{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# HDF-N master catalogue\n",
    "## Preparation of CANDELS-GOODS-N data\n",
    "\n",
    "CANDELS-GOODS-N catalogue: the catalogue comes from `dmu0_CANDELS-GOODS-N`.\n",
    "\n",
    "In the catalogue, we keep:\n",
    "\n",
    "- The identifier (it's unique in the catalogue);\n",
    "- The position;\n",
    "- The stellarity;\n",
    "- The total magnitude.\n",
    "\n",
    "We don't know when the maps have been observed. We will use the year of the reference paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This notebook was run with herschelhelp_internal version: \n",
      "0246c5d (Thu Jan 25 17:01:47 2018 +0000) [with local modifications]\n"
     ]
    }
   ],
   "source": [
    "from herschelhelp_internal import git_version\n",
    "print(\"This notebook was run with herschelhelp_internal version: \\n{}\".format(git_version()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "#%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('figure', figsize=(10, 6))\n",
    "\n",
    "from collections import OrderedDict\n",
    "import os\n",
    "\n",
    "from astropy import units as u\n",
    "from astropy.coordinates import SkyCoord\n",
    "from astropy.table import Column, Table\n",
    "import numpy as np\n",
    "\n",
    "from herschelhelp_internal.flagging import  gaia_flag_column\n",
    "from herschelhelp_internal.masterlist import nb_astcor_diag_plot, remove_duplicates\n",
    "from herschelhelp_internal.utils import astrometric_correction, flux_to_mag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "OUT_DIR =  os.environ.get('TMP_DIR', \"./data_tmp\")\n",
    "try:\n",
    "    os.makedirs(OUT_DIR)\n",
    "except FileExistsError:\n",
    "    pass\n",
    "\n",
    "RA_COL = \"candels-gn_ra\"\n",
    "DEC_COL = \"candels-gn_dec\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I - Column selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: UnitsWarning: '0 use, gt 1 no-use' did not parse as fits unit: At col 2, Unit 'use' not supported by the FITS standard. Did you mean uS or us? [astropy.units.core]\n",
      "WARNING: UnitsWarning: '0 galaxy, 1 star' did not parse as fits unit: At col 2, Unit 'galaxy' not supported by the FITS standard.  [astropy.units.core]\n"
     ]
    }
   ],
   "source": [
    "imported_columns = OrderedDict({\n",
    "        'ID': \"candels-gn_id\",\n",
    "        'RA': \"candels-gn_ra\",\n",
    "        'DEC': \"candels-gn_dec\",\n",
    "        'CLASS_STAR':  \"candels-gn_stellarity\",\n",
    "    #HST data\n",
    "        'ACS_F435W_FLUX': \"f_acs_f435w\", \n",
    "        'ACS_F435W_FLUXERR': \"ferr_acs_f435w\", \n",
    "        'ACS_F606W_FLUX': \"f_acs_f606w\", \n",
    "        'ACS_F606W_FLUXERR': \"ferr_acs_f606w\", \n",
    "        'ACS_F775W_FLUX': \"f_acs_f775w\", \n",
    "        'ACS_F775W_FLUXERR': \"ferr_acs_f775w\", \n",
    "        'ACS_F814W_FLUX': \"f_acs_f814w\", \n",
    "        'ACS_F814W_FLUXERR': \"ferr_acs_f814w\", \n",
    "        'ACS_F850LP_FLUX': \"f_acs_f850lp\", \n",
    "        'ACS_F850LP_FLUXERR': \"ferr_acs_f850lp\", \n",
    "    \n",
    "        'WFC3_F105W_FLUX': \"f_wfc3_f105w\", \n",
    "        'WFC3_F105W_FLUXERR': \"ferr_wfc3_f105w\", \n",
    "        'WFC3_F125W_FLUX': \"f_wfc3_f125w\", \n",
    "        'WFC3_F125W_FLUXERR': \"ferr_wfc3_f125w\", \n",
    "        'WFC3_F140W_FLUX': \"f_wfc3_f140w\", \n",
    "        'WFC3_F140W_FLUXERR': \"ferr_wfc3_f140w\", \n",
    "        'WFC3_F160W_FLUX': \"f_wfc3_f160w\", \n",
    "        'WFC3_F160W_FLUXERR': \"ferr_wfc3_f160w\", \n",
    "    #MOIRCS. There is a Ks and K. We believe this to be K.\n",
