E_Fig_3_histogram_panels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Based on CRTS_sel_g_cut_vs_r_cut.ipynb,   taking only the code needed to make Fig. 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A testbed for making Fig.3 :  the 4 x 4 histogram plot. It shows that   0   < log(tau) < 1.7 (short timescales bin), does not exhibit any variability, because chi_ij for qso and stars is almost undistinguishable for uncorrected points. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "** What happens here : **\n",
    "\n",
    "We run the cells below for different magnitude  cuts (changing Min and  Max  parameters below) :  17-18 ,  18-18.5 ,  18.5-19.  \n",
    "\n",
    "Each run reads in xi, ei points for quasars  , blue stars.  We read in xi (mi  : magnitude  difference) , tau (time difference),   ei (magnitude difference error)  points separately for 4 timescale bins in log(delta t)  space . \n",
    "\n",
    "A list of xi, tau,  ei  per magnitude per timescale per object type (quasar or a star) is saved as a .txt file in the folder structure data_products/Fig_3_data/year-month-day/r_cut_Min-Max_object_mi_tau_ei_log_tau_min_max.txt \n",
    "\n",
    "\n",
    "Then we read in each xi,tau,ei file,  and  for every point in a given  magnitude-timescale-object bin we calculate  chi quantity.   Thus we make a histogram of chi values for magnitude-timescale-object grid, resulting in  a  4 x 3 x 2  histograms .  The robust width of the chi distribution for each bin is a signature of intrinsic variability. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "from astroML.stats import median_sigmaG\n",
    "from scipy.stats import binned_statistic\n",
    "from scipy.optimize import curve_fit\n",
    "import CRTS_paper_modules as mod\n",
    "import datetime\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zipping CRTS-SDSS quasars catalog from ../data_products/CRTS_SDSS_catalogs/CRTS_SDSS_cross_matched_qso_DB_QSO_catalog.txt\n",
      "Read in 7601 quasars from CRTS\n",
      "zipping CRTS-SDSS stars catalog...\n",
      "Read in catalog for 48250 stars from CRTS \n"
     ]
    }
   ],
   "source": [
    "cols1, qso_cat = mod.get_qso_catalog() \n",
    "cols2 , star_cat= mod.get_stars_catalog()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  {mag_ranges} x {object_types} x { quantities } x {delta_t_bins}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Today we will save our Fig_3 files in /Users/chris/GradResearch/CRTS_PROJECT/data_products/Fig_3_data/2017-08-08/\n",
      "\n",
      "Using now only lightcurves with SDSS  17.000000< r < 18.000000\n",
      "\n",
      "Choosing stars with  SDSS   -1.00<g-i<1.00\n",
      " These cuts reduced the number of stars  in the sample from 48250 to 2795\n",
      "\n",
      " Returning only QSO with  an SDSS counterpart within 2.000000 arcsec\n",
      "\n",
      " These cuts reduced the number of qso  in the sample from 7601 to 185\n",
      "\n",
      "Reading in tau,xi,ei  for 185 objects\n",
      "\n",
      "Using structure function master files from ../data_products/sf_file_per_LC/qso/\n",
      "[##########] 100.00%\n",
      "Finished reading all master files for the selected objects ...\n",
      "\n",
      "Reading in tau,xi,ei  for 2795 objects\n",
      "\n",
      "Using structure function master files from ../data_products/sf_file_per_LC/stars/\n",
      "[##########] 100.00%\n",
      "Finished reading all master files for the selected objects ...\n",
      "Saved 17-18_qso_mi_tau_ei-log_t_0-1.7.txt\n",
      "Saved 17-18_qso_mi_tau_ei-log_t_2.3-2.5.txt\n",
      "Saved 17-18_qso_mi_tau_ei-log_t_2.8-3.0.txt\n",
      "Saved 17-18_qso_mi_tau_ei-log_t_3.2-3.4.txt\n",
      "Saved 17-18_starsB_mi_tau_ei-log_t_0-1.7.txt\n",
      "Saved 17-18_starsB_mi_tau_ei-log_t_2.3-2.5.txt\n",
      "Saved 17-18_starsB_mi_tau_ei-log_t_2.8-3.0.txt\n",
      "Saved 17-18_starsB_mi_tau_ei-log_t_3.2-3.4.txt\n",
      "\n",
      "Using now only lightcurves with SDSS  18.000000< r < 18.500000\n",
      "\n",
      "Choosing stars with  SDSS   -1.00<g-i<1.00\n",
