mle_implementation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TOC\n",
    "\n",
    "* [Plot samples](#Plot-samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LaMassa S82 (x-ray) catalog *versus* UKIDSS\n",
    "\n",
    "In this notebook the cross-matching procedure applied by [LaMassa et al. 2016] (LM hereafter) to multi-wavelength catalogs will  be reproduced. Particularly, we will cross-match the x-ray data from XMM-Newton AO 13 cycle to UKIDSS near-infrared. The goal here is to verify whether we can recover the very same results therein, showing us our algorithm for Maximum Likelihood Estimator to be correct.\n",
    "\n",
    "The UKIDSS catalog here in use is the same used in LM: UKIDSS-LAS Data Release 8, *primary* objects, cleaned from spurious/noisy detections; \"?*apermag3*\" magnitude measurements and accordingly errors were retrieved. The table file `ukidss.fits` here used can be taken from [my github repository][github_ukidss].\n",
    "\n",
    "The LaMassa catalog --from where we'll take the x-ray sources-- was downloaded from [CDS].\n",
    "\n",
    "[LaMassa et al. 2016]: http://arxiv.org/abs/1510.00852\n",
    "[github_ukidss]: https://github.com/chbrandt/uks82\n",
    "[CDS]: http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J%2FApJ%2F817%2F172"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximum Likelihood Estimator (MLE)\n",
    "\n",
    "MLE is applied by LM to find the correct --or most possible-- counterpart to their x-ray sources. MLE was first proposed by [Sutherland & Saunders in 1992] and is being adopted as a better alternative to the simplistic *nearest-neighbour* algorithm.\n",
    "\n",
    "What MLE does is to estimate how probable a given counterpart candidate is to be real counterpart from a source in its vicinity. The method was developed having in mind that multiple candidates can be nearby in the (RA,Dec) sky-projected plan. Accordingly, the method includes the ancillary magnitudes as a third component to help differentiating background objects from candidate(s).\n",
    "\n",
    "Consider the situation where there is a source \"S\" (which was observed by instrument \"A\") and in the vicinities, within a distance \"da\", of S there are $N$ objects (\"N1\", \"N2\", ..., \"NN\") that were observed by a different instrument (\"B\"). Also observed using \"B\", but distant a bit further from \"S\". there are $M$ objects (\"M1\", \"M2\", ..., \"MM\") that can not be related to \"S\", but will be of our help further on. The \"M\" objects lie beyond the distance \"da\" and before distance \"db\", and $db > da$. *We want now to answer the following question: which of the objects observed by \"B\" is in fact \"S\" (observed by a different instrument)?* Before coming with any answer, we are taught that instruments \"A\" and \"B\" suffer from different physical effects that lead to uncorrelated errors and different image resolutions when registering the pictures; which means that \"S\" and its (true) counterpart may *not* be one over the other, but shifted by some amount.\n",
    "\n",
    "The distance \"da\" from \"S\" is considered to be \"vicinity\", and objects inside this distance are considered, *a priori*, candidates to the (true) counterpart. Such objects will be called *ancillary*  objects. The objects from sample `M` will be called *background* objects, they compose the sample of objects observed by \"B\" definitely *not* candidate to be \"S\" counterpart.\n",
    "\n",
    "The MLE method will eventually give a score called *Reliability* ($R$) to each of the candidates. Such score --reliability-- is the probability of being the true counterpart, and is given by:\n",
    "$$\n",
    "R_j = \\frac{LR_j}{\\sum_j{LR_j}+(1-Q)}\n",
    "$$\n",
    "\n",
    "The central figure in MLE is the likelihood ratio, $LR$:\n",
    "$$\n",
    "LR_j = \\frac{q(m) f(r)}{n(m)}\n",
    "$$\n",
    ". \n",
    "\n",
    "$f(r)$ is the prior regarding the position of the candidate object relative to the source. Typically, $f(r)$ is modelled as a bidimensional Gaussian with $\\sigma$ being the quadrature sum of source's positional error and objects' average positional error:\n",
    "$$\n",
    "f(r) = \\frac{1}{2 \\pi \\sigma} exp^{-r^2/2\\sigma^2} ; \n",
    "$$\n",
    "$$\n",
    "\\sigma = \\frac{1}{2}\\Big[\\sqrt{\\sigma^2_{\\alpha_S} + \\sigma^2_{\\delta_S}} + \\sqrt{\\sigma^2_{\\alpha_O} + \\sigma^2_{\\delta_O}}\\Big]\n",
    "$$\n",
    "\n",
    "$q(m)$ is the likelihood of the object being a (good) candidate given its magnitude. It is computed by drawing the ancillary objects normalized magnitude distribution and subtracting from it the normalized background magnitude distribution.\n",
    "\n",
    "Finally, $n(m)$ is the surface density of background objects with magnitude $m$.It is computed by counting the number of background objects per magnitude bin per square-degree; normalized by the number of objects.\n",
    "\n",
    "\n",
    "[Sutherland & Saunders in 1992]: http://mnras.oxfordjournals.org/cgi/doi/10.1093/mnras/259.3.413\n",
    "\n",
    "\n",
    "## The algorithm\n",
    "\n",
    "Let's put it all together to build an algorithm.\n",
    "\n",
    "To compute MLE quantities we need to define the background and ancillary samples. \n",
    "To do that we have to define the *search radius* ($r_s$) --from where the *ancillary* sample will come out-- and the *inner & outer radii* ($r_i$, $r_o$) for the background sample.\n",
    "\n",
    "### Search radii\n",
    "\n",
    "There are different ways to estimate the (best) *search radius*. \n",
    "Typically, the instrument's (nominal) error radius, systematic plus statistical, is used, as [LaMassa et al. 2016]. \n",
    "[Timlin et al. 2016] have used the Rayleigh Criterion to estimate such radius, considering then a physical limitation on resolving close by objects; similarly, the overall PSF (FWHM) is a valid estimator. \n",
    "Another way of estimating $r_s$, data driven, is by directly estimating the typical distance between the objects in each catalog.\n",
    "\n",
    "Analogously, we have to define the *inner and outer radii*, from the primary source, of the annulus defining the background region. \n",
    "Trully speaking, the background region does *not* need to be drawn as an annulus centered centered in the source, but that is a straightforward, generic choice for sampling background sources.\n",
    "It is important to notice that the background region should avoid other sources' ancillary sample, which is to say that the (annulus) region should not intersect with another source's search area.\n",
    "\n",
    "* Estimate samples radii\n",
    "  * (ancillary) search radius: $r_{s}$\n",
    "  * background (annulus) radii: $r_{i} \\lt r_{o}$\n",
    "\n",
    "\n",
    "### Samples definition\n",
    "\n",
    "Once we have the radii defined we cross-match the catalogs to define the *ancillary* and *background* samples; At this point, each source has two lists of objects related to it:\n",
    "\n",
    "* Source\n",
    "  * ancillary sample (within Rs)\n",
    "  * background sample (between Ri and Ro)\n",
    "  \n",
    "But before looping through each primary source, we may define $q(m)$ and $n(m)$ as they are globally defined functions. And after we have $q(m)$ we may estimate $Q$.\n",
    "\n",
    "* Estimate magnitude distributions\n",
    "  * $n(m)$: background surface brightness distribution\n",
    "  * $q(m)$: ancillary brightness distribution\n",
    "  * $Q$: expected counterpart recover rate\n",
    "  \n",
    "  \n",
    "#### Radial prior\n",
    "\n",
    "The radial profile $f(r) \\propto \\sigma^{-1} \\exp^{-r^2/\\sigma^2}$ is ideally defined for each source, for $\\sigma$ is a function of the source' and ancillary objects' positional errors, $\\sigma_s$ and $\\sigma_o$, resp.:\n",
    "$$\n",
    "\\sigma = \\sqrt{\\frac{\\sigma_s^2 + \\sigma_o^2}{2}}\n",
    "$$\n",
    "\n",
    "If the positional errors are well behaved --i.e, their dispersion is small--, we may approximate $f(r)$ as a global function.\n",
    "We may consider $\\sigma_s$ and $\\sigma_o$ as the mean of the respective positional errors.\n",
    "\n",
    "* Compute mean positional errors\n",
    "  * primary sources catalog\n",
    "  * ancillary objects\n",
    "* define $f(r)$\n",
    "\n",
    "\n",
    "#### Likelood Ratio threshold\n",
    "\n",
    "The LR-threshold, $LR_{th}$, is the minimum value an ancillary object may score to be considered a counterpart candidate.\n",
    "There are different ways to compute $LR_{th}$, the simplest one is based on the reliability parameter in a assintotic case: consider there is only *one* ancillary object within the *search radius* around a source; in this case we would expect such object to be the true source' counterpart.\n",
    "Considering the Reliability parameter, $R$ a probability score, $R_j=0.5$ is the minimal (reasonable) value for such parameter so that the object can be considered a candidate.\n",
    "Using the definition of $R$ above we should have:\n",
    "$$\n",
    "0.5 = \\frac{LR_{th}}{LR_{th} + (1-Q)}\n",
    "$$\n",
    "\n",
    "$$\n",
    "LR_{th} = \\frac{0.5(Q-1)}{-0.5}\n",
    "$$\n",
    "\n",
    "$$\n",
    "LR_{th} = 1-Q\n",
    "$$\n",
    "\n",
    "\n",
    "### Counterpart evaluation\n",
    "\n",
    "Now that we have all the ingredients in place we may visit each primary source' neighbourhood and evaluate each ancillary object.\n",
    "\n",
    "For each source,\n",
    "* Loop over the respective ancillary sample:\n",
    "  * evaluate each object's $LR$\n",
    "  * remove objects with $LR_j < LR_{th}$\n",
    "* Sum all ancillaries' $LR_j$\n",
    "* Loop over all candidates:\n",
    "  * compute $R_j$\n",
    "  \n",
    "The highest $R_j$ is said to be the true counterpart.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "[Timlin et al. 2016]: http://arxiv.org/abs/1603.08488"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Coding\n",
    "\n",
    "## Read X-ray and IR catalogs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import booq\n",
    "from booq import table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### X-Ray (Lamassa-XMM-AO13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: UnitsWarning: '[10-7W]' did not parse as unit: Invalid character at col 0 [astropy.units.core]\n",
      "WARNING:astropy:UnitsWarning: '[10-7W]' did not parse as unit: Invalid character at col 0\n"
     ]
    }
   ],
   "source": [
    "tab_lm = table.ATable.read('lamassa/cds/xmmao13.dat',readme='lamassa/cds/ReadMe',format='cds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      Seq        ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM InChandra  \\\n",
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       "\n",
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       "1   1.68   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN        NaN   \n",
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       "\n",
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       "[5 rows x 121 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_lm = tab_lm.to_dataframe()\n",
    "del tab_lm\n",
    "df_lm.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "      <td>291.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.02</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2362</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.142</td>\n",
       "      <td>-0.442</td>\n",
       "      <td>3.4</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.95</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2363</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.154</td>\n",
       "      <td>-0.448</td>\n",
       "      <td>2.1</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>7.25</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 121 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Seq        ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM InChandra  \\\n",
       "0  2359  742830101.0  14.097  0.166    4.7   515.8      0.0    no        no   \n",
       "1  2360  742830101.0  14.115 -0.353    3.5   171.7      0.0    no        no   \n",
       "2  2361  742830101.0  14.115 -0.160    5.8   291.7      0.0    no        no   \n",
       "3  2362  742830101.0  14.142 -0.442    3.4    49.1      0.0    no        no   \n",
       "4  2363  742830101.0  14.154 -0.448    2.1    49.1      0.0    no        no   \n",
       "\n",
       "   FSoft   ...     rH  F250  e_F250  F350  e_F350  F500  e_F500  XMMAO10CP  \\\n",
       "0   1.61   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN        NaN   \n",
       "1   1.68   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN        NaN   \n",
       "2   2.02   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN        NaN   \n",
       "3   0.95   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN        NaN   \n",
       "4   7.25   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN        NaN   \n",
       "\n",
       "   ChCP  CPCoord  \n",
       "0   NaN      0.0  \n",
       "1   NaN      0.0  \n",
       "2   NaN      0.0  \n",
       "3   NaN      0.0  \n",
       "4   NaN      0.0  \n",
       "\n",
       "[5 rows x 121 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ID_column_lm = 'Seq'\n",
    "df_lm[ID_column_lm] = df_lm[ID_column_lm].astype(int).astype(str)\n",
    "\n",
    "df_lm.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### IR (UKIDSS-DR8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  file: ukidss/ukidss.fits\n",
      "  extension: 1\n",
      "  type: BINARY_TBL\n",
      "  rows: 3501552\n",
      "  column info:\n",
      "    SOURCEID            i8  \n",
      "    RA                  f8  \n",
      "    DEC                 f8  \n",
      "    SIGRA               f4  \n",
      "    SIGDEC              f4  \n",
      "    EPOCH               f8  \n",
      "    EBV                 f4  \n",
      "    AY                  f4  \n",
      "    AJ                  f4  \n",
      "    AH                  f4  \n",
      "    AK                  f4  \n",
      "    MERGEDCLASS         i2  \n",
      "    MERGEDCLASSSTAT     f4  \n",
      "    YHALLMAG            f4  \n",
      "    YHALLMAGERR         f4  \n",
      "    YPETROMAG           f4  \n",
      "    YPETROMAGERR        f4  \n",
      "    YPSFMAG             f4  \n",
      "    YPSFMAGERR          f4  \n",
      "    YAPERMAG3           f4  \n",
      "    YAPERMAG3ERR        f4  \n",
      "    J_1HALLMAG          f4  \n",
      "    J_1HALLMAGERR       f4  \n",
      "    J_1PETROMAG         f4  \n",
      "    J_1PETROMAGERR      f4  \n",
      "    J_1PSFMAG           f4  \n",
      "    J_1PSFMAGERR        f4  \n",
      "    J_1APERMAG3         f4  \n",
      "    J_1APERMAG3ERR      f4  \n",
      "    HHALLMAG            f4  \n",
      "    HHALLMAGERR         f4  \n",
      "    HPETROMAG           f4  \n",
      "    HPETROMAGERR        f4  \n",
      "    HPSFMAG             f4  \n",
      "    HPSFMAGERR          f4  \n",
      "    HAPERMAG3           f4  \n",
      "    HAPERMAG3ERR        f4  \n",
      "    KHALLMAG            f4  \n",
      "    KHALLMAGERR         f4  \n",
      "    KPETROMAG           f4  \n",
      "    KPETROMAGERR        f4  \n",
      "    KPSFMAG             f4  \n",
      "    KPSFMAGERR          f4  \n",
      "    KAPERMAG3           f4  \n",
      "    KAPERMAG3ERR        f4  \n"
     ]
    }
   ],
   "source": [
    "from booq.io import fits\n",
    "uk = fits.open('ukidss/ukidss.fits')\n",
    "uk.info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# cat_uk = table.read('ukidss/ukidss.fits',\n",
    "#                     columns=['SOURCEID','RA','DEC','SIGRA','SIGDEC',\n",
    "#                              'YAPERMAG3','J_1APERMAG3','HAPERMAG3','KAPERMAG3']\n",
    "#                    )\n",
    "# cat_uk['SOURCEID'] = cat_uk['SOURCEID'].astype(int).astype(str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from booq import table\n",
    "tab_uk_pos = table.ATable.read('ukidss/ukidss.fits',columns=['RA','DEC'])\n",
    "#TODO: at init/reading be able to specific specific region(s) to load\n",
    "#cat_uk = table.ATable.read('ukidss/ukidss.fits',conesearch=(ra,dec,radius),\n",
    "#                          columns={'ra':'RA2000','dec':'DE2000'})\n",
    "#cat_uk = table.ATable.read('ukidss/ukidss.fits',around=(cat_lm,radius),\n",
    "#                          columns={'ra':'RA2000','dec':'DE2000'})\n",
    "#cat_uk = table.ATable.read('ukidss/ukidss.fits',region=booq.region.Region,\n",
    "#                          columns={'ra':'RA2000','dec':'DE2000'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.021207</td>\n",
       "      <td>0.021641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.022647</td>\n",
       "      <td>0.021643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6.021880</td>\n",
       "      <td>0.021649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.021893</td>\n",
       "      <td>0.021659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.022186</td>\n",
       "      <td>0.021660</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         RA       DEC\n",
       "0  6.021207  0.021641\n",
       "1  6.022647  0.021643\n",
       "2  6.021880  0.021649\n",
       "3  6.021893  0.021659\n",
       "4  6.022186  0.021660"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_uk_pos = tab_uk_pos.to_dataframe()\n",
    "del tab_uk_pos\n",
    "df_uk_pos.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**For some reason, UKIDSS positional columns (RA,Dec) are in radians; transform to degrees**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 RA           DEC\n",
      "count  3.501552e+06  3.501552e+06\n",
      "mean   1.841558e+02 -3.185555e-02\n",
      "std    1.530424e+02  7.262582e-01\n",
      "min    1.004211e-05 -1.249998e+00\n",
      "25%    3.243559e+01 -6.691321e-01\n",
      "50%    3.134817e+02 -5.326323e-02\n",
      "75%    3.349581e+02  6.023953e-01\n",
      "max    3.600000e+02  1.250000e+00\n",
      "\n",
      "Total number of rows: 3501552 (3.5e+06)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "RA     0\n",
      "DEC    0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "from astropy.coordinates import Angle\n",
    "ra = Angle(df_uk_pos['RA'].values,'rad').to('deg')\n",
    "dec= Angle(df_uk_pos['DEC'].values,'rad').to('deg')\n",
    "df_uk_pos['RA'] = ra\n",
    "df_uk_pos['DEC'] = dec\n",
    "\n",
    "df_uk_pos.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define a sub sample\n",
    "\n",
    "Because the UKIDSS catalog is quite big, we should define a sub-sample to better explorer the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  RA            DEC\n",
      "count  231338.000000  231338.000000\n",
      "mean       21.215457       0.013751\n",
      "std         4.365869       0.389857\n",
      "min        13.597006      -0.721999\n",
      "25%        17.474631      -0.301291\n",
      "50%        21.748381       0.031961\n",
      "75%        24.765722       0.342271\n",
      "max        28.543990       0.703997\n",
      "\n",
      "Total number of rows: 231338 (2.3e+05)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "RA     0\n",
      "DEC    0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "ra_min = df_lm.RAdeg.min() - 0.5\n",
    "ra_max = df_lm.RAdeg.max() + 0.5\n",
    "dec_min = df_lm.DEdeg.min() - 0.1\n",
    "dec_max = df_lm.DEdeg.max() + 0.1\n",
    "df_uk_sample = df_uk_pos.crop(RA=(ra_min,ra_max),\n",
    "                           DEC=(dec_min,dec_max))\n",
    "del df_uk_pos\n",
    "\n",
    "df_uk_sample.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>601783</th>\n",
       "      <td>23.367877</td>\n",
       "      <td>0.687888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>601784</th>\n",
       "      <td>23.460531</td>\n",
       "      <td>0.688232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>601785</th>\n",
       "      <td>23.414002</td>\n",
       "      <td>0.687667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>601786</th>\n",
       "      <td>23.280570</td>\n",
       "      <td>0.687302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>601787</th>\n",
       "      <td>23.474184</td>\n",
       "      <td>0.687547</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               RA       DEC\n",
       "601783  23.367877  0.687888\n",
       "601784  23.460531  0.688232\n",
       "601785  23.414002  0.687667\n",
       "601786  23.280570  0.687302\n",
       "601787  23.474184  0.687547"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_uk_sample.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we get the positional-index of those selected lines to load the whole UKIDSS catalog."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;ATable length=231338&gt;\n",
       "<table id=\"table140394044087264\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>SOURCEID</th><th>RA</th><th>DEC</th><th>SIGRA</th><th>SIGDEC</th><th>EPOCH</th><th>EBV</th><th>AY</th><th>AJ</th><th>AH</th><th>AK</th><th>MERGEDCLASS</th><th>MERGEDCLASSSTAT</th><th>YHALLMAG</th><th>YHALLMAGERR</th><th>YPETROMAG</th><th>YPETROMAGERR</th><th>YPSFMAG</th><th>YPSFMAGERR</th><th>YAPERMAG3</th><th>YAPERMAG3ERR</th><th>J_1HALLMAG</th><th>J_1HALLMAGERR</th><th>J_1PETROMAG</th><th>J_1PETROMAGERR</th><th>J_1PSFMAG</th><th>J_1PSFMAGERR</th><th>J_1APERMAG3</th><th>J_1APERMAG3ERR</th><th>HHALLMAG</th><th>HHALLMAGERR</th><th>HPETROMAG</th><th>HPETROMAGERR</th><th>HPSFMAG</th><th>HPSFMAGERR</th><th>HAPERMAG3</th><th>HAPERMAG3ERR</th><th>KHALLMAG</th><th>KHALLMAGERR</th><th>KPETROMAG</th><th>KPETROMAGERR</th><th>KPSFMAG</th><th>KPSFMAGERR</th><th>KAPERMAG3</th><th>KAPERMAG3ERR</th></tr></thead>\n",
       "<thead><tr><th>int64</th><th>float64</th><th>float64</th><th>float32</th><th>float32</th><th>float64</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>int16</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th></tr></thead>\n",
       "<tr><td>433827929919</td><td>0.407846390194</td><td>0.0120059039264</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0220508</td><td>0.0267036</td><td>0.0196032</td><td>0.0127454</td><td>0.0079383</td><td>1</td><td>4.93475</td><td>19.8162</td><td>0.339393</td><td>19.7927</td><td>0.352423</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.6622</td><td>0.129669</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.5194</td><td>0.341595</td><td>18.6227</td><td>0.444583</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.5062</td><td>0.151259</td><td>16.8393</td><td>0.166297</td><td>17.0132</td><td>0.244477</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.5441</td><td>0.124013</td></tr>\n",
       "<tr><td>433827929920</td><td>0.409463516869</td><td>0.012011917063</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0236491</td><td>0.028639</td><td>0.021024</td><td>0.0136692</td><td>0.00851367</td><td>-1</td><td>0.421079</td><td>17.9835</td><td>0.0401669</td><td>17.9463</td><td>0.0584219</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.8783</td><td>0.0279219</td><td>17.4947</td><td>0.0500438</td><td>17.5421</td><td>0.0748066</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.3798</td><td>0.0304339</td><td>16.9268</td><td>0.0543857</td><td>16.9449</td><td>0.0858596</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>16.8934</td><td>0.035704</td><td>16.618</td><td>0.0808161</td><td>16.6613</td><td>0.118318</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>16.5653</td><td>0.0519861</td></tr>\n",
       "<tr><td>433827929921</td><td>0.408651420325</td><td>0.0120020568056</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0226826</td><td>0.0274686</td><td>0.0201648</td><td>0.0131105</td><td>0.00816573</td><td>1</td><td>2.94201</td><td>19.834</td><td>0.366881</td><td>19.834</td><td>0.366881</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.2877</td><td>0.228542</td><td>19.2812</td><td>0.234339</td><td>19.2812</td><td>0.234339</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.6216</td><td>0.228677</td><td>18.7383</td><td>0.383572</td><td>18.7283</td><td>0.389533</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.6331</td><td>0.170696</td><td>17.6925</td><td>0.398679</td><td>17.6925</td><td>0.398679</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.7641</td><td>0.152736</td></tr>\n",
       "<tr><td>433827929922</td><td>0.406322596785</td><td>0.0119956787088</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0225056</td><td>0.0272542</td><td>0.0200075</td><td>0.0130082</td><td>0.00810201</td><td>1</td><td>16.0753</td><td>17.4584</td><td>0.0395172</td><td>17.2767</td><td>0.0590367</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.841</td><td>0.0268707</td><td>16.9499</td><td>0.0415769</td><td>16.7474</td><td>0.0635827</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.2757</td><td>0.0275967</td><td>16.1115</td><td>0.0399464</td><td>16.0146</td><td>0.0600487</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>16.5572</td><td>0.0260672</td><td>15.3375</td><td>0.0384352</td><td>15.0854</td><td>0.0602332</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>15.8079</td><td>0.0255751</td></tr>\n",
       "<tr><td>433827929923</td><td>0.409701804291</td><td>0.0119999505893</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0239274</td><td>0.0289761</td><td>0.0212715</td><td>0.0138301</td><td>0.00861388</td><td>1</td><td>0.782843</td><td>20.1834</td><td>0.387817</td><td>20.1834</td><td>0.387817</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.3265</td><td>0.239728</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433827929924</td><td>0.409192913378</td><td>0.0120002894351</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0233148</td><td>0.0282342</td><td>0.0207268</td><td>0.0134759</td><td>0.00839331</td><td>1</td><td>15.8572</td><td>18.3361</td><td>0.11912</td><td>18.4298</td><td>0.200747</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.941</td><td>0.0686888</td><td>17.7032</td><td>0.105149</td><td>17.7141</td><td>0.127878</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.4453</td><td>0.0785382</td><td>17.0186</td><td>0.134257</td><td>17.1364</td><td>0.218883</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.5933</td><td>0.0666682</td><td>16.3074</td><td>0.130962</td><td>16.4882</td><td>0.237619</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>16.8477</td><td>0.0668407</td></tr>\n",
       "<tr><td>433827929925</td><td>0.407144874736</td><td>0.0119879010813</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0219588</td><td>0.0265921</td><td>0.0195214</td><td>0.0126922</td><td>0.00790517</td><td>1</td><td>10.203</td><td>18.5988</td><td>0.166848</td><td>18.6272</td><td>0.239986</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.2887</td><td>0.0926362</td><td>18.2093</td><td>0.111538</td><td>18.1836</td><td>0.116781</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.0402</td><td>0.133803</td><td>17.1965</td><td>0.157632</td><td>17.3195</td><td>0.225639</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.0303</td><td>0.097468</td><td>16.7118</td><td>0.220821</td><td>16.7333</td><td>0.258675</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.5643</td><td>0.125003</td></tr>\n",
       "<tr><td>433827929926</td><td>0.409655117277</td><td>0.011988087937</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0238767</td><td>0.0289147</td><td>0.0212264</td><td>0.0138007</td><td>0.00859561</td><td>1</td><td>3.84407</td><td>19.8644</td><td>0.403661</td><td>20.653</td><td>0.987575</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.6256</td><td>0.127254</td><td>18.9018</td><td>0.18113</td><td>18.8652</td><td>0.185378</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.2267</td><td>0.160163</td><td>17.9615</td><td>0.274414</td><td>17.9615</td><td>0.274414</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.3873</td><td>0.137669</td><td>17.5568</td><td>0.221735</td><td>17.4939</td><td>0.304165</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.6057</td><td>0.133668</td></tr>\n",
       "<tr><td>433827929927</td><td>0.406068068638</td><td>0.0119687939775</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.0228351</td><td>0.0276533</td><td>0.0203004</td><td>0.0131987</td><td>0.00822064</td><td>1</td><td>1.64003</td><td>19.6853</td><td>0.295783</td><td>19.7383</td><td>0.269282</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.8526</td><td>0.155415</td><td>19.2255</td><td>0.223597</td><td>19.2255</td><td>0.223597</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.4793</td><td>0.201637</td><td>18.274</td><td>0.283236</td><td>18.2174</td><td>0.28653</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.6206</td><td>0.167925</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433827929928</td><td>0.406560901188</td><td>0.0119668732539</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2005.90215116</td><td>0.022154</td><td>0.0268285</td><td>0.0196949</td><td>0.012805</td><td>0.00797543</td><td>1</td><td>2.52627</td><td>19.6839</td><td>0.340545</td><td>19.6585</td><td>0.304635</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.6698</td><td>0.129848</td><td>19.0392</td><td>0.185266</td><td>19.1449</td><td>0.245873</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.0803</td><td>0.138229</td><td>17.9178</td><td>0.193481</td><td>17.9172</td><td>0.199938</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.1842</td><td>0.111608</td><td>17.4144</td><td>0.194213</td><td>17.4593</td><td>0.292663</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.5409</td><td>0.121203</td></tr>\n",
       "<tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "<tr><td>433837305044</td><td>0.34025866932</td><td>-0.0104056767725</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0342745</td><td>0.0415064</td><td>0.03047</td><td>0.0198106</td><td>0.0123388</td><td>-2</td><td>0.709851</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.8969</td><td>0.223847</td><td>19.8969</td><td>0.223847</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.808</td><td>0.186296</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.4788</td><td>0.227545</td><td>17.4788</td><td>0.227545</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>17.8522</td><td>0.164637</td></tr>\n",
       "<tr><td>433837305050</td><td>0.340506321416</td><td>-0.0109826421143</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0346866</td><td>0.0420055</td><td>0.0308364</td><td>0.0200489</td><td>0.0124872</td><td>-1</td><td>-3.11877</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.7356</td><td>0.366901</td><td>20.7356</td><td>0.366901</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.414</td><td>0.325283</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433837305053</td><td>0.340841774497</td><td>-0.0121659783303</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0352021</td><td>0.0426297</td><td>0.0312946</td><td>0.0203468</td><td>0.0126727</td><td>-1</td><td>-1.70577</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.5132</td><td>0.29812</td><td>20.5132</td><td>0.29812</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.2891</td><td>0.289107</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.0736</td><td>0.329767</td><td>18.1151</td><td>0.366375</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.0793</td><td>0.202633</td></tr>\n",
       "<tr><td>433837305055</td><td>0.341219413239</td><td>-0.0104824705603</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0359505</td><td>0.043536</td><td>0.03196</td><td>0.0207794</td><td>0.0129422</td><td>-1</td><td>-1.43004</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>21.152</td><td>0.71656</td><td>21.152</td><td>0.71656</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.7076</td><td>0.429333</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433837305057</td><td>0.341218704583</td><td>-0.0112323250807</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.035303</td><td>0.042752</td><td>0.0313844</td><td>0.0204052</td><td>0.0127091</td><td>1</td><td>1.08339</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.4278</td><td>0.156925</td><td>19.4278</td><td>0.156925</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.4976</td><td>0.141521</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433837305058</td><td>0.341219993198</td><td>-0.0109830742323</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0354352</td><td>0.0429121</td><td>0.0315019</td><td>0.0204816</td><td>0.0127567</td><td>-1</td><td>-3.96188</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>24.3294</td><td>13.8604</td><td>23.1295</td><td>5.28247</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>20.3296</td><td>0.303181</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433837305060</td><td>0.341247091418</td><td>-0.0120141150356</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0353353</td><td>0.0427911</td><td>0.0314131</td><td>0.0204238</td><td>0.0127207</td><td>1</td><td>2.99593</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.493</td><td>0.132775</td><td>19.3929</td><td>0.131533</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.5533</td><td>0.14854</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433837305062</td><td>0.34221406482</td><td>-0.0123296423311</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0361872</td><td>0.0438227</td><td>0.0321704</td><td>0.0209162</td><td>0.0130274</td><td>1</td><td>4.67382</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>18.4883</td><td>0.0883277</td><td>18.4883</td><td>0.0883277</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.1478</td><td>0.103815</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433837305063</td><td>0.342633797848</td><td>-0.0104163954124</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0368925</td><td>0.0446768</td><td>0.0327974</td><td>0.0213239</td><td>0.0132813</td><td>1</td><td>2.10527</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.5584</td><td>0.124152</td><td>19.5276</td><td>0.124712</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.3396</td><td>0.125078</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "<tr><td>433837305064</td><td>0.342778182631</td><td>-0.0113454301968</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>2006.96990376</td><td>0.0366883</td><td>0.0444295</td><td>0.0326159</td><td>0.0212058</td><td>0.0132078</td><td>-1</td><td>-1.25256</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.959</td><td>0.20353</td><td>19.9632</td><td>0.206217</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>19.606</td><td>0.158622</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td><td>-9.99999e+08</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<ATable length=231338>\n",
       "  SOURCEID         RA             DEC        ...  KAPERMAG3   KAPERMAG3ERR\n",
       "   int64        float64         float64      ...   float32      float32   \n",
       "------------ -------------- ---------------- ... ------------ ------------\n",
       "433827929919 0.407846390194  0.0120059039264 ...      17.5441     0.124013\n",
       "433827929920 0.409463516869   0.012011917063 ...      16.5653    0.0519861\n",
       "433827929921 0.408651420325  0.0120020568056 ...      17.7641     0.152736\n",
       "433827929922 0.406322596785  0.0119956787088 ...      15.8079    0.0255751\n",
       "433827929923 0.409701804291  0.0119999505893 ... -9.99999e+08 -9.99999e+08\n",
       "433827929924 0.409192913378  0.0120002894351 ...      16.8477    0.0668407\n",
       "433827929925 0.407144874736  0.0119879010813 ...      17.5643     0.125003\n",
       "433827929926 0.409655117277   0.011988087937 ...      17.6057     0.133668\n",
       "433827929927 0.406068068638  0.0119687939775 ... -9.99999e+08 -9.99999e+08\n",
       "433827929928 0.406560901188  0.0119668732539 ...      17.5409     0.121203\n",
       "         ...            ...              ... ...          ...          ...\n",
       "433837305044  0.34025866932 -0.0104056767725 ...      17.8522     0.164637\n",
       "433837305050 0.340506321416 -0.0109826421143 ... -9.99999e+08 -9.99999e+08\n",
       "433837305053 0.340841774497 -0.0121659783303 ...      18.0793     0.202633\n",
       "433837305055 0.341219413239 -0.0104824705603 ... -9.99999e+08 -9.99999e+08\n",
       "433837305057 0.341218704583 -0.0112323250807 ... -9.99999e+08 -9.99999e+08\n",
       "433837305058 0.341219993198 -0.0109830742323 ... -9.99999e+08 -9.99999e+08\n",
       "433837305060 0.341247091418 -0.0120141150356 ... -9.99999e+08 -9.99999e+08\n",
       "433837305062  0.34221406482 -0.0123296423311 ... -9.99999e+08 -9.99999e+08\n",
       "433837305063 0.342633797848 -0.0104163954124 ... -9.99999e+08 -9.99999e+08\n",
       "433837305064 0.342778182631 -0.0113454301968 ... -9.99999e+08 -9.99999e+08"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 'rows' contains the positions of our interest (the ones in df_uk_sample aget df_uk)\n",
    "rows = df_uk_sample.index.values\n",
    "del df_uk_sample\n",
    "\n",
    "tab_uk_sample = table.ATable.read('ukidss/ukidss.fits',rows=rows)\n",
    "tab_uk_sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           SOURCEID             RA            DEC        SIGRA       SIGDEC  \\\n",
      "count  2.313380e+05  231338.000000  231338.000000     231338.0     231338.0   \n",
      "mean   4.338322e+11      21.215457       0.013751 -999999488.0 -999999488.0   \n",
      "std    2.958270e+06       4.365869       0.389857          0.0          0.0   \n",
      "min    4.338279e+11      13.597006      -0.721999 -999999488.0 -999999488.0   \n",
      "25%    4.338291e+11      17.474631      -0.301291 -999999488.0 -999999488.0   \n",
      "50%    4.338325e+11      21.748381       0.031961 -999999488.0 -999999488.0   \n",
      "75%    4.338345e+11      24.765722       0.342271 -999999488.0 -999999488.0   \n",
      "max    4.338373e+11      28.543990       0.703997 -999999488.0 -999999488.0   \n",
      "\n",
      "               EPOCH            EBV             AY             AJ  \\\n",
      "count  231338.000000  231338.000000  231338.000000  231338.000000   \n",
      "mean     2006.341197       0.032063       0.038828       0.028504   \n",
      "std         0.630836       0.005339       0.006466       0.004747   \n",
      "min      2005.686836       0.020811       0.025202       0.018501   \n",
      "25%      2005.896787       0.028523       0.034542       0.025357   \n",
      "50%      2005.924034       0.031697       0.038385       0.028179   \n",
      "75%      2006.890816       0.034540       0.041828       0.030706   \n",
      "max      2008.774788       0.062102       0.075205       0.055209   \n",
      "\n",
      "                  AH      ...          HAPERMAG3  HAPERMAG3ERR      KHALLMAG  \\\n",
      "count  231338.000000      ...       2.313380e+05  2.313380e+05  2.313380e+05   \n",
      "mean        0.018532      ...      -4.116270e+08 -4.116270e+08 -2.973526e+08   \n",
      "std         0.003086      ...       4.921291e+08  4.921291e+08  4.570939e+08   \n",
      "min         0.012029      ...      -9.999995e+08 -9.999995e+08 -9.999995e+08   \n",
      "25%         0.016486      ...      -9.999995e+08 -9.999995e+08 -9.999995e+08   \n",
      "50%         0.018321      ...       1.625615e+01  2.266635e-02  1.654052e+01   \n",
      "75%         0.019964      ...       1.814290e+01  1.224565e-01  1.752031e+01   \n",
      "max         0.035895      ...       1.983346e+01  5.110809e-01  2.880482e+01   \n",
      "\n",
      "        KHALLMAGERR     KPETROMAG  KPETROMAGERR      KPSFMAG   KPSFMAGERR  \\\n",
      "count  2.313380e+05  2.313380e+05  2.313380e+05     231338.0     231338.0   \n",
      "mean  -2.973526e+08 -2.972316e+08 -2.972316e+08 -999999488.0 -999999488.0   \n",
      "std    4.570939e+08  4.570402e+08  4.570402e+08          0.0          0.0   \n",
      "min   -9.999995e+08 -9.999995e+08 -9.999995e+08 -999999488.0 -999999488.0   \n",
      "25%   -9.999995e+08 -9.999995e+08 -9.999995e+08 -999999488.0 -999999488.0   \n",
      "50%    1.029659e-01  1.648322e+01  1.356286e-01 -999999488.0 -999999488.0   \n",
      "75%    2.378411e-01  1.751610e+01  2.668378e-01 -999999488.0 -999999488.0   \n",
      "max    6.197548e+03  2.535833e+01  2.745251e+02 -999999488.0 -999999488.0   \n",
      "\n",
      "          KAPERMAG3  KAPERMAG3ERR  \n",
      "count  2.313380e+05  2.313380e+05  \n",
      "mean  -2.964405e+08 -2.964405e+08  \n",
      "std    4.566884e+08  4.566884e+08  \n",
      "min   -9.999995e+08 -9.999995e+08  \n",
      "25%   -9.999995e+08 -9.999995e+08  \n",
      "50%    1.687404e+01  6.536197e-02  \n",