    "        'MOIRCS_K_FLUX':\"f_moircs_k\",\n",
    "        'MOIRCS_K_FLUXERR':\"ferr_moircs_k\",\n",
    "    #CFHT WIRCAM\n",
    "        'CFHT_Ks_FLUX': \"f_candels-wircam_k\",# 33 WIRCAM_K_FLUX Flux density (in μJy) in the Ks-band (CFHT/WIRCam) (3)\n",
    "        'CFHT_Ks_FLUXERR': \"ferr_candels-wircam_k\",# 34 WIRCAM_K_FLUXERR \n",
    "    #Spitzer/IRAC\n",
    "        'IRAC_CH1_SCANDELS_FLUX': \"f_candels-irac_i1\",# 47 IRAC_CH1_FLUX Flux density (in μJy) in the 3.6μm-band (Spitzer/IRAC) (3)\n",
    "        'IRAC_CH1_SCANDELS_FLUXERR': \"ferr_candels-irac_i1\",# 48 IRAC_CH1_FLUXERR Flux uncertainty (in μJy) in the 3.6μm-band (Spitzer/IRAC) (3)\n",
    "        'IRAC_CH2_SCANDELS_FLUX': \"f_candels-irac_i2\",# 49 IRAC_CH2_FLUX Flux density (in μJy) in the 4.5μm-band (Spitzer/IRAC) (3)\n",
    "        'IRAC_CH2_SCANDELS_FLUXERR': \"ferr_candels-irac_i2\",# 50 IRAC_CH2_FLUXERR Flux uncertainty (in μJy) in the 4.5μm-band (Spitzer/IRAC) (3)\n",
    "        'IRAC_CH3_FLUX': \"f_candels-irac_i3\",# 51 IRAC_CH3_FLUX Flux density (in μJy) in the 5.8μm-band (Spitzer/IRAC) (3)\n",
    "        'IRAC_CH3_FLUXERR': \"ferr_candels-irac_i3\",# 52 IRAC_CH3_FLUXERR Flux uncertainty (in μJy) in the 5.8μm-band (Spitzer/IRAC) (3)\n",
    "        'IRAC_CH4_FLUX': \"f_candels-irac_i4\",# 53 IRAC_CH4_FLUX Flux density (in μJy) in the 8.0μm-band (Spitzer/IRAC) (3)\n",
    "        'IRAC_CH4_FLUXERR': \"ferr_candels-irac_i4\"# 54 IRAC_CH4_FLUXERR\n",
    "    \n",
    "    \n",
    "    })\n",
    "\n",
    "\n",
    "catalogue = Table.read(\"../../dmu0/dmu0_CANDELS-GOODS-N/data/CANDELS.GOODSN.F160W.v1_1.photom.fits\")[list(imported_columns)]\n",
    "for column in imported_columns:\n",
    "    catalogue[column].name = imported_columns[column]\n",
    "\n",
    "epoch = 2011\n",
    "\n",
    "# Clean table metadata\n",
    "catalogue.meta = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/herschelhelp_internal/herschelhelp_internal/utils.py:76: RuntimeWarning: divide by zero encountered in log10\n",
      "  magnitudes = 2.5 * (23 - np.log10(fluxes)) - 48.6\n",
      "/opt/herschelhelp_internal/herschelhelp_internal/utils.py:76: RuntimeWarning: invalid value encountered in log10\n",
      "  magnitudes = 2.5 * (23 - np.log10(fluxes)) - 48.6\n",
      "/opt/herschelhelp_internal/herschelhelp_internal/utils.py:80: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  errors = 2.5 / np.log(10) * errors_on_fluxes / fluxes\n"
     ]
    }
   ],
   "source": [
    "# Adding flux and band-flag columns\n",
    "for col in catalogue.colnames:\n",
    "    if col.startswith('f_'):\n",
    "        \n",
    "        errcol = \"ferr{}\".format(col[1:])\n",
    "        \n",
    "        # Some object have a magnitude to 0, we suppose this means missing value\n",
    "        #catalogue[col][catalogue[col] <= 0] = np.nan\n",
    "        #catalogue[errcol][catalogue[errcol] <= 0] = np.nan  \n",
    "        \n",
    "\n",
    "        mag, error = flux_to_mag(np.array(catalogue[col])*1.e-6, np.array(catalogue[errcol])*1.e-6)\n",
    "        \n",
    "        # Fluxes are added in µJy\n",
    "        catalogue.add_column(Column(mag, name=\"m{}\".format(col[1:])))\n",
    "        catalogue.add_column(Column(error, name=\"m{}\".format(errcol[1:])))\n",
    "        \n",
    "\n",
    "        \n",
    "        # Band-flag column\n",
    "        if \"ap\" not in col:\n",
    "            catalogue.add_column(Column(np.zeros(len(catalogue), dtype=bool), name=\"flag{}\".format(col[1:])))\n",
    "        \n",
    "# TODO: Set to True the flag columns for fluxes that should not be used for SED fitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Table length=10&gt;\n",
