dx = [0.01, 0.01, 0.01, 0.01, 0.01,\n",
    "      0.01, 0.01, 0.01, 0.01, 0.01]                                                                                       \n",
    "\n",
    "data_t = [0.3304071 , 0.28373072, 0.44070176, 0.49827658, 0.45374148, \n",
    "     0.52819172, 0.64219285, 0.60636401, 0.59992293, 0.55806461]                                                                                                                     \n",
    "                                                                                                                                                                                                                                                 \n",
    "data_dt = [0.05, 0.05, 0.05, 0.05, 0.05,  \n",
    "      0.05, 0.05, 0.05, 0.05, 0.05]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a figure (by default the figure numbering start from 1)\n",
    "plt.figure(1) \n",
    "\n",
    "# plot measurement with errors\n",
    "plt.errorbar(data_x, data_t, xerr=data_dx, yerr=data_dt,\n",
    "             marker='o', color='black', label='data', linestyle='none')\n",
    "\n",
    "# legend\n",
    "plt.legend(loc='upper left',fontsize='15', numpoints=1)\n",
    "\n",
    "# set axis range\n",
    "plt.xlim([0,2.0])\n",
    "plt.ylim([0,0.8])\n",
    "\n",
    "# grid lines (sometimes useful)\n",
    "plt.grid(False)\n",
    "\n",
    "# always label the axes (the r'$...$' make the axes have a latex style)\n",
    "plt.xlabel(r'height $h$ [m]')\n",
    "plt.ylabel(r'time $t$ [s]')\n",
    "\n",
    "# make the plot appear\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Any function you draw is computed in on a finite number of points\n",
    "# With a large enough number of points you achieve what graphically \n",
    "# seems a smooth curve\n",
    "def Falltime(x, g):\n",
    "    return np.sqrt(2*x/g)\n",
    "\n",
    "# create a dataset\n",
    "true_g = 9.8\n",
    "function_x = np.arange(0, 2.0, 0.01)\n",
    "function_y = Falltime(function_x, true_g)\n",
    "\n",
    "# the simplest way to plot\n",
    "plt.plot(function_x, function_y,color='blue',label='theory')\n",
    "\n",
    "# set axis range\n",
    "plt.xlim([0,2.0])\n",
    "plt.ylim([0,0.8])\n",
    "\n",
    "# always label the axes (the r'$...$' make the axes have a latex style)\n",
    "plt.xlabel(r'height $h$ [m]')\n",
    "plt.ylabel(r'time $t$ [s]')\n",
    "\n",
    "# legend\n",
    "plt.legend(loc='upper left',fontsize='15', numpoints=1)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# you can also overlap the two plots by putting them together on the same figure\n",
    "\n",
    "# plot mean value on top\n",
    "plt.plot(function_x, function_y, color='blue', label='theory')\n",
    "\n",
    "# always label the axes (the r'$...$' make the axes have a latex style)\n",
    "plt.xlabel(r'height $h$ [m]')\n",
    "plt.ylabel(r'time $t$ [s]')\n",
    "\n",
    "# plot measurement with errors\n",
    "plt.errorbar(data_x, data_t, xerr=data_dx, yerr=data_dt,\n",
    "             marker='o', color='black', label='data', linestyle='none')\n",
    "\n",
    "# legend\n",
    "plt.legend(loc='upper left',fontsize='15', numpoints=1)\n",
    "\n",
    "# set axis range\n",
    "plt.xlim([0,2.0])\n",
    "plt.ylim([0,0.8])\n",
    "\n",
    "# grid lines (sometimes useful)\n",
    "plt.grid(False)\n",
    "\n",
    "# always label the axes (the r'$...$' make the axes have a latex style)\n",
    "plt.xlabel(r'height $h$ [m]')\n",
    "plt.ylabel(r'time $t$ [s]')\n",
    "\n",
    "# make the plot appear\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histograms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data are 100 points gaussian distributed around mu = 5 with sigma = 1\n",
    "x = [-0.69, -0.77, -0.037, -0.047, -0.88, 0.5, -1.7, -0.89, 1.4, 0.47, \n",
    "     -0.081, 1.7, 0.27, -0.77, -0.19, -0.47, 1.1, 0.86, -1.4, 1, -0.78, \n",
    "     0.36, -0.08, -0.62, -0.31, -0.63, 0.33, -1.1, -1.3, 1.3, 1.2, 1.2, \n",
    "     -0.45, 0.058, -1.2, 0.73, -0.3, 1.2, -0.48, -0.27, -0.25, 0.077, \n",
    "     1.8, 2.4, 0.51, 1.3, 2.1, -0.72, 1.1, 0.83, 0.055, -1.2, -3.8, -0.95, \n",
    "     -0.25, 0.11, -0.38, 0.9, 0.16, 0.38, 2, -0.34, 0.16, -0.41, -1.8, 0.27, \n",
    "     -1.3, -0.33, -0.33, -0.36, 1.7, -0.52, 0.84, 0.97, 1.8, 1.3, 1.1, -0.21, \n",
    "     -1.1, -0.039, -0.33, -0.2, 0.81, -1.5, 0.73, 0.37, -0.39, 0.45, -0.44, \n",
    "     -1.6, 2, -0.44, -0.19, -0.57, -0.094, 0.68, -0.19, 0.56, -0.37, -1.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAJQCAYAAADG07NDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xu0XXV57//3xwBiERRkqwwuDdpUi7aApnihehREo1ig/sRiaxsrp6mnUPVo1diLF2rPQNt6qcVLKkjqkSKilghUS1Gw2iOSCF4AKQFRIhSiqOClaPD5/bFm6HKzL3PvZK6Ztff7NUbGmvf57Jbx+FlzzfmdqSokSZI0WvfpuwBJkqTFyBAmSZLUA0OYJElSDwxhkiRJPTCESZIk9cAQJkmS1ANDmCRJUg8MYZIkST0whEmSJPVgp74LaGPvvfeupUuX9l2GpBHasGHDt6pqou86tpX9S1p82vavsQhhS5cuZf369X2XIWmEkny97xq2B/uXtPi07V/+HClJktQDQ5gkSVIPDGGSJEk9MIRJkiT1wBAmSZLUA0OYJElSDwxhkiRJPTCESZIk9cAQJkmS1ANDmCRJUg/G4rVF2rEtXX1BZ8e+8dSjOzu2JNm/1CevhEmSJPXAECZJktQDQ5gkSVIPDGGSJEk9MIRJkiT1wBAmSZLUA0OYJElSDzoPYUmWJLkiyfnN/IFJLktyXZIPJtml6xokaViSFUmuTbIxyeoZtntukkqyfGjZa5r9rk3yjNFULGkhGsWVsJcC1wzNvwl4a1UtA74DnDiCGiQJGHwxBE4DngkcBDw/yUFTbLc78BLgsqFlBwEnAI8CVgDvbI4nSXPWaQhLsh9wNPDeZj7AEcC5zSZrgeO6rEGSJjkM2FhVN1TVj4GzgWOn2O4vgDcD/zW07Fjg7Kq6q6q+BmxsjidJc9b1lbC3Aa8CftrMPwj4blVtaeY3AftOtWOSVUnWJ1m/efPmjsuUtIjsC9w0NH+vPpTkUGD/qjp/rvs2+9u/JM2qsxCW5NnAbVW1YXjxFJvWVPtX1ZqqWl5VyycmJjqpUdKiNGMfSnIf4K3AK+a67z0L7F+SWujyBd6HA8ckeRawK7AHgytjD0yyU3M1bD/g5g5rkKTJNgH7D81P7kO7A48GLhncQcFDgXVJjmmxryS11tmVsKp6TVXtV1VLGdzI+smq+m3gU8Bzm81WAud1VYMkTeFyYFnzpPYuDPrTuq0rq+p7VbV3VS1t+tfngGOqan2z3QlJ7pvkQGAZ8PnR/wmSFoI+xgl7NfDyJBsZ3CN2eg81SFqkmqvwJwOfYPDk9jlVdVWSU5qrXTPtexVwDnA18HHgpKq6u+uaJS1MXf4ceY+qugS4pJm+AZ8mktSjqroQuHDSstdOs+1TJs3/JfCXnRUnadFwxHxJkqQeGMIkSZJ6YAiTJEnqgSFMkiSpB4YwSZKkHhjCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQeGMIkSZJ6YAiTJEnqgSFMkiSpB4YwSZKkHhjCJEmSemAIkyRJ6kFnISzJrkk+n+SLSa5K8oZm+ZlJvpbkyubfIV3VIElTSbIiybVJNiZZPcX6Fyf5ctOjPpPkoGb50iQ/Gupf7x599ZIWip06PPZdwBFV9f0kOwOfSfLPzbpXVtW5HZ5bkqaUZAlwGnAUsAm4PMm6qrp6aLOzqurdzfbHAG8BVjTrrq8qvzxK2madXQmrge83szs3/6qr80lSS4cBG6vqhqr6MXA2cOzwBlV1x9Dsbti7JHWg03vCkixJciVwG3BRVV3WrPrLJF9K8tYk951m31VJ1idZv3nz5i7LlLS47AvcNDS/qVn2M5KclOR64M3AS4ZWHZjkiiSXJnnSVCewf0lqo9MQVlV3N5ft9wMOS/Jo4DXAI4FfBfYCXj3NvmuqanlVLZ+YmOiyTEmLS6ZYdq8rXVV1WlU9nEGP+rNm8S3AAVV1KPBy4Kwke0yxr/1L0qxG8nRkVX0XuARYUVW3ND9V3gW8j8FPA5I0KpuA/Yfm9wNunmH7s4HjAKrqrqr6djO9Abge+MWO6pS0wHX5dOREkgc20/cDngZ8Nck+zbIwaGxf6aoGSZrC5cCyJAcm2QU4AVg3vEGSZUOzRwPXNcsnmhv7SfIwYBlww0iqlrTgdPl05D7A2qZh3Qc4p6rOT/LJJBMMfhK4EnhxhzVI0s+oqi1JTgY+ASwBzqiqq5KcAqyvqnXAyUmeBvwE+A6wstn9ycApSbYAdwMvrqrbR/9XSFoIOgthVfUl4NAplh/R1TklqY2quhC4cNKy1w5Nv3Sa/T4MfLjb6iQtFo6YL0mS1ANDmCRJUg8MYZIkST0whEmSJPXAECZJktQDQ5gkSVIPDGGSJEk9MIRJkiT1wBAmSZLUA0OYJElSDwxhkiRJPTCESZIk9cAQJkmS1ANDmCRJUg8MYZIkST2YVwhL8s/buxBJ2lb2JknjZKfpViR5zHSrgEO6KUeSZmZvkrRQTBvCgMuBSxk0tske2E05kjQre5OkBWGmEHYN8AdVdd3kFUlu6q4kSZqRvUnSgjDTPWGvn2H9H8124CS7Jvl8ki8muSrJG5rlBya5LMl1ST6YZJe5ly1pEXs929CbAJKsSHJtko1JVk+x/sVJvpzkyiSfSXLQ0LrXNPtdm+QZ8/oLJIkZQlhVnVtV106z7p9aHPsu4IiqOpjBfRorkjweeBPw1qpaBnwHOHHuZUtarLa1NyVZApwGPBM4CHj+cMhqnFVVv1xVhwBvBt7S7HsQcALwKGAF8M7meJI0Z50NUVED329md27+FXAEcG6zfC1wXFc1SNIUDgM2VtUNVfVj4Gzg2OENquqOodndGPQumu3Orqq7quprwMbmeJI0Z52OE5ZkSZIrgduAi4Drge9W1ZZmk03AvtPsuyrJ+iTrN2/e3GWZkhaXfYHhe8em7ENJTkpyPYMrYS+Z4772L0mz6jSEVdXdzeX8/Rh8W/ylqTabZt81VbW8qpZPTEx0WaakxWWqpyrv1Yeq6rSqejjwauDP5riv/UvSrFqFsCSPHP6cq6r6LnAJ8HjggUm2PpW5H3DzfI4pSfPsTZuA/YfmZ+tDZ/Pft03MdV9JmlbbK2FnTfqcVZKJJA9spu8HPI3Bo+WfAp7bbLYSOK/tMSVpkjn3JgbjjC1rntTehcGN9uuGN0iybGj2aGDrcBjrgBOS3DfJgcAy4PPzqlzSojfTOGFTmepS/HT2AdY2Tw7dBzinqs5PcjVwdpI3AlcAp8+xBkmarHVvqqotSU4GPgEsAc6oqquSnAKsr6p1wMlJngb8hMFT3Cubfa9Kcg5wNbAFOKmq7t7Of4ukRWKuIay1qvoScOgUy2/Ap4kk9aiqLgQunLTstUPTL51h378E/rK76iQtFp3emC9JkqSpzTWETfkkoyT1zN4kaey0DWGZ9ClJOwJ7k6Sx1TaEPWnSpyTtCOxNksZWqxC29fVDQ68hkqTe2ZskjTNvzJckSeqBIUySJKkHbV9bdL8kj+i6GEmaC3uTpHE2awhL8uvAlcDHm/lDkqybeS9J6pa9SdK4a3Ml7PUMRrj/LkBVXQks7a4kSWrl9dibJI2xNiFsS1V9r/NKJGlu7E2Sxlqbd0d+JclvAUuSLANeAvx7t2VJ0qzsTZLGWpsrYX8EPAq4CzgL+B7wsi6LkqQW7E2SxlqbK2GPBV5bVX+6dUGSxwBf6KwqSZqdvUnSWGtzJewTwCeTPGRo2Xs7qkeS2rI3SRprbULYtcBfAZckeWKzzJflSuqbvUnSWGvzc2RV1flJrgU+mOQMoDquS5JmY2+SNNbahLAAVNV1SZ4EvA/4lU6rkhpLV1/Q2bFvPPXozo6tkbA3aYdm/9JsZg1hVXXo0PQPgOclOaDTqiRpFvYmSeNu2hCW5FVV9eYkfzvNJi+Z6cBJ9gf+AXgo8FNgTVW9Pcnrgd8HNjeb/klVXTjnyiUtStvam5pjrADeDiwB3ltVp05a/3LgfwJbGPSqF1XV15t1dwNfbjb9RlUdM7+/RNJiN9OVsGuazw3zPPYW4BVV9YUkuwMbklzUrHtrVf31PI8raXHbpt6UZAlwGnAUsAm4PMm6qrp6aLMrgOVV9cMk/wt4M/CbzbofVdUh8ytdkv7btCGsqj7WfK7duizJfYD7V9Udsx24qm4Bbmmm70xyDbDvNlcsaVHb1t7E4H2TG6vqhmbfs4FjgXtCWFV9amj7zwEv2A6lS9LPmHWIiiRnJdkjyW4MmtS1SV45l5MkWQocClzWLDo5yZeSnJFkz2n2WZVkfZL1mzdvnmoTSYvYNvSmfYGbhuY3MfMXxBOBfx6a37XpTZ9Lctw0tdm/JM2qzThhBzXfLo8DLgQOAH6n7QmS3B/4MPCy5jjvAh4OHMLgStnfTLVfVa2pquVVtXxiYqLt6SQtHvPtTVONJTbl0BZJXgAsZzAe2VYHVNVy4LeAtyV5+L0OZv+S1EKbELZzkp0ZNLrzquontByLp9nvw8AHquojAFV1a1XdXVU/Bf6ewU8DkjRX8+1Nm4D9h+b3A26evFGSpwF/ChxTVXdtXV5VNzefNwCXMLjKL0lz1iaEvQe4EdgN+HSSnwdmve8iSYDTgWuq6i1Dy/cZ2uw3gK/MpWBJasyrNwGXA8uSHJhkF+AEYN3wBkkObY5/TFXdNrR8zyT3bab3Bg5n6F4ySZqLNuOE/S1wz6PgSb4BPLXFsQ9n8NPAl5Nc2Sz7E+D5SQ5h8I31RuAP5lizJM27N1XVliQnM3j35BLgjKq6KskpwPqqWsfg58f7Ax8afJ+8ZyiKXwLek+SnDL7EnjrpqUpJaq3NiPk/o6qKwfATs233Gaa+98IxwSRtd217U7PthUzqRVX12qHpp02z378Dv7wNZUrSPdr8HClJkqTtzBAmSZLUgzbjhB3fjHhPkj9L8pEkj+m+NEmanr1J0rhrcyXsz5sR738NeAawlsFYX5LUJ3uTpLHWJoTd3XweDbyrqs4DdumuJElqxd4kaay1CWHfTPIe4HnAhc0YOd5LJqlv9iZJY61Nw3oeg/F0VlTVd4G9gDm9O1KSOmBvkjTWZg1hVfVD4DzgB0kOAHYGvtp1YZI0E3uTpHE362CtSf4IeB1wK/DTZnEBv9JhXZI0I3uTpHHXZsT8lwKPqKpvd12MJM2BvUnSWGtzT9hNwPe6LkSS5sjeJGmstbkSdgNwSZILgLu2Lqyqt3RWlSTNzt4kaay1CWHfaP7tgmPwSNpx2JskjbVZQ1hVvWEUhUjSXNibJI27aUNYkrdV1cuSfIzBE0c/o6qO6bQySZqCvUnSQjHTlbD3N59/PYpCJKkle5OkBWHaEFZVG5rPS5PsAjySwbfOa6vqxyOqT5J+hr1J0kLRZrDWo4F3A9cDAQ5M8gdV9c9dFydJ07E3SRp3bZ6O/BvgqVW1ESDJw4ELABudpD7ZmySNtTaDtd62tck1bgBum22nJPsn+VSSa5JcleSlzfK9klyU5Lrmc8951i5pcZtXbwJIsiLJtUk2Jlk9xfqXJ7k6yZeSXJzk54fWrWz613VJVm77nyFpsZrp6cjnNJNXJbkQOIfBfRfHA5e3OPYW4BVV9YUkuwMbklwEvBC4uKpObZrfauDV2/A3SFpEtrU3JVkCnAYcBWwCLk+yrqquHtrsCmB5Vf0wyf8C3gz8ZpK9GLyvcnlzzg3Nvt/ZTn+epEVkpp8jf31o+lbgfzTTm4FZr15V1S3ALc30nUmuAfYFjgWe0my2FrgEQ5ik9rapNwGHARur6gaAJGcz6Ev3hLCq+tTQ9p8DXtBMPwO4qKpub/a9CFgB/OPc/wxJi91MT0f+3vY6SZKlwKHAZcBDmoBGVd2S5MHT7LMKWAVwwAEHbK9SJI257dCb9mXw3smtNgGPm2H7E/nv+8ym2nffyTvYvyS10eaesG2S5P7Ah4GXVdUdbferqjVVtbyqlk9MTHRXoKTFJlMsu9egrwBJXsDgp8e/msu+9i9JbXQawpLszCCAfaCqPtIsvjXJPs36fWh5I60kbSebgP2H5vcDbp68UZKnAX8KHFNVd81lX0lqY9oQluQJSab61tdKs+/pwDVV9ZahVeuArU8UrQTOm+85JC0+29qbGNy8vyzJgc1grycw6EvD5zgUeA+DADb8RfETwNOT7Nk82f30ZpkkzdlMV8JWMnjy5+wkL0zy0Dke+3Dgd4AjklzZ/HsWcCpwVJLrGDyddOq8Kpe0WG1Tb6qqLcDJDMLTNcA5VXVVklOSbH3v5F8B9wc+1PSudc2+twN/wSDIXQ6csvUmfUmaq5luzH8xQJJHAs8EzkzyAOBTwMeBz1bV3TPs/xmmvn8C4Mh5VyxpUdvW3tQc40LgwknLXjs0/bQZ9j0DOGPef4AkNWa9J6yqvlpVb62qFcARwGcYjMdzWdfFSdJ07E2Sxl2b1xbdo6p+xODb44WzbStJo2JvkjSOOh+iQpIkSfdmCJMkSerBrCEsyW5J7tNM/2KSY5rxvySpN/YmSeOuzZWwTwO7JtkXuBj4PeDMLouSpBbsTZLGWpsQlqr6IfAc4B1V9RvAQd2WJUmzsjdJGmutQliSJwC/DVzQLJvTU5WS1AF7k6Sx1iaEvQx4DfDRZlTphzEYFFGS+mRvkjTWZv3WWFWXApcm2a2ZvwF4SdeFSdJM7E2Sxl2bpyOfkORqBu9YI8nBSd7ZeWWSNAN7k6Rx1+bnyLcBzwC+DVBVXwSe3GVRktSCvUnSWGs1WGtV3TRp0Ywvx5WkUbA3SRpnbZ4kuinJE4FKsguDey6u6bYsSZqVvUnSWGtzJezFwEnAvsAm4JBmXpL6ZG+SNNbaPB35LQbj8EjSDsPeJGncTRvCkryqqt6c5B1ATV5fVT4KLmnk7E2SFoqZroRtvbdi/SgKkaSW7E2SFoRpQ1hVfSzJEuDRVfXKEdYkSdOyN0laKGa8Mb+q7gYeO58DJzkjyW1JvjK07PVJvpnkyubfs+ZzbEmL27b0JoAkK5Jcm2RjktVTrH9yki8k2ZLkuZPW3T3Uw9bNtwZJajNExRVNo/kQ8IOtC6vqI7Psdybwd8A/TFr+1qr667kUKUlTmFdvaq6inQYcxeCpysuTrKuqq4c2+wbwQuCPpzjEj6rqkG2sXZJahbC9GIxIfcTQsgJmbHRV9ekkS+ddmSTNbF69CTgM2Ni8a5IkZwPHAveEsKq6sVn30+1YryT9jDYh7L1V9dnhBUkO34ZznpzkdxncVPuKqvrOVBslWQWsAjjggAO24XTS1JauvqCzY9946tGdHVv3mG9v2hcYHml/E/C4OZx31yTrgS3AqVX1T5M3sH+pa/avhaHNYK3vaLmsjXcBD2cwqOItwN9Mt2FVramq5VW1fGJiYp6nk7SAzbc3ZYpl9xrqYgYHVNVy4LeAtyV5+L0OZv+S1MJM44Q9AXgiMJHk5UOr9gCWzOdkVXXr0PH/Hjh/PseRtHhth960Cdh/aH4/4Oa256+qm5vPG5JcAhwKXN92f0naaqYrYbsA92cQ1HYf+ncH8NwZ9ptWkn2GZn8D+Mp020rSNLa1N10OLEtyYPPOyROAVk85JtkzyX2b6b2Bwxm6l0yS5mKmccIuBS5NcmZVfX2uB07yj8BTgL2TbAJeBzwlySEMLv3fCPzBfIqWtHhta2+qqi1JTgY+weDK2RlVdVWSU4D1VbUuya8CHwX2BH49yRuq6lHALwHvaW7Yvw+De8IMYZLmpc2N+fdNsgZYOrx9VR0x7R6D9c+fYvHpc6pOkqY3r97UbHMhcOGkZa8dmr6cwc+Uk/f7d+CX51+yJP23NiHsQ8C7gfcCd3dbjiS1Zm+SNNbahLAtVfWuziuRpLmxN0kaa22GqPhYkj9Msk+Svbb+67wySZqZvUnSWGtzJWxl8zn8otwCHrb9y5Gk1uxNksbarCGsqg4cRSGSNBf2JknjbtqfI5O8amj6+Enr/k+XRUnSdOxNkhaKme4JO2Fo+jWT1q3ooBZJasPeJGlBmCmEZZrpqeYlaVTsTZIWhJlCWE0zPdW8JI2KvUnSgjDTjfkHJ7mDwTfL+zXTNPO7dl6ZJE3N3iRpQZjp3ZFLRlmIJLVhb5K0ULQZJ0wLwNLVF/RdgiTNi/1LC1WbEfMlSZK0nRnCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSepBZyEsyRlJbkvylaFleyW5KMl1zeeeXZ1fkqaTZEWSa5NsTLJ6ivVPTvKFJFuSPHfSupVND7suycrRVS1poenyStiZwIpJy1YDF1fVMuDiZl6SRibJEuA04JnAQcDzkxw0abNvAC8Ezpq0717A64DHAYcBr/PLpKT56iyEVdWngdsnLT4WWNtMrwWO6+r8kjSNw4CNVXVDVf0YOJtBb7pHVd1YVV8Cfjpp32cAF1XV7VX1HeAi7v1lU5JaGfU9YQ+pqlsAms8HT7dhklVJ1idZv3nz5pEVKGnB2xe4aWh+U7Nsu+1r/5LUxg57Y35Vramq5VW1fGJiou9yJC0cmWJZbc997V+S2hh1CLs1yT4AzedtIz6/JG0C9h+a3w+4eQT7StLPGHUIWwdsfZpoJXDeiM8vSZcDy5IcmGQX4AQGvamNTwBPT7Jnc0P+05tlkjRnXQ5R8Y/A/wMekWRTkhOBU4GjklwHHNXMS9LIVNUW4GQG4eka4JyquirJKUmOAUjyq0k2AccD70lyVbPv7cBfMAhylwOnNMskac526urAVfX8aVYd2dU5JamNqroQuHDSstcOTV/O4KfGqfY9Azij0wIlLQo77I35kiRJC5khTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQeGMIkSZJ6YAiTJEnqgSFMkiSpB4YwSZKkHhjCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQe9BLCktyY5MtJrkyyvo8aJC1eSVYkuTbJxiSrp1h/3yQfbNZflmRps3xpkh81vevKJO8ede2SFo6dejz3U6vqWz2eX9IilGQJcBpwFLAJuDzJuqq6emizE4HvVNUvJDkBeBPwm82666vqkJEWLWlB8udISYvNYcDGqrqhqn4MnA0cO2mbY4G1zfS5wJFJMsIaJS0CfYWwAv4lyYYkq6baIMmqJOuTrN+8efOIy5O0gO0L3DQ0v6lZNuU2VbUF+B7woGbdgUmuSHJpkidNdQL7l6Q2+gphh1fVY4BnAiclefLkDapqTVUtr6rlExMTo69Q0kI11RWtarnNLcABVXUo8HLgrCR73GtD+5ekFnoJYVV1c/N5G/BRBj8PSNIobAL2H5rfD7h5um2S7AQ8ALi9qu6qqm8DVNUG4HrgFzuvWNKCNPIQlmS3JLtvnQaeDnxl1HVIWrQuB5YlOTDJLsAJwLpJ26wDVjbTzwU+WVWVZKK5sZ8kDwOWATeMqG5JC0wfT0c+BPhoc4/rTsBZVfXxHuqQtAhV1ZYkJwOfAJYAZ1TVVUlOAdZX1TrgdOD9STYCtzMIagBPBk5JsgW4G3hxVd0++r9C0kIw8hBWVTcAB4/6vJK0VVVdCFw4adlrh6b/Czh+iv0+DHy48wIlLQp9jhMmLVhLV1/Q2bFvPPXozo4tSfav0XGcMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQeGMIkSZJ6YAiTJEnqgSFMkiSpB4YwSZKkHhjCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHO/VdwLhZuvqCzo5946lHd3ZsSbJ/STsWr4RJkiT1oJcQlmRFkmuTbEyyuo8aJC1es/WgJPdN8sFm/WVJlg6te02z/Nokzxhl3ZIWlpGHsCRLgNOAZwIHAc9PctCo65C0OLXsQScC36mqXwDeCryp2fcg4ATgUcAK4J3N8SRpzvq4EnYYsLGqbqiqHwNnA8f2UIekxalNDzoWWNtMnwscmSTN8rOr6q6q+hqwsTmeJM1ZHzfm7wvcNDS/CXjc5I2SrAJWNbPfT3LtCGprY2/gW10cOG/q4qj36Kzujln3JIvov5Of7+i4bXrQPdtU1ZYk3wMe1Cz/3KR99518AvvXdrcj/Xc5F9Y9ySL676RV/+ojhGWKZXWvBVVrgDXdlzM3SdZX1fK+65gr6x4t696htelB021j/+qBdY+WdY9OHz9HbgL2H5rfD7i5hzokLU5tetA92yTZCXgAcHvLfSWplT5C2OXAsiQHJtmFwU2u63qoQ9Li1KYHrQNWNtPPBT5ZVdUsP6F5evJAYBnw+RHVLWmBGfnPkc39FScDnwCWAGdU1VWjrmMb7HA/MbRk3aNl3Tuo6XpQklOA9VW1DjgdeH+SjQyugJ3Q7HtVknOAq4EtwElVdXcvf8j8jOv/f617tKx7RDL4cidJkqRRcsR8SZKkHhjCJEmSemAIm6ckf5ykkuzddy1tJPmrJF9N8qUkH03ywL5rmsk4vtoqyf5JPpXkmiRXJXlp3zXNRZIlSa5Icn7ftah79rBu2cNGbxx7mCFsHpLsDxwFfKPvWubgIuDRVfUrwH8Ar+m5nmmN8auttgCvqKpfAh4PnDQmdW/1UuCavotQ9+xh3bKH9WbsepghbH7eCryKKQZp3FFV1b9U1ZZm9nMMxjfaUY3lq62q6paq+kIzfSeDZnCv0dR3REn2A44G3tt3LRoJe1i37GEjNq49zBA2R0mOAb5ZVV/su5Zt8CLgn/suYgZTvVZmLBrBVkmWAocCl/VbSWtvY/A/yj/tuxB1yx42Evaw0RvLHtbHa4t2eEn+FXjoFKv+FPgT4OmjraidmequqvOabf6UwSXnD4yytjlq9WqYHVWS+wMfBl5WVXf0Xc9skjwbuK2qNiR5St/1aNvZw3pnDxuhce5hhrApVNXTplqe5JeBA4EvJoHB5fAvJDmsqv5zhCVOabq6t0qyEng2cGTt2APEje2rYZLszKB5faCqPtJ3PS0dDhyT5FnArsAeSf5vVb2g57o0T/aw3tnDRmtse5iDtW6DJDcCy6tqR3lr+7SSrADeAvyPqtrcdz0zad7V9x/AkcANuk/1AAAa9UlEQVQ3Gbxm5rd29DcrZPC/amuB26vqZX3XMx/Nt8g/rqpn912LumcP64Y9rD/j1sO8J2zx+Dtgd+CiJFcmeXffBU2nufl262tlrgHO2dGbV+Nw4HeAI5r/G1/ZfDOTtO3sYd2zh42YV8IkSZJ64JUwSZKkHhjCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCNNIJVma5EdJrtyGYyxP8rfN9FOSPHGW7Z+U5OokX5nvOSXJ/qXtzRCmPlxfVYfMd+eqWl9VL2lmnwLM2MSq6t8ABxyUtD3Yv7TdGMK03ST51SRfSrJrkt2SXJXk0bPss3T4G16SP07y+mb6kiRvSvL5JP+R5EnN8qckOT/JUuDFwP9uRnZ+UpLjk3wlyReTfLqzP1bSgmL/Uh98gbe2m6q6PMk64I3A/YD/W1Xbegl9p6o6rHl1xuuAe17wW1U3Nq8u+X5V/TVAki8Dz6iqbyZ54DaeW9IiYf9SHwxh2t5OYfCy2v8CXjLLtm18pPncACxtsf1ngTOTnDO0ryS1Yf/SSPlzpLa3vYD7M3jR7q4ttt/Cz/53OHmfu5rPu2nxpaGqXgz8GbA/cGWSB7WoQZLA/qURM4Rpe1sD/DnwAeBNLba/FXhwkgcluS/w7Dme704GDROAJA+vqsuq6rXAtxg0M0lqw/6lkfLnSG03SX4X2FJVZyVZAvx7kiOq6pPT7VNVP0lyCnAZ8DXgq3M87ceAc5McC/wRg5tclwEBLga+OJ+/RdLiYv9SH1JVfdegRaR5Iuj8qprxqaOFcl5JC4f9S9ubP0dq1O4GHrAtgx3OVfNo+McYXN6XpPmyf2m78kqYJElSD7wSJkmS1ANDmCRJUg8MYZIkST0whEmSJPXAECZJktQDQ5gkSVIPDGGSJEk9MIRJkiT1wBAmSZLUA0OYJElSDwxhkiRJPTCESZIk9cAQJkmS1ANDmCRJUg8MYZIkST0whEmSJPVgp74LaGPvvfeupUuX9l2GpBHasGHDt6pqou86JKkrnYWwJI8APji06GHAa4F/aJYvBW4EnldV35npWEuXLmX9+vXdFCpph5Tk633XIEld6uznyKq6tqoOqapDgMcCPwQ+CqwGLq6qZcDFzbwkSdKiMqp7wo4Erq+qrwPHAmub5WuB40ZUgyRJ0g5jVCHsBOAfm+mHVNUtAM3ng0dUgyRJ0g6j8xCWZBfgGOBDc9xvVZL1SdZv3ry5m+IkSZJ6MoorYc8EvlBVtzbztybZB6D5vG2qnapqTVUtr6rlExM+ICVJkhaWUYSw5/PfP0UCrANWNtMrgfNGUIMkSdIOpdMQluTngKOAjwwtPhU4Ksl1zbpTu6xBkiRpR9TpYK1V9UPgQZOWfZvB05KSJEmLlq8tkiRJ6sFYvLZIO7alqy/ou4R5ufHUo/suQZK0iHklTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQeGMIkSZJ6YAiTJEnqgSFMkiSpB4YwSZKkHhjCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQeGMIkSZJ6YAiTJEnqgSFMkiSpB4YwSZKkHhjCJEmSemAIkyRJ6kGnISzJA5Ocm+SrSa5J8oQkeyW5KMl1zeeeXdYgSZK0I+r6StjbgY9X1SOBg4FrgNXAxVW1DLi4mZckSVpUOgthSfYAngycDlBVP66q7wLHAmubzdYCx3VVgyRJ0o6qyythDwM2A+9LckWS9ybZDXhIVd0C0Hw+eKqdk6xKsj7J+s2bN3dYpiRJ0uh1GcJ2Ah4DvKuqDgV+wBx+eqyqNVW1vKqWT0xMdFWjJElSL7oMYZuATVV1WTN/LoNQdmuSfQCaz9s6rEGSJGmH1FkIq6r/BG5K8ohm0ZHA1cA6YGWzbCVwXlc1SJIk7ah26vj4fwR8IMkuwA3A7zEIfuckORH4BnB8xzVIkiTtcDoNYVV1JbB8ilVHdnleSZKkHZ0j5kuSJPXAECZJktQDQ5gkSVIPDGGSJEk9MIRJkiT1wBAmSZLUA0OYJElSDwxhkiRJPTCESZIk9cAQJkmS1ANDmCRJUg8MYZIkST0whEmSJPXAECZJktSDWUNYkp9L8udJ/r6ZX5bk2d2XJkmStHC1uRL2PuAu4AnN/CbgjZ1VJEmStAi0CWEPr6o3Az8BqKofAem0KkmSpAWuTQj7cZL7AQWQ5OEMroxJkiRpnnZqsc3rgY8D+yf5AHA48MIOa5IkSVrwZg1hVfUvSTYAj2fwM+RLq+pbnVcmSZK0gLV5OvJi4HFVdUFVnV9V30qyZgS1SZIkLVht7gk7EHh1ktcNLVveUT2SJEmLQpsQ9l3gSOAhST6W5AEd1yRJkrTgtQlhqaotVfWHwIeBzwAP7rYsSZKkha3N05Hv3jpRVWcm+TJwUnclSZIkLXzThrAke1TVHcCHkuw1tOprwB+3OXiSG4E7gbuBLVW1vDnWB4GlwI3A86rqO/OqXpIkaUzN9HPkWc3nBmB987lhaL6tp1bVIVW19Wb+1cDFVbUMuLiZlyRJWlSmvRJWVc9uPg/czuc8FnhKM70WuAR49XY+hyRJ0g6tzThhhyfZrZl+QZK3JDmg5fEL+JckG5KsapY9pKpuAWg+vclfkiQtOm2ejnwX8MMkBwOvAr4OvL/l8Q+vqscAzwROSvLktoUlWZVkfZL1mzdvbrubJEnSWGgTwrZUVTH4GfHtVfV2YPc2B6+qm5vP24CPAocBtybZB6D5vG2afddU1fKqWj4xMdHmdJIkSWOjTQi7M8lrgBcAFyRZAuw8205Jdkuy+9Zp4OnAV4B1wMpms5XAefMpXJIkaZy1GSfsN4HfAk6sqv9s7gf7qxb7PQT4aJKt5zmrqj6e5HLgnCQnAt8Ajp9f6ZIkSeNr1hBWVf8JvGVo/hvAP7TY7wbg4CmWf5vBa5AkSZIWrTY/R0qSJGk7M4RJkiT1YE4hLMmeSX6lq2IkSZIWizaDtV6SZI/mnY9fBN6X5C2z7SdJkqTptbkS9oDmRd7PAd5XVY8FntZtWZIkSQtbmxC2UzOo6vOA8zuuR5IkaVFoE8JOAT4BbKyqy5M8DLiu27IkSZIWtjbjhH0I+NDQ/A3A/9dlUZIkSQvdrCEsyQTw+8DS4e2r6kXdlSVJkrSwtXlt0XnAvwH/CtzdbTmSJEmLQ5sQ9nNV9erOK5EkSVpE2tyYf36SZ3VeiSRJ0iLSJoS9lEEQ+1GSO5LcmeSOrguTJElayNo8Hbn7KAqRJElaTKYNYUkeWVVfTfKYqdZX1Re6K0uSJGlhm+lK2MuBVcDfTLGugCM6qUiSJGkRmDaEVdWq5vOpoytHkiRpcWgzWOuuwB8Cv8bgCti/Ae+uqv/quDZJkqQFq804Yf8A3Am8o5l/PvB+4PiuipIkSVro2oSwR1TVwUPzn0ryxa4KkiRJWgzajBN2RZLHb51J8jjgs92VJEmStPDNNETFlxncA7Yz8LtJvtHM/zxw9WjKkyRJWphm+jny2SOrQpIkaZGZaYiKr4+yEEmSpMWkzT1hkiRJ2s4MYZIkST1oFcKS/HySpzXT90vS+qXeSZYkuSLJ+c38gUkuS3Jdkg8m2WV+pUuSJI2vWUNYkt8HzgXe0yzaD/inOZzjpcA1Q/NvAt5aVcuA7wAnzuFYkiRJC0KbK2EnAYcDdwBU1XXAg9scPMl+wNHAe5v5MHjx97nNJmuB4+ZWsiRJ0vhrE8Luqqofb51JshOD8cLaeBvwKuCnzfyDgO9W1ZZmfhOw71Q7JlmVZH2S9Zs3b255OkmSpPHQJoRdmuRPgPslOQr4EPCx2XZK8mzgtqraMLx4ik2nDHRVtaaqllfV8omJiRZlSpIkjY82745czeC+rS8DfwBcSPPz4iwOB45J8ixgV2APBlfGHphkp+Zq2H7AzfMpXJIkaZzNeiWsqn5aVX9fVcdX1XOb6Vl/jqyq11TVflW1FDgB+GRV/TbwKeC5zWYrgfO2oX5JkqSx1ObdkVOqql+Z5zlfDZyd5I3AFcDp8zyOJEnS2BrJuyOr6hLgkmb6BuCw7XVsSZKkcdTq3ZFJHsogOBVweVX95whqkyRJWrDaDNb6P4HPA89hcC/X55K8qOvCJEmSFrI2T0e+Eji0qr4NkORBwL8DZ3RZmCRJ0kLWZpywTcCdQ/N3Ajd1U44kSdLiMNPTkS9vJr8JXJbkPAb3hB3L4OdJSZIkzdNMP0fu3nxe3/zbynG9JEmSttFMT0e+YZSFSJIkLSaz3pifZILBS7gfxeD1QwBU1REd1iVJkrSgtbkx/wPAV4EDgTcANwKXd1iTJEnSgtcmhD2oqk4HflJVl1bVi4DHd1yXJEnSgtZmnLCfNJ+3JDkauBnYr7uSJEmSFr42IeyNSR4AvAJ4B7AH8L87rUqSJGmBmzWEVdX5zeT3gKd2W44kSdLiMNNgra+qqjcneQeDQVp/RlW9pNPKJEmSFrCZroRd03yuH0UhkiRJi8lMg7V+LMkS4NFV9coR1iRJkrTgzThERVXdDTx2RLVIkiQtGm2ejrwiyTrgQ8APti6sqo90VpUkSdIC1yaE7QV8Gxh+TVEBhjBJkqR5ajNExe+NohBJkqTFpM0LvHcFTuTeL/B+UYd1SZIkLWht3h35fuChwDOASxm8sujOLouSJEla6NqEsF+oqj8HflBVa4GjgV/utixJkqSFrU0I2/oC7+8meTTwAGBpZxVJkiQtAm2ejlyTZE/gz4F1wP2baUmSJM1TmxD2vmbQ1kuBh7U9cHND/6eB+zbnObeqXpfkQOBsBkNffAH4nar68ZwrlyRJGmNtfo78WpI1SY5Mkjkc+y7giKo6GDgEWJHk8cCbgLdW1TLgOwyevJQkSVpU2oSwRwD/CpwE3Jjk75L82mw71cD3m9mdm3/FYNDXc5vla4Hj5ly1JEnSmJs1hFXVj6rqnKp6DoMrWnsw+GlyVkmWJLkSuA24CLge+G5VbWk22QTsO6/KJUmSxlibK2Ek+R9J3sngHq5dgee12a+q7q6qQxiMLXYY8EtTbTbNOVclWZ9k/ebNm9ucTpIkaWy0GTH/a8CVwDnAK6vqB7Psci9V9d0klwCPBx6YZKfmath+wM3T7LMGWAOwfPnyKYOaJEnSuGrzdOTBVXXHXA+cZAL4SRPA7gc8jcFN+Z8CnsvgCcmVwHlzPbYkSdK4a/MC7zkHsMY+wNokSxj87HlOVZ2f5Grg7CRvBK4ATp/n8SVJksZWmyth81JVXwIOnWL5DQzuD5MkSVq0pr0xP8kT5jgumCRJklqa6enIlcCGJGcneWGSh46qKEmSpIVu2p8jq+rFAEkeCTwTODPJAxjcWP9x4LPN64wkSZI0R20Ga/1qVb21qlYwGO3+M8DxwGVdFydJkrRQzenG/Kr6EXBh80+SJEnz1GrEfEmSJG1fhjBJkqQezBrCkuyW5D7N9C8mOSbJzt2XJkmStHC1uRL2aWDXJPsCFwO/B5zZZVGSJEkLXZsQlqr6IfAc4B1V9RvAQd2WJUmStLC1CmFJngD8NnBBs6yz1x1JkiQtBm1C2MuA1wAfraqrkjyMwYCtkiRJmqdZr2hV1aXApUl2a+ZvAF7SdWGSJEkLWZunI5+Q5Grgmmb+4CTv7LwySZKkBazNz5FvA54BfBugqr4IPLnLoiRJkha6VoO1VtVNkxb54m5JkqRt0OYpx5uSPBGoJLswuB/smm7LkiRJWtjaXAl7MXASsC+wCTikmZckSdI8tXk68lsMxgiTJEnSdjJtCEvyqqp6c5J3ADV5fVU5TIUkSdI8zXQlbOt9X+tHUYgkSdJiMm0Iq6qPJVkCPLqqXjnCmiRJkha8GW/Mr6q7gceOqBZJkqRFo80QFVckWQd8CPjB1oVV9ZHOqpIkSVrg2oSwvRiMln/E0LICDGGSJEnz1CaEvbeqPju8IMnhHdUjSZK0KLQZrPUdLZf9jCT7J/lUkmuSXJXkpc3yvZJclOS65nPPuRYtSZI07mYaJ+wJwBOBiSQvH1q1B7CkxbG3AK+oqi8k2R3YkOQi4IXAxVV1apLVwGrg1fP9AyRJksbRTFfCdgHuzyCo7T707w7gubMduKpuqaovNNN3Mhh3bF/gWGBts9la4Lj5Fi9JkjSuZhon7FLg0iRnVtXXt+UkSZYChwKXAQ+pqluac9yS5MHbcmxJkqRx1ObG/PsmWQMsHd6+qo6Ydo8hSe4PfBh4WVXdkaRVYUlWAasADjjggFb7SJIkjYs2IexDwLuB9wJ3z+XgSXZmEMA+MDSu2K1J9mmugu0D3DbVvlW1BlgDsHz58nu9u1KSJGmctQlhW6rqXXM9cAaXvE4HrqmqtwytWgesBE5tPs+b67ElSZLGXZsQ9rEkfwh8FLhr68Kqun2W/Q4Hfgf4cpIrm2V/wiB8nZPkROAbwPFzrlqSJGnMtQlhK5vP4Zd4F/CwmXaqqs8A090AdmSL80qSJC1Ys4awqjpwFIVIkiQtJtOOE5bkVUPTx09a93+6LEqSJGmhm2mw1hOGpl8zad2KDmqRJElaNGYKYZlmeqp5SZIkzcFMIaymmZ5qXpIkSXMw0435Bye5g8FVr/s10zTzu3ZemSRJ0gI207sjl4yyEEmSpMVkpp8jJUmS1BFDmCRJUg8MYZIkST0whEmSJPXAECZJktSDNi/wlhakpasv6OzYN556dGfHliQtDF4JkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQeGMIkSZJ6YAiTJEnqgSPm70C6HMFdkiTtWLwSJkmS1ANDmCRJUg8MYZIkST3oLIQlOSPJbUm+MrRsryQXJbmu+dyzq/NLkiTtyLq8EnYmsGLSstXAxVW1DLi4mZckSVp0OgthVfVp4PZJi48F1jbTa4Hjujq/JEnSjmzU94Q9pKpuAWg+HzzdhklWJVmfZP3mzZtHVqAkSdIo7LA35lfVmqpaXlXLJyYm+i5HkiRpuxp1CLs1yT4AzedtIz6/JEnSDmHUIWwdsLKZXgmcN+LzS5Ik7RC6HKLiH4H/BzwiyaYkJwKnAkcluQ44qpmXJEladDp7d2RVPX+aVUd2dU5JkqRxscPemC9JkrSQGcIkSZJ6YAiTJEnqgSFMkiSpB4YwSZKkHhjCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQeGMIkSZJ6YAiTJEnqwU59FyAtREtXX9B3CTucG089uu8SJGmH4pUwSZKkHhjCJEmSemAIkyRJ6oEhTJIkqQeGMEmSpB4YwiRJknpgCJMkSeqBIUySJKkHhjBJkqQe9DJifpIVwNuBJcB7q+rU7XVsRyqXJEnjYORXwpIsAU4DngkcBDw/yUGjrkOS/v/27jdUz7qO4/j7gysnWkkTEXR0Rvgg0EhYQ5ThcKWjhj4SIvoDPRDBmkojNP8k4pOhVEQPYoQYuAjJSTqUsn8ohctNN92cG6ukNvMfPlAhraNfH9zXYm3nz32fP/fvPjvv15P7vq5zXef63Ifz4Hv/ftf1+0pSSy2mI1cBB6vqb1X1H+AXwJUNckiSJDXTogg7G/jnUduHun2SJEmLRot7wjLBvjruoORq4Opu8+0k++c1Vf/OAF5vHWIGzD1c5j5GNg18yifmIYYkjYwWRdghYPlR2+cALx17UFVtBjYPK1S/kuyoqpWtcwzK3MNlbknSdFpMRz4FnJtkRZIPA18CHmqQQ5IkqZmhj4RV1XiSbwK/prdExT1VtXfYOSRJklpqsk5YVT0CPNLi2nNg5KZI+2Tu4TK3JGlKqTrunnhJkiTNM9sWSZIkNWARNkNJNiapJGe0ztKPJHcleSHJs0keTHJ660xTSbIuyf4kB5Pc2DpPP5IsT/KHJPuS7E1yXetMg0hyUpJnkmxrnUWSFgOLsBlIshz4PPCP1lkG8BhwXlV9GjgA3NQ4z6QWcGurceDbVfUp4ELg2gWS+4jrgH2tQ0jSYmERNjM/AL7DBIvMjqqq+k1VjXebT9Jbn21ULcjWVlX1r6p6unv/Fr2CZkF0g0hyDvBF4Kets0jSYmERNqAkVwCHq2p36yyz8A3g0dYhprDgW1slGQMuALa3TdK3H9L7YvF+6yCStFg0WaJi1CX5LXDWBD+6GfgucNlwE/VnqtxV9avumJvpTZttGWa2AfXV2mpUJTkNeAC4vqrebJ1nOknWA69W1c4ka1rnkaTFwiJsAlX1uYn2JzkfWAHsTgK9Kb2nk6yqqpeHGHFCk+U+IsnXgfXA2hrttUn6am01ipJ8iF4BtqWqtrbO06eLgSuSfAFYCnw0yX1V9ZXGuSTphOY6YbOQ5EVgZVWNfKPmJOuA7wOXVNVrrfNMJckSeg8PrAUO02t19eVR76yQXmX+M+CNqrq+dZ6Z6EbCNlbV+tZZJOlE5z1hi8ePgY8AjyXZleQnrQNNpnuA4Ehrq33A/aNegHUuBr4KXNr9jXd1o0uSJB3HkTBJkqQGHAmTJElqwCJMkiSpAYswSZKkBizCJEmSGrAIkyRJasAiTJIkqQGLMA1VkrEk/06yaxa/Y2WSH3Xv1yS5aJrjVyd5PsmemV5TkqS5ZhGmFv5aVZ+Z6clVtaOqNnSba4Api7CqegJw0VRJ0kixCNOcSfLZJM8mWZrk1CR7k5w3zTljR49QJdmY5Pbu/R+TbErylyQHkqzu9q9Jsi3JGHANcEO3Ov3qJFcl2ZNkd5LH5+3DSpI0Szbw1pypqqeSPATcCZwC3FdVs50CXFJVq7r2P98D/tekvKpe7NovvV1VdwMkeQ64vKoOJzl9lteWJGneWIRprt1Br+H2O8CGaY7tx9budScw1sfxfwLuTXL/UedKkjRynI7UXPs4cBq9ZuFL+zh+nP//Pzz2nHe71/fo40tDVV0D3AIsB3YlWdZHBkmShs4iTHNtM3ArsAXY1MfxrwBnJlmW5GRg/YDXe4tewQdAkk9W1faqug14nV4xJknSyHE6UnMmydeA8ar6eZKTgD8nubSqfj/ZOVX13yR3ANuBvwMvDHjZh4FfJrkS+Ba9m/TPBQL8Dtg9k88iSdJ8S1W1zqBFpHuicVtVTfnU5IlyXUmSJuN0pIbtPeBjs1msdVDd0hYP05uelCRpJDgSJkmS1IAjYZIkSQ1YhEmSJDVgESZJktSARZgkSVIDFmGSJEkNfAAjwJ3+ZhcjcgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[10, 10])\n",