      "75%    1.775938e+01  1.459568e-01  \n",
      "max    2.030012e+01  1.511550e+00  \n",
      "\n",
      "[8 rows x 45 columns]\n",
      "\n",
      "Total number of rows: 231338 (2.3e+05)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "SOURCEID           0\n",
      "RA                 0\n",
      "DEC                0\n",
      "SIGRA              0\n",
      "SIGDEC             0\n",
      "EPOCH              0\n",
      "EBV                0\n",
      "AY                 0\n",
      "AJ                 0\n",
      "AH                 0\n",
      "AK                 0\n",
      "MERGEDCLASS        0\n",
      "MERGEDCLASSSTAT    0\n",
      "YHALLMAG           0\n",
      "YHALLMAGERR        0\n",
      "YPETROMAG          0\n",
      "YPETROMAGERR       0\n",
      "YPSFMAG            0\n",
      "YPSFMAGERR         0\n",
      "YAPERMAG3          0\n",
      "YAPERMAG3ERR       0\n",
      "J_1HALLMAG         0\n",
      "J_1HALLMAGERR      0\n",
      "J_1PETROMAG        0\n",
      "J_1PETROMAGERR     0\n",
      "J_1PSFMAG          0\n",
      "J_1PSFMAGERR       0\n",
      "J_1APERMAG3        0\n",
      "J_1APERMAG3ERR     0\n",
      "HHALLMAG           0\n",
      "HHALLMAGERR        0\n",
      "HPETROMAG          0\n",
      "HPETROMAGERR       0\n",
      "HPSFMAG            0\n",
      "HPSFMAGERR         0\n",
      "HAPERMAG3          0\n",
      "HAPERMAG3ERR       0\n",
      "KHALLMAG           0\n",
      "KHALLMAGERR        0\n",
      "KPETROMAG          0\n",
      "KPETROMAGERR       0\n",
      "KPSFMAG            0\n",
      "KPSFMAGERR         0\n",
      "KAPERMAG3          0\n",
      "KAPERMAG3ERR       0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "df_uk = tab_uk_sample.to_dataframe()\n",
    "del tab_uk_sample\n",
    "\n",
    "from astropy.coordinates import Angle\n",
    "ra = Angle(df_uk['RA'].values,'rad').to('deg')\n",
    "dec= Angle(df_uk['DEC'].values,'rad').to('deg')\n",
    "df_uk['RA'] = ra\n",
    "df_uk['DEC'] = dec\n",
    "\n",
    "df_uk.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Clean table null values\n",
    "\n",
    "I assume every negative value in *semi-positive* columns to be `Null/NaN`.\n",
    "Such columns are the positional (RA,Dec) standard deviations and the magnitude columns.\n",
    "(Physically speaking, magnitudes are/can be negative; It just does not happen in our case --galaxies.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cols = ['SIGRA','SIGDEC']\n",
    "cols.extend( [ c for c in df_uk.filter(like='MAG',axis=1).columns ] )\n",
    "for col in cols:\n",
    "    idx = df_uk[col] < 0\n",
    "    df_uk.loc[idx,col] = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SOURCEID</th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "      <th>SIGRA</th>\n",
       "      <th>SIGDEC</th>\n",
       "      <th>EPOCH</th>\n",
       "      <th>EBV</th>\n",
       "      <th>AY</th>\n",
       "      <th>AJ</th>\n",
       "      <th>AH</th>\n",
       "      <th>...</th>\n",
       "      <th>HAPERMAG3</th>\n",
       "      <th>HAPERMAG3ERR</th>\n",
       "      <th>KHALLMAG</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>433827929919</td>\n",
       "      <td>23.367877</td>\n",
       "      <td>0.687888</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022051</td>\n",
       "      <td>0.026704</td>\n",
       "      <td>0.019603</td>\n",
       "      <td>0.012745</td>\n",
       "      <td>...</td>\n",
       "      <td>18.506187</td>\n",
       "      <td>0.151259</td>\n",
       "      <td>16.839336</td>\n",
       "      <td>0.166297</td>\n",
       "      <td>17.013243</td>\n",
       "      <td>0.244477</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.544065</td>\n",
       "      <td>0.124013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>433827929920</td>\n",
       "      <td>23.460531</td>\n",
       "      <td>0.688232</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.023649</td>\n",
       "      <td>0.028639</td>\n",
       "      <td>0.021024</td>\n",
       "      <td>0.013669</td>\n",
       "      <td>...</td>\n",
       "      <td>16.893356</td>\n",
       "      <td>0.035704</td>\n",
       "      <td>16.618038</td>\n",
       "      <td>0.080816</td>\n",
       "      <td>16.661270</td>\n",
       "      <td>0.118318</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.565256</td>\n",
       "      <td>0.051986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>433827929921</td>\n",
       "      <td>23.414002</td>\n",
       "      <td>0.687667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022683</td>\n",
       "      <td>0.027469</td>\n",
       "      <td>0.020165</td>\n",
       "      <td>0.013111</td>\n",
       "      <td>...</td>\n",
       "      <td>18.633087</td>\n",
       "      <td>0.170696</td>\n",
       "      <td>17.692490</td>\n",
       "      <td>0.398679</td>\n",
       "      <td>17.692490</td>\n",
       "      <td>0.398679</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.764069</td>\n",
       "      <td>0.152736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>433827929922</td>\n",
       "      <td>23.280570</td>\n",
       "      <td>0.687302</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022506</td>\n",
       "      <td>0.027254</td>\n",
       "      <td>0.020007</td>\n",
       "      <td>0.013008</td>\n",
       "      <td>...</td>\n",
       "      <td>16.557207</td>\n",
       "      <td>0.026067</td>\n",
       "      <td>15.337543</td>\n",
       "      <td>0.038435</td>\n",
       "      <td>15.085359</td>\n",
       "      <td>0.060233</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.807901</td>\n",
       "      <td>0.025575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>433827929923</td>\n",
       "      <td>23.474184</td>\n",
       "      <td>0.687547</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.023927</td>\n",
       "      <td>0.028976</td>\n",
       "      <td>0.021271</td>\n",
       "      <td>0.013830</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 45 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       SOURCEID         RA       DEC  SIGRA  SIGDEC        EPOCH       EBV  \\\n",
       "0  433827929919  23.367877  0.687888    NaN     NaN  2005.902151  0.022051   \n",
       "1  433827929920  23.460531  0.688232    NaN     NaN  2005.902151  0.023649   \n",
       "2  433827929921  23.414002  0.687667    NaN     NaN  2005.902151  0.022683   \n",
       "3  433827929922  23.280570  0.687302    NaN     NaN  2005.902151  0.022506   \n",
       "4  433827929923  23.474184  0.687547    NaN     NaN  2005.902151  0.023927   \n",
       "\n",
       "         AY        AJ        AH      ...       HAPERMAG3  HAPERMAG3ERR  \\\n",
       "0  0.026704  0.019603  0.012745      ...       18.506187      0.151259   \n",
       "1  0.028639  0.021024  0.013669      ...       16.893356      0.035704   \n",
       "2  0.027469  0.020165  0.013111      ...       18.633087      0.170696   \n",
       "3  0.027254  0.020007  0.013008      ...       16.557207      0.026067   \n",
       "4  0.028976  0.021271  0.013830      ...             NaN           NaN   \n",
       "\n",
       "    KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  KPSFMAG  KPSFMAGERR  \\\n",
       "0  16.839336     0.166297  17.013243      0.244477      NaN         NaN   \n",
       "1  16.618038     0.080816  16.661270      0.118318      NaN         NaN   \n",
       "2  17.692490     0.398679  17.692490      0.398679      NaN         NaN   \n",
       "3  15.337543     0.038435  15.085359      0.060233      NaN         NaN   \n",
       "4        NaN          NaN        NaN           NaN      NaN         NaN   \n",
       "\n",
       "   KAPERMAG3  KAPERMAG3ERR  \n",
       "0  17.544065      0.124013  \n",
       "1  16.565256      0.051986  \n",
       "2  17.764069      0.152736  \n",
       "3  15.807901      0.025575  \n",
       "4        NaN           NaN  \n",
       "\n",
       "[5 rows x 45 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ID_column_uk = 'SOURCEID'\n",
    "df_uk[ID_column_uk] = df_uk[ID_column_uk].astype(int).astype(str)\n",
    "\n",
    "df_uk.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot table distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from bokeh.io import output_notebook\n",
    "# output_notebook()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# from booq.plot import PlotHisto\n",
    "# p = PlotHisto()\n",
    "# for col in ['YAPERMAG3','J_1APERMAG3','HAPERMAG3','KAPERMAG3']:\n",
    "#     ds_label = p.add_dataset(df_uk,label=col,x=col)\n",
    "#     p.plot(ds_label)\n",
    "# p.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# from booq.plot import PlotHisto\n",
    "# p = PlotHisto()\n",
    "# for col in ['YAPERMAG3','J_1APERMAG3','HAPERMAG3','KAPERMAG3']:\n",
    "#     ds_label = p.add_dataset(df_uk_sample,label=col,x=col)\n",
    "#     p.plot(ds_label)\n",
    "# p.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot sky distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from booq.plot import PlotScatter\n",
    "# scatter = PlotScatter()\n",
    "\n",
    "# # uk_label = scatter.add_dataset(cat_uk,x='RA',y='DEC',label='scatter_uk')\n",
    "# # scatter.plot(uk_label)\n",
    "\n",
    "# uks_label = scatter.add_dataset(df_uk,x='RA',y='DEC',label='scatter_uk_sample')\n",
    "# scatter.plot(uks_label)\n",
    "\n",
    "# lm_label = scatter.add_dataset(df_lm,x='RAdeg',y='DEdeg',label='scatter_lm')\n",
    "# scatter.plot(lm_label)\n",
    "\n",
    "# scatter.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Radii definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import NearestNeighbors\n",
    "\n",
    "X = df_uk[['RA','DEC']].values\n",
    "nbrs = NearestNeighbors(n_neighbors=2, algorithm='ball_tree').fit(X)\n",
    "distances_uk, indices_uk = nbrs.kneighbors(X)\n",
    "distances_uk = distances_uk.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = df_lm[['RAdeg','DEdeg']].values\n",
    "nbrs = NearestNeighbors(n_neighbors=2, algorithm='ball_tree').fit(X)\n",
    "distances_lm, indices_lm = nbrs.kneighbors(X)\n",
    "distances_lm = distances_lm.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# from booq.plot import PlotHisto\n",
    "# p = PlotHisto()\n",
    "# ds_label = p.add_dataset(distances_uk,label='1st-neighbour ukidss',x=1)\n",
    "# p.plot(ds_label)\n",
    "# ds_label = p.add_dataset(distances_lm,label='1st-neighbour lamassa',x=1)\n",
    "# p.plot(ds_label)\n",
    "# p.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##### Nearest neighbours\n",
    "\n",
    "Let's take the nearest neighbours plot above as a guide to define the search radii when cross-matching. The typical distance among \"LaMassa\" (x-ray) sources -- *i.e.*, the peak of the distribution, is around 90 arcsec; beggining at $\\approx 30\"$. On \"UKIDSS\", if we consider the first peak, it is around $7.2\"$.\n",
    "\n",
    "We may then take $r_s = 7 arcsec$ as the search radius. If we sextuple this radius, the corresponding circle area would be 36 times bigger; we may consider such radius as the background area outer radius. By defining the inner and outer radii as $r_i = 7\"$ and $r_o = 42 arcsec$ the annular region is 35 times the ancillary area, which should give us a good background sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.units import arcsec\n",
    "\n",
    "rs = 7 * arcsec\n",
    "ri = rs\n",
    "ro = 6 * ri"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Cross-Match\n",
    "\n",
    "Defined the corresponding radii for ancillary and background samples search, we proceed now with the corresponding cross-matchings as the first step of samples definition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from booq.pipelines.xmatch import xmatch\n",
    "import warnings\n",
    "warnings.filterwarnings(action='ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ancillary cross-matching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"10\" halign=\"left\">A</th>\n",
       "      <th>...</th>\n",
       "      <th colspan=\"7\" halign=\"left\">B</th>\n",
       "      <th colspan=\"3\" halign=\"left\">AB</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Seq</th>\n",
       "      <th>ObsID</th>\n",
       "      <th>RAdeg</th>\n",
       "      <th>DEdeg</th>\n",
       "      <th>e_Pos</th>\n",
       "      <th>DistNN</th>\n",
       "      <th>ExtFlag</th>\n",
       "      <th>InXMM</th>\n",
       "      <th>InChandra</th>\n",
       "      <th>FSoft</th>\n",
       "      <th>...</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "      <th>separation</th>\n",
       "      <th>duplicates</th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2359</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.097</td>\n",
       "      <td>0.166</td>\n",
       "      <td>4.7</td>\n",
       "      <td>515.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.61</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2360</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.353</td>\n",
       "      <td>3.5</td>\n",
       "      <td>171.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.68</td>\n",
       "      <td>...</td>\n",
       "      <td>0.031406</td>\n",
       "      <td>15.165094</td>\n",
       "      <td>0.047093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "      <td>2.558296</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2361</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>5.8</td>\n",
       "      <td>291.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.02</td>\n",
       "      <td>...</td>\n",
       "      <td>0.234180</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
       "      <td>0.738626</td>\n",
       "      <td>433834423638</td>\n",
       "      <td>5.6150290842272454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2362</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.142</td>\n",
       "      <td>-0.442</td>\n",
       "      <td>3.4</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.95</td>\n",
       "      <td>...</td>\n",
       "      <td>0.112740</td>\n",
       "      <td>16.943735</td>\n",
       "      <td>0.177616</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "      <td>6.797695</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2363</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.154</td>\n",
       "      <td>-0.448</td>\n",
       "      <td>2.1</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>7.25</td>\n",
       "      <td>...</td>\n",
       "      <td>0.049313</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>3.585183</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 169 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      A                                                                   \\\n",
       "    Seq        ObsID   RAdeg  DEdeg e_Pos DistNN ExtFlag InXMM InChandra   \n",
       "0  2359  742830101.0  14.097  0.166   4.7  515.8     0.0    no        no   \n",
       "1  2360  742830101.0  14.115 -0.353   3.5  171.7     0.0    no        no   \n",
       "2  2361  742830101.0  14.115 -0.160   5.8  291.7     0.0    no        no   \n",
       "3  2362  742830101.0  14.142 -0.442   3.4   49.1     0.0    no        no   \n",
       "4  2363  742830101.0  14.154 -0.448   2.1   49.1     0.0    no        no   \n",
       "\n",
       "                ...                   B                                  \\\n",
       "  FSoft         ...         KHALLMAGERR  KPETROMAG KPETROMAGERR KPSFMAG   \n",
       "0  1.61         ...                 NaN        NaN          NaN     NaN   \n",
       "1  1.68         ...            0.031406  15.165094     0.047093     NaN   \n",
       "2  2.02         ...            0.234180  17.763853     0.258605     NaN   \n",
       "3  0.95         ...            0.112740  16.943735     0.177616     NaN   \n",
       "4  7.25         ...            0.049313  15.984794     0.066120     NaN   \n",
       "\n",
       "                                             AB                \\\n",
       "  KPSFMAGERR  KAPERMAG3 KAPERMAG3ERR separation    duplicates   \n",
       "0        NaN        NaN          NaN        NaN           NaN   \n",
       "1        NaN  15.644726     0.019929   2.558296          None   \n",
       "2        NaN  17.884663     0.145093   0.738626  433834423638   \n",
       "3        NaN  17.142780     0.078272   6.797695          None   \n",
       "4        NaN  16.248377     0.034981   3.585183          None   \n",
       "\n",
       "                       \n",
       "            distances  \n",
       "0                 NaN  \n",
       "1                None  \n",
       "2  5.6150290842272454  \n",
       "3                None  \n",
       "4                None  \n",
       "\n",
       "[5 rows x 169 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "match_ancillary = xmatch(df_lm, df_uk,\n",
    "                         columns_A=dict(ra='RAdeg',dec='DEdeg',id=ID_column_lm),\n",
    "                         columns_B=dict(ra='RA',dec='DEC',id=ID_column_uk),\n",
    "                         method='gc',radius=rs)\n",
    "match_ancillary.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A                                                       \\\n",
      "         Seq         ObsID        RAdeg        DEdeg        e_Pos   \n",
      "count   2862  2.862000e+03  2862.000000  2862.000000  2862.000000   \n",
      "unique  2862           NaN          NaN          NaN          NaN   \n",
      "top     3111           NaN          NaN          NaN          NaN   \n",
      "freq       1           NaN          NaN          NaN          NaN   \n",
      "mean     NaN  7.466381e+08    20.942283    -0.064055     2.985814   \n",
      "std      NaN  1.720502e+06     4.334022     0.292446     0.928504   \n",
      "min      NaN  7.428301e+08    14.097000    -0.622000     0.400000   \n",
      "25%      NaN  7.473901e+08    17.102750    -0.322750     2.400000   \n",
      "50%      NaN  7.474001e+08    19.970000    -0.065500     2.900000   \n",
      "75%      NaN  7.474301e+08    25.257250     0.170750     3.500000   \n",
      "max      NaN  7.474401e+08    28.044000     0.604000    11.500000   \n",
      "\n",
      "                                                               \\\n",
      "             DistNN      ExtFlag InXMM InChandra        FSoft   \n",
      "count   2862.000000  2862.000000  2862      2862  2862.000000   \n",
      "unique          NaN          NaN     9        35          NaN   \n",
      "top             NaN          NaN    no        no          NaN   \n",
      "freq            NaN          NaN  2854      2828          NaN   \n",
      "mean     127.227708     0.017820   NaN       NaN     1.592338   \n",
      "std       78.304843     0.219697   NaN       NaN     3.073713   \n",
      "min       16.400000     0.000000   NaN       NaN     0.000000   \n",
      "25%       71.750000     0.000000   NaN       NaN     0.522500   \n",
      "50%      112.700000     0.000000   NaN       NaN     0.860000   \n",
      "75%      165.100000     0.000000   NaN       NaN     1.540000   \n",
      "max      765.400000     6.000000   NaN       NaN    51.610000   \n",
      "\n",
      "              ...                    B                                    \\\n",
      "              ...          KHALLMAGERR    KPETROMAG KPETROMAGERR KPSFMAG   \n",
      "count         ...          1271.000000  1271.000000  1271.000000     0.0   \n",
      "unique        ...                  NaN          NaN          NaN     NaN   \n",
      "top           ...                  NaN          NaN          NaN     NaN   \n",
      "freq          ...                  NaN          NaN          NaN     NaN   \n",
      "mean          ...             0.196477    16.518888     0.228675     NaN   \n",
      "std           ...             0.309029     1.837397     0.313333     NaN   \n",
      "min           ...             0.000260     8.473408     0.000292     NaN   \n",
      "25%           ...             0.064819    15.979828     0.093961     NaN   \n",
      "50%           ...             0.158628    17.022558     0.197185     NaN   \n",
      "75%           ...             0.258799    17.660066     0.296021     NaN   \n",
      "max           ...             9.074115    21.520224     9.074115     NaN   \n",
      "\n",
      "                                                      AB                \\\n",
      "       KPSFMAGERR    KAPERMAG3 KAPERMAG3ERR   separation    duplicates   \n",
      "count         0.0  1273.000000  1273.000000  1481.000000           323   \n",
      "unique        NaN          NaN          NaN          NaN           323   \n",
      "top           NaN          NaN          NaN          NaN  433830543803   \n",
      "freq          NaN          NaN          NaN          NaN             1   \n",
      "mean          NaN    16.703365     0.097445     2.662259           NaN   \n",
      "std           NaN     1.680402     0.068511     1.470225           NaN   \n",
      "min           NaN     9.880221     0.000552     0.116544           NaN   \n",
      "25%           NaN    16.332140     0.040163     1.577137           NaN   \n",
      "50%           NaN    17.210604     0.088342     2.431352           NaN   \n",
      "75%           NaN    17.762251     0.147168     3.482694           NaN   \n",
      "max           NaN    18.688906     0.324966     6.979402           NaN   \n",
      "\n",
      "                           \n",
      "                distances  \n",
      "count                 323  \n",
      "unique                323  \n",
      "top     6.959285377000077  \n",
      "freq                    1  \n",
      "mean                  NaN  \n",
      "std                   NaN  \n",
      "min                   NaN  \n",
      "25%                   NaN  \n",
      "50%                   NaN  \n",
      "75%                   NaN  \n",
      "max                   NaN  \n",
      "\n",
      "[11 rows x 169 columns]\n",
      "\n",
      "Total number of rows: 2862 (2.9e+03)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "A   Seq                  0\n",
      "    ObsID                0\n",
      "    RAdeg                0\n",
      "    DEdeg                0\n",
      "    e_Pos                0\n",
      "    DistNN               0\n",
      "    ExtFlag              0\n",
      "    InXMM                0\n",
      "    InChandra            0\n",
      "    FSoft                0\n",
      "    e_FSoft              0\n",
      "    CtSoft               0\n",
      "    SoftDetml            0\n",
      "    FHard                0\n",
      "    e_FHard              0\n",
      "    CtHard               0\n",
      "    HardDetml            0\n",
      "    FFull                0\n",
      "    e_FFull              0\n",
      "    CtFull               0\n",
      "    FullDetml            0\n",
      "    logLSoft             0\n",
      "    logLHard             0\n",
      "    logLFull             0\n",
      "    RejS                 0\n",
      "    SDSS               602\n",
      "    RASdeg             424\n",
      "    DESdeg             424\n",
      "    RelS               428\n",
      "    rS                 424\n",
      "                      ... \n",
      "B   YPSFMAGERR        2862\n",
      "    YAPERMAG3         1661\n",
      "    YAPERMAG3ERR      1661\n",
      "    J_1HALLMAG        1841\n",
      "    J_1HALLMAGERR     1841\n",
      "    J_1PETROMAG       1841\n",
      "    J_1PETROMAGERR    1841\n",
      "    J_1PSFMAG         2862\n",
      "    J_1PSFMAGERR      2862\n",
      "    J_1APERMAG3       1841\n",
      "    J_1APERMAG3ERR    1841\n",
      "    HHALLMAG          1783\n",
      "    HHALLMAGERR       1783\n",
      "    HPETROMAG         1782\n",
      "    HPETROMAGERR      1782\n",
      "    HPSFMAG           2862\n",
      "    HPSFMAGERR        2862\n",
      "    HAPERMAG3         1782\n",
      "    HAPERMAG3ERR      1782\n",
      "    KHALLMAG          1591\n",
      "    KHALLMAGERR       1591\n",
      "    KPETROMAG         1591\n",
      "    KPETROMAGERR      1591\n",
      "    KPSFMAG           2862\n",
      "    KPSFMAGERR        2862\n",
      "    KAPERMAG3         1589\n",
      "    KAPERMAG3ERR      1589\n",
      "AB  separation        1381\n",
      "    duplicates        2539\n",
      "    distances         2539\n",
      "Length: 169, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "match_ancillary.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We may remove non-matching sources.** \n",
    "They are of no value on building the ancillary sample.\n",
    "Notice that the reasons why they have not matched can be various.\n",
    "Of real (scientific) value would be to have **no** counterpart -- that would tell us something about the physical nature of such sources.\n",
    "But the lack of matching objects can be also a void space in the ancillary catalog, there are regions where UKIDSS has no coverage -- and that is a *false* lack of counterparts.\n",
    "\n",
    "That said, may remove the non-matching sources, but we must apply the same cleaning to the *background* matching results. So we'll have a fair pair of ancillary and background samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"10\" halign=\"left\">A</th>\n",
       "      <th>...</th>\n",
       "      <th colspan=\"7\" halign=\"left\">B</th>\n",
       "      <th colspan=\"3\" halign=\"left\">AB</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Seq</th>\n",
       "      <th>ObsID</th>\n",
       "      <th>RAdeg</th>\n",
       "      <th>DEdeg</th>\n",
       "      <th>e_Pos</th>\n",
       "      <th>DistNN</th>\n",
       "      <th>ExtFlag</th>\n",
       "      <th>InXMM</th>\n",
       "      <th>InChandra</th>\n",
       "      <th>FSoft</th>\n",
       "      <th>...</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "      <th>separation</th>\n",
       "      <th>duplicates</th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2360</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.353</td>\n",
       "      <td>3.5</td>\n",
       "      <td>171.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.68</td>\n",
       "      <td>...</td>\n",
       "      <td>0.031406</td>\n",
       "      <td>15.165094</td>\n",
       "      <td>0.047093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "      <td>2.558296</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2361</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>5.8</td>\n",
       "      <td>291.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.02</td>\n",
       "      <td>...</td>\n",
       "      <td>0.234180</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
       "      <td>0.738626</td>\n",
       "      <td>433834423638</td>\n",
       "      <td>5.6150290842272454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2362</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.142</td>\n",
       "      <td>-0.442</td>\n",
       "      <td>3.4</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.95</td>\n",
       "      <td>...</td>\n",
       "      <td>0.112740</td>\n",
       "      <td>16.943735</td>\n",
       "      <td>0.177616</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "      <td>6.797695</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2363</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.154</td>\n",
       "      <td>-0.448</td>\n",
       "      <td>2.1</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>7.25</td>\n",
       "      <td>...</td>\n",
       "      <td>0.049313</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>3.585183</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2365</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.162</td>\n",
       "      <td>0.038</td>\n",
       "      <td>4.0</td>\n",
       "      <td>224.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.64</td>\n",
       "      <td>...</td>\n",
       "      <td>0.169763</td>\n",
       "      <td>17.494886</td>\n",
       "      <td>0.185832</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
       "      <td>5.428978</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 169 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      A                                                                   \\\n",
       "    Seq        ObsID   RAdeg  DEdeg e_Pos DistNN ExtFlag InXMM InChandra   \n",
       "1  2360  742830101.0  14.115 -0.353   3.5  171.7     0.0    no        no   \n",
       "2  2361  742830101.0  14.115 -0.160   5.8  291.7     0.0    no        no   \n",
       "3  2362  742830101.0  14.142 -0.442   3.4   49.1     0.0    no        no   \n",
       "4  2363  742830101.0  14.154 -0.448   2.1   49.1     0.0    no        no   \n",
       "6  2365  742830101.0  14.162  0.038   4.0  224.1     0.0    no        no   \n",
       "\n",
       "                ...                   B                                  \\\n",
       "  FSoft         ...         KHALLMAGERR  KPETROMAG KPETROMAGERR KPSFMAG   \n",
       "1  1.68         ...            0.031406  15.165094     0.047093     NaN   \n",
       "2  2.02         ...            0.234180  17.763853     0.258605     NaN   \n",
       "3  0.95         ...            0.112740  16.943735     0.177616     NaN   \n",
       "4  7.25         ...            0.049313  15.984794     0.066120     NaN   \n",
       "6  1.64         ...            0.169763  17.494886     0.185832     NaN   \n",
       "\n",
       "                                             AB                \\\n",
       "  KPSFMAGERR  KAPERMAG3 KAPERMAG3ERR separation    duplicates   \n",
       "1        NaN  15.644726     0.019929   2.558296          None   \n",
       "2        NaN  17.884663     0.145093   0.738626  433834423638   \n",
       "3        NaN  17.142780     0.078272   6.797695          None   \n",
       "4        NaN  16.248377     0.034981   3.585183          None   \n",
       "6        NaN  17.446341     0.103341   5.428978          None   \n",
       "\n",
       "                       \n",
       "            distances  \n",
       "1                None  \n",
       "2  5.6150290842272454  \n",
       "3                None  \n",
       "4                None  \n",
       "6                None  \n",
       "\n",
       "[5 rows x 169 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "match_ancillary = match_ancillary.loc[~match_ancillary.loc[:,('AB','separation')].isnull()]\n",
    "match_ancillary.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A                                                       \\\n",
      "         Seq         ObsID        RAdeg        DEdeg        e_Pos   \n",
      "count   1481  1.481000e+03  1481.000000  1481.000000  1481.000000   \n",
      "unique  1481           NaN          NaN          NaN          NaN   \n",
      "top     3684           NaN          NaN          NaN          NaN   \n",
      "freq       1           NaN          NaN          NaN          NaN   \n",
      "mean     NaN  7.465086e+08    20.866885    -0.034976     2.844227   \n",
      "std      NaN  1.827515e+06     4.354893     0.287542     0.907481   \n",
      "min      NaN  7.428301e+08    14.115000    -0.617000     0.400000   \n",
      "25%      NaN  7.473901e+08    17.016000    -0.282000     2.300000   \n",
      "50%      NaN  7.474001e+08    19.871000    -0.028000     2.800000   \n",
      "75%      NaN  7.474301e+08    25.148000     0.189000     3.400000   \n",
      "max      NaN  7.474401e+08    28.044000     0.604000     7.300000   \n",
      "\n",
      "                                                               \\\n",
      "             DistNN      ExtFlag InXMM InChandra        FSoft   \n",
      "count   1481.000000  1481.000000  1481      1481  1481.000000   \n",
      "unique          NaN          NaN     6        24          NaN   \n",
      "top             NaN          NaN    no        no          NaN   \n",
      "freq            NaN          NaN  1476      1458          NaN   \n",
      "mean     127.068332     0.017556   NaN       NaN     2.014450   \n",
      "std       79.524362     0.234727   NaN       NaN     3.664386   \n",
      "min       16.400000     0.000000   NaN       NaN     0.000000   \n",
      "25%       72.700000     0.000000   NaN       NaN     0.620000   \n",
      "50%      112.800000     0.000000   NaN       NaN     1.050000   \n",
      "75%      163.100000     0.000000   NaN       NaN     1.900000   \n",
      "max      765.400000     6.000000   NaN       NaN    46.740000   \n",
      "\n",
      "              ...                    B                                    \\\n",
      "              ...          KHALLMAGERR    KPETROMAG KPETROMAGERR KPSFMAG   \n",
      "count         ...          1271.000000  1271.000000  1271.000000     0.0   \n",
      "unique        ...                  NaN          NaN          NaN     NaN   \n",
      "top           ...                  NaN          NaN          NaN     NaN   \n",
      "freq          ...                  NaN          NaN          NaN     NaN   \n",
      "mean          ...             0.196477    16.518888     0.228675     NaN   \n",
      "std           ...             0.309029     1.837397     0.313333     NaN   \n",
      "min           ...             0.000260     8.473408     0.000292     NaN   \n",
      "25%           ...             0.064819    15.979828     0.093961     NaN   \n",
      "50%           ...             0.158628    17.022558     0.197185     NaN   \n",
      "75%           ...             0.258799    17.660066     0.296021     NaN   \n",
      "max           ...             9.074115    21.520224     9.074115     NaN   \n",
      "\n",
      "                                                      AB                \\\n",
      "       KPSFMAGERR    KAPERMAG3 KAPERMAG3ERR   separation    duplicates   \n",
      "count         0.0  1273.000000  1273.000000  1481.000000           323   \n",
      "unique        NaN          NaN          NaN          NaN           323   \n",
      "top           NaN          NaN          NaN          NaN  433830663398   \n",
      "freq          NaN          NaN          NaN          NaN             1   \n",
      "mean          NaN    16.703365     0.097445     2.662259           NaN   \n",
      "std           NaN     1.680402     0.068511     1.470225           NaN   \n",
      "min           NaN     9.880221     0.000552     0.116544           NaN   \n",
      "25%           NaN    16.332140     0.040163     1.577137           NaN   \n",
      "50%           NaN    17.210604     0.088342     2.431352           NaN   \n",
      "75%           NaN    17.762251     0.147168     3.482694           NaN   \n",
      "max           NaN    18.688906     0.324966     6.979402           NaN   \n",
      "\n",
      "                           \n",
      "                distances  \n",
      "count                 323  \n",
      "unique                323  \n",
      "top     6.959285377000077  \n",
      "freq                    1  \n",
      "mean                  NaN  \n",
      "std                   NaN  \n",
      "min                   NaN  \n",
      "25%                   NaN  \n",
      "50%                   NaN  \n",
      "75%                   NaN  \n",
      "max                   NaN  \n",
      "\n",
      "[11 rows x 169 columns]\n",
      "\n",
      "Total number of rows: 1481 (1.5e+03)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "A   Seq                  0\n",
      "    ObsID                0\n",
      "    RAdeg                0\n",
      "    DEdeg                0\n",
      "    e_Pos                0\n",
      "    DistNN               0\n",
      "    ExtFlag              0\n",
      "    InXMM                0\n",
      "    InChandra            0\n",
      "    FSoft                0\n",
      "    e_FSoft              0\n",
      "    CtSoft               0\n",
      "    SoftDetml            0\n",
      "    FHard                0\n",
      "    e_FHard              0\n",
      "    CtHard               0\n",
      "    HardDetml            0\n",
      "    FFull                0\n",
      "    e_FFull              0\n",
      "    CtFull               0\n",
      "    FullDetml            0\n",
      "    logLSoft             0\n",
      "    logLHard             0\n",
      "    logLFull             0\n",
      "    RejS                 0\n",
      "    SDSS               143\n",
      "    RASdeg              78\n",
      "    DESdeg              78\n",
      "    RelS                81\n",
      "    rS                  78\n",
      "                      ... \n",
      "B   YPSFMAGERR        1481\n",
      "    YAPERMAG3          280\n",
      "    YAPERMAG3ERR       280\n",
      "    J_1HALLMAG         460\n",
      "    J_1HALLMAGERR      460\n",
      "    J_1PETROMAG        460\n",
      "    J_1PETROMAGERR     460\n",
      "    J_1PSFMAG         1481\n",
      "    J_1PSFMAGERR      1481\n",
      "    J_1APERMAG3        460\n",
      "    J_1APERMAG3ERR     460\n",
      "    HHALLMAG           402\n",
      "    HHALLMAGERR        402\n",
      "    HPETROMAG          401\n",
      "    HPETROMAGERR       401\n",
      "    HPSFMAG           1481\n",
      "    HPSFMAGERR        1481\n",
      "    HAPERMAG3          401\n",
      "    HAPERMAG3ERR       401\n",
      "    KHALLMAG           210\n",
      "    KHALLMAGERR        210\n",
      "    KPETROMAG          210\n",
      "    KPETROMAGERR       210\n",
      "    KPSFMAG           1481\n",
      "    KPSFMAGERR        1481\n",
      "    KAPERMAG3          208\n",
      "    KAPERMAG3ERR       208\n",
      "AB  separation           0\n",
      "    duplicates        1158\n",
      "    distances         1158\n",
      "Length: 169, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "match_ancillary.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# non_matching_ancillary = match_ancillary.loc[match_ancillary.loc[:,('AB','dist')].isnull()]\n",
    "# non_matching_ancillary.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Background cross-matching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"10\" halign=\"left\">A</th>\n",
       "      <th>...</th>\n",
       "      <th colspan=\"7\" halign=\"left\">B</th>\n",
       "      <th colspan=\"3\" halign=\"left\">AB</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Seq</th>\n",
       "      <th>ObsID</th>\n",
       "      <th>RAdeg</th>\n",
       "      <th>DEdeg</th>\n",
       "      <th>e_Pos</th>\n",
       "      <th>DistNN</th>\n",
       "      <th>ExtFlag</th>\n",
       "      <th>InXMM</th>\n",
       "      <th>InChandra</th>\n",
       "      <th>FSoft</th>\n",
       "      <th>...</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "      <th>separation</th>\n",
       "      <th>duplicates</th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2359</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.097</td>\n",
       "      <td>0.166</td>\n",
       "      <td>4.7</td>\n",
       "      <td>515.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.61</td>\n",
       "      <td>...</td>\n",
       "      <td>0.212726</td>\n",
       "      <td>17.259270</td>\n",
       "      <td>0.266500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.693806</td>\n",
       "      <td>0.135874</td>\n",
       "      <td>8.145277</td>\n",
       "      <td>433830679408;433830679023;433830678980;4338306...</td>\n",
       "      <td>10.794982638045562;35.13669682682967;26.195491...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2360</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.353</td>\n",
       "      <td>3.5</td>\n",
       "      <td>171.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.68</td>\n",
       "      <td>...</td>\n",
       "      <td>0.031406</td>\n",
       "      <td>15.165094</td>\n",
       "      <td>0.047093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "      <td>2.558296</td>\n",
       "      <td>433834423106;433834423147;433834423635</td>\n",
       "      <td>20.97624189523573;37.473506355347666;25.140110...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2361</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>5.8</td>\n",
       "      <td>291.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.02</td>\n",
       "      <td>...</td>\n",
       "      <td>0.234180</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
       "      <td>0.738626</td>\n",
       "      <td>433834423127;433834423131;433834423632;4338344...</td>\n",
