ExoMult-tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import all the necessary Python packages and the stellar sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: VerifyWarning: It is strongly recommended that column names contain only upper and lower-case ASCII letters, digits, or underscores for maximum compatibility with other software (got '[Fe/H]'). [astropy.io.fits.column]\n",
      "WARNING: VerifyWarning: It is strongly recommended that column names contain only upper and lower-case ASCII letters, digits, or underscores for maximum compatibility with other software (got '[Fe/H]_err'). [astropy.io.fits.column]\n"
     ]
    }
   ],
   "source": [
    "import ExoMultSimple as ExoMult\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy.io import fits\n",
    "from astropy.table import Table, unique\n",
    "from astropy.stats import mad_std\n",
    "\n",
    "stellar=pd.read_csv(\"stellar_samples.csv\",sep=\",\", engine='python', header=0)\n",
    "laMOST= Table.read('table-03.fits', format='fits')\n",
    "\n",
    "\n",
    "LAMOST=laMOST[\"EPIC_1\",\"[Fe/H]\",\"[Fe/H]_err\",\"logg\",\"logg_err\", \"Teff\",\"Teff_err\"]\n",
    "LAMOST[\"EPIC\"]=LAMOST[\"EPIC_1\"]\n",
    "LAMOST=LAMOST.to_pandas()\n",
    "stellar=pd.merge(stellar,LAMOST[[\"EPIC\", '[Fe/H]', '[Fe/H]_err',\"logg\",\"logg_err\", \"Teff\", \"Teff_err\"]], on=\"EPIC\", how=\"left\")\n",
    "# stellar[\"FeH\"]=np.where(np.isfinite(stellar[\"[Fe/H]\"]),stellar[\"[Fe/H]\"],stellar.FeH)\n",
    "stellar[\"U_FeH\"]=np.where(np.isfinite(stellar[\"[Fe/H]_err\"]),stellar[\"[Fe/H]_err\"],stellar.U_FeH)\n",
    "\n",
    "\n",
    "\n",
    "stellar[\"logg\"]=np.where(np.isfinite(stellar[\"logg_y\"]),stellar[\"logg_y\"],stellar.logg_x)\n",
    "stellar[\"U_logg\"]=np.where(np.isfinite(stellar[\"logg_err\"]),stellar[\"logg_err\"],stellar.U_logg)\n",
    "\n",
    "stellar[\"Teff\"]=np.where(np.isfinite(stellar[\"Teff_y\"]),stellar[\"Teff_y\"],stellar.Teff_x)\n",
    "stellar[\"U_Teff\"]=np.where(np.isfinite(stellar[\"Teff_err\"]),stellar[\"Teff_err\"],stellar.U_Teff)\n",
    "stellarOG=stellar\n",
    "\n",
    "# stellar=stellar.drop(['[Fe/H]','[Fe/H]_err',\"logg_y\",\"logg_x\",\"logg_err\", \"Teff_y\", \"Teff_x\", \"Teff_err\"], axis=1)\n",
    "# print(stellar)\n",
    "\n",
    "\n",
    "# LAMOST=pd.read_csv(\"table3.dat\", engine='python', names=[\"id\",\"EPIC\",\"RA\",\"Dec\",\"Teff\",\"U_Teff\",\"logg\",\"U_logg\",\"FeH\",\"U_FeH\",\"RV\",\"U_RV\",\"nSpec\"], delim_whitespace=True)\n",
    "# stellar=pd.merge(stellar,LAMOST[[\"EPIC\", 'FeH', 'U_FeH',]], on=\"EPIC\", how=\"left\")\n",
    "# stellar[\"FeH\"]=np.where(np.isfinite(stellar.FeH_y),stellar.FeH_y,stellar.FeH_x)\n",
    "# stellar[\"U_FeH\"]=np.where(np.isfinite(stellar.U_FeH_y),stellar.U_FeH_y,stellar.U_FeH_x)\n",
    "# stellar=stellar.drop(['FeH_x', 'FeH_y','U_FeH_x', 'U_FeH_y'], axis=1)\n",
    "# print(stellar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.backends.backend_pdf import PdfPages\n",
    "with PdfPages('k2Star.pdf')as pdf:\n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    im=plt.scatter(stellar.Teff_y,stellar.logg_y, c=stellar['[Fe/H]'], s=.02, alpha=.2, cmap='viridis', vmin=-2,vmax=0.6, rasterized=True)\n",
    "    plt.ylim(5.5, 0)\n",
    "    plt.xlim(8500, 3000)\n",
    "    plt.text(8300,.25, \"K2\", horizontalalignment=\"left\",verticalalignment='top', color=\"black\", fontsize=16)\n",
    "\n",
    "\n",
    "    plt.ylabel(\"$\\log g$\")\n",
    "    plt.xlabel(\"$T_{\\mathrm{eff}}$ [K]\")\n",
    "    cbar =plt.colorbar(im)\n",
    "    cbar.set_label(\"[Fe/H]\")\n",
    "    cbar.set_alpha(1)\n",
    "    cbar.draw_all()\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "#     plt.rcParams.update({'font.size': 14})\n",
    "\n",
    "# plt.ylim(5.5, 0)\n",
    "# plt.xlim(8500, 3000)\n",
    "# plt.text(8300,.25, \"K2\", horizontalalignment=\"left\",verticalalignment='top', color=\"black\", fontsize=16)\n",
    "\n",
    "\n",
    "#     plt.ylabel(\"$\\log g$\")\n",
    "#     plt.xlabel(\"$T_{\\mathrm{eff}}$ [K]\")\n",
    "#     cbar =plt.colorbar(im)\n",
    "#     cbar.set_label(\"[Fe/H]\")\n",
    "#     cbar.set_alpha(1)\n",
    "#     cbar.draw_all()\n",
    "#     pdf.savefig(bbox_inches = \"tight\", dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we trim the stellar sample to meet our selection criterion. I am focusing on the metal-poor FGK targets, but you will likely have your own interesting sample.\n",
    "\n",
    "#### I strongly recommend you remove targets with CDPP 8hr greater that 1200 ppm. These targets are super noisy and are unlikely to yield meaningful detections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "284691\n",
      "221770\n",
      "130731\n",
      "94091\n",
      "81000\n",
      "46545\n",
      "81000\n",
      "81000 Stars in Sample\n",
      "0.2505\n"
     ]
    },
    {
     "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.07500000000000001\n",
      "-0.05799999999999998\n",
      "-0.047\n",
      "-0.035500000000000004\n",
      "stellar  201864\n"
     ]
    },
    {
     "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": [
    "####Remove Really Noisy Targets####\n",
    "print(len(stellar))\n",
    "\n",
    "# stellar=stellar[stellar.Ncomp<1]\n",
    "#stellar=stellar[stellar.d_mag<4]\n",
    "# stellar=stellar[stellar.CDPP8<=1200]\n",
    "# stellar=stellar[stellar.RUWE<1.2]\n",
    "\n",
    "\n",
    "####Only Select FGK Dwarf Stars####\n",
    "# stellar=stellar[(stellar.Teff<3500) &  (stellar.Teff>3000)]\n",
    "stellar=stellar[(stellar.Teff>4000) & (stellar.Teff<6500)]\n",
    "print(len(stellar))\n",
    "stellar=stellar[stellar.logg>=1/4.671*np.arctan((stellar.Teff-6300)/-67.172)+3.876]\n",
    "print(len(stellar))\n",
    "# stellar=stellar[stellar.logg>=4]\n",
    "# print(len(stellar))\n",
    "stellar=stellar[stellar.RUWE<1.2]\n",
    "print(len(stellar))\n",
    "stellar=stellar[stellar.CDPP8<=1200]\n",
    "print(len(stellar))\n",
    "# stellar=stellar[stellar.logg<5]\n",
    "# stellar=stellar[stellar.Rad<2]\n",
    "# stellar=stellar[stellar.Mass<2]\n",
    "# stellar=stellar[stellar.FeH<0.4]\n",
    "# stellar=stellar[stellar.FeH>0.2]\n",
    "print(len(stellar[stellar.U_FeH==.235]))\n",
    "print(len(stellar))\n",
    "####Only Select Low Metallicity Targets####\n",
    "# stellar=stellar[(stellar.FeH>0.2) & (stellar.FeH<0.4)]\n",
    "\n",
    "print(len(stellar), \"Stars in Sample\")\n",
    "print(np.median(stellar.FeH[(stellar.FeH>0.2) & (stellar.FeH<.4)]))\n",
    "# print(np.sort(stellar.FeH)[int(len(stellar)*.84)]-np.median(stellar.FeH))\n",
    "# print(np.median(stellar.FeH)-np.sort(stellar.FeH)[int(len(stellar)*.16)])\n",
    "plt.hist(stellar.FeH)\n",
    "plt.show()\n",
    "plt.scatter(stellar.Teff,stellar.logg)\n",
    "plt.show()\n",
    "\n",
    "print(np.sort(stellar.FeH[(stellar.FeH>-.4) & (stellar.FeH<-.2)])[np.int(.16*len(stellar.FeH[(stellar.FeH>-.40) & (stellar.FeH<-.2)]))]\n",
    "      -np.median(stellar.FeH[(stellar.FeH>-.4) & (stellar.FeH<-0.2)]))\n",
    "\n",
    "print(np.sort(stellar.FeH[(stellar.FeH>-.2) & (stellar.FeH<0)])[np.int(.16*len(stellar.FeH[(stellar.FeH>-.20) & (stellar.FeH<0.0)]))]\n",
    "      -np.median(stellar.FeH[(stellar.FeH>-.2) & (stellar.FeH<-0.0)]))\n",
    "\n",
    "print(np.sort(stellar.FeH[(stellar.FeH>-0) & (stellar.FeH<0.2)])[np.int(.16*len(stellar.FeH[(stellar.FeH>0) & (stellar.FeH<0.2)]))]\n",
    "      -np.median(stellar.FeH[(stellar.FeH>-0) & (stellar.FeH<0.2)]))\n",
    "\n",
    "print(np.sort(stellar.FeH[(stellar.FeH>.2) & (stellar.FeH<0.4)])[np.int(.16*len(stellar.FeH[(stellar.FeH>.20) & (stellar.FeH<0.4)]))]\n",
    "      -np.median(stellar.FeH[(stellar.FeH>.2) & (stellar.FeH<0.4)]))\n",
    "\n",
    "stellarOG=stellarOG[~stellarOG['EPIC'].isin(stellar.EPIC.values.tolist())]\n",
    "print(\"stellar \",str(len(stellarOG)))\n",
    "from matplotlib.backends.backend_pdf import PdfPages\n",
    "with PdfPages('k2Star2.pdf')as pdf:\n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    im2=plt.scatter(stellarOG.Teff,stellarOG.logg, c=\"grey\", s=.02, alpha=.05, rasterized=True)\n",
    "    im=plt.scatter(stellar.Teff,stellar.logg, c=stellar['[Fe/H]'], s=.04, alpha=.2, cmap='viridis', vmin=-2,vmax=0.6, rasterized=True)\n",
    "\n",
    "    plt.ylim(5.25, 3)\n",
    "    plt.xlim(7000, 3500)\n",
    "    plt.text(6900,3.05, \"K2\", horizontalalignment=\"left\",verticalalignment='top', color=\"black\", fontsize=16)\n",
    "\n",
    "\n",
    "    plt.ylabel(\"$\\log g$\")\n",
    "    plt.xlabel(\"$T_{\\mathrm{eff}}$ [K]\")\n",
    "    cbar =plt.colorbar(im)\n",
    "    cbar.set_label(\"[Fe/H]\")\n",
    "    cbar.set_alpha(1)\n",
    "    cbar.draw_all()\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()\n",
    "    \n",
    "    \n",
    "plt.hist(stellarOG.FeH)\n",
    "plt.hist(stellar.FeH)\n",
    "plt.show()\n",
    "\n",
    "    \n",
    "# with PdfPages('k2StarMetal.pdf')as pdf:\n",
    "#     plt.rcParams.update({'font.size': 14})\n",
    "#     im2=plt.scatter(stellarOG.Teff,stellarOG.logg, c=\"grey\", s=.02, alpha=.05, rasterized=True)\n",
    "#     im=plt.scatter(stellar.Teff,stellar.logg, c=stellar['[Fe/H]'], s=.04, alpha=.2, cmap='viridis', vmin=-2,vmax=0.6, rasterized=True)\n",
    "\n",
    "#     plt.ylim(5.25, 3)\n",
    "#     plt.xlim(7000, 3500)\n",
    "#     plt.text(6900,3.05, \"K2\", horizontalalignment=\"left\",verticalalignment='top', color=\"black\", fontsize=16)\n",
    "\n",
    "\n",
    "#     plt.ylabel(\"$\\log g$\")\n",
    "#     plt.xlabel(\"$T_{\\mathrm{eff}}$ [K]\")\n",
    "#     cbar =plt.colorbar(im)\n",
    "#     cbar.set_label(\"[Fe/H]\")\n",
    "#     cbar.set_alpha(1)\n",
    "#     cbar.draw_all()\n",
    "#     pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "#     plt.close()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34395\n",
      "-0.001999923706054396\n",
      "0.04447795344159575\n",
      "223915\n"
     ]
    }
   ],
   "source": [
    "###KEPLER STARS\n",
    "stellarkep=pd.read_csv(\"stellar_samples_kepler.csv\",sep=\",\", engine='python', header=0)\n",
    "LAMOST=pd.read_csv(\"lamostClean.csv\",sep=\",\", engine='python', header=0)\n",
    "stellarkep=pd.merge(stellarkep,LAMOST[[\"KIC\", 'FeH', 'U_FeH',\"logg\",\"U_logg\"]], on=\"KIC\", how=\"left\")\n",
    "\n",
    "from astropy.stats import mad_std\n",
    "# print(steFeH[np.isfinite(steFeH)])\n",
    "# print(len(steFeH[np.isfinite(steFeH)]))\n",
    "# print(len(lamFeH[np.isfinite(lamFeH)]))\n",
    "steFeH=stellar[\"logg_x\"][np.isfinite(stellar[\"logg_y\"])]\n",
    "lamFeH=stellar[\"logg_y\"][np.isfinite(stellar[\"logg_y\"])]\n",
    "print(len(lamFeH))\n",
    "# plt.scatter(steFeH,lamFeH)\n",
    "# plt.xlim([0,6])\n",
    "# plt.ylim([0,6])\n",
    "# plt.plot([0,6],[0,6],color=\"red\")\n",
    "# plt.show()\n",
    "diff=steFeH-lamFeH\n",
    "\n",
    "\n",
    "print(np.median(diff))\n",
    "print(mad_std(diff))\n",
    "# diff=diff[abs(diff)<1]\n",
    "# plt.hist(diff)\n",
    "# plt.xlim([-2.5,1])\n",
    "\n",
    "stellarkep[\"FeH\"]=np.where(np.isfinite(stellarkep[\"FeH_y\"]),stellarkep[\"FeH_y\"],stellarkep.FeH_x)\n",
    "stellarkep[\"U_FeH\"]=np.where(np.isfinite(stellarkep[\"U_FeH_y\"]),stellarkep[\"U_FeH_y\"],stellarkep.U_FeH_x)\n",
    "stellarkep[\"logg\"]=np.where(np.isfinite(stellarkep[\"logg_y\"]),stellarkep[\"logg_y\"],stellarkep.logg_x)\n",
    "stellarkep[\"U_logg\"]=np.where(np.isfinite(stellarkep[\"U_logg_y\"]),stellarkep[\"U_logg_y\"],stellarkep.U_logg_x)\n",
    "# stellar=stellar.drop(['FeH_y','FeH_x',\"logg_y\",\"logg_x\",\"U_FeH_y\",\"U_FeH_x\",\"U_logg_x\",\"U_logg_y\"], axis=1)\n",
    "print(len(stellarkep))\n",
    "stellarkep=stellarkep[(stellarkep.Teff>4000) &  (stellarkep.Teff<6500)]\n",
    "stellarkep=stellarkep[stellarkep.logg>=1/4.671*np.arctan((stellarkep.Teff-6300)/-67.172)+3.876]\n",
    "stellarkep=stellarkep[stellarkep.RUWE<1.2]\n",
    "stellarkep=stellarkep[stellarkep.CDPP7_5<=1000]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.012\n",
      "0.08895613311033612\n",
      "-0.14800000000000002\n",
      "0.17642966400216667\n",
      "0.956\n",
      "0.17642966400216664\n",
      "0.895\n",
      "0.1645688462541218\n",
      "1.015\n",
      "0.28169442151606466\n",
      "0.888\n",
      "0.25352497936445784\n",
      "5705.3\n",
      "550.1936832874281\n",
      "5413.0\n",
      "704.236053790161\n"
     ]
    }
   ],
   "source": [
    "\n",
    "with PdfPages('K2KepMet.pdf')as pdf:\n",
    "    \n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.hist(stellarkep.FeH[(stellarkep.FeH<.6) &( stellarkep.FeH>-1.5)],bins=25,color=\"#39558C\")\n",
    "    plt.hist(stellar.FeH[(stellar.FeH<.6) &( stellar.FeH>-1.5)],bins=25,alpha=.75,color=\"#73D055\")\n",
    "    plt.xlabel(\"[Fe/H]\")\n",
    "    plt.ylabel(\"Number of Stars [k]\")\n",
    "    plt.yticks([0,10000, 20000, 30000,40000], ['0',\"10\", \"20\", \"30\", \"40\"])\n",
    "    plt.xlim([-1.5,.6])\n",
    "    plt.ylim([0,40000])\n",
    "    ax.set_aspect((.6+1.5)/40000)\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()\n",
    "print(np.median(stellarkep.FeH))\n",
    "print(mad_std(stellarkep.FeH))\n",
    "print(np.median(stellar.FeH))\n",
    "print(mad_std(stellar.FeH))  \n",