       "<table id=\"table140686318638864-397166\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>idx</th><th>candels-gn_id</th><th>candels-gn_ra</th><th>candels-gn_dec</th><th>candels-gn_stellarity</th><th>f_acs_f435w</th><th>ferr_acs_f435w</th><th>f_acs_f606w</th><th>ferr_acs_f606w</th><th>f_acs_f775w</th><th>ferr_acs_f775w</th><th>f_acs_f814w</th><th>ferr_acs_f814w</th><th>f_acs_f850lp</th><th>ferr_acs_f850lp</th><th>f_wfc3_f105w</th><th>ferr_wfc3_f105w</th><th>f_wfc3_f125w</th><th>ferr_wfc3_f125w</th><th>f_wfc3_f140w</th><th>ferr_wfc3_f140w</th><th>f_wfc3_f160w</th><th>ferr_wfc3_f160w</th><th>f_moircs_k</th><th>ferr_moircs_k</th><th>f_candels-wircam_k</th><th>ferr_candels-wircam_k</th><th>f_candels-irac_i1</th><th>ferr_candels-irac_i1</th><th>f_candels-irac_i2</th><th>ferr_candels-irac_i2</th><th>f_candels-irac_i3</th><th>ferr_candels-irac_i3</th><th>f_candels-irac_i4</th><th>ferr_candels-irac_i4</th><th>m_acs_f435w</th><th>merr_acs_f435w</th><th>flag_acs_f435w</th><th>m_acs_f606w</th><th>merr_acs_f606w</th><th>flag_acs_f606w</th><th>m_acs_f775w</th><th>merr_acs_f775w</th><th>flag_acs_f775w</th><th>m_acs_f814w</th><th>merr_acs_f814w</th><th>flag_acs_f814w</th><th>m_acs_f850lp</th><th>merr_acs_f850lp</th><th>flag_acs_f850lp</th><th>m_wfc3_f105w</th><th>merr_wfc3_f105w</th><th>flag_wfc3_f105w</th><th>m_wfc3_f125w</th><th>merr_wfc3_f125w</th><th>flag_wfc3_f125w</th><th>m_wfc3_f140w</th><th>merr_wfc3_f140w</th><th>flag_wfc3_f140w</th><th>m_wfc3_f160w</th><th>merr_wfc3_f160w</th><th>flag_wfc3_f160w</th><th>m_moircs_k</th><th>merr_moircs_k</th><th>flag_moircs_k</th><th>m_candels-wircam_k</th><th>merr_candels-wircam_k</th><th>flag_candels-wircam_k</th><th>m_candels-irac_i1</th><th>merr_candels-irac_i1</th><th>flag_candels-irac_i1</th><th>m_candels-irac_i2</th><th>merr_candels-irac_i2</th><th>flag_candels-irac_i2</th><th>m_candels-irac_i3</th><th>merr_candels-irac_i3</th><th>flag_candels-irac_i3</th><th>m_candels-irac_i4</th><th>merr_candels-irac_i4</th><th>flag_candels-irac_i4</th></tr></thead>\n",
       "<thead><tr><th></th><th></th><th></th><th></th><th>0 galaxy, 1 star</th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr></thead>\n",
       "<tr><td>0</td><td>1</td><td>189.15216178</td><td>62.09177764</td><td>0</td><td>-0.03041</td><td>0.03046</td><td>-0.01637</td><td>0.03921</td><td>0.036</td><td>0.0591</td><td>-0.00105</td><td>64894254393.4</td><td>-0.07984</td><td>0.07474</td><td>-0.07928</td><td>0.05425</td><td>0.00583</td><td>0.03354</td><td>-2e-05</td><td>40607499435.5</td><td>0.73155</td><td>0.37962</td><td>0.01084</td><td>1444.70263</td><td>-0.20261</td><td>0.09029</td><td>-0.08455</td><td>0.13695</td><td>-0.18952</td><td>0.13653</td><td>-0.37712</td><td>1.00009</td><td>-0.35061</td><td>1.52074</td><td>nan</td><td>-1.08752136787</td><td>False</td><td>nan</td><td>-2.60059356069</td><td>False</td><td>27.5092437481</td><td>1.78241693614</td><td>False</td><td>nan</td><td>-6.71028966435e+13</td><td>False</td><td>nan</td><td>-1.01638181292</td><td>False</td><td>nan</td><td>-0.742951426692</td><td>False</td><td>29.4858286131</td><td>6.2462422483</td><td>False</td><td>nan</td><td>-2.20445161609e+15</td><td>False</td><td>24.2393899634</td><td>0.563416277835</td><td>False</td><td>28.8124267945</td><td>144701.65595</td><td>False</td><td>nan</td><td>-0.483841478346</td><td>False</td><td>nan</td><td>-1.75862298334</td><td>False</td><td>nan</td><td>-0.782163170302</td><td>False</td><td>nan</td><td>-2.8792795954</td><td>False</td><td>nan</td><td>-4.70928517733</td><td>False</td></tr>\n",