       "      <td>14.680191352777541;36.46523760569112;27.639894...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2362</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.142</td>\n",
       "      <td>-0.442</td>\n",
       "      <td>3.4</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.95</td>\n",
       "      <td>...</td>\n",
       "      <td>0.112740</td>\n",
       "      <td>16.943735</td>\n",
       "      <td>0.177616</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "      <td>6.797695</td>\n",
       "      <td>433836362985;433836362987;433836362444;4338363...</td>\n",
       "      <td>29.201881886120077;16.895045273815764;40.55821...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2363</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.154</td>\n",
       "      <td>-0.448</td>\n",
       "      <td>2.1</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>7.25</td>\n",
       "      <td>...</td>\n",
       "      <td>0.049313</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>3.585183</td>\n",
       "      <td>433836362503;433836363001;433836362478;4338363...</td>\n",
       "      <td>26.838219103542556;36.09115181194094;28.849663...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 169 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      A                                                                   \\\n",
       "    Seq        ObsID   RAdeg  DEdeg e_Pos DistNN ExtFlag InXMM InChandra   \n",
       "0  2359  742830101.0  14.097  0.166   4.7  515.8     0.0    no        no   \n",
       "1  2360  742830101.0  14.115 -0.353   3.5  171.7     0.0    no        no   \n",
       "2  2361  742830101.0  14.115 -0.160   5.8  291.7     0.0    no        no   \n",
       "3  2362  742830101.0  14.142 -0.442   3.4   49.1     0.0    no        no   \n",
       "4  2363  742830101.0  14.154 -0.448   2.1   49.1     0.0    no        no   \n",
       "\n",
       "                               ...                                   B  \\\n",
       "  FSoft                        ...                         KHALLMAGERR   \n",
       "0  1.61                        ...                            0.212726   \n",
       "1  1.68                        ...                            0.031406   \n",
       "2  2.02                        ...                            0.234180   \n",
       "3  0.95                        ...                            0.112740   \n",
       "4  7.25                        ...                            0.049313   \n",
       "\n",
       "                                                                      \\\n",
       "   KPETROMAG KPETROMAGERR KPSFMAG KPSFMAGERR  KAPERMAG3 KAPERMAG3ERR   \n",
       "0  17.259270     0.266500     NaN        NaN  17.693806     0.135874   \n",
       "1  15.165094     0.047093     NaN        NaN  15.644726     0.019929   \n",
       "2  17.763853     0.258605     NaN        NaN  17.884663     0.145093   \n",
       "3  16.943735     0.177616     NaN        NaN  17.142780     0.078272   \n",
       "4  15.984794     0.066120     NaN        NaN  16.248377     0.034981   \n",
       "\n",
       "          AB                                                     \\\n",
       "  separation                                         duplicates   \n",
       "0   8.145277  433830679408;433830679023;433830678980;4338306...   \n",
       "1   2.558296             433834423106;433834423147;433834423635   \n",
       "2   0.738626  433834423127;433834423131;433834423632;4338344...   \n",
       "3   6.797695  433836362985;433836362987;433836362444;4338363...   \n",
       "4   3.585183  433836362503;433836363001;433836362478;4338363...   \n",
       "\n",
       "                                                      \n",
       "                                           distances  \n",
       "0  10.794982638045562;35.13669682682967;26.195491...  \n",
       "1  20.97624189523573;37.473506355347666;25.140110...  \n",
       "2  14.680191352777541;36.46523760569112;27.639894...  \n",
       "3  29.201881886120077;16.895045273815764;40.55821...  \n",
       "4  26.838219103542556;36.09115181194094;28.849663...  \n",
       "\n",
       "[5 rows x 169 columns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "match_background = xmatch(df_lm, df_uk,\n",
    "                         columns_A=dict(ra='RAdeg',dec='DEdeg',id=ID_column_lm),\n",
    "                         columns_B=dict(ra='RA',dec='DEC',id=ID_column_uk),\n",
    "                         method='gc',radius=ro)\n",
    "match_background.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A                                                       \\\n",
      "         Seq         ObsID        RAdeg        DEdeg        e_Pos   \n",
      "count   2862  2.862000e+03  2862.000000  2862.000000  2862.000000   \n",
      "unique  2862           NaN          NaN          NaN          NaN   \n",
      "top     3111           NaN          NaN          NaN          NaN   \n",
      "freq       1           NaN          NaN          NaN          NaN   \n",
      "mean     NaN  7.466381e+08    20.942283    -0.064055     2.985814   \n",
      "std      NaN  1.720502e+06     4.334022     0.292446     0.928504   \n",
      "min      NaN  7.428301e+08    14.097000    -0.622000     0.400000   \n",
      "25%      NaN  7.473901e+08    17.102750    -0.322750     2.400000   \n",
      "50%      NaN  7.474001e+08    19.970000    -0.065500     2.900000   \n",
      "75%      NaN  7.474301e+08    25.257250     0.170750     3.500000   \n",
      "max      NaN  7.474401e+08    28.044000     0.604000    11.500000   \n",
      "\n",
      "                                                               \\\n",
      "             DistNN      ExtFlag InXMM InChandra        FSoft   \n",
      "count   2862.000000  2862.000000  2862      2862  2862.000000   \n",
      "unique          NaN          NaN     9        35          NaN   \n",
      "top             NaN          NaN    no        no          NaN   \n",
      "freq            NaN          NaN  2854      2828          NaN   \n",
      "mean     127.227708     0.017820   NaN       NaN     1.592338   \n",
      "std       78.304843     0.219697   NaN       NaN     3.073713   \n",
      "min       16.400000     0.000000   NaN       NaN     0.000000   \n",
      "25%       71.750000     0.000000   NaN       NaN     0.522500   \n",
      "50%      112.700000     0.000000   NaN       NaN     0.860000   \n",
      "75%      165.100000     0.000000   NaN       NaN     1.540000   \n",
      "max      765.400000     6.000000   NaN       NaN    51.610000   \n",
      "\n",
      "                              ...                                    B  \\\n",
      "                              ...                          KHALLMAGERR   \n",
      "count                         ...                          1872.000000   \n",
      "unique                        ...                                  NaN   \n",
      "top                           ...                                  NaN   \n",
      "freq                          ...                                  NaN   \n",
      "mean                          ...                             0.213265   \n",
      "std                           ...                             0.315744   \n",
      "min                           ...                             0.000260   \n",
      "25%                           ...                             0.071128   \n",
      "50%                           ...                             0.166825   \n",
      "75%                           ...                             0.274401   \n",
      "max                           ...                             9.074115   \n",
      "\n",
      "                                                                               \\\n",
      "          KPETROMAG KPETROMAGERR KPSFMAG KPSFMAGERR    KAPERMAG3 KAPERMAG3ERR   \n",
      "count   1872.000000  1872.000000     0.0        0.0  1874.000000  1874.000000   \n",
      "unique          NaN          NaN     NaN        NaN          NaN          NaN   \n",
      "top             NaN          NaN     NaN        NaN          NaN          NaN   \n",
      "freq            NaN          NaN     NaN        NaN          NaN          NaN   \n",
      "mean      16.652637     0.241801     NaN        NaN    16.806101     0.101962   \n",
      "std        1.706284     0.294813     NaN        NaN     1.555981     0.069800   \n",
      "min        8.473408     0.000292     NaN        NaN     9.880221     0.000552   \n",
      "25%       16.100899     0.104010     NaN        NaN    16.384849     0.043298   \n",
      "50%       17.051500     0.203932     NaN        NaN    17.286014     0.096088   \n",
      "75%       17.713838     0.307784     NaN        NaN    17.797832     0.153670   \n",
      "max       21.520224     9.074115     NaN        NaN    18.783207     0.330045   \n",
      "\n",
      "                 AB                                          \\\n",
      "         separation                              duplicates   \n",
      "count   2274.000000                                    2199   \n",
      "unique          NaN                                    2198   \n",
      "top             NaN  433830541289;433830541573;433830541648   \n",
      "freq            NaN                                       2   \n",
      "mean       8.283049                                     NaN   \n",
      "std        9.133926                                     NaN   \n",
      "min        0.116544                                     NaN   \n",
      "25%        1.994775                                     NaN   \n",
      "50%        3.586436                                     NaN   \n",
      "75%       12.900086                                     NaN   \n",
      "max       41.464279                                     NaN   \n",
      "\n",
      "                                                           \n",
      "                                                distances  \n",
      "count                                                2199  \n",
      "unique                                               2199  \n",
      "top     36.295362601549414;25.60172644637104;23.911665...  \n",
      "freq                                                    1  \n",
      "mean                                                  NaN  \n",
      "std                                                   NaN  \n",
      "min                                                   NaN  \n",
      "25%                                                   NaN  \n",
      "50%                                                   NaN  \n",
      "75%                                                   NaN  \n",
      "max                                                   NaN  \n",
      "\n",
      "[11 rows x 169 columns]\n",
      "\n",
      "Total number of rows: 2862 (2.9e+03)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "A   Seq                  0\n",
      "    ObsID                0\n",
      "    RAdeg                0\n",
      "    DEdeg                0\n",
      "    e_Pos                0\n",
      "    DistNN               0\n",
      "    ExtFlag              0\n",
      "    InXMM                0\n",
      "    InChandra            0\n",
      "    FSoft                0\n",
      "    e_FSoft              0\n",
      "    CtSoft               0\n",
      "    SoftDetml            0\n",
      "    FHard                0\n",
      "    e_FHard              0\n",
      "    CtHard               0\n",
      "    HardDetml            0\n",
      "    FFull                0\n",
      "    e_FFull              0\n",
      "    CtFull               0\n",
      "    FullDetml            0\n",
      "    logLSoft             0\n",
      "    logLHard             0\n",
      "    logLFull             0\n",
      "    RejS                 0\n",
      "    SDSS               602\n",
      "    RASdeg             424\n",
      "    DESdeg             424\n",
      "    RelS               428\n",
      "    rS                 424\n",
      "                      ... \n",
      "B   YPSFMAGERR        2862\n",
      "    YAPERMAG3         1070\n",
      "    YAPERMAG3ERR      1070\n",
      "    J_1HALLMAG        1382\n",
      "    J_1HALLMAGERR     1382\n",
      "    J_1PETROMAG       1382\n",
      "    J_1PETROMAGERR    1382\n",
      "    J_1PSFMAG         2862\n",
      "    J_1PSFMAGERR      2862\n",
      "    J_1APERMAG3       1382\n",
      "    J_1APERMAG3ERR    1382\n",
      "    HHALLMAG          1287\n",
      "    HHALLMAGERR       1287\n",
      "    HPETROMAG         1286\n",
      "    HPETROMAGERR      1286\n",
      "    HPSFMAG           2862\n",
      "    HPSFMAGERR        2862\n",
      "    HAPERMAG3         1286\n",
      "    HAPERMAG3ERR      1286\n",
      "    KHALLMAG           990\n",
      "    KHALLMAGERR        990\n",
      "    KPETROMAG          990\n",
      "    KPETROMAGERR       990\n",
      "    KPSFMAG           2862\n",
      "    KPSFMAGERR        2862\n",
      "    KAPERMAG3          988\n",
      "    KAPERMAG3ERR       988\n",
      "AB  separation         588\n",
      "    duplicates         663\n",
      "    distances          663\n",
      "Length: 169, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "match_background.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We may remove non-matching sources.** They are of no value on building the background sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"10\" halign=\"left\">A</th>\n",
       "      <th>...</th>\n",
       "      <th colspan=\"7\" halign=\"left\">B</th>\n",
       "      <th colspan=\"3\" halign=\"left\">AB</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Seq</th>\n",
       "      <th>ObsID</th>\n",
       "      <th>RAdeg</th>\n",
       "      <th>DEdeg</th>\n",
       "      <th>e_Pos</th>\n",
       "      <th>DistNN</th>\n",
       "      <th>ExtFlag</th>\n",
       "      <th>InXMM</th>\n",
       "      <th>InChandra</th>\n",
       "      <th>FSoft</th>\n",
       "      <th>...</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "      <th>separation</th>\n",
       "      <th>duplicates</th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2360</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.353</td>\n",
       "      <td>3.5</td>\n",
       "      <td>171.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.68</td>\n",
       "      <td>...</td>\n",
       "      <td>0.031406</td>\n",
       "      <td>15.165094</td>\n",
       "      <td>0.047093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "      <td>2.558296</td>\n",
       "      <td>433834423106;433834423147;433834423635</td>\n",
       "      <td>20.97624189523573;37.473506355347666;25.140110...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2361</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>5.8</td>\n",
       "      <td>291.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.02</td>\n",
       "      <td>...</td>\n",
       "      <td>0.234180</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
       "      <td>0.738626</td>\n",
       "      <td>433834423127;433834423131;433834423632;4338344...</td>\n",
       "      <td>14.680191352777541;36.46523760569112;27.639894...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2362</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.142</td>\n",
       "      <td>-0.442</td>\n",
       "      <td>3.4</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.95</td>\n",
       "      <td>...</td>\n",
       "      <td>0.112740</td>\n",
       "      <td>16.943735</td>\n",
       "      <td>0.177616</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "      <td>6.797695</td>\n",
       "      <td>433836362985;433836362987;433836362444;4338363...</td>\n",
       "      <td>29.201881886120077;16.895045273815764;40.55821...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2363</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.154</td>\n",
       "      <td>-0.448</td>\n",
       "      <td>2.1</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>7.25</td>\n",
       "      <td>...</td>\n",
       "      <td>0.049313</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>3.585183</td>\n",
       "      <td>433836362503;433836363001;433836362478;4338363...</td>\n",
       "      <td>26.838219103542556;36.09115181194094;28.849663...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2365</td>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.162</td>\n",
       "      <td>0.038</td>\n",
       "      <td>4.0</td>\n",
       "      <td>224.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.64</td>\n",
       "      <td>...</td>\n",
       "      <td>0.169763</td>\n",
       "      <td>17.494886</td>\n",
       "      <td>0.185832</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
       "      <td>5.428978</td>\n",
       "      <td>433832563106;433832563116;433832563641;4338327...</td>\n",
       "      <td>36.648784584264334;33.61796887568458;32.780057...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 169 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      A                                                                   \\\n",
       "    Seq        ObsID   RAdeg  DEdeg e_Pos DistNN ExtFlag InXMM InChandra   \n",
       "1  2360  742830101.0  14.115 -0.353   3.5  171.7     0.0    no        no   \n",
       "2  2361  742830101.0  14.115 -0.160   5.8  291.7     0.0    no        no   \n",
       "3  2362  742830101.0  14.142 -0.442   3.4   49.1     0.0    no        no   \n",
       "4  2363  742830101.0  14.154 -0.448   2.1   49.1     0.0    no        no   \n",
       "6  2365  742830101.0  14.162  0.038   4.0  224.1     0.0    no        no   \n",
       "\n",
       "                               ...                                   B  \\\n",
       "  FSoft                        ...                         KHALLMAGERR   \n",
       "1  1.68                        ...                            0.031406   \n",
       "2  2.02                        ...                            0.234180   \n",
       "3  0.95                        ...                            0.112740   \n",
       "4  7.25                        ...                            0.049313   \n",
       "6  1.64                        ...                            0.169763   \n",
       "\n",
       "                                                                      \\\n",
       "   KPETROMAG KPETROMAGERR KPSFMAG KPSFMAGERR  KAPERMAG3 KAPERMAG3ERR   \n",
       "1  15.165094     0.047093     NaN        NaN  15.644726     0.019929   \n",
       "2  17.763853     0.258605     NaN        NaN  17.884663     0.145093   \n",
       "3  16.943735     0.177616     NaN        NaN  17.142780     0.078272   \n",
       "4  15.984794     0.066120     NaN        NaN  16.248377     0.034981   \n",
       "6  17.494886     0.185832     NaN        NaN  17.446341     0.103341   \n",
       "\n",
       "          AB                                                     \\\n",
       "  separation                                         duplicates   \n",
       "1   2.558296             433834423106;433834423147;433834423635   \n",
       "2   0.738626  433834423127;433834423131;433834423632;4338344...   \n",
       "3   6.797695  433836362985;433836362987;433836362444;4338363...   \n",
       "4   3.585183  433836362503;433836363001;433836362478;4338363...   \n",
       "6   5.428978  433832563106;433832563116;433832563641;4338327...   \n",
       "\n",
       "                                                      \n",
       "                                           distances  \n",
       "1  20.97624189523573;37.473506355347666;25.140110...  \n",
       "2  14.680191352777541;36.46523760569112;27.639894...  \n",
       "3  29.201881886120077;16.895045273815764;40.55821...  \n",
       "4  26.838219103542556;36.09115181194094;28.849663...  \n",
       "6  36.648784584264334;33.61796887568458;32.780057...  \n",
       "\n",
       "[5 rows x 169 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# match_background = match_background.loc[~match_background.loc[:,('AB','duplicates')].isnull()]\n",
    "match_background = match_background.loc[match_ancillary.index]\n",
    "match_background.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A                                                       \\\n",
      "         Seq         ObsID        RAdeg        DEdeg        e_Pos   \n",
      "count   1481  1.481000e+03  1481.000000  1481.000000  1481.000000   \n",
      "unique  1481           NaN          NaN          NaN          NaN   \n",
      "top     3684           NaN          NaN          NaN          NaN   \n",
      "freq       1           NaN          NaN          NaN          NaN   \n",
      "mean     NaN  7.465086e+08    20.866885    -0.034976     2.844227   \n",
      "std      NaN  1.827515e+06     4.354893     0.287542     0.907481   \n",
      "min      NaN  7.428301e+08    14.115000    -0.617000     0.400000   \n",
      "25%      NaN  7.473901e+08    17.016000    -0.282000     2.300000   \n",
      "50%      NaN  7.474001e+08    19.871000    -0.028000     2.800000   \n",
      "75%      NaN  7.474301e+08    25.148000     0.189000     3.400000   \n",
      "max      NaN  7.474401e+08    28.044000     0.604000     7.300000   \n",
      "\n",
      "                                                               \\\n",
      "             DistNN      ExtFlag InXMM InChandra        FSoft   \n",
      "count   1481.000000  1481.000000  1481      1481  1481.000000   \n",
      "unique          NaN          NaN     6        24          NaN   \n",
      "top             NaN          NaN    no        no          NaN   \n",
      "freq            NaN          NaN  1476      1458          NaN   \n",
      "mean     127.068332     0.017556   NaN       NaN     2.014450   \n",
      "std       79.524362     0.234727   NaN       NaN     3.664386   \n",
      "min       16.400000     0.000000   NaN       NaN     0.000000   \n",
      "25%       72.700000     0.000000   NaN       NaN     0.620000   \n",
      "50%      112.800000     0.000000   NaN       NaN     1.050000   \n",
      "75%      163.100000     0.000000   NaN       NaN     1.900000   \n",
      "max      765.400000     6.000000   NaN       NaN    46.740000   \n",
      "\n",
      "                              ...                                    B  \\\n",
      "                              ...                          KHALLMAGERR   \n",
      "count                         ...                          1271.000000   \n",
      "unique                        ...                                  NaN   \n",
      "top                           ...                                  NaN   \n",
      "freq                          ...                                  NaN   \n",
      "mean                          ...                             0.196477   \n",
      "std                           ...                             0.309029   \n",
      "min                           ...                             0.000260   \n",
      "25%                           ...                             0.064819   \n",
      "50%                           ...                             0.158628   \n",
      "75%                           ...                             0.258799   \n",
      "max                           ...                             9.074115   \n",
      "\n",
      "                                                                               \\\n",
      "          KPETROMAG KPETROMAGERR KPSFMAG KPSFMAGERR    KAPERMAG3 KAPERMAG3ERR   \n",
      "count   1271.000000  1271.000000     0.0        0.0  1273.000000  1273.000000   \n",
      "unique          NaN          NaN     NaN        NaN          NaN          NaN   \n",
      "top             NaN          NaN     NaN        NaN          NaN          NaN   \n",
      "freq            NaN          NaN     NaN        NaN          NaN          NaN   \n",
      "mean      16.518888     0.228675     NaN        NaN    16.703365     0.097445   \n",
      "std        1.837397     0.313333     NaN        NaN     1.680402     0.068511   \n",
      "min        8.473408     0.000292     NaN        NaN     9.880221     0.000552   \n",
      "25%       15.979828     0.093961     NaN        NaN    16.332140     0.040163   \n",
      "50%       17.022558     0.197185     NaN        NaN    17.210604     0.088342   \n",
      "75%       17.660066     0.296021     NaN        NaN    17.762251     0.147168   \n",
      "max       21.520224     9.074115     NaN        NaN    18.688906     0.324966   \n",
      "\n",
      "                 AB                                                     \\\n",
      "         separation                                         duplicates   \n",
      "count   1481.000000                                               1467   \n",
      "unique          NaN                                               1467   \n",
      "top             NaN  433832768420;433832768425;433832768079;4338327...   \n",
      "freq            NaN                                                  1   \n",
      "mean       2.662259                                                NaN   \n",
      "std        1.470225                                                NaN   \n",
      "min        0.116544                                                NaN   \n",
      "25%        1.577137                                                NaN   \n",
      "50%        2.431352                                                NaN   \n",
      "75%        3.482694                                                NaN   \n",
      "max        6.979402                                                NaN   \n",
      "\n",
      "                                                           \n",
      "                                                distances  \n",
      "count                                                1467  \n",
      "unique                                               1467  \n",
      "top     36.295362601549414;25.60172644637104;23.911665...  \n",
      "freq                                                    1  \n",
      "mean                                                  NaN  \n",
      "std                                                   NaN  \n",
      "min                                                   NaN  \n",
      "25%                                                   NaN  \n",
      "50%                                                   NaN  \n",
      "75%                                                   NaN  \n",
      "max                                                   NaN  \n",
      "\n",
      "[11 rows x 169 columns]\n",
      "\n",
      "Total number of rows: 1481 (1.5e+03)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "A   Seq                  0\n",
      "    ObsID                0\n",
      "    RAdeg                0\n",
      "    DEdeg                0\n",
      "    e_Pos                0\n",
      "    DistNN               0\n",
      "    ExtFlag              0\n",
      "    InXMM                0\n",
      "    InChandra            0\n",
      "    FSoft                0\n",
      "    e_FSoft              0\n",
      "    CtSoft               0\n",
      "    SoftDetml            0\n",
      "    FHard                0\n",
      "    e_FHard              0\n",
      "    CtHard               0\n",
      "    HardDetml            0\n",
      "    FFull                0\n",
      "    e_FFull              0\n",
      "    CtFull               0\n",
      "    FullDetml            0\n",
      "    logLSoft             0\n",
      "    logLHard             0\n",
      "    logLFull             0\n",
      "    RejS                 0\n",
      "    SDSS               143\n",
      "    RASdeg              78\n",
      "    DESdeg              78\n",
      "    RelS                81\n",
      "    rS                  78\n",
      "                      ... \n",
      "B   YPSFMAGERR        1481\n",
      "    YAPERMAG3          280\n",
      "    YAPERMAG3ERR       280\n",
      "    J_1HALLMAG         460\n",
      "    J_1HALLMAGERR      460\n",
      "    J_1PETROMAG        460\n",
      "    J_1PETROMAGERR     460\n",
      "    J_1PSFMAG         1481\n",
      "    J_1PSFMAGERR      1481\n",
      "    J_1APERMAG3        460\n",
      "    J_1APERMAG3ERR     460\n",
      "    HHALLMAG           402\n",
      "    HHALLMAGERR        402\n",
      "    HPETROMAG          401\n",
      "    HPETROMAGERR       401\n",
      "    HPSFMAG           1481\n",
      "    HPSFMAGERR        1481\n",
      "    HAPERMAG3          401\n",
      "    HAPERMAG3ERR       401\n",
      "    KHALLMAG           210\n",
      "    KHALLMAGERR        210\n",
      "    KPETROMAG          210\n",
      "    KPETROMAGERR       210\n",
      "    KPSFMAG           1481\n",
      "    KPSFMAGERR        1481\n",
      "    KAPERMAG3          208\n",
      "    KAPERMAG3ERR       208\n",
      "AB  separation           0\n",
      "    duplicates          14\n",
      "    distances           14\n",
      "Length: 169, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "match_background.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the samples\n",
    "\n",
    "Building the samples is pretty much the process of compiling the list(s) of counterpart matches, including the multiple matches that may appear in columns `AB/duplicates` and `AB/distances`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Background sample\n",
    "\n",
    "Notice that the *background matches* are contaminated with *ancillary* objects; we clean the sample by simply removing the objects closer then $r_s$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">2360</th>\n",
       "      <th>433834423106</th>\n",
       "      <td>20.976242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423147</th>\n",
       "      <td>37.473506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423635</th>\n",
       "      <td>25.140111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2361</th>\n",
       "      <th>433834423127</th>\n",
       "      <td>14.680191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423131</th>\n",
       "      <td>36.465238</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       distances\n",
       "(A, Seq) duplicates             \n",
       "2360     433834423106  20.976242\n",
       "         433834423147  37.473506\n",
       "         433834423635  25.140111\n",
       "2361     433834423127  14.680191\n",
       "         433834423131  36.465238"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "from numpy import nan\n",
    "def expand_duplicates(group):\n",
    "    '''\n",
    "    Expand duplicates/distances ;-separated strings in multiple entries\n",
    "    '''\n",
    "    assert len(group)==1\n",
    "    df_row = group.iloc[0]\n",
    "    assert ('AB','duplicates') in df_row.index\n",
    "    assert ('AB','distances') in df_row.index\n",
    "    if not df_row[('AB','duplicates')]:\n",
    "        assert not df_row[('AB','distances')]\n",
    "        return None\n",
    "    dups = str(df_row[('AB','duplicates')]).split(';')\n",
    "    seps = [ float(sep) for sep in str(df_row[('AB','distances')]).split(';') ]\n",
    "    df = DataFrame({'distances':seps}, index=dups)\n",
    "    df.index.name = 'duplicates'\n",
    "    # Notice that the nearest objects from column ('B','\"id\"') is not included; conciously\n",
    "    return df\n",
    "\n",
    "# Grouping by the Object-ID --which are unique-- will produce length-1 groups;\n",
    "# The goal is to the Object-ID (A/Seq) as the returned DataFrame's index.\n",
    "background_sample = match_background.groupby(by=[('A','Seq')]).apply(expand_duplicates)\n",
    "\n",
    "background_sample = background_sample.loc[background_sample.distances > rs]\n",
    "background_sample.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10859.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>27.205650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.843440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>7.000223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>19.299350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>28.512622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>35.807267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>41.988813</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          distances\n",
       "count  10859.000000\n",
       "mean      27.205650\n",
       "std        9.843440\n",
       "min        7.000223\n",
       "25%       19.299350\n",
       "50%       28.512622\n",
       "75%       35.807267\n",
       "max       41.988813"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "background_sample.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ancillary sample\n",
    "\n",
    "The `expand_sample` function below is slightly modified to include the nearest object, in column `B/SOURCEID`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>2.558296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>0.738626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423638</th>\n",
       "      <td>5.615029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>6.797695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>3.585183</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       distances\n",
       "(A, Seq) duplicates             \n",
       "2360     433834423123   2.558296\n",
       "2361     433834423565   0.738626\n",
       "         433834423638   5.615029\n",
       "2362     433836362467   6.797695\n",
       "2363     433836362494   3.585183"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "from numpy import nan\n",
    "def expand_duplicates(group):\n",
    "    assert len(group)==1\n",
    "    df_row = group.iloc[0]\n",
    "    assert ('AB','duplicates') in df_row.index\n",
    "    assert ('AB','distances') in df_row.index\n",
    "    dups = [ str(df_row[('B','SOURCEID')]) ]\n",
    "    seps = [ float(df_row[('AB','separation')]) ]\n",
    "    if df_row[('AB','duplicates')] != None:\n",
    "        dups.extend( str(df_row[('AB','duplicates')]).split(';') )\n",
    "        seps.extend( [ float(sep) for sep in str(df_row[('AB','distances')]).split(';') ] )\n",
    "    df = DataFrame({'distances':seps}, index=dups)\n",
    "    df.index.name = 'duplicates'\n",
    "    # Notice that the nearest objects from column ('B','\"id\"') is not included; conciously\n",
    "    return df\n",
    "\n",
    "# Grouping by the Object-ID --which are unique-- will produce length-1 groups;\n",
    "# The goal is to the Object-ID (A/Seq) as the returned DataFrame's index.\n",
    "ancillary_sample = match_ancillary.groupby(by=[('A','Seq')]).apply(expand_duplicates)\n",
    "ancillary_sample.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1986.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.253892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.781674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.116544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.818475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.959127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.541647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>6.998498</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         distances\n",
       "count  1986.000000\n",
       "mean      3.253892\n",
       "std       1.781674\n",
       "min       0.116544\n",
       "25%       1.818475\n",
       "50%       2.959127\n",
       "75%       4.541647\n",
       "max       6.998498"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ancillary_sample.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# from booq.plot import PlotHisto\n",
    "# p = PlotHisto()\n",
    "# ds_label = p.add_dataset(background_sample,label='Background distances',x='distances')\n",
    "# p.plot(ds_label)\n",
    "# ds_label = p.add_dataset(ancillary_sample,label='Ancillary distances',x='distances')\n",
    "# p.plot(ds_label)\n",
    "# p.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define (brightness) distributions\n",
    "\n",
    "* $n(m)$ : the background brightness distributions\n",
    "* $q(m)$ : the ancillary brightness distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $n(m)$\n",
    "\n",
    "To build $n(m)$ we have to recover the magnitude information from the input table.\n",
    "\n",
    "Another quantity we need to compute $n(m)$ is the amount of square-degrees the background sample/region covers.\n",
    "The area it covers will be each annulus area times the number of (primary) sources:\n",
    "$$\n",
    "A = \\pi(r^2_o - r^2_i) * N_{sources}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area of each individual annulus: 1.496619833585138 arcmin2\n",
      "Total area covered by background sample: 2195.5412958693973 arcmin2\n"
     ]
    }
   ],
   "source": [
    "N_sources_bkg = len(background_sample.index.droplevel(1).unique())\n",
    "\n",
    "from astropy import units\n",
    "import math\n",
    "Area_annulus = math.pi * (ro**2 - ri**2)\n",
    "Area_annulus = Area_annulus.to('arcmin2')\n",
    "Area_total_background = Area_annulus * N_sources_bkg\n",
    "print('Area of each individual annulus: {}'.format(Area_annulus))\n",
    "print('Total area covered by background sample: {}'.format(Area_total_background))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "      <th>SIGRA</th>\n",
       "      <th>SIGDEC</th>\n",
       "      <th>EPOCH</th>\n",
       "      <th>EBV</th>\n",
       "      <th>AY</th>\n",
       "      <th>AJ</th>\n",
       "      <th>AH</th>\n",
       "      <th>...</th>\n",
       "      <th>HAPERMAG3</th>\n",
       "      <th>HAPERMAG3ERR</th>\n",
       "      <th>KHALLMAG</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SOURCEID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>433834423106</th>\n",
       "      <td>20.976242</td>\n",
       "      <td>14.120546</td>\n",
       "      <td>-0.351212</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.890867</td>\n",
       "      <td>0.024186</td>\n",
       "      <td>0.029290</td>\n",
       "      <td>0.021502</td>\n",
       "      <td>0.013980</td>\n",
       "      <td>...</td>\n",
       "      <td>18.227285</td>\n",
       "      <td>0.138568</td>\n",
       "      <td>16.983847</td>\n",
       "      <td>0.189038</td>\n",
       "      <td>16.983847</td>\n",
       "      <td>0.189038</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.809649</td>\n",
       "      <td>0.136995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423147</th>\n",
       "      <td>37.473506</td>\n",
       "      <td>14.107016</td>\n",
       "      <td>-0.346320</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.890867</td>\n",
       "      <td>0.023933</td>\n",
       "      <td>0.028983</td>\n",
       "      <td>0.021276</td>\n",
       "      <td>0.013833</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.809454</td>\n",
       "      <td>0.321708</td>\n",
       "      <td>17.809454</td>\n",
       "      <td>0.321708</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.178520</td>\n",
       "      <td>0.191387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423635</th>\n",
       "      <td>25.140111</td>\n",
       "      <td>14.118664</td>\n",
       "      <td>-0.347055</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.768465</td>\n",
       "      <td>0.024067</td>\n",
       "      <td>0.029146</td>\n",
       "      <td>0.021396</td>\n",
       "      <td>0.013911</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.346136</td>\n",
       "      <td>0.382614</td>\n",
       "      <td>18.380192</td>\n",
       "      <td>0.441398</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.145107</td>\n",
       "      <td>0.185927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423127</th>\n",
       "      <td>14.680191</td>\n",
       "      <td>14.114177</td>\n",
       "      <td>-0.163994</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.890867</td>\n",
       "      <td>0.021455</td>\n",
       "      <td>0.025982</td>\n",
       "      <td>0.019073</td>\n",
       "      <td>0.012401</td>\n",
       "      <td>...</td>\n",
       "      <td>17.876492</td>\n",
       "      <td>0.098539</td>\n",
       "      <td>17.177437</td>\n",
       "      <td>0.124891</td>\n",
       "      <td>17.400656</td>\n",
       "      <td>0.230916</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.014196</td>\n",
       "      <td>0.065776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423131</th>\n",