    "    \n",
    "with PdfPages('K2KepMass.pdf')as pdf:\n",
    "    \n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.hist(stellarkep.Mass[(stellarkep.Mass<2.25)],bins=25,color=\"#39558C\")\n",
    "    plt.hist(stellar.Mass[(stellar.Mass<2.25)],bins=25,alpha=.75,color=\"#73D055\")\n",
    "    plt.xlabel(\"Mass [$M_{\\odot}$]\")\n",
    "    plt.ylabel(\"Number of Stars [k]\")\n",
    "    plt.yticks([0,5000, 10000, 15000,20000], ['0',\"5\", \"10\", \"15\", \"20\"])\n",
    "    plt.xlim([0,2.25])\n",
    "    plt.ylim([0,20000])\n",
    "    ax.set_aspect((2.25)/20000)\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()\n",
    "\n",
    "    \n",
    "print(np.median(stellarkep.Mass))\n",
    "print(mad_std(stellarkep.Mass))\n",
    "print(np.median(stellar.Mass))\n",
    "print(mad_std(stellar.Mass)) \n",
    "\n",
    "with PdfPages('K2KepRad.pdf')as pdf:\n",
    "    \n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.hist(stellarkep.Rad[(stellarkep.Rad<3)],bins=25,color=\"#39558C\")\n",
    "    plt.hist(stellar.Rad[(stellar.Rad<3)],bins=25,alpha=.75,color=\"#73D055\")\n",
    "    plt.xlabel(\"Radius [$R_{\\odot}$]\")\n",
    "    plt.ylabel(\"Number of Stars [k]\")\n",
    "    plt.yticks([0,5000, 10000, 15000,20000,25000], ['0',\"5\", \"10\", \"15\", \"20\",\"25\"])\n",
    "    plt.xlim([0.5,3])\n",
    "    plt.ylim([0,25000])\n",
    "    ax.set_aspect((3-.5)/25000)\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()\n",
    "    \n",
    "print(np.median(stellarkep.Rad))\n",
    "print(mad_std(stellarkep.Rad))\n",
    "print(np.median(stellar.Rad))\n",
    "print(mad_std(stellar.Rad))       \n",
    "\n",
    "with PdfPages('K2KepTeff.pdf')as pdf:\n",
    "    \n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.hist(stellarkep.Teff,bins=25,color=\"#39558C\")\n",
    "    plt.hist(stellar.Teff,bins=25,alpha=.75,color=\"#73D055\")\n",
    "    plt.xlabel(\"$T_{\\mathrm{eff}}$ [K]\")\n",
    "    plt.ylabel(\"Number of Stars [k]\")\n",
    "    plt.yticks([0,3000,6000,9000 ], ['0',\"3\", \"6\", \"9\"])\n",
    "    plt.xlim([4000,6500])\n",
    "    plt.ylim([0,9000])\n",
    "    ax.set_aspect((6500-4000)/9000)\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()\n",
    "print(np.median(stellarkep.Teff))\n",
    "print(mad_std(stellarkep.Teff))\n",
    "print(np.median(stellar.Teff))\n",
    "print(mad_std(stellar.Teff))      \n",
    "\n",
    "with PdfPages('K2Keplogg.pdf')as pdf:\n",
    "    \n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.hist(stellarkep.logg,bins=25,color=\"#39558C\")\n",
    "    plt.hist(stellar.logg,bins=25,alpha=.75,color=\"#73D055\")\n",
    "    plt.xlabel(\"$\\log g$\")\n",
    "    plt.ylabel(\"Number of Stars [k]\")\n",
    "    plt.yticks([0,5000, 10000, 15000,20000], ['0',\"5\", \"10\", \"15\", \"20\"])\n",
    "    plt.xlim([3.5,5])\n",
    "    plt.ylim([0,20000])\n",
    "    ax.set_aspect((5-3.5)/20000)\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()      \n",
    "        \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'DataFrame' object has no attribute 'dec'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-140-8faa65887991>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mstellar\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdec\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/miniconda3/lib/python3.6/site-packages/pandas/core/generic.py\u001b[0m in \u001b[0;36m__getattr__\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m   4374\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_info_axis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_can_hold_identifiers_and_holds_name\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4375\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4376\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   4377\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4378\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__setattr__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'DataFrame' object has no attribute 'dec'"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from astropy.stats import mad_std\n",
    "# # print(steFeH[np.isfinite(steFeH)])\n",
    "# # print(len(steFeH[np.isfinite(steFeH)]))\n",
    "# # print(len(lamFeH[np.isfinite(lamFeH)]))\n",
    "# steFeH=stellar[\"FeH\"][np.isfinite(stellar[\"[Fe/H]\"])]\n",
    "# lamFeH=stellar[\"[Fe/H]\"][np.isfinite(stellar[\"[Fe/H]\"])]\n",
    "# plt.scatter(stellar[\"[Fe/H]\"][np.isfinite(stellar[\"[Fe/H]\"])],stellar[\"FeH\"][np.isfinite(stellar[\"[Fe/H]\"])])\n",
    "# plt.xlim([-2.5,1])\n",
    "# plt.ylim([-2.5,1])\n",
    "# plt.plot([-2.5,1],[-2.5,1],color=\"red\")\n",
    "# plt.show()\n",
    "# diff=steFeH-lamFeH\n",
    "\n",
    "# print(np.median(diff))\n",
    "# print(mad_std(diff))\n",
    "# diff=diff[abs(diff)<1]\n",
    "# plt.hist(diff)\n",
    "# # plt.xlim([-2.5,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "with PdfPages('k2fieldMetals.pdf')as pdf:\n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    plt.hist(stellar.FeH, bins=25, color=\"#453781\")\n",
    "    plt.hist(stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"[Fe/H]\"], bins=25, color=\"#3CBB75\")\n",
    "    plt.text(-.96,.96*20000, \"Field\", horizontalalignment=\"left\",verticalalignment='top', color=\"#453781\", fontsize=16)\n",
    "    plt.text(-.96,.88*20000, \"LAMOST\", horizontalalignment=\"left\",verticalalignment='top', color=\"#3CBB75\", fontsize=16)\n",
    "    plt.text(.46,.96*20000, \"K2\", horizontalalignment=\"right\",verticalalignment='top', color=\"black\", fontsize=16)\n",
    "    plt.xlabel(\"[Fe/H]\")\n",
    "    plt.ylabel(\"Number of Stars\")\n",
    "    plt.xlim([-1.,.5])\n",
    "    plt.ylim([0,20000])\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.06375190334903896\n",
      "0.00040875813789574246\n"
     ]
    }
   ],
   "source": [
    "\n",
    "with PdfPages('k2fieldLAMOST.pdf')as pdf:\n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    xvalue=np.arange(-1,1,.01)\n",
    "    print(mad_std(stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"FeH\"]-stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"[Fe/H]\"]))\n",
    "    print(np.mean(stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"FeH\"]-stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"[Fe/H]\"]))\n",
    "    plt.scatter(stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"FeH\"],stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"[Fe/H]\"], color=\"#453781\", alpha =.1, s=5, rasterized=True)\n",
    "    plt.plot(xvalue,xvalue-(np.median(stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"FeH\"]-stellar[np.isfinite(stellar[\"[Fe/H]\"])][\"[Fe/H]\"])), color=\"#3CBB75\")\n",
    "    plt.text(-.96,.45, \"Offset = -0.002\", horizontalalignment=\"left\",verticalalignment='top', color=\"black\", fontsize=16)\n",
    "    plt.text(-.96,.3, \"RMS = 0.064\", horizontalalignment=\"left\",verticalalignment='top', color=\"black\", fontsize=16)\n",
    "    # plt.text(-.96,40000*.88, \"LAMOST\", horizontalalignment=\"left\",verticalalignment='top', color=\"#3CBB75\", fontsize=16)\n",
    "    plt.text(.46,-.96, \"K2\", horizontalalignment=\"right\",verticalalignment='bottom', color=\"black\", fontsize=16)\n",
    "\n",
    "\n",
    "    plt.xlabel(\"HU20 [Fe/H]\")\n",
    "    plt.ylabel(\"LAMOST [Fe/H]\")\n",
    "    plt.xlim([-1.,.5])\n",
    "    plt.ylim([-1.,.5])\n",
    "# plt.ylim([0,40000])\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We must now provide ExoMult with the population input parameters.\n",
    " <b>pMax</b> and <b>pMin</b> - Period distribution limits. \n",
    "<br> <b>rMax</b> and <b>rMin</b> - Radius distribution limits.\n",
    "<br>\n",
    "<br>ExoMult assums a broken power-law distribution in both period and radius space. \n",
    "<br> <b>alpha_1</b> and <b>alpha_2</b> - Radius distribution powers.\n",
    "<br> <b>rad_break</b> - Location of the break between the defined powers.\n",
    "<br>\n",
    "<br> <b>beta_1</b> and <b>beta_2</b> - Period distribution powers.\n",
    "<br> <b>rad_break</b> - Location of the break between the defined powers.\n",
    "<br> \n",
    "<br> <b>mut_Ray</b> - Magnitude of mutual inclination between planets in a fixed system. A 0 here assumes a perfectly flat disk.\n",
    "<br>\n",
    "<br>ExoMult does not assume a system multiplicity distribution, it requires you manually input the fraction of stars with at least one planet (<b>frac_m1</b>), at least two planets (<b>frac_m2</b>), and so forth.\n",
    "<br>\n",
    "<br>In the provided example I created a variable call <b>occurFact</b>. This can be considered the overall occurrence factor or the number planets expected per star. If you use the code that follows it will just max out each multiplicity order (i.e., <b>occurFact = 2.5</b> means that 100% of the stars have two planets and 50% have three)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = ExoMult.PopParams(stellar=stellar)\n",
    "\n",
    "####Distribution Limits####\n",
    "params.pMax=40 #days\n",
    "params.pMin=0.5 #days\n",
    "params.rMax=6 #Earth Radii\n",
    "params.rMin=0.5 #Earth Radii\n",
    "\n",
    "####Kepler Distribtuion Shape####\n",
    "params.alpha_1=-1.61\n",
    "params.rad_break=3.03 #Earth Radii\n",
    "params.alpha_2=-6.56\n",
    "params.beta_1=0.91\n",
    "params.per_break=6.83  #days\n",
    "params.beta_2=-0.59\n",
    "params.mut_Ray=0 #degrees\n",
    "\n",
    "####Occurrence Factor (Number of Planets Per Star)####\n",
    "occurFact=2.5\n",
    "\n",
    "params.frac_m1=occurFact\n",
    "params.frac_m2=params.frac_m1-1\n",
    "params.frac_m3=params.frac_m2-1\n",
    "params.frac_m4=params.frac_m3-1\n",
    "params.frac_m5=params.frac_m4-1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have all the inputs defined we can run ExoMult.\n",
    "<br> However, let's first turn on <b>prettyPrint</b>. This will just give provide a little insight into what is happening under the hood.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drawing exoplanet population from broken power-law distribution\n",
      "Applying population completeness corrections for K2\n",
      "----- Removing non-transiting exoplanets\n",
      "----- Removing undetected exoplanets\n",
      "Drawing planet radii from stellar uncertainties\n",
      "----- Reasserting maximum radius threshold\n",
      "144 Expected Obs. Hosting Targets\n",
      "165 Expected Obs. Planet Candidates\n"
     ]
    }
   ],
   "source": [
    "params.prettyPrint=True\n",
    "outputPopulation=ExoMult.Simulate(params)\n",
    "print(len(outputPopulation), \"Expected Obs. Hosting Targets\")\n",
    "print(np.sum(outputPopulation.m), \"Expected Obs. Planet Candidates\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br>Now that have the output population, we can look at the expected observated radius and period distribution given our input parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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"
    }
   ],
   "source": [
    "plt.hist(np.concatenate([outputPopulation.rad_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.rad_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.rad_m3[outputPopulation.rad_m3>0]], axis=0))\n",
    "plt.title(\"Expected Obs. Radius Distribution\")\n",
    "plt.ylabel(\"Number of Planets\")\n",
    "plt.xlabel(\"Radius [Earth]\")\n",
    "plt.show()\n",
    "\n",
    "plt.hist(np.concatenate([outputPopulation.per_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.per_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.per_m3[outputPopulation.rad_m3>0]], axis=0))\n",
    "plt.title(\"Expected Obs. Period Distribution\")\n",
    "plt.ylabel(\"Number of Planets\")\n",
    "plt.xlabel(\"Period [Days]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, let's try it again, but with a flat distribution in period and radius."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = ExoMult.PopParams(stellar=stellar)\n",
    "params.pMax=40\n",
    "params.pMin=0.5\n",
    "params.rMax=6\n",
    "params.rMin=0.5 \n",
    "\n",
    "#### Flat Period and Radius distribution ###\n",
    "params.alpha_1=0\n",
    "params.rad_break=2\n",
    "params.alpha_2=0\n",
    "params.beta_1=0\n",
    "params.per_break=10\n",
    "params.beta_2=0\n",
    "params.mut_Ray=0\n",
    "\n",
    "occurFact=2.5\n",
    "params.frac_m1=occurFact\n",
    "params.frac_m2=params.frac_m1-1\n",
    "params.frac_m3=params.frac_m2-1\n",
    "params.frac_m4=params.frac_m3-1\n",
    "params.frac_m5=params.frac_m4-1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: I am not going to turn on <b>prettyPrint</b> because it just gets in the way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "474 Expected Obs. Hosting Targets\n",
      "740 Expected Obs. Planet Candidates\n"
     ]
    }
   ],
   "source": [
    "outputPopulation=ExoMult.Simulate(params)\n",
    "print(len(outputPopulation), \"Expected Obs. Hosting Targets\")\n",
    "print(np.sum(outputPopulation.m), \"Expected Obs. Planet Candidates\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Clearly, a flat distribution yields a lot more planets.\n",
