Early Prototype SSO detections.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding solar system object (SSO) metric capabilities to [MAF](https://confluence.lsstcorp.org/display/SIM/MAF+documentation) moves far enough beyond the current concepts of slicers + metrics in MAF that it seems worthwhile to prototype the functionality required, test the best approaches, and then see how we should map this back into classes for MAF. \n",
    "\n",
    "The general concept in MAF (for stationary objects) is: \n",
    "* read the pointing history from the opsim sqlite database\n",
    "* determine how to subdivide the pointing history appropriately for a desired metric measurement + use the appropriate `slicer` to do so\n",
    "* iterate over the `slicer` and apply a `metric` (python class which makes a measurement on a given data slice) at each slice|\n",
    "* consolidate the metric results at each slicepoint, as appropriate given the slicer (i.e. make a skymap, etc.)\n",
    "\n",
    "For moving objects, we have additional steps and instead of the metric being applied per \"subdivision of the pointing history\" (per RA/Dec pointing, for example), we probably want to think of the metric being applied \"per SSO\". \n",
    "So the steps could be:\n",
    "* read the orbital parameters and Hmag for each SSO\n",
    "* read the pointing history from the opsim sqlite database\n",
    "* determine when each individual object would be detected and what its magnitude would be in each detection (potentially, only record observations where the detection is > 5sigma??)\n",
    "* apply metric based on observations\n",
    "*  .. additional wrinkles: because this is slow (per object), we are also interested in (a) saving the pointing history for all objects, potentially also saving steps needed to create this pointing history for different opsim runs, and (b) allowing each object to be cloned to a variety of different H mags (equivalent to cloning over the size distribution, so that each single orbital parameter set represents a range of different objects). \n",
    "\n",
    "The 'generation of observations' steps here are joined in a single python class, 'moObs'. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from itertools import repeat\n",
    "from scipy import interpolate\n",
    "\n",
    "import pandas as pd\n",
    "import pyoorb as oo\n",
    "\n",
    "import lsst.sims.photUtils.Bandpass as Bandpass\n",
    "import lsst.sims.photUtils.Sed as Sed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the pointing history information from the opsim sqlite output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from lsst.sims.maf.db import OpsimDatabase\n",
    "from lsst.sims.utils import haversine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dbAddress = 'enigma_1189_sqlite.db'\n",
    "ops = OpsimDatabase(dbAddress)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('obsHistID', 'expMJD', 'night', 'fieldRA', 'fieldDec', 'rotSkyPos', 'filter', 'finSeeing', 'fiveSigmaDepth', 'visitExpTime')\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lynnej/anaconda/lib/python2.7/site-packages/sqlalchemy/sql/elements.py:3758: SAWarning: Textual SQL expression '' should be explicitly declared as text('') (this warning may be suppressed after 10 occurrences)\n",
      "  {\"expr\": util.ellipses_string(element)})\n"
     ]
    }
   ],
   "source": [
    "dbcols = ['expMJD', 'night', 'fieldRA', 'fieldDec', 'rotSkyPos', 'filter', \n",
    "          'finSeeing', 'fiveSigmaDepth', 'visitExpTime']\n",
    "simdata = ops.fetchMetricData(dbcols, sqlconstraint='')\n",