       "      <td>36.465238</td>\n",
       "      <td>14.112243</td>\n",
       "      <td>-0.150253</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.890867</td>\n",
       "      <td>0.021741</td>\n",
       "      <td>0.026329</td>\n",
       "      <td>0.019328</td>\n",
       "      <td>0.012566</td>\n",
       "      <td>...</td>\n",
       "      <td>17.903620</td>\n",
       "      <td>0.101870</td>\n",
       "      <td>17.322979</td>\n",
       "      <td>0.132065</td>\n",
       "      <td>17.316591</td>\n",
       "      <td>0.225728</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.402369</td>\n",
       "      <td>0.094191</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 45 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              distances         RA       DEC  SIGRA  SIGDEC        EPOCH  \\\n",
       "SOURCEID                                                                   \n",
       "433834423106  20.976242  14.120546 -0.351212    NaN     NaN  2006.890867   \n",
       "433834423147  37.473506  14.107016 -0.346320    NaN     NaN  2006.890867   \n",
       "433834423635  25.140111  14.118664 -0.347055    NaN     NaN  2005.768465   \n",
       "433834423127  14.680191  14.114177 -0.163994    NaN     NaN  2006.890867   \n",
       "433834423131  36.465238  14.112243 -0.150253    NaN     NaN  2006.890867   \n",
       "\n",
       "                   EBV        AY        AJ        AH      ...       HAPERMAG3  \\\n",
       "SOURCEID                                                  ...                   \n",
       "433834423106  0.024186  0.029290  0.021502  0.013980      ...       18.227285   \n",
       "433834423147  0.023933  0.028983  0.021276  0.013833      ...             NaN   \n",
       "433834423635  0.024067  0.029146  0.021396  0.013911      ...             NaN   \n",
       "433834423127  0.021455  0.025982  0.019073  0.012401      ...       17.876492   \n",
       "433834423131  0.021741  0.026329  0.019328  0.012566      ...       17.903620   \n",
       "\n",
       "              HAPERMAG3ERR   KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  \\\n",
       "SOURCEID                                                                      \n",
       "433834423106      0.138568  16.983847     0.189038  16.983847      0.189038   \n",
       "433834423147           NaN  17.809454     0.321708  17.809454      0.321708   \n",
       "433834423635           NaN  18.346136     0.382614  18.380192      0.441398   \n",
       "433834423127      0.098539  17.177437     0.124891  17.400656      0.230916   \n",
       "433834423131      0.101870  17.322979     0.132065  17.316591      0.225728   \n",
       "\n",
       "              KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \n",
       "SOURCEID                                                    \n",
       "433834423106      NaN         NaN  17.809649      0.136995  \n",
       "433834423147      NaN         NaN  18.178520      0.191387  \n",
       "433834423635      NaN         NaN  18.145107      0.185927  \n",
       "433834423127      NaN         NaN  17.014196      0.065776  \n",
       "433834423131      NaN         NaN  17.402369      0.094191  \n",
       "\n",
       "[5 rows x 45 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "primary_key = ID_column_uk\n",
    "\n",
    "# Because I don't want to have the same object twice in the likelihood sample, let's remove the duplicates\n",
    "bgs = background_sample.copy()\n",
    "bgs.index = background_sample.index.droplevel(0).astype(df_uk[primary_key].dtype)\n",
    "bgs = bgs.loc[~bgs.index.duplicated()]\n",
    "\n",
    "import pandas\n",
    "background_sample_magnitudes = pandas.merge(bgs, df_uk, left_index=True, right_on=primary_key,\n",
    "                                            sort=False, how='inner')\n",
    "background_sample_magnitudes.set_index(primary_key, inplace=True)\n",
    "del bgs\n",
    "background_sample_magnitudes.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "      <th>SIGRA</th>\n",
       "      <th>SIGDEC</th>\n",
       "      <th>EPOCH</th>\n",
       "      <th>EBV</th>\n",
       "      <th>AY</th>\n",
       "      <th>AJ</th>\n",
       "      <th>AH</th>\n",
       "      <th>...</th>\n",
       "      <th>HAPERMAG3</th>\n",
       "      <th>HAPERMAG3ERR</th>\n",
       "      <th>KHALLMAG</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10401.000000</td>\n",
       "      <td>10401.000000</td>\n",
       "      <td>10401.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10401.000000</td>\n",
       "      <td>10401.000000</td>\n",
       "      <td>10401.000000</td>\n",
       "      <td>10401.000000</td>\n",
       "      <td>10401.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>5767.000000</td>\n",
       "      <td>5767.000000</td>\n",
       "      <td>6680.000000</td>\n",
       "      <td>6680.000000</td>\n",
       "      <td>6679.000000</td>\n",
       "      <td>6679.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6681.000000</td>\n",
       "      <td>6681.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>27.208721</td>\n",
       "      <td>21.092817</td>\n",
       "      <td>-0.052897</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.423965</td>\n",
       "      <td>0.032625</td>\n",
       "      <td>0.039509</td>\n",
       "      <td>0.029004</td>\n",
       "      <td>0.018857</td>\n",
       "      <td>...</td>\n",
       "      <td>17.536470</td>\n",
       "      <td>0.110895</td>\n",
       "      <td>16.880636</td>\n",
       "      <td>0.212533</td>\n",
       "      <td>16.857033</td>\n",
       "      <td>0.240138</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.092848</td>\n",
       "      <td>0.114462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.842257</td>\n",
       "      <td>4.305663</td>\n",
       "      <td>0.296030</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.660693</td>\n",
       "      <td>0.005325</td>\n",
       "      <td>0.006448</td>\n",
       "      <td>0.004734</td>\n",
       "      <td>0.003078</td>\n",
       "      <td>...</td>\n",
       "      <td>1.424200</td>\n",
       "      <td>0.071076</td>\n",
       "      <td>1.314710</td>\n",
       "      <td>0.253860</td>\n",
       "      <td>1.340714</td>\n",
       "      <td>0.261833</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.256614</td>\n",
       "      <td>0.069386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>7.008305</td>\n",
       "      <td>14.107016</td>\n",
       "      <td>-0.626600</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.686836</td>\n",
       "      <td>0.021368</td>\n",
       "      <td>0.025877</td>\n",
       "      <td>0.018996</td>\n",
       "      <td>0.012351</td>\n",
       "      <td>...</td>\n",
       "      <td>10.107296</td>\n",
       "      <td>0.000458</td>\n",
       "      <td>8.475052</td>\n",
       "      <td>0.000363</td>\n",
       "      <td>8.575525</td>\n",
       "      <td>0.000390</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.577841</td>\n",
       "      <td>0.000502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>19.302151</td>\n",
       "      <td>17.238457</td>\n",
       "      <td>-0.302214</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.896804</td>\n",
       "      <td>0.029373</td>\n",
       "      <td>0.035571</td>\n",
       "      <td>0.026113</td>\n",
       "      <td>0.016978</td>\n",
       "      <td>...</td>\n",
       "      <td>17.122291</td>\n",
       "      <td>0.049612</td>\n",
       "      <td>16.379802</td>\n",
       "      <td>0.091832</td>\n",
       "      <td>16.312389</td>\n",
       "      <td>0.119152</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.707462</td>\n",
       "      <td>0.056648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>28.476797</td>\n",
       "      <td>20.317843</td>\n",
       "      <td>-0.039732</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.924070</td>\n",
       "      <td>0.032119</td>\n",
       "      <td>0.038896</td>\n",
       "      <td>0.028554</td>\n",
       "      <td>0.018565</td>\n",
       "      <td>...</td>\n",
       "      <td>18.004902</td>\n",
       "      <td>0.110099</td>\n",
       "      <td>17.149163</td>\n",
       "      <td>0.177955</td>\n",
       "      <td>17.140457</td>\n",
       "      <td>0.211157</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.482964</td>\n",
       "      <td>0.113730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>35.823040</td>\n",
       "      <td>25.217041</td>\n",
       "      <td>0.179750</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.890881</td>\n",
       "      <td>0.034539</td>\n",
       "      <td>0.041827</td>\n",
       "      <td>0.030706</td>\n",
       "      <td>0.019964</td>\n",
       "      <td>...</td>\n",
       "      <td>18.470686</td>\n",
       "      <td>0.166042</td>\n",
       "      <td>17.724091</td>\n",
       "      <td>0.275941</td>\n",
       "      <td>17.730078</td>\n",
       "      <td>0.304179</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.903210</td>\n",
       "      <td>0.166821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>41.988813</td>\n",
       "      <td>28.050635</td>\n",
       "      <td>0.612749</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2007.731502</td>\n",
       "      <td>0.061104</td>\n",
       "      <td>0.073997</td>\n",
       "      <td>0.054322</td>\n",
       "      <td>0.035318</td>\n",
       "      <td>...</td>\n",
       "      <td>19.574642</td>\n",
       "      <td>0.392515</td>\n",
       "      <td>21.895563</td>\n",
       "      <td>11.746733</td>\n",
       "      <td>21.895563</td>\n",
       "      <td>11.746733</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.901745</td>\n",
       "      <td>0.403689</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 45 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          distances            RA           DEC  SIGRA  SIGDEC         EPOCH  \\\n",
       "count  10401.000000  10401.000000  10401.000000    0.0     0.0  10401.000000   \n",
       "mean      27.208721     21.092817     -0.052897    NaN     NaN   2006.423965   \n",
       "std        9.842257      4.305663      0.296030    NaN     NaN      0.660693   \n",
       "min        7.008305     14.107016     -0.626600    NaN     NaN   2005.686836   \n",
       "25%       19.302151     17.238457     -0.302214    NaN     NaN   2005.896804   \n",
       "50%       28.476797     20.317843     -0.039732    NaN     NaN   2005.924070   \n",
       "75%       35.823040     25.217041      0.179750    NaN     NaN   2006.890881   \n",
       "max       41.988813     28.050635      0.612749    NaN     NaN   2007.731502   \n",
       "\n",
       "                EBV            AY            AJ            AH      ...       \\\n",
       "count  10401.000000  10401.000000  10401.000000  10401.000000      ...        \n",
       "mean       0.032625      0.039509      0.029004      0.018857      ...        \n",
       "std        0.005325      0.006448      0.004734      0.003078      ...        \n",
       "min        0.021368      0.025877      0.018996      0.012351      ...        \n",
       "25%        0.029373      0.035571      0.026113      0.016978      ...        \n",
       "50%        0.032119      0.038896      0.028554      0.018565      ...        \n",
       "75%        0.034539      0.041827      0.030706      0.019964      ...        \n",
       "max        0.061104      0.073997      0.054322      0.035318      ...        \n",
       "\n",
       "         HAPERMAG3  HAPERMAG3ERR     KHALLMAG  KHALLMAGERR    KPETROMAG  \\\n",
       "count  5767.000000   5767.000000  6680.000000  6680.000000  6679.000000   \n",
       "mean     17.536470      0.110895    16.880636     0.212533    16.857033   \n",
       "std       1.424200      0.071076     1.314710     0.253860     1.340714   \n",
       "min      10.107296      0.000458     8.475052     0.000363     8.575525   \n",
       "25%      17.122291      0.049612    16.379802     0.091832    16.312389   \n",
       "50%      18.004902      0.110099    17.149163     0.177955    17.140457   \n",
       "75%      18.470686      0.166042    17.724091     0.275941    17.730078   \n",
       "max      19.574642      0.392515    21.895563    11.746733    21.895563   \n",
       "\n",
       "       KPETROMAGERR  KPSFMAG  KPSFMAGERR    KAPERMAG3  KAPERMAG3ERR  \n",
       "count   6679.000000      0.0         0.0  6681.000000   6681.000000  \n",
       "mean       0.240138      NaN         NaN    17.092848      0.114462  \n",
       "std        0.261833      NaN         NaN     1.256614      0.069386  \n",
       "min        0.000390      NaN         NaN     9.577841      0.000502  \n",
       "25%        0.119152      NaN         NaN    16.707462      0.056648  \n",
       "50%        0.211157      NaN         NaN    17.482964      0.113730  \n",
       "75%        0.304179      NaN         NaN    17.903210      0.166821  \n",
       "max       11.746733      NaN         NaN    18.901745      0.403689  \n",
       "\n",
       "[8 rows x 45 columns]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "background_sample_magnitudes.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Spline(object):\n",
    "    _tck = None\n",
    "    _q = 1\n",
    "\n",
    "    def fit(self,x,y,normal=False):\n",
    "        from scipy.interpolate import splrep\n",
    "        tck = splrep(x, y, s=0)\n",
    "        self._tck = tck\n",
    "        if normal:\n",
    "            self.normalize()\n",
    "            \n",
    "    @property\n",
    "    def Q(self):\n",
    "        return self._q\n",
    "\n",
    "    @property\n",
    "    def nodes(self):\n",
    "        if self._tck is None:\n",
    "            print(\"None curve has been fit. Try 'Spline.fit()' first.\")\n",
    "            return None\n",
    "        return self._tck[0]\n",
    "    \n",
    "    @property\n",
    "    def coefficients(self):\n",
    "        if self._tck is None:\n",
    "            print(\"None curve has been fit. Try 'Spline.fit()' first.\")\n",
    "            return None\n",
    "        return self._tck[1]\n",
    "\n",
    "    @property\n",
    "    def degree(self):\n",
    "        if self._tck is None:\n",
    "            print(\"None curve has been fit. Try 'Spline.fit()' first.\")\n",
    "            return None\n",
    "        return self._tck[2]\n",
    "\n",
    "    def evaluate(self,x):\n",
    "        if self._tck is None:\n",
    "            print(\"None curve has been fit. Try 'Spline.fit()' first.\")\n",
    "            return None\n",
    "        from scipy.interpolate import splev\n",
    "        return splev(x,self._tck,der=0)\n",
    "    \n",
    "    def integrate(self,a,b):\n",
    "        if self._tck is None:\n",
    "            print(\"None curve has been fit. Try 'Spline.fit()' first.\")\n",
    "            return None\n",
    "        from scipy.interpolate import splint\n",
    "        return splint(a,b,self._tck)\n",
    "    \n",
    "    def normalize(self,a=None,b=None):\n",
    "        if self._tck is None:\n",
    "            print(\"None curve has been fit. Try 'Spline.fit()' first.\")\n",
    "            return None\n",
    "        if a is None:\n",
    "            a = self.nodes.min()\n",
    "        if b is None:\n",
    "            b = self.nodes.max()\n",
    "        assert a<b, \"Integration limits are inverted(?): a={};b={}\".format(a,b)\n",
    "        q = self.integrate(a,b)\n",
    "        t,c,k = self._tck\n",
    "        c = c/q\n",
    "        self._tck = (t,c,k)\n",
    "        self._q = q\n",
    "        \n",
    "    \n",
    "def compile_interpolation_function(x,y,normal=False):\n",
    "    spl = Spline()\n",
    "    spl.fit(x,y,normal=normal)\n",
    "    return spl\n",
    "# def compile_interpolation_function(x,y):\n",
    "#     from scipy import interpolate\n",
    "#     tck = interpolate.splrep(x, y, s=0)\n",
    "#     def f(x,tck=tck):\n",
    "#         return interpolate.splev(x, tck, der=0)\n",
    "#     return f\n",
    "\n",
    "def surface_density(sample,area_total):\n",
    "    import pandas\n",
    "    from numpy import histogram,diff\n",
    "    hist = {}\n",
    "    bins = {}\n",
    "    func_nm = {}\n",
    "    for col in ['YAPERMAG3','J_1APERMAG3','HAPERMAG3','KAPERMAG3']:\n",
    "        vec = sample[col]\n",
    "        minmax = (vec.min(),vec.max())\n",
    "\n",
    "        h,b = histogram(vec, bins='auto', range=minmax)\n",
    "        h = h/area_total\n",
    "\n",
    "        hist[col] = h\n",
    "        bins[col] = b\n",
    "\n",
    "        x = diff(b)/2 + b[:-1]\n",
    "        func_nm[col] = compile_interpolation_function(x,h)\n",
    "    return func_nm,hist,bins\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I8FHuFM4Z3BOW/IVfe9+g7OnnWHbR9ez75G8MObKK9d5Cvuf9b7KGT+KSmhf4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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fafecee1748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "func_nm_b,hist_b,bins_b = surface_density(background_sample_magnitudes,Area_total_background)\n",
    "\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "from numpy import diff\n",
    "b = bins_b['HAPERMAG3']\n",
    "x = b[:-1] + diff(b)/2\n",
    "y = hist_b['HAPERMAG3']\n",
    "C = func_nm_b['HAPERMAG3']\n",
    "_=plt.plot(x,y,'*',b,C.evaluate(b),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $q(m)$\n",
    "\n",
    "Now we have to proceed alike to get the ancillary brightness distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
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       "      <th>2360</th>\n",
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       "      <th rowspan=\"2\" valign=\"top\">2361</th>\n",
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       "      <th>433834423638</th>\n",
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       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>6.797695</td>\n",
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       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
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       "    </tr>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       distances\n",
       "(A, Seq) duplicates             \n",
       "2360     433834423123   2.558296\n",
       "2361     433834423565   0.738626\n",
       "         433834423638   5.615029\n",
       "2362     433836362467   6.797695\n",
       "2363     433836362494   3.585183"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ancillary_sample.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area of each individual annulus: 0.04276056667386108 arcmin2\n",
      "Total area covered by background sample: 63.32839924398826 arcmin2\n"
     ]
    }
   ],
   "source": [
    "N_sources_anc = len(ancillary_sample.index.droplevel(1).unique())\n",
    "\n",
    "from astropy import units\n",
    "import math\n",
    "Area_radius = math.pi * rs**2\n",
    "Area_radius = Area_radius.to('arcmin2')\n",
    "Area_total_ancillary = Area_radius * N_sources_anc\n",
    "print('Area of each individual annulus: {}'.format(Area_radius))\n",
    "print('Total area covered by background sample: {}'.format(Area_total_ancillary))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>SOURCEID</th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "      <th>SIGRA</th>\n",
       "      <th>SIGDEC</th>\n",
       "      <th>EPOCH</th>\n",
       "      <th>EBV</th>\n",
       "      <th>AY</th>\n",
       "      <th>AJ</th>\n",
       "      <th>AH</th>\n",
       "      <th>...</th>\n",
       "      <th>HAPERMAG3</th>\n",
       "      <th>HAPERMAG3ERR</th>\n",
       "      <th>KHALLMAG</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
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       "      <td>2005.902151</td>\n",
       "      <td>0.022051</td>\n",
       "      <td>0.026704</td>\n",
       "      <td>0.019603</td>\n",
       "      <td>0.012745</td>\n",
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       "      <td>0.151259</td>\n",
       "      <td>16.839336</td>\n",
       "      <td>0.166297</td>\n",
       "      <td>17.013243</td>\n",
       "      <td>0.244477</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.544065</td>\n",
       "      <td>0.124013</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>433827929920</td>\n",
       "      <td>23.460531</td>\n",
       "      <td>0.688232</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.023649</td>\n",
       "      <td>0.028639</td>\n",
       "      <td>0.021024</td>\n",
       "      <td>0.013669</td>\n",
       "      <td>...</td>\n",
       "      <td>16.893356</td>\n",
       "      <td>0.035704</td>\n",
       "      <td>16.618038</td>\n",
       "      <td>0.080816</td>\n",
       "      <td>16.661270</td>\n",
       "      <td>0.118318</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.565256</td>\n",
       "      <td>0.051986</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>433827929921</td>\n",
       "      <td>23.414002</td>\n",
       "      <td>0.687667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022683</td>\n",
       "      <td>0.027469</td>\n",
       "      <td>0.020165</td>\n",
       "      <td>0.013111</td>\n",
       "      <td>...</td>\n",
       "      <td>18.633087</td>\n",
       "      <td>0.170696</td>\n",
       "      <td>17.692490</td>\n",
       "      <td>0.398679</td>\n",
       "      <td>17.692490</td>\n",
       "      <td>0.398679</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.764069</td>\n",
       "      <td>0.152736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>433827929922</td>\n",
       "      <td>23.280570</td>\n",
       "      <td>0.687302</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022506</td>\n",
       "      <td>0.027254</td>\n",
       "      <td>0.020007</td>\n",
       "      <td>0.013008</td>\n",
       "      <td>...</td>\n",
       "      <td>16.557207</td>\n",
       "      <td>0.026067</td>\n",
       "      <td>15.337543</td>\n",
       "      <td>0.038435</td>\n",
       "      <td>15.085359</td>\n",
       "      <td>0.060233</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.807901</td>\n",
       "      <td>0.025575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>433827929923</td>\n",
       "      <td>23.474184</td>\n",
       "      <td>0.687547</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.023927</td>\n",
       "      <td>0.028976</td>\n",
       "      <td>0.021271</td>\n",
       "      <td>0.013830</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 45 columns</p>\n",
       "</div>"
      ],
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       "       SOURCEID         RA       DEC  SIGRA  SIGDEC        EPOCH       EBV  \\\n",
       "0  433827929919  23.367877  0.687888    NaN     NaN  2005.902151  0.022051   \n",
       "1  433827929920  23.460531  0.688232    NaN     NaN  2005.902151  0.023649   \n",
       "2  433827929921  23.414002  0.687667    NaN     NaN  2005.902151  0.022683   \n",
       "3  433827929922  23.280570  0.687302    NaN     NaN  2005.902151  0.022506   \n",
       "4  433827929923  23.474184  0.687547    NaN     NaN  2005.902151  0.023927   \n",
       "\n",
       "         AY        AJ        AH      ...       HAPERMAG3  HAPERMAG3ERR  \\\n",
       "0  0.026704  0.019603  0.012745      ...       18.506187      0.151259   \n",
       "1  0.028639  0.021024  0.013669      ...       16.893356      0.035704   \n",
       "2  0.027469  0.020165  0.013111      ...       18.633087      0.170696   \n",
       "3  0.027254  0.020007  0.013008      ...       16.557207      0.026067   \n",
       "4  0.028976  0.021271  0.013830      ...             NaN           NaN   \n",
       "\n",
       "    KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  KPSFMAG  KPSFMAGERR  \\\n",
       "0  16.839336     0.166297  17.013243      0.244477      NaN         NaN   \n",
       "1  16.618038     0.080816  16.661270      0.118318      NaN         NaN   \n",
       "2  17.692490     0.398679  17.692490      0.398679      NaN         NaN   \n",
       "3  15.337543     0.038435  15.085359      0.060233      NaN         NaN   \n",
       "4        NaN          NaN        NaN           NaN      NaN         NaN   \n",
       "\n",
       "   KAPERMAG3  KAPERMAG3ERR  \n",
       "0  17.544065      0.124013  \n",
       "1  16.565256      0.051986  \n",
       "2  17.764069      0.152736  \n",
       "3  15.807901      0.025575  \n",
       "4        NaN           NaN  \n",
       "\n",
       "[5 rows x 45 columns]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_uk.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.012431</td>\n",
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       "      <td>18.644693</td>\n",
       "      <td>0.198955</td>\n",
       "      <td>17.770628</td>\n",
       "      <td>0.234180</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
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       "      <td>-0.160856</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>0.025993</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>0.210202</td>\n",
       "      <td>17.539215</td>\n",
       "      <td>0.210202</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>16.968500</td>\n",
       "      <td>0.112740</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>0.049189</td>\n",
       "      <td>16.122658</td>\n",
       "      <td>0.049313</td>\n",
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       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
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       "</table>\n",
       "<p>5 rows × 45 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              distances         RA       DEC  SIGRA  SIGDEC        EPOCH  \\\n",
       "SOURCEID                                                                   \n",
       "433834423123   2.558296  14.114893 -0.352297    NaN     NaN  2006.890867   \n",
       "433834423565   0.738626  14.114795 -0.160001    NaN     NaN  2006.969972   \n",
       "433834423638   5.615029  14.116304 -0.160856    NaN     NaN  2005.768465   \n",
       "433836362467   6.797695  14.141094 -0.440343    NaN     NaN  2006.882247   \n",
       "433836362494   3.585183  14.154556 -0.447174    NaN     NaN  2006.882247   \n",
       "\n",
       "                   EBV        AY        AJ        AH      ...       HAPERMAG3  \\\n",
       "SOURCEID                                                  ...                   \n",
       "433834423123  0.024134  0.029226  0.021455  0.013949      ...       16.420605   \n",
       "433834423565  0.021508  0.026046  0.019120  0.012431      ...       18.644693   \n",
       "433834423638  0.021464  0.025993  0.019082  0.012406      ...             NaN   \n",
       "433836362467  0.024106  0.029192  0.021430  0.013933      ...       17.760912   \n",
       "433836362494  0.024283  0.029406  0.021587  0.014035      ...       17.173470   \n",
       "\n",
       "              HAPERMAG3ERR   KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  \\\n",
       "SOURCEID                                                                      \n",
       "433834423123      0.027337  15.266109     0.031406  15.165094      0.047093   \n",
       "433834423565      0.198955  17.770628     0.234180  17.763853      0.258605   \n",
       "433834423638           NaN  17.539215     0.210202  17.539215      0.210202   \n",
       "433836362467      0.083793  16.968500     0.112740  16.943735      0.177616   \n",
       "433836362494      0.049189  16.122658     0.049313  15.984794      0.066120   \n",
       "\n",
       "              KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \n",
       "SOURCEID                                                    \n",
       "433834423123      NaN         NaN  15.644726      0.019929  \n",
       "433834423565      NaN         NaN  17.884663      0.145093  \n",
       "433834423638      NaN         NaN  18.211197      0.195287  \n",
       "433836362467      NaN         NaN  17.142780      0.078272  \n",
       "433836362494      NaN         NaN  16.248377      0.034981  \n",
       "\n",
       "[5 rows x 45 columns]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "primary_key = ID_column_uk\n",
    "\n",
    "acs = ancillary_sample.copy()\n",
    "acs.index = ancillary_sample.index.droplevel(0).astype(df_uk[primary_key].dtype)\n",
    "acs = acs.loc[~acs.index.duplicated()]\n",
    "\n",
    "import pandas\n",
    "ancillary_sample_magnitudes = pandas.merge(acs, df_uk, sort=False, how='inner',\n",
    "                                               left_index=True, right_on=primary_key)\n",
    "ancillary_sample_magnitudes.set_index(primary_key, inplace=True)\n",
    "del acs\n",
    "ancillary_sample_magnitudes.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "      <th>SIGRA</th>\n",
       "      <th>SIGDEC</th>\n",
       "      <th>EPOCH</th>\n",
       "      <th>EBV</th>\n",
       "      <th>AY</th>\n",
       "      <th>AJ</th>\n",
       "      <th>AH</th>\n",
       "      <th>...</th>\n",
       "      <th>HAPERMAG3</th>\n",
       "      <th>HAPERMAG3ERR</th>\n",
       "      <th>KHALLMAG</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1986.000000</td>\n",
       "      <td>1986.000000</td>\n",
       "      <td>1986.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1986.000000</td>\n",
       "      <td>1986.000000</td>\n",
       "      <td>1986.000000</td>\n",
       "      <td>1986.000000</td>\n",
       "      <td>1986.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1320.000000</td>\n",
       "      <td>1320.000000</td>\n",
       "      <td>1545.000000</td>\n",
       "      <td>1545.000000</td>\n",
       "      <td>1545.000000</td>\n",
       "      <td>1545.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1547.000000</td>\n",
       "      <td>1547.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.253892</td>\n",
       "      <td>20.948839</td>\n",
       "      <td>-0.041642</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.478207</td>\n",
       "      <td>0.032459</td>\n",
       "      <td>0.039308</td>\n",
       "      <td>0.028856</td>\n",
       "      <td>0.018761</td>\n",
       "      <td>...</td>\n",
       "      <td>17.211620</td>\n",
       "      <td>0.100770</td>\n",
       "      <td>16.524746</td>\n",
       "      <td>0.192030</td>\n",
       "      <td>16.493393</td>\n",
       "      <td>0.222760</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.719076</td>\n",
       "      <td>0.100069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.781674</td>\n",
       "      <td>4.343018</td>\n",
       "      <td>0.290443</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.678600</td>\n",
       "      <td>0.005218</td>\n",
       "      <td>0.006319</td>\n",
       "      <td>0.004639</td>\n",
       "      <td>0.003016</td>\n",
       "      <td>...</td>\n",
       "      <td>1.863755</td>\n",
       "      <td>0.069903</td>\n",
       "      <td>1.842760</td>\n",
       "      <td>0.287458</td>\n",
       "      <td>1.859436</td>\n",
       "      <td>0.292445</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.716015</td>\n",
       "      <td>0.070200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.116544</td>\n",
       "      <td>14.114795</td>\n",
       "      <td>-0.616043</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.686836</td>\n",
       "      <td>0.021464</td>\n",
       "      <td>0.025993</td>\n",
       "      <td>0.019082</td>\n",
       "      <td>0.012406</td>\n",
       "      <td>...</td>\n",
       "      <td>10.107296</td>\n",
       "      <td>0.000458</td>\n",
       "      <td>8.269741</td>\n",
       "      <td>0.000260</td>\n",
       "      <td>8.473408</td>\n",
       "      <td>0.000292</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.577841</td>\n",
       "      <td>0.000502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.818475</td>\n",
       "      <td>17.050568</td>\n",
       "      <td>-0.295672</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.896808</td>\n",
       "      <td>0.029166</td>\n",
       "      <td>0.035320</td>\n",
       "      <td>0.025929</td>\n",
       "      <td>0.016858</td>\n",
       "      <td>...</td>\n",
       "      <td>16.883600</td>\n",
       "      <td>0.039884</td>\n",
       "      <td>16.105494</td>\n",
       "      <td>0.065911</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.094301</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.362699</td>\n",
       "      <td>0.040900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.959127</td>\n",
       "      <td>19.975227</td>\n",
       "      <td>-0.041050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.924078</td>\n",
       "      <td>0.031954</td>\n",
       "      <td>0.038697</td>\n",
       "      <td>0.028407</td>\n",
       "      <td>0.018470</td>\n",
       "      <td>...</td>\n",
       "      <td>17.848999</td>\n",
       "      <td>0.095547</td>\n",
       "      <td>17.050779</td>\n",
       "      <td>0.157007</td>\n",
       "      <td>17.000351</td>\n",
       "      <td>0.190011</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.263138</td>\n",
       "      <td>0.093453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.541647</td>\n",
       "      <td>25.234287</td>\n",
       "      <td>0.187365</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.890888</td>\n",
       "      <td>0.034515</td>\n",
       "      <td>0.041798</td>\n",
       "      <td>0.030684</td>\n",
       "      <td>0.019950</td>\n",
       "      <td>...</td>\n",
       "      <td>18.380485</td>\n",
       "      <td>0.153957</td>\n",
       "      <td>17.632435</td>\n",
       "      <td>0.253736</td>\n",
       "      <td>17.645555</td>\n",
       "      <td>0.288566</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.791502</td>\n",
       "      <td>0.151584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>6.998498</td>\n",
       "      <td>28.042850</td>\n",
       "      <td>0.604937</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2007.731498</td>\n",
       "      <td>0.061432</td>\n",
       "      <td>0.074394</td>\n",
       "      <td>0.054613</td>\n",
       "      <td>0.035508</td>\n",
       "      <td>...</td>\n",
       "      <td>19.299809</td>\n",
       "      <td>0.346629</td>\n",
       "      <td>21.520224</td>\n",
       "      <td>9.074115</td>\n",
       "      <td>21.520224</td>\n",
       "      <td>9.074115</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.786821</td>\n",
       "      <td>0.334490</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 45 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         distances           RA          DEC  SIGRA  SIGDEC        EPOCH  \\\n",
       "count  1986.000000  1986.000000  1986.000000    0.0     0.0  1986.000000   \n",
       "mean      3.253892    20.948839    -0.041642    NaN     NaN  2006.478207   \n",
       "std       1.781674     4.343018     0.290443    NaN     NaN     0.678600   \n",
       "min       0.116544    14.114795    -0.616043    NaN     NaN  2005.686836   \n",
       "25%       1.818475    17.050568    -0.295672    NaN     NaN  2005.896808   \n",
       "50%       2.959127    19.975227    -0.041050    NaN     NaN  2005.924078   \n",
       "75%       4.541647    25.234287     0.187365    NaN     NaN  2006.890888   \n",
       "max       6.998498    28.042850     0.604937    NaN     NaN  2007.731498   \n",
       "\n",
       "               EBV           AY           AJ           AH      ...       \\\n",
       "count  1986.000000  1986.000000  1986.000000  1986.000000      ...        \n",
       "mean      0.032459     0.039308     0.028856     0.018761      ...        \n",
       "std       0.005218     0.006319     0.004639     0.003016      ...        \n",
       "min       0.021464     0.025993     0.019082     0.012406      ...        \n",
       "25%       0.029166     0.035320     0.025929     0.016858      ...        \n",
       "50%       0.031954     0.038697     0.028407     0.018470      ...        \n",
       "75%       0.034515     0.041798     0.030684     0.019950      ...        \n",
       "max       0.061432     0.074394     0.054613     0.035508      ...        \n",
       "\n",
       "         HAPERMAG3  HAPERMAG3ERR     KHALLMAG  KHALLMAGERR    KPETROMAG  \\\n",
       "count  1320.000000   1320.000000  1545.000000  1545.000000  1545.000000   \n",
       "mean     17.211620      0.100770    16.524746     0.192030    16.493393   \n",
       "std       1.863755      0.069903     1.842760     0.287458     1.859436   \n",
       "min      10.107296      0.000458     8.269741     0.000260     8.473408   \n",
       "25%      16.883600      0.039884    16.105494     0.065911    15.984794   \n",
       "50%      17.848999      0.095547    17.050779     0.157007    17.000351   \n",
       "75%      18.380485      0.153957    17.632435     0.253736    17.645555   \n",
       "max      19.299809      0.346629    21.520224     9.074115    21.520224   \n",
       "\n",
       "       KPETROMAGERR  KPSFMAG  KPSFMAGERR    KAPERMAG3  KAPERMAG3ERR  \n",
       "count   1545.000000      0.0         0.0  1547.000000   1547.000000  \n",
       "mean       0.222760      NaN         NaN    16.719076      0.100069  \n",
       "std        0.292445      NaN         NaN     1.716015      0.070200  \n",
       "min        0.000292      NaN         NaN     9.577841      0.000502  \n",
       "25%        0.094301      NaN         NaN    16.362699      0.040900  \n",
       "50%        0.190011      NaN         NaN    17.263138      0.093453  \n",
       "75%        0.288566      NaN         NaN    17.791502      0.151584  \n",
       "max        9.074115      NaN         NaN    18.786821      0.334490  \n",
       "\n",
       "[8 rows x 45 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ancillary_sample_magnitudes.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FT8LAc6HTEX5HUz9p7aBVIC567vVZOGwK8DDwzGHazHbOnReRiESkZVgyDfZ95ZU/xpM4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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fafeb743f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "func_nm_a,hist_a,bins_a = surface_density(ancillary_sample_magnitudes,Area_total_ancillary)\n",
    "\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "from numpy import diff\n",
    "b = bins_a['HAPERMAG3']\n",
    "x = b[:-1] + diff(b)/2\n",
    "y = hist_a['HAPERMAG3']\n",
    "C = func_nm_a['HAPERMAG3']\n",
    "_=plt.plot(x,y,'*',b,C.evaluate(b),'-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$34.669142 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 34.669142471303175>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Area_total_background / Area_total_ancillary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.467774420946626"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(background_sample.index.droplevel(1))/len(ancillary_sample.index.droplevel(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import histogram,diff\n",
    "func_qm = {}\n",
    "hist_diff = {}\n",
    "x_diff = {}\n",
    "for col in ['YAPERMAG3','J_1APERMAG3','HAPERMAG3','KAPERMAG3']:\n",
    "    veca = ancillary_sample_magnitudes[col]\n",
    "    vecb = background_sample_magnitudes[col]\n",
    "    _min = min(veca.min(),vecb.min())\n",
    "    _max = min(veca.max(),vecb.max())\n",
    "\n",
    "    hb,bb = histogram(vecb, bins=50, range=(_min,_max))\n",
    "    hb = hb/ Area_total_background\n",
    "\n",
    "    ha,ba = histogram(veca, bins=50, range=(_min,_max))\n",
    "    ha = ha/ Area_total_ancillary\n",
    "\n",
    "    x = diff(ba)/2 + ba[:-1]\n",
    "\n",
    "    h_diff = ha - hb\n",
    "    hist_diff[col] = h_diff\n",
    "    x_diff[col] = x\n",
    "    func = compile_interpolation_function(x, h_diff/h_diff.sum(),normal=True)\n",
    "    func_qm[col] = func\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q=0.183\n"
     ]
    },
    {
     "data": {
      "image/png": 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bN4e/2aTO2mesPciWoyeYseZgrbb/c5RqZoIrw6oV7+oKKKVMwHvAMCAZ2KKU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\naIT+H6l4l7dPhjsnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fafeb696128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_curve_fit(col):\n",
    "    from matplotlib import pyplot as plt\n",