    "<br> Let's take a quick look at the output period and radius distributions. We should expect them to look different given our flat input distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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svaGZmQ1sXZtAJC0J/AiYEBGP5uJVgZeBJ0vVp+dp9eazl6TJkibPnDmzZfGamQ00XZlAcp/HL4EVgS8szLwi4vSIGBkRI4cOHdqM8MzMjC5MIDl5/Bp4N/CBiHiqMHkaMAgYUvrYsDzNzMzapKsSiKQlgPNJyWN0RJSTwt+B/1LobM9DeNcBrm9XnGZm1uZRWJKWBd6R3y4GDJe0ITALeBz4HfBe4CNASKr1a8yOiHkRMVvSz4GjJc0AngKOA+4ErmrfmpiZWbuPQEYCt+XHYOC7+fX3gLeQzv14E+lI44nCY9fCPA4ELiIdqVwHzAE+EhEvt2UNzMwMaP95IBMB9VKlt2m1ebwA7JcfZmbWIV3VB2JmZv2Hb2lrZh3RyVvLWnP4CMTMzBriBGJmZg1xAjEzs4Y4gZiZWUOcQMzMrCFOIGZm1hAnEDMza4gTiJmZNcQJxMzMGuIEYmZmDXECMTOzhjiBmJlZQ5xAzMysIU4gZmbWECcQMzNrSKUEImldSWsX3m8r6ZeSxkoa1LrwzMysW1U9AjkT2AhA0luBi4E3AvsAP2hNaGZm1s2qJpB3Arfm17sAN0XE/wCfA3ZrRWBmZtbdqiaQQcCL+fUHgMvy64eAYc0OyszMul/VBHIX8BVJW5ISyJ9z+ZuBJ1sRmJmZdbeqCeSbwJ7ARODXEfGPXL4TcHPVhUnaStIfJT0mKSSNKU2XpHGSHpc0T9JESeuV6qwk6VxJs/PjXEkrVo3BzMyao1ICiYhJwFBgSET8b2HSacCXF2B5y5KOZg4A5tWZfjDwNWA/4L3ADOBKScsV6pwHbAzskB8bA+cuQAxmZtYEVYfxngksExFPlybNBI6qurCIuCwiDo2IC4BXSssQcCAwPiIujIi7gD2A5YDdc511SEljr4i4ISJuAL4EfLg4zNjMzFqvahPWHsDgOuWDgc83KZY1gFWBK2oFETEPmARslos2BeYA1xc+dx0wt1DHzMzaYPHeJkp6I6D8WEnSS4XJg4AdgelNimXV/Fye33RSZ32tzsyIiNrEiAhJMwqfn4+kvYC9AIYPH96kUM3MrNcEQhphFflxd53pARze7KCaKSJOB04HGDlyZPRR3czMKuorgYwmHX38FfgEMKsw7UXg4Yh4vEmxTMvPw4BHCuXDCtOmAUMlqXYUkvtOVinUMTOzNug1gUTENQCS1gAeKTYdtcAUUhLYFrglL3dpYEvgG7nODaSRXJvyWj/IpsAbmL9fxMzMWqzqMN6HgfUlnSTpT5JWA5C0s6SNqi5M0rKSNpS0YV728Px+eE5OJwDflPRxSesDZ5E6zc/LcdxDOonxNEmbStqUNJT4koi4r2ocZma28KoO492OdFTwZmAbXhuR9XYWrA9kJHBbfgwGvptffy9PPxo4HjgZmAysBmwXEc8V5rE7cAdweX7cQboml5mZtVFffSA13wcOiohTJBV35hNJJ/5VEhETSX0qPU0PYFx+9FTnaeCzVZdpZmatUfU8kPV57QKKRbNIl3U3M7MBpmoCmcVr52IUbQw82rxwzMysv6iaQM4DjpH0FtK5H4tL2ho4FjinVcGZmVn3qppADiMNs32YNIz2btK5IdcCR7QmNDMz62aVOtEj4r/AZyR9h3Rr28WA2yLigVYGZ2atN+KQSzsdgvVTVUdhARARD5HuQmhmZgNc5QQiaVfS3QhXodT0FRE7NTkuMzPrcpUSiKRjSPfquBp4nNSRbmZmA1jVI5DPA7vlG0GZmZlVHoW1GHB7C+MwM7N+pmoCOR1fPsTMzAqqNmGtCOwuaVvgTuC/xYkRsX+T4zIzsy5XNYGsy2tNWO8sTXOHutlC8rkY1h9VPZFwdKsDMTOz/qVqH4iZmdl8FuREwtHAbsBwYMnitIjYpslxmZlZl6t6IuEY4FTgImAUcDGwFrAG8MsWxWZmtkjpVF/X1PE7tmS+VZuwvg7sGxG7kUZgjY2IjUjJY05LIjMzs65WNYG8Dbgqv36BdEl3gJOAMU2OyczM+oGqCeQpYLn8+jHSLW4BVgYGNzsoMzPrflU70f8GbAf8A/gt8ON8UuEHgCtbFJuZmXWxqglkX2Dp/PqHwEvA5qRk8oMWxGVmZl2uUhNWRMyKiMfz61ci4qiI2Ckivh4RzzQrGEmDJH1f0hRJz+fnH0havFBHksZJelzSPEkTJa3XrBjMzKyaHo9AJL2x6kwiYlZzwuGbwD7AHqTmsncDZ5M67r+f6xwMfI3UeX8f8B3gSklrR8RzTYrDzMz60FsT1pP0fZ0r5TqDmhTPZsCEiJiQ30+V9EdgE0hHH6QbW42PiAtz2R7ADGB34LQmxWFmZn3oLYF04vpX1wJ7S3pnRNwraV1gG1K/C6QTF1cFrqh9ICLmSZpESj6vSyCS9gL2Ahg+fHiLwzczGzh6TCARcU07A8mOIg0XvlvSy6T4joiIU/L0VfPz9NLnpgNvrjfDiDiddD8TRo4c6SsHm5k1Sa+d6LnD+huSrpN0s6QjJS3d22cW0q6k2+fuDmycX+8t6f9auEwzM2tAX6OwDgHGA3OBJ4CDgB+3MJ5jgGMj4jcR8Y+IOBc4Dhibp0/Lz8NKnxtWmGZmZm3QVwIZA+wXEdtFxEeBnYHP587sVlgGeLlU9jKvxTmFlCi2rU3MR0RbAte3KCYzM6ujrxMJVwcuKby/nDTy6k2kS5o02wTgEElTgH8CG5GOes4BiIiQdAJwqKR7gfuBw0gXdDyvBfGYmVkP+kogSwLzam/yDvxFYKkWxbMf6XyPU4BVSM1mZwDfK9Q5mnT9rZOBlYCbgO18DoiZWXtVuZTJDyX9p/B+SeBwSbNrBRGxfzOCyUngwPzoqU4A4/LDzMw6pK8EMgl4e6nsetJdCWs8NNbMbADqNYFExKg2xWFmZv1M1fuBmJmZzccJxMzMGuIEYmZmDXECMTOzhvSYQCSdKWm5/Hqr4k2dzMzMeksKnwUOBZ4DrgZWI913w6ylRhxyaceWPXX8jh1btll/01sCmQrsJ+kK0uVLNpX0dL2KETGpBbGZmVkX6y2BfAP4GelKuAFc1EO9Zt6R0MzM+onebih1MXCxpBWBWcB6uAnLzMyyPjvGI+IZSaOBByLipTbEZGZm/UClkVURcY2kpSR9HliX1Gx1N3BeRLzQygDNzKw7VToPRNK6pHtvHAdsArwfOB64X9I6rQvPzMy6VdUTCU8EbgeGR8SWEbEl6Yq8dwAntCY0MzPrZlVPDtwceG9EPFsriIhnJX0LuLElkZl1QCfPQTHrb6oegTwPrFinfIU8zczMBpiqCWQCcIakzSUNyo8tgNOAP7YuPDMz61ZVm7AOAM4G/ga8nMsWIyWPA5sflnUDN+eYWW+qDuN9BviopHcAtVFX90TEg60KzMzMutsCXWE3JwwnDTMz6777gUhaTdLZkmZKel7S3ZK2LkyXpHGSHpc0T9JESet1MmYzs4GoqxJIvu7WdaSr/+5Iai7bj/mvwXUw8LVc/t487cravUvMzKw9uu0mUQcDT0TE5wtlU2ovJInUaT8+Ii7MZXuQksjupFFhZmbWBn0egUhaXNLekt7Uhnh2Bm6SdL6kGZJul7RvThwAawCrAlfUPhAR84BJwGZtiM/MzLI+E0i+Au8xwBKtD4e3AXsD/wK2J11CZTywT56+an6eXvrc9MK0+UjaS9JkSZNnzpzZ/IjNzAaoqn0gNwIbtzKQbDHg1ogYGxG3RcQvgB/zWgJZYBFxekSMjIiRQ4cObVqgZmYDXdU+kDOAH0laHfg7MLc4MSJubVI8T5AuE190D+lERoBp+XkY8EihzrDCNDMza4OqCeS8/HxcnWnNvKXtdcDapbK1gIfz6ymkRLEtcAuApKWBLUm34DUzszapmkDWaGkUrzkeuD5f5fd8YCNgf+BQgIgISScAh0q6l3SPksOAObyW5MzMrA2qXsrk4b5rLbyIuEXSzsCRwLdJzVTfBk4pVDsaGAycDKwE3ARsFxHPtSNGMzNLKp8HIulDpM7stwHbR8S/JX0RmBIRf2lWQBFxKdDjVfwiIoBx+WFmZh1S9Za2nwF+CzxAas6qDekdRDr5z8zMBpiqw3gPBvaMiK8CLxXKbwQ2bHZQZmbW/aomkDWBG+qUzwGWb144ZmbWX1RNII+ThtOWbQU81LxwzMysv6iaQE4Hfixp8/z+rfkihkcDP21JZGZm1tWqDuM9WtIKwJXA0sDVwAvAsRFxcgvjMzOzLlV5GG9EfEvSEcC6pCOXuyNiTssiMzOzrrag9wMJ4Pn8+uUmx2JmZv1I1fNAlsqXEJkF3AHcCcySdGK+FpWZmQ0wVY9AfgpsB3yR14bzbgr8EFgO+N/mh2ZmZt2sagL5JPDxiLiyUPYvSTOAC3ECMTMbcKoO450LPFan/DFgXvPCMTOz/qJqAvkJcLikwbWC/PrbeZqZmQ0wPTZhSfpjqWgU8JikO/P7d+XPv6E1oZmZWTfrrQ/kqdL7C0vvpzQ5FjMz60d6TCAR8YV2BmJmZv1L1T4QMzOz+VQaxitpJdIdAEcDq1BKPBGxStMjMzOzrlb1PJBzgPWAs4HppEuamJnZAFY1gYwCto6IW1sYi5mZ9SNV+0AeWoC6ZmY2AFRNCgcAP5S0gaRBrQzIzMz6h6oJ5EFgMHAr8KKkl4uPVgUnaaykkHRSoUySxkl6XNI8SRMlrdeqGMzMrL6qfSC/BlYA9qdNneiS3g/sRbp0fNHBwNeAMcB9wHeAKyWtHRHPtTouMzNLqiaQkcD7IuKuVgZTk2+f+yvSVX4PL5QLOBAYHxEX5rI9gBnA7sBp7YjPzMyqN2HdDSzfykBKTgcuiIirS+VrAKsCV9QKImIeMAnYrH3hmZlZ1QRyGHCcpA9KGibpjcVHMwOStCfwjrzMslXz8/RS+fTCtPL89pI0WdLkmTNnNi9QM7MBrmoT1mX5+Qrm7/9Qft+UkVmS1gaOBLaIiP82Y54RcTrpiIaRI0f6BEgzsyapmkBGtzSK12wKDAH+mbo7gJSctpL0ZdLZ8ADDgEcKnxsGTGtTjGZmRsUEEhHXtDqQ7A/A5FLZL4AHSEcm95MSxbbALQCSlga2BL7RphjNzIzqF1PcuLfpzbrESUQ8AzxTWvZcYFZtBJikE4BDJd1LSiiHAXOA85oRg5mZVVO1CWsyqa9DhbJif0I7z04/mnRS48nASsBNwHY+B8TMrL2qJpA1Su+XADYCvgWMbWpEJRExqvQ+SJeWH9fK5ZqZWe+q9oE8XKf4QUmzSSf6/ampUZmZWddb2CvsTgE2bEIcZmbWz1TtRC+fLChgNVIz0n1NjsnMzPqBqn0gT/L6CygK+Dewa1MjMjOzfqHREwlfAWYCD0bES80NyczM+oNuO5HQzMz6iV4TSNULJUbErOaEY2Zm/UVfRyD1+j7KosJ8zMxsEdPXjr+3iyjuQLpXuvtAzMwGoF4TSL2+D0kbAceQLmB4GvD91oRmZmbdrPKJhJLWkHQecDPwFLBuROwfEb5Lk5nZANRnApG0sqQTgXtJd/3bLCJ2jYiHWh6dmZl1rV4TiKRvAQ8BWwMfjYhtIuKWtkRmZmZdra9O9O8D84BHgb0l7V2vUkTs1OzAzMysu/WVQM6h72G8ZmY2APU1CmtMm+IwM7N+ZmEv525mZgOUE4iZmTXECcTMzBriBGJmZg3xRRC73IhDLu10CGZmdfkIxMzMGtJVCUTSWEm3SHpW0kxJEyStX6ojSeMkPS5pnqSJktbrVMxmZgNVVyUQYBRwCrAZsA3pUvFXlW5sdTDwNWA/4L3ADOBKScu1N1Qzs4Gtq/pAImL74ntJnwNmA5sDEyQJOBAYHxEX5jp7kJLI7qTLy5uZWRt02xFI2XKkGJ/O79cgXRH4ilqFiJgHTCIdtbyOpL0kTZY0eeZMX3nezKxZuj2BnAjcDtyQ36+an6eX6k0vTJtPRJweESMjYuTQoUNbEqSZ2UDUVU1YRZKOA7YAtoiIlzsdj5mZza8rj0AkHQ/sBmwTEf8qTJqWn4eVPjKsMM3MzNqg6xJIvvthLXncW5o8hZQoti3UX5p0f/br2xakmZl1VxOWpJOBzwE7A09LqvVrzImIORERkk4ADpV0L3A/cBgwBzivAyGbmQ1YXZVAgNodD/9SKv8uMC6/PhoYDJwMrATcBGwXEc+1I0AzM0u6KoFEhCrUCVIyGdfqeMzMrGdd1wdiZmb9gxOImZk1xAnEzMwa4gRiZmYNcQIxM7OGOIGYmVlDnEDMzKwhTiBmZtYQJxAzM2uIE4iZmTXECcTMzBriBGJmZg1xAjEzs4Z01dV4u9mIQy7tdAhmZl3FRyBmZtYQJxAzM2uIE4iZmTXECcTMzBriBGJmZg1xAjEzs4Y4gZiZWUP6bQKRtLekKZKel/R3SVt2OiYzs4GkXyYQSbsCJwJHAhsB1wN/kjS8o4GZmQ0g/TKBAAcBZ0XEGRFxT0TsBzwBfKXDcZmZDRj9LoFIWhJ4D3BFadIVwGbtj8jMbGDqj9fCGgIMAqaXyqcDHyxXlrQXsFd+O0fSfS2I58kmz7NbDaR1Ba/vom7ArK+OWqh17fFz/TGBLJCIOB04vVXzlzQ5Ika2av7dZCCtK3h9F3UDaX1bta79rgmLlA1fBoaVyocB09ofjpnZwNTvEkhEvAj8Hdi2NGlb0mgsMzNrg/7ahHUccK6km4HrgC8DbwJO7UAsLWse60IDaV3B67uoG0jr25J1VUS0Yr4tJ2lv4GBgNeAu4KsRMamzUZmZDRz9NoGYmVln9bs+EDMz6w5OIGZm1hAnkAZI2krSHyU9Jikkjel0TK0iaaykWyQ9K2mmpAmS1u90XK0iaR9Jd+b1fVbSDZJ27HRc7ZD/1iHppE7H0gqSxuX1Kz4W6aH/klaTdHb+331e0t2Stm7W/J1AGrMsqeP+AGBeh2NptVHAKaTLxGwDvARcJemNnQyqhR4FvglsDIwE/gr8QdK7OxpVi0l6P+mKDXd2OpYWu4808Kb2eFdnw2kdSSuSRqkK2BFYB9gPmNG0ZbgTfeFImgPsGxFndTqWdpC0LDAb2DkiJnQ6nnaQNAsYGxGndTqWVpC0AnAr8EXgcOCuiNi3s1E1n6RxwC4RscgeQRdJOhLYOiI2b9UyfARiC2o50vfm6U4H0mqSBkn6NOmIc1E+SfV04IKIuLrTgbTB2yQ9nu8l9BtJb+t0QC20M3CTpPMlzZB0u6R9JalZC3ACsQV1InA7cEOH42gZSe/KR5YvkE5O/VhE/KPDYbWEpD2BdwCHdTqWNrgJGAPsAOwJrApcL2nlTgbVQm8D9gb+BWxP+t8dD+zTrAX01zPRrQMkHQdsAWwRES93Op4Wug/YEFgB2AU4W9KoiLiro1E1maS1STdl2yIi/tvpeFotIv5UfC/pRtLOdQ/S1S0WNYsBkyNibH5/m6Q1SQmkKQMlfARilUg6HtgN2CYi/tXpeFopIl6MiAcj4u/5n+924KsdDqsVNiVd0vyfkl6S9BKwNbB3fr9UZ8NrrYiYA/wTWLPTsbTIE8DdpbJ7gKbdudVHINYnSScCuwKjI+LeTsfTAYsBi+LO9A/A5FLZL4AHSEcmL7Y7oHaStDTwTmBR7fu5Dli7VLYW8HCzFuAE0oA8Eukd+e1iwHBJGwKzIuKRjgXWApJOBj5H6pB7WtKqedKc/AtukSJpPHAp8G/SgIHdSUOZF7lzQSLiGeCZYpmkuaTv8SLVXAcg6VhgAvAIsArwbeANwNmdjKuFjif18XwLOB/YCNgfOLRZC/Aw3gZIGkX9Xy1nR8SYtgbTYpJ6+oJ8NyLGtTOWdpB0FjCa1ME6m3RexDERcXkn42oXSRNZdIfx/gbYitRsNxO4Efh2RJSbeRYZ+STYI0lHIo+Q+j5+Ek3a8TuBmJlZQ9yJbmZmDXECMTOzhjiBmJlZQ5xAzMysIU4gZmbWECcQMzNriBOIWS8knZTPjai9P0vSJS1e5tTCDY9W7fsTLYujz3XNdWqx7tKu2Kw7OIFYv1faib0k6RFJP5W0UgsWdwDw2RbMt+x7pBsezQCQNKLO3fRqjx0WZkGFeY9s4OMH5DhtAPKlTGxRcRXpkiuLA+sCZwIrki4A2TQRMbuZ8+vFcxFR73arOwB3lMpmNboQSUs2+ll4dXvMbuItJqwf8RGILSpeiIhpEfFoRFxBuvbPdrWJ+eZQP883Epon6QFJB0tarFTnWElP58cJwKDiQsrNOpImlu8hXqfOVpJulDRH0mxJN6vx+8o/ldez+HgxL+ftki6WNE3SXEm3SvpwKbapSvcGP1PSM8CvgCl58i35SGRi6TMHSHosb5NfSFqmwdhtEeMEYoucfJe5HYDiPS4WAx4DPkW6N/S3SBeV+0KhztdINxr6EulS54OAzyxkLIsDFwPXAhsAmwAnAK24n8qywJ+AbfOyLgR+L+mdpXoHAfeS7vl+KPC+XL4DqTnq44W6WwLrAx8kXZH5Y6RmKzM3YdkiY4d8F8FBwNK57KDaxHzDpO8U6k+VtDGpievnuexA4OiI+C2kX96kO7ktjOVJTWkTIuKhXLYwl8SfJOmVUtmbI2J2RNzB/M1bR0j6COmmWD8olF8TEUfX3kgakV8+VafZ7Fngy/kGYvdI+h3wAeCHC7EOtohwArFFxSRgL2Aw6Sji7cCPixUkfRn4IrB6rrcE+d4IklYg/fp+9Va9EfGKpJuAtzYaVETMylf4vVzSX4C/kO4/3uhl/3cHypdafw5A0huAw4EPk9ZlCVIyvbNUv3wPkN7cXbr75OOkoygzN2HZIuM/+S6C/4iI/YFlSPd7AEDSrqSmo7NIRxUbAqcAC9WJDLwClHuQlyi+iYgvkHa6k4CdgPskNXpk82hez+KjdkRyLPBJ0npvTVrHm3n9Os5dgOWVb3UbeL9hmb8Itqj6LvBNSW/K77cAboqIkyLi1oh4kHSUArw6mugJ4P21MqWhRe+jdzN5/TDWDcqVIuKOiDgqIkYBE0n34W62LYBzIuLCiLgTeJTCOvaidufBQb3WMitxArFFUkRMJN0P+rBcdD+wsaQPSVpTUu1XetGJwMGSdpG0NumIpa9zHP4KfEjSTpLWlnQchSYvSWtIGi9pM0mrSxoNvJvX36u6qpUlrVp6DC6s48ckbSzpXcAvea0/qDczgHnA9pKG5eY8sz45gdii7EfA/0laHTgN+C1wHnALMCJPL9f/BfAz4CbS/8ev+ljGmYXHdaT+iIsK0/9Dug/170g7+LPzPI9qcJ3+TDpSKj5qI8UOIiWDv5FGY92YX/cqIl4i3er0i6Q+josbjM0GGN+R0KzLSJoKnBQRx3Y6lqqUbn38yYi4oNOxWPv4CMSsOx2RTzxcpdOB9EbSqXn4tA1APgIx6zK5ya02kmtKaRhtV8kJbvn89omIWJARXtbPOYGYmVlD3IRlZmYNcQIxM7OGOIGYmVlDnEDMzKwhTiBmZtaQ/we/3rWPnT+fJgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lx6l15aYW1q0ETI+IqK3Mz6cVyswlIs6OiBERMWL55ZdvUuhmZtaW+4FIOgXYknQo6u12xGBmZn3T7y0QST8FdgW2jYgnCqum5McV616yYmHdFGD53F9S256AFQplzMysH/RrApF0GnOSx8N1qyeSksB2hfKLAFsxp8/jdmBxUl9IzWbAYszdL2JmZi3Wb4ewJJ0B7Al8HnhRUq3PYkZEzIiIkHQqcLSkh4EJwHdIneYXAETEQ5KuJo3I2ie//izgco/AMjPrX/3ZB7J/fryhbvn3gDH5+UnAUOAMYBngTmD7iHi1UH434HTgmjx/KXBAC+I1M7Nu9Od5ICpRJkjJZEw3ZV4E9mhaYGZmVomvhWVmZpU4gZiZWSVOIGZmVokTiJmZVeIEYmZmlTiBmJlZJU4gZmZWiROImZlV4gRiZmaVOIGYmVklTiBmZlaJE4iZmVXiBGJmZpWUSiCS1pH0ocL8dpJ+K+koSUNaF56ZmXWqsi2Q3wAbAEj6AHAJsCzwDeD41oRmZmadrGwC+TBwb36+C3BnRHyKdIfBXVsRmJmZdbayCWQI8EZ+/gngyvz8cWDFZgdlZmadr2wCeQDYT9JWpARydV7+PuC5VgRmZmadrWwC+TbwdeAm4PcRcX9e/lngrhbEZWZmHa7UPdEjYpyk5YEl8z3Ja84CXmtJZGZm1tHKDuP9DbBoXfIAmA78qOlRmZlZxyt7CGtvYGiD5UOBvZoXjpmZDRTdHsKStCygPC0j6a3C6iHAKGBq68IzM7NO1VMfyHNA5OnBBusDOK7ZQZmZWefrKYFsQ2p93AjsDLxQWPcGMDkinm1RbGZm1sG6TSARcTOApNWAJyMi+iUqMzPreKU60SNiMrCepJ9LukrSygCSPi9pg5ZGaGZmHansMN7tgbtJZ55vy5wRWWvgPhAzs0Gp7DDeHwCHRcQXmHNNLEhnpn+s2UGZmVnnK5tA1mPOBRSLXiBd1t3MzAaZsgnkBdLhq3obAk83LxwzMxsoyiaQC4AfS3o/6dyP90j6OHAycF6rgjMzs85VNoF8B5gITAYWJ51UeCPwN+CHrQnNzMw6Wdmr8b4J7C7pWNKtbRcA/h4Rj7YyODMz61ylEkhNRDxOuguhmZkNcqUTiKQvke5GuAJ1h74i4rNNjsvMzDpcqQQi6cfAIcBfgWdJHelmZjaIlW2B7AXsGhEX9mVnkrYGvgVsBKwCfCUixhbWjyXde6TozojYtFBmYdLor11JZ8TfAOwfER5ObGbWj8qOwloA+EcT9rc48ABwMDCzizLXAysXpk/VrT+VdGXgXYGtgCWByyUNaUJ8ZmZWUtkWyNnAHsCYvuwsIq4kn9GeWxuNzI6IKY1WSFoK+E9Sy+W6vGxP0vDiTwLX9CU+MzMrr2wCWRrYTdJ2wH3Am8WVEXFQE2PaUtI04CXgZuCYiJiW120ELAhcW9j3U5IeAjanQQKRtA+wD8CwYcOaGKaZ2eBWNoGsw5xDWB+uW9fMDvWrgYtJJy0OB44HbpS0UUTMBlYC3ibdKbFoal43j4g4m9SCYsSIEe78NzNrkrInEm7T6kDyfv63MHu/pHtIh6dGkRKLmZl1iLKd6G2Rb5f7NLBmXjQFGAIsV1d0xbzOzMz6SW9OJNyGNPJpGLBQcV1EbNvkuGr7XI50FeB/5UX3kPpftiNd4JF8gce1gdtaEYOZmTVW9o6Eo4GrgCWAkcB0YBnS5dwfLLszSYtLWl/S+nnfw/L8sLzuZEmbSRouaSRwGTAN+DNARLwM/Bo4SdIn8+10zyd17F9fNg4zM+u7soewvgUcEBG7kloAR0XEBsBvgRm92N8I4O95Ggp8Lz//Pqlz/CPAJcAE4FzgEWCziHi1sI1DSAnlD8Ctef+fiYi3exGHmZn1UdlDWKsz5xf+bNIJgQA/J93W9sgyG4mImwB1U2SHEtuYDRyYJzMza5OyLZDnSYevAJ4h3eIW4L2kloSZmQ0yZVsgtwDbA/cDfwR+lk8q/ARwXYtiMzOzDlY2gRwALJKfnwC8BWxBSibHtyAuMzPrcGVPJHyh8Pwd4Ecti8jMzAaELhOIpGXLbqSYYMzMbHDorgXyHD1f50q5jC+lbmY2yHSXQPrl+ldmZjYwdZlAIuLm/gzEzMwGlm7PA1FyuKRbJd0l6b8lLdLda8zMbHDo6UTCI4ETgddIFzQ8DPhZq4MyM7PO11MCGQ0cGBHbR8TngM8De0nq7nIkZmY2CPSUQFYFLi/MX0MaebVKyyIyM7MBoacEshAwszYTEQG8ASzcyqDMzKzzlTkT/QRJrxfmFwKOk/RybUFEHNT0yMzMrKP1lEDGAWvULbuNdFfCmp5ONjQzs/lQtwkkIkb2UxxmZjbAlL0fiJmZ2VycQMzMrBInEDMzq6TsDaWsTYYfeUXb9j3pxFFt27eZdb4uWyCSfiNpifx8a0lONmZm9q7uDmHtASyWn/8VKH2DKTMzm/9116qYBBwo6VrS5Us2k/Rio4IRMa4FsZmZWQfrLoEcDvwKOIp0suCfuyjnOxKamQ1C3d1Q6hLgEklLAy8A6wLT+ikuMzPrcD12jEfES5K2AR6NiLf6ISYzMxsASo2sioibJS0saS9gHdJhqweBCyJidisDNDOzzlTqREJJ6wATgFOATYBNgZ8CEySt3brwzMysU5U9E/004B/AsIjYKiK2Il2R9/+AU1sTmpmZdbKyJwduAWwcEa/UFkTEK5KOAe5oSWRmZtbRyrZAZgFLN1i+VF5nZmaDTNkEchlwjqQtJA3J05bAWcClrQvPzMw6VdkEcjDwKHALqcUxC7iZ1LF+SEsiMzOzjlZ2GO9LwOckfRCojbp6KCIea1VgZmbW2Xp1hd2cMJw0zMzMN5QyM7NqnEDMzKySfk0g+cZUl0p6RlJIGl23XpLGSHpW0kxJN0lat67MMpLOl/Ryns7PF3w0M7N+1GMCkfQeSftLWqUJ+1sceIA0qmtmg/VHAN8EDgQ2Jl3997ranRGzC4ANgR3ztCFwfhNiMzOzXugxgeQr8P4YWLCvO4uIKyPi6Ii4EHinuE6SSEOCT4yIiyLiAWBvYAlgt1xmbVLS2Ccibo+I24F9gU9L+lBf4zMzs/LKHsK6g/RLv5VWA1YCrq0tiIiZwDhg87xoM2AGcFvhdbcCrxXKzEXSPpLGSxo/ffr0VsRtZjYolR3Gew7wE0mrAveQvrDfFRH3NiGWlfLj1LrlU4H3FcpMj4go7DskTSu8fi4RcTZwNsCIESOiURkzM+u9sgnkgvx4SoN1vqWtmdkgVDaBrNbSKJIp+XFF4MnC8hUL66YAy0tSrRWS+05WKJQxM7N+UPZSJpNbHQgwkZQEtgPuBpC0CLAVcHgucztpJNdmzOkH2QxYjLn7RczMrMVKnwci6d8lXS7pQUkfyMu+JukTvdjG4pLWl7R+3vewPD8styhOBb4taSdJ6wFjSZ3mFwBExEPA1cBZkjaTtBnpisCXR8QjZeMwM7O+K3tL292BP5KuyLsac4b0DiGdu1HWCODveRoKfC8//35efxLpVrlnAOOBlYHtI+LVwjZ2I90J8Zo8/R+wZy9iMDOzJijbB3IE8PWI+F9JXyssv4M5X/49ioibAHWzPoAxeeqqzIvAHmX3aWZmrVH2ENaapP6HejOAJZsXjpmZDRRlE8izwFoNlm8NPN68cMzMbKAom0DOBn4maYs8/wFJe5P6LH7RksjMzKyjlR3Ge5KkpYDrgEWAvwKzgZMj4owWxmdtNPzIK9qy30knjmrLfs2sd0rfkTAijpH0Q2AdUsvlwYiY0bLIzMyso/Xqlraky5bMys/fbnIsZmY2gJQ9D2RhSacCL5DOu7gPeEHSaflscTMzG2TKtkB+AWwPfI05w3k3A04g3a/jq80PzczMOlnZBPJFYKeIuK6w7Il8GfWLcAIxMxt0yg7jfQ14psHyZ2h8a1ozM5vPlU0gpwPHSRpaW5CffzevMzOzQabLQ1iSLq1bNBJ4RtJ9ef4j+fWLtSY0MzPrZN31gTxfN39R3fzEJsdiZmYDSJcJJCK+0p+BmJnZwFL6hlJmZmZFpYbxSlqGdI+ObUj3H58r8UTECk2PzMzMOlrZ80DOA9YFzgWmki5pYtYS7bqII/hCjma9UTaBjAQ+HhH3tjAWMzMbQMr2gTzei7JmZjYIlE0KBwMnSPqopCGtDMjMzAaGsoewHgOGAvcCSJprZUQ4qZiZDTJlE8jvgaWAg3AnupmZUT6BjAA+FhEPtDIYMzMbOMr2gTwILNnKQMzMbGApm0C+A5wi6ZOSVpS0bHFqZYBmZtaZyh7CujI/Xsvc/R/K8+5ENzMbZMomkG1aGoWZmQ04pRJIRNzc6kDMrD3adekYXzZm4Ct7McUNu1vvS5yYmQ0+ZQ9hjSf1dRTPICz2hbgPxOYL7byQo9lAUzaBrFY3vyCwAXAMcFRTIzIzswGhbB/I5AaLH5P0MnAccFVTozIzs47X1yvsTgTWb0IcZmY2wJTtRK8/WVDAyqS7FD7S5JjMzGwAKNsH8hzzXkBRwFPAl5oakZmZDQhVTyR8B5gOPBYRbzU3JDMzGwh8IqGZmVXSbSd6/UUTu5qaFYykMZKibppSWK9c5llJMyXdJGndZu3fzMzK66kF0qjvo16U2E5vPAKMLMy/XXh+BPBNYHQudyxwnaQPRcSrTYzBzMx60NMXf3cXUdyRdK/0ZveBvBURU+oXKt1H9xDgxIi4KC/bG5gG7Aac1eQ4zMysG90mkEZ9H5I2AH4MbEX60v5Bk2NaXdKzwGzgTuDoiHiCdDb8SqRLytfimylpHLA5TiBmZv2q9ImEklaTdAFwF/A8sE5EHBQR05sYz52kw1M7Al8nJYzbJL03P4d0T/aiqYV1jeLeR9J4SeOnT29mqGZmg1uPfRf5y/tY4L+AW4HNI+LuVgQTEXNdEkXSHcATwN7AHRW3eTZwNsCIESN66s8xM7OSehqFdQzwOPBx4HMRsW2rkkcjETED+CewJlDrF1mxrtiKhXVmZtZPemqB/ACYCTwN7C9p/0aFIuKzzQ4MQNIiwIeBv5KuuzUF2A64u7B+K+DwVuzfzMy61lMCOY+eh/E2jaSTgcuAJ4EVgO8CiwHnRkRIOhU4WtLDwATgO8AM4IL+itHMzJKeRmGN7qc4at4P/B5YjnSplDuATQuXkz8JGAqcASxD6nTf3ueAmJn1v2aeANhnEfHlHtYH6QrAY/ojHjMz61pf7wdiZmaDlBOImZlV4gRiZmaVOIGYmVklTiBmZlaJE4iZmVXiBGJmZpU4gZiZWSVOIGZmVokTiJmZVeIEYmZmlTiBmJlZJU4gZmZWSUddjdfMBo/hR17Rlv1OOnFUW/Y7P3ILxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq8QXUzSzQaVdF3GE+e9Cjm6BmJlZJU4gZmZWiROImZlV4gRiZmaVOIGYmVklTiBmZlaJE4iZmVXiBGJmZpX4REIzs37SrpMYW3UCo1sgZmZWyYBNIJL2lzRR0ixJ90jaqt0xmZkNJgMygUj6EnAa8N/ABsBtwFWShrU1MDOzQWRAJhDgMGBsRJwTEQ9FxIHAv4D92hyXmdmgMeASiKSFgI2Aa+tWXQts3v8RmZkNTgNxFNZywBBgat3yqcAn6wtL2gfYJ8/OkPRIL/bzXNUg7V2ux+ZxXTbHoKtH/ajPm1i10cKBmEB6JSLOBs7u7eskjY+IES0IaVBxPTaP67I5XI/NM+AOYZF+ObwNrFi3fEVgSv+HY2Y2OA24BBIRbwD3ANvVrdqONBrLzMz6wUA9hHUKcL6ku4Bbgf8CVgF+2cR99PqwlzXkemwe12VzuB6bRBHR7hgqkbQ/cASwMvAAcGhEjGtvVGZmg8eATSBmZtZeA64PxMzMOoMTiJmZVeIEUscXaew9SVtLulTSM5JC0ui69ZI0RtKzkmZKuknSum0Kt2NJOkrS3ZJekTRd0mWS1qsr47rsgaRvSLov1+Mrkm6XNKqw3nXYJE4gBb5IY2WLkwYyHAzMbLD+COCbwIHAxsA04DpJS/RbhAPDSOBM0iV5tgXeAq6XtGyhjOuyZ08D3wY2BEYANwJ/kfRveb3rsFkiwlOegDuBc+qWPQqc0O7YBsoEzABGF+ZFutDlMYVlQ4FXgX3bHW8nT6TE/DbwGddln+vyBWBf12FzJ7dAMl+ksWVWA1aiUK8RMRMYh+u1J0uQjhK8mOddl70kaYikL5OS8W24DpvKCWSO7i7SuFL/hzPfqNWd67X3TgP+Adye512XJUn6iKQZwGzSCcZfiIj7cR021UA9E91svibpFGBLYMuIeLvd8QxAjwDrA0sBuwDnShrZxnjmS26BzOGLNLZGre5cryVJ+imwK7BtRDxRWOW6LCki3oiIxyLinog4itSSOxTXYVM5gWThizS2ykTSP+a79SppEWArXK/zkHQac5LHw3WrXZfVLQAsjOuwqXwIa279cZHG+Y6kxYEP5tkFgGGS1gdeiIgnJZ0KHC3pYWAC8B3SaK0L2hBux5J0BrAn8HngRUm1Y/IzImJGRITrsmeSTgSuAJ4iDUTYjTREepTrsMnaPQys0yZgf2ASqfPtHmDrdsfU6RPpnzMaTGPzegFjSMMnZwE3A+u1O+5Om7qowwDGFMq4Lnuux7HA5Pw/PA24HtjBddj8yRdTNDOzStwHYmZmlTiBmJlZJU4gZmZWiROImZlV4gRiZmaVOIGYmVklTiBmJUgamW+WtVwft/OApDHdrB+T9xOSjuzLvlpF0thCjLu0Ox5rHycQm6/Ufbm9KekJSSdLWqyPm74NWBl4vglh9uSRvK/TawvyXfNq7+sNSf+SdLWkPSSpH2IqOjjHZ4OcE4jNj64nfcGtTrpMxf7AyVU3JmnBSBfnmxL9c+btW3lfr9Ut/x/mvK/Pki7zfhbwZ0lD+iEuACLi5YjwhQfNCcTmS7PzF/BTEXEB8DvS9aVq98M+QtLj+X7Y90vao/ZCScPzr/xdJd0oaSawb6NDWJJ2yq+fLekpSccUWwOSVpB0Sd7PZElf7eP7ej2/r6cj4u6I+B6wE/A5YK/Cfg/L9wR/Tek+9b+StHRet1i+T/hch54kbZdbbCvm+WNzzLMlTZF0Xh9jt/mQE4gNBjOBBfPz44H/BL4BrAOcAJwlaVTda04g3Z98HeAv9RuUtBHwJ+Bi4CPAkcBRwAGFYmNJF5n8JCmB7QUM7/O7KYiIa4D7gZ0Li98BDgHWJV1I8GPkw2G5VfN7oD6ZfRW4PCKmStoZ+Bap5bYm8GngrmbGbfMHX43X5muSPkb6Er0h94McBmwfEbfkIhNzmW+QruBac3pEXFjYzgeZ22HAzRFxXJ6fIGlN4NvA6ZLWAv6ddEOoW/M29gaeoPkeBP6tNhMRpxbWTZJ0BHCJpL0j4h3gHOAOSe+LiGckLUNKcF/Mr1mVdKHBayPiTeBJYHwL4rYBzi0Qmx/tKGmGpFmkfoJxwIGk1sQiwNV5/Yx829P9gDXqttHTF+bapEv+F/0NeJ+kJfP6dyj8co+IycCzFd9Td0S6am+akbaVdJ2kpyW9SmolLUS+ZWtEjCe1WvbOL9kNeAG4Ks//iVRPEyX9WtIXJS3cgrhtgHMCsfnRONLtTD8ELBIRO0XENOZ83j+T19emdYHt67ZR34HdG9HF81ZZh9yykbQqqSX1EKlFsRFzDlctVHjNr4DR+flXgXMj3zo3Ip4i1d2+wCvAT4B7mjCSzeYzTiA2P3o90u1MJ+dDMDUPku4RsWpeX5wm93IfDwFb1C3bEng6Il4FHib9f32stlLSMNINyppG0g7AekDtcNsIUqI4NCJuj4gJXezzd8D7JR0AbEga4fWuiJgVEVdExKHAxqQkW/9+bZBzH4gNGhHxqqSTgZPzaKlxwOLApsA7EXF2Lzb3E+DufFLgBaQv2W8CR+d9PSLpalIH/T6kjvxT8mNVi+a7FL6HNJz3U8ARwCXAb3OZR0mJ6xBJF+f3dkj9hiLiJUl/yu9jXEQ8WlsnaXTex52kO/V9CXgzb9vsXW6B2GDzXdLd6L4F/BO4jjSCaWJvNhIR95IOEe0MPACcmKefF4qNztu9EbiMlGgm9SH2r5A6t5/I29uMdNvlLxQOP91HOtHvMFKL62uk99rIr0mtlV/XLX+JNFLtFtJ72xnYKSJ6VUc2//MdCc06SG7R7BIR6/XDvr5EOhFxlYh4vcLrA/hicbSaDS5ugZh1nrXzCLHDWrFxSYtKWp10uO2c3iYPSb/Mo9dskHMLxKyDSFoWWDbPPhcRL7VgH2OAY0jDjj8XEa/08vUrAEvm2X81uOSKDRJOIGZmVokPYZmZWSVOIGZmVokTiJmZVeIEYmZmlTiBmJlZJf8Pto+fbnoEPt8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.concatenate([outputPopulation.rad_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.rad_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.rad_m3[outputPopulation.rad_m3>0]], axis=0))\n",
    "plt.title(\"Expected Obs. Radius Distribution\")\n",
    "plt.ylabel(\"Number of Planets\")\n",
    "plt.xlabel(\"Radius [Earth]\")\n",
    "plt.show()\n",
    "\n",
    "plt.hist(np.concatenate([outputPopulation.per_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.per_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.per_m3[outputPopulation.rad_m3>0]], axis=0))\n",
    "plt.title(\"Expected Obs. Period Distribution\")\n",
    "plt.ylabel(\"Number of Planets\")\n",
    "plt.xlabel(\"Period [Days]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "391\n",
      "283\n",
      "69\n",
      "214\n"
     ]
    }
   ],
   "source": [
    "import emcee\n",
    "from scipy import stats\n",
    "from scipy.special import gamma, factorial\n",
    "from scipy.stats import norm, uniform, beta, poisson, binom, binned_statistic\n",
    "planet=pd.read_csv(\"planet_sample.csv\",sep=\",\", engine='python', header=0)\n",
    "planet=planet[planet['EPIC'].isin(stellar.EPIC.values.tolist())]\n",
    "print(len(planet))\n",
    "planet=planet.drop_duplicates([\"CAND\"])\n",
    "planet=planet[(planet.Rad>1) & (planet.Rad<4)]\n",
    "print(len(planet))\n",
    "# planet=planet[planet['EPIC'].isin(stellar.EPIC.values.tolist())]\n",
    "# planet=pd.merge(planet,stellar[[\"EPIC\", \"FeH\", \"U_FeH\",\"k2_kepmag\"]], on=\"EPIC\", how=\"left\")\n",
    "\n",
    "# planet.FeH=planet[\"FeH_y\"]\n",
    "\n",
    "# planet=planet.drop_duplicates([\"CAND\"])\n",
    "# # planet[\"FeH\"]=planet[\"FeH_y\"]\n",
    "# plt.scatter(planet.Rad,1/planet.MajAxis**2*215**2*(planet.Teff/5700)**4)\n",
    "# plt.yscale('log')\n",
    "# # plt.ylim([500,2500])\n",
    "# plt.xlim([0,30])\n",
    "# planetNew=planet[1/planet.MajAxis**2*215**2*(planet.Teff/5700)**4>1e3]\n",
    "\n",
    "perBr=np.arange(.5,40)\n",
    "radBr=10**(-0.09*np.log10(perBr) + 0.37)\n",
    "with PdfPages('k2planet.pdf')as pdf:\n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    plt.scatter(planet.Period[(np.log10(planet.Rad)<-0.09*np.log10(planet.Period) + 0.37)],planet.Rad[(np.log10(planet.Rad)<-0.09*np.log10(planet.Period) + 0.37)], color=\"#43AF7F\", s=20)\n",
    "    plt.scatter(planet.Period[(np.log10(planet.Rad)>-0.09*np.log10(planet.Period) + 0.37) & (planet.Rad<4)],planet.Rad[(np.log10(planet.Rad)>-0.09*np.log10(planet.Period) + 0.37)& (planet.Rad<4)],color=\"#39558C\", s=20)\n",
    "    plt.plot(perBr,radBr, color= \"grey\", ls=\":\")\n",
    "    plt.xlim([.5,40])\n",
    "    plt.ylim([1,4])\n",
    "    plt.yscale('log')\n",
    "    plt.xscale('log')\n",
    "    plt.xlabel('Period [days]')\n",
    "    plt.ylabel(\"Radius [$R_{\\oplus}$]\")\n",
    "    plt.yticks([1, 2, 3,4], ['1', \"2\", \"3\", \"4\"])\n",
    "    plt.xticks([ 1,3, 10,30], ['1', \"3\", \"10\", \"30\"])\n",
    "    pdf.savefig(bbox_inches = \"tight\", dpi=300)\n",
    "    plt.close()\n",
    "print(len(planet.Period[(np.log10(planet.Rad)<-0.09*np.log10(planet.Period) + 0.37)]))\n",
    "print(len(planet.Period[(np.log10(planet.Rad)>-0.09*np.log10(planet.Period) + 0.37)]))\n",
    "# plt.scatter(planet.Period[(planet.Rad>1) & (planet.Rad<1.8)],planet.Rad[(planet.Rad>1)& (planet.Rad<1.8)])\n",
    "# plt.scatter(planet.Period[(planet.Rad>1.8) & (planet.Rad<4)],planet.Rad[(planet.Rad>1.8)& (planet.Rad<4)])\n",
    "# plt.scatter(planet.Period[(planet.Rad>8)],planet.Rad[(planet.Rad>8)])\n",
    "\n",
    "# plt.scatter(planet.Period[(planet.Rad>4) & (planet.Rad<8)],planet.Rad[(planet.Rad>4)& (planet.Rad<8)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        vertical-align: top;\n",
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       "\n",
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       "        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>EPIC</th>\n",
       "      <th>CAMP</th>\n",
       "      <th>CAND</th>\n",
       "      <th>MULT</th>\n",
       "      <th>Score</th>\n",
       "      <th>Period</th>\n",
       "      <th>u_Period</th>\n",
       "      <th>U_Period</th>\n",
       "      <th>Ratio</th>\n",
       "      <th>u_Ratio</th>\n",
       "      <th>...</th>\n",
       "      <th>M*</th>\n",
       "      <th>u_M*</th>\n",
       "      <th>U_M*</th>\n",
       "      <th>Teff</th>\n",
       "      <th>u_Teff</th>\n",
       "      <th>logg</th>\n",
       "      <th>u_logg</th>\n",
       "      <th>FeH</th>\n",
       "      <th>u_FeH</th>\n",
       "      <th>SpT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>203776696</td>\n",
       "      <td>2</td>\n",
       "      <td>2.037767e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.90</td>\n",
       "      <td>3.535323</td>\n",
       "      <td>0.000090</td>\n",
       "      <td>0.000086</td>\n",
       "      <td>0.075440</td>\n",
       "      <td>0.001043</td>\n",
       "      <td>...</td>\n",
       "      <td>2.143</td>\n",
       "      <td>0.678</td>\n",
       "      <td>1.043</td>\n",
       "      <td>6177</td>\n",
       "      <td>138</td>\n",
       "      <td>4.118</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.330</td>\n",
       "      <td>0.235</td>\n",
       "      <td>F2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>204748201</td>\n",
       "      <td>2</td>\n",
       "      <td>2.047482e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.68</td>\n",
       "      <td>3.682157</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>0.000031</td>\n",
       "      <td>0.109754</td>\n",
       "      <td>0.000237</td>\n",
       "      <td>...</td>\n",
       "      <td>0.893</td>\n",
       "      <td>0.279</td>\n",
       "      <td>0.400</td>\n",
       "      <td>6021</td>\n",
       "      <td>138</td>\n",
       "      <td>4.241</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.460</td>\n",
       "      <td>0.235</td>\n",
       "      <td>G0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>161</th>\n",
       "      <td>210958990</td>\n",
       "      <td>4</td>\n",
       "      <td>2.109590e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.98</td>\n",
       "      <td>1.702324</td>\n",
       "      <td>0.000023</td>\n",
       "      <td>0.000023</td>\n",
       "      <td>0.149780</td>\n",
       "      <td>0.001425</td>\n",
       "      <td>...</td>\n",
       "      <td>1.726</td>\n",
       "      <td>0.197</td>\n",
       "      <td>0.211</td>\n",
       "      <td>6256</td>\n",
       "      <td>26</td>\n",
       "      <td>4.359</td>\n",
       "      <td>0.043</td>\n",
       "      <td>0.160</td>\n",
       "      <td>0.025</td>\n",
       "      <td>F8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>211002562</td>\n",
       "      <td>4</td>\n",
       "      <td>2.110026e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.98</td>\n",
       "      <td>3.347857</td>\n",
       "      <td>0.000033</td>\n",
       "      <td>0.000033</td>\n",
       "      <td>0.115895</td>\n",
       "      <td>0.000745</td>\n",
       "      <td>...</td>\n",
       "      <td>1.491</td>\n",
       "      <td>0.465</td>\n",
       "      <td>0.663</td>\n",
       "      <td>5826</td>\n",
       "      <td>138</td>\n",
       "      <td>3.939</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.259</td>\n",
       "      <td>0.235</td>\n",
       "      <td>G0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>286</th>\n",
       "      <td>212688722</td>\n",
       "      <td>6</td>\n",
       "      <td>2.126887e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.80</td>\n",
       "      <td>5.734172</td>\n",
       "      <td>0.001401</td>\n",
       "      <td>0.000787</td>\n",
       "      <td>0.020669</td>\n",
       "      <td>0.001015</td>\n",
       "      <td>...</td>\n",
       "      <td>1.147</td>\n",
       "      <td>0.371</td>\n",
       "      <td>0.525</td>\n",
       "      <td>5192</td>\n",
       "      <td>138</td>\n",
       "      <td>3.618</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.447</td>\n",
       "      <td>0.235</td>\n",
       "      <td>G8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>327</th>\n",
       "      <td>217671466</td>\n",
       "      <td>7</td>\n",
       "      <td>2.176715e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.86</td>\n",
       "      <td>1.915295</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>0.090127</td>\n",