    "print simdata.dtype.names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "Read the moving object orbital information. Since the data from different moving object orbit files can have different keywords for the same values, or even need converting from Keplerian to Cometary orbits, we'll do some additional gymnastics to 'regularize' the output orbit array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def _updateColMap(colMap, outCol, alternativeNames, ssoCols):\n",
    "    for a in alternativeNames:\n",
    "        if a in ssoCols:\n",
    "            colMap[outCol] = a\n",
    "    return colMap\n",
    "\n",
    "def readOrbits(orbitfile='pha20141031.des'):\n",
    "    \"\"\"\n",
    "    Read the orbits from file 'orbitfile', returning a numpy structured array with the columns:\n",
    "    'objID q e inc node argPeri tPeri epoch H g a meanAnom'\n",
    "    \"\"\"\n",
    "    orbits = pd.read_table(orbitfile, sep='\\s*', engine='python')\n",
    "    # Normalize the column names, as different inputs tend to have some commonly-different names. \n",
    "    ssoCols = orbits.columns.values.tolist()\n",
    "    nSso = len(orbits)\n",
    "    outCols = ['objId', 'q', 'e', 'inc', 'node', 'argPeri', 'tPeri', 'epoch', 'H', 'g', 'a', 'meanAnom']\n",
    "    # Create mapping between column names read from disk and desired column names.\n",
    "    colMap = {}\n",
    "    for o in outCols:\n",
    "        if o in ssoCols:\n",
    "            colMap[o] = o\n",
    "        else:\n",
    "            # Try to find corresponding value\n",
    "            if o == 'objId':\n",
    "                alternatives = ['!!ObjID','objid', '!!OID']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'inc':\n",
    "                alternatives = ['i']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'node':\n",
    "                alternatives = ['BigOmega', 'Omega/node', 'Omega']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'argPeri':\n",
    "                alternatives = ['argperi', 'omega/argperi']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'tPeri':\n",
    "                alternatives = ['t_p', 'timeperi']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'epoch':\n",
    "                alternatives = ['t_0']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'H':\n",
    "                alternatives = ['magH', 'magHv', 'Hv']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'g':\n",
    "                alternatives = ['phaseV', 'phase', 'gV']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'a':\n",
    "                alternatives = ['semimajor']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "            elif o == 'meanAnom':\n",
    "                alternative = ['meanAnomaly', 'meananomaly', 'M']\n",
    "                colMap = _updateColMap(colMap, o, alternatives, ssoCols)\n",
    "                \n",
    "    # Add the columns we can generate. \n",
    "    if 'objId' not in colMap:\n",
    "        orbids = np.arange(0, nSso, 1)\n",
    "    else:\n",
    "        orbids = orbits[colMap['objId']]\n",
    "    if 'H' not in colMap:\n",
    "        Hval = np.zeros(nSso) + 20.0\n",
    "    else:\n",
    "        Hval = orbits[colMap['H']]\n",
    "    if 'g' not in colMap:\n",
    "        gval = np.zeros(nSso) + 0.15\n",
    "    else:\n",
    "        gval = orbits[colMap['g']]\n",
    "    \n",
    "    # And some columns that can be converted from different orbit types.\n",
    "    if 'a' not in colMap:\n",
    "        aval = orbits[colMap['q']] / (1 + orbits[colMap['e']])\n",
    "    else:\n",
    "        aval = orbits[colMap['a']]\n",
    "    period = np.sqrt(aval**3)\n",
    "    if 'meanAnom' not in colMap:\n",
    "        meanAnomval = 360.0*(orbits[colMap['epoch']] - orbits[colMap['tPeri']]) / (period*365.25)\n",
    "    else:\n",