    "    fig,ax = plt.subplots()\n",
    "    from numpy import diff,linspace\n",
    "    x = x_diff[col]\n",
    "    xx = linspace(x.min(),x.max(),500)\n",
    "    y = hist_diff[col]\n",
    "    y = y/y.sum()\n",
    "    C = func_qm[col]\n",
    "    _=ax.plot(x,y,'*',x,C.evaluate(x),'r-',xx,C.evaluate(xx),'g-')\n",
    "    print(\"Q={:.3f}\".format(C.Q))\n",
    "    \n",
    "plot_curve_fit('HAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q=0.214\n"
     ]
    },
    {
     "data": {
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EoSdy56iY2sSG2JN7pn85CampcN55jd5XY8j0A0KIkw4d4qXP7yXQqpg85QOj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fafeb5f2e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_curve_fit('YAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q=0.214\n"
     ]
    },
    {
     "data": {
      "image/png": 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oKPVq7Lwvp8qeN5DOEZ1ZH7YbfpXiLoQw2IpfPqY0zH37209lIjBX6xnVky99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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fafeb5eb828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_curve_fit('J_1APERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q=0.184\n"
     ]
    },
    {
     "data": {
      "image/png": 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7mqzi5tBBzH1khdEvwa4uLNRnVNavnp6Zx5SYvSzdfZi8Qiu+Xh4M6dScSddd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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fafeb3ea358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_curve_fit('KAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.18484205740928 1 / arcmin2\n",
      "17.849910700360645 1 / arcmin2\n",
      "18.219774839753114 1 / arcmin2\n",
      "21.387055434323845 1 / arcmin2\n"
     ]
    }
   ],
   "source": [
    "for k in hist_diff.keys():\n",
    "    h = hist_diff[k]\n",
    "    print(h.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral q(m)[9.578 : 18.787]: 1.0\n"
     ]
    }
   ],
   "source": [
    "col = 'KAPERMAG3'\n",
    "sample = ancillary_sample_magnitudes\n",
    "_min = sample[col].min()\n",
    "_max = sample[col].max()\n",
    "C = func_qm[col]\n",
    "I = C.integrate(_min,_max)\n",
    "print('Integral q(m)[{:.3f} : {:.3f}]: {}'.format(_min,_max,I))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define $f(r)$\n",
    "\n",
    "$f(r)$ is defined as a bi-dimensional gaussian, where $\\sigma$ is the positional error of the source and ancillary objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def define_fr(sigma_x,sigma_y):\n",
    "    from cmath import sqrt,pi,exp\n",
    "    sigma = sqrt(sigma_x**2 + sigma_y**2)\n",
    "    f_2_pi_sigma = 1/(2 * pi * sigma)\n",
    "    f_2_sigma_2 = -1/(2 * sigma**2)\n",
    "    def gr(r):\n",
    "        gaussian = f_2_pi_sigma * exp( r**2 * f_2_sigma_2 )\n",
    "        return gaussian.real\n",
    "    return gr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = define_fr(2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UFeC0+JXljDGs2V7B3DEpDBusUzScqTFpCUzNHqy7e1SftPiV5baVneTI8VYWF+jlFQdq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\nCjNa/EopFWa0+JVSKsz8P5arbgs+1ce6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fafeb6d4da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy\n",
    "x = numpy.linspace(-10,10,100)\n",
    "from matplotlib import pyplot as plt\n",
    "y = [ f(r) for r in x ]\n",
    "_=plt.plot(x,y,'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Likelihood Ratio\n",
    "\n",
    "Now we can compute $LR$ for all ancillary objects. The information we need to relate in a unique table is *magnitude* for each ancillary object --to be used by $q(m)$ and $n(m)$-- and *position error* from the sources table --to be used by $f(r)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
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       "      <th>(A, Seq)</th>\n",
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       "                       distances\n",
       "(A, Seq) duplicates             \n",
       "2360     433834423123   2.558296\n",
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       "         433834423638   5.615029\n",
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       "2369     433836363145   2.324095\n",
       "2370     433834437127   4.105510"
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     "execution_count": 67,
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   "source": [
    "ancillary_sample.head(10)"
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  {
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       "      <td>224.1</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>29.8</td>\n",
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       "      <td>742830101.0</td>\n",
       "      <td>14.170</td>\n",
       "      <td>-0.244</td>\n",
       "      <td>2.7</td>\n",
       "      <td>283.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0.20</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.172</td>\n",
       "      <td>-0.400</td>\n",
       "      <td>4.3</td>\n",
       "      <td>29.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.51</td>\n",
       "      <td>0.18</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
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       "            ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM InChandra  \\\n",
       "Seq                                                                        \n",
       "2359  742830101.0  14.097  0.166    4.7   515.8      0.0    no        no   \n",
       "2360  742830101.0  14.115 -0.353    3.5   171.7      0.0    no        no   \n",
       "2361  742830101.0  14.115 -0.160    5.8   291.7      0.0    no        no   \n",
       "2362  742830101.0  14.142 -0.442    3.4    49.1      0.0    no        no   \n",
       "2363  742830101.0  14.154 -0.448    2.1    49.1      0.0    no        no   \n",
       "2364  742830101.0  14.162 -0.357    5.2   145.3      0.0    no        no   \n",
       "2365  742830101.0  14.162  0.038    4.0   224.1      0.0    no        no   \n",
       "2366  742830101.0  14.163 -0.400    3.8    29.8      0.0    no        no   \n",
       "2367  742830101.0  14.170 -0.244    2.7   283.6      0.0    no        no   \n",
       "2368  742830101.0  14.172 -0.400    4.3    29.8      0.0    no        no   \n",
       "\n",
       "      FSoft  e_FSoft   ...     rH  F250  e_F250  F350  e_F350  F500  e_F500  \\\n",
       "Seq                    ...                                                    \n",
       "2359   1.61     0.52   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2360   1.68     0.38   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2361   2.02     0.50   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2362   0.95     0.26   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2363   7.25     0.63   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2364   0.69     0.20   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2365   1.64     0.44   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2366   1.24     0.38   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2367   0.89     0.20   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2368   0.51     0.18   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "\n",
       "      XMMAO10CP  ChCP  CPCoord  \n",
       "Seq                             \n",
       "2359        NaN   NaN      0.0  \n",
       "2360        NaN   NaN      0.0  \n",
       "2361        NaN   NaN      0.0  \n",
       "2362        NaN   NaN      0.0  \n",
       "2363        NaN   NaN      0.0  \n",
       "2364        NaN   NaN      0.0  \n",
       "2365        NaN   NaN      0.0  \n",
       "2366        NaN   NaN      0.0  \n",
       "2367        NaN   NaN      0.0  \n",
       "2368        NaN   NaN      0.0  \n",
       "\n",
       "[10 rows x 120 columns]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_lm.set_index(ID_column_lm,inplace=True)\n",
    "df_lm.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
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       "      <th>433836019770</th>\n",
       "      <td>0.746982</td>\n",
       "      <td>17.318093</td>\n",
       "      <td>-0.534814</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.882288</td>\n",
       "      <td>0.038986</td>\n",
       "      <td>0.047212</td>\n",
       "      <td>0.034659</td>\n",
       "      <td>0.022534</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433828771062</th>\n",
       "      <td>1.364488</td>\n",
       "      <td>19.003348</td>\n",
       "      <td>0.362151</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006.876850</td>\n",
       "      <td>0.029718</td>\n",
       "      <td>0.035988</td>\n",
       "      <td>0.026419</td>\n",
       "      <td>0.017177</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.388758</td>\n",
       "      <td>0.181505</td>\n",
       "      <td>17.388758</td>\n",
       "      <td>0.181505</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.948137</td>\n",
       "      <td>0.171602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433832676448</th>\n",
       "      <td>2.058248</td>\n",
       "      <td>25.107189</td>\n",
       "      <td>0.042461</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.896816</td>\n",
       "      <td>0.028853</td>\n",
       "      <td>0.034941</td>\n",
       "      <td>0.025650</td>\n",
       "      <td>0.016677</td>\n",
       "      <td>...</td>\n",
       "      <td>17.929939</td>\n",
       "      <td>0.096629</td>\n",
       "      <td>16.884718</td>\n",
       "      <td>0.129574</td>\n",
       "      <td>16.813383</td>\n",
       "      <td>0.141358</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.158628</td>\n",
       "      <td>0.081468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433830588187</th>\n",
       "      <td>0.940338</td>\n",
       "      <td>26.909776</td>\n",
       "      <td>0.166134</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.924036</td>\n",
       "      <td>0.032919</td>\n",
       "      <td>0.039865</td>\n",
       "      <td>0.029265</td>\n",
       "      <td>0.019027</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.759869</td>\n",
       "      <td>0.171323</td>\n",
       "      <td>16.701662</td>\n",
       "      <td>0.187717</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.170341</td>\n",
       "      <td>0.106814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433836352140</th>\n",
       "      <td>6.123352</td>\n",
       "      <td>16.983057</td>\n",
       "      <td>-0.414667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.989634</td>\n",
       "      <td>0.038476</td>\n",
       "      <td>0.046595</td>\n",
       "      <td>0.034205</td>\n",
       "      <td>0.022239</td>\n",
       "      <td>...</td>\n",
       "      <td>18.782997</td>\n",
       "      <td>0.209874</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834460905</th>\n",
       "      <td>4.043837</td>\n",
       "      <td>27.700620</td>\n",
       "      <td>-0.299937</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.924042</td>\n",
       "      <td>0.031768</td>\n",
       "      <td>0.038471</td>\n",
       "      <td>0.028242</td>\n",
       "      <td>0.018362</td>\n",
       "      <td>...</td>\n",
       "      <td>18.412802</td>\n",
       "      <td>0.166715</td>\n",
       "      <td>17.369020</td>\n",
       "      <td>0.211877</td>\n",
       "      <td>17.206861</td>\n",
       "      <td>0.229076</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.338112</td>\n",
       "      <td>0.108962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834420696</th>\n",
       "      <td>6.425187</td>\n",
       "      <td>25.212197</td>\n",
       "      <td>-0.276324</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.896818</td>\n",
       "      <td>0.030723</td>\n",
       "      <td>0.037206</td>\n",
       "      <td>0.027313</td>\n",
       "      <td>0.017758</td>\n",
       "      <td>...</td>\n",
       "      <td>17.653343</td>\n",
       "      <td>0.080364</td>\n",
       "      <td>16.416468</td>\n",
       "      <td>0.132516</td>\n",
       "      <td>16.334234</td>\n",
       "      <td>0.169916</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.044228</td>\n",
       "      <td>0.071858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433830797900</th>\n",
       "      <td>0.758633</td>\n",
       "      <td>24.715791</td>\n",
       "      <td>0.084028</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.782085</td>\n",
       "      <td>0.037652</td>\n",
       "      <td>0.045596</td>\n",
       "      <td>0.033472</td>\n",
       "      <td>0.021763</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.947081</td>\n",
       "      <td>0.343615</td>\n",
       "      <td>17.947081</td>\n",
       "      <td>0.343615</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.175064</td>\n",
       "      <td>0.201067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433830642893</th>\n",
       "      <td>2.069061</td>\n",
       "      <td>26.772892</td>\n",
       "      <td>0.084565</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.924032</td>\n",
       "      <td>0.030782</td>\n",
       "      <td>0.037278</td>\n",
       "      <td>0.027366</td>\n",
       "      <td>0.017792</td>\n",
       "      <td>...</td>\n",
       "      <td>18.204731</td>\n",
       "      <td>0.160133</td>\n",
       "      <td>16.879576</td>\n",
       "      <td>0.162226</td>\n",
       "      <td>17.045557</td>\n",
       "      <td>0.258378</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.055212</td>\n",
       "      <td>0.094585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834318350</th>\n",
       "      <td>6.206586</td>\n",
       "      <td>19.354767</td>\n",
       "      <td>-0.338292</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2007.731485</td>\n",
       "      <td>0.033067</td>\n",
       "      <td>0.040044</td>\n",
       "      <td>0.029396</td>\n",
       "      <td>0.019113</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 45 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              distances         RA       DEC  SIGRA  SIGDEC        EPOCH  \\\n",
       "SOURCEID                                                                   \n",
       "433836019770   0.746982  17.318093 -0.534814    NaN     NaN  2006.882288   \n",
       "433828771062   1.364488  19.003348  0.362151    NaN     NaN  2006.876850   \n",
       "433832676448   2.058248  25.107189  0.042461    NaN     NaN  2005.896816   \n",
       "433830588187   0.940338  26.909776  0.166134    NaN     NaN  2005.924036   \n",
       "433836352140   6.123352  16.983057 -0.414667    NaN     NaN  2005.989634   \n",
       "433834460905   4.043837  27.700620 -0.299937    NaN     NaN  2005.924042   \n",
       "433834420696   6.425187  25.212197 -0.276324    NaN     NaN  2005.896818   \n",
       "433830797900   0.758633  24.715791  0.084028    NaN     NaN  2005.782085   \n",
       "433830642893   2.069061  26.772892  0.084565    NaN     NaN  2005.924032   \n",
       "433834318350   6.206586  19.354767 -0.338292    NaN     NaN  2007.731485   \n",
       "\n",
       "                   EBV        AY        AJ        AH      ...       HAPERMAG3  \\\n",
       "SOURCEID                                                  ...                   \n",
       "433836019770  0.038986  0.047212  0.034659  0.022534      ...             NaN   \n",
       "433828771062  0.029718  0.035988  0.026419  0.017177      ...             NaN   \n",
       "433832676448  0.028853  0.034941  0.025650  0.016677      ...       17.929939   \n",
       "433830588187  0.032919  0.039865  0.029265  0.019027      ...             NaN   \n",
       "433836352140  0.038476  0.046595  0.034205  0.022239      ...       18.782997   \n",
       "433834460905  0.031768  0.038471  0.028242  0.018362      ...       18.412802   \n",
       "433834420696  0.030723  0.037206  0.027313  0.017758      ...       17.653343   \n",
       "433830797900  0.037652  0.045596  0.033472  0.021763      ...             NaN   \n",
       "433830642893  0.030782  0.037278  0.027366  0.017792      ...       18.204731   \n",
       "433834318350  0.033067  0.040044  0.029396  0.019113      ...             NaN   \n",
       "\n",
       "              HAPERMAG3ERR   KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  \\\n",
       "SOURCEID                                                                      \n",
       "433836019770           NaN        NaN          NaN        NaN           NaN   \n",
       "433828771062           NaN  17.388758     0.181505  17.388758      0.181505   \n",
       "433832676448      0.096629  16.884718     0.129574  16.813383      0.141358   \n",
       "433830588187           NaN  16.759869     0.171323  16.701662      0.187717   \n",
       "433836352140      0.209874        NaN          NaN        NaN           NaN   \n",
       "433834460905      0.166715  17.369020     0.211877  17.206861      0.229076   \n",
       "433834420696      0.080364  16.416468     0.132516  16.334234      0.169916   \n",
       "433830797900           NaN  17.947081     0.343615  17.947081      0.343615   \n",
       "433830642893      0.160133  16.879576     0.162226  17.045557      0.258378   \n",
       "433834318350           NaN        NaN          NaN        NaN           NaN   \n",
       "\n",
       "              KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \n",
       "SOURCEID                                                    \n",
       "433836019770      NaN         NaN        NaN           NaN  \n",
       "433828771062      NaN         NaN  17.948137      0.171602  \n",
       "433832676448      NaN         NaN  17.158628      0.081468  \n",
       "433830588187      NaN         NaN  17.170341      0.106814  \n",
       "433836352140      NaN         NaN        NaN           NaN  \n",
       "433834460905      NaN         NaN  17.338112      0.108962  \n",
       "433834420696      NaN         NaN  17.044228      0.071858  \n",
       "433830797900      NaN         NaN  18.175064      0.201067  \n",
       "433830642893      NaN         NaN  17.055212      0.094585  \n",
       "433834318350      NaN         NaN        NaN           NaN  \n",
       "\n",
       "[10 rows x 45 columns]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ancillary_sample_magnitudes.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>key_0</th>\n",
       "      <th>distances</th>\n",
       "      <th>e_Pos</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>2360</td>\n",
       "      <td>2.558296</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>2361</td>\n",
       "      <td>0.738626</td>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423638</th>\n",
       "      <td>2361</td>\n",
       "      <td>5.615029</td>\n",
       "      <td>5.8</td>\n",
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       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>2362</td>\n",
       "      <td>6.797695</td>\n",
       "      <td>3.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>2363</td>\n",
       "      <td>3.585183</td>\n",
       "      <td>2.1</td>\n",
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       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <th>433832563084</th>\n",
       "      <td>2365</td>\n",
       "      <td>5.428978</td>\n",
       "      <td>4.0</td>\n",
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       "    <tr>\n",
       "      <th>2366</th>\n",
       "      <th>433836363120</th>\n",
       "      <td>2366</td>\n",
       "      <td>4.329322</td>\n",
       "      <td>3.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <th>433836362527</th>\n",
       "      <td>2368</td>\n",
       "      <td>6.895045</td>\n",
       "      <td>4.3</td>\n",
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       "    <tr>\n",
       "      <th>2369</th>\n",
       "      <th>433836363145</th>\n",
       "      <td>2369</td>\n",
       "      <td>2.324095</td>\n",
       "      <td>4.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2370</th>\n",
       "      <th>433834437127</th>\n",
       "      <td>2370</td>\n",
       "      <td>4.105510</td>\n",
       "      <td>3.6</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      key_0  distances  e_Pos\n",
       "(A, Seq) duplicates                          \n",
       "2360     433834423123  2360   2.558296    3.5\n",
       "2361     433834423565  2361   0.738626    5.8\n",
       "         433834423638  2361   5.615029    5.8\n",
       "2362     433836362467  2362   6.797695    3.4\n",
       "2363     433836362494  2363   3.585183    2.1\n",
       "2365     433832563084  2365   5.428978    4.0\n",
       "2366     433836363120  2366   4.329322    3.8\n",
       "2368     433836362527  2368   6.895045    4.3\n",
       "2369     433836363145  2369   2.324095    4.4\n",
       "2370     433834437127  2370   4.105510    3.6"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_keys = ancillary_sample.index.droplevel(1).values\n",
    "ancillary_sample_poserror = ancillary_sample.merge( df_lm[['e_Pos']], left_on=_keys, right_index=True )\n",
    "ancillary_sample_poserror.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ancillary_sample_poserror.drop('key_0',axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>433834423123</td>\n",
       "      <td>2.558296</td>\n",
       "      <td>3.5</td>\n",
       "      <td>17.424122</td>\n",
       "      <td>0.033594</td>\n",
       "      <td>17.339571</td>\n",
       "      <td>0.047153</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.924706</td>\n",
       "      <td>...</td>\n",
       "      <td>16.420605</td>\n",
       "      <td>0.027337</td>\n",
       "      <td>15.266109</td>\n",
       "      <td>0.031406</td>\n",
       "      <td>15.165094</td>\n",
       "      <td>0.047093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>433834423565</td>\n",
       "      <td>0.738626</td>\n",
       "      <td>5.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>18.644693</td>\n",
       "      <td>0.198955</td>\n",
       "      <td>17.770628</td>\n",
       "      <td>0.234180</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423638</th>\n",
       "      <td>433834423638</td>\n",
       "      <td>5.615029</td>\n",
       "      <td>5.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.539215</td>\n",
       "      <td>0.210202</td>\n",
       "      <td>17.539215</td>\n",
       "      <td>0.210202</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.211197</td>\n",
       "      <td>0.195287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>433836362467</td>\n",
       "      <td>6.797695</td>\n",
       "      <td>3.4</td>\n",
       "      <td>18.844223</td>\n",
       "      <td>0.132539</td>\n",
       "      <td>18.781025</td>\n",
       "      <td>0.171607</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.888762</td>\n",
       "      <td>...</td>\n",
       "      <td>17.760912</td>\n",
       "      <td>0.083793</td>\n",
       "      <td>16.968500</td>\n",
       "      <td>0.112740</td>\n",
       "      <td>16.943735</td>\n",
       "      <td>0.177616</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>433836362494</td>\n",
       "      <td>3.585183</td>\n",
       "      <td>2.1</td>\n",
       "      <td>18.274193</td>\n",
       "      <td>0.072648</td>\n",
       "      <td>18.210474</td>\n",
       "      <td>0.095541</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.222660</td>\n",
       "      <td>...</td>\n",
       "      <td>17.173470</td>\n",
       "      <td>0.049189</td>\n",
       "      <td>16.122658</td>\n",
       "      <td>0.049313</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <th>433832563084</th>\n",
       "      <td>433832563084</td>\n",
       "      <td>5.428978</td>\n",
       "      <td>4.0</td>\n",
       "      <td>18.948622</td>\n",
       "      <td>0.091160</td>\n",
       "      <td>18.862259</td>\n",
       "      <td>0.121492</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.878496</td>\n",
       "      <td>...</td>\n",
       "      <td>17.777243</td>\n",
       "      <td>0.096601</td>\n",
       "      <td>17.553614</td>\n",
       "      <td>0.169763</td>\n",
       "      <td>17.494886</td>\n",
       "      <td>0.185832</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2366</th>\n",
       "      <th>433836363120</th>\n",
       "      <td>433836363120</td>\n",
       "      <td>4.329322</td>\n",
       "      <td>3.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.838139</td>\n",
       "      <td>0.317437</td>\n",
       "      <td>17.724998</td>\n",
       "      <td>0.303445</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.112112</td>\n",
       "      <td>0.189446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <th>433836362527</th>\n",
       "      <td>433836362527</td>\n",
       "      <td>6.895045</td>\n",
       "      <td>4.3</td>\n",
       "      <td>20.190485</td>\n",
       "      <td>0.328694</td>\n",
       "      <td>20.190479</td>\n",
       "      <td>0.328940</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.279314</td>\n",
       "      <td>...</td>\n",
       "      <td>18.432409</td>\n",
       "      <td>0.153373</td>\n",
       "      <td>17.352652</td>\n",
       "      <td>0.137550</td>\n",
       "      <td>17.437912</td>\n",
       "      <td>0.219109</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.248894</td>\n",
       "      <td>0.086354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2369</th>\n",
       "      <th>433836363145</th>\n",
       "      <td>433836363145</td>\n",
       "      <td>2.324095</td>\n",
       "      <td>4.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.910995</td>\n",
       "      <td>0.299177</td>\n",
       "      <td>17.910995</td>\n",
       "      <td>0.299177</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.370745</td>\n",
       "      <td>0.240838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2370</th>\n",
       "      <th>433834437127</th>\n",
       "      <td>433834437127</td>\n",
       "      <td>4.105510</td>\n",
       "      <td>3.6</td>\n",
       "      <td>20.370106</td>\n",
       "      <td>0.413753</td>\n",
       "      <td>20.370106</td>\n",
       "      <td>0.413753</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.141270</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.955881</td>\n",
       "      <td>0.764128</td>\n",
       "      <td>18.777044</td>\n",
       "      <td>0.610249</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.318068</td>\n",
       "      <td>0.225548</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                              key_0  distances  e_Pos   YHALLMAG  YHALLMAGERR  \\\n",
       "(A, Seq) duplicates                                                             \n",
       "2360     433834423123  433834423123   2.558296    3.5  17.424122     0.033594   \n",
       "2361     433834423565  433834423565   0.738626    5.8        NaN          NaN   \n",
       "         433834423638  433834423638   5.615029    5.8        NaN          NaN   \n",
       "2362     433836362467  433836362467   6.797695    3.4  18.844223     0.132539   \n",
       "2363     433836362494  433836362494   3.585183    2.1  18.274193     0.072648   \n",
       "2365     433832563084  433832563084   5.428978    4.0  18.948622     0.091160   \n",
       "2366     433836363120  433836363120   4.329322    3.8        NaN          NaN   \n",
       "2368     433836362527  433836362527   6.895045    4.3  20.190485     0.328694   \n",
       "2369     433836363145  433836363145   2.324095    4.4        NaN          NaN   \n",
       "2370     433834437127  433834437127   4.105510    3.6  20.370106     0.413753   \n",
       "\n",
       "                       YPETROMAG  YPETROMAGERR  YPSFMAG  YPSFMAGERR  \\\n",
       "(A, Seq) duplicates                                                   \n",
       "2360     433834423123  17.339571      0.047153      NaN         NaN   \n",
       "2361     433834423565        NaN           NaN      NaN         NaN   \n",
       "         433834423638        NaN           NaN      NaN         NaN   \n",
       "2362     433836362467  18.781025      0.171607      NaN         NaN   \n",
       "2363     433836362494  18.210474      0.095541      NaN         NaN   \n",
       "2365     433832563084  18.862259      0.121492      NaN         NaN   \n",
       "2366     433836363120        NaN           NaN      NaN         NaN   \n",
       "2368     433836362527  20.190479      0.328940      NaN         NaN   \n",
       "2369     433836363145        NaN           NaN      NaN         NaN   \n",
       "2370     433834437127  20.370106      0.413753      NaN         NaN   \n",
       "\n",
       "                       YAPERMAG3      ...       HAPERMAG3  HAPERMAG3ERR  \\\n",
       "(A, Seq) duplicates                   ...                                 \n",
       "2360     433834423123  17.924706      ...       16.420605      0.027337   \n",
       "2361     433834423565        NaN      ...       18.644693      0.198955   \n",
       "         433834423638        NaN      ...             NaN           NaN   \n",
       "2362     433836362467  18.888762      ...       17.760912      0.083793   \n",
       "2363     433836362494  18.222660      ...       17.173470      0.049189   \n",
       "2365     433832563084  18.878496      ...       17.777243      0.096601   \n",
       "2366     433836363120        NaN      ...             NaN           NaN   \n",
       "2368     433836362527  20.279314      ...       18.432409      0.153373   \n",
       "2369     433836363145        NaN      ...             NaN           NaN   \n",
       "2370     433834437127  20.141270      ...             NaN           NaN   \n",
       "\n",
       "                        KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  \\\n",
       "(A, Seq) duplicates                                                      \n",
       "2360     433834423123  15.266109     0.031406  15.165094      0.047093   \n",
       "2361     433834423565  17.770628     0.234180  17.763853      0.258605   \n",
       "         433834423638  17.539215     0.210202  17.539215      0.210202   \n",
       "2362     433836362467  16.968500     0.112740  16.943735      0.177616   \n",
       "2363     433836362494  16.122658     0.049313  15.984794      0.066120   \n",
       "2365     433832563084  17.553614     0.169763  17.494886      0.185832   \n",
       "2366     433836363120  17.838139     0.317437  17.724998      0.303445   \n",
       "2368     433836362527  17.352652     0.137550  17.437912      0.219109   \n",
       "2369     433836363145  17.910995     0.299177  17.910995      0.299177   \n",
       "2370     433834437127  18.955881     0.764128  18.777044      0.610249   \n",
       "\n",
       "                       KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \n",
       "(A, Seq) duplicates                                                  \n",
       "2360     433834423123      NaN         NaN  15.644726      0.019929  \n",
       "2361     433834423565      NaN         NaN  17.884663      0.145093  \n",
       "         433834423638      NaN         NaN  18.211197      0.195287  \n",
       "2362     433836362467      NaN         NaN  17.142780      0.078272  \n",
       "2363     433836362494      NaN         NaN  16.248377      0.034981  \n",
       "2365     433832563084      NaN         NaN  17.446341      0.103341  \n",
       "2366     433836363120      NaN         NaN  18.112112      0.189446  \n",
       "2368     433836362527      NaN         NaN  17.248894      0.086354  \n",
       "2369     433836363145      NaN         NaN  18.370745      0.240838  \n",
       "2370     433834437127      NaN         NaN  18.318068      0.225548  \n",
       "\n",
       "[10 rows x 35 columns]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we define the vector to 'join' the left table because it is using a multindex index\n",
    "_keys = ancillary_sample.index.droplevel(0).values\n",
    "\n",
    "_cols = [ c for c in df_uk.filter(like='MAG',axis=1).columns ]\n",
    "ancillary_joined = ancillary_sample_poserror.merge(ancillary_sample_magnitudes[_cols], left_on=_keys, right_index=True )\n",
    "ancillary_joined.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ancillary_joined.drop('key_0',axis=1,inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.82870090634\n"
     ]
    }
   ],
   "source": [
    "e_pos = ancillary_joined['e_Pos'].mean()\n",
    "print(e_pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def define_LR(func_qm, func_fr, func_nm):\n",
    "    def LR(r,m, qm=func_qm, fr=func_fr, nm=func_nm):\n",
    "        return qm(m)*fr(r)/nm(m)\n",
    "    return LR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "func_fr = define_fr(e_pos,e_pos)\n",
    "\n",
    "df = ancillary_joined.copy()\n",
    "\n",
    "for mag_col in 'YAPERMAG3 J_1APERMAG3 HAPERMAG3 KAPERMAG3'.split():\n",
    "    \n",
    "    LR = define_LR(func_qm=func_qm[mag_col].evaluate, func_fr=func_fr, func_nm=func_nm_b[col].evaluate)\n",
    "    \n",
    "    colname = 'LR_{}'.format(mag_col)\n",
    "    df[colname] = ancillary_joined.apply(lambda df:LR(df['e_Pos'],df[mag_col]), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "      <th>e_Pos</th>\n",
       "      <th>YHALLMAG</th>\n",
       "      <th>YHALLMAGERR</th>\n",
       "      <th>YPETROMAG</th>\n",
       "      <th>YPETROMAGERR</th>\n",
       "      <th>YPSFMAG</th>\n",
       "      <th>YPSFMAGERR</th>\n",
       "      <th>YAPERMAG3</th>\n",
       "      <th>YAPERMAG3ERR</th>\n",
       "      <th>...</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "      <th>LR_YAPERMAG3</th>\n",
       "      <th>LR_J_1APERMAG3</th>\n",
       "      <th>LR_HAPERMAG3</th>\n",
       "      <th>LR_KAPERMAG3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>2.558296</td>\n",
       "      <td>3.5</td>\n",
       "      <td>17.424122</td>\n",
       "      <td>0.033594</td>\n",
       "      <td>17.339571</td>\n",
       "      <td>0.047153</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.924706</td>\n",
       "      <td>0.023942</td>\n",
       "      <td>...</td>\n",
       "      <td>15.165094</td>\n",
       "      <td>0.047093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "      <td>0.015332</td>\n",
       "      <td>0.028080</td>\n",
       "      <td>0.071227</td>\n",
       "      <td>0.081955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>0.738626</td>\n",
       "      <td>5.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.005289</td>\n",
       "      <td>0.843252</td>\n",
       "      <td>0.025315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423638</th>\n",
       "      <td>5.615029</td>\n",
       "      <td>5.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>17.539215</td>\n",
       "      <td>0.210202</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.211197</td>\n",
       "      <td>0.195287</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.026147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>6.797695</td>\n",
       "      <td>3.4</td>\n",
       "      <td>18.844223</td>\n",
       "      <td>0.132539</td>\n",
       "      <td>18.781025</td>\n",
       "      <td>0.171607</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.888762</td>\n",
       "      <td>0.070068</td>\n",
       "      <td>...</td>\n",
       "      <td>16.943735</td>\n",
       "      <td>0.177616</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "      <td>-2.800060</td>\n",
       "      <td>0.177738</td>\n",
       "      <td>0.035366</td>\n",
       "      <td>0.077586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>3.585183</td>\n",
       "      <td>2.1</td>\n",
       "      <td>18.274193</td>\n",
       "      <td>0.072648</td>\n",
       "      <td>18.210474</td>\n",
       "      <td>0.095541</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.222660</td>\n",
       "      <td>0.039503</td>\n",
       "      <td>...</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>0.046278</td>\n",
       "      <td>0.029622</td>\n",
       "      <td>0.055195</td>\n",
       "      <td>0.110417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <th>433832563084</th>\n",
       "      <td>5.428978</td>\n",
       "      <td>4.0</td>\n",
       "      <td>18.948622</td>\n",
       "      <td>0.091160</td>\n",
       "      <td>18.862259</td>\n",
       "      <td>0.121492</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.878496</td>\n",
       "      <td>0.053765</td>\n",
       "      <td>...</td>\n",
       "      <td>17.494886</td>\n",
       "      <td>0.185832</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
       "      <td>-4.183243</td>\n",
       "      <td>0.311976</td>\n",
       "      <td>0.030268</td>\n",
       "      <td>0.069000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2366</th>\n",
       "      <th>433836363120</th>\n",
       "      <td>4.329322</td>\n",
       "      <td>3.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>17.724998</td>\n",
       "      <td>0.303445</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.112112</td>\n",
       "      <td>0.189446</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.042469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <th>433836362527</th>\n",
       "      <td>6.895045</td>\n",
       "      <td>4.3</td>\n",
       "      <td>20.190485</td>\n",
       "      <td>0.328694</td>\n",
       "      <td>20.190479</td>\n",
       "      <td>0.328940</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.279314</td>\n",
       "      <td>0.241452</td>\n",
       "      <td>...</td>\n",
       "      <td>17.437912</td>\n",
       "      <td>0.219109</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.248894</td>\n",
       "      <td>0.086354</td>\n",
       "      <td>-0.000918</td>\n",
       "      <td>-0.012953</td>\n",
       "      <td>0.260244</td>\n",
       "      <td>0.064378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2369</th>\n",
       "      <th>433836363145</th>\n",
       "      <td>2.324095</td>\n",
       "      <td>4.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>17.910995</td>\n",
       "      <td>0.299177</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.370745</td>\n",
       "      <td>0.240838</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.050331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2370</th>\n",
       "      <th>433834437127</th>\n",
       "      <td>4.105510</td>\n",
       "      <td>3.6</td>\n",
       "      <td>20.370106</td>\n",
       "      <td>0.413753</td>\n",
       "      <td>20.370106</td>\n",
       "      <td>0.413753</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.141270</td>\n",
       "      <td>0.159393</td>\n",
       "      <td>...</td>\n",
       "      <td>18.777044</td>\n",
       "      <td>0.610249</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.318068</td>\n",
       "      <td>0.225548</td>\n",
       "      <td>-0.002145</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.058400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 38 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                       distances  e_Pos   YHALLMAG  YHALLMAGERR  YPETROMAG  \\\n",
       "(A, Seq) duplicates                                                          \n",
       "2360     433834423123   2.558296    3.5  17.424122     0.033594  17.339571   \n",
       "2361     433834423565   0.738626    5.8        NaN          NaN        NaN   \n",
       "         433834423638   5.615029    5.8        NaN          NaN        NaN   \n",
       "2362     433836362467   6.797695    3.4  18.844223     0.132539  18.781025   \n",
       "2363     433836362494   3.585183    2.1  18.274193     0.072648  18.210474   \n",
       "2365     433832563084   5.428978    4.0  18.948622     0.091160  18.862259   \n",
       "2366     433836363120   4.329322    3.8        NaN          NaN        NaN   \n",
       "2368     433836362527   6.895045    4.3  20.190485     0.328694  20.190479   \n",
       "2369     433836363145   2.324095    4.4        NaN          NaN        NaN   \n",
       "2370     433834437127   4.105510    3.6  20.370106     0.413753  20.370106   \n",