       "      <td>0.000207</td>\n",
       "      <td>...</td>\n",
       "      <td>1.157</td>\n",
       "      <td>0.357</td>\n",
       "      <td>0.514</td>\n",
       "      <td>5621</td>\n",
       "      <td>138</td>\n",
       "      <td>4.150</td>\n",
       "      <td>0.150</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.235</td>\n",
       "      <td>G4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>329</th>\n",
       "      <td>218131080</td>\n",
       "      <td>7</td>\n",
       "      <td>2.181311e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.98</td>\n",
       "      <td>3.142733</td>\n",
       "      <td>0.000015</td>\n",
       "      <td>0.000015</td>\n",
       "      <td>0.063973</td>\n",
       "      <td>0.000164</td>\n",
       "      <td>...</td>\n",
       "      <td>0.639</td>\n",
       "      <td>0.218</td>\n",
       "      <td>0.343</td>\n",
       "      <td>6119</td>\n",
       "      <td>138</td>\n",
       "      <td>4.349</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.355</td>\n",
       "      <td>0.235</td>\n",
       "      <td>F2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>448</th>\n",
       "      <td>246331347</td>\n",
       "      <td>12</td>\n",
       "      <td>2.463313e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.82</td>\n",
       "      <td>1.082361</td>\n",
       "      <td>0.000052</td>\n",
       "      <td>0.000057</td>\n",
       "      <td>0.038088</td>\n",
       "      <td>0.001916</td>\n",
       "      <td>...</td>\n",
       "      <td>1.159</td>\n",
       "      <td>0.351</td>\n",
       "      <td>0.530</td>\n",
       "      <td>5556</td>\n",
       "      <td>138</td>\n",
       "      <td>4.032</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.376</td>\n",
       "      <td>0.235</td>\n",
       "      <td>G7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>474</th>\n",
       "      <td>246911830</td>\n",
       "      <td>13</td>\n",
       "      <td>2.469118e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.82</td>\n",
       "      <td>2.626702</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>0.098947</td>\n",
       "      <td>0.000151</td>\n",
       "      <td>...</td>\n",
       "      <td>1.376</td>\n",
       "      <td>0.422</td>\n",
       "      <td>0.591</td>\n",
       "      <td>6692</td>\n",
       "      <td>138</td>\n",
       "      <td>4.107</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.098</td>\n",
       "      <td>0.235</td>\n",
       "      <td>F3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>488</th>\n",
       "      <td>247281516</td>\n",
       "      <td>13</td>\n",
       "      <td>2.472815e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.78</td>\n",
       "      <td>6.770834</td>\n",
       "      <td>0.000025</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>0.103924</td>\n",
       "      <td>0.000145</td>\n",
       "      <td>...</td>\n",
       "      <td>1.895</td>\n",
       "      <td>0.593</td>\n",
       "      <td>0.809</td>\n",
       "      <td>6310</td>\n",
       "      <td>138</td>\n",
       "      <td>4.014</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.021</td>\n",
       "      <td>0.235</td>\n",
       "      <td>F5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>247382651</td>\n",
       "      <td>13</td>\n",
       "      <td>2.473827e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.86</td>\n",
       "      <td>1.971544</td>\n",
       "      <td>0.000523</td>\n",
       "      <td>0.000282</td>\n",
       "      <td>0.032426</td>\n",
       "      <td>0.001233</td>\n",
       "      <td>...</td>\n",
       "      <td>2.256</td>\n",
       "      <td>0.686</td>\n",
       "      <td>0.997</td>\n",
       "      <td>7678</td>\n",
       "      <td>138</td>\n",
       "      <td>3.953</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>0.235</td>\n",
       "      <td>AV</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>247708770</td>\n",
       "      <td>13</td>\n",
       "      <td>2.477088e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.82</td>\n",
       "      <td>4.420394</td>\n",
       "      <td>0.000571</td>\n",
       "      <td>0.000533</td>\n",
       "      <td>0.032784</td>\n",
       "      <td>0.000891</td>\n",
       "      <td>...</td>\n",
       "      <td>2.489</td>\n",
       "      <td>0.955</td>\n",
       "      <td>1.607</td>\n",
       "      <td>5943</td>\n",
       "      <td>138</td>\n",
       "      <td>3.917</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.240</td>\n",
       "      <td>0.235</td>\n",
       "      <td>F8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>508</th>\n",
       "      <td>247909155</td>\n",
       "      <td>13</td>\n",
       "      <td>2.479092e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.81</td>\n",
       "      <td>1.741584</td>\n",
       "      <td>0.000164</td>\n",
       "      <td>0.000157</td>\n",
       "      <td>0.093735</td>\n",
       "      <td>0.003225</td>\n",
       "      <td>...</td>\n",
       "      <td>0.688</td>\n",
       "      <td>0.456</td>\n",
       "      <td>0.988</td>\n",
       "      <td>5008</td>\n",
       "      <td>167</td>\n",
       "      <td>4.718</td>\n",
       "      <td>0.165</td>\n",
       "      <td>-0.200</td>\n",
       "      <td>0.573</td>\n",
       "      <td>K2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>549</th>\n",
       "      <td>248740905</td>\n",
       "      <td>14</td>\n",
       "      <td>2.487409e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.82</td>\n",
       "      <td>2.491154</td>\n",
       "      <td>0.000039</td>\n",
       "      <td>0.000038</td>\n",
       "      <td>0.050971</td>\n",
       "      <td>0.000384</td>\n",
       "      <td>...</td>\n",
       "      <td>1.490</td>\n",
       "      <td>0.094</td>\n",
       "      <td>0.103</td>\n",
       "      <td>6362</td>\n",
       "      <td>15</td>\n",
       "      <td>4.122</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.065</td>\n",
       "      <td>0.013</td>\n",
       "      <td>F6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>620</th>\n",
       "      <td>250062008</td>\n",
       "      <td>15</td>\n",
       "      <td>2.500620e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.76</td>\n",
       "      <td>23.510312</td>\n",
       "      <td>0.004800</td>\n",
       "      <td>0.005360</td>\n",
       "      <td>0.025405</td>\n",
       "      <td>0.000509</td>\n",
       "      <td>...</td>\n",
       "      <td>2.721</td>\n",
       "      <td>0.830</td>\n",
       "      <td>1.189</td>\n",
       "      <td>7251</td>\n",
       "      <td>138</td>\n",
       "      <td>4.005</td>\n",
       "      <td>0.150</td>\n",
       "      <td>-0.064</td>\n",
       "      <td>0.235</td>\n",
       "      <td>AIV</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>743</th>\n",
       "      <td>211309648</td>\n",
       "      <td>18</td>\n",
       "      <td>2.113096e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.90</td>\n",
       "      <td>3.139404</td>\n",
       "      <td>0.000072</td>\n",
       "      <td>0.000073</td>\n",
       "      <td>0.098272</td>\n",
       "      <td>0.001064</td>\n",
       "      <td>...</td>\n",
       "      <td>0.952</td>\n",
       "      <td>0.288</td>\n",
       "      <td>0.431</td>\n",
       "      <td>5716</td>\n",
       "      <td>138</td>\n",
       "      <td>4.047</td>\n",
       "      <td>0.151</td>\n",
       "      <td>-0.136</td>\n",
       "      <td>0.198</td>\n",
       "      <td>G3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>750</th>\n",
       "      <td>211393988</td>\n",
       "      <td>18</td>\n",
       "      <td>2.113940e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.92</td>\n",
       "      <td>4.871902</td>\n",
       "      <td>0.000131</td>\n",
       "      <td>0.000137</td>\n",
       "      <td>0.077531</td>\n",
       "      <td>0.000663</td>\n",
       "      <td>...</td>\n",
       "      <td>1.564</td>\n",
       "      <td>0.477</td>\n",
       "      <td>0.699</td>\n",
       "      <td>6466</td>\n",
       "      <td>138</td>\n",
       "      <td>4.113</td>\n",
       "      <td>0.151</td>\n",
       "      <td>-0.239</td>\n",
       "      <td>0.198</td>\n",
       "      <td>F0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>789</th>\n",
       "      <td>211962097</td>\n",
       "      <td>18</td>\n",
       "      <td>2.119621e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.92</td>\n",
       "      <td>5.839233</td>\n",
       "      <td>0.000112</td>\n",
       "      <td>0.000095</td>\n",
       "      <td>0.094654</td>\n",
       "      <td>0.000509</td>\n",
       "      <td>...</td>\n",
       "      <td>1.677</td>\n",
       "      <td>0.525</td>\n",
       "      <td>0.730</td>\n",
       "      <td>6187</td>\n",
       "      <td>138</td>\n",
       "      <td>3.986</td>\n",
       "      <td>0.151</td>\n",
       "      <td>-0.194</td>\n",
       "      <td>0.198</td>\n",
       "      <td>F2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>799</th>\n",
       "      <td>212085740</td>\n",
       "      <td>18</td>\n",
       "      <td>2.120857e+08</td>\n",
       "      <td>0</td>\n",
       "      <td>0.72</td>\n",
       "      <td>2.422830</td>\n",
       "      <td>0.000098</td>\n",
       "      <td>0.000113</td>\n",
       "      <td>0.072474</td>\n",
       "      <td>0.001386</td>\n",
       "      <td>...</td>\n",
       "      <td>0.985</td>\n",
       "      <td>0.115</td>\n",
       "      <td>0.130</td>\n",
       "      <td>5723</td>\n",
       "      <td>29</td>\n",
       "      <td>4.294</td>\n",
       "      <td>0.048</td>\n",
       "      <td>-0.178</td>\n",
       "      <td>0.028</td>\n",
       "      <td>G3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>19 rows × 37 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          EPIC  CAMP          CAND  MULT  Score     Period  u_Period  \\\n",
       "31   203776696     2  2.037767e+08     0   0.90   3.535323  0.000090   \n",
       "40   204748201     2  2.047482e+08     0   0.68   3.682157  0.000029   \n",
       "161  210958990     4  2.109590e+08     0   0.98   1.702324  0.000023   \n",
       "165  211002562     4  2.110026e+08     0   0.98   3.347857  0.000033   \n",
       "286  212688722     6  2.126887e+08     0   0.80   5.734172  0.001401   \n",
       "327  217671466     7  2.176715e+08     0   0.86   1.915295  0.000006   \n",
       "329  218131080     7  2.181311e+08     0   0.98   3.142733  0.000015   \n",
       "448  246331347    12  2.463313e+08     0   0.82   1.082361  0.000052   \n",
       "474  246911830    13  2.469118e+08     0   0.82   2.626702  0.000007   \n",
       "488  247281516    13  2.472815e+08     0   0.78   6.770834  0.000025   \n",
       "491  247382651    13  2.473827e+08     0   0.86   1.971544  0.000523   \n",
       "503  247708770    13  2.477088e+08     0   0.82   4.420394  0.000571   \n",
       "508  247909155    13  2.479092e+08     0   0.81   1.741584  0.000164   \n",
       "549  248740905    14  2.487409e+08     0   0.82   2.491154  0.000039   \n",
       "620  250062008    15  2.500620e+08     0   0.76  23.510312  0.004800   \n",
       "743  211309648    18  2.113096e+08     0   0.90   3.139404  0.000072   \n",
       "750  211393988    18  2.113940e+08     0   0.92   4.871902  0.000131   \n",
       "789  211962097    18  2.119621e+08     0   0.92   5.839233  0.000112   \n",
       "799  212085740    18  2.120857e+08     0   0.72   2.422830  0.000098   \n",
       "\n",
       "     U_Period     Ratio   u_Ratio ...      M*   u_M*   U_M*  Teff  u_Teff  \\\n",
       "31   0.000086  0.075440  0.001043 ...   2.143  0.678  1.043  6177     138   \n",
       "40   0.000031  0.109754  0.000237 ...   0.893  0.279  0.400  6021     138   \n",
       "161  0.000023  0.149780  0.001425 ...   1.726  0.197  0.211  6256      26   \n",
       "165  0.000033  0.115895  0.000745 ...   1.491  0.465  0.663  5826     138   \n",
       "286  0.000787  0.020669  0.001015 ...   1.147  0.371  0.525  5192     138   \n",
       "327  0.000006  0.090127  0.000207 ...   1.157  0.357  0.514  5621     138   \n",
       "329  0.000015  0.063973  0.000164 ...   0.639  0.218  0.343  6119     138   \n",
       "448  0.000057  0.038088  0.001916 ...   1.159  0.351  0.530  5556     138   \n",
       "474  0.000007  0.098947  0.000151 ...   1.376  0.422  0.591  6692     138   \n",
       "488  0.000026  0.103924  0.000145 ...   1.895  0.593  0.809  6310     138   \n",
       "491  0.000282  0.032426  0.001233 ...   2.256  0.686  0.997  7678     138   \n",
       "503  0.000533  0.032784  0.000891 ...   2.489  0.955  1.607  5943     138   \n",
       "508  0.000157  0.093735  0.003225 ...   0.688  0.456  0.988  5008     167   \n",
       "549  0.000038  0.050971  0.000384 ...   1.490  0.094  0.103  6362      15   \n",
       "620  0.005360  0.025405  0.000509 ...   2.721  0.830  1.189  7251     138   \n",
       "743  0.000073  0.098272  0.001064 ...   0.952  0.288  0.431  5716     138   \n",
       "750  0.000137  0.077531  0.000663 ...   1.564  0.477  0.699  6466     138   \n",