    "\n",
    "# histogram of the data (default color is blue)\n",
    "plt.subplot(221)\n",
    "plt.hist(x, bins=10, range=[-5,5])\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'Entries / bins size = 1')\n",
    "\n",
    "\n",
    "# histogram of the data with area normalized to unity\n",
    "plt.subplot(222)\n",
    "plt.hist(x, bins=10, range=[-5,5], \n",
    "         density=True)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'Entries / bins size = 1')\n",
    "\n",
    "\n",
    "# histogram of the data\n",
    "plt.subplot(223)\n",
    "plt.hist(x, bins=[-5,-3,-1,1,2,5])\n",
    "\n",
    "# always label the axes (the r'$...$' make the axes have a latex style)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'Entries / variable bins size')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Choice of the binning\n",
    "\n",
    "plt.figure(figsize=[15, 15])\n",
    "\n",
    "j = 0\n",
    "for i in [1,2,3,5,10,50,100,200,300]:\n",
    "    j+=1\n",
    "    plt.subplot(330+j)\n",
    "    plt.hist(x, bins=i, range=[-5,5])\n",
    "    plt.xlabel(r'x [units]')\n",
    "    binsize = 10./i\n",
    "    label = \"Entries / bins size = \" + str( float('%.1g' % binsize ) )\n",
    "    plt.ylabel(label)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Normalized Entries / bins size = 0.2')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Shape comparison by overlapping normalized histograms\n",
    "\n",
    "# generate two gaussian distributed samples\n",
    "import scipy.stats\n",
    "# set the seed to always get the same samples\n",
    "np.random.seed(seed=12345)\n",
    "#mu = 1,   sigma = 1\n",
    "x1 = scipy.stats.norm.rvs(loc=1.0, scale=1, size=10000)\n",
    "#mu = 1.2, sigma = 1\n",
    "x2 = scipy.stats.norm.rvs(loc=1.2, scale=1, size=2000)\n",
    "\n",
    "plt.figure(figsize=[10,5])\n",
    "plt.subplot(121)\n",
    "plt.hist(x1, bins=50, range=[-5,5], color='blue', alpha=0.5)\n",
    "plt.hist(x2, bins=50, range=[-5,5], color='green',alpha=0.5)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'Entries / bins size = 0.2')\n",
    "\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.hist(x1, bins=50, range=[-5,5], color='blue', alpha=0.5, density=True)\n",
    "plt.hist(x2, bins=50, range=[-5,5], color='green',alpha=0.5, density=True)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'Normalized Entries / bins size = 0.2')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mauro/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:23: RuntimeWarning: divide by zero encountered in true_divide\n",
      "/Users/mauro/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:23: RuntimeWarning: invalid value encountered in true_divide\n",
      "/Users/mauro/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:46: RuntimeWarning: divide by zero encountered in true_divide\n",
      "/Users/mauro/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:46: RuntimeWarning: invalid value encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'ratio')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAE6CAYAAADndn5bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzt3Xu8XGV97/HP18jFclG59GISmkhDNXiBZotVi26tSCgKnr5EEdsi9RxKC6LHWg6oxTStrajHeqNijkWslaZ4DxiLeInWC5odLrEJoCFFs4nKliAoIBj4nj9mbRiGmVlrdvaamb339/167dfMetaz1voNYc9vP8+z1vPINhEREd08YtABRETE8EuyiIiIUkkWERFRKskiIiJKJVlERESpJIuIiCiVZBExDSS9QtLnazjvqKTx6T5vRK+SLGJOknSTpLsl/VzSjyRdJGnviscukmRJj5wss/1R2y+oL+JKcV0k6e8GGUPMXkkWMZe9yPbewGHA4cA5A44nYmglWcScZ/tHwOU0kgYAko6VdLWkOyRtk7Si6ZCvFq8/LVomz5D0Sklfazr+mZLWS7q9eH1mp+sXrZxzJG2WdJukD0nas0PdJ0paJ+mnkjZJOq4oPxV4BXBWEdOlU/4PEtFGkkXMeZIWAMcAW5qK7wT+BHgMcCzw55JeXOx7dvH6GNt72/5my/n2Az4LvAfYH3gn8FlJ+3cJ4xXA0cDBwCHAm9rEuRtwKfB54FeBVwMflfTbtlcBHwXeVsT0oqqfP6KKJIuYyz4t6WfANuAW4M2TO2yvs/0d2/fb3gj8G/Cciuc9Fvie7Y/Y3mn734DrgW5f4O+zvc32DuAtwMvb1PldYG/grbbvtf0l4LIOdSOmVZJFzGUvtr0PMAo8AThgcoekp0v6sqQJSbcDpzXvL/E44PstZd8H5nc5ZltL3cd1OO822/f3cN6IaZFkEXOe7a8AFwHvaCq+GFgDLLT9aOACQJOHlJxyO/CbLWUHATd3OWZhS93tHc67UNIjWupOnjdTSEdtkiwiGt4FHCVpcpB7H2CH7V9IOgI4qanuBHA/8PgO51oLHCLpJEmPlPQyYCmNLqNOTpe0oBjveAPw723qfIvGWMpZknaTNEqja2t1sf/HXWKK2CVJFhGA7QngX4C/Lor+AlhZjGmcC1zSVPcuGuMKXy/uSvrdlnPdCrwQ+EvgVuAs4IW2f9IlhItpDFxvLX4e9ryE7XuB42gMxv8E+CfgT2xfX1T5Z2BpEdOne/j4EaWUxY8iBkvSTcD/tP2FQccS0UlaFhERUSrJIiIiSqUbKiIiSqVlERERpR5ZXmVmOOCAA7xo0aJBhxERMaNs2LDhJ7YPLKs3a5LFokWLGBsbG3QYEREziqTW2QbaSjdURESUSrKIiIhSSRYREVEqySIiIkolWURERKkki4iIKJVkERERpZIsIiKiVJJFRESUmjVPcEdEdStW9FYeUWvLQtJySTdI2iLp7C71XiLJkkaays4pjrtB0tF1xhkREd3V1rKQNA84HzgKGAfWS1pje3NLvX2AM2msLzxZthQ4ETgUeBzwBUmH2L6vrngjIqKzOlsWRwBbbG8t1g5eDRzfpt7fAm8DftFUdjyw2vY9tv8b2FKcLyIiBqDOZDEf2Na0PV6UPUDS4cBC25f1emxx/KmSxiSNTUxMTE/UERHxMHUOcKtN2QPL8kl6BPCPwCt7PfaBAnsVsApgZGQkS/5F7KJuA9wZ/J7b6kwW48DCpu0FwPam7X2AJwHrJAH8OrBG0nEVjo2IiD6qsxtqPbBE0mJJu9MYsF4zudP27bYPsL3I9iLgSuA422NFvRMl7SFpMbAE+HaNsUZERBe1tSxs75R0BnA5MA+40PYmSSuBMdtruhy7SdIlwGZgJ3B67oSK6CIPTkTNan0oz/ZaYG1L2bkd6o62bL8FeEttwUVERGWZ7iMiIkolWURERKkki4iIKJVkERERpTLrbMQssGLdaPvyvkYRs1mSRcRs1unW2Q7JhdEO5THnJVlEzCQdn5sY7WMQMRdlzCIiIkolWURERKkki4iIKJUxi4hhlDmdYsikZREREaXSsoiYQTo9TzFd9SM6ScsiIiJKJVlERESpdENFxIPWreuyc7RPQcQwqrVlIWm5pBskbZF0dpv9p0n6jqRrJH1N0tKifJGku4vyayRdUGecERHRXW0tC0nzgPOBo4BxYL2kNbY3N1W72PYFRf3jgHcCy4t9N9o+rK74IiKiujpbFkcAW2xvtX0vsBo4vrmC7TuaNvcCXGM8ERExRXUmi/nAtqbt8aLsISSdLulG4G3AmU27Fku6WtJXJB3Z7gKSTpU0JmlsYmJiOmOPiIgmdQ5wq03Zw1oOts8Hzpd0EvAm4GTgh8BBtm+VtAz4tKRDW1oi2F4FrAIYGRlJqySiRp0eKs/D5nNDnS2LcWBh0/YCYHuX+quBFwPYvsf2rcX7DcCNwCE1xRkRESXqTBbrgSWSFkvaHTgRWNNcQdKSps1jge8V5QcWA+RIejywBNhaY6wREdFFbd1QtndKOgO4HJgHXGh7k6SVwJjtNcAZkp4P/BK4jUYXFMCzgZWSdgL3AafZ3lFXrBER0V2tD+XZXgusbSk7t+n9azoc9wngE3XGFhER1WW6j4iIKJVkERERpZIsIiKiVJJFRESUSrKIiIhSSRYREVGq662zkvYFDrR9Y0v5U2xvrDWyiJgRMg3I3NAxWUh6KfAu4BZJuwGvtL2+2H0R8Dv1hxcxN2Xt7Bg23bqh3gAsK9aUOAX4iKQ/LPa1myQwIiJmqW7dUPNs/xDA9rclPRe4TNICsu5ERMSc0q1l8TNJB09uFIljlMYCRofWHFdERAyRbi2LP