    "        meanAnomval = orbits[colMap['meanAnom']]\n",
    "    if 'q' not in colMap:\n",
    "        qval = orbits[colMap['a']] * (1 - orbits[colMap['e']])\n",
    "    else:\n",
    "        qval = orbits[colMap['q']]\n",
    "    if 'tPeri' not in colMap:\n",
    "        tPerival = orbits[colMap['epoch']] - (orbits[colMap['meanAnom']]/360.0) * (period*365.25)\n",
    "    else:\n",
    "        tPerival = orbits[colMap['tPeri']]\n",
    "        \n",
    "    # Put it all together and turn it into a numpy array. \n",
    "    orbits = np.rec.fromarrays([orbids, qval, orbits[colMap['e']], orbits[colMap['inc']],\n",
    "                                 orbits[colMap['node']], orbits[colMap['argPeri']], tPerival,\n",
    "                                 orbits[colMap['epoch']], Hval, gval, aval, meanAnomval], \n",
    "                                names = outCols)\n",
    "    return orbits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "orbitfile = 'pha20141031.des'\n",
    "orbits = readOrbits(orbitfile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('objId', 'q', 'e', 'inc', 'node', 'argPeri', 'tPeri', 'epoch', 'H', 'g', 'a', 'meanAnom')\n",
      "1510 (0, 0.1865233429220149, 0.82696095, 22.827817, 88.02446399999998, 31.358208, 49090.767295844285, 49353.16, 20.0, 0.15, 0.1020948712242672, 7927.89962516944)\n"
     ]
    }
   ],
   "source": [
    "print orbits.dtype.names\n",
    "print len(orbits), orbits[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have some options to test. It's too expensive to calculate ephemerides for every object at the time of every opsim pointing, so we want to calculate positions on a coarse grid of times - let's start with calculating the positions every 2 hours for PHAs.  There are a few options for doing this: \n",
    "* (1) We could calculate the rough positions using [OpenOrb](https://code.google.com/p/oorb/wiki/OpenOrb) directly at the command line, for the full ten years. This is is efficient because it calculates the positions for all objects at once, meaning we only have to calculate things like the positions of the planets and Earth once for each time. A test on my laptop created a 10 year 2-hr grid of ephemerides in about 2 hours, producing a 42GB output file. The problems here are that you have to keep a fairly large output file (not something you'd like to read into memory as-is) and that the contents of the file are not in the order that we'd like (ordered by time, then object). I'll come back to this if the approaches below don't work out.\n",
    "* (2) We could calculate the rough positions using the python bindings to OpenOrb, for each object over the full ten years, then calculate the actual observations matching opsim pointings, then write to disk. This is less efficient because the calculation of the Earth and planets' positions are repeated, but will be tested below. \n",
    "* (3) We could calculate the rough positions using the python bindings to OpenOrb, but do it for all objects at once .. since the full results won't fit in memory, we could do it month-by-month (or some other time step). This is efficient only if we can also propagate and save the orbits at each interval; otherwise we have to re-propagate the orbits over the gap between their epoch and the start of observations every time. I'm not entirely sure the propagation routines have working python bindings, but will test below. This is a nice approach, although it doesn't quite fit into the \"per object\" concept as cleanly. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing ephemeris generation, along the style of option (2) above. <br>\n",
    "\n",