       "789  0.000095  0.094654  0.000509 ...   1.677  0.525  0.730  6187     138   \n",
       "799  0.000113  0.072474  0.001386 ...   0.985  0.115  0.130  5723      29   \n",
       "\n",
       "      logg  u_logg    FeH  u_FeH  SpT  \n",
       "31   4.118   0.150 -0.330  0.235   F2  \n",
       "40   4.241   0.150 -0.460  0.235   G0  \n",
       "161  4.359   0.043  0.160  0.025   F8  \n",
       "165  3.939   0.150 -0.259  0.235   G0  \n",
       "286  3.618   0.150 -0.447  0.235   G8  \n",
       "327  4.150   0.150  0.000  0.235   G4  \n",
       "329  4.349   0.150 -0.355  0.235   F2  \n",
       "448  4.032   0.150 -0.376  0.235   G7  \n",
       "474  4.107   0.150 -0.098  0.235   F3  \n",
       "488  4.014   0.150 -0.021  0.235   F5  \n",
       "491  3.953   0.150 -0.003  0.235   AV  \n",
       "503  3.917   0.150 -0.240  0.235   F8  \n",
       "508  4.718   0.165 -0.200  0.573   K2  \n",
       "549  4.122   0.024  0.065  0.013   F6  \n",
       "620  4.005   0.150 -0.064  0.235  AIV  \n",
       "743  4.047   0.151 -0.136  0.198   G3  \n",
       "750  4.113   0.151 -0.239  0.198   F0  \n",
       "789  3.986   0.151 -0.194  0.198   F2  \n",
       "799  4.294   0.048 -0.178  0.028   G3  \n",
       "\n",
       "[19 rows x 37 columns]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "planetNew[(planetNew.Rad>6) & (planetNew.Rad<30) & (planetNew.b<.8)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "93 Planet Candidates Observed\n",
      "109 Expected Obs. Planet Candidates\n"
     ]
    }
   ],
   "source": [
    "###### Planets only in Samaple ###\n",
    "planet=planet[planet['EPIC'].isin(stellar.EPIC.values.tolist())]\n",
    "planet=planet.drop_duplicates([\"CAND\"])\n",
    "\n",
    "planet=planet[(planet.Period>.5) & (planet.Period<50)]\n",
    "planet=planet[(planet.Rad<4) & (planet.Rad>.5)]\n",
    "\n",
    "print(len(planet), \"Planet Candidates Observed\")\n",
    "\n",
    "params = ExoMult.PopParams(stellar=stellar)\n",
    "\n",
    "####Distribution Limits####\n",
    "params.pMax=50 #days\n",
    "params.pMin=0.5 #days\n",
    "params.rMax=4 #Earth Radii\n",
    "params.rMin=0.5 #Earth Radii\n",
    "\n",
    "####Kepler Distribtuion Shape####\n",
    "# params.alpha_1=-0.8416112186408303\n",
    "# # params.alpha_1=-10\n",
    "# # params.rad_break=3.03 #Earth Radii\n",
    "# params.rad_break=1.8 #Earth Radii\n",
    "# params.alpha_2=-10\n",
    "# # params.alpha_2=-2.5\n",
    "# # params.alpha_2=-8\n",
    "# params.beta_1=0.7425142511899641\n",
    "# # params.beta_1=.5\n",
    "# params.per_break=10.065194185750743  #days\n",
    "# # params.per_break=10  #days\n",
    "# params.beta_2=-0.1775957773311858\n",
    "params.mut_Ray=0 #degrees\n",
    "\n",
    "# params.alpha_1=-0.5717755446364347\n",
    "# params.rad_break=1 #Earth Radii\n",
    "# params.alpha_2=-0.5717755446364347\n",
    "# params.beta_1=0.9099833959997778\n",
    "# params.per_break=6.574778525573955  #days\n",
    "# params.beta_2=-0.7864727916655461\n",
    "\n",
    "# params.alpha_1=-1.0001\n",
    "params.rad_break=1.8 #Earth Radii\n",
    "# params.alpha_2=-1.0001\n",
    "# params.beta_1=-1.0001\n",
    "#params.per_break=10  #days\n",
    "# params.beta_2=-1.0001\n",
    "params.mut_Ray=0 #degrees\n",
    "\n",
    "####Occurrence Factor (Number of Planets Per Star)####\n",
    "occurFact=2.55471253258464\n",
    "\n",
    "params.frac_m1=occurFact\n",
    "params.frac_m2=params.frac_m1-1\n",
    "params.frac_m3=params.frac_m2-1\n",
    "params.frac_m4=params.frac_m3-1\n",
    "params.frac_m5=params.frac_m4-1\n",
    "outputPopulation=ExoMult.Simulate(params)\n",
    "print(np.sum(outputPopulation.m), \"Expected Obs. Planet Candidates\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "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"
    }
   ],
   "source": [
    "plt.hist(planet.Rad, color=\"Red\")\n",
    "plt.title(\"Observed Radius Distribution\")\n",
    "plt.ylabel(\"Number of Planets\")\n",
    "plt.xlabel(\"Radius [Earth]\")\n",
    "plt.show()\n",
    "plt.hist(planet.Period, color=\"Red\")\n",
    "plt.title(\"Observed Period Distribution\")\n",
    "plt.ylabel(\"Number of Planets\")\n",
    "plt.xlabel(\"Period [Days]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.7750962156775406\n",
      "-0.47639231038615565\n"
     ]
    }
   ],
   "source": [
    "radiusObs = np.sort(planet.Rad)\n",
    "periodObs = np.sort(planet.Period)\n",
    "covarObs=(planet.Rad-np.mean(planet.Rad))*(planet.Period-np.mean(planet.Period))\n",
    "covarObs=np.sort(covarObs)\n",
    "# radiusExp=np.sort(np.concatenate([outputPopulation.rad_m1[outputPopulation.rad_m1>0],\n",
    "#                          outputPopulation.rad_m2[outputPopulation.rad_m2>0],\n",
    "#                          outputPopulation.rad_m3[outputPopulation.rad_m3>0]], axis=0))\n",
    "# periodExp=np.sort(np.concatenate([outputPopulation.per_m1[outputPopulation.rad_m1>0],\n",
    "#                          outputPopulation.per_m2[outputPopulation.rad_m2>0],\n",
    "#                          outputPopulation.per_m3[outputPopulation.rad_m3>0]], axis=0))\n",
    "\n",
    "radiusExp=np.sort(outputPopulation.rad_m1[outputPopulation.rad_m1>0])\n",
    "periodExp=np.sort(outputPopulation.per_m1[outputPopulation.rad_m1>0])\n",
    "covar=(outputPopulation.rad_m1[outputPopulation.rad_m1>0]-np.mean(outputPopulation.rad_m1[outputPopulation.rad_m1>0]))*(outputPopulation.per_m1[outputPopulation.rad_m1>0]-np.mean(outputPopulation.per_m1[outputPopulation.rad_m1>0]))\n",
    "covar=np.sort(covar)\n",
    "\n",
    "yObs = np.arange(len(radiusObs)) / float(len(radiusObs))\n",
    "\n",
    "yExp = np.arange(len(radiusExp)) / float(len(radiusExp))\n",
    "\n",
    "plt.plot(radiusObs,yObs, color=\"red\", label=\"Obs. Planets\")\n",
    "plt.plot(radiusExp,yExp, label=\"Exp. Planets\")\n",
    "plt.show()\n",
    "# plt.plot(covarObs,yObs,color=\"red\", label=\"Obs. Planets\")\n",
    "# plt.plot(covar,yExp, label=\"Exp. Planets\")\n",
    "plt.plot(periodObs,yObs,color=\"red\", label=\"Obs. Planets\")\n",
    "plt.plot(periodExp,yExp, label=\"Exp. Planets\")\n",
    "plt.show()\n",
    "\n",
    "pv_rad=stats.anderson_ksamp([radiusObs,radiusExp]).statistic\n",
    "pv_per=stats.anderson_ksamp([periodObs,periodExp]).statistic\n",
    "\n",
    "print(pv_rad)\n",
    "print(pv_per)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.7194751330029803\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import gamma, factorial\n",
    "# from scipy.stats import norm, uniform, beta, poisson, binom, binned_statistic\n",
    "def logSamePois(x1,x2):\n",
    "    if (x1==0) | (x2==0):\n",
    "        return(np.log(2**(-x1-x2-1)*gamma(x1+x2+1)/(factorial(x1)* factorial(x2))))\n",
    "    else:\n",
    "        return(np.log(2)*(-x1-x2-1)+(x1+x2)*np.log((x1+x2))-(x1+x2)-x1*np.log(x1)+x1-x2*np.log(x2)+x2)\n",
    "        \n",
    "\n",
    "likelihood=logSamePois(10,9)#-pv_rad-pv_per\n",
    "print(likelihood)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "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": [
    "samplesSuperEarths_Kepler=pd.read_csv(\"./Kepler_chains/SuperEarths.csv\", delimiter=\",\", names=[\"occurFact\", \"Alpha\", \"Beta_1\",\"Per_Break\",\"Beta_2\"])\n",
    "\n",
    "alp=np.median(samplesSuperEarths_Kepler.Alpha)\n",
    "aCon=np.median(samplesSuperEarths_Kepler.Beta_1)\n",
    "bCon=np.median(samplesSuperEarths_Kepler.Beta_2)\n",
    "xmix=np.median(samplesSuperEarths_Kepler.Per_Break)\n",
    "\n",
    "low_alp=alp-np.sort(samplesSuperEarths_Kepler.Alpha)[int(len(samplesSuperEarths_Kepler)*.16)]\n",
    "low_aCon=aCon-np.sort(samplesSuperEarths_Kepler.Beta_1)[int(len(samplesSuperEarths_Kepler)*.16)]\n",
    "low_bCon=bCon-np.sort(samplesSuperEarths_Kepler.Beta_2)[int(len(samplesSuperEarths_Kepler)*.16)]\n",
    "low_xmix=xmix-np.sort(samplesSuperEarths_Kepler.Per_Break)[int(len(samplesSuperEarths_Kepler)*.16)]\n",
    "\n",
    "high_alp=np.sort(samplesSuperEarths_Kepler.Alpha)[int(len(samplesSuperEarths_Kepler)*.84)]-alp\n",
    "high_aCon=np.sort(samplesSuperEarths_Kepler.Beta_1)[int(len(samplesSuperEarths_Kepler)*.84)]-aCon\n",
    "high_bCon=np.sort(samplesSuperEarths_Kepler.Beta_2)[int(len(samplesSuperEarths_Kepler)*.84)]-bCon\n",
    "high_xmix=np.sort(samplesSuperEarths_Kepler.Per_Break)[int(len(samplesSuperEarths_Kepler)*.84)]-xmix\n",
    "plt.hist(stellar.FeH[stellar.FeH>-.1])\n",
    "\n",
    "\n",
    "ndim = 1\n",
    "nwalkers = 20\n",
    "pos_min = np.array([0])#,-2,0,5,0])\n",
    "pos_max = np.array([.4])#,-1,1,7,2])\n",
    "psize = pos_max - pos_min\n",
    "pos = [pos_min + psize*np.random.rand(ndim) for i in range(nwalkers)]\n",
    "\n",
    "def lnprior(theta):\n",
    "    a1=theta\n",
    "# Alpha = -0.456132743382628 +0.3614233955323064 -0.40044242082158854\n",
    "# Beta_1 = 0.6758748895276029 +0.2572448739820613 -0.18938929791474807\n",
    "# Per Break = 7.474210034413118 +3.097912497636986 -1.8531438811980516\n",
    "# Beta_2 = -1.02749185905701 +0.3170930465170043 -0.6431590758031733\n",
    "    occurPrior=uniform.pdf(a1,0,5)\n",
    "#     alphaPrior=np.where(a2>alp  ,-((a2-alp)/high_alp)**2,-((a2-alp)/low_alp)**2)\n",
    "#     beta1Prior=np.where(a3>aCon ,-((a3-aCon )/high_aCon)**2,-((a3-aCon)/low_aCon)**2)\n",
    "#     perBreakPrior=np.where(a4>xmix,-((a4-xmix)/high_xmix)**2,-((a4-xmix)/low_xmix)**2)\n",
    "#     beta2Prior=np.where(a5>bCon,-((a5-bCon)/high_bCon)**2,-((a5-bCon)/low_bCon)**2)\n",
    "#     alphaPrior=uniform.pdf(a2,-20,40)\n",
    "#     beta1Prior=uniform.pdf(a3,-20,40)\n",
    "#     perBreakPrior=uniform.pdf(a4,0,20)\n",
    "#     beta2Prior=uniform.pdf(a5,-20,40)\n",
    "    return(np.log(occurPrior))#+alphaPrior/2+beta1Prior/2+perBreakPrior/2+beta2Prior/2)\n",
    "#     return(np.log(occurPrior)+np.log(alphaPrior)+np.log(beta1Prior)+np.log(beta2Prior)-(a4-10)**2)\n",
    "#     return(np.log(occurPrior)-((a2+0.6021775825595477)/0.33)**2-((a3-0.73389770663693)/0.24)**2-((a4-6.565839465395051)/2)**2-((a5+0.8995804978719887)/0.3)**2)\n",
    "\n",
    "\n",
    "def lnlike(theta, x, y):\n",
    "    a1=theta\n",
    "    \n",
    "    multAmp=25\n",
    "    stellarMult=stellar.sample(n=multAmp*len(stellar), replace=True)\n",
    "    params = ExoMult.PopParams(stellar=stellarMult)\n",
    "    \n",
    "    ####Distribution Limits####\n",
    "    params.pMax=40 #days\n",
    "    params.pMin=0.5 #days\n",
    "    params.rMax=4 #Earth Radii\n",
    "    params.rMin=0.5 #Earth Radii\n",
    "\n",
    "    ####Kepler Distribtuion Shape####\n",
    "    params.alpha_1=alp\n",
    "    params.rad_break=1.8 #Earth Radii\n",
    "#     params.alpha_2=alp\n",
    "#     params.beta_1=aCon\n",
    "#     params.per_break=10  #days\n",
    "#     params.beta_2=aCon\n",
    "    params.mut_Ray=0 #degrees\n",
    "    \n",
    "    ####Occurrence Factor (Number of Planets Per Star)####\n",
    "    occurFact=a1\n",
    "\n",
    "    params.frac_m1=occurFact\n",
    "    params.frac_m2=params.frac_m1-1\n",
    "    params.frac_m3=params.frac_m2-1\n",
    "    params.frac_m4=params.frac_m3-1\n",
    "    params.frac_m5=params.frac_m4-1\n",
    "\n",
    "\n",
    "    outputPopulation=ExoMult.Simulate(params)\n",
    "    if np.max(outputPopulation.m)==1:\n",
    "        radiusExp=np.sort(outputPopulation.rad_m1[outputPopulation.rad_m1>0])\n",
    "        periodExp=np.sort(outputPopulation.per_m1[outputPopulation.rad_m1>0])\n",
    "        \n",
    "    elif np.max(outputPopulation.m)==2:\n",
    "        radiusExp=np.sort(np.concatenate([outputPopulation.rad_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.rad_m2[outputPopulation.rad_m2>0]], axis=0))\n",
    "        periodExp=np.sort(np.concatenate([outputPopulation.per_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.per_m2[outputPopulation.rad_m2>0]], axis=0))\n",
    "    elif np.max(outputPopulation.m)==3:\n",
    "        radiusExp=np.sort(np.concatenate([outputPopulation.rad_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.rad_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.rad_m3[outputPopulation.rad_m3>0]],axis=0))\n",
    "        periodExp=np.sort(np.concatenate([outputPopulation.per_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.per_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.per_m3[outputPopulation.rad_m3>0]], axis=0))    \n",
    "        \n",
    "        \n",
    "#     pv_rad=stats.anderson_ksamp([planetNew.Rad,radiusExp]).statistic\n",
    "#     pv_per=stats.anderson_ksamp([planetNew.Period,periodExp]).statistic\n",
    "    \n",
    "    likelihood=logSamePois(len(planet),len(radiusExp))#-pv_rad-pv_per\n",
    "    \n",
    "    return(likelihood)\n",
    "    \n",
    "def lnprob(theta, x, y):\n",
    "    try:\n",
    "        lp = lnprior(theta)\n",
    "        if not np.isfinite(lp):\n",
    "            return -np.inf\n",
    "        else:\n",
    "            lk = lnlike(theta,x, y)\n",
    "        if not np.isfinite(lk):\n",
    "            return -np.inf\n",
    "\n",
    "        return lp + lk    \n",
    "    except:\n",
    "        return -np.inf\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Burn In\n",