       "\n",
       "                       YPETROMAGERR  YPSFMAG  YPSFMAGERR  YAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                   \n",
       "2360     433834423123      0.047153      NaN         NaN  17.924706   \n",
       "2361     433834423565           NaN      NaN         NaN        NaN   \n",
       "         433834423638           NaN      NaN         NaN        NaN   \n",
       "2362     433836362467      0.171607      NaN         NaN  18.888762   \n",
       "2363     433836362494      0.095541      NaN         NaN  18.222660   \n",
       "2365     433832563084      0.121492      NaN         NaN  18.878496   \n",
       "2366     433836363120           NaN      NaN         NaN        NaN   \n",
       "2368     433836362527      0.328940      NaN         NaN  20.279314   \n",
       "2369     433836363145           NaN      NaN         NaN        NaN   \n",
       "2370     433834437127      0.413753      NaN         NaN  20.141270   \n",
       "\n",
       "                       YAPERMAG3ERR      ...       KPETROMAG  KPETROMAGERR  \\\n",
       "(A, Seq) duplicates                      ...                                 \n",
       "2360     433834423123      0.023942      ...       15.165094      0.047093   \n",
       "2361     433834423565           NaN      ...       17.763853      0.258605   \n",
       "         433834423638           NaN      ...       17.539215      0.210202   \n",
       "2362     433836362467      0.070068      ...       16.943735      0.177616   \n",
       "2363     433836362494      0.039503      ...       15.984794      0.066120   \n",
       "2365     433832563084      0.053765      ...       17.494886      0.185832   \n",
       "2366     433836363120           NaN      ...       17.724998      0.303445   \n",
       "2368     433836362527      0.241452      ...       17.437912      0.219109   \n",
       "2369     433836363145           NaN      ...       17.910995      0.299177   \n",
       "2370     433834437127      0.159393      ...       18.777044      0.610249   \n",
       "\n",
       "                       KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \\\n",
       "(A, Seq) duplicates                                                   \n",
       "2360     433834423123      NaN         NaN  15.644726      0.019929   \n",
       "2361     433834423565      NaN         NaN  17.884663      0.145093   \n",
       "         433834423638      NaN         NaN  18.211197      0.195287   \n",
       "2362     433836362467      NaN         NaN  17.142780      0.078272   \n",
       "2363     433836362494      NaN         NaN  16.248377      0.034981   \n",
       "2365     433832563084      NaN         NaN  17.446341      0.103341   \n",
       "2366     433836363120      NaN         NaN  18.112112      0.189446   \n",
       "2368     433836362527      NaN         NaN  17.248894      0.086354   \n",
       "2369     433836363145      NaN         NaN  18.370745      0.240838   \n",
       "2370     433834437127      NaN         NaN  18.318068      0.225548   \n",
       "\n",
       "                       LR_YAPERMAG3  LR_J_1APERMAG3  LR_HAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                 \n",
       "2360     433834423123      0.015332        0.028080      0.071227   \n",
       "2361     433834423565           NaN       -0.005289      0.843252   \n",
       "         433834423638           NaN             NaN           NaN   \n",
       "2362     433836362467     -2.800060        0.177738      0.035366   \n",
       "2363     433836362494      0.046278        0.029622      0.055195   \n",
       "2365     433832563084     -4.183243        0.311976      0.030268   \n",
       "2366     433836363120           NaN             NaN           NaN   \n",
       "2368     433836362527     -0.000918       -0.012953      0.260244   \n",
       "2369     433836363145           NaN             NaN           NaN   \n",
       "2370     433834437127     -0.002145             NaN           NaN   \n",
       "\n",
       "                       LR_KAPERMAG3  \n",
       "(A, Seq) duplicates                  \n",
       "2360     433834423123      0.081955  \n",
       "2361     433834423565      0.025315  \n",
       "         433834423638      0.026147  \n",
       "2362     433836362467      0.077586  \n",
       "2363     433836362494      0.110417  \n",
       "2365     433832563084      0.069000  \n",
       "2366     433836363120      0.042469  \n",
       "2368     433836362527      0.064378  \n",
       "2369     433836363145      0.050331  \n",
       "2370     433834437127      0.058400  \n",
       "\n",
       "[10 rows x 38 columns]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Q = 1\n",
    "\n",
    "bla = df.copy()\n",
    "for mag_col in 'YAPERMAG3 J_1APERMAG3 HAPERMAG3 KAPERMAG3'.split():\n",
    "    lr_col = 'LR_{}'.format(mag_col)\n",
    "    r_col = 'R_{}'.format(mag_col)\n",
    "    bla[r_col] = df.groupby(level=0)[lr_col].apply(lambda s:s/s.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>distances</th>\n",
       "      <th>e_Pos</th>\n",
       "      <th>YHALLMAG</th>\n",
       "      <th>YHALLMAGERR</th>\n",
       "      <th>YPETROMAG</th>\n",
       "      <th>YPETROMAGERR</th>\n",
       "      <th>YPSFMAG</th>\n",
       "      <th>YPSFMAGERR</th>\n",
       "      <th>YAPERMAG3</th>\n",
       "      <th>YAPERMAG3ERR</th>\n",
       "      <th>...</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "      <th>LR_YAPERMAG3</th>\n",
       "      <th>LR_J_1APERMAG3</th>\n",
       "      <th>LR_HAPERMAG3</th>\n",
       "      <th>LR_KAPERMAG3</th>\n",
       "      <th>R_YAPERMAG3</th>\n",
       "      <th>R_J_1APERMAG3</th>\n",
       "      <th>R_HAPERMAG3</th>\n",
       "      <th>R_KAPERMAG3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>2.558296</td>\n",
       "      <td>3.5</td>\n",
       "      <td>17.424122</td>\n",
       "      <td>0.033594</td>\n",
       "      <td>17.339571</td>\n",
       "      <td>0.047153</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.924706</td>\n",
       "      <td>0.023942</td>\n",
       "      <td>...</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "      <td>0.015332</td>\n",
       "      <td>0.028080</td>\n",
       "      <td>0.071227</td>\n",
       "      <td>0.081955</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>0.738626</td>\n",
       "      <td>5.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.005289</td>\n",
       "      <td>0.843252</td>\n",
       "      <td>0.025315</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.491914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433834423638</th>\n",
       "      <td>5.615029</td>\n",
       "      <td>5.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>18.211197</td>\n",
       "      <td>0.195287</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.026147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.508086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>6.797695</td>\n",
       "      <td>3.4</td>\n",
       "      <td>18.844223</td>\n",
       "      <td>0.132539</td>\n",
       "      <td>18.781025</td>\n",
       "      <td>0.171607</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.888762</td>\n",
       "      <td>0.070068</td>\n",
       "      <td>...</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "      <td>-2.800060</td>\n",
       "      <td>0.177738</td>\n",
       "      <td>0.035366</td>\n",
       "      <td>0.077586</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>3.585183</td>\n",
       "      <td>2.1</td>\n",
       "      <td>18.274193</td>\n",
       "      <td>0.072648</td>\n",
       "      <td>18.210474</td>\n",
       "      <td>0.095541</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.222660</td>\n",
       "      <td>0.039503</td>\n",
       "      <td>...</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>0.046278</td>\n",
       "      <td>0.029622</td>\n",
       "      <td>0.055195</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <th>433832563084</th>\n",
       "      <td>5.428978</td>\n",
       "      <td>4.0</td>\n",
       "      <td>18.948622</td>\n",
       "      <td>0.091160</td>\n",
       "      <td>18.862259</td>\n",
       "      <td>0.121492</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.878496</td>\n",
       "      <td>0.053765</td>\n",
       "      <td>...</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
       "      <td>-4.183243</td>\n",
       "      <td>0.311976</td>\n",
       "      <td>0.030268</td>\n",
       "      <td>0.069000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2366</th>\n",
       "      <th>433836363120</th>\n",
       "      <td>4.329322</td>\n",
       "      <td>3.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>18.112112</td>\n",
       "      <td>0.189446</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.042469</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <th>433836362527</th>\n",
       "      <td>6.895045</td>\n",
       "      <td>4.3</td>\n",
       "      <td>20.190485</td>\n",
       "      <td>0.328694</td>\n",
       "      <td>20.190479</td>\n",
       "      <td>0.328940</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.279314</td>\n",
       "      <td>0.241452</td>\n",
       "      <td>...</td>\n",
       "      <td>17.248894</td>\n",
       "      <td>0.086354</td>\n",
       "      <td>-0.000918</td>\n",
       "      <td>-0.012953</td>\n",
       "      <td>0.260244</td>\n",
       "      <td>0.064378</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2369</th>\n",
       "      <th>433836363145</th>\n",
       "      <td>2.324095</td>\n",
       "      <td>4.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>18.370745</td>\n",
       "      <td>0.240838</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.050331</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2370</th>\n",
       "      <th>433834437127</th>\n",
       "      <td>4.105510</td>\n",
       "      <td>3.6</td>\n",
       "      <td>20.370106</td>\n",
       "      <td>0.413753</td>\n",
       "      <td>20.370106</td>\n",
       "      <td>0.413753</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.141270</td>\n",
       "      <td>0.159393</td>\n",
       "      <td>...</td>\n",
       "      <td>18.318068</td>\n",
       "      <td>0.225548</td>\n",
       "      <td>-0.002145</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.058400</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2371</th>\n",
       "      <th>433836363155</th>\n",
       "      <td>2.352554</td>\n",
       "      <td>3.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>17.672789</td>\n",
       "      <td>0.126915</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.063354</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2372</th>\n",
       "      <th>433829058905</th>\n",
       "      <td>2.172553</td>\n",
       "      <td>4.7</td>\n",
       "      <td>20.290100</td>\n",
       "      <td>0.246336</td>\n",
       "      <td>20.290100</td>\n",
       "      <td>0.246336</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.627474</td>\n",
       "      <td>0.219280</td>\n",
       "      <td>...</td>\n",
       "      <td>18.438936</td>\n",
       "      <td>0.241503</td>\n",
       "      <td>-0.000037</td>\n",
       "      <td>-0.002648</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.047626</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2373</th>\n",
       "      <th>433832563245</th>\n",
       "      <td>2.146502</td>\n",
       "      <td>1.3</td>\n",
       "      <td>18.332699</td>\n",
       "      <td>0.063843</td>\n",
       "      <td>18.261703</td>\n",
       "      <td>0.090970</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.467182</td>\n",
       "      <td>0.038477</td>\n",
       "      <td>...</td>\n",
       "      <td>16.323315</td>\n",
       "      <td>0.038072</td>\n",
       "      <td>0.226794</td>\n",
       "      <td>0.053318</td>\n",
       "      <td>0.060528</td>\n",
       "      <td>0.116486</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2374</th>\n",
       "      <th>433832563006</th>\n",
       "      <td>2.928150</td>\n",
       "      <td>3.4</td>\n",
       "      <td>20.211857</td>\n",
       "      <td>0.379707</td>\n",
       "      <td>20.234011</td>\n",
       "      <td>0.376071</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.095844</td>\n",
       "      <td>0.152174</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.002657</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.084783</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433832563005</th>\n",
       "      <td>5.038435</td>\n",
       "      <td>3.4</td>\n",
       "      <td>19.264446</td>\n",
       "      <td>0.171967</td>\n",
       "      <td>19.245205</td>\n",
       "      <td>0.206013</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>19.307280</td>\n",
       "      <td>0.076326</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.028681</td>\n",
       "      <td>-0.033419</td>\n",
       "      <td>0.890196</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.915217</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2375</th>\n",
       "      <th>433836363033</th>\n",
       "      <td>0.898566</td>\n",
       "      <td>3.1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>18.311871</td>\n",
       "      <td>0.229123</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.177510</td>\n",
       "      <td>0.064352</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2377</th>\n",
       "      <th>433830897005</th>\n",
       "      <td>1.941389</td>\n",
       "      <td>2.9</td>\n",
       "      <td>19.524969</td>\n",
       "      <td>0.182216</td>\n",
       "      <td>19.526970</td>\n",
       "      <td>0.197271</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.111305</td>\n",
       "      <td>0.142833</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.002775</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2378</th>\n",
       "      <th>433832563193</th>\n",
       "      <td>3.424471</td>\n",
       "      <td>4.6</td>\n",
       "      <td>16.337986</td>\n",
       "      <td>0.018466</td>\n",
       "      <td>16.166098</td>\n",
       "      <td>0.023612</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.243748</td>\n",
       "      <td>0.015382</td>\n",
       "      <td>...</td>\n",
       "      <td>15.357374</td>\n",
       "      <td>0.016536</td>\n",
       "      <td>0.010406</td>\n",
       "      <td>0.013628</td>\n",
       "      <td>0.034200</td>\n",
       "      <td>0.072981</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.005723</td>\n",
       "      <td>0.480826</td>\n",
       "      <td>0.605098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433832563562</th>\n",
       "      <td>5.528915</td>\n",
       "      <td>4.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>17.662270</td>\n",
       "      <td>0.127713</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.367595</td>\n",
       "      <td>0.036928</td>\n",
       "      <td>0.047630</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.994277</td>\n",
       "      <td>0.519174</td>\n",
       "      <td>0.394902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2379</th>\n",
       "      <th>433834437256</th>\n",
       "      <td>0.640801</td>\n",
       "      <td>1.6</td>\n",
       "      <td>19.390974</td>\n",
       "      <td>0.183926</td>\n",
       "      <td>19.395226</td>\n",
       "      <td>0.193301</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>19.261967</td>\n",
       "      <td>0.074662</td>\n",
       "      <td>...</td>\n",
       "      <td>17.580620</td>\n",
       "      <td>0.117012</td>\n",
       "      <td>-0.045075</td>\n",
       "      <td>-1.037225</td>\n",
       "      <td>0.391700</td>\n",
       "      <td>0.093590</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>20 rows × 42 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                       distances  e_Pos   YHALLMAG  YHALLMAGERR  YPETROMAG  \\\n",
       "(A, Seq) duplicates                                                          \n",
       "2360     433834423123   2.558296    3.5  17.424122     0.033594  17.339571   \n",
       "2361     433834423565   0.738626    5.8        NaN          NaN        NaN   \n",
       "         433834423638   5.615029    5.8        NaN          NaN        NaN   \n",
       "2362     433836362467   6.797695    3.4  18.844223     0.132539  18.781025   \n",
       "2363     433836362494   3.585183    2.1  18.274193     0.072648  18.210474   \n",
       "2365     433832563084   5.428978    4.0  18.948622     0.091160  18.862259   \n",
       "2366     433836363120   4.329322    3.8        NaN          NaN        NaN   \n",
       "2368     433836362527   6.895045    4.3  20.190485     0.328694  20.190479   \n",
       "2369     433836363145   2.324095    4.4        NaN          NaN        NaN   \n",
       "2370     433834437127   4.105510    3.6  20.370106     0.413753  20.370106   \n",
       "2371     433836363155   2.352554    3.4        NaN          NaN        NaN   \n",
       "2372     433829058905   2.172553    4.7  20.290100     0.246336  20.290100   \n",
       "2373     433832563245   2.146502    1.3  18.332699     0.063843  18.261703   \n",
       "2374     433832563006   2.928150    3.4  20.211857     0.379707  20.234011   \n",
       "         433832563005   5.038435    3.4  19.264446     0.171967  19.245205   \n",
       "2375     433836363033   0.898566    3.1        NaN          NaN        NaN   \n",
       "2377     433830897005   1.941389    2.9  19.524969     0.182216  19.526970   \n",
       "2378     433832563193   3.424471    4.6  16.337986     0.018466  16.166098   \n",
       "         433832563562   5.528915    4.6        NaN          NaN        NaN   \n",
       "2379     433834437256   0.640801    1.6  19.390974     0.183926  19.395226   \n",
       "\n",
       "                       YPETROMAGERR  YPSFMAG  YPSFMAGERR  YAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                   \n",
       "2360     433834423123      0.047153      NaN         NaN  17.924706   \n",
       "2361     433834423565           NaN      NaN         NaN        NaN   \n",
       "         433834423638           NaN      NaN         NaN        NaN   \n",
       "2362     433836362467      0.171607      NaN         NaN  18.888762   \n",
       "2363     433836362494      0.095541      NaN         NaN  18.222660   \n",
       "2365     433832563084      0.121492      NaN         NaN  18.878496   \n",
       "2366     433836363120           NaN      NaN         NaN        NaN   \n",
       "2368     433836362527      0.328940      NaN         NaN  20.279314   \n",
       "2369     433836363145           NaN      NaN         NaN        NaN   \n",
       "2370     433834437127      0.413753      NaN         NaN  20.141270   \n",
       "2371     433836363155           NaN      NaN         NaN        NaN   \n",
       "2372     433829058905      0.246336      NaN         NaN  20.627474   \n",
       "2373     433832563245      0.090970      NaN         NaN  18.467182   \n",
       "2374     433832563006      0.376071      NaN         NaN  20.095844   \n",
       "         433832563005      0.206013      NaN         NaN  19.307280   \n",
       "2375     433836363033           NaN      NaN         NaN        NaN   \n",
       "2377     433830897005      0.197271      NaN         NaN  20.111305   \n",
       "2378     433832563193      0.023612      NaN         NaN  17.243748   \n",
       "         433832563562           NaN      NaN         NaN        NaN   \n",
       "2379     433834437256      0.193301      NaN         NaN  19.261967   \n",
       "\n",
       "                       YAPERMAG3ERR     ...       KAPERMAG3  KAPERMAG3ERR  \\\n",
       "(A, Seq) duplicates                     ...                                 \n",
       "2360     433834423123      0.023942     ...       15.644726      0.019929   \n",
       "2361     433834423565           NaN     ...       17.884663      0.145093   \n",
       "         433834423638           NaN     ...       18.211197      0.195287   \n",
       "2362     433836362467      0.070068     ...       17.142780      0.078272   \n",
       "2363     433836362494      0.039503     ...       16.248377      0.034981   \n",
       "2365     433832563084      0.053765     ...       17.446341      0.103341   \n",
       "2366     433836363120           NaN     ...       18.112112      0.189446   \n",
       "2368     433836362527      0.241452     ...       17.248894      0.086354   \n",
       "2369     433836363145           NaN     ...       18.370745      0.240838   \n",
       "2370     433834437127      0.159393     ...       18.318068      0.225548   \n",
       "2371     433836363155           NaN     ...       17.672789      0.126915   \n",
       "2372     433829058905      0.219280     ...       18.438936      0.241503   \n",
       "2373     433832563245      0.038477     ...       16.323315      0.038072   \n",
       "2374     433832563006      0.152174     ...             NaN           NaN   \n",
       "         433832563005      0.076326     ...             NaN           NaN   \n",
       "2375     433836363033           NaN     ...       18.311871      0.229123   \n",
       "2377     433830897005      0.142833     ...             NaN           NaN   \n",
       "2378     433832563193      0.015382     ...       15.357374      0.016536   \n",
       "         433832563562           NaN     ...       17.662270      0.127713   \n",
       "2379     433834437256      0.074662     ...       17.580620      0.117012   \n",
       "\n",
       "                       LR_YAPERMAG3  LR_J_1APERMAG3  LR_HAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                 \n",
       "2360     433834423123      0.015332        0.028080      0.071227   \n",
       "2361     433834423565           NaN       -0.005289      0.843252   \n",
       "         433834423638           NaN             NaN           NaN   \n",
       "2362     433836362467     -2.800060        0.177738      0.035366   \n",
       "2363     433836362494      0.046278        0.029622      0.055195   \n",
       "2365     433832563084     -4.183243        0.311976      0.030268   \n",
       "2366     433836363120           NaN             NaN           NaN   \n",
       "2368     433836362527     -0.000918       -0.012953      0.260244   \n",
       "2369     433836363145           NaN             NaN           NaN   \n",
       "2370     433834437127     -0.002145             NaN           NaN   \n",
       "2371     433836363155           NaN             NaN           NaN   \n",
       "2372     433829058905     -0.000037       -0.002648           NaN   \n",
       "2373     433832563245      0.226794        0.053318      0.060528   \n",
       "2374     433832563006     -0.002657             NaN           NaN   \n",
       "         433832563005     -0.028681       -0.033419      0.890196   \n",
       "2375     433836363033           NaN             NaN      2.177510   \n",
       "2377     433830897005     -0.002775             NaN           NaN   \n",
       "2378     433832563193      0.010406        0.013628      0.034200   \n",
       "         433832563562           NaN        2.367595      0.036928   \n",
       "2379     433834437256     -0.045075       -1.037225      0.391700   \n",
       "\n",
       "                       LR_KAPERMAG3  R_YAPERMAG3  R_J_1APERMAG3  R_HAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                            \n",
       "2360     433834423123      0.081955     1.000000       1.000000     1.000000   \n",
       "2361     433834423565      0.025315          NaN       1.000000     1.000000   \n",
       "         433834423638      0.026147          NaN            NaN          NaN   \n",
       "2362     433836362467      0.077586     1.000000       1.000000     1.000000   \n",
       "2363     433836362494      0.110417     1.000000       1.000000     1.000000   \n",
       "2365     433832563084      0.069000     1.000000       1.000000     1.000000   \n",
       "2366     433836363120      0.042469          NaN            NaN          NaN   \n",
       "2368     433836362527      0.064378     1.000000       1.000000     1.000000   \n",
       "2369     433836363145      0.050331          NaN            NaN          NaN   \n",
       "2370     433834437127      0.058400     1.000000            NaN          NaN   \n",
       "2371     433836363155      0.063354          NaN            NaN          NaN   \n",
       "2372     433829058905      0.047626     1.000000       1.000000          NaN   \n",
       "2373     433832563245      0.116486     1.000000       1.000000     1.000000   \n",
       "2374     433832563006           NaN     0.084783            NaN          NaN   \n",
       "         433832563005           NaN     0.915217       1.000000     1.000000   \n",
       "2375     433836363033      0.064352          NaN            NaN     1.000000   \n",
       "2377     433830897005           NaN     1.000000            NaN          NaN   \n",
       "2378     433832563193      0.072981     1.000000       0.005723     0.480826   \n",
       "         433832563562      0.047630          NaN       0.994277     0.519174   \n",
       "2379     433834437256      0.093590     1.000000       1.000000     1.000000   \n",
       "\n",
       "                       R_KAPERMAG3  \n",
       "(A, Seq) duplicates                 \n",
       "2360     433834423123     1.000000  \n",
       "2361     433834423565     0.491914  \n",
       "         433834423638     0.508086  \n",
       "2362     433836362467     1.000000  \n",
       "2363     433836362494     1.000000  \n",
       "2365     433832563084     1.000000  \n",
       "2366     433836363120     1.000000  \n",
       "2368     433836362527     1.000000  \n",
       "2369     433836363145     1.000000  \n",
       "2370     433834437127     1.000000  \n",
       "2371     433836363155     1.000000  \n",
       "2372     433829058905     1.000000  \n",
       "2373     433832563245     1.000000  \n",
       "2374     433832563006          NaN  \n",
       "         433832563005          NaN  \n",
       "2375     433836363033     1.000000  \n",
       "2377     433830897005          NaN  \n",
       "2378     433832563193     0.605098  \n",
       "         433832563562     0.394902  \n",
       "2379     433834437256     1.000000  \n",
       "\n",
       "[20 rows x 42 columns]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bla.head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "final_matches_perMag = {}\n",
    "for mag_col in 'YAPERMAG3 J_1APERMAG3 HAPERMAG3 KAPERMAG3'.split():\n",
    "    r_col = 'R_{}'.format(mag_col)\n",
    "    temp_df = bla.filter(like=mag_col, axis=1)\n",
    "    mask = temp_df.groupby(level=0)[r_col].apply(lambda x:x==x.max())\n",
    "    final_matches_perMag[mag_col] = temp_df.loc[mask]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                       YAPERMAG3  YAPERMAG3ERR  LR_YAPERMAG3  R_YAPERMAG3\n",
      "(A, Seq) duplicates                                                      \n",
      "2360     433834423123  17.924706      0.023942      0.015332     1.000000\n",
      "2362     433836362467  18.888762      0.070068     -2.800060     1.000000\n",
      "2363     433836362494  18.222660      0.039503      0.046278     1.000000\n",
      "2365     433832563084  18.878496      0.053765     -4.183243     1.000000\n",
      "2368     433836362527  20.279314      0.241452     -0.000918     1.000000\n",
      "2370     433834437127  20.141270      0.159393     -0.002145     1.000000\n",
      "2372     433829058905  20.627474      0.219280     -0.000037     1.000000\n",
      "2373     433832563245  18.467182      0.038477      0.226794     1.000000\n",
      "2374     433832563005  19.307280      0.076326     -0.028681     0.915217\n",
      "2377     433830897005  20.111305      0.142833     -0.002775     1.000000\n",
      "2378     433832563193  17.243748      0.015382      0.010406     1.000000\n",
      "2379     433834437256  19.261967      0.074662     -0.045075     1.000000\n",
      "2382     433836362683  19.693525      0.143666     -0.006553     1.000000\n",
      "2383     433836362697  12.286665      0.001154      0.156943     1.000000\n",
      "2384     433830897040  19.761644      0.106287     -0.007018     1.000000\n",
      "2387     433836362717  18.612921      0.055962      0.814559     1.000000\n",
      "2388     433834437241  19.308516      0.077915     -0.038544     1.000000\n",
      "2390     433830897120  17.206987      0.014441      0.018890     1.000000\n",
      "2397     433834437536  18.786797      0.051230      1.841838     1.000000\n",
      "2401     433836362818  18.598341      0.056047      0.870764     1.000000\n",
      "2402     433832563277  18.082695      0.028678      0.027571     1.000000\n",
      "2404     433834437412  19.350780      0.081926     -0.028273     1.000000\n",
      "2405     433832563133  18.338087      0.034732      0.081959     0.700880\n",
      "2409     433832563275  20.224939      0.175372     -0.001940     1.000000\n",
      "2411     433830897250  19.829821      0.115345     -0.004704     1.000000\n",
      "2412     433830897263  19.274771      0.071970     -0.023961     1.000000\n",
      "2413     433832563431  18.342751      0.035465      0.096456     1.000000\n",
      "2420     433836386700  19.102766      0.079107     -0.102617     1.000000\n",
      "2421     433836386718  14.326086      0.002991      0.079609     1.000000\n",
      "2425     433830897359  18.179745      0.029720      0.032246     0.703697\n",
      "...                          ...           ...           ...          ...\n",
      "5153     433828816617  19.770571      0.159796     -0.006353     1.000000\n",
      "5155     433834400093  19.892611      0.161539     -0.004732     1.000000\n",
      "5158     433834400072  20.409607      0.259317     -0.000493     1.000000\n",
      "5159     433834400069  18.928713      0.068551     -0.898528     1.000000\n",
      "5162     433834400044  19.715792      0.138307     -0.006834     1.000000\n",
      "5163     433828816927  18.860825      0.070377    112.181076     1.000000\n",
      "5165     433832635058  18.793072      0.062503      2.242093     1.002083\n",
      "5167     433834399972  19.333525      0.098514     -0.026757     1.000000\n",
      "5171     433832635011  11.481219      0.000751      0.370844     0.807589\n",
      "5172     433834399940  18.469696      0.046156      0.187696     1.000000\n",
      "5174     433834399926  19.695276      0.136011     -0.005579     1.000000\n",
      "5176     433834399931  19.035408      0.074045     -0.218905     1.000000\n",
      "5179     433836104567  19.662977      0.154926     -0.010035     1.000000\n",
      "5180     433828816906  20.143066      0.219097     -0.001792     1.000000\n",
      "5183     433830580450  19.599760      0.132040     -0.011647     1.000000\n",
      "5184     433832634906  17.878853      0.028373      0.018509     1.000000\n",
      "5187     433828816521  18.594954      0.055405      0.811773     4.512995\n",
      "5190     433836104311  19.188871      0.100056     -0.035744     1.000000\n",
      "5197     433828816714  19.525652      0.126027     -0.016430     1.000000\n",
      "5205     433832634787  19.249189      0.089863     -0.042358     1.396051\n",
      "5206     433832462816  20.104740      0.202568     -0.002841     1.000000\n",
      "5207     433836104468  16.551403      0.011193      0.016532     1.000000\n",
      "5208     433834204976  17.394588      0.020709      0.013246     1.971503\n",
      "5209     433828958021  19.983400      0.161413     -0.003960     1.000000\n",
      "5211     433832463003  18.766121      0.063113      1.766090     1.000000\n",
      "5212     433836104298  19.309853      0.110118     -0.027205     1.000000\n",
      "5213     433832462768  19.046249      0.078378     -0.160426     1.000000\n",
      "5215     433836104605  14.058876      0.002430      0.086563     1.000000\n",
      "5219     433834204873  18.654671      0.057811      1.162458     1.000000\n",
      "5220     433830737812  18.549906      0.045479      0.310773     1.000000\n",
      "\n",
      "[1254 rows x 4 columns]\n",
      "                       J_1APERMAG3  J_1APERMAG3ERR  LR_J_1APERMAG3  \\\n",
      "(A, Seq) duplicates                                                  \n",
      "2360     433834423123    17.245426        0.019872        0.028080   \n",
      "2361     433834423565    19.491657        0.146564       -0.005289   \n",
      "2362     433836362467    18.414364        0.067330        0.177738   \n",
      "2363     433836362494    17.871763        0.041378        0.029622   \n",
      "2365     433832563084    18.501507        0.062208        0.311976   \n",
      "2368     433836362527    19.435019        0.169515       -0.012953   \n",
      "2372     433829058905    19.613602        0.154692       -0.002648   \n",
      "2373     433832563245    18.165794        0.046680        0.053318   \n",
      "2374     433832563005    19.322327        0.131315       -0.033419   \n",
      "2378     433832563562    18.779383        0.081248        2.367595   \n",
      "2379     433834437256    18.953220        0.094430       -1.037225   \n",
      "2380     433836362941    19.408398        0.167378       -0.020944   \n",
      "2382     433836362683    19.722084        0.222832       -0.001266   \n",
      "2383     433836362697    10.400075        0.000396        0.816701   \n",
      "2384     433830897040    19.368000        0.121436       -0.031867   \n",
      "2387     433836362717    18.004446        0.047505        0.028425   \n",
      "2388     433834437241    19.207781        0.119614       -0.091619   \n",
      "2390     433830897120    16.677595        0.011365        0.023643   \n",
      "2397     433834437536    18.620321        0.071769        1.232126   \n",
      "2401     433836362818    18.304895        0.062746        0.121768   \n",
      "2402     433832563277    17.938627        0.038730        0.031888   \n",
      "2404     433834437412    18.717354        0.077851        3.031077   \n",
      "2405     433832563136    17.501858        0.026037        0.031203   \n",
      "2411     433830897250    19.352989        0.121814       -0.028239   \n",
      "2412     433830897263    18.979040        0.087405       -0.387824   \n",
      "2413     433832563431    18.013477        0.041633        0.035540   \n",
      "2415     433836387102    19.801624        0.247407       -0.000670   \n",
      "2420     433836386700    18.383923        0.067130        0.165462   \n",
      "2421     433836386718    13.765009        0.002105        0.113650   \n",
      "2425     433830875274    18.523653        0.056274        0.474472   \n",
      "...                            ...             ...             ...   \n",
      "5148     433834400166    19.441866        0.204901       -0.016281   \n",
      "5155     433834400093    18.824003        0.116695        5.622640   \n",
      "5158     433834400072    19.502253        0.217013       -0.010503   \n",
      "5159     433834400069    18.717474        0.105312        2.709628   \n",
      "5161     433832635285    19.530439        0.242557       -0.003861   \n",
      "5162     433834400044    19.400953        0.197615       -0.021178   \n",
      "5163     433828816927    18.188662        0.081228        0.039488   \n",
      "5165     433832635058    18.305901        0.079742        0.094240   \n",
      "5167     433834399972    18.958704        0.132173       -0.729220   \n",
      "5171     433832635011    11.194613        0.000628        0.356016   \n",
      "5172     433834399940    17.782789        0.045579        0.025784   \n",
      "5174     433834399926    19.301725        0.180800       -0.029702   \n",
      "5176     433834399931    18.519619        0.087055        0.528360   \n",
      "5179     433836104567    19.468880        0.223129       -0.015495   \n",
      "5183     433830580450    19.396421        0.223834       -0.023108   \n",
      "5184     433832634906    17.135004        0.027658        0.037199   \n",
      "5187     433828816519    18.292645        0.088890        0.109362   \n",
      "5189     433836104795    19.801432        0.304974       -0.000838   \n",
      "5197     433828816714    19.483612        0.263749       -0.013251   \n",
      "5205     433832634787    18.622391        0.103220        1.627290   \n",
      "5206     433832462816    19.123638        0.155889       -0.134059   \n",
      "5207     433836104468    15.991566        0.010443        0.043902   \n",
      "5208     433834204976    16.877903        0.022895        0.022040   \n",
      "5209     433828958021    19.652857        0.227387       -0.002833   \n",
      "5211     433832463003    18.805693        0.119651        3.747695   \n",
      "5213     433832462768    18.478634        0.086141        0.297527   \n",
      "5215     433836104605    13.485350        0.001809        0.131035   \n",
      "5217     433836104787    19.280344        0.189581       -0.042255   \n",
      "5219     433834205134    18.927177        0.141996       -1.377019   \n",
      "5220     433830737812    17.979549        0.052182        0.021589   \n",
      "\n",
      "                       R_J_1APERMAG3  \n",
      "(A, Seq) duplicates                   \n",
      "2360     433834423123       1.000000  \n",
      "2361     433834423565       1.000000  \n",
      "2362     433836362467       1.000000  \n",
      "2363     433836362494       1.000000  \n",
      "2365     433832563084       1.000000  \n",
      "2368     433836362527       1.000000  \n",
      "2372     433829058905       1.000000  \n",
      "2373     433832563245       1.000000  \n",
      "2374     433832563005       1.000000  \n",
      "2378     433832563562       0.994277  \n",
      "2379     433834437256       1.000000  \n",
      "2380     433836362941       1.000000  \n",
      "2382     433836362683       1.000000  \n",
      "2383     433836362697       1.000000  \n",
      "2384     433830897040       1.000000  \n",
      "2387     433836362717       1.000000  \n",
      "2388     433834437241       1.000000  \n",
      "2390     433830897120       1.000000  \n",
      "2397     433834437536       1.000000  \n",
      "2401     433836362818       1.000000  \n",
      "2402     433832563277       1.000000  \n",
      "2404     433834437412       1.000000  \n",
      "2405     433832563136       0.439587  \n",
      "2411     433830897250       1.000000  \n",
      "2412     433830897263       1.000000  \n",
      "2413     433832563431       1.000000  \n",
      "2415     433836387102       1.000000  \n",
      "2420     433836386700       1.000000  \n",
      "2421     433836386718       1.157280  \n",
      "2425     433830875274       1.039591  \n",
      "...                              ...  \n",
      "5148     433834400166       1.000000  \n",
      "5155     433834400093       1.000000  \n",
      "5158     433834400072       1.000000  \n",
      "5159     433834400069       1.000000  \n",
      "5161     433832635285       1.000000  \n",
      "5162     433834400044       1.000000  \n",
      "5163     433828816927       1.000000  \n",
      "5165     433832635058       1.736839  \n",
      "5167     433834399972       1.000000  \n",
      "5171     433832635011       0.902275  \n",
      "5172     433834399940       1.000000  \n",
      "5174     433834399926       1.000000  \n",
      "5176     433834399931       1.000000  \n",
      "5179     433836104567       1.000000  \n",
      "5183     433830580450       1.000000  \n",
      "5184     433832634906       1.000000  \n",
      "5187     433828816519       0.774730  \n",
      "5189     433836104795       1.000000  \n",
      "5197     433828816714       1.000000  \n",
      "5205     433832634787       0.988267  \n",
      "5206     433832462816       1.000000  \n",
      "5207     433836104468       1.000000  \n",
      "5208     433834204976       1.000000  \n",
      "5209     433828958021       1.000000  \n",
      "5211     433832463003       1.000000  \n",
      "5213     433832462768       1.000000  \n",
      "5215     433836104605       1.283242  \n",
      "5217     433836104787       1.000000  \n",