    ">Try generating SPK files with SPICE (http://naif.jpl.nasa.gov/naif/toolkit_C_MacIntel_OSX_AppleC_64bit.html).. basically just generating interpolation with chebychev instead of polynomial! But SPICE does automatic generation of what size window/how many coefficient. \n",
    "\n",
    "... and also, see how big a gap in the coarse grid I can get (1 day?)\n",
    "\n",
    "Because pyoorb is a python interface to a Fortran program (OpenOrb), written very simply with f2py, we have to do some awkwardness with array-rearranging."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def setTimes(timestep=1., nyears=1., timestart=49353.):\n",
    "    # Extend times beyond first/last observation, so that interpolation doesn't fail\n",
    "    timestart = timestart - timestep\n",
    "    timeend = timestart + 365 * nyears + timestep \n",
    "    times = np.arange(timestart, timeend + timestep/2.0, timestep)\n",
    "    # For pyoorb, we need to tag times with timescales;\n",
    "    # 1= MJD_UTC, 2=UT1, 3=TT, 4=TAI\n",
    "    ephTimes = np.array(zip(times, repeat(4, len(times))), dtype='double', order='F')\n",
    "    return ephTimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nyears = 10\n",
    "ephTimes = setTimes(timestep=2./24., nyears=nyears)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up pyoorb (reads in JPL ephemerides for major planets, etc.). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oo.pyoorb.oorb_init(ephemeris_fname=\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python oorb element format: \n",
    "        # Translate orbital elements into array that pyoorb will like.\n",
    "        # PyOrb wants ::\n",
    "        # 0: orbitId  (cannot be a string)\n",
    "        # 1 - 6: orbital elements, using radians for angles\n",
    "        # 7: element type code, where 2 = cometary - means timescale is TT, too\n",
    "        # 8: epoch\n",
    "        # 9: timescale for the epoch; 1= MJD_UTC, 2=UT1, 3=TT, 4=TAI\n",
    "        # 10: magHv\n",
    "        # 11: G\n",
    "so we have to do a little translating from the orbits DataFrame to the elements we want in this array. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def packOorbElem(sso):\n",
    "    \"\"\"\n",
    "    Convert numpy structured array of orbital elements into the array OpenOrb needs as input.\n",
    "    'sso' can be the orbital elements of a single object or of multiple objects.\n",
    "    To normalize the column names to those expected here, read in data using 'readOrbits'.\n",
    "    \"\"\"\n",
    "    if len(sso.shape) == 0:\n",
    "        # Passed a single SSO\n",
    "        nSso = 0\n",
    "        sso0 = sso\n",
    "        elem_type = 2\n",
    "        epoch_type = 3\n",
    "    else:\n",
    "        nSso = len(sso)\n",
    "        sso0 = sso[0]        \n",
    "        elem_type = np.zeros(nSso) + 2\n",
    "        epoch_type = np.zeros(nSso) + 3\n",
    "    # Check on orbit id type - pyoorb needs numbers not strings.\n",
    "    if (isinstance(sso0['objId'], float) or isinstance(sso0['objId'], int)):\n",
    "        orbids = sso['objId']\n",
    "    else:\n",
    "        if nSso == 0:\n",
    "            orbids = 0\n",
    "        else:\n",
    "            orbids = np.arange(0, nSso, 1)\n",
    "    # Convert to format for pyoorb, INCLUDING converting inclination, node, argperi to RADIANS\n",
    "    oorbArray = np.column_stack((orbids, sso['q'], sso['e'], np.radians(sso['inc']),\n",
    "                                 np.radians(sso['node']), np.radians(sso['argPeri']),\n",
    "                                 sso['tPeri'], elem_type, sso['epoch'], epoch_type, \n",
    "                                 sso['H'], sso['g']))                                            \n",
    "    return oorbArray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10  (years of ephemerides)\n",