6elu8n2zyQtB15aa1QRETFUOiYL29d2KP8l8NHaIoqIiKEzpecsJK2a7kAiImJ4TfWhvA9MaxQRETHUppQsiqVOIyJijuiYLCQ9WtJbJV0v6dbi57qi7DFVTi5puaQbJG2RdHab/adJ+o6kayR9TdLSpn3nFMfdIOnoqX28iIiYDt1aFpfQWOp01Pb+tvcHnluUfazsxMUa2ucDxwBLgZc3J4PCxbafXDz49zbgncWxS2ms2X0osBz4p8k1uSMiov+63Tq7yPZ5zQW2fwScJ+lPK5z7CGCL7a0AklbTeEZjc9P57miqvxcPPux3PLDa9j3Af0vaUpzvmxWuGxF1WLeuffnoaD+jiAHpliy+L+ks4MO2fwwg6deAVwLbKpx7fku9ceDprZUknQ68DtgdeF7TsVe2HDu/wjUjZpaOs+2N9jGIiHLduqFeBuwPfEXSDkk7gHXAflR7KK/d/FEPmybE9vm2Dwb+D/CmXo6VdKqkMUljExMTFUKKiIip6PZQ3m00vsD/zxTPPQ4sbNpeAGzvUn818P5ejrW9ClgFMDIykvmqIiJqUufiR+uBJZIWS9qdxoD1muYKkpY0bR4LfK94vwY4UdIekhYDS4Bv1xhrRER00XXxo11he6ekM4DLgXnAhbY3SVoJjNleA5wh6fnAL2ncZXVycewmSZfQGAzfCZxu+766Yo2IiO5qSxYAttcCa1vKzm16/5oux74FeEt90UVERFWVkoWkJ9i+fvK17qAiZp2sMRozXNUxi4tbXiMiYg7pdYA7y6lGRMxBdd4NFRERs0SSRURElOo1WeTBt4iIOahqslDLa0REzCFVk8WRLa8RETGHVEoWtn/e/BoREXNLBrgjIqJUkkVERJSqlCwkPUrSb9cdTEREDKfSuaEkvQh4B42V7BZLOgxYafu4uoOLiJmr03RYmSZrZqrSslhBY/3rnwLYvgZYVF9IERExbKrMOrvT9u1SHrGIiDbWrWtfPjrazyiiZlWSxX9JOgmYV6xsdybwjXrDioiIYVKlG+rVwKHAPTSmKL8deG2dQUVExHCpkiyWAefaflrx8yZgaZWTS1ou6QZJWySd3Wb/6yRtlrRR0hcl/WbTvvskXVP8rGk9NiIi+qdKsrgc+JKkX2sq+2DZQZLmAecDx9BILi+X1JpkrgZGbD8F+DjwtqZ9d9s+rPjJnVcREQNUJVncALwdWCfpmUVZldHuI4AttrfavhdYDRzfXMH2l23fVWxeCSyoFnZERPRTlWRh25cBxwHvk3QG1aYqnw9sa9oeL8o6eRXwuabtPSWNSbpS0ovbHSDp1KLO2MTERIWQIiJiKqrcDSUA29+TdCTwIeApVY9r0TbJSPojYAR4TlPxQba3S3o8jW6w79i+8SEns1cBqwBGRkay1kZERE1Kk4Xtw5ve3wm8VNJBFc49Dixs2l4AbG+tJOn5wBuB59i+p+la24vXrZLWAYcDN7YeHzGTrVg3OugQIirpmCwknWX7bZLe06HKmSXnXg8skbQYuBk4ETip5RqHAx8Altu+pan8scBdtu+RdADwLB46+B0REX3UrWVxXfG6YSontr2zGN+4HJgHXGh7k6SVwJjtNTQGzvcGPlY8If6D4s6nJwIfkHQ/jXGVt9rePJU4IiJi13VMFrYvLV4/PFkm6RHA3rbvqHJy22uBtS1l5za9f36H474BPLnKNSIion6ld0NJuljSvpL2AjYDN0j6q/pDi4iIYVHl1tmlRUvixTRaCQcBf1xrVBERMVSqJIvdJO1GI1l8xvYvqfacRUREzBJVnrP4AHATcC3w1WL+pkpjFhExh3WaupzRPgYR06W0ZWH7Pbbn2/4D2wZ+ADy3/tAiImJYVGlZPESRMHbWEEtERAypnpNFRHSRBaZjlqoywB0REXNclecsTpC0T/H+TZI+Kel36g8tIiKGRZWWxV/b/pmk3wOOBj4MvL/esCIiYphUSRb3Fa/HAu+3/Rlg9/pCioiIYVMlWdws6QPAS4G1kvaoeFxERMwSVe6GeimwHHiH7Z9K+g0gc0NF9CDrVjyo0w1juZFsuFV5KO8u4DPAncWiR7sB19cdWEREDI/SloWkVwNvBn4M3F8Um2pLq0ZExCxQpRvqNcBv27617mAiImI4VRmo3gbcPpWTS1ou6QZJWySd3Wb/6yRtlrRR0heLSQon950s6XvFz8lTuX5EREyPKi2LrcA6SZ8F7pkstP3ObgdJmgecDxwFjAPrJa1pWR71amDE9l2S/pzGOtsvk7Qfja6vERpdXhuKY2/r4bNFRMQ0qdKy+AFwBY1nK/Zp+ilzBLDF9lbb9wKrgeObK9j+cjGADnAlsKB4fzRwhe0dRYK4gsYdWRERMQClLQvbfzPFc8+n0YU1aRx4epf6rwI+1+XY+a0HSDoVOBXgoIMOmmKYERFRpmOykPQu26+VdCltVsazfVzJudWmrO0Ke5L+iEaX03N6Odb2KmAVwMjISFbvi4ioSbeWxUeK13dM8dzjwMKm7QXA9tZKkp4PvBF4ju17mo4dbTl23RTjiIiIXdQxWdjeULx+RdLuwBNo/HV/QzEGUWY9sETSYuBm4ETgpOYKkg6nsWzrctu3NO26HPh7SY8ttl8AnFPtI0VExHSr8lDescAFwI00uocWS/oz25/rdpztnZLOoPHFPw+40PYmSSuBMdtrgLcDewMfkwTwA9vH2d4h6W9pJByAlbZ3TPEzRkTELqpy6+z/BZ5rewuApIOBz/LgYHRHttcCa1vKzm16//wux14IXFghvoiIqFmVW2dvmUwUha3ALZ0qR0TE7NPtbqg/LN5ukrQWuITGmMUJPNg9FBERc0C3bqgXNb3/MQ/e1joBPPbh1SMiYrbqdjfUKf0MJCIihldWvIuIiFJJFhERUapjspD0DBUPP0RExNzWbYD7ZOB8Sd8F/gP4D9s/6k9YETFrrVvXYcdoH4OIXnUb4D4NQNITgGOAiyQ9GvgyjeTxddv39SXKiGGzYsWgI4joqypTlF8PXA/8o6RHAc+l8azFO2nMFBsRscs65d/k5eFQZbqPB9i+m8b0HWvL6kbMRSvWjQ46hIha5G6oiIgolWQRERGlSpOFpL0kPaJ4f4ik4yTtVn9oERExLKq0LL4K7ClpPvBF4BTgojqDioiI4VIlWcj2XcAfAu+1/T+ApfWGFRERw6RSspD0DOAVNBY9gh7vooqIiJmtSrJ4LY31rz9VLIv6eBoP5pWStFzSDZK2SDq7zf5nS7pK0k5JL2nZd5+ka4qfNVWuFxER9ajyUN5XgK9I2qvY3gqcWXacpHnA+cBRwDiwXtIa25ubqv0AeCXw+januNv2YaWfICIialflbqhnSNoMXFdsP1XSP1U49xHAFttbbd8LrAaOb65g+ybbG4H7ew89IiL6pUo31LuAo4FbAWxfCzy7wnHzgW1N2+NFWVV7ShqTdKWkF7erIOnUos7YxMRED6eOiIheVHooz/a2lqIqEwi2m97cVa5XOMj2CHAS8C5JB7eJa5XtEdsjBx54YA+njoiIXlRJFtskPROwpN0lvZ6iS6rEOLCwaXsBsL1qYLa3F69bgXXA4VWPjYiI6VUlWZwGnE6jC2kcOKzYLrMeWCJpsaTdgROBSnc1SXqspD2K9wcAzwI2dz8qIiLqUuVuqJ/QeMaiJ7Z3SjoDuByYB1xY3Hq7EhizvUbS04BPAY8FXiTpb2wfCjwR+ICk+2kktLe23EUVERF91DFZSDrL9tskvZc2Yw22S2+ftf2w6cxtn9v0fj2N7qnW474BPLns/BER0R/dWhaT4xJj/QgkIiKGV7dlVS8tHqx7ku2/6mNMERExZLqOWdi+T9KyfgUTMVNkRbwarFvXYcdoH4OITqpMCHh1MTfTx4A7Jwttf7K2qCIiYqhUSRb70Xh6+3lNZQaSLCIi5ogqyeKDtr/eXCDpWTXFExERQ6jKQ3nvrVgWERGzVLfnLJ4BPBM4UNLrmnbtS+Mhu4iImCO6dUPtDuxd1NmnqfwO4CVtj4iIiFmp23MWk4seXWT7+32MKWJ4rFjRYcdoH4OY2zr9E3T8p4laVBng3kPSKmBRc33bz+t4REREzCpVksXHgAuAD1JtHYuIiJhlqiSLnbbfX3skERExtKrcOnuppL+Q9BuS9pv8qT2yiIgYGlVaFicXr82TCRp4/PSHExERw6jK4keL+xFIREQMr47dUJLOanp/Qsu+v69ycknLJd0gaYuks9vsf7akqyTtlPSSln0nS/pe8XNy67EREdE/3cYsTmx6f07LvuVlJy7WwjgfOAZYCrxc0tKWaj8AXglc3HLsfsCbgacDRwBvlvTYsmtGREQ9uiULdXjfbrudI4AttrfavhdYDRzfXMH2TbY3Ave3HHs0cIXtHbZvA66gQoKKiIh6dEsW7vC+3XY784FtTdvjRVkVlY6VdKqkMUljExMTFU8dERG96jbA/VRJd9BoRTyqeE+xvWeFc7drfVRJMpWPtb0KWAUwMjJS9dwREdGjbnND7erMsuPAwqbtBcD2Ho4dbTl23S7GExGzSOaM6q8qz1lM1XpgiaTFwM00BsxPqnjs5cDfNw1qv4CHD7JH1C5rbUc0VHmCe0ps7wTOoPHFfx1wie1NklZKOg5A0tMkjQMnAB+QtKk4dgfwtzQSznpgZVEWEREDUGfLAttrgbUtZec2vV9Po4up3bEXAhfWGV/EAzIVeURXtbUsIiJi9qi1ZRERscvWrWtfPjrazyjmvLQsIiKiVJJFRESUSrKIiIhSSRYREVEqySIiIkolWURERKkki4iIKJXnLGLuyAxzEVOWlkVERJRKyyIiZpVMXV6PtCwiIqJUkkVERJRKN1QEWeRoRsoEg32VlkVERJSqNVlIWi7pBklbJJ3dZv8ekv692P8tSYuK8kWS7pZ0TfFzQZ1xRkREd7V1Q0maB5wPHAWMA+slrbG9uanaq4DbbP+WpBOB84CXFftutH1YXfFFRER1dY5ZHAFssb0VQNJq4HigOVkcD6wo3n8ceJ8k1RhTzGEZl4iYujq7oeYD25q2x4uytnVs7wRuB/Yv9i2WdLWkr0g6st0FJJ0qaUzS2MTExPRGHxERD6izZdGuheCKdX4IHGT7VknLgE9LOtT2HQ+paK8CVgGMjIy0njsi5qJOd0kx2scgZp86WxbjwMKm7QXA9k51JD0SeDSww/Y9tm8FsL0BuBE4pMZYIyKiizpbFuuBJZIWAzcDJwIntdRZA5wMfBN4CfAl25Z0II2kcZ+kxwNLgK01xhoRs1ymAdk1tSUL2zslnQFcDswDLrS9SdJKYMz2GuCfgY9I2gLsoJFQAJ4NrJS0E7gPOM32jrpijYiI7mp9gtv2WmBtS9m5Te9/AZzQ5rhPAJ+oM7aIiKgu033E7NOxX2G0j0FEzC6Z7iMiIkolWURERKkki4iIKJUxi4iY03JLbTVJFjFz5bc5epH1L3ZJkkXMOpkwMGL6ZcwiIiJKJVlERESpJIuIiCiVZBEREaUywB3Dr8NdTxnIjmmR9S8qSbKIiGij253Zc/Gu7XRDRUREqbQsYnikuyliaCVZRERMk9k8dUiSRfRfWhAxE3Qc+IYVK0b7FsawqDVZSFoOvJvGsqoftP3Wlv17AP8CLANuBV5m+6Zi3znAq2gsq3qm7cvrjDVqMBv+nIoIoMZkIWkecD5wFDAOrJe0xvbmpmqvAm6z/VuSTgTOA14maSnwx8VxC4BLJZ1l+111xRsRUVmPkxLOhu6pOlsWRwBbbG8FkLQaOB5oThbHAyuK9x8H3idJRfmngY/bvkrSF4DXSfp8S7KJOkzT/8HpVoo5p0vXVXujbUuHMbnUmSzmA9uatseBp3eqY3unpNuB/YvyK21fVdT7PrBvUf5AspB0KnAqwP7778/IyEgNHyOm7rJBBxBRv7vvhhtvBBskOPhgeNSjKpVftmdTeQWX1fMr9TtVKtWZLNSmzBXrtJbvDSwGvtXpYnvttRdjY2M9BRgR0ZONG2HDBli2DJ7ylEbZhz4EK1fC/vvDrbfC618Pp5zSe/mASLqqvFa9yWIcWNi0vQDY3qHOuKRHAo8GdjQfK2lvYDnwD7bvaD7Y9ipgFcDIyEhrIoqImD4bN8IJJ8C998Luu8PHPtZIGMuWNbZvvbXxumxZo36v5UOuzmSxHlgiaTFwM3AicFJLnTXAycA3gZcAX7JtSWuAiyW9B1gL7ATeXmOsERHdbdjQSBSTLYINGxrJ4ilPaSSO1hZHr+VDrrZkUYxBnAFcTuPW2Qttb5K0EhizvQb4Z+AjkrbQaFGcWBy7SdIlwI+AXwKvsH1fXbFGRDxEu+6mbi2CyaTRqtfyISZ7OHtvJP0e8J/Ad4D7i+I32F7brv7IyIgzZhERu6xTd9PkvhnWIigjaYPt0ruDhvYJbttfo/0AeEREfTp1N8GMbBFMl8w6GxGzw8aNjTuNNm7ctfozdAC6bkPbsoiIqKxb11Gv9WfoAHTd+pYsJD0VOLLY/E/b1/br2hExi7QbN+jWddROWf053N3USV+ShaTXAP8L+GRR9K+SVtl+bz+uHxGzRK/POkwe08udTdFWv1oWrwKebvtOAEnn0Xi2IskiIh6u011HvT7r0Cm5pKupZ/1KFqIx1fik+8idThGzT6+3lrar3208oddnHXJn07TpV7L4EPAtSZ8qtl9M44G8iJiJev2S76V+2Rd8Ly2CdDdNm74kC9vvlLQO+D0aLYpTbF/dj2tHRIlOrYFu5b18yfdav+wLvpcWQbqbpk3dK+Xta/sOSfsBNxU/k/v2s72jzutHRIlOX+TdWgm9fsn3Wn+6v+DT3TQt6m5ZXAy8ENjAQ6cnV7H9+JqvHzF7TaVFUPWW025dQb1+yU8lKczlL/ghnVKk1mRh+4XF6+I6rxMx5/TaIpiu6bWh9y/5JIXqen24sI/69ZzFF23/fllZRLTo9RbSXsunOo12r1/ySQrV9PpwYR/VPWaxJ/ArwAGSHsuDt8vuCzyuzmtHTJtu3QLT1WUwXbeQTrWlMEum0Z7xhvjurbpbFn8GvJZGYtjAg8niDuD8mq8dc12vffqdztHtdtBep7Ku+xbSWbbgzpwzxP9OdY9ZvBt4t6RXZ2qP6Kup3OXT65xDvd4q2q9bSNNSmNmG9N+pX89ZvFfSk4ClwJ5N5f/Sj+vHDDJd3Tq99t1PZc6hXm8VHfQtpBG7oF8D3G8GRmkki7XAMcDXgCSLeNB0detA7333vQ4AQ++3iuYW0pjB+jXdx0uApwJX2z5F0q8BH+zTtaNudbcGptKl1Gvf/VQGgDvtm8q4QZJCDLl+JYtf2L5f0k5J+wK3kAfyZofpvC98urp1JvXSd9+vp4aTFGKGqj1ZSBKwUdJjgP9H466onwPfrvva0QdlX9i9tDqmq1tnqvJFHtFR7cnCtiUdZvunwAWS/gPY13bFhXJjqJUtOtPrGMR0detExLTqVzfUlZKeZnu97Zv6dM3oh25f2L2OQZRdJ906EQPTr2TxXODPJH0fuJNiIkHb+S2fDTp9Yfc6BhERQ6tfyeKYPl0nhslU7jyKiKHUr4fyvj+V4yQtB94NzAM+aPut0xpY1K8fdx5FRO361bLomaR5NOaPOgoYB9ZLWmN787RfbDrWBehW3o9rDPLaU5Gxhoje9OP3shvbQ/kDPAO4vGn7HOCcTvWXLVvmKbn2WvuQQ+xFixqv1147veX9uMYgrx0R9avx9xIYc4Xv5EfUl4Z22XxgW9P2eFH2AEmnShqTNDYxMTG1qzQPtt57b2N7Osv7cY1BXjsi6jcEv5fDnCzUpswP2bBX2R6xPXLggQdO7SrTtS7AVCacmw3Xjoj6DcHvpRqtkOEj6RnACttHF9vnANj+hw71J4ApDaTvBY/aC37lTrjrTrh7uss77DsA+MmArj3t1+jBAcBPpnjsTJbPPbdM++eu8ffyN22X/rU9zMnikcB3gd8HbgbWAyfZ3jTQwKaJpDHbI4OOo9/yueeWfO7ZY2jvhrK9U9IZwOU0bp29cLYkioiImWZokwWA7bU01r+IiIgBGuYB7tlu1aADGJB87rkln3uWGNoxi4iIGB5pWURERKkki4iIKJVkMWCSXi/Jkg4YdCz9IOntkq6XtFHSp4oVFGctScsl3SBpi6SzBx1Pv0haKOnLkq6TtEnSawYdU79ImifpakmXDTqW6ZRkMUCSFtKYKPEHg46lj64AnuTGWibfpTHn16zUNBnmMcBS4OWSlg42qr7ZCfyl7SeHVuXtAAADfklEQVQCvwucPoc++2uA6wYdxHRLshisfwTOomUak9nM9udt7yw2rwQWDDKemh0BbLG91fa9wGrg+AHH1Be2f2j7quL9z2h8ec7vftTMJ2kBcCzwwUHHMt2SLAZE0nHAzbavHXQsA/SnwOcGHUSNSifDnAskLQIOB7412Ej64l00/gC8f9CBTLehfihvppP0BeDX2+x6I/AG4AX9jag/un1u258p6ryRRlfFR/sZW5+VToY520naG/gE8Frbdww6njpJeiFwi+0NkkYHHc90S7Koke3ntyuX9GRgMXCtJGh0xVwl6QjbP+pjiLXo9LknSToZeCHw+57dD/qMAwubthcA2wcUS99J2o1Govio7U8OOp4+eBZwnKQ/APYE9pX0r7b/aMBxTYs8lDcEJN0EjNie9bNzFkvlvhN4ju0pLkIyM8z2yTC7UeOvoA8DO2y/dtDx9FvRsni97RcOOpbpkjGL6Lf3AfsAV0i6RtIFgw6oLsVA/uRkmNcBl8yFRFF4FvDHwPOKf+drir+4Y4ZKyyIiIkqlZREREaWSLCIiolSSRURElEqyiIiIUkkWERFRKskiIiJKJVlETIGkRZLulnTNLpxjRNJ7ivejkp5ZUv9ISZsl/ddUrxkxVUkWEVN3o+3Dpnqw7THbZxabo0DXZGH7P4E82BYDkWQR0ULS04rFmfaUtFexeM+TSo5Z1PwXf7Go1Yri/TpJ50n6tqTvSjqyKB+VdFkxK+tpwP8unnQ+UtIJkv5L0rWSvlrbh42oKBMJRrSwvV7SGuDvgEcB/2p7V7t+Hmn7iGLKizcDD0y2aPumYtqTn9t+B4Ck7wBH2755tq8mGDNDkkVEeytpTPz3C+DMkrpVTM66ugFYVKH+14GLJF3SdGzEwKQbKqK9/YC9aUx6uGeF+jt56O9T6zH3FK/3UeGPNNunAW+iMcX5NZL2rxBDRG2SLCLaWwX8NY3Fmc6rUP/HwK9K2l/SHjTW6+jFz2gkJgAkHWz7W7bPBX7CQ9fFiOi7dENFtJD0J8BO2xdLmgd8Q9LzbH+p0zG2fylpJY2lQ/8buL7Hy14KfFzS8cCraQx2L6Gx2t4Xgbm8/G4MgUxRHjEFxR1Ml9nuepfUbLluRLqhIqbmPuDRu/JQXq+KW24vpdEtFdFXaVlERESptCwiIqJUkkVERJRKsoiIiFJJFhERUer/Axvg9fPvB088AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Ratio plot\n",
    "\n",
    "# generate three gaussian distributed samples centered at 0.8, 1.0, 1.2\n",
    "import scipy.stats\n",
    "# set the seed to always get the same samples\n",
    "np.random.seed(seed=12345)\n",
    "#mu = 1.0,   sigma = 1\n",
    "x1 = scipy.stats.norm.rvs(loc=1.0, scale=1, size=10000)\n",
    "#mu = 1.2,   sigma = 1\n",
    "x2 = scipy.stats.norm.rvs(loc=1.2, scale=1, size=10000)\n",
    "\n",
    "# Plot the two normalized histograms and their ratio\n",
    "fig, main_ax = plt.subplots()\n",
    "entries1, bins1, patches1 = main_ax.hist(x1, bins=50, range=[-5,5], color='red', alpha=0.5, density=True)\n",
    "entries2, bins2, patches2 = main_ax.hist(x2, bins=50, range=[-5,5], color='blue',alpha=0.5, density=True)\n",
    "\n",
    "plt.title('Ratio plot', axes=main_ax)\n",
    "plt.xlabel(r'x [units]', axes=main_ax)\n",
    "plt.ylabel(r'Entries / bins size = 0.2', axes=main_ax)\n",
    "\n",
    "\n",
    "# if numerator or denominator are zero set the ratio to zero\n",
    "ratio12 = np.nan_to_num(entries1/entries2, nan=0, posinf=0, neginf=0)\n",
    "# zoom between 0 and 2 to avoid the outliers\n",
    "ratio12 = np.clip(ratio12, 0,2.)\n",
    "\n",
    "# get the bin center\n",
    "binscenter = bins1[0:50]+(bins1[1]-bins1[0])*0.5\n",
    "bottom_inset_ax = fig.add_axes([0.125, 0., .775, 0.125])\n",
    "bottom_inset_ax.plot(binscenter, ratio12, marker=\".\", linestyle=\"\", alpha=0.8, color=\"r\")\n",
    "plt.xlabel(r'x [units]', axes=bottom_inset_ax)\n",
    "plt.ylabel(r'ratio'    , axes=bottom_inset_ax)\n",
    "\n",
    "\n",
    "# Or the other way around\n",
    "# Plot the two normalized histograms and their ratio\n",
    "fig, main_ax = plt.subplots()\n",
    "entries1, bins1, patches1 = main_ax.hist(x1, bins=50, range=[-5,5], color='red', alpha=0.5, density=True)\n",
    "entries2, bins2, patches2 = main_ax.hist(x2, bins=50, range=[-5,5], color='blue',alpha=0.5, density=True)\n",
    "\n",
    "plt.title('Ratio plot', axes=main_ax)\n",
    "plt.xlabel(r'x [units]', axes=main_ax)\n",
    "plt.ylabel(r'Entries / bins size = 0.2', axes=main_ax)\n",
    "\n",
    "# if numerator or denominator are zero set the ratio to zero\n",
    "ratio21 = np.nan_to_num(entries2/entries1, nan=0, posinf=0, neginf=0)\n",
    "# zoom between 0 and 2 to avoid the outliers\n",
    "ratio21 = np.clip(ratio21, 0,2.)\n",
    "\n",
    "# get the bin center\n",
    "binscenter = bins1[0:50]+(bins1[1]-bins1[0])*0.5\n",
    "bottom_inset_ax = fig.add_axes([0.125, 0., .775, 0.125])\n",
    "bottom_inset_ax.plot(binscenter, ratio21, marker=\".\", linestyle=\"\", alpha=0.8, color=\"r\")\n",
    "plt.xlabel(r'x [units]', axes=bottom_inset_ax)\n",