      " These cuts reduced the number of stars  in the sample from 48250 to 1400\n",
      "\n",
      " Returning only QSO with  an SDSS counterpart within 2.000000 arcsec\n",
      "\n",
      " These cuts reduced the number of qso  in the sample from 7601 to 333\n",
      "\n",
      "Reading in tau,xi,ei  for 333 objects\n",
      "\n",
      "Using structure function master files from ../data_products/sf_file_per_LC/qso/\n",
      "[######### ] 99.10%\n",
      "Finished reading all master files for the selected objects ...\n",
      "\n",
      "Reading in tau,xi,ei  for 1400 objects\n",
      "\n",
      "Using structure function master files from ../data_products/sf_file_per_LC/stars/\n",
      "[##########] 100.00%\n",
      "Finished reading all master files for the selected objects ...\n",
      "Saved 18-18.5_qso_mi_tau_ei-log_t_0-1.7.txt\n",
      "Saved 18-18.5_qso_mi_tau_ei-log_t_2.3-2.5.txt\n",
      "Saved 18-18.5_qso_mi_tau_ei-log_t_2.8-3.0.txt\n",
      "Saved 18-18.5_qso_mi_tau_ei-log_t_3.2-3.4.txt\n",
      "Saved 18-18.5_starsB_mi_tau_ei-log_t_0-1.7.txt\n",
      "Saved 18-18.5_starsB_mi_tau_ei-log_t_2.3-2.5.txt\n",
      "Saved 18-18.5_starsB_mi_tau_ei-log_t_2.8-3.0.txt\n",
      "Saved 18-18.5_starsB_mi_tau_ei-log_t_3.2-3.4.txt\n",
      "\n",
      "Using now only lightcurves with SDSS  18.500000< r < 19.000000\n",
      "\n",
      "Choosing stars with  SDSS   -1.00<g-i<1.00\n",
      " These cuts reduced the number of stars  in the sample from 48250 to 1496\n",
      "\n",
      " Returning only QSO with  an SDSS counterpart within 2.000000 arcsec\n",
      "\n",
      " These cuts reduced the number of qso  in the sample from 7601 to 747\n",
      "\n",
      "Reading in tau,xi,ei  for 747 objects\n",
      "\n",
      "Using structure function master files from ../data_products/sf_file_per_LC/qso/\n",
      "[######### ] 99.73%\n",
      "Finished reading all master files for the selected objects ...\n",
      "\n",
      "Reading in tau,xi,ei  for 1496 objects\n",
      "\n",
      "Using structure function master files from ../data_products/sf_file_per_LC/stars/\n",
      "[######### ] 99.93%\n",
      "Finished reading all master files for the selected objects ...\n",
      "Saved 18.5-19_qso_mi_tau_ei-log_t_0-1.7.txt\n",
      "Saved 18.5-19_qso_mi_tau_ei-log_t_2.3-2.5.txt\n",
      "Saved 18.5-19_qso_mi_tau_ei-log_t_2.8-3.0.txt\n",
      "Saved 18.5-19_qso_mi_tau_ei-log_t_3.2-3.4.txt\n",
      "Saved 18.5-19_starsB_mi_tau_ei-log_t_0-1.7.txt\n",
      "Saved 18.5-19_starsB_mi_tau_ei-log_t_2.3-2.5.txt\n",
      "Saved 18.5-19_starsB_mi_tau_ei-log_t_2.8-3.0.txt\n",
      "Saved 18.5-19_starsB_mi_tau_ei-log_t_3.2-3.4.txt\n"
     ]
    }
   ],
   "source": [
    "# Make it in a loop : \n",
    "# Loop over all magnitude ranges,\n",
    "# at each range reading in xi, ei \n",
    "# for QSO and blue stars \n",
    "\n",
    "# Subsequently, save  these arrays \n",
    "# of xi, ei  , grouped into \n",
    "# four delta_t  bins \n",
    "\n",
    "inDirStars   = '../data_products/sf_file_per_LC/stars/'\n",
    "inDirQSO = '../data_products/sf_file_per_LC/qso/'\n",
    "\n",
    "###  set the output directory  to save the results...\n",
    "outDir = os.path.join(os.getcwd()[:-4]+'data_products/'+'Fig_3_data/')\n",
    "if not os.path.exists(outDir): os.system('mkdir %s' % outDir)\n",
    "                      \n",
    "outDir = os.path.join(os.getcwd()[:-4],'data_products/'+'Fig_3_data', \n",
    "                      datetime.datetime.now().strftime('%Y-%m-%d')+ '/')\n",
    "if not os.path.exists(outDir): os.system('mkdir %s' % outDir)\n",
    "\n",
    "print('Today we will save our Fig_3 files in %s'%outDir)\n",
    "\n",
    "# loop over magnitudes ...\n",
    "for Min, Max in zip([17,18,18.5], [18,18.5, 19]):\n",
    "    \n",
    "    # select objects that satisfy magnitude cut ... \n",
    "    cut_mag = 'r'\n",
    "    print('\\nUsing now only lightcurves with SDSS  %f< %s < %f' % (Min, cut_mag, Max))\n",
    "\n",
    "    good_ids_S_blue = mod.cut_stars(star_cat = star_cat, mMin = Min, \n",
    "                                    mMax=Max, mErrMax = 0.3, gi_Min = -1,  \n",