      "(0, 0.1865233429220149, 0.82696095, 22.827817, 88.02446399999998, 31.358208, 49090.767295844285, 49353.16, 20.0, 0.15, 0.1020948712242672, 7927.89962516944)\n",
      "10  (years of ephemerides)\n",
      "(0, 0.1865233429220149, 0.82696095, 22.827817, 88.02446399999998, 31.358208, 49090.767295844285, 49353.16, 20.0, 0.15, 0.1020948712242672, 7927.89962516944)\n",
      "10  (years of ephemerides)\n",
      "(0, 0.1865233429220149, 0.82696095, 22.827817, 88.02446399999998, 31.358208, 49090.767295844285, 49353.16, 20.0, 0.15, 0.1020948712242672, 7927.89962516944)\n",
      "10  (years of ephemerides)\n",
      "(0, 0.1865233429220149, 0.82696095, 22.827817, 88.02446399999998, 31.358208, 49090.767295844285, 49353.16, 20.0, 0.15, 0.1020948712242672, 7927.89962516944)\n",
      "1 loops, best of 3: 8.04 s per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "print nyears, ' (years of ephemerides)'\n",
    "for sso in orbits[0:1]:\n",
    "    print sso\n",
    "    oorbelems = packOorbElem(sso)\n",
    "    oorbephs, err = oo.pyoorb.oorb_ephemeris(in_orbits = oorbelems, in_obscode=807, in_date_ephems=ephTimes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Just about 8 seconds per object to calculate the coarse grid over 10 years (for 2 hour timesteps). 1 second for 1 day timesteps. For many simulations, I think we'd have on the order of 1000-2000 objects = 2.5 - 5 hours for this step, done like this.  I tested ephemeris generation separately of the numpy-array-reordering and the time was very similar, so most of the time is indeed going into pyoorb."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And also, more awkwardness with the ephems and elems arrays:\n",
    "\n",
    "Python oorb ephem array format:\n",
    "    #   [objid][time][ephemeris information @ that time]\n",
    "    # 0 = distance (geocentric distance)\n",
    "    # 1 = ra (deg)\n",
    "    # 2 = dec (deg)\n",
    "    # 3 = mag\n",
    "    # 4 = ephem mjd\n",
    "    # 5 = ephem mjd timescale\n",
    "    # 6 = dra/dt (deg/day) sky motion\n",
    "    # 7 = ddec/dt (deg/day) sky motion\n",
    "    # 8 = phase angle (deg)\n",
    "    # 9 = solar elongation angle (deg)\n",
    "So usually we want to swap the axes at least, so that instead of all the ephemeris information @ a particular time being the accessible bit of information, we have all the RA values over time for a single object ('byObject') Alternatively, we may want all the RA values for all objects at one time. This is also an option, by setting 'byObject' to False."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def unpackEphs(oorbephems, byObject=True):\n",
    "    \"\"\"\n",
    "    Given oorb ephemeris array (shape = object / times / eph@time),\n",
    "    Return an array aranged with \n",
    "     columns = ['delta', 'ra', 'dec', 'mag', 'time', 'timescale', 'dradt', 'ddecdt', 'phase', 'solarelon']\n",
    "     as the second\n",
    "    grouped either by object (i.e. length of ra array == length of times) (default)\n",
    "    or grouped by time (i.e. length of ra array == number of objects) (if byObject not true).\n",
    "    \"\"\"\n",
    "    ephs = np.swapaxes(oorbephems, 2, 0)\n",
    "    # oorbcols=['delta', 'ra', 'dec', 'magV', 'time', 'timescale', 'dradt', 'ddecdt', 'phase', 'solarelon']\n",
    "    velocity = np.sqrt(ephs[6]**2 + ephs[7]**2)\n",
    "    if byObject:\n",
    "        ephs = np.swapaxes(ephs, 2, 1)\n",
    "        velocity = np.swapaxes(velocity, 1, 0)\n",
    "    # Create numpy structured array\n",
    "    ephs = np.rec.fromarrays([ephs[0], ephs[1], ephs[2], ephs[3], ephs[4], \n",
    "                              ephs[6], ephs[7], ephs[8], ephs[9], velocity], \n",