      "5219     433834205134       1.195113  \n",
      "5220     433830737812       1.000000  \n",
      "\n",
      "[1082 rows x 4 columns]\n",
      "                       HAPERMAG3  HAPERMAG3ERR  LR_HAPERMAG3  R_HAPERMAG3\n",
      "(A, Seq) duplicates                                                      \n",
      "2360     433834423123  16.420605      0.027337      0.071227     1.000000\n",
      "2361     433834423565  18.644693      0.198955      0.843252     1.000000\n",
      "2362     433836362467  17.760912      0.083793      0.035366     1.000000\n",
      "2363     433836362494  17.173470      0.049189      0.055195     1.000000\n",
      "2365     433832563084  17.777243      0.096601      0.030268     1.000000\n",
      "2368     433836362527  18.432409      0.153373      0.260244     1.000000\n",
      "2373     433832563245  17.186298      0.056870      0.060528     1.000000\n",
      "2374     433832563005  18.563437      0.196922      0.890196     1.000000\n",
      "2375     433836363033  18.796801      0.215325      2.177510     1.000000\n",
      "2378     433832563562  18.007706      0.119877      0.036928     0.519174\n",
      "2379     433834437256  18.419258      0.170482      0.391700     1.000000\n",
      "2380     433836362941  18.785177      0.212911      2.142263     1.000000\n",
      "2383     433836362697  12.846084      0.001766      0.282490     1.000000\n",
      "2387     433836362717  17.309542      0.055377      0.049880     1.000000\n",
      "2388     433834437241  18.468391      0.178951      0.561063     1.000000\n",
      "2390     433830897120  15.996914      0.017716      0.052473     1.000000\n",
      "2401     433836362818  17.956501      0.099511      0.060198     1.000000\n",
      "2402     433832563277  17.703932      0.092394      0.048986     1.000000\n",
      "2404     433834437412  18.047419      0.123982      0.063055     1.000000\n",
      "2405     433832563133  17.289087      0.062637      0.053998     0.361351\n",
      "2411     433830897250  18.366116      0.147660      0.213970     1.000000\n",
      "2412     433830897263  18.327894      0.142333      0.123293     1.000000\n",
      "2413     433832563431  17.627716      0.086638      0.057320     1.000000\n",
      "2415     433836387102  18.410160      0.150617      0.254346     1.000000\n",
      "2420     433836386700  17.409685      0.059674      0.054777     1.000000\n",
      "2421     433836386718  13.082668      0.002039      0.124279     1.000000\n",
      "2425     433830897355  16.479706      0.027119      0.067856     0.400962\n",
      "2426     433832563239  17.523548      0.078247      0.052167     1.000000\n",
      "2427     433832732119  18.046804      0.128108      0.058552     1.000000\n",
      "2429     433830874662  18.366051      0.153193      0.218272     1.000000\n",
      "...                          ...           ...           ...          ...\n",
      "5145     433830580657  18.312771      0.182195      0.183103     0.413292\n",
      "5146     433832635230  17.016855      0.050636      0.056138     1.000000\n",
      "5148     433834400166  18.587337      0.210662      1.168414     1.000000\n",
      "5156     433834400445  18.813341      0.256349      2.730966     1.000000\n",
      "5159     433834400069  18.458633      0.184885      0.395872     1.000000\n",
      "5161     433832635285  18.493805      0.193700      0.251524     1.000000\n",
      "5163     433828816927  17.436222      0.080430      0.043148     1.000000\n",
      "5165     433832635058  17.810293      0.103662      0.036280     1.000000\n",
      "5171     433832635011  11.804230      0.001065      0.212199     1.000000\n",
      "5172     433834399940  17.131571      0.055327      0.047724     1.000000\n",
      "5174     433834399926  18.512144      0.195419      0.452883     1.000000\n",
      "5176     433834400436  18.665960      0.220892      2.289900     0.972480\n",
      "5179     433836104567  18.438868      0.170007      0.416666     1.000000\n",
      "5181     433832635335  17.861996      0.105737      0.034445     1.000000\n",
      "5182     433832635334  18.554668      0.203572      0.892736     1.000000\n",
      "5183     433830580450  18.489006      0.212166      0.533617     1.000000\n",
      "5184     433832634906  16.317656      0.026407      0.079873     1.000000\n",
      "5187     433828816519  18.048309      0.137467      0.073980     0.559725\n",
      "5197     433828816714  18.234837      0.165025      0.123757     1.000000\n",
      "5205     433832634794  16.459311      0.029782      0.080858     0.662659\n",
      "5206     433832462816  18.623259      0.213969      1.617397     1.000000\n",
      "5207     433836104468  15.119283      0.009284      0.040499     1.000000\n",
      "5208     433834204976  16.326229      0.027215      0.074642     1.000000\n",
      "5211     433832463003  18.069792      0.131175      0.057320     1.000000\n",
      "5212     433836104298  18.054272      0.117542      0.053774     1.000000\n",
      "5213     433832462768  17.786472      0.099437      0.035240     1.000000\n",
      "5215     433836104605  13.036633      0.002181      0.210709     1.000000\n",
      "5217     433836104787  18.339977      0.154737      0.174833     1.000000\n",
      "5219     433834205134  18.424446      0.180232      0.325414     0.884359\n",
      "5220     433830737812  17.293871      0.057284      0.038252     1.000000\n",
      "\n",
      "[1143 rows x 4 columns]\n",
      "                       KAPERMAG3  KAPERMAG3ERR  LR_KAPERMAG3  R_KAPERMAG3\n",
      "(A, Seq) duplicates                                                      \n",
      "2360     433834423123  15.644726      0.019929      0.081955     1.000000\n",
      "2361     433834423638  18.211197      0.195287      0.026147     0.508086\n",
      "2362     433836362467  17.142780      0.078272      0.077586     1.000000\n",
      "2363     433836362494  16.248377      0.034981      0.110417     1.000000\n",
      "2365     433832563084  17.446341      0.103341      0.069000     1.000000\n",
      "2366     433836363120  18.112112      0.189446      0.042469     1.000000\n",
      "2368     433836362527  17.248894      0.086354      0.064378     1.000000\n",
      "2369     433836363145  18.370745      0.240838      0.050331     1.000000\n",
      "2370     433834437127  18.318068      0.225548      0.058400     1.000000\n",
      "2371     433836363155  17.672789      0.126915      0.063354     1.000000\n",
      "2372     433829058905  18.438936      0.241503      0.047626     1.000000\n",
      "2373     433832563245  16.323315      0.038072      0.116486     1.000000\n",
      "2375     433836363033  18.311871      0.229123      0.064352     1.000000\n",
      "2378     433832563193  15.357374      0.016536      0.072981     0.605098\n",
      "2379     433834437256  17.580620      0.117012      0.093590     1.000000\n",
      "2380     433836362941  17.913157      0.159587      0.055038     1.000000\n",
      "2383     433836362697  10.791451      0.000817      0.580437     1.000000\n",
      "2384     433830897040  17.816031      0.138683      0.064601     1.000000\n",
      "2387     433836362717  16.377665      0.040097      0.102404     1.000000\n",
      "2388     433834437241  17.449163      0.104403      0.106916     1.000000\n",
      "2390     433830897120  15.245141      0.014406      0.118758     1.000000\n",
      "2391     433830897541  17.755636      0.132772      0.059633     1.000000\n",
      "2397     433834437536  18.018436      0.177411      0.044476     1.000000\n",
      "2401     433836362818  17.689283      0.134518      0.085402     1.000000\n",
      "2402     433832563277  16.903563      0.065317      0.110363     1.000000\n",
      "2404     433834437412  17.178679      0.082832      0.091393     1.000000\n",
      "2405     433832563134  14.919018      0.011598      0.134923     0.322397\n",
      "2409     433832563275  18.006271      0.177882      0.062318     1.000000\n",
      "2411     433830897250  17.816755      0.141371      0.052061     1.000000\n",
      "2412     433830897263  17.460295      0.103712      0.058446     1.000000\n",
      "...                          ...           ...           ...          ...\n",
      "5156     433834400445  17.844395      0.164684      0.060354     1.000000\n",
      "5158     433834400072  17.684925      0.143023      0.067406     1.000000\n",
      "5159     433834400069  17.634108      0.135766      0.068031     1.000000\n",
      "5161     433832635285  17.556959      0.135754      0.036354     1.000000\n",
      "5162     433834400044  17.909420      0.175526      0.052902     1.000000\n",
      "5163     433828816927  16.554800      0.063353      0.069468     1.000000\n",
      "5165     433832635058  17.550945      0.134909      0.077524     1.000000\n",
      "5170     433834400495  17.770426      0.154547      0.060376     1.000000\n",
      "5171     433832635011  10.910043      0.000928      0.612140     0.856009\n",
      "5172     433834399940  16.315331      0.041304      0.093844     1.000000\n",
      "5174     433834399926  17.922951      0.177518      0.039891     1.000000\n",
      "5176     433834399931  18.221453      0.231463      0.065373     0.510091\n",
      "5179     433836104567  18.013350      0.167276      0.060315     1.000000\n",
      "5181     433832635335  17.298538      0.105734      0.076432     1.000000\n",
      "5183     433830580450  18.162489      0.257294      0.053442     1.000000\n",
      "5184     433832634906  15.368078      0.018944      0.133076     1.000000\n",
      "5187     433828816521  16.453400      0.056428      0.130106     0.550767\n",
      "5198     433836104989  18.084858      0.178164      0.056444     1.000000\n",
      "5201     433830580778  17.508984      0.140621      0.062975     1.000000\n",
      "5205     433832634794  16.404646      0.047353      0.113885     0.419653\n",
      "5206     433832462816  17.827826      0.168309      0.055873     1.000000\n",
      "5207     433836104468  14.375650      0.007200      0.050778     1.000000\n",
      "5208     433834204976  16.029503      0.035247      0.118444     0.600930\n",
      "5211     433832463003  17.281328      0.103570      0.076980     1.000000\n",
      "5212     433836104298  17.411783      0.094905      0.075910     0.563673\n",
      "5213     433832462768  16.925835      0.074258      0.088931     1.000000\n",
      "5215     433836104605  12.797623      0.002469      0.271363     1.000000\n",
      "5217     433836104787  17.639168      0.117859      0.064807     1.000000\n",
      "5219     433834204873  17.171953      0.099276      0.084595     0.539992\n",
      "5220     433830737812  16.625101      0.057040      0.060177     1.000000\n",
      "\n",
      "[1315 rows x 4 columns]\n"
     ]
    }
   ],
   "source": [
    "for c in final_matches_perMag.keys():\n",
    "    print(final_matches_perMag[c])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "col = 'YAPERMAG3'\n",
    "mle_match = final_matches_perMag[col]\n",
    "for col in 'J_1APERMAG3 HAPERMAG3 KAPERMAG3'.split():\n",
    "    tab = final_matches_perMag[col]\n",
    "    mle_match = mle_match.merge(tab, how='outer', left_index=True, right_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>YAPERMAG3</th>\n",
       "      <th>YAPERMAG3ERR</th>\n",
       "      <th>LR_YAPERMAG3</th>\n",
       "      <th>R_YAPERMAG3</th>\n",
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       "      <th>R_KAPERMAG3</th>\n",
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       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>0.070068</td>\n",
       "      <td>-2.800060</td>\n",
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       "      <td>0.311976</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.777243</td>\n",
       "      <td>0.096601</td>\n",
       "      <td>0.030268</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
       "      <td>0.069000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2366</th>\n",
       "      <th>433836363120</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.112112</td>\n",
       "      <td>0.189446</td>\n",
       "      <td>0.042469</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <th>433836362527</th>\n",
       "      <td>20.279314</td>\n",
       "      <td>0.241452</td>\n",
       "      <td>-0.000918</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>19.435019</td>\n",
       "      <td>0.169515</td>\n",
       "      <td>-0.012953</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.432409</td>\n",
       "      <td>0.153373</td>\n",
       "      <td>0.260244</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.248894</td>\n",
       "      <td>0.086354</td>\n",
       "      <td>0.064378</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2369</th>\n",
       "      <th>433836363145</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.370745</td>\n",
       "      <td>0.240838</td>\n",
       "      <td>0.050331</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2370</th>\n",
       "      <th>433834437127</th>\n",
       "      <td>20.141270</td>\n",
       "      <td>0.159393</td>\n",
       "      <td>-0.002145</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.318068</td>\n",
       "      <td>0.225548</td>\n",
       "      <td>0.058400</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2371</th>\n",
       "      <th>433836363155</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.672789</td>\n",
       "      <td>0.126915</td>\n",
       "      <td>0.063354</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2372</th>\n",
       "      <th>433829058905</th>\n",
       "      <td>20.627474</td>\n",
       "      <td>0.219280</td>\n",
       "      <td>-0.000037</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>19.613602</td>\n",
       "      <td>0.154692</td>\n",
       "      <td>-0.002648</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.438936</td>\n",
       "      <td>0.241503</td>\n",
       "      <td>0.047626</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2373</th>\n",
       "      <th>433832563245</th>\n",
       "      <td>18.467182</td>\n",
       "      <td>0.038477</td>\n",
       "      <td>0.226794</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.165794</td>\n",
       "      <td>0.046680</td>\n",
       "      <td>0.053318</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.186298</td>\n",
       "      <td>0.056870</td>\n",
       "      <td>0.060528</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>16.323315</td>\n",
       "      <td>0.038072</td>\n",
       "      <td>0.116486</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2374</th>\n",
       "      <th>433832563005</th>\n",
       "      <td>19.307280</td>\n",
       "      <td>0.076326</td>\n",
       "      <td>-0.028681</td>\n",
       "      <td>0.915217</td>\n",
       "      <td>19.322327</td>\n",
       "      <td>0.131315</td>\n",
       "      <td>-0.033419</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.563437</td>\n",
       "      <td>0.196922</td>\n",
       "      <td>0.890196</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2375</th>\n",
       "      <th>433836363033</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.796801</td>\n",
       "      <td>0.215325</td>\n",
       "      <td>2.177510</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.311871</td>\n",
       "      <td>0.229123</td>\n",
       "      <td>0.064352</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2377</th>\n",
       "      <th>433830897005</th>\n",
       "      <td>20.111305</td>\n",
       "      <td>0.142833</td>\n",
       "      <td>-0.002775</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">2378</th>\n",
       "      <th>433832563193</th>\n",
       "      <td>17.243748</td>\n",
       "      <td>0.015382</td>\n",
       "      <td>0.010406</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.357374</td>\n",
       "      <td>0.016536</td>\n",
       "      <td>0.072981</td>\n",
       "      <td>0.605098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433832563562</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.779383</td>\n",
       "      <td>0.081248</td>\n",
       "      <td>2.367595</td>\n",
       "      <td>0.994277</td>\n",
       "      <td>18.007706</td>\n",
       "      <td>0.119877</td>\n",
       "      <td>0.036928</td>\n",
       "      <td>0.519174</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2379</th>\n",
       "      <th>433834437256</th>\n",
       "      <td>19.261967</td>\n",
       "      <td>0.074662</td>\n",
       "      <td>-0.045075</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.953220</td>\n",
       "      <td>0.094430</td>\n",
       "      <td>-1.037225</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.419258</td>\n",
       "      <td>0.170482</td>\n",
       "      <td>0.391700</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.580620</td>\n",
       "      <td>0.117012</td>\n",
       "      <td>0.093590</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2380</th>\n",
       "      <th>433836362941</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>19.408398</td>\n",
       "      <td>0.167378</td>\n",
       "      <td>-0.020944</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.785177</td>\n",
       "      <td>0.212911</td>\n",
       "      <td>2.142263</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.913157</td>\n",
       "      <td>0.159587</td>\n",
       "      <td>0.055038</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       YAPERMAG3  YAPERMAG3ERR  LR_YAPERMAG3  R_YAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                         \n",
       "2360     433834423123  17.924706      0.023942      0.015332     1.000000   \n",
       "2361     433834423565        NaN           NaN           NaN          NaN   \n",
       "         433834423638        NaN           NaN           NaN          NaN   \n",
       "2362     433836362467  18.888762      0.070068     -2.800060     1.000000   \n",
       "2363     433836362494  18.222660      0.039503      0.046278     1.000000   \n",
       "2365     433832563084  18.878496      0.053765     -4.183243     1.000000   \n",
       "2366     433836363120        NaN           NaN           NaN          NaN   \n",
       "2368     433836362527  20.279314      0.241452     -0.000918     1.000000   \n",
       "2369     433836363145        NaN           NaN           NaN          NaN   \n",
       "2370     433834437127  20.141270      0.159393     -0.002145     1.000000   \n",
       "2371     433836363155        NaN           NaN           NaN          NaN   \n",
       "2372     433829058905  20.627474      0.219280     -0.000037     1.000000   \n",
       "2373     433832563245  18.467182      0.038477      0.226794     1.000000   \n",
       "2374     433832563005  19.307280      0.076326     -0.028681     0.915217   \n",
       "2375     433836363033        NaN           NaN           NaN          NaN   \n",
       "2377     433830897005  20.111305      0.142833     -0.002775     1.000000   \n",
       "2378     433832563193  17.243748      0.015382      0.010406     1.000000   \n",
       "         433832563562        NaN           NaN           NaN          NaN   \n",
       "2379     433834437256  19.261967      0.074662     -0.045075     1.000000   \n",
       "2380     433836362941        NaN           NaN           NaN          NaN   \n",
       "\n",
       "                       J_1APERMAG3  J_1APERMAG3ERR  LR_J_1APERMAG3  \\\n",
       "(A, Seq) duplicates                                                  \n",
       "2360     433834423123    17.245426        0.019872        0.028080   \n",
       "2361     433834423565    19.491657        0.146564       -0.005289   \n",
       "         433834423638          NaN             NaN             NaN   \n",
       "2362     433836362467    18.414364        0.067330        0.177738   \n",
       "2363     433836362494    17.871763        0.041378        0.029622   \n",
       "2365     433832563084    18.501507        0.062208        0.311976   \n",
       "2366     433836363120          NaN             NaN             NaN   \n",
       "2368     433836362527    19.435019        0.169515       -0.012953   \n",
       "2369     433836363145          NaN             NaN             NaN   \n",
       "2370     433834437127          NaN             NaN             NaN   \n",
       "2371     433836363155          NaN             NaN             NaN   \n",
       "2372     433829058905    19.613602        0.154692       -0.002648   \n",
       "2373     433832563245    18.165794        0.046680        0.053318   \n",
       "2374     433832563005    19.322327        0.131315       -0.033419   \n",
       "2375     433836363033          NaN             NaN             NaN   \n",
       "2377     433830897005          NaN             NaN             NaN   \n",
       "2378     433832563193          NaN             NaN             NaN   \n",
       "         433832563562    18.779383        0.081248        2.367595   \n",
       "2379     433834437256    18.953220        0.094430       -1.037225   \n",
       "2380     433836362941    19.408398        0.167378       -0.020944   \n",
       "\n",
       "                       R_J_1APERMAG3  HAPERMAG3  HAPERMAG3ERR  LR_HAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                           \n",
       "2360     433834423123       1.000000  16.420605      0.027337      0.071227   \n",
       "2361     433834423565       1.000000  18.644693      0.198955      0.843252   \n",
       "         433834423638            NaN        NaN           NaN           NaN   \n",
       "2362     433836362467       1.000000  17.760912      0.083793      0.035366   \n",
       "2363     433836362494       1.000000  17.173470      0.049189      0.055195   \n",
       "2365     433832563084       1.000000  17.777243      0.096601      0.030268   \n",
       "2366     433836363120            NaN        NaN           NaN           NaN   \n",
       "2368     433836362527       1.000000  18.432409      0.153373      0.260244   \n",
       "2369     433836363145            NaN        NaN           NaN           NaN   \n",
       "2370     433834437127            NaN        NaN           NaN           NaN   \n",
       "2371     433836363155            NaN        NaN           NaN           NaN   \n",
       "2372     433829058905       1.000000        NaN           NaN           NaN   \n",
       "2373     433832563245       1.000000  17.186298      0.056870      0.060528   \n",
       "2374     433832563005       1.000000  18.563437      0.196922      0.890196   \n",
       "2375     433836363033            NaN  18.796801      0.215325      2.177510   \n",
       "2377     433830897005            NaN        NaN           NaN           NaN   \n",
       "2378     433832563193            NaN        NaN           NaN           NaN   \n",
       "         433832563562       0.994277  18.007706      0.119877      0.036928   \n",
       "2379     433834437256       1.000000  18.419258      0.170482      0.391700   \n",
       "2380     433836362941       1.000000  18.785177      0.212911      2.142263   \n",
       "\n",
       "                       R_HAPERMAG3  KAPERMAG3  KAPERMAG3ERR  LR_KAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                         \n",
       "2360     433834423123     1.000000  15.644726      0.019929      0.081955   \n",
       "2361     433834423565     1.000000        NaN           NaN           NaN   \n",
       "         433834423638          NaN  18.211197      0.195287      0.026147   \n",
       "2362     433836362467     1.000000  17.142780      0.078272      0.077586   \n",
       "2363     433836362494     1.000000  16.248377      0.034981      0.110417   \n",
       "2365     433832563084     1.000000  17.446341      0.103341      0.069000   \n",
       "2366     433836363120          NaN  18.112112      0.189446      0.042469   \n",
       "2368     433836362527     1.000000  17.248894      0.086354      0.064378   \n",
       "2369     433836363145          NaN  18.370745      0.240838      0.050331   \n",
       "2370     433834437127          NaN  18.318068      0.225548      0.058400   \n",
       "2371     433836363155          NaN  17.672789      0.126915      0.063354   \n",
       "2372     433829058905          NaN  18.438936      0.241503      0.047626   \n",
       "2373     433832563245     1.000000  16.323315      0.038072      0.116486   \n",
       "2374     433832563005     1.000000        NaN           NaN           NaN   \n",
       "2375     433836363033     1.000000  18.311871      0.229123      0.064352   \n",
       "2377     433830897005          NaN        NaN           NaN           NaN   \n",
       "2378     433832563193          NaN  15.357374      0.016536      0.072981   \n",
       "         433832563562     0.519174        NaN           NaN           NaN   \n",
       "2379     433834437256     1.000000  17.580620      0.117012      0.093590   \n",
       "2380     433836362941     1.000000  17.913157      0.159587      0.055038   \n",
       "\n",
       "                       R_KAPERMAG3  \n",
       "(A, Seq) duplicates                 \n",
       "2360     433834423123     1.000000  \n",
       "2361     433834423565          NaN  \n",
       "         433834423638     0.508086  \n",
       "2362     433836362467     1.000000  \n",
       "2363     433836362494     1.000000  \n",
       "2365     433832563084     1.000000  \n",
       "2366     433836363120     1.000000  \n",
       "2368     433836362527     1.000000  \n",
       "2369     433836363145     1.000000  \n",
       "2370     433834437127     1.000000  \n",
       "2371     433836363155     1.000000  \n",
       "2372     433829058905     1.000000  \n",
       "2373     433832563245     1.000000  \n",
       "2374     433832563005          NaN  \n",
       "2375     433836363033     1.000000  \n",
       "2377     433830897005          NaN  \n",
       "2378     433832563193     0.605098  \n",
       "         433832563562          NaN  \n",
       "2379     433834437256     1.000000  \n",
       "2380     433836362941     1.000000  "
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mle_match.head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>YAPERMAG3</th>\n",
       "      <th>YAPERMAG3ERR</th>\n",
       "      <th>LR_YAPERMAG3</th>\n",
       "      <th>R_YAPERMAG3</th>\n",
       "      <th>J_1APERMAG3</th>\n",
       "      <th>J_1APERMAG3ERR</th>\n",
       "      <th>LR_J_1APERMAG3</th>\n",
       "      <th>R_J_1APERMAG3</th>\n",
       "      <th>HAPERMAG3</th>\n",
       "      <th>HAPERMAG3ERR</th>\n",
       "      <th>LR_HAPERMAG3</th>\n",
       "      <th>R_HAPERMAG3</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "      <th>LR_KAPERMAG3</th>\n",
       "      <th>R_KAPERMAG3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>17.924706</td>\n",
       "      <td>0.023942</td>\n",
       "      <td>0.015332</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.245426</td>\n",
       "      <td>0.019872</td>\n",
       "      <td>0.028080</td>\n",
       "      <td>1.0</td>\n",
       "      <td>16.420605</td>\n",
       "      <td>0.027337</td>\n",
       "      <td>0.071227</td>\n",
       "      <td>1.0</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
       "      <td>0.081955</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>19.491657</td>\n",
       "      <td>0.146564</td>\n",
       "      <td>-0.005289</td>\n",
       "      <td>1.0</td>\n",
       "      <td>18.644693</td>\n",
       "      <td>0.198955</td>\n",
       "      <td>0.843252</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>18.888762</td>\n",
       "      <td>0.070068</td>\n",
       "      <td>-2.800060</td>\n",
       "      <td>1.0</td>\n",
       "      <td>18.414364</td>\n",
       "      <td>0.067330</td>\n",
       "      <td>0.177738</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.760912</td>\n",
       "      <td>0.083793</td>\n",
       "      <td>0.035366</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
       "      <td>0.077586</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>18.222660</td>\n",
       "      <td>0.039503</td>\n",
       "      <td>0.046278</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.871763</td>\n",
       "      <td>0.041378</td>\n",
       "      <td>0.029622</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.173470</td>\n",
       "      <td>0.049189</td>\n",
       "      <td>0.055195</td>\n",
       "      <td>1.0</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <th>433832563084</th>\n",
       "      <td>18.878496</td>\n",
       "      <td>0.053765</td>\n",
       "      <td>-4.183243</td>\n",
       "      <td>1.0</td>\n",
       "      <td>18.501507</td>\n",
       "      <td>0.062208</td>\n",
       "      <td>0.311976</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.777243</td>\n",
       "      <td>0.096601</td>\n",
       "      <td>0.030268</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
       "      <td>0.069000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2366</th>\n",
       "      <th>433836363120</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.112112</td>\n",
       "      <td>0.189446</td>\n",
       "      <td>0.042469</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <th>433836362527</th>\n",
       "      <td>20.279314</td>\n",
       "      <td>0.241452</td>\n",
       "      <td>-0.000918</td>\n",
       "      <td>1.0</td>\n",
       "      <td>19.435019</td>\n",
       "      <td>0.169515</td>\n",
       "      <td>-0.012953</td>\n",
       "      <td>1.0</td>\n",
       "      <td>18.432409</td>\n",
       "      <td>0.153373</td>\n",
       "      <td>0.260244</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.248894</td>\n",
       "      <td>0.086354</td>\n",
       "      <td>0.064378</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2369</th>\n",
       "      <th>433836363145</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.370745</td>\n",
       "      <td>0.240838</td>\n",
       "      <td>0.050331</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2370</th>\n",
       "      <th>433834437127</th>\n",
       "      <td>20.141270</td>\n",
       "      <td>0.159393</td>\n",
       "      <td>-0.002145</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.318068</td>\n",
       "      <td>0.225548</td>\n",
       "      <td>0.058400</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2371</th>\n",
       "      <th>433836363155</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.672789</td>\n",
       "      <td>0.126915</td>\n",
       "      <td>0.063354</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       YAPERMAG3  YAPERMAG3ERR  LR_YAPERMAG3  R_YAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                         \n",
       "2360     433834423123  17.924706      0.023942      0.015332          1.0   \n",
       "2361     433834423565        NaN           NaN           NaN          NaN   \n",
       "2362     433836362467  18.888762      0.070068     -2.800060          1.0   \n",
       "2363     433836362494  18.222660      0.039503      0.046278          1.0   \n",
       "2365     433832563084  18.878496      0.053765     -4.183243          1.0   \n",
       "2366     433836363120        NaN           NaN           NaN          NaN   \n",
       "2368     433836362527  20.279314      0.241452     -0.000918          1.0   \n",
       "2369     433836363145        NaN           NaN           NaN          NaN   \n",
       "2370     433834437127  20.141270      0.159393     -0.002145          1.0   \n",
       "2371     433836363155        NaN           NaN           NaN          NaN   \n",
       "\n",
       "                       J_1APERMAG3  J_1APERMAG3ERR  LR_J_1APERMAG3  \\\n",
       "(A, Seq) duplicates                                                  \n",
       "2360     433834423123    17.245426        0.019872        0.028080   \n",
       "2361     433834423565    19.491657        0.146564       -0.005289   \n",
       "2362     433836362467    18.414364        0.067330        0.177738   \n",
       "2363     433836362494    17.871763        0.041378        0.029622   \n",
       "2365     433832563084    18.501507        0.062208        0.311976   \n",
       "2366     433836363120          NaN             NaN             NaN   \n",
       "2368     433836362527    19.435019        0.169515       -0.012953   \n",
       "2369     433836363145          NaN             NaN             NaN   \n",
       "2370     433834437127          NaN             NaN             NaN   \n",
       "2371     433836363155          NaN             NaN             NaN   \n",
       "\n",
       "                       R_J_1APERMAG3  HAPERMAG3  HAPERMAG3ERR  LR_HAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                           \n",
       "2360     433834423123            1.0  16.420605      0.027337      0.071227   \n",
       "2361     433834423565            1.0  18.644693      0.198955      0.843252   \n",
       "2362     433836362467            1.0  17.760912      0.083793      0.035366   \n",
       "2363     433836362494            1.0  17.173470      0.049189      0.055195   \n",
       "2365     433832563084            1.0  17.777243      0.096601      0.030268   \n",
       "2366     433836363120            NaN        NaN           NaN           NaN   \n",
       "2368     433836362527            1.0  18.432409      0.153373      0.260244   \n",
       "2369     433836363145            NaN        NaN           NaN           NaN   \n",
       "2370     433834437127            NaN        NaN           NaN           NaN   \n",
       "2371     433836363155            NaN        NaN           NaN           NaN   \n",
       "\n",
       "                       R_HAPERMAG3  KAPERMAG3  KAPERMAG3ERR  LR_KAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                         \n",
       "2360     433834423123          1.0  15.644726      0.019929      0.081955   \n",
       "2361     433834423565          1.0        NaN           NaN           NaN   \n",
       "2362     433836362467          1.0  17.142780      0.078272      0.077586   \n",
       "2363     433836362494          1.0  16.248377      0.034981      0.110417   \n",
       "2365     433832563084          1.0  17.446341      0.103341      0.069000   \n",
       "2366     433836363120          NaN  18.112112      0.189446      0.042469   \n",
       "2368     433836362527          1.0  17.248894      0.086354      0.064378   \n",
       "2369     433836363145          NaN  18.370745      0.240838      0.050331   \n",
       "2370     433834437127          NaN  18.318068      0.225548      0.058400   \n",
       "2371     433836363155          NaN  17.672789      0.126915      0.063354   \n",
       "\n",
       "                       R_KAPERMAG3  \n",
       "(A, Seq) duplicates                 \n",
       "2360     433834423123          1.0  \n",
       "2361     433834423565          NaN  \n",
       "2362     433836362467          1.0  \n",
       "2363     433836362494          1.0  \n",
       "2365     433832563084          1.0  \n",
       "2366     433836363120          1.0  \n",
       "2368     433836362527          1.0  \n",
       "2369     433836363145          1.0  \n",
       "2370     433834437127          1.0  \n",
       "2371     433836363155          1.0  "
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp_df = mle_match.filter(regex=\"^R_\", axis=1)\n",
    "\n",
    "mask = temp_df.agg('sum',axis=1).groupby(level=0).apply(lambda x:x==x.max())\n",
    "\n",
    "mle_match_final = mle_match.loc[mask]\n",
    "mle_match_final.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>LR_YAPERMAG3</th>\n",
       "      <th>R_YAPERMAG3</th>\n",
       "      <th>LR_J_1APERMAG3</th>\n",
       "      <th>R_J_1APERMAG3</th>\n",
       "      <th>LR_HAPERMAG3</th>\n",
       "      <th>R_HAPERMAG3</th>\n",
       "      <th>LR_KAPERMAG3</th>\n",
       "      <th>R_KAPERMAG3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(A, Seq)</th>\n",
       "      <th>duplicates</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>0.015332</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.028080</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.071227</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.081955</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.005289</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.843252</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>-2.800060</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.177738</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.035366</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.077586</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>0.046278</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.029622</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.055195</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <th>433832563084</th>\n",
       "      <td>-4.183243</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.311976</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.030268</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.069000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2366</th>\n",
       "      <th>433836363120</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.042469</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2368</th>\n",
       "      <th>433836362527</th>\n",
       "      <td>-0.000918</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.012953</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.260244</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.064378</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2369</th>\n",
       "      <th>433836363145</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.050331</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2370</th>\n",
       "      <th>433834437127</th>\n",
       "      <td>-0.002145</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.058400</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2371</th>\n",
       "      <th>433836363155</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.063354</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       LR_YAPERMAG3  R_YAPERMAG3  LR_J_1APERMAG3  \\\n",
       "(A, Seq) duplicates                                                \n",
       "2360     433834423123      0.015332          1.0        0.028080   \n",
       "2361     433834423565           NaN          NaN       -0.005289   \n",
       "2362     433836362467     -2.800060          1.0        0.177738   \n",
       "2363     433836362494      0.046278          1.0        0.029622   \n",
       "2365     433832563084     -4.183243          1.0        0.311976   \n",
       "2366     433836363120           NaN          NaN             NaN   \n",
       "2368     433836362527     -0.000918          1.0       -0.012953   \n",
       "2369     433836363145           NaN          NaN             NaN   \n",
       "2370     433834437127     -0.002145          1.0             NaN   \n",
       "2371     433836363155           NaN          NaN             NaN   \n",
       "\n",
       "                       R_J_1APERMAG3  LR_HAPERMAG3  R_HAPERMAG3  LR_KAPERMAG3  \\\n",
       "(A, Seq) duplicates                                                             \n",
       "2360     433834423123            1.0      0.071227          1.0      0.081955   \n",
       "2361     433834423565            1.0      0.843252          1.0           NaN   \n",
       "2362     433836362467            1.0      0.035366          1.0      0.077586   \n",
       "2363     433836362494            1.0      0.055195          1.0      0.110417   \n",
       "2365     433832563084            1.0      0.030268          1.0      0.069000   \n",
       "2366     433836363120            NaN           NaN          NaN      0.042469   \n",
       "2368     433836362527            1.0      0.260244          1.0      0.064378   \n",
       "2369     433836363145            NaN           NaN          NaN      0.050331   \n",
       "2370     433834437127            NaN           NaN          NaN      0.058400   \n",
       "2371     433836363155            NaN           NaN          NaN      0.063354   \n",
       "\n",