    "                                    gi_Max=1, cut_mag=cut_mag + '_mMed')\n",
    "    good_ids_QSO = mod.cut_qso(qso_cat = qso_cat, mMin = Min, \n",
    "                               mMax=Max, mErrMax = 0.3, \n",
    "                                cut_mag=cut_mag)\n",
    "    out_dic = {}\n",
    "\n",
    "    # read xi, ei the fastest way for selected objects \n",
    "    out_dic['qso'] = mod.faster_read_xi_ei(inDirSF = inDirQSO,\n",
    "                                           good_ids = good_ids_QSO )\n",
    "    out_dic['starsB'] = mod.faster_read_xi_ei(inDirSF = inDirStars,\n",
    "                                              good_ids = good_ids_S_blue )\n",
    "    \n",
    "    # split into four log(delta_t) bins , and save in an\n",
    "    # appropriate directory \n",
    "    log_tau_min = [0,   2.3, 2.8, 3.2]\n",
    "    log_tau_max = [1.7, 2.5, 3.0, 3.4]\n",
    "    \n",
    "    ## Save to a file points for log(tau) samples  for QSO, stars \n",
    "    for obj in out_dic.keys():\n",
    "        m_ij = out_dic[obj]['xi']\n",
    "        tau =  out_dic[obj]['tau']\n",
    "        e_ij =  out_dic[obj]['ei']\n",
    "\n",
    "        for i in range(len(log_tau_min)):\n",
    "            # select those points that fall into given\n",
    "            # delta  t  bin \n",
    "            m1 = log_tau_min[i] < np.log10(tau)\n",
    "            m2 = np.log10(tau) < log_tau_max[i]\n",
    "            mask =  m1 * m2 \n",
    "            \n",
    "            data = np.column_stack((m_ij[mask], tau[mask], e_ij[mask]))\n",
    "\n",
    "            fname = str(Min)+'-'+str(Max)+'_'+obj+'_mi_tau_ei-log_t_'+\\\n",
    "                    str(log_tau_min[i])+'-'+str(log_tau_max[i])+'.txt'\n",
    "            print('Saved %s' % fname)\n",
    "            np.savetxt(outDir+fname, data, fmt='%s', delimiter= ' ')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--> Now go up, and change Min, Max to the next magnitude bin, until all options have been exhausted "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the histogram grid for qso and starsB "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'/Users/chris/GradResearch/CRTS_PROJECT/data_products/Fig_3_data/2017-08-08/'"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#outDir = os.path.join(os.getcwd()[:-4],'data_products/'+'Fig_3_data/2017-01-10/')\n",
    "outDir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note : if the files saved above already exist, can just rerun the cells below to remake the figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Define function used to plot each histogram in the grid ... \n",
    "\n",
    "# Use today's data... \n",
    "# --> do not change the outDir \n",
    "\n",
    "# Use data from another day : \n",
    "#outDir = os.path.join(os.getcwd()[:-4],'data_products/'+'Fig_3_data/2016-06-07/')\n",
    "\n",
    "def plot2Chistograms(chiQSO, chiSTAR, Xmin, Xmax, Ymin, Ymax, ax, bins=20, \n",
    "                     title='', axes_text_size=25):\n",
    "    limits = [(Xmin, Xmax, Ymin, Ymax)]\n",
    "    ax.set_xlim(Xmin, Xmax)\n",
    "    ax.set_ylim(Ymin, Ymax)        \n",
    "        \n",
    "    #plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "    xTitle = Xmin + 0.05*(Xmax-Xmin)\n",
    "    yTitle = Ymax - 0.2*(Ymax-Ymin)\n",
    "    ax.text(xTitle, yTitle, title, fontsize=axes_text_size) # , fontsize=12 \n",
    "\n",
    "    # plot a histogram\n",
    "    ax.hist(chiSTAR, bins=bins, normed=True, facecolor='blue', \n",
    "            histtype='stepfilled', alpha=0.4)\n",
    "    ax.hist(chiQSO, bins=bins, normed=True, facecolor='red', \n",
    "            histtype='stepfilled', alpha=0.2,  hatch=\"//\")\n",
    "\n",
    "    # plot the robust width of both distributions\n",
    "    stdev_rob_QSO = 0.7414 *(np.percentile(chiQSO,75) - np.percentile(chiQSO,25) )\n",
    "    stdev_rob_S = 0.7414 *(np.percentile(chiSTAR,75) - np.percentile(chiSTAR,25) )\n",
    "    \n",
    "    \n",
    "    xTitle = Xmin + 0.65*(Xmax-Xmin)\n",
    "    yTitle = Ymax - 0.2*(Ymax-Ymin)\n",