       "<tr><td>1</td><td>2</td><td>189.14883356</td><td>62.09202743</td><td>0</td><td>-0.04039</td><td>0.12865</td><td>0.02556</td><td>0.15445</td><td>0.05139</td><td>0.23871</td><td>-0.00188</td><td>264842218594.0</td><td>-0.18039</td><td>0.3039</td><td>-0.0424</td><td>0.25053</td><td>0.23843</td><td>0.15215</td><td>-0.00038</td><td>165724690769.0</td><td>1.09767</td><td>0.38818</td><td>0.00992</td><td>1395.40524</td><td>0.00836</td><td>0.08557</td><td>0.05314</td><td>0.13861</td><td>0.62588</td><td>0.13547</td><td>-0.54797</td><td>0.99801</td><td>-1.1307</td><td>1.33768</td><td>nan</td><td>-3.45828083046</td><td>False</td><td>27.8810978763</td><td>6.56071818564</td><td>False</td><td>27.1228034558</td><td>5.04331756057</td><td>False</td><td>nan</td><td>-1.5295148153e+14</td><td>False</td><td>nan</td><td>-1.82912152905</td><td>False</td><td>nan</td><td>-6.41531819288</td><td>False</td><td>25.456597753</td><td>0.692843868448</td><td>False</td><td>nan</td><td>-4.73508675765e+14</td><td>False</td><td>23.7988205129</td><td>0.383959732855</td><td>False</td><td>28.9087208196</td><td>152726.006994</td><td>False</td><td>29.0944843064</td><td>11.1132113686</td><td>False</td><td>27.0864461248</td><td>2.8320266342</td><td>False</td><td>24.4087723153</td><td>0.235004607367</td><td>False</td><td>nan</td><td>-1.97743597224</td><td>False</td><td>nan</td><td>-1.28448536869</td><td>False</td></tr>\n",
       "<tr><td>2</td><td>3</td><td>189.15133834</td><td>62.09213218</td><td>0</td><td>0.01698</td><td>0.0183</td><td>-0.01012</td><td>0.0216</td><td>-0.05957</td><td>0.03347</td><td>-0.00107</td><td>37153131237.0</td><td>-0.03646</td><td>0.04346</td><td>0.02456</td><td>0.03178</td><td>-0.00887</td><td>0.01767</td><td>-2e-05</td><td>23193730332.7</td><td>0.36765</td><td>0.04515</td><td>0.01055</td><td>1448.69502</td><td>-0.01034</td><td>0.08998</td><td>0.11392</td><td>0.14662</td><td>0.27129</td><td>0.14499</td><td>0.90009</td><td>1.01676</td><td>0.47453</td><td>1.55453</td><td>28.3251557852</td><td>1.17013972598</td><td>False</td><td>nan</td><td>-2.3173816228</td><td>False</td><td>nan</td><td>-0.61003174036</td><td>False</td><td>nan</td><td>-3.76995324338e+13</td><td>False</td><td>nan</td><td>-1.29418802685</td><td>False</td><td>27.9244290938</td><td>1.40491435616</td><td>False</td><td>nan</td><td>-2.1629040291</td><td>False</td><td>nan</td><td>-1.25911363728e+15</td><td>False</td><td>24.9864135742</td><td>0.133336025146</td><td>False</td><td>28.8418688509</td><td>149090.107381</td><td>False</td><td>nan</td><td>-9.44821505843</td><td>False</td><td>26.2585000593</td><td>1.39738976775</td><td>False</td><td>25.3164155361</td><td>0.580267950635</td><td>False</td><td>24.0142851582</td><td>1.22646973475</td><td>False</td><td>24.7093408152</td><td>3.55680252541</td><td>False</td></tr>\n",
       "<tr><td>3</td><td>4</td><td>189.14960603</td><td>62.09211704</td><td>0</td><td>-0.02057</td><td>0.06794</td><td>0.06738</td><td>0.08303</td><td>-0.08115</td><td>0.12626</td><td>-0.00202</td><td>142937077016.0</td><td>-0.0238</td><td>0.16321</td><td>0.16267</td><td>0.12396</td><td>-0.08133</td><td>0.06801</td><td>-0.00034</td><td>89442699180.2</td><td>2.03812</td><td>0.36995</td><td>0.01363</td><td>1618.73109</td><td>0.0057</td><td>0.09325</td><td>0.55563</td><td>0.13483</td><td>0.30043</td><td>0.13159</td><td>-0.06876</td><td>0.97509</td><td>1.99878</td><td>1.36655</td><td>nan</td><td>-3.58604364372</td><td>False</td><td>26.8286724834</td><td>1.33791447137</td><td>False</td><td>nan</td><td>-1.68927976849</td><td>False</td><td>nan</td><td>-7.68277027319e+13</td><td>False</td><td>nan</td><td>-7.44550445288</td><td>False</td><td>25.8717313333</td><td>0.827367430638</td><td>False</td><td>nan</td><td>-0.907917364879</td><td>False</td><td>nan</td><td>-2.85621108092e+14</td><td>False</td><td>23.1269256232</td><td>0.197077752512</td><td>False</td><td>28.5637603604</td><td>128944.603828</td><td>False</td><td>29.5103128608</td><td>17.7622633498</td><td>False</td><td>24.5380357839</td><td>0.263466357986</td><td>False</td><td>25.2056417555</td><td>0.475558456826</td><td>False</td><td>nan</td><td>-15.3968952283</td><td>False</td><td>23.148087512</td><td>0.742309213927</td><td>False</td></tr>\n",