      "True Distribution\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(2000, 1)"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(radiusObs, periodObs), threads=10, a=2)\n",
    "\n",
    "nburnsteps = 100\n",
    "nsteps=100\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "width = 1\n",
    "print(\"Burn In\")\n",
    "result=sampler.run_mcmc(pos, nburnsteps)\n",
    "\n",
    "pos,prob,state=result\n",
    "sampler.reset()\n",
    "\n",
    "########## perform MCMC\n",
    "print(\"True Distribution\")\n",
    "result=sampler.run_mcmc(pos, nsteps)\n",
    "samples = sampler.flatchain\n",
    "\n",
    "samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "occurFact = 1.594393647184482 +0.30680826404712325 -0.22519830307931432\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([ 21., 153., 368., 546., 428., 218., 158.,  79.,  21.,   8.]),\n",
       " array([0.95515849, 1.12237619, 1.2895939 , 1.45681161, 1.62402932,\n",
       "        1.79124702, 1.95846473, 2.12568244, 2.29290014, 2.46011785,\n",
       "        2.62733556]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "numsamp=len(samples[:,0])\n",
    "\n",
    "theta=np.sort(samples[:,0])\n",
    "low=np.median(theta)-theta[int(.16*numsamp)]\n",
    "high=theta[int((1-.16)*numsamp)]-np.median(theta)\n",
    "print(\"occurFact = \"+str(np.median(theta))+\" +\"+str(high)+\" -\"+str(low))\n",
    "plt.hist(samples[:,0])\n",
    "\n",
    "\n",
    "# theta=np.sort(samples[:,1])\n",
    "# low=np.median(theta)-theta[int(.16*numsamp)]\n",
    "# high=theta[int((1-.16)*numsamp)]-np.median(theta)\n",
    "# print(\"Alpha = \"+str(np.median(theta))+\" +\"+str(high)+\" -\"+str(low))\n",
    "# plt.hist(samples[:,1])\n",
    "\n",
    "\n",
    "# theta=np.sort(samples[:,2])\n",
    "# low=np.median(theta)-theta[int(.16*numsamp)]\n",
    "# high=theta[int((1-.16)*numsamp)]-np.median(theta)\n",
    "# print(\"Beta_1 = \"+str(np.median(theta))+\" +\"+str(high)+\" -\"+str(low))\n",
    "# plt.hist(samples[:,2])\n",
    "\n",
    "\n",
    "# theta=np.sort(samples[:,3])\n",
    "# low=np.median(theta)-theta[int(.16*numsamp)]\n",
    "# high=theta[int((1-.16)*numsamp)]-np.median(theta)\n",
    "# print(\"Per Break = \"+str(np.median(theta))+\" +\"+str(high)+\" -\"+str(low))\n",
    "# plt.hist(samples[:,3])\n",
    "\n",
    "\n",
    "# theta=np.sort(samples[:,4])\n",
    "# low=np.median(theta)-theta[int(.16*numsamp)]\n",
    "# high=theta[int((1-.16)*numsamp)]-np.median(theta)\n",
    "# print(\"Beta_2 = \"+str(np.median(theta))+\" +\"+str(high)+\" -\"+str(low))\n",
    "# plt.hist(samples[:,4])\n",
    "# plt.show()\n",
    "\n",
    "# samplesSuperEarths=samples\n",
    "# samplesSubNeptunes=samples\n",
    "# samplesSubSaturns=samples\n",
    "# samplesJupiters=samples\n",
    "\n",
    "# np.savetxt(\"./K2_chains/SuperEarths.csv\", samplesSuperEarths, delimiter=\",\")\n",
    "# np.savetxt(\"./K2_chains/SubNeptunes.csv\", samplesSubNeptunes, delimiter=\",\")\n",
    "# np.savetxt(\"./K2_chains/SubSaturns.csv\", samplesSubSaturns, delimiter=\",\")\n",
    "# np.savetxt(\"./K2_chains/Jupiters.csv\", samplesJupiters, delimiter=\",\")\n",
    "\n",
    "# np.savetxt(\"./K2_chains/SubNeptunes_FeH_high.csv\", samplesSubNeptunes, delimiter=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 637,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12943c3c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.array([-0.5,-0.3,-0.1,0.1,0.3])\n",
    "y=np.array([0.048,0.028,0.056,0.078,0.12])\n",
    "yerr=np.array([0.033,0.013,0.014,0.024,0.10])\n",
    "\n",
    "y2=np.array([0.16,0.122,0.071,0.14,0.30])\n",
    "yerr2=np.array([0.16,0.055,0.036,0.06,0.27])\n",
    "\n",
    "y3=np.array([0.043,0.011,0.026,0.033,0.13])\n",
    "yerr3=np.array([0.035,0.011,0.012,0.019,0.15])\n",
    "\n",
    "y4=np.array([0.093,0.039,0.044,0.082,0.18])\n",
    "yerr4=np.array([0.078,0.022,0.021,0.056,0.19])\n",
    "\n",
    "plt.errorbar(x,y,yerr=yerr)\n",
    "plt.errorbar(x,y2,yerr=yerr2)\n",
    "plt.errorbar(x,y3,yerr=yerr3)\n",
    "plt.errorbar(x,y4,yerr=yerr4)\n",
    "plt.yscale(\"log\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 871,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x137675390>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples=samplesSuperEarths\n",
    "aCon=samples[:,2]\n",
    "bCon=samples[:,4]\n",
    "xmix=samples[:,3]\n",
    "xmin=.5\n",
    "xmax=40\n",
    "constant1=((xmix**(aCon+1)-xmin**(aCon+1))/(aCon+1)+(xmix**aCon/xmix**bCon)*(xmax**(bCon+1)-xmix**(bCon+1))/(bCon+1))**-1\n",
    "constant2=constant1*(xmix**aCon/xmix**bCon)\n",
    "def model(x):\n",
    "    y=np.where(x<xmix,constant1*samples[:,0]*x**aCon,constant2*samples[:,0]*x**bCon)\n",
    "    return(y)\n",
    "\n",
    "xvar=np.logspace(np.log10(xmin),np.log10(xmax),40)\n",
    "y=np.zeros(len(xvar))\n",
    "u_y=np.zeros(len(xvar))\n",
    "U_y=np.zeros(len(xvar))\n",
    "for i in range(len(xvar)):\n",
    "    y[i]=np.median(model(xvar[i]))\n",
    "    u_y[i]=y[i]-np.sort(model(xvar[i]))[int(.16*len(model(xvar[i])))]\n",
    "    U_y[i]=np.sort(model(xvar[i]))[int(.84*len(model(xvar[i])))]-y[i]\n",
    "plt.fill_between(xvar,-u_y*100+y*100,y*100+U_y*100, color=\"blue\", alpha=.5)\n",
    "\n",
    "\n",
    "\n",
    "samples=samplesSubNeptunes\n",
    "aCon=samples[:,2]\n",
    "bCon=samples[:,4]\n",
    "xmix=samples[:,3]\n",
    "constant1=((xmix**(aCon+1)-xmin**(aCon+1))/(aCon+1)+(xmix**aCon/xmix**bCon)*(xmax**(bCon+1)-xmix**(bCon+1))/(bCon+1))**-1\n",
    "constant2=constant1*(xmix**aCon/xmix**bCon)\n",
    "def model(x):\n",
    "    y=np.where(x<xmix,constant1*samples[:,0]*x**aCon,constant2*samples[:,0]*x**bCon)\n",
    "    return(y)\n",
    "xvar=np.logspace(np.log10(xmin),np.log10(xmax),40)\n",
    "y=np.zeros(len(xvar))\n",
    "u_y=np.zeros(len(xvar))\n",
    "U_y=np.zeros(len(xvar))\n",
    "for i in range(len(xvar)):\n",
    "    y[i]=np.median(model(xvar[i]))\n",
    "    u_y[i]=y[i]-np.sort(model(xvar[i]))[int(.16*len(model(xvar[i])))]\n",
    "    U_y[i]=np.sort(model(xvar[i]))[int(.84*len(model(xvar[i])))]-y[i]\n",
    "plt.fill_between(xvar,-u_y*100+y*100,y*100+U_y*100, color=\"red\", alpha=.5)\n",
    "\n",
    "\n",
    "samples=samplesSubSaturns\n",
    "aCon=samples[:,2]\n",
    "bCon=samples[:,4]\n",
    "xmix=samples[:,3]\n",
    "constant1=((xmix**(aCon+1)-xmin**(aCon+1))/(aCon+1)+(xmix**aCon/xmix**bCon)*(xmax**(bCon+1)-xmix**(bCon+1))/(bCon+1))**-1\n",
    "constant2=constant1*(xmix**aCon/xmix**bCon)\n",
    "def model(x):\n",
    "    y=np.where(x<xmix,constant1*samples[:,0]*x**aCon,constant2*samples[:,0]*x**bCon)\n",
    "    return(y)\n",
    "xvar=np.logspace(np.log10(xmin),np.log10(xmax),40)\n",
    "y=np.zeros(len(xvar))\n",
    "u_y=np.zeros(len(xvar))\n",
    "U_y=np.zeros(len(xvar))\n",
    "for i in range(len(xvar)):\n",
    "    y[i]=np.median(model(xvar[i]))\n",
    "    u_y[i]=y[i]-np.sort(model(xvar[i]))[int(.16*len(model(xvar[i])))]\n",
    "    U_y[i]=np.sort(model(xvar[i]))[int(.84*len(model(xvar[i])))]-y[i]\n",
    "plt.fill_between(xvar,-u_y*100+y*100,y*100+U_y*100, color=\"yellow\", alpha=.5)\n",
    "\n",
    "\n",
    "samples=samplesJupiters\n",
    "aCon=samples[:,2]\n",
    "bCon=samples[:,4]\n",
    "xmix=samples[:,3]\n",
    "constant1=((xmix**(aCon+1)-xmin**(aCon+1))/(aCon+1)+(xmix**aCon/xmix**bCon)*(xmax**(bCon+1)-xmix**(bCon+1))/(bCon+1))**-1\n",
    "constant2=constant1*(xmix**aCon/xmix**bCon)\n",
    "def model(x):\n",
    "    y=np.where(x<xmix,constant1*samples[:,0]*x**aCon,constant2*samples[:,0]*x**bCon)\n",
    "    return(y)\n",
    "xvar=np.logspace(np.log10(xmin),np.log10(xmax),40)\n",
    "y=np.zeros(len(xvar))\n",
    "u_y=np.zeros(len(xvar))\n",
    "U_y=np.zeros(len(xvar))\n",
    "for i in range(len(xvar)):\n",
    "    y[i]=np.median(model(xvar[i]))\n",
    "    u_y[i]=y[i]-np.sort(model(xvar[i]))[int(.16*len(model(xvar[i])))]\n",
    "    U_y[i]=np.sort(model(xvar[i]))[int(.84*len(model(xvar[i])))]-y[i]\n",
    "plt.fill_between(xvar,-u_y*100+y*100,y*100+U_y*100, color=\"black\", alpha=.5)\n",
    "\n",
    "\n",
    "plt.yscale(\"log\")\n",
    "plt.xscale(\"log\")\n",
    "\n",
    "# plt.xlim([1,40])\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 738,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-21.391827830428376"
      ]
     },
     "execution_count": 738,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lnprior(pos_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 Planet Candidates Observed\n"
     ]
    }
   ],
   "source": [
    "import emcee\n",
    "from scipy import stats\n",
    "from scipy.special import gamma, factorial\n",
    "from scipy.stats import norm, uniform, beta, poisson, binom, binned_statistic\n",
    "planet=pd.read_csv(\"planet_sample.csv\",sep=\",\", engine='python', header=0)\n",
    "\n",
    "###### Planets only in Samaple ###\n",
    "planet=planet[planet['EPIC'].isin(stellar.EPIC.values.tolist())]\n",
    "planet=planet.drop_duplicates([\"CAND\"])\n",
    "\n",
    "planet=planet[(planet.Period>.5) & (planet.Period<10)]\n",
    "planet=planet[(planet.Rad>8) & (planet.Rad<24)]\n",
    "\n",
    "radiusObs = np.sort(planet.Rad)\n",
    "periodObs = np.sort(planet.Period)\n",
    "\n",
    "print(len(planet), \"Planet Candidates Observed\")\n",
    "\n",
    "ndim = 1\n",
    "nwalkers = 10\n",
    "pos_min = np.array([0])\n",
    "pos_max = np.array([.4])\n",
    "psize = pos_max - pos_min\n",
    "pos = [pos_min + psize*np.random.rand(ndim) for i in range(nwalkers)]\n",
    "\n",
    "def lnprior(theta):\n",
    "    a1=theta\n",
    "    occurPrior=uniform.pdf(a1,0,5)\n",
    "    return(np.log(occurPrior))\n",
    "\n",
    "def lnlike(theta, x, y):\n",
    "    a1=theta\n",
    "    params = ExoMult.PopParams(stellar=stellar)\n",
    "    \n",
    "    ####Distribution Limits####\n",
    "    params.pMax=10 #days\n",
    "    params.pMin=0.5 #days\n",
    "    params.rMax=24 #Earth Radii\n",
    "    params.rMin=8 #Earth Radii\n",
    "\n",
    "    ####Kepler Distribtuion Shape####\n",
    "    params.alpha_1=-2.1558177298387826\n",
    "    params.rad_break=params.rMin #Earth Radii\n",
    "    params.alpha_2=-2.1558177298387826\n",
    "    params.beta_1=1.6274914284598139\n",
    "    params.per_break=params.pMin  #days\n",
    "    params.beta_2=1.6274914284598139\n",
    "    params.mut_Ray=0 #degrees\n",
    "    \n",
    "    ####Occurrence Factor (Number of Planets Per Star)####\n",
    "    occurFact=a1\n",
    "\n",
    "    params.frac_m1=occurFact\n",
    "    params.frac_m2=params.frac_m1-1\n",
    "    params.frac_m3=params.frac_m2-1\n",
    "    params.frac_m4=params.frac_m3-1\n",
    "    params.frac_m5=params.frac_m4-1\n",
    "\n",
    "\n",
    "    outputPopulation=ExoMult.Simulate(params)\n",
    "    if np.max(outputPopulation.m)==1:\n",
    "        radiusExp=np.sort(outputPopulation.rad_m1[outputPopulation.rad_m1>0])\n",
    "        periodExp=np.sort(outputPopulation.per_m1[outputPopulation.rad_m1>0])\n",
    "        \n",
    "    elif np.max(outputPopulation.m)==2:\n",
    "        radiusExp=np.sort(np.concatenate([outputPopulation.rad_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.rad_m2[outputPopulation.rad_m2>0]], axis=0))\n",
    "        periodExp=np.sort(np.concatenate([outputPopulation.per_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.per_m2[outputPopulation.rad_m2>0]], axis=0))\n",
    "    elif np.max(outputPopulation.m)==3:\n",
    "        radiusExp=np.sort(np.concatenate([outputPopulation.rad_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.rad_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.rad_m3[outputPopulation.rad_m3>0]],axis=0))\n",
    "        periodExp=np.sort(np.concatenate([outputPopulation.per_m1[outputPopulation.rad_m1>0],\n",
    "                         outputPopulation.per_m2[outputPopulation.rad_m2>0],\n",
    "                         outputPopulation.per_m3[outputPopulation.rad_m3>0]], axis=0))    \n",
    "        \n",
    "        \n",
    "#     pv_rad=stats.anderson_ksamp([x,radiusExp]).statistic\n",
    "#     pv_per=stats.anderson_ksamp([y,periodExp]).statistic\n",
    "    \n",
    "    likelihood=logSamePois(len(radiusObs),len(radiusExp))#-pv_rad-pv_per\n",
    "    return(likelihood)\n",
    "    \n",
    "def lnprob(theta, x, y):\n",
    "    try:\n",
    "        lp = lnprior(theta)\n",
    "        if not np.isfinite(lp):\n",
    "            return -np.inf\n",
    "        else:\n",
    "            lk = lnlike(theta,x, y)\n",
    "        if not np.isfinite(lk):\n",
    "            return -np.inf\n",
    "        return lp + lk    \n",
    "    except:\n",
    "        return -np.inf\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Burn In\n",
      "True Distribution\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(2000, 1)"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(radiusObs, periodObs), threads=10, a=2)\n",
    "\n",
    "nburnsteps = 200\n",
    "nsteps=200\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "width = 1\n",
    "print(\"Burn In\")\n",
    "result=sampler.run_mcmc(pos, nburnsteps)\n",
    "\n",
    "pos,prob,state=result\n",
    "sampler.reset()\n",
    "\n",
    "########## perform MCMC\n",
    "print(\"True Distribution\")\n",
    "result=sampler.run_mcmc(pos, nsteps)\n",