    "    StarSigmaG = r'$'+str(stdev_rob_S)[:4]+'$'\n",
    "    ax.text(xTitle, yTitle, StarSigmaG, fontsize=axes_text_size) #  fontsize=12\n",
    "    \n",
    "    \n",
    "    xTitle = Xmin + 0.65*(Xmax-Xmin)\n",
    "    yTitle = Ymax - 0.35*(Ymax-Ymin)\n",
    "    QSOSigmaG = r'$'+str(stdev_rob_QSO)[:4]+'$'\n",
    "    ax.text(xTitle, yTitle, QSOSigmaG, fontsize=axes_text_size) #  fontsize=12\n",
    "    ax.tick_params(axis='x', pad=10)\n",
    "    ax.locator_params(tight=True, nbins=4)\n",
    "    \n",
    "    \n",
    "    #start, end = ax.get_xlim()\n",
    "    #stepsize=5\n",
    "    #ax.xaxis.set_ticks(np.arange(start, end, stepsize))\n",
    "    \n",
    "Min_arr = [17, 18, 18.5]\n",
    "Max_arr = [18, 18.5, 19]\n",
    "log_tau_min = [0,   2.3, 2.8, 3.2]\n",
    "log_tau_max = [1.7, 2.5, 3.0, 3.4]\n",
    "xlims_arr = [4.9,10,10,10]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\Plot the uncorrected histograms "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: because we are plotting histograms of hundreds of thousands of points, the plotting itself takes ~few minutes... If you need to tweak any details of the plot, set $\\verb|testing=True|$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rcParams['text.usetex'] = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving plot to: /Users/chris/GradResearch/CRTS_PROJECT/data_products/Fig_3_data/2017-08-08/Fig_3_histogram_panels.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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3pQxh6enkPZLkLQaMrydp0zO44nqdrT19+jS+F/OXjZ1dPnbbHpy/eva/O7ej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Iaid2cnZtbQvGBkFjYA8BjX7AA4acFJa0fSefBU3zk32PF9szLOwmVmPefc2uxrkWtQdrp2J5iu\n+rnm+26x38ysKakdLHYmqSap65ybBK+H+zx0Hry+VIAlfM+65jPHnQVPPTjnOsHz9W3rOPb9kfX0\nJck519m2bLB8TdKlpOh+PdP8556uLHsp6UJSXcv7tRc8F1q895D3JGznpea/u3CZM0lvwt/dMdsI\nAIVwzvHgwYPHyT4k3UT+fy/JSbrc8p569H1lekhqSmpseH0U7IPWlvU0JPWC/7eC9zQkXUm6Wt3H\nwevhCX9/5fVe8Hp9y/e8XN224HfR13yChfst729teP+9pMc99uOjpOaOy7aC5Vf3S311mxP2azPY\nh42V9d0c+p6E3+d9zO+msfqZSOP78eDBg0deD4axAThpzrl25Mvuyr9rghb63sr7yuTCrbTSrwh/\n9m3X7nQkvQn+H/aS3Gje23W9suwo+PetpJpb7w0JX08cPhf0JPQltV1k6Jib9xqEvUeJP1fw/hvN\nexri3l+XdJv0/pV1NYP37tITdRX5vkv7xcX3eLxU/H6N9q681PznHR3xntWf507zyRaWfjfB+wea\n33i2lsb3A4A8UewAQCA4CZ5pft1Kc/X14GTvRtKn+67bzC7N7DGFx/2hP1/wM208+QxOVsfafu1O\n3X2Yhex58O/YxQ8BDIdu1WIKIWl52NOaYL/3g/XHXSMTFg2xP1swRK2v+c0/477/3296f4yO5gXA\nRsH+7ilhvwTD+VYLnrj9ujqM7FNJzyLrPOQ94TbUNf+5pzFFaOgu+PfFsd8PAPL2e0VvAAB4ZqD5\nUKyOVi7i17xnouMOmGrYOTcws3cpbN8x2htOaKO6mp/gvlIwPXVU2LsVeeo88r44jeDfpN6i8IQ5\n6dqOt8G/STOfhYVpUk9Lf+XfVRdb3r+qpeVrb5KE32/p5w4KjI7m2/1x5Pmalrcx3K9LBUNw/M0O\nfc8u27gi/Fmfp/D9ACBXTFAAABFBa/udJDnnLPL86jCdUtln6FWw/J3mRcrFtveYmdOGSQ3M7FHz\nXh1LeP1e896dtZtzJv0+Yr7/zDn3JOa1cNIFxa1/2/tjlm1JeuWce75luWgvWrQQONO8J2ly7H49\n9j3RfasNN0YNjv2WpGu3MrHFIdsIAHmiZwcAIpxzEzObSaqZWdM5Nw5mmOqXtdAJ7NqrE+pqfrLe\n04eelzWR4X6xJ+5BsVHb8npd85P/uJPtl1vWv61XJxyKF7v+4IR/0/tXdSR9ucNyYW/RcM/9Hm7X\ntp8rjfcs9u2W3spwHy0NoTxkGwEgb1yzAwDrwpb4dnCB+f2uPSI+2uVanVXBzzuR1Ii7fikinKgh\naf3NLa+HxUjSELPwRDup0AyLiqQC5KPg36TJB7Zt30IwhKupHa7X0bzAk5KH5m2zbb+m8Z5t+zZa\njErS6jDMQ7YRAHJFsQMA68IT50tpfr3NsSsseIKCpRnM9hDOuLXpeo5trfvtLa+HvR6LE+mViRHC\n2b7+XvGWvr+Z1VaKs7DouFO8fa7XudT2XpBVSdu9zSG9Jof2tGzaxvD3M4j5uenZAeA9hrEBwIro\nUDaldCJX1AQFh/TqhJxzQzObKujdWe3dCno66ppfs5FUADQ1vx5mrfcg0muwKCCC7T2LLDbVvAci\n6f3hzV3D7/9Cy70405V/V7c/3L5demCiUy5vExZXZ5sWiruWKrJfk4b2xa1n7/fowz5Julanpvlk\nHVOtTD5x4PcDgNzRswMAKyLXcUgfrms4mnNulsZjz2/bObBXJ7Tpvjthy37s+ne4HiZ8/03kuc5K\nT1pYqNW0Lhz6Fi1uVu8jtOn94Sxvu9wvp675DTN33ZdhYbvteqdOzBDJvHp1wv3XSHj9RvNC6IJe\nHQBlRc8OAEQEJ7WvNL9PSDgLVeJNRn0WnEw3gtm0DhUWCXG9O+EQsEOv11nqdQlu/Ll07U3QI9bV\nfDhVJ1iupmAacM17UMJeoYZWhmQFvVMTzYvWRaFiZv3Iz7ZLz1dHCUVdHOfczMw6knpm1ov2HAXH\nWFfza8Hibk67bb/G2fs9QQ/mtaRXZrYYpha5n9SZpOcJvV6HbCMA5I6ppwEgEJ7kOecugq/DgHy2\n4zAnr5jZSB8KjjSMw30TrL8v6TxpGuZgcodXkn60YVrjnuY9C1NJdwk33wyLG0l6CP7tBgVFI3jt\nVvPhaLGFabCtZ5F19DTv2Whqh99vMH12e9+JKsLem8h2n2n+s77ZsE827te03hN5b0vzYjDcxrrm\nsw8mFnfHfD8AyBPFDgAEguKgHWnhXvTsOOeuC904pG7X++sEBcvNLvfhAQD4hWt2AECLwqaz0toe\nDqlK7bod+GHPe8S0tT7tMgCgBOjZAXDygiE5sTcNjQxle17ym4qenGD4mxJuJtrXfCrpi21D04Jj\ngN8/AJQQPTsATlpwzchow4lseA3JpnvNwDPBtTyPkn6V8Fp4z5xthU5L86m1KXQAoIQodgCcrGD2\nr/st0wmHRU4znErZzK5WpqeGf86Df1fvDdSQ9JWkYXSyhQ06+jBFMwCgZBjGBuBkmdll3OxfMcs1\nNC96zjSf9eueCQv8FzMDm4Kv3+zSUxMMg3tUSWfjAwBQ7AAAECuYxKC7Yw8QAMBDFDsAAAAAKolr\ndgAAAABUEsUOAAAAgEqi2AEAAABQSRQ7AAAAACqJYgcAAABAJVHsAAAAAKik/x9wD4JpAqTKJQAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a0dca90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#import matplotlib \n",