       "<tr><td>4</td><td>5</td><td>189.14808454</td><td>62.09249699</td><td>0</td><td>0.03149</td><td>0.04246</td><td>-0.05597</td><td>0.05101</td><td>-0.02036</td><td>0.07891</td><td>-0.00161</td><td>87996244750.6</td><td>-0.06562</td><td>0.10256</td><td>0.22797</td><td>0.08041</td><td>0.15102</td><td>0.04451</td><td>-0.00032</td><td>55063541332.5</td><td>1.88213</td><td>0.40744</td><td>0.01539</td><td>1705.73592</td><td>0.41502</td><td>0.10039</td><td>8.86312</td><td>0.12774</td><td>4.06394</td><td>0.12548</td><td>4.95255</td><td>0.96467</td><td>2.10368</td><td>1.29263</td><td>27.6545683484</td><td>1.4639682202</td><td>False</td><td>nan</td><td>-0.989519453363</td><td>False</td><td>nan</td><td>-4.20802769732</td><td>False</td><td>nan</td><td>-5.93420551606e+13</td><td>False</td><td>nan</td><td>-1.69693851204</td><td>False</td><td>25.5053057519</td><td>0.382962882066</td><td>False</td><td>25.9524138352</td><td>0.319998135835</td><td>False</td><td>nan</td><td>-1.86826501209e+14</td><td>False</td><td>23.2133759571</td><td>0.235038153192</td><td>False</td><td>28.4319034504</td><td>120336.53308</td><td>False</td><td>24.8548274348</td><td>0.26263085537</td><td>False</td><td>21.5310334266</td><td>0.0156482077187</td><td>False</td><td>22.3776317815</td><td>0.033523668896</td><td>False</td><td>22.162927828</td><td>0.211482396875</td><td>False</td><td>23.0925508048</td><td>0.667142906885</td><td>False</td></tr>\n",
       "<tr><td>5</td><td>6</td><td>189.14870539</td><td>62.09269735</td><td>0</td><td>0.00072</td><td>0.05542</td><td>-0.00956</td><td>0.06588</td><td>-0.04616</td><td>0.10169</td><td>-0.0039</td><td>114216919405.0</td><td>-0.16295</td><td>0.12953</td><td>-0.02333</td><td>0.09892</td><td>0.02109</td><td>0.05702</td><td>-0.00022</td><td>71471096072.1</td><td>1.07439</td><td>0.24742</td><td>0.01249</td><td>1542.03164</td><td>0.14265</td><td>0.09545</td><td>-4.62312</td><td>0.12194</td><td>-1.85403</td><td>0.11972</td><td>-3.1253</td><td>0.87925</td><td>-2.1586</td><td>1.23912</td><td>31.7566687589</td><td>83.5715284274</td><td>False</td><td>nan</td><td>-7.48203987128</td><td>False</td><td>nan</td><td>-2.39186556893</td><td>False</td><td>nan</td><td>-3.17972934857e+13</td><td>False</td><td>nan</td><td>-0.863058672</td><td>False</td><td>nan</td><td>-4.60355873873</td><td>False</td><td>28.0898085507</td><td>2.93545179684</td><td>False</td><td>nan</td><td>-3.52721620905e+14</td><td>False</td><td>23.8220951064</td><td>0.250032904049</td><td>False</td><td>28.6585939041</td><td>134046.403557</td><td>False</td><td>26.01432056</td><td>0.726488052886</td><td>False</td><td>nan</td><td>-0.028637515965</td><td>False</td><td>nan</td><td>-0.0701090804537</td><td>False</td><td>nan</td><td>-0.305453415043</td><td>False</td><td>nan</td><td>-0.623254630798</td><td>False</td></tr>\n",