    "samples = sampler.flatchain\n",
    "\n",
    "samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "occurFact = 0.009875478342039846 +0.007099961823266556 -0.004664980261493276\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12aaffb00>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numsamp=len(samples[:,0])\n",
    "theta=np.sort(samples[:,0])\n",
    "low=np.median(theta)-theta[int(.16*numsamp)]\n",
    "high=theta[int((1-.16)*numsamp)]-np.median(theta)\n",
    "print(\"occurFact = \"+str(np.median(theta))+\" +\"+str(high)+\" -\"+str(low))\n",
    "plt.hist(samples[:,0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6931471805599453"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logSamePois(0,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x12b32f630>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13bf16668>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dMag=np.zeros(len(planet))\n",
    "for i in range(len(planet)):\n",
    "#     print(stellar.d_mag[stellar.EPIC==planet.EPIC.iloc[i]].iloc[0])\n",
    "    dMag[i]=stellar.d_mag[stellar.EPIC==planet.EPIC.iloc[i]].iloc[0]\n",
    "\n",
    "plt.scatter(planet.Rad,dMag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30\n",
      "65\n"
     ]
    }
   ],
   "source": [
    "from matplotlib.backends.backend_pdf import PdfPages\n",
    "offset=np.sqrt(1+10**(-clustNumber/2.5))/np.sqrt(1+10**(clustNumber/2.5))\n",
    "# print(len(offset[planet.Ratio*offset>1.04]))\n",
    "x=np.arange(0,2,.1)\n",
    "y=np.ones(len(x))*30\n",
    "guy=planet.Ratio*np.sqrt(1+10**(-clustNumber/2.5))/np.sqrt(1+10**(clustNumber/2.5))+planet.b\n",
    "guy2=planet.Ratio*np.sqrt(1+10**(-clustNumber/2.5))/np.sqrt(1+10**(clustNumber/2.5))\n",
    "with PdfPages('fluxDilution.pdf')as pdf:\n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    plt.fill_between(x,np.ones(len(x))*1.05,np.ones(len(x))*5,color=\"#FDE725\", alpha=.75)\n",
    "    plt.scatter(planet.Ratio+planet.b,np.where(guy2<1,guy,planet.Ratio+planet.b), color =\"black\", s=2)\n",
    "    plt.text(.01,1.95, \"Potentially Diluted Background EBs\", horizontalalignment=\"left\",verticalalignment='top', color=\"#3CBB75\", fontsize=13)\n",
    "    plt.scatter((planet.Ratio+ planet.b)[((guy>1.04) | (guy2>.3))& (guy2<1)],guy[((guy>1.04) | (guy2>.3)) &(guy2<1)],color=\"#3CBB75\", s=15)\n",
    "    plt.xlabel(\"Catalog [$R_{\\mathrm{pl}}/R_{\\star}+b$]\")\n",
    "    plt.ylabel(\"Diluted [$R_{\\mathrm{pl}}/R_{\\star}+b$]\")\n",
    "#     plt.yscale(\"log\")\n",
    "#     plt.xscale(\"log\")\n",
    "    plt.xlim([0,1.04])\n",
    "    plt.ylim([0,2])\n",
    "#     plt.yticks([1,10,100,1000],[\"1\",\"10\",\"100\",\"1000\"])\n",
    "#     plt.xticks([.3,1,3,10,30],[\"0.3\",\"1\",\"3\",\"10\",\"30\"])\n",
    "    pdf.savefig(bbox_inches = \"tight\")\n",
    "    plt.close()\n",
    "print(len((planet.Ratio+ planet.b)[((guy>1.04) | (guy2>.3))& (guy2<1)]))\n",
    "print(len((planet.Ratio+ planet.b)[((guy2<=1))]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12752fbe0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(planet.Ratio+ planet.b,planet.Ratio*np.sqrt(1+10**(dMag/2.5))/np.sqrt(1+10**(-dMag/2.5))+planet.b, color =\"black\", s=2)\n",
    "guy=planet.Ratio*np.sqrt(1+10**(dMag/2.5))/np.sqrt(1+10**(-dMag/2.5))+planet.b\n",
    "print(len(guy[guy>1.04]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    }
   ],
   "source": [
    "print(len((planet.Ratio+ planet.b)[(guy2>1)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "stellarCoord=pd.read_csv(\"epic_coords.csv\",sep=\",\", engine='python', header=0)\n",
    "stellarCoord=stellarCoord[stellarCoord['epic_number'].isin(planet.EPIC.values.tolist())]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "672"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(dMag[dMag==0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "stellarCoord.to_csv(\"starHost.csv\", index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        0.000137\n",
       "1        0.006400\n",
       "2        0.009894\n",
       "3        0.004371\n",
       "4        0.000084\n",
       "5        0.013020\n",
       "6        0.015905\n",
       "7        0.000101\n",
       "8        0.005536\n",
       "9        0.008035\n",
       "10       0.000140\n",
       "11       0.014783\n",
       "12       0.000156\n",
       "13       0.011608\n",
       "14       0.002271\n",
       "15       0.007854\n",
       "16       0.000061\n",
       "17       0.014714\n",
       "18       0.015334\n",
       "19       0.000149\n",
       "20       0.016342\n",
       "21       0.007103\n",
       "22       0.000111\n",
       "23       0.006381\n",
       "24       0.003197\n",
       "25       0.000166\n",
       "26       0.005244\n",
       "27       0.005614\n",
       "28       0.000102\n",
       "29       0.008358\n",
       "           ...   \n",
       "13926    0.008429\n",
       "13927    0.015534\n",
       "13928    0.000041\n",
       "13929    0.004551\n",
       "13930    0.013450\n",
       "13931    0.012386\n",
       "13932    0.009058\n",
       "13933    0.002360\n",
       "13934    0.013996\n",
       "13935    0.009383\n",
       "13936    0.014386\n",
       "13937    0.000069\n",
       "13938    0.014117\n",
       "13939    0.014693\n",
       "13940    0.004668\n",
       "13941    0.014422\n",
       "13942    0.005605\n",
       "13943    0.010606\n",
       "13944    0.000030\n",
       "13945    0.006055\n",
       "13946    0.010937\n",
       "13947    0.005395\n",
       "13948    0.000042\n",
       "13949    0.010622\n",
       "13950    0.015177\n",
       "13951    0.012163\n",
       "13952    0.000006\n",
       "13953    0.002342\n",
       "13954    0.003471\n",
       "13955    0.014224\n",
       "Name: angdist, Length: 13956, dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster=pd.read_csv(\"K2Planet-result.csv\",sep=\",\", engine='python', header=0)\n",
    "cluster.angdist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "clustNumber=np.zeros(len(planet))\n",
    "clustB=np.zeros(len(planet))\n",
    "for i in range(len(planet)):\n",
    "    epi=planet.EPIC.iloc[i]\n",
    "    dummy=cluster[cluster.epic_number==epi].drop_duplicates()\n",
    "#     print(cluster[cluster.epic_number==epi].phot_g_mean_mag.drop_duplicates())\n",
    "# clustB[i]=np.median(cluster[cluster.epic_number==epi].b.drop_duplicates())\n",
    "    try:\n",
    "        clustNumber[i]=np.sort(dummy.phot_g_mean_mag[dummy.angdist<.0012])[0]-np.sort(dummy.phot_g_mean_mag[dummy.angdist<.0012])[1]\n",
    "#     clustB[i]=np.median(cluster[cluster.epic_number==epi].b.drop_duplicates())\n",
    "    except:\n",
    "        clustNumber[i]=-np.inf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(clustNumber[clustNumber>-1000])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "kepCluster=pd.read_csv(\"./kepCluster.csv\", delimiter=\",\", names=[\"num\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4769"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(stellar.Ncomp[stellar.Ncomp>1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins=np.arange(0,6,.3)\n",
    "bins2=np.arange(0,6,.6)\n",
    "with PdfPages('seperation.pdf')as pdf:\n",
    "    plt.rcParams.update({'font.size': 14})\n",
    "    plt.hist(np.log(kepCluster.num[(kepCluster.num>0) & (kepCluster.num<100000)]), bins=bins, color = \"#33638D\")\n",
    "    plt.hist(np.log(clustNumber[(clustNumber>0) & (clustNumber<100000)]), bins=bins2,  color = \"#73D055\", alpha=.75)\n",
    "    plt.xticks([0,2,4,6],[\"1\",\"100\",\"10000\",\"100000\"])\n",
    "    plt.text(0.1,960, \"Kepler\", horizontalalignment=\"left\",verticalalignment='top', color=\"#33638D\", fontsize=14)\n",
    "    plt.text(0.1,875, \"K2\", horizontalalignment=\"left\",verticalalignment='top', color=\"#73D055\", fontsize=14)\n",
    "    plt.xlim([0,6])\n",
    "    plt.xlabel(\"Stars within One Arcminute Radius\")\n",
    "    plt.ylabel(\"Number of Candidates\")\n",
    "    pdf.savefig(bbox_inches = \"tight\")\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "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>num</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>29.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>79.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>17.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>99.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>40.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>71.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>15.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>23.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>19.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>78.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>66.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>30.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>30.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>30.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>30.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>30.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>51.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>76.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4582</th>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4583</th>\n",
       "      <td>76.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4584</th>\n",
       "      <td>119.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4585</th>\n",
       "      <td>43.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4586</th>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4587</th>\n",
       "      <td>72.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4588</th>\n",
       "      <td>52.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4589</th>\n",
       "      <td>27.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4590</th>\n",
       "      <td>129.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4591</th>\n",
       "      <td>140.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4592</th>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4593</th>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4594</th>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4595</th>\n",
       "      <td>64.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4596</th>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4597</th>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4598</th>\n",
       "      <td>29.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4599</th>\n",
       "      <td>36.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4600</th>\n",
       "      <td>42.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4601</th>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4602</th>\n",
       "      <td>44.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4603</th>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4604</th>\n",
       "      <td>40.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4605</th>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4606</th>\n",
       "      <td>28.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4607</th>\n",
       "      <td>27.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4608</th>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4609</th>\n",
       "      <td>43.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4610</th>\n",
       "      <td>33.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4611</th>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4612 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        num\n",
       "0      19.0\n",
       "1      29.0\n",
       "2      50.0\n",
       "3      79.0\n",
       "4      21.0\n",
       "5      17.0\n",
       "6      99.0\n",
       "7      40.0\n",
       "8      71.0\n",
       "9      13.0\n",
       "10     15.0\n",
       "11     46.0\n",
       "12     46.0\n",
       "13     46.0\n",
       "14     23.0\n",
       "15     14.0\n",
       "16     14.0\n",
       "17     37.0\n",
       "18     19.0\n",
       "19     78.0\n",
       "20     66.0\n",
       "21     30.0\n",
       "22     30.0\n",
       "23     30.0\n",
       "24     30.0\n",
       "25     30.0\n",
       "26     10.0\n",
       "27     10.0\n",
       "28     51.0\n",
       "29     76.0\n",
       "...     ...\n",
       "4582   34.0\n",
       "4583   76.0\n",
       "4584  119.0\n",
       "4585   43.0\n",
       "4586   31.0\n",
       "4587   72.0\n",
       "4588   52.0\n",
       "4589   27.0\n",
       "4590  129.0\n",
       "4591  140.0\n",
       "4592   46.0\n",
       "4593   50.0\n",
       "4594   18.0\n",
       "4595   64.0\n",
       "4596   37.0\n",
       "4597   48.0\n",
       "4598   29.0\n",
       "4599   36.0\n",
       "4600   42.0\n",
       "4601   21.0\n",
       "4602   44.0\n",
       "4603   35.0\n",
       "4604   40.0\n",
       "4605   22.0\n",
       "4606   28.0\n",
       "4607   27.0\n",
       "4608   34.0\n",
       "4609   43.0\n",
       "4610   33.0\n",
       "4611   31.0\n",
       "\n",
       "[4612 rows x 1 columns]"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kepCluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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