    "#matplotlib.rc('xtick', labelsize=15) \n",
    "#matplotlib.rc('ytick', labelsize=15) \n",
    "\n",
    "from matplotlib import rcParams\n",
    "\n",
    "rcParams['ytick.labelsize'] = 25\n",
    "rcParams['xtick.labelsize'] = 25\n",
    "#rcParams['axes.labelsize'] = 35\n",
    "axes_label_font = 30 \n",
    "#rcParams['font.size'] = 25\n",
    "axes_text_size = 18\n",
    "rcParams['axes.linewidth'] = 2\n",
    "rcParams.update({'figure.autolayout': False})\n",
    "\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "fig, axs = plt.subplots(4,3, figsize=(12,12))\n",
    "# plot the same timescale-magnitude range before we get too specific... \n",
    "# if with one bin range it looks good, set testing = False, and run for all ... \n",
    "\n",
    "testing = False\n",
    "if testing is True : \n",
    "    # just for testing  - load only 1/16 files (one for QSO one for Stars) and experiment with how it looks \n",
    "    j=0\n",
    "    i=0\n",
    "\n",
    "    datafileS = outDir+str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+'starsB'+'_mi_tau_ei-log_t_'+\\\n",
    "                            str(log_tau_min[i])+'-'+str(log_tau_max[i])+'.txt'\n",
    "    vS = np.loadtxt(datafileS, unpack=True)\n",
    "\n",
    "    datafileQ = outDir+str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+'qso'+'_mi_tau_ei-log_t_'+\\\n",
    "            str(log_tau_min[i])+'-'+str(log_tau_max[i])+'.txt'\n",
    "    vQ = np.loadtxt(datafileQ, unpack=True)\n",
    "    print('Read in the xi,tau,ei  data from \\n %s and \\n %s for testing...'%(datafileS, \n",
    "                                                                             datafileQ))\n",
    "    \n",
    "    \n",
    "# initiate a storage array for the robust widths of chi distributions ... \n",
    "store_fc_starB = np.zeros((3,4))\n",
    "\n",
    "for i in range(len(log_tau_max)):  # \n",
    "    for j in range(len(Min_arr) ):  # \n",
    "        \n",
    "        #a = coeffs['a'][coeffs['rMagMin'] == Min_arr[j]]\n",
    "        #b = coeffs['b'][coeffs['rMagMin'] == Min_arr[j]]\n",
    "        #tau = (tau_max_arr[i] + tau_min_arr[i])/2.0\n",
    "        #bin_fc = 1.0/ ( a* tau + b)\n",
    "    \n",
    "        if testing is not True: \n",
    "            datafileS = outDir+str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+\\\n",
    "                'starsB'+'_mi_tau_ei-log_t_'+\\\n",
    "                str(log_tau_min[i])+'-'+str(log_tau_max[i])+'.txt'\n",
    "            vS = np.loadtxt(datafileS, unpack=True)\n",
    "        \n",
    "            datafileQ = outDir +str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+\\\n",
    "                'qso'+'_mi_tau_ei-log_t_'+\\\n",
    "                 str(log_tau_min[i])+'-'+str(log_tau_max[i])+'.txt'\n",
    "            vQ = np.loadtxt(datafileQ, unpack=True)\n",
    "        \n",
    "        # calculate the robust width of the chi distribution .... \n",
    "        #chiS = vS[0]/(bin_fc*vS[2]) # applying the error correction : ei_corr = fc * ei \n",
    "        chiS = vS[0] / vS[2]\n",
    "        chiSok = chiS[np.abs(chiS)<5]\n",
    "        stdev_rob_S = 0.7414 *(np.percentile(chiSok,75) - np.percentile(chiSok,25) )\n",
    "        \n",
    "        #chiQ = vQ[0]/(bin_fc*vQ[2]) # applying the correction  \n",
    "        chiQ = vQ[0]/vQ[2]\n",
    "        chiQok = chiQ[np.abs(chiQ)<xlims_arr[i]]\n",
    "\n",
    "        # plot histograms\n",
    "        \n",
    "        Xmin = -xlims_arr[i]\n",
    "        Xmax = xlims_arr[i]\n",
    "        bins = 40 \n",
    "        title= r'$ '+' '+ str(log_tau_min[i])+'-'+str(log_tau_max[i])+'$'\n",