       "<tr><td>6</td><td>7</td><td>189.14636359</td><td>62.09288181</td><td>0</td><td>0.11011</td><td>0.14499</td><td>0.00357</td><td>0.16921</td><td>1.09122</td><td>0.27022</td><td>-0.01357</td><td>292273460385.0</td><td>1.98403</td><td>0.35271</td><td>2.74672</td><td>0.32787</td><td>3.65231</td><td>0.15878</td><td>-0.00097</td><td>182889756397.0</td><td>4.56103</td><td>2.85484</td><td>0.01711</td><td>1758.97257</td><td>2.1676</td><td>0.10799</td><td>51.32974</td><td>0.09993</td><td>39.13622</td><td>0.10128</td><td>33.16982</td><td>0.7209</td><td>22.66882</td><td>1.04269</td><td>26.2954330934</td><td>1.42966935181</td><td>False</td><td>30.0183294597</td><td>51.4614630832</td><td>False</td><td>23.805219207</td><td>0.268862041797</td><td>False</td><td>nan</td><td>-2.3384810437e+13</td><td>False</td><td>23.1561294132</td><td>0.193016243091</td><td>False</td><td>22.8029640255</td><td>0.129601972336</td><td>False</td><td>22.493580919</td><td>0.0472011397147</td><td>False</td><td>nan</td><td>-2.04711371134e+14</td><td>False</td><td>22.252342678</td><td>0.679584029658</td><td>False</td><td>28.3168749761</td><td>111617.779218</td><td>False</td><td>23.0600521441</td><td>0.0540914618711</td><td>False</td><td>19.6240773389</td><td>0.00211373794104</td><td>False</td><td>19.9185528082</td><td>0.00280975942025</td><td>False</td><td>20.0981422131</td><td>0.0235969694744</td><td>False</td><td>20.511427715</td><td>0.0499402387658</td><td>False</td></tr>\n",
       "<tr><td>7</td><td>8</td><td>189.14509981</td><td>62.09340188</td><td>0</td><td>0.0178</td><td>0.02649</td><td>-0.02002</td><td>0.03159</td><td>-0.01046</td><td>0.04839</td><td>-0.00229</td><td>52742979131.0</td><td>-0.04317</td><td>0.06216</td><td>0.03731</td><td>0.04688</td><td>0.01265</td><td>0.02578</td><td>-5e-05</td><td>33003853966.8</td><td>1.4936</td><td>0.21241</td><td>0.01142</td><td>1471.11023</td><td>-0.10997</td><td>0.08489</td><td>0.46067</td><td>0.14588</td><td>0.20961</td><td>0.13888</td><td>2.10853</td><td>0.90842</td><td>5.19303</td><td>1.35599</td><td>28.2739499942</td><td>1.61579505978</td><td>False</td><td>nan</td><td>-1.71320712829</td><td>False</td><td>nan</td><td>-5.02282743291</td><td>False</td><td>nan</td><td>-2.50065336198e+13</td><td>False</td><td>nan</td><td>-1.56333941366</td><td>False</td><td>27.4704368774</td><td>1.36422710477</td><td>False</td><td>28.6447736862</td><td>2.21267030503</td><td>False</td><td>nan</td><td>-7.16669582967e+14</td><td>False</td><td>23.4644142376</td><td>0.154406284984</td><td>False</td><td>28.7558347402</td><td>139863.190709</td><td>False</td><td>nan</td><td>-0.838120818604</td><td>False</td><td>24.741525173</td><td>0.343819214514</td><td>False</td><td>25.5964700051</td><td>0.71936951537</td><td>False</td><td>23.0900505387</td><td>0.467768769297</td><td>False</td><td>22.1114479212</td><td>0.283504512065</td><td>False</td></tr>\n",
       "<tr><td>8</td><td>9</td><td>189.14428042</td><td>62.09353138</td><td>0</td><td>-0.00789</td><td>0.04863</td><td>-0.02897</td><td>0.05807</td><td>-0.09221</td><td>0.08945</td><td>-0.00363</td><td>101034871370.0</td><td>0.06439</td><td>0.11654</td><td>0.25504</td><td>0.09269</td><td>0.05482</td><td>0.0502</td><td>0.0001</td><td>63222445815.3</td><td>1.96327</td><td>0.45921</td><td>0.01395</td><td>1625.22483</td><td>-0.0231</td><td>0.09401</td><td>1.17544</td><td>0.17931</td><td>1.10055</td><td>0.16543</td><td>1.08135</td><td>0.94592</td><td>-2.24309</td><td>1.45174</td><td>nan</td><td>-6.69193303389</td><td>False</td><td>nan</td><td>-2.17634454299</td><td>False</td><td>nan</td><td>-1.05323829862</td><td>False</td><td>nan</td><td>-3.02196192257e+13</td><td>False</td><td>26.8779539373</td><td>1.96508304554</td><td>False</td><td>25.3834792507</td><td>0.394592569083</td><td>False</td><td>27.052652422</td><td>0.994234904758</td><td>False</td><td>33.9</td><td>6.8642898375e+14</td><td>False</td><td>23.1675499241</td><td>0.253954332612</td><td>False</td><td>28.538564481</td><td>126492.146151</td><td>False</td><td>nan</td><td>-4.41861734239</td><td>False</td><td>23.724498836</td><td>0.16562594337</td><td>False</td><td>23.7959755547</td><td>0.16320325324</td><td>False</td><td>23.8150842886</td><td>0.949756869473</td><td>False</td><td>nan</td><td>-0.702694353724</td><td>False</td></tr>\n",