    "                             names=['delta', 'ra', 'dec', 'magV', 'time', 'dradt', \n",
    "                                    'ddecdt', 'phase', 'solarelon','velocity'])\n",
    "    return ephs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All right, let's test interpolating the coarse ephemerides to all the times in opsim. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Linear interpolation\n",
    "def interpolateEphs(ephs, i=0):\n",
    "    interpfuncs = {}\n",
    "    for n in ephs.dtype.names:\n",
    "        if n == 'time':\n",
    "            continue\n",
    "        interpfuncs[n] = interpolate.interp1d(ephs['time'][i], ephs[n][i], kind='linear', \n",
    "                                              assume_sorted=True, copy=False)\n",
    "    return interpfuncs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f0c510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pWkVkI4CjYl76hKp+z1/nSgAHVfUbZcZC1M1cqisIcqWYjIpRasJQ1eVpr4vI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\nDCIiMsKEQURERpgwiIjICBMGEREZ+f/ljgNaUA92hwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x130d0d890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Sb4hths2ABCbv5pKsEaj+QvAdA6uqG+fRR/ekgvpe2B579KqmFx2GUY52a0Bq\ndFoH5AIzIFHQeHO54opAMpzQ/Y1zQmZ5649+VJEU4NFHqyurLCEWMsa6E6FRjF3hO9K52GUVGa2i\nvK5d61eHC4puW3rvveCqKx5DJGJXEZ7bRWBNZi+G7wX5cudVu6lTOTZurK6sWB8AbBpvwbxlVqf2\noqnXVcNFg/f52o6z27JjmHpbVVnuVik3pxWdmr5oUXU93WzZq1bBWWcVywvhphO30lTVtdZLWdny\n2kXibadh7H5i03iD0hhDqjgiuxBRRJKLvPgq2d7O9c6dvZdhxM0550DZnlq1btLG6+zss4sfOViR\nCdz93oqMgeRRxYr4dpgBaUnvF0PyVNQ4iFt0lexpp0FvbpzGYz/wgR6KMnK5886w9V97bdj6q6Cq\nXn0VK/N7JQkN40ZD8TGQ6lfEt63NXFj5XHABXHNNr0Ha8v3OjUHO2gVAc+8CMhdW+bKKlhdDG7vU\nsHQpXHZZeB0xuBhdlbXffsXi4rVy5ZkLyzNXX93b8e1CZ7/hDb2V7ZJBGKyvUfUakPHjzSWYx6WX\nhlZg1Ehcgv46BdYDqTB/u2OzFNlWNvvZ/fcXn+td/Mm0tbZe6HUXQBe7zJUtp8bGjTB3brfXUG3v\ni8HtgcSiw3ogrTVYD8RwEs55n32qL3OMuJ7Yr7qqt+PLLdRqNB4hVm7HspGUMXgEMyAiMl5ENojI\nTen7aSKyTkQeEZHbRKTSCDdz5oTuaZWpv9wNeOLE4nkffBB8dHmLrgFxyYUXhlYQJkzOypXte8OD\nSuhJDsNAyB7IR4BNjN29LgbWqeps4Gvp+8p4+GGo/xFlVzsXoeheB1Ut+kmmDnd/c+9mCq+vhXUh\ntgoeRoosUvQxI8/VYslumDcvtIL2izsHgSBjICJyMHA98DfABar6OyKyGThBVbeJyAxgVFXnZI4r\nPQZSZjyh7PhA/vhHqwU+7X2mVeyncc457ad8xrBXhQtNMXwv92MPzWm+93wpqmPKFHjuOZdjIJ01\n5B9X5bhFOQ35ZVUzBrJwIVxzzWCNgVwDXATUT5OZrqq1nTe2AdNdCvAZeOzww5vTLrjAX/2DsF7A\nyOeAA0IrKE7WeFTNwoUQei3IjBlBq09pbONrrnFYk+8eiIi8B/htVT1fREaAv0p7INtVdWpdvp+o\n6rTMsbp48eLd70dGRhgZGSlYb/dPGStWwPnn994DSGZB5OVrjlHkogcSZqc664G40lDPjh0wdWr1\n11C3rF3ZVoQTAAATUElEQVQLp5zSnY7LL69+CnC337VoyJ+iFDkfRSnfAwEYTf9qfMJJDySEAbkC\n+GPgJWAvYF/g34G3ASOqulVEDgDucOnCcjnFL++YcePyjm3MN3ky/PSn7csqEsMohptcaAMyZw48\n/HD47+XHfRTegMSio/vz0/j+2GPhrrv8aihSzrRp8OMfFzvuzjth3rxsb8+NCyvoOhAROQG4MO2B\nfBr4sap+SkQuBqao6sWZ/NEbkOSCbD4mbw1BNt+WLc2D2mXWMoS+yVWx9qFqA1SmjF51uV4DUlST\nGZB2+Rvfb9/e+w6HLgzIHnvAiy+W1+DKgMSwDqTWvFcC7xaRR4B3pu/7kHw/b5Exl/wZUd2d8zlz\nOudxT+NNMwaSwIO+Cd8Og7wbogti2B43j733Dq0gn6AGRFW/rqrvTV//RFXfpaqzVfUkVd0RUltV\nJEERy5Msfit+E8hOV+6FbCThX/u1cuXEsAYkhokErfZ6cU8YI1Y88rQ7Okej7Q8D+8ILoRXkMzSh\nTKpyYZ13XjK4Xqae5m5lMU3duU0a855+eufFa/mD/rVKuncDxTAA7m4PjvLnIoTrqMwYWnkdzWnt\ntISaTtyY3/04WZHfYKdypkxJ3GtlNQzkGEi3hDEgzWllL8gQBqT8rLF8V1ynNSVlNVRdhhkQvxqS\nuprThtOAdKehdTk2BmIMGEX3MzHC4XONUT2+I8HmkTzph9Ww//7Vl9m9AfLjtrQeSAfypsS17ilA\nu15FVT2QhQtbh5t33QMpUqb1QNxqaK6nOa1opIPqtYTvDYU+R1WtBanXNmFCLURRMZqXDVgPJAjd\nxXBqfdOtEpcrSyEvGGP/PGRALDPR/BHDCmxjjBhmct13H/i4JsyAOKS6/Z79zqLJrszNcvTRrY+t\nehOnMmQXEIbAZzu07o16k9CSWgDSqgKMGsXwFarJTqtDqtrvedUqKPI04e6G0Vjwvfd2yjuWv0zU\n47w6eyHMfvCN7dDrdO5yhDCkjfVddFGqRMMZ9XazJvuFWEcabAykxLGtVqt2qmP8eNjV8GBara+2\n7OrrTmMzeRQdr8lbXV+ErDHs5XxVeYkXLTuGsYduxs6q09Gclqfllluqe8Bq1lD8d+BrrKzM9612\nHNDGQALS2O5lfewbNoBPX3VVC/iK9oDyqGq/EdscqHdcGw9I1kkVuVZcGY+ECHx3GQ3J3j6Dh/VA\nCh3bnNYc5weK9CgadbjtgZRdLJmnq6peWFF6mUtvPZD8c+brpx5ayyWXwCc/GfY8VbEWxHogA0Ky\nj3Wns+fXx1t0d8QirFoldNvDmDmzuvrz2Hdft+VXhfWM4sPVSvtuKNoTc4v7+9FA9UAaA8cljacK\n/OpXyF4Tqc6a5/VAivk8q+qBFNFQftwg7wmy+Zgqe0FZHn8cZs2qpkflsgfSqvzQPZAie8340jJ3\nLtx/f/geWS/5XGpwdfz8+bBmTa0MC2VS0IA0ttG++8Jzm59GDpyBy5NZ7oLtxoA0p/k0IEceCQ8+\n6M6N1llTsbJcb5t69NHNs9Caz4OfMO6NdbZ3Q/rQMKYlL9UMSIjFsGNlmAurLa3m3f/0pyAHOt0d\n1wudovK6nvP/wAOd88SwBsT1tqm33w6dXRONxiMGfA7ijh/vr66inHpqaAWDycAYkPY/2sbP9tnH\nh55qufDCTjn8jsHk09jOydhRWBJfdHWUWWW8fHm1Gspw883+6vr+9yE2/391i3rL8/jjoRVUzwAZ\nkHraX7wPPth7DfWD2OWf/scOTKbKVsfll/dydLEvtHRp+8/LhLCumhgWkS1YEFqBX6qauj1ovPa1\noRVUT4g90WcCXwD2J7nT/6OqfkZEpgH/BhwCbAHmZzeVajUG0uxzbu8PLudLbE5rFbCuXR2tghSW\nDXpY5LMitNJVPxmg0/es2p9cVWDIqqlqPMydplqF/gfQ8/WA7zGQvC2kfU926GkqryoyDmwMpJmd\nwEJVfSPwduB8ETkcuBhYp6qzga+l7wuSdV+FdeX09vRfnOuvd19H40yy0C4yoxgxjMGErd9XLKh2\nJOFrSlqkX/6yIhVuz4N3A6KqW1X1vvT1z4CHgIOA9wKfT7N9Hvhd39rakfixi10Ml17qVMpuzj7b\nTz01LOprzLS+UbzpTR5lpIyMQGzXiu8xiK98pfyxMmnP6oQ4JOgYiIjMAt4M3A1MV9Vt6UfbgNJT\np1xsbBOHHzvsU52PUBj9TqiZaEnYmvxrvsgMuqq54w7/dXZi1qzQCrqhsRdZdiJGL2GIilA6Vmqv\niMg+wJeBj6jq8yL1vj5VaVwVWHfcEkTgz/4MzjhjhBNPPKEpj9s4O+FYtKg5RAPEsf9ADKHDW1wy\nngnjPupu35oQhLhAIrgo2zAW/mh3Cnvume+96vYBdnR0lNHR0fSdw9+Fqnr/A/YAvgr8ZV3aZmBG\n+voAYHPOcZoMJSV/yYj6roa0/PRdTZ+XIa+cPfborvw8vd1oyqurVRv08t1alZPNt2pVdRo61VXm\nO7igna7sZ1dd5UZDEV0u26CYntZ/Pjj22Pbn6kMfqu7e0Ips+QsXtv6s3W+6dw2oOriXe3dhSdLV\nuBbYpKp/V/fRjcCZ6eszgVIeRJ9TR6+/vvPmSyHwuf6i1TjMokX+NLQihvUXndfvDC7HHQchx0Hu\nuqv95ytXgvvfbmP5td1EY+ixV0GIabzHA98ANjJ2dS0C7gFWA6+hzTTe+gtStfU0vLIhQ9prz0tt\nLPu009oPnvUyjTfv+HZt0A1FdRXd76GKy6rbMkPsuT1uHLz8sn8NnXTVKLsfS1X0er1XXf/y5WPu\noOxn69dX7wos+nupZ/ZseOSR6q6jRIPFwmoyIAlxGZDON7n89LIGZPVqmD/fnwH54AfhuuvcGLFO\nmmI0INl6YjMgoX/esRmQ+rp9nKulS+Gyyzr/XpqpTlvymzUDkmNAil8ceXm65YIL4JprsuV2d6Lv\nvBPmzSv/Q3cVqK6bH7qv/R46/cgmT05inbXT5YJW9YwbB8nvyQxIjfAGpDnNpwHJqyetjdb3kZqQ\nKhflDs5CQmcUCRjXyxhJFdNY458tExN5P7oxnn/en5IiZI2HkY/PuFTHHgshx2HyKXKd9Md1NFAG\npD5g3Lhx+ScghgB/vRDHRjV+KPJdx6VXcNlthl3S79eaK3xOs88bSJ8xw1/9RZjeYcVbEok7TgbK\nhVX/VfJi4WTzlNPQemylaPm9uhqq0FBEU6uymvO62/+is6+4tU/Ztwsr5PhHXv0hNGSpYmtXVxr8\nubCaam+q14XLvVGDubBS6luzdXv4iYXTWP+73+2jzvb4eerNtnuj8Xj1q13X3/kXZU//ceAiKkQV\nvOEN/uqaOxeK3reyVL0dQdX0YQ+k9rTbyOGHw6ZN2fwueiCtPys7k6qbY5uPr+Yp6s1vVu67r1gP\nZNo02L69IVeDhu3bq1sdX2QAcuZMeOIJf0//rc6f9UDyCd0uCxbA5z6XN2gNIa8ZSPYmev5595MN\nXPVABsaAFHO19H5Cjj8evvnN3k52jAZkxw6YOrWYrua87m4QRVxYrjVkydfkfxvbLGZA2mnIpvht\nq07T93ud3t+5fnNhpYSdnXD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1278a91d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ssvOBqaloa4BzJM2RdBhwOHB/3ndffXU8AUm50/Y974mVcoGHvaJwVrdhrOEpX8x6TXic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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102a85dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6MT4ezsO6lSg0kB9oNBygGsIErOSFv3ixJxkp1q/3rcAfnSL85iFqdZi/qNav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\nyQ2NBiGEkNzQaBBCCMkNjQYhhJDc/H9e3ib3K1wYWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118e8ee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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k/4EwZeKtw/bysUFfw6pVUnwgilIOYRPWUUdZFqgFPa0PKaTMtwL4W2b+TyL6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\nyzU6am7E0sgRjDpKfz4AdNE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/TESNGesfhKNEGsx3h3pDRNTIUXsonEmKDZ6BN2FxYjIj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\nFCUTqkAURVGUTPx/VAwnvQ2CgCsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1190f9a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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f77j6/EZjCMYTPsZJvyeWEFKKuqJotC1v6658wz+oNJlBOYbgp92awazCX+y0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\nUAsm1wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1191ac350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