    "        plot2Chistograms(chiQok, chiSok, Xmin=Xmin, Xmax=Xmax, Ymin=0.0, \n",
    "                             Ymax=0.55, ax=axs[i,j],bins=bins,  \n",
    "                         title=title, axes_text_size=axes_text_size)\n",
    "        # alter manually ticks for the first row....\n",
    "        if i == 0 : \n",
    "            axs[i,j].set_xticks([-4,-2,0,2,4])\n",
    "            \n",
    "            #minorLocator = AutoMinorLocator(5)\n",
    "            #ax[i].xaxis.set_minor_locator(minorLocator)\n",
    "            #minorLocator = AutoMinorLocator(5)\n",
    "            #ax[i].yaxis.set_minor_locator(minorLocator)\n",
    "            \n",
    "        # Make more ticks, on both sides...\n",
    "        axs[i,j].tick_params(which='both', direction='in', width='1')\n",
    "        axs[i,j].tick_params(which='major', length=5)\n",
    "        #axs[i,j].tick_params(which='minor', length=5, color='black' ) \n",
    "        axs[i,j].yaxis.set_ticks_position('both')\n",
    "        axs[i,j].xaxis.set_ticks_position('both')\n",
    "        axs[i,j].locator_params(nbins=5, axis='x')\n",
    "\n",
    "    \n",
    "    #stepsize=5\n",
    "    #ax.xaxis.set_ticks(np.arange(start, end, stepsize))\n",
    "        \n",
    "        \n",
    "        # save the value of robust width of stellar chi distribution...\n",
    "        stdev_rob_S = 0.7414 *(np.percentile(chiSok,75) - np.percentile(chiSok,25) )\n",
    "        #store_fc_starB[row,column] = [magnitude_max, deltaTrange]\n",
    "        store_fc_starB[j,i] = stdev_rob_S\n",
    "        \n",
    "Xlabel = '$\\chi = \\Delta mag / error$'\n",
    "Ylabel = '$n / (N\\Delta_{bin})$'\n",
    "fig.text(0.5, 0.04, Xlabel, ha='center', va='center', fontsize=axes_label_font)\n",
    "fig.text(0.03, 0.5, Ylabel, ha='center', va='center', rotation='vertical', \n",
    "         fontsize=axes_label_font)\n",
    "\n",
    "#name = 'poster_r_cut_qso_starsB_histogram_grid.png'\n",
    "#name = None\n",
    "name = outDir+'Fig_3_histogram_panels.png'\n",
    "if (name is None):\n",
    "    plt.show() \n",
    "else:\n",
    "    print('saving plot to: %s'%name)\n",
    "    fig.subplots_adjust(wspace=0.46, hspace=0.36, left=0.12, right=0.94, \n",
    "                        bottom=0.10, top=0.95)\n",
    "    plt.savefig(name, bbox_inches='tight')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.axis.XTick at 0x12295e160>,\n",
       " <matplotlib.axis.XTick at 0x11a2a2fd0>,\n",
       " <matplotlib.axis.XTick at 0x119f586a0>,\n",
       " <matplotlib.axis.XTick at 0x126abc668>,\n",
       " <matplotlib.axis.XTick at 0x11b18cfd0>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax = axs[0,0]\n",
    "xticks = ax.get_xticks()\n",
    "ax.set_xticks([-4,-2,0,2,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5. , -2.5,  0. ,  2.5,  5. ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xticks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "17-18_qso_mi_tau_ei-log_t_0-1.7.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([array([0, 1, 2]), array([0, 1, 2, 3]), 0.0, 0.0], dtype=object)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np \n",
    "\n",
    "A = list(np.zeros(4))\n",
    "A[0] = np.arange(3)\n",
    "A[1] = np.arange(4)\n",
    "\n",
    "B = np.ravel(A)\n",
    "B "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate corrrection factors,  show that they work... "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Save the robust width of chi distritbution for stars and quasars ... \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saved r_cut_starsB_chi_robust_width.txt\n"
     ]
    }
   ],
   "source": [
    "data = np.column_stack((store_fc_starB[0], store_fc_starB[1], store_fc_starB[2]))\n",
    "fname = b+'_starsB_chi_robust_width.txt'\n",
    "print('Saved %s' % fname)\n",
    "np.savetxt(outDir+fname, data, fmt='%s', delimiter= ' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read-in the robust widths, calculate their mean to use as a correction factor... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file = outDir + fname\n",
