{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cauchMC.py -- simple Monte Carlo program to make histogram of uniformly and Cauchy\n",
    "# distributed random values and plot\n",
    "# G. Cowan, RHUL Physics, October 2019\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate data and store in numpy array, put into histogram\n",
    "\n",
    "numVal = 10000\n",
    "nBins = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate uniformly distributed numbers\n",
    "rMin = 0.\n",
    "rMax = 1.\n",
    "rData = np.random.uniform(rMin, rMax, numVal)\n",
    "rHist, rbin_edges = np.histogram(rData, bins=nBins, range=(rMin, rMax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using transformation method, generate Cauchy distributed numbers\n",
    "xMin=-10.\n",
    "xMax=10.\n",
    "xData = np.tan(np.pi*(rData - 0.5))\n",
    "xHist, xbin_edges = np.histogram(xData, bins=nBins, range=(xMin, xMax))"
   ]
  },
  {
   "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"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make plots and save in file\n",
    "binLo, binHi = rbin_edges[:-1], rbin_edges[1:]\n",
    "xPlot = np.array([binLo, binHi]).T.flatten()\n",
    "yPlot = np.array([rHist, rHist]).T.flatten()\n",
    "fig, ax = plt.subplots(1,1)\n",
    "plt.gcf().subplots_adjust(bottom=0.15)\n",
    "plt.gcf().subplots_adjust(left=0.15)\n",
    "ax.set_xlim((rMin, rMax))\n",
    "ax.set_ylim((0., 150))\n",
    "plt.xlabel(r'$r$', labelpad=0)\n",
    "plt.plot(xPlot, yPlot)\n",
    "\n",
    "binLo, binHi = xbin_edges[:-1], xbin_edges[1:]\n",
    "xPlot = np.array([binLo, binHi]).T.flatten()\n",
    "yPlot = np.array([xHist, xHist]).T.flatten()\n",
    "fig, ax = plt.subplots(1,1)\n",
    "plt.gcf().subplots_adjust(bottom=0.15)\n",
    "plt.gcf().subplots_adjust(left=0.15)\n",
    "ax.set_xlim((xMin, xMax))\n",
    "ax.set_ylim((0., 800))\n",
    "plt.xlabel(r'$x$', labelpad=0)\n",
    "plt.plot(xPlot, yPlot)\n",
    "\n",
    "plt.show()\n",
    "plt.savefig(\"histograms.pdf\", format='pdf')"
   ]
  },
  {
   "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}