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relW9X1VvAHCDiHwRwG0ArjCtZ2ho6MjzSqWCSqXS/mCJiCwbfa/5blHDw8MY\nHh5uXzAJRNVuI4uIfADAelVdYnhPbcdHRFSE2f1j2Hug58jyihXAAw80ty4Rgaq2vUHEVi+pk0OL\nKwFsshEHEZEr+o5yfy4pW20YXxWRUwFMANgB4CpLcRAROWFiwv1hcVYShqr+po3tEhG5qpU2jKK4\nn9KIiKaAvt6JyDKnBiEiIqNwwujvB775TYvBJGDCICJywOLjgskH33sP+MM/tBhMAiYMIiIHzOyP\nVkmNjVkKJAUTBhGRAzj5IBERZTKyuw+cfJCIiOra8doM2yHUxYRBROSAhccdsh1CXUwYREQOmNnn\n/tQgTBhERA6YN3scbPQmIqK6Rt6YATZ6ExFRXTt2HWU7hLqYMIiIHMBGbyIiymTkjV7bIdTFhEFE\n5ICF8x2cCySGCYOIyAEjr0dLGJzenIiIjMYPBz2kuro4vTkRESUY3R/cAHVigtObExFRgviQPU5v\nTkREmYyP246gFhMGEZGDtmyxHUEtJgwiIgf0z5iMLJ95pqVAUjBhEBE5oO+oaMJgt9oYEfmCiEyK\nyBybcRAR2TYx4fbEg4DFhCEiCwBcAGDEVgxERK4YO8yEkeZWAH9scftERM6YcVS0Yy2rpHwishLA\nK6r6jI3tExG5ZvGJQT9aV0d6T6//keaIyAYA8w1v3QBgDYCPhz+etJ6hoaEjzyuVCiqVSnsCJCJy\nyMiuoEhRHel9zz3Z/nZ4eBjDw8P5BBYiqsXeElBElgB4GMAB/6WTALwK4FxV3R37rBYdHxGRDcuX\nHsSPnppxZHnFCuCBB5pbl4hAVdveKJJbCSOJqj4L4Ljqsoi8CGCpqr5ddCxERK4Y2VX46bhhLozD\nYBGCiKa8hSccjiy7ODWI9ZSmqj9nOwYiItviJQxODUJEREbjsXEYp51mKZAUTBhERA4Y3Rc9HW/b\nZimQFEwYREQOGIu1WXDyQSIiShCtkuJIbyIiKi0mDCIiB7hYoohjwiAicgJnqyUioia4OHCPCYOI\nyAH9/dHlJ56wE0caJgwiIgf09UWXR0ftxJGGCYOIyAG7dkWXlyyxE0eawqc3bwSnNyeiqUKkdnly\nstl15TO9OUsYREQOiicQFzBhEBE54Pbbo8suVq6wSoqIyBHhUsXGjcDy5c2uh1VSREQdbeNGYNq0\n1pJFnljCICLqMCxhEBGRVUwYRESUCRMGERFlwoRBRESZMGEQEVEmVhKGiAyJyCsissl/XGgjDiIi\nys5WCUNAuR5rAAAGUklEQVQB3KqqH/IfD7Vz5cPDw+1cXWHKGHcZYwYYd9EYd2ewWSWV20wpZf2S\nyxh3GWMGGHfRGHdnsJkw/kBEnhaRvxGRQYtxEBFRBrklDBHZICJbDI9PAvhvABYDOAfAawD+PK84\niIioPaxPDSIiiwDcr6pnGt7jvCBERE3IY2qQ6e1eYRYicryqvuYvXgJgi+lzefyHiYioOVYSBoA/\nFZFz4PWWehHA71uKg4iIMrJeJUVEROXg9EhvEenyB/bd7y+fLSL/JiLPiMh9IjLgv75IRA6GBgJ+\nJ7SOpX5j+09F5Juh13tF5O/91x8TkYVtinmnH98mEXncf22O3wngBRH5QbhXmIis8WPYJiIfL0Pc\nJdjfq0TkORGZEJEPxz7v8v42xl2C/b1WRLaK1+vxn0RkVujzLu9vY9wl2N83+zFvFpGHRWRB6PP5\n7m9VdfYB4PMA7gRwn7/8EwDn+8+vAHCT/3wRgC0J63gcwLn+8/UALvSffxbAd/znnwbw/TbF/CKA\nObHX/gzAH/vPrwPwNf/5GQA2A+j2/w8/Q1Dqczlu1/f3aQBOAfAIgA+HXnd9fyfF7fr+vgDANP/5\n10p0fCfF7fr+Hgg9/wMA/6Oo/d3yfyivB4CTAPwQwC/D60UFAHtD7y8A8FzaFwzgeABbQ8u/BeCv\n/OcPAfio/3w6gDfb+AUfE3ttG4Dj/OfzAWzzn68BcF3ocw8BOK8EcTu9v0PvxU+8Tu/vlLhLsb/9\n9y8BcEeZ9rch7jLt7zUIEl3u+9vlKqnbAFwLYDL02nMistJ/vgpe0qha7BfbhkWkenPDEwG8EvrM\nq/5r1fdeBgBVPQxgn4jMaUPcCuCHIvKEiPye/9pxqvqG//wNAMf5z0+IxfeKH1f8ddfiBtze30lc\n399pyrK/r4R3BQuUa3+H4wYc398i8hUReQnA5QC+6r+c+/621UsqlYh8AsBuVd0kIpXQW1cC+JaI\nfAnAfQDG/Nd3AVigqqPi1f3eKyIfLDTowDJVfU1E5gHYICLbwm+qqoqb40saidvp/a2qGy3F0ohG\n4i7F/haRGwCMqepdlmJL00jczu9vVb0BwA0i8kUA34BXRZ87V0sYHwPwSRF5EcD3APwnEfk7Vd2u\nqr+qqh8B8H0AOwBAVcdUddR//pT/+snwMulJofWehCDTvgrgAwAgItMBzFLVt1sNXP3xJar6JoB7\nAJwL4A0Rme9v63gAu0MxhEtJ1ficjrsE+zuJ6/s76bPO728RuRzACgCXhj7u/P42xV2G/R1yF4Bf\nCMWQ6/52MmGo6vWqukBVF8Orb/s/qvqf/SwLEZkG4E/gTTECEZkrIl3+85+D9+X+P39nvyMiHxUR\nAfA7AP63v5n7APyu//w3ATzcatwi0idBz61+AB+HNygxvK3fBXBvKIbfEpEeEVnsx/24qr7uctwl\n2N+Rj4Weu76/jXG7vr/Fuz3BtQBWqur7oT9xen8nxV2C/f3zoY+tBLApFEO++7sdDTN5PgD8EoJe\nUlcD2O4/bgl95jcAPOvvuCcBXBx6bym8H+PPAHwr9HovgLsB/BTAYwAWtSHWxfB6KWz241njvz4H\nXgP+CwB+AGAw9DfX+7FtA/CrZYi7BPv7Enj1sgcBvA7gwZLsb2PcAD7l+P7+KYARP75N8HvdlGB/\nG+Muwf7+Bz+GzQD+EcCxRe1vDtwjIqJMnKySIiIi9zBhEBFRJkwYRESUCRMGERFlwoRBRESZMGEQ\nEVEmTBhEPhE5RoIprV8TkVf85/tF5C9tx0dkG8dhEBmIyI0A9qvqrbZjIXIFSxhEyQQARKQiwU28\nhkTkf4rI/xXv5ja/ISJfF+8mNw/68/FUb1gzLN4sow9V5+QiKjMmDKLGLYZ3n5ZPArgDwAZVPQve\nlB4Xi0g3gL8A8Cn1Jsq8HcBXbAVL1C5OTm9O5DCFN8fThIg8C++Obf/iv7cF3s13TgHwQXj3MQCA\nLnhTZhOVGhMGUePGAEBVJ0VkPPT6JLzflMC7G+THbARHlBdWSRE1Rup/BNsBzBOR8wBARLpF5Ix8\nwyLKHxMGUTIN/Wt6jthzwLs54Ti8ewv8qYhshjdN9n/MM1CiIrBbLRERZcISBhERZcKEQUREmTBh\nEBFRJkwYRESUCRMGERFlwoRBRESZMGEQEVEmTBhERJTJ/welv1IWcmQTzgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119580490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7NzLeoxLJLJbXb7+5UdLDSxt133BrnBiqjqN3+6