    "sigmaG_chi_blue_stars = np.loadtxt(file, unpack=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the mean, and save as a correction-factor file : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.88971443,  1.10721   ,  1.2876506 ])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fc = np.mean(sigmaG_chi_blue_stars, axis = 1)\n",
    "fc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saved r_cut_minMag_maxMag_mean_fc.txt\n"
     ]
    }
   ],
   "source": [
    "data  = np.column_stack((Min_arr, Max_arr, fc))\n",
    "fname = b+'_minMag_maxMag_mean_fc.txt'\n",
    "print('Saved %s' % fname)\n",
    "np.savetxt(outDir+fname, data, fmt='%s', delimiter= ' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the corrected histograms, to show that it works ... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# plot the same timescale-magnitude range before we get too specific... \n",
    "# if with one bin range it looks good, set testing = False, and run for all ... \n",
    "b = 'r_cut'\n",
    "testing = False\n",
    "\n",
    "if testing is True : \n",
    "    # just for testing  - load only 1/16 files (one for QSO one for Stars) and experiment with how it looks \n",
    "    # if you use that, make sure to comment out those lines below !  \n",
    "    j=0\n",
    "    i=0\n",
    "\n",
    "    datafileS = outDir+b+'_'+str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+'starsB'+'_mi_tau_ei-log_tau_'+\\\n",
    "                            str(tau_min_arr[i])+'-'+str(tau_max_arr[i])+'.txt'\n",
    "    vS = np.loadtxt(datafileS, unpack=True)\n",
    "\n",
    "    datafileQ = outDir+b+'_'+str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+'qso'+'_mi_tau_ei-log_tau_'+\\\n",
    "            str(tau_min_arr[i])+'-'+str(tau_max_arr[i])+'.txt'\n",
    "    vQ = np.loadtxt(datafileQ, unpack=True)\n",
    "    print('Read in the xi,tau,ei  data from \\n %s and \\n %s for testing...'%(datafileS, datafileQ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'plt' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-20d2d9335b55>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmagic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'matplotlib inline'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots_adjust\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwspace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.46\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhspace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.36\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mleft\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.94\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbottom\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtop\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.95\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'plt' is not defined"
     ]
    }
   ],
   "source": [
    "import matplotlib \n",
    "matplotlib.rc('xtick', labelsize=15) \n",
    "matplotlib.rc('ytick', labelsize=15) \n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "fig, axs = plt.subplots(4,3, figsize=(8, 8))\n",
    "fig.subplots_adjust(wspace=0.46, hspace=0.36, left=0.12, right=0.94, bottom=0.10, top=0.95)\n",
    "\n",
    "# initiate a storage array for the robust widths of chi distributions ... \n",
    "store_fc_starB = np.zeros((3,4))\n",
    "\n",
    "for i in range(len(tau_max_arr)):  # \n",
    "    \n",
    "    for j in range(len(Min_arr) ):  # \n",
    "        \n",
    "        bin_fc = fc[j]\n",
    "       \n",
    "        if testing is not True: \n",
    "            datafileS = outDir+'r_cut_'+str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+'starsB'+'_mi_tau_ei-log_tau_'+\\\n",
    "                        str(tau_min_arr[i])+'-'+str(tau_max_arr[i])+'.txt'\n",
    "            vS = np.loadtxt(datafileS, unpack=True)\n",
    "        \n",
    "            datafileQ = outDir+'r_cut_'+str(Min_arr[j])+'-'+str(Max_arr[j])+'_'+'qso'+'_mi_tau_ei-log_tau_'+\\\n",
    "                        str(tau_min_arr[i])+'-'+str(tau_max_arr[i])+'.txt'\n",