       "                       R_KAPERMAG3  \n",
       "(A, Seq) duplicates                 \n",
       "2360     433834423123          1.0  \n",
       "2361     433834423565          NaN  \n",
       "2362     433836362467          1.0  \n",
       "2363     433836362494          1.0  \n",
       "2365     433832563084          1.0  \n",
       "2366     433836363120          1.0  \n",
       "2368     433836362527          1.0  \n",
       "2369     433836363145          1.0  \n",
       "2370     433834437127          1.0  \n",
       "2371     433836363155          1.0  "
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mle_match_reliability = mle_match_final.filter(like='R_',axis=1)\n",
    "mle_match_reliability.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ObsID</th>\n",
       "      <th>RAdeg</th>\n",
       "      <th>DEdeg</th>\n",
       "      <th>e_Pos</th>\n",
       "      <th>DistNN</th>\n",
       "      <th>ExtFlag</th>\n",
       "      <th>InXMM</th>\n",
       "      <th>InChandra</th>\n",
       "      <th>FSoft</th>\n",
       "      <th>e_FSoft</th>\n",
       "      <th>...</th>\n",
       "      <th>rH</th>\n",
       "      <th>F250</th>\n",
       "      <th>e_F250</th>\n",
       "      <th>F350</th>\n",
       "      <th>e_F350</th>\n",
       "      <th>F500</th>\n",
       "      <th>e_F500</th>\n",
       "      <th>XMMAO10CP</th>\n",
       "      <th>ChCP</th>\n",
       "      <th>CPCoord</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Seq</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2359</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.097</td>\n",
       "      <td>0.166</td>\n",
       "      <td>4.7</td>\n",
       "      <td>515.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.61</td>\n",
       "      <td>0.52</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
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       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.353</td>\n",
       "      <td>3.5</td>\n",
       "      <td>171.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.68</td>\n",
       "      <td>0.38</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2361</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>5.8</td>\n",
       "      <td>291.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.02</td>\n",
       "      <td>0.50</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.142</td>\n",
       "      <td>-0.442</td>\n",
       "      <td>3.4</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.26</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.154</td>\n",
       "      <td>-0.448</td>\n",
       "      <td>2.1</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>7.25</td>\n",
       "      <td>0.63</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
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       "</table>\n",
       "<p>5 rows × 120 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM InChandra  \\\n",
       "Seq                                                                        \n",
       "2359  742830101.0  14.097  0.166    4.7   515.8      0.0    no        no   \n",
       "2360  742830101.0  14.115 -0.353    3.5   171.7      0.0    no        no   \n",
       "2361  742830101.0  14.115 -0.160    5.8   291.7      0.0    no        no   \n",
       "2362  742830101.0  14.142 -0.442    3.4    49.1      0.0    no        no   \n",
       "2363  742830101.0  14.154 -0.448    2.1    49.1      0.0    no        no   \n",
       "\n",
       "      FSoft  e_FSoft   ...     rH  F250  e_F250  F350  e_F350  F500  e_F500  \\\n",
       "Seq                    ...                                                    \n",
       "2359   1.61     0.52   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2360   1.68     0.38   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2361   2.02     0.50   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2362   0.95     0.26   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "2363   7.25     0.63   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "\n",
       "      XMMAO10CP  ChCP  CPCoord  \n",
       "Seq                             \n",
       "2359        NaN   NaN      0.0  \n",
       "2360        NaN   NaN      0.0  \n",
       "2361        NaN   NaN      0.0  \n",
       "2362        NaN   NaN      0.0  \n",
       "2363        NaN   NaN      0.0  \n",
       "\n",
       "[5 rows x 120 columns]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_lm.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# cat_lm.set_index('Seq', inplace=True)\n",
    "match_mle_a = df_lm.loc[mle_match_reliability.index.droplevel(1).values]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>SOURCEID</th>\n",
       "      <th>RA</th>\n",
       "      <th>DEC</th>\n",
       "      <th>SIGRA</th>\n",
       "      <th>SIGDEC</th>\n",
       "      <th>EPOCH</th>\n",
       "      <th>EBV</th>\n",
       "      <th>AY</th>\n",
       "      <th>AJ</th>\n",
       "      <th>AH</th>\n",
       "      <th>...</th>\n",
       "      <th>HAPERMAG3</th>\n",
       "      <th>HAPERMAG3ERR</th>\n",
       "      <th>KHALLMAG</th>\n",
       "      <th>KHALLMAGERR</th>\n",
       "      <th>KPETROMAG</th>\n",
       "      <th>KPETROMAGERR</th>\n",
       "      <th>KPSFMAG</th>\n",
       "      <th>KPSFMAGERR</th>\n",
       "      <th>KAPERMAG3</th>\n",
       "      <th>KAPERMAG3ERR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>433827929919</td>\n",
       "      <td>23.367877</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022051</td>\n",
       "      <td>0.026704</td>\n",
       "      <td>0.019603</td>\n",
       "      <td>0.012745</td>\n",
       "      <td>...</td>\n",
       "      <td>18.506187</td>\n",
       "      <td>0.151259</td>\n",
       "      <td>16.839336</td>\n",
       "      <td>0.166297</td>\n",
       "      <td>17.013243</td>\n",
       "      <td>0.244477</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.544065</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>433827929920</td>\n",
       "      <td>23.460531</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.023649</td>\n",
       "      <td>0.028639</td>\n",
       "      <td>0.021024</td>\n",
       "      <td>0.013669</td>\n",
       "      <td>...</td>\n",
       "      <td>16.893356</td>\n",
       "      <td>0.035704</td>\n",
       "      <td>16.618038</td>\n",
       "      <td>0.080816</td>\n",
       "      <td>16.661270</td>\n",
       "      <td>0.118318</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.565256</td>\n",
       "      <td>0.051986</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>433827929921</td>\n",
       "      <td>23.414002</td>\n",
       "      <td>0.687667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022683</td>\n",
       "      <td>0.027469</td>\n",
       "      <td>0.020165</td>\n",
       "      <td>0.013111</td>\n",
       "      <td>...</td>\n",
       "      <td>18.633087</td>\n",
       "      <td>0.170696</td>\n",
       "      <td>17.692490</td>\n",
       "      <td>0.398679</td>\n",
       "      <td>17.692490</td>\n",
       "      <td>0.398679</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.764069</td>\n",
       "      <td>0.152736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>433827929922</td>\n",
       "      <td>23.280570</td>\n",
       "      <td>0.687302</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.022506</td>\n",
       "      <td>0.027254</td>\n",
       "      <td>0.020007</td>\n",
       "      <td>0.013008</td>\n",
       "      <td>...</td>\n",
       "      <td>16.557207</td>\n",
       "      <td>0.026067</td>\n",
       "      <td>15.337543</td>\n",
       "      <td>0.038435</td>\n",
       "      <td>15.085359</td>\n",
       "      <td>0.060233</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.807901</td>\n",
       "      <td>0.025575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>433827929923</td>\n",
       "      <td>23.474184</td>\n",
       "      <td>0.687547</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005.902151</td>\n",
       "      <td>0.023927</td>\n",
       "      <td>0.028976</td>\n",
       "      <td>0.021271</td>\n",
       "      <td>0.013830</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 45 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       SOURCEID         RA       DEC  SIGRA  SIGDEC        EPOCH       EBV  \\\n",
       "0  433827929919  23.367877  0.687888    NaN     NaN  2005.902151  0.022051   \n",
       "1  433827929920  23.460531  0.688232    NaN     NaN  2005.902151  0.023649   \n",
       "2  433827929921  23.414002  0.687667    NaN     NaN  2005.902151  0.022683   \n",
       "3  433827929922  23.280570  0.687302    NaN     NaN  2005.902151  0.022506   \n",
       "4  433827929923  23.474184  0.687547    NaN     NaN  2005.902151  0.023927   \n",
       "\n",
       "         AY        AJ        AH      ...       HAPERMAG3  HAPERMAG3ERR  \\\n",
       "0  0.026704  0.019603  0.012745      ...       18.506187      0.151259   \n",
       "1  0.028639  0.021024  0.013669      ...       16.893356      0.035704   \n",
       "2  0.027469  0.020165  0.013111      ...       18.633087      0.170696   \n",
       "3  0.027254  0.020007  0.013008      ...       16.557207      0.026067   \n",
       "4  0.028976  0.021271  0.013830      ...             NaN           NaN   \n",
       "\n",
       "    KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  KPSFMAG  KPSFMAGERR  \\\n",
       "0  16.839336     0.166297  17.013243      0.244477      NaN         NaN   \n",
       "1  16.618038     0.080816  16.661270      0.118318      NaN         NaN   \n",
       "2  17.692490     0.398679  17.692490      0.398679      NaN         NaN   \n",
       "3  15.337543     0.038435  15.085359      0.060233      NaN         NaN   \n",
       "4        NaN          NaN        NaN           NaN      NaN         NaN   \n",
       "\n",
       "   KAPERMAG3  KAPERMAG3ERR  \n",
       "0  17.544065      0.124013  \n",
       "1  16.565256      0.051986  \n",
       "2  17.764069      0.152736  \n",
       "3  15.807901      0.025575  \n",
       "4        NaN           NaN  \n",
       "\n",
       "[5 rows x 45 columns]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_uk.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_uk.set_index('SOURCEID', inplace=True)\n",
    "match_mle_b = df_uk.loc[mle_match_reliability.index.droplevel(0).values]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "            ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM InChandra  \\\n",
       "Seq                                                                        \n",
       "2360  742830101.0  14.115 -0.353    3.5   171.7      0.0    no        no   \n",
       "2361  742830101.0  14.115 -0.160    5.8   291.7      0.0    no        no   \n",
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       "\n",
       "      FSoft  e_FSoft   ...     rH  F250  e_F250  F350  e_F350  F500  e_F500  \\\n",
       "Seq                    ...                                                    \n",
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       "2365   1.64     0.44   ...    NaN   NaN     NaN   NaN     NaN   NaN     NaN   \n",
       "\n",
       "      XMMAO10CP  ChCP  CPCoord  \n",
       "Seq                             \n",
       "2360        NaN   NaN      0.0  \n",
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       "\n",
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       "                     RA       DEC  SIGRA  SIGDEC        EPOCH       EBV  \\\n",
       "SOURCEID                                                                  \n",
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       "\n",
       "                    AY        AJ        AH        AK      ...       HAPERMAG3  \\\n",
       "SOURCEID                                                  ...                   \n",
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       "\n",
       "              HAPERMAG3ERR   KHALLMAG  KHALLMAGERR  KPETROMAG  KPETROMAGERR  \\\n",
       "SOURCEID                                                                      \n",
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     "execution_count": 91,
     "metadata": {},
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   "source": [
    "match_mle_b.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "final_mle_match = pandas.concat([ match_mle_a.reset_index(), match_mle_b.reset_index()], axis=1).set_index([ID_column_lm,ID_column_uk])"
   ]
  },
  {
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   "execution_count": 93,
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   "outputs": [
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
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       "      <th>2360</th>\n",
       "      <th>433834423123</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.353</td>\n",
       "      <td>3.5</td>\n",
       "      <td>171.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.68</td>\n",
       "      <td>0.38</td>\n",
       "      <td>...</td>\n",
       "      <td>16.420605</td>\n",
       "      <td>0.027337</td>\n",
       "      <td>15.266109</td>\n",
       "      <td>0.031406</td>\n",
       "      <td>15.165094</td>\n",
       "      <td>0.047093</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.644726</td>\n",
       "      <td>0.019929</td>\n",
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       "    <tr>\n",
       "      <th>2361</th>\n",
       "      <th>433834423565</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.115</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>5.8</td>\n",
       "      <td>291.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.02</td>\n",
       "      <td>0.50</td>\n",
       "      <td>...</td>\n",
       "      <td>18.644693</td>\n",
       "      <td>0.198955</td>\n",
       "      <td>17.770628</td>\n",
       "      <td>0.234180</td>\n",
       "      <td>17.763853</td>\n",
       "      <td>0.258605</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.884663</td>\n",
       "      <td>0.145093</td>\n",
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       "    <tr>\n",
       "      <th>2362</th>\n",
       "      <th>433836362467</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.142</td>\n",
       "      <td>-0.442</td>\n",
       "      <td>3.4</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.26</td>\n",
       "      <td>...</td>\n",
       "      <td>17.760912</td>\n",
       "      <td>0.083793</td>\n",
       "      <td>16.968500</td>\n",
       "      <td>0.112740</td>\n",
       "      <td>16.943735</td>\n",
       "      <td>0.177616</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.142780</td>\n",
       "      <td>0.078272</td>\n",
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       "    <tr>\n",
       "      <th>2363</th>\n",
       "      <th>433836362494</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.154</td>\n",
       "      <td>-0.448</td>\n",
       "      <td>2.1</td>\n",
       "      <td>49.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>7.25</td>\n",
       "      <td>0.63</td>\n",
       "      <td>...</td>\n",
       "      <td>17.173470</td>\n",
       "      <td>0.049189</td>\n",
       "      <td>16.122658</td>\n",
       "      <td>0.049313</td>\n",
       "      <td>15.984794</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.248377</td>\n",
       "      <td>0.034981</td>\n",
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       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <th>433832563084</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>14.162</td>\n",
       "      <td>0.038</td>\n",
       "      <td>4.0</td>\n",
       "      <td>224.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.64</td>\n",
       "      <td>0.44</td>\n",
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       "      <td>17.777243</td>\n",
       "      <td>0.096601</td>\n",
       "      <td>17.553614</td>\n",
       "      <td>0.169763</td>\n",
       "      <td>17.494886</td>\n",
       "      <td>0.185832</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.446341</td>\n",
       "      <td>0.103341</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 164 columns</p>\n",
       "</div>"
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      "text/plain": [
       "                         ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM  \\\n",
       "Seq  SOURCEID                                                                 \n",
       "2360 433834423123  742830101.0  14.115 -0.353    3.5   171.7      0.0    no   \n",
       "2361 433834423565  742830101.0  14.115 -0.160    5.8   291.7      0.0    no   \n",
       "2362 433836362467  742830101.0  14.142 -0.442    3.4    49.1      0.0    no   \n",
       "2363 433836362494  742830101.0  14.154 -0.448    2.1    49.1      0.0    no   \n",
       "2365 433832563084  742830101.0  14.162  0.038    4.0   224.1      0.0    no   \n",
       "\n",
       "                  InChandra  FSoft  e_FSoft      ...       HAPERMAG3  \\\n",
       "Seq  SOURCEID                                    ...                   \n",
       "2360 433834423123        no   1.68     0.38      ...       16.420605   \n",
       "2361 433834423565        no   2.02     0.50      ...       18.644693   \n",
       "2362 433836362467        no   0.95     0.26      ...       17.760912   \n",
       "2363 433836362494        no   7.25     0.63      ...       17.173470   \n",
       "2365 433832563084        no   1.64     0.44      ...       17.777243   \n",
       "\n",
       "                   HAPERMAG3ERR   KHALLMAG  KHALLMAGERR  KPETROMAG  \\\n",
       "Seq  SOURCEID                                                        \n",
       "2360 433834423123      0.027337  15.266109     0.031406  15.165094   \n",
       "2361 433834423565      0.198955  17.770628     0.234180  17.763853   \n",
       "2362 433836362467      0.083793  16.968500     0.112740  16.943735   \n",
       "2363 433836362494      0.049189  16.122658     0.049313  15.984794   \n",
       "2365 433832563084      0.096601  17.553614     0.169763  17.494886   \n",
       "\n",
       "                   KPETROMAGERR  KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \n",
       "Seq  SOURCEID                                                                  \n",
       "2360 433834423123      0.047093      NaN         NaN  15.644726      0.019929  \n",
       "2361 433834423565      0.258605      NaN         NaN  17.884663      0.145093  \n",
       "2362 433836362467      0.177616      NaN         NaN  17.142780      0.078272  \n",
       "2363 433836362494      0.066120      NaN         NaN  16.248377      0.034981  \n",
       "2365 433832563084      0.185832      NaN         NaN  17.446341      0.103341  \n",
       "\n",
       "[5 rows x 164 columns]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_mle_match.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
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       "      <td>12.797623</td>\n",
       "      <td>0.002469</td>\n",
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       "                         ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM  \\\n",
       "Seq  SOURCEID                                                                 \n",
       "5213 433832462768  747440101.0  27.994  0.063    3.3   138.7      0.0    no   \n",
       "5215 433836104605  747440101.0  28.000 -0.415    2.5   174.1      0.0    no   \n",
       "5217 433836104787  747440101.0  28.007 -0.463    3.5   141.3      0.0    no   \n",
       "5219 433834205134  747440101.0  28.024 -0.263    3.1   242.2      0.0    no   \n",
       "5220 433830737812  747440101.0  28.044  0.134    4.1   167.0      0.0    no   \n",
       "\n",
       "                  InChandra  FSoft  e_FSoft      ...       HAPERMAG3  \\\n",
       "Seq  SOURCEID                                    ...                   \n",
       "5213 433832462768        no   0.99     0.26      ...       17.786472   \n",
       "5215 433836104605        no   1.15     0.25      ...       13.036633   \n",
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       "5220 433830737812        no   0.79     0.22      ...       17.293871   \n",
       "\n",
       "                   HAPERMAG3ERR   KHALLMAG  KHALLMAGERR  KPETROMAG  \\\n",
       "Seq  SOURCEID                                                        \n",
       "5213 433832462768      0.099437  16.651016     0.118230  16.779015   \n",
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       "\n",
       "                   KPETROMAGERR  KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \n",
       "Seq  SOURCEID                                                                  \n",
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       "5215 433836104605      0.003539      NaN         NaN  12.797623      0.002469  \n",
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       "\n",
       "[5 rows x 164 columns]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "final_mle_match.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3054</th>\n",
       "      <th>433830832449</th>\n",
       "      <td>747390101.0</td>\n",
       "      <td>17.034</td>\n",
       "      <td>0.077</td>\n",
       "      <td>3.7</td>\n",
       "      <td>66.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.10</td>\n",
       "      <td>...</td>\n",
       "      <td>18.645838</td>\n",
       "      <td>0.203443</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3629</th>\n",
       "      <th>433828292717</th>\n",
       "      <td>747400101.0</td>\n",
       "      <td>19.402</td>\n",
       "      <td>0.562</td>\n",
       "      <td>2.3</td>\n",
       "      <td>86.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>3.07</td>\n",
       "      <td>0.44</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.317797</td>\n",
       "      <td>0.312936</td>\n",
       "      <td>18.156382</td>\n",
       "      <td>0.351777</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.165691</td>\n",
       "      <td>0.184878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2817</th>\n",
       "      <th>433832583778</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>15.938</td>\n",
       "      <td>-0.121</td>\n",
       "      <td>2.9</td>\n",
       "      <td>193.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.53</td>\n",
       "      <td>0.24</td>\n",
       "      <td>...</td>\n",
       "      <td>18.212225</td>\n",
       "      <td>0.149940</td>\n",
       "      <td>17.668640</td>\n",
       "      <td>0.176986</td>\n",
       "      <td>17.776709</td>\n",
       "      <td>0.286265</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.455675</td>\n",
       "      <td>0.101515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3574</th>\n",
       "      <th>433834318228</th>\n",
       "      <td>747400101.0</td>\n",
       "      <td>19.210</td>\n",
       "      <td>-0.307</td>\n",
       "      <td>1.7</td>\n",
       "      <td>76.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.28</td>\n",
       "      <td>0.22</td>\n",
       "      <td>...</td>\n",
       "      <td>17.596136</td>\n",
       "      <td>0.060489</td>\n",
       "      <td>16.403347</td>\n",
       "      <td>0.086130</td>\n",
       "      <td>16.509922</td>\n",
       "      <td>0.160516</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.863695</td>\n",
       "      <td>0.051403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2635</th>\n",
       "      <th>433830901006</th>\n",
       "      <td>742830101.0</td>\n",
       "      <td>15.247</td>\n",
       "      <td>0.205</td>\n",
       "      <td>2.1</td>\n",
       "      <td>214.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>1.72</td>\n",
       "      <td>0.19</td>\n",
       "      <td>...</td>\n",
       "      <td>17.111403</td>\n",
       "      <td>0.049267</td>\n",
       "      <td>16.229816</td>\n",
       "      <td>0.059616</td>\n",
       "      <td>16.244713</td>\n",
       "      <td>0.088863</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.150557</td>\n",
       "      <td>0.033153</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 164 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                         ObsID   RAdeg  DEdeg  e_Pos  DistNN  ExtFlag InXMM  \\\n",
       "Seq  SOURCEID                                                                 \n",
       "3054 433830832449  747390101.0  17.034  0.077    3.7    66.1      0.0    no   \n",
       "3629 433828292717  747400101.0  19.402  0.562    2.3    86.3      0.0    no   \n",
       "2817 433832583778  742830101.0  15.938 -0.121    2.9   193.3      0.0    no   \n",
       "3574 433834318228  747400101.0  19.210 -0.307    1.7    76.1      0.0    no   \n",
       "2635 433830901006  742830101.0  15.247  0.205    2.1   214.9      0.0    no   \n",
       "\n",
       "                  InChandra  FSoft  e_FSoft      ...       HAPERMAG3  \\\n",
       "Seq  SOURCEID                                    ...                   \n",
       "3054 433830832449        no   0.38     0.10      ...       18.645838   \n",
       "3629 433828292717        no   3.07     0.44      ...             NaN   \n",
       "2817 433832583778        no   1.53     0.24      ...       18.212225   \n",
       "3574 433834318228        no   2.28     0.22      ...       17.596136   \n",
       "2635 433830901006        no   1.72     0.19      ...       17.111403   \n",
       "\n",
       "                   HAPERMAG3ERR   KHALLMAG  KHALLMAGERR  KPETROMAG  \\\n",
       "Seq  SOURCEID                                                        \n",
       "3054 433830832449      0.203443        NaN          NaN        NaN   \n",
       "3629 433828292717           NaN  18.317797     0.312936  18.156382   \n",
       "2817 433832583778      0.149940  17.668640     0.176986  17.776709   \n",
       "3574 433834318228      0.060489  16.403347     0.086130  16.509922   \n",
       "2635 433830901006      0.049267  16.229816     0.059616  16.244713   \n",
       "\n",
       "                   KPETROMAGERR  KPSFMAG  KPSFMAGERR  KAPERMAG3  KAPERMAG3ERR  \n",
       "Seq  SOURCEID                                                                  \n",
       "3054 433830832449           NaN      NaN         NaN        NaN           NaN  \n",
       "3629 433828292717      0.351777      NaN         NaN  18.165691      0.184878  \n",
       "2817 433832583778      0.286265      NaN         NaN  17.455675      0.101515  \n",
       "3574 433834318228      0.160516      NaN         NaN  16.863695      0.051403  \n",
       "2635 433830901006      0.088863      NaN         NaN  16.150557      0.033153  \n",
       "\n",
       "[5 rows x 164 columns]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_mle_match.sample(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "               ObsID        RAdeg        DEdeg        e_Pos       DistNN  \\\n",
      "count   1.492000e+03  1492.000000  1492.000000  1492.000000  1492.000000   \n",
      "unique           NaN          NaN          NaN          NaN          NaN   \n",
      "top              NaN          NaN          NaN          NaN          NaN   \n",
      "freq             NaN          NaN          NaN          NaN          NaN   \n",
      "mean    7.465153e+08    20.871196    -0.035375     2.842091   127.074665   \n",
      "std     1.822402e+06     4.348811     0.287653     0.906100    79.624401   \n",
      "min     7.428301e+08    14.115000    -0.617000     0.400000    16.400000   \n",
      "25%     7.473901e+08    17.036250    -0.282250     2.300000    72.700000   \n",
      "50%     7.474001e+08    19.875000    -0.027500     2.800000   112.600000   \n",
      "75%     7.474301e+08    25.142750     0.189000     3.400000   162.875000   \n",
      "max     7.474401e+08    28.044000     0.604000     7.300000   765.400000   \n",
      "\n",
      "            ExtFlag InXMM InChandra        FSoft      e_FSoft      ...       \\\n",
      "count   1492.000000  1492      1492  1492.000000  1492.000000      ...        \n",
      "unique          NaN     6        24          NaN          NaN      ...        \n",
      "top             NaN    no        no          NaN          NaN      ...        \n",
      "freq            NaN  1487      1469          NaN          NaN      ...        \n",
      "mean       0.017426   NaN       NaN     2.013003     0.264102      ...        \n",
      "std        0.233865   NaN       NaN     3.653750     0.272522      ...        \n",
      "min        0.000000   NaN       NaN     0.000000     0.000000      ...        \n",
      "25%        0.000000   NaN       NaN     0.620000     0.140000      ...        \n",
      "50%        0.000000   NaN       NaN     1.050000     0.200000      ...        \n",
      "75%        0.000000   NaN       NaN     1.900000     0.300000      ...        \n",
      "max        6.000000   NaN       NaN    46.740000     4.560000      ...        \n",
      "\n",
      "          HAPERMAG3  HAPERMAG3ERR     KHALLMAG  KHALLMAGERR    KPETROMAG  \\\n",
      "count   1133.000000   1133.000000  1300.000000  1300.000000  1300.000000   \n",
      "unique          NaN           NaN          NaN          NaN          NaN   \n",
      "top             NaN           NaN          NaN          NaN          NaN   \n",
      "freq            NaN           NaN          NaN          NaN          NaN   \n",
      "mean      17.174982      0.098265    16.484390     0.192466    16.457329   \n",
      "std        1.894588      0.067923     1.899052     0.304378     1.914559   \n",
      "min       10.107296      0.000458     8.269741     0.000260     8.473408   \n",
      "25%       16.898626      0.040606    16.070085     0.064300    15.947272   \n",
      "50%       17.814739      0.093174    17.024106     0.155186    16.995995   \n",
      "75%       18.357952      0.150079    17.631047     0.254555    17.645322   \n",
      "max       19.299809      0.346629    21.520224     9.074115    21.520224   \n",
      "\n",
      "        KPETROMAGERR  KPSFMAG  KPSFMAGERR    KAPERMAG3  KAPERMAG3ERR  \n",
      "count    1300.000000      0.0         0.0  1301.000000   1301.000000  \n",
      "unique           NaN      NaN         NaN          NaN           NaN  \n",
      "top              NaN      NaN         NaN          NaN           NaN  \n",
      "freq             NaN      NaN         NaN          NaN           NaN  \n",
      "mean        0.225341      NaN         NaN    16.648907      0.095469  \n",
      "std         0.310005      NaN         NaN     1.754564      0.067781  \n",
      "min         0.000292      NaN         NaN     9.577841      0.000502  \n",
      "25%         0.092062      NaN         NaN    16.328405      0.039451  \n",
      "50%         0.194100      NaN         NaN    17.183228      0.086354  \n",
      "75%         0.292292      NaN         NaN    17.713430      0.143673  \n",
      "max         9.074115      NaN         NaN    18.688906      0.324966  \n",
      "\n",
      "[11 rows x 164 columns]\n",
      "\n",
      "Total number of rows: 1492 (1.5e+03)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "ObsID                0\n",
      "RAdeg                0\n",
      "DEdeg                0\n",
      "e_Pos                0\n",
      "DistNN               0\n",
      "ExtFlag              0\n",
      "InXMM                0\n",
      "InChandra            0\n",
      "FSoft                0\n",
      "e_FSoft              0\n",
      "CtSoft               0\n",
      "SoftDetml            0\n",
      "FHard                0\n",
      "e_FHard              0\n",
      "CtHard               0\n",
      "HardDetml            0\n",
      "FFull                0\n",
      "e_FFull              0\n",
      "CtFull               0\n",
      "FullDetml            0\n",
      "logLSoft             0\n",
      "logLHard             0\n",
      "logLFull             0\n",
      "RejS                 0\n",
      "SDSS               144\n",
      "RASdeg              79\n",
      "DESdeg              79\n",
      "RelS                82\n",
      "rS                  79\n",
      "CoaddS               0\n",
      "                  ... \n",
      "YPETROMAG          255\n",
      "YPETROMAGERR       255\n",
      "YPSFMAG           1492\n",
      "YPSFMAGERR        1492\n",
      "YAPERMAG3          253\n",
      "YAPERMAG3ERR       253\n",
      "J_1HALLMAG         420\n",
      "J_1HALLMAGERR      420\n",
      "J_1PETROMAG        420\n",
      "J_1PETROMAGERR     420\n",
      "J_1PSFMAG         1492\n",
      "J_1PSFMAGERR      1492\n",
      "J_1APERMAG3        420\n",
      "J_1APERMAG3ERR     420\n",
      "HHALLMAG           360\n",
      "HHALLMAGERR        360\n",
      "HPETROMAG          359\n",
      "HPETROMAGERR       359\n",
      "HPSFMAG           1492\n",
      "HPSFMAGERR        1492\n",
      "HAPERMAG3          359\n",
      "HAPERMAG3ERR       359\n",
      "KHALLMAG           192\n",
      "KHALLMAGERR        192\n",
      "KPETROMAG          192\n",
      "KPETROMAGERR       192\n",
      "KPSFMAG           1492\n",
      "KPSFMAGERR        1492\n",
      "KAPERMAG3          191\n",
      "KAPERMAG3ERR       191\n",
      "Length: 164, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "final_mle_match.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    1492.000000\n",
      "mean       -0.000087\n",
      "std         0.000646\n",
      "min        -0.001874\n",
      "25%        -0.000508\n",
      "50%        -0.000090\n",
      "75%         0.000295\n",
      "max         0.001933\n",
      "dtype: float64\n",
      "\n",
      "Total number of rows: 1492 (1.5e+03)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "0 (0.000%)\n"
     ]
    }
   ],
   "source": [
    "RA_diff = final_mle_match['RAdeg'] - final_mle_match['RA']\n",
    "RA_diff.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    1492.000000\n",
      "mean       -0.000126\n",
      "std         0.000637\n",
      "min        -0.001886\n",
      "25%        -0.000537\n",
      "50%        -0.000134\n",
      "75%         0.000265\n",
      "max         0.001909\n",
      "dtype: float64\n",
      "\n",
      "Total number of rows: 1492 (1.5e+03)\n",
      "\n",
      "-> Has Nil? (How many?)\n",
      "0 (0.000%)\n"
     ]
    }
   ],
   "source": [
    "DEC_diff = final_mle_match['DEdeg'] - final_mle_match['DEC']\n",
    "DEC_diff.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "final_mle_match.to_csv('lamassa_ukidss_MatchMLE.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot samples\n",
    "\n",
    "## ancillary *vs* background\n",
    "\n",
    "Trying to find the difference between them..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_ = plot_distros('KAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_ = plot_distros('J_1APERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_ = plot_distros('YAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_ = plot_distros('HAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from booq.plot import PlotHisto\n",
    "p = PlotHisto()\n",
    "# for col in ['YAPERMAG3','J_1APERMAG3','HAPERMAG3','KAPERMAG3']:\n",
    "#     ds_label = p.add_dataset(cat_uk_sample,label=col,x=col)\n",
    "#     p.plot(ds_label)\n",
    "col = 'KAPERMAG3'\n",
    "dsl = p.add_dataset(background_sample_magnitudes, label='background',x=col)\n",
    "p.plot(dsl)\n",
    "dsl = p.add_dataset(ancillary_sample_magnitudes, label='ancillary', x=col)\n",
    "p.plot(dsl)\n",
    "p.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_colors(col1,col2,col3):\n",
    "    from booq import plot\n",
    "    p = plot.PlotScatter()\n",
    "\n",
    "    bkg_12 = background_sample_magnitudes[col1] - background_sample_magnitudes[col2]\n",
    "    bkg_23 = background_sample_magnitudes[col2] - background_sample_magnitudes[col3]\n",
    "\n",
    "    anc_12 = ancillary_sample_magnitudes[col1] - ancillary_sample_magnitudes[col2]\n",
    "    anc_23 = ancillary_sample_magnitudes[col2] - ancillary_sample_magnitudes[col3]\n",
    "\n",
    "\n",
    "    db = {12:bkg_12.values, 23:bkg_23.values}\n",
    "    dsl = p.add_dataset(db, label='bkg', x=12, y=23)\n",
    "    p.plot(dsl)\n",
    "\n",
    "    da = {12:anc_12.values, 23:anc_23.values}\n",
    "    dsl = p.add_dataset(da, label='anc', x=12, y=23)\n",
    "    p.plot(dsl)\n",
    "\n",
    "    p.show()\n",
    "    \n",
    "plot_colors('YAPERMAG3','J_1APERMAG3','HAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot_colors('J_1APERMAG3','HAPERMAG3','KAPERMAG3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_grid_scatter(cols):\n",
    "    dfb = background_sample_magnitudes[cols]\n",
    "    dfb['sample'] = 'background'\n",
    "\n",
    "    dfa = ancillary_sample_magnitudes[cols]\n",
    "    dfa['sample'] = 'ancillary'\n",
    "\n",
    "    df = dfb.append(dfa)\n",
    "\n",
    "    import matplotlib.pyplot as plt\n",
    "    import seaborn as sns\n",
    "    sns.set()\n",
    "    g = sns.PairGrid(df, hue=\"sample\")\n",
    "#     try:\n",
    "    gg = g.map_diag(sns.kdeplot)\n",
    "    gg = gg.map_offdiag(plt.scatter)\n",
    "#     except:\n",
    "#         gg = g.map(plt.scatter)\n",
    "    g = gg.add_legend()\n",
    "\n",
    "plot_grid_scatter(['YAPERMAG3','J_1APERMAG3','HAPERMAG3','KAPERMAG3'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ancillary_sample_magnitudes.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cols = ['YHALLMAG','YPETROMAG','YAPERMAG3']\n",
    "plot_grid_scatter(cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "cols = ['J_1HALLMAG','J_1PETROMAG','J_1APERMAG3']\n",
    "plot_grid_scatter(cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cols = ['HHALLMAG','HPETROMAG','HAPERMAG3']\n",
    "plot_grid_scatter(cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "cols = ['KHALLMAG','KPETROMAG','KAPERMAG3']\n",
    "plot_grid_scatter(cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bkg_ratio_PetroHall_K = background_sample_magnitudes['KPETROMAG']/background_sample_magnitudes['KHALLMAG']\n",
    "anc_ratio_PetroHall_K = ancillary_sample_magnitudes['KPETROMAG']/ancillary_sample_magnitudes['KHALLMAG']\n",
    "d = {'bkg':bkg_ratio_PetroHall_K, 'anc':anc_ratio_PetroHall_K}\n",
    "\n",
    "from booq.plot import PlotHisto\n",
    "p = PlotHisto()\n",
    "dsl = p.add_dataset(d, label='background',x='bkg')\n",
    "p.plot(dsl)\n",
    "dsl = p.add_dataset(d, label='ancillary', x='anc')\n",
    "p.plot(dsl)\n",
    "p.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cdf(vec,bins):\n",
    "    import numpy as np\n",
    "    h,b = np.histogram(vec,bins=bins)\n",
    "    cdf = np.cumsum(h)\n",
    "    cdf = cdf/cdf.sum()\n",
    "    return cdf,h\n",
    "def ks_test(vec1,vec2):\n",
    "    import numpy as np\n",
    "    vmin = min(vec1.min(),vec2.min())\n",
    "    vmax = max(vec1.max(),vec2.max())\n",
    "    bins = np.linspace(vmin,vmax,50)\n",
    "    cdf1,h1 = cdf(vec1,bins)\n",
    "    cdf2,h2 = cdf(vec2,bins)\n",
    "    assert len(cdf1)==len(cdf2)\n",
    "    dist = 0\n",
    "    dist_i = None\n",
    "    for i in range(len(cdf1)):\n",
    "        diff = abs(cdf1[i]-cdf2[i])\n",
    "        if diff > dist:\n",
    "            dist = diff\n",
    "            dist_i = i\n",
    "    i = dist_i\n",
    "    \n",
    "    from matplotlib import pyplot as plt\n",
    "    fig,ax = plt.subplots()\n",
    "    x = bins[:-1] + np.diff(bins)/2\n",
    "    ax.plot(x,cdf1,'b-')\n",
    "    ax.plot(x,cdf2,'r-')\n",
    "    test_x = [x[i],x[i]]\n",
    "    _my = min(cdf1[i],cdf2[i])\n",
    "    test_y = [_my, (dist+_my)]\n",
    "    ax.plot(test_x,test_y,'g-')\n",
    "    return dist,h1.sum(),h2.sum()\n",
    "\n",
    "df = DataFrame(d)\n",
    "vec1 = df['bkg'].dropna()\n",
    "vec2 = df['anc'].dropna()\n",
    "ks_dist,n1,n2 = ks_test(vec1,vec2)\n",
    "print('KS distance: {}'.format(ks_dist))\n",
    "print('Number of points, vec1: {}'.format(n1))\n",
    "print('Number of points, vec2: {}'.format(n2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = DataFrame(d)\n",
    "vec1 = df['bkg'].dropna()\n",
    "vec2 = df['anc'].dropna()\n",
    "ks_dist,n1,n2 = ks_test(vec1,vec2)\n",
    "print('KS distance: {}'.format(ks_dist))\n",
    "print('Number of points, vec1: {}'.format(n1))\n",
    "print('Number of points, vec2: {}'.format(n2))"
   ]
  }
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