       "<tr><td>9</td><td>10</td><td>189.15491217</td><td>62.09411161</td><td>0</td><td>0.02194</td><td>0.00754</td><td>0.085</td><td>0.00929</td><td>0.25559</td><td>0.01553</td><td>0.28142</td><td>0.04471</td><td>0.34715</td><td>0.0201</td><td>0.40775</td><td>0.02116</td><td>0.50832</td><td>0.00891</td><td>2e-05</td><td>9395352460.95</td><td>0.4747</td><td>0.03888</td><td>0.01088</td><td>1479.21105</td><td>0.54232</td><td>0.09135</td><td>-0.02745</td><td>0.15104</td><td>0.06979</td><td>0.14957</td><td>-0.63339</td><td>1.0126</td><td>-1.79954</td><td>1.52496</td><td>28.0469084419</td><td>0.373129032993</td><td>False</td><td>26.5764526857</td><td>0.118664580497</td><td>False</td><td>25.3811403551</td><td>0.065970825384</td><td>False</td><td>25.2766126032</td><td>0.172494015048</td><td>False</td><td>25.048707076</td><td>0.0628641731691</td><td>False</td><td>24.8740150757</td><td>0.0563437844088</td><td>False</td><td>24.6346570063</td><td>0.0190311409828</td><td>False</td><td>35.6474250108</td><td>5.10043716166e+14</td><td>False</td><td>24.7089519207</td><td>0.088926529684</td><td>False</td><td>28.8084277616</td><td>147613.326421</td><td>False</td><td>24.5643609477</td><td>0.182884648002</td><td>False</td><td>nan</td><td>-5.97412008622</td><td>False</td><td>26.7905170042</td><td>2.3268887254</td><td>False</td><td>nan</td><td>-1.73576545405</td><td>False</td><td>nan</td><td>-0.920070841886</td><td>False</td></tr>\n",
       "</table><style>table.dataTable {clear: both; width: auto !important; margin: 0 !important;}\n",
       ".dataTables_info, .dataTables_length, .dataTables_filter, .dataTables_paginate{\n",
       "display: inline-block; margin-right: 1em; }\n",
       ".paginate_button { margin-right: 5px; }\n",
       "</style>\n",
       "<script>\n",
       "require.config({paths: {\n",
       "    datatables: 'https://cdn.datatables.net/1.10.12/js/jquery.dataTables.min'\n",
       "}});\n",
       "require([\"datatables\"], function(){\n",
       "    console.log(\"$('#table140686318638864-397166').dataTable()\");\n",
       "    $('#table140686318638864-397166').dataTable({\n",
       "        \"order\": [],\n",
       "        \"iDisplayLength\": 50,\n",
       "        \"aLengthMenu\": [[10, 25, 50, 100, 500, 1000, -1], [10, 25, 50, 100, 500, 1000, 'All']],\n",
       "        \"pagingType\": \"full_numbers\"\n",
       "    });\n",
       "});\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "catalogue[:10].show_in_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II - Removal of duplicated sources"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We remove duplicated objects from the input catalogues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The initial catalogue had 35445 sources.\n",
      "The cleaned catalogue has 35423 sources (22 removed).\n",
      "The cleaned catalogue has 21 sources flagged as having been cleaned\n"
     ]
    }
   ],
   "source": [
    "SORT_COLS = [\"merr_acs_f435w\",\"ferr_acs_f606w\",\n",
    "             \"ferr_acs_f775w\",\"ferr_acs_f814w\",\n",
    "             \"ferr_acs_f850lp\", \"ferr_wfc3_f105w\",\n",
    "             \"ferr_wfc3_f125w\",\"ferr_wfc3_f140w\",\"ferr_wfc3_f160w\"]\n",
    "FLAG_NAME = 'candels-gn_flag_cleaned'\n",
    "\n",
    "nb_orig_sources = len(catalogue)\n",
    "\n",
    "catalogue = remove_duplicates(catalogue, RA_COL, DEC_COL, sort_col=SORT_COLS,flag_name=FLAG_NAME)\n",
    "\n",