    "            vQ = np.loadtxt(datafileQ, unpack=True)\n",
    "        \n",
    "        # calculate the robust width of the chi distribution .... \n",
    "        chiS = vS[0]/(bin_fc*vS[2]) # applying the error correction : ei_corr = fc * ei \n",
    "        chiSok = chiS[np.abs(chiS)<5]\n",
    "        stdev_rob_S = 0.7414 *(np.percentile(chiSok,75) - np.percentile(chiSok,25) )\n",
    "        \n",
    "        chiQ = vQ[0]/(bin_fc*vQ[2]) # applying the correction  \n",
    "        chiQok = chiQ[np.abs(chiQ)<xlims_arr[i]]\n",
    "\n",
    "        # plot histograms\n",
    "        \n",
    "        Xmin = -xlims_arr[i]\n",
    "        Xmax = xlims_arr[i]\n",
    "        bins = 40 \n",
    "        title= r'$ '+' '+ str(tau_min_arr[i])+'-'+str(tau_max_arr[i])+'$'\n",
    "        plot2Chistograms(chiQok, chiSok, Xmin=Xmin, Xmax=Xmax, Ymin=0.0, \n",
    "                             Ymax=0.55, ax=axs[i,j],bins=bins,  \n",
    "                         title=title)\n",
    "        # save the value of robust width of stellar chi distribution...\n",
    "        stdev_rob_S = 0.7414 *(np.percentile(chiSok,75) - np.percentile(chiSok,25) )\n",
    "        #store_fc_starB[row,column] = [magnitude_max, deltaTrange]\n",
    "        store_fc_starB[j,i] = stdev_rob_S\n",
    "\n",
    "Xlabel = '$\\chi = \\Delta mag / error$'\n",
    "Ylabel = '$n / (N\\Delta_{bin})$'\n",
    "fig.text(0.5, 0.04, Xlabel, ha='center', va='center',fontsize=20)\n",
    "fig.text(0.03, 0.5, Ylabel, ha='center', va='center', rotation='vertical',fontsize=20)\n",
    "\n",
    "name = outDir+'Fig_3_histogram_panels_corrected.png'\n",
    "if (name is None):\n",
    "    plt.show() \n",
    "else:\n",
    "    print('saving plot to: %s'%name)\n",
    "    plt.savefig(name, bbox_inches='tight')\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Illustration only ] Calculating the full linear fit along timescales ... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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atGhZ63FsKcvT0xNPT0+zbdavX4WzszOzZ78MwPnzGVy8WEhGxu/89tsvPPfc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\nHKeU/D+Zuc7CvBLn9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e55ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func(x, a, b):\n",
    "    return a * x + b\n",
    "\n",
    "from scipy.optimize import curve_fit\n",
    "# popt is func(x, popt*)\n",
    "\n",
    "fig,ax = plt.subplots()\n",
    "\n",
    "aCoeffArr = np.zeros(len(Min_arr))\n",
    "bCoeffArr =np.zeros(len(Min_arr))\n",
    "stdArr = np.zeros(len(Min_arr))\n",
    "colors = ['']\n",
    "for i in range(len(Min_arr)):\n",
    "    tau_cen = (np.array(tau_max_arr) + np.array(tau_min_arr)) / 2.0\n",
    "    popt, pcov = curve_fit(func, tau_cen, store_fc_starB[i,:])\n",
    "    a,b = popt[0], popt[1]\n",
    "    aCoeffArr[i] = a\n",
    "    bCoeffArr[i] = b\n",
    "    \n",
    "    x = np.sort(np.append(np.array(tau_min_arr), tau_max_arr)) #np.linspace(tau_min_arr[0], tau_min_arr[-1])\n",
    "    y = a * x + b\n",
    "    std = np.std(a * np.array(tau_cen)  - store_fc_starB[i,:] )\n",
    "    stdArr[i] = std\n",
    "    ax.plot(x,y)\n",
    "    ax.scatter(tau_cen, store_fc_starB[i,:])\n",
    "    ax.text(x=0, y=store_fc_starB[i,0]+0.05,  s=r'$y='+str(a)[:6]+'x + '+str(b)[:5]+'$ ', fontsize=20)\n",
    "\n",
    "for j in range(len(tau_min_arr)):\n",
    "    ax.fill_between(x=[tau_min_arr[j],tau_max_arr[j]],y1=[0.8,0.8],y2=[1.4,1.4],alpha=0.1)\n",
    "\n",
    "ax.set_ylim(0.8,1.4)\n",
    "ax.set_xlabel(r'$log_{10} (\\Delta _{t})$ [days]',fontsize=20)\n",
    "ax.set_ylabel(r'$\\sigma_{G}(\\chi_{Blue})$',fontsize=20)\n",
    "plt.tight_layout()\n",
    "plt.savefig(outDir + 'Blue_Stars_coefficients.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Store the linear correction coefficients \n",
    "data = np.column_stack((aCoeffArr, bCoeffArr, stdArr, Min_arr, Max_arr))\n",
    "np.savetxt(outDir+'fc_starsB_a_b_coeff.txt',data, header='  a      b     stddev   rMagMin  rMagMax',fmt='%2.5f    %2.5f    %2.5f  %2.2f  %2.2f  ')\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}