    "plt.ylabel(r'ratio'    , axes=bottom_inset_ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mauro/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:23: RuntimeWarning: divide by zero encountered in true_divide\n",
      "/Users/mauro/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:23: RuntimeWarning: invalid value encountered in true_divide\n",
      "/Users/mauro/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:46: RuntimeWarning: invalid value encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'ratio')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Ratio plot\n",
    "\n",
    "# generate three gaussian distributed samples centered at 0.8, 1.0, 1.2\n",
    "import scipy.stats\n",
    "# set the seed to always get the same samples\n",
    "np.random.seed(seed=12345)\n",
    "#mu = 1.0,   sigma = 1\n",
    "x1 = scipy.stats.norm.rvs(loc=1.0, scale=1, size=10000)\n",
    "#mu = 1.0,   sigma = 0.9\n",
    "x2 = scipy.stats.norm.rvs(loc=1.0, scale=0.9, size=10000)\n",
    "\n",
    "# Plot the two normalized histograms and their ratio\n",
    "fig, main_ax = plt.subplots()\n",
    "entries1, bins1, patches1 = main_ax.hist(x1, bins=50, range=[-5,5], color='red', alpha=0.5, density=True)\n",
    "entries2, bins2, patches2 = main_ax.hist(x2, bins=50, range=[-5,5], color='blue',alpha=0.5, density=True)\n",
    "\n",
    "plt.title('Ratio plot', axes=main_ax)\n",
    "plt.xlabel(r'x [units]', axes=main_ax)\n",
    "plt.ylabel(r'Entries / bins size = 0.2', axes=main_ax)\n",
    "\n",
    "\n",
    "# if numerator or denominator are zero set the ratio to zero\n",
    "ratio12 = np.nan_to_num(entries1/entries2, nan=0, posinf=0, neginf=0)\n",
    "# zoom between 0 and 2 to avoid the outliers\n",
    "ratio12 = np.clip(ratio12, 0,2.)\n",
    "\n",
    "# get the bin center\n",
    "binscenter = bins1[0:50]+(bins1[1]-bins1[0])*0.5\n",
    "bottom_inset_ax = fig.add_axes([0.125, 0., .775, 0.125])\n",
    "bottom_inset_ax.plot(binscenter, ratio12, marker=\".\", linestyle=\"\", alpha=0.8, color=\"r\")\n",
    "plt.xlabel(r'x [units]', axes=bottom_inset_ax)\n",
    "plt.ylabel(r'ratio'    , axes=bottom_inset_ax)\n",
    "\n",
    "\n",
    "# Or the other way around\n",
    "# Plot the two normalized histograms and their ratio\n",
    "fig, main_ax = plt.subplots()\n",
    "entries1, bins1, patches1 = main_ax.hist(x1, bins=50, range=[-5,5], color='red', alpha=0.5, density=True)\n",
    "entries2, bins2, patches2 = main_ax.hist(x2, bins=50, range=[-5,5], color='blue',alpha=0.5, density=True)\n",
    "\n",
    "plt.title('Ratio plot', axes=main_ax)\n",
    "plt.xlabel(r'x [units]', axes=main_ax)\n",
    "plt.ylabel(r'Entries / bins size = 0.2', axes=main_ax)\n",
    "\n",
    "# if numerator or denominator are zero set the ratio to zero\n",
    "ratio21 = np.nan_to_num(entries2/entries1, nan=0, posinf=0, neginf=0)\n",
    "# zoom between 0 and 2 to avoid the outliers\n",
    "ratio21 = np.clip(ratio21, 0,2.)\n",
    "\n",
    "# get the bin center\n",
    "binscenter = bins1[0:50]+(bins1[1]-bins1[0])*0.5\n",
    "bottom_inset_ax = fig.add_axes([0.125, 0., .775, 0.125])\n",
    "bottom_inset_ax.plot(binscenter, ratio21, marker=\".\", linestyle=\"\", alpha=0.8, color=\"r\")\n",
    "plt.xlabel(r'x [units]', axes=bottom_inset_ax)\n",
    "plt.ylabel(r'ratio'    , axes=bottom_inset_ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2D distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4.0, 4.0)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate two gaussian distributed samples\n",
    "import scipy.stats\n",
    "# set the seed to always get the same samples\n",
    "np.random.seed(seed=12346)\n",
    "#mu = 0, sigma = 1\n",
    "x = scipy.stats.norm.rvs(loc=0.0, scale=1, size=10000)\n",
    "#mu = 0, sigma = 1\n",
    "y = scipy.stats.norm.rvs(loc=0.0, scale=1, size=10000)\n",
    "\n",
    "plt.figure( figsize=[6,5])\n",
    "plt.hist2d(x, y, bins=(40, 40), cmap='Blues')\n",
    "cb = plt.colorbar()\n",
    "cb.set_label('Entires / bin (0.2 x 0.2)')\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'y [units]')\n",
    "plt.xlim([-4.0,4.0])\n",
    "plt.ylim([-4.0,4.0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log scales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Shape comparison by overlapping normalized histograms\n",
    "\n",
    "# generate two gaussian distributed samples\n",
    "import scipy.stats\n",
    "# set the seed to always get the same samples\n",
    "np.random.seed(seed=12346)\n",
    "#mu = 0,   sigma = 1\n",
    "x1 = scipy.stats.norm.rvs(loc=0.0, scale=1, size=10000)\n",
    "\n",
    "plt.figure(figsize=[10, 5])\n",
    "plt.subplot(121)\n",
    "plt.hist(x1, bins=50, range=[-5,5], color='blue', alpha=0.5)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'Entries / bins size = 1')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.hist(x1, bins=50, range=[-5,5], color='blue', alpha=0.5)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'Entries / bins size = 1')\n",
    "plt.yscale('log', nonposy='clip')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example log-scale; exponential\n",
    "x = np.arange(0.1, 4, 0.1)\n",
    "y = np.exp(-x)\n",
    "\n",
    "# linear scale\n",
    "plt.figure(figsize=[10, 5])\n",
    "plt.subplot(121)\n",
    "plt.scatter(x, y)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'exp(-x)')\n",
    "\n",
    "# log-scale\n",
    "plt.subplot(122)\n",
    "plt.scatter(x, y)\n",
    "plt.yscale('log', nonposy='clip')\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'exp(-x)')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example log-log scale: power law\n",
    "x = np.arange(0.1, 4, 0.05)\n",
    "y = 1.5*x**0.3\n",
    "\n",
    "# linear scale\n",
    "plt.figure(figsize=[15, 5])\n",
    "plt.subplot(121)\n",
    "plt.scatter(x, y)\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'$1.5*x^{0.3}$')\n",
    "\n",
    "# log-log\n",
    "plt.subplot(122)\n",
    "plt.scatter(x, y)\n",
    "plt.yscale('log', nonposy='clip')\n",
    "plt.xscale('log', nonposx='clip')\n",
    "plt.xlabel(r'x [units]')\n",
    "plt.ylabel(r'$1.5*x^{0.3}$')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}