    "nb_sources = len(catalogue)\n",
    "\n",
    "print(\"The initial catalogue had {} sources.\".format(nb_orig_sources))\n",
    "print(\"The cleaned catalogue has {} sources ({} removed).\".format(nb_sources, nb_orig_sources - nb_sources))\n",
    "print(\"The cleaned catalogue has {} sources flagged as having been cleaned\".format(np.sum(catalogue[FLAG_NAME])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III - Astrometry correction\n",
    "\n",
    "We match the astrometry to the Gaia one. We limit the Gaia catalogue to sources with a g band flux between the 30th and the 70th percentile. Some quick tests show that this give the lower dispersion in the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gaia = Table.read(\"../../dmu0/dmu0_GAIA/data/GAIA_HDF-N.fits\")\n",
    "gaia_coords = SkyCoord(gaia['ra'], gaia['dec'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SG0/vEWcSk5yOajKHleQas5kVLugXT05GTEMSdzocfL783yx4aC611VUhxTOZ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\n9qjZEUIIcXv/HxRI0m70wmFiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff417fddeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WOTlY3yYCsetCMJjuEkkWUmCQi+N5mE9bEnc4Nor1vMyebvZi5/X3fWgPg2cT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff415f7d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nb_astcor_diag_plot(catalogue[RA_COL], catalogue[DEC_COL], \n",
    "                    gaia_coords.ra, gaia_coords.dec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RA correction: 0.02082349079728374 arcsec\n",
      "Dec correction: -0.02865639995377478 arcsec\n"
     ]
    }
   ],
   "source": [
    "delta_ra, delta_dec =  astrometric_correction(\n",
    "    SkyCoord(catalogue[RA_COL], catalogue[DEC_COL]),\n",
    "    gaia_coords\n",
    ")\n",
    "\n",
    "print(\"RA correction: {}\".format(delta_ra))\n",
    "print(\"Dec correction: {}\".format(delta_dec))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "catalogue[RA_COL].unit = u.deg\n",
    "catalogue[DEC_COL].unit = u.deg\n",
    "catalogue[RA_COL] = catalogue[RA_COL] +  delta_ra.to(u.deg)\n",
    "catalogue[DEC_COL] = catalogue[DEC_COL] + delta_dec.to(u.deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xetiT68TZhEckR3eJ5uGhiVhNvgt2hcPFkdOFPPDaIn44eCLoeOnp6Vx77bXY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff415d93b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HKTDIxckI4A8twAaD+FlZ2HRujugJuVlY62M9D2s49xBTScyYjk0QX/xZOjrV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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff415e5cc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nb_astcor_diag_plot(catalogue[RA_COL], catalogue[DEC_COL], \n",
    "                    gaia_coords.ra, gaia_coords.dec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV - Flagging Gaia objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "catalogue.add_column(\n",
    "    gaia_flag_column(SkyCoord(catalogue[RA_COL], catalogue[DEC_COL]), epoch, gaia)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102 sources flagged.\n"
     ]
    }
   ],
   "source": [
    "GAIA_FLAG_NAME = \"candels-gn_flag_gaia\"\n",
    "\n",
    "catalogue['flag_gaia'].name = GAIA_FLAG_NAME\n",
    "print(\"{} sources flagged.\".format(np.sum(catalogue[GAIA_FLAG_NAME] > 0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# V - Saving to disk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "catalogue.write(\"{}/CANDELS-GOODS-N.fits\".format(OUT_DIR), overwrite=True)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python (herschelhelp_internal)",
   "language": "python",
   "name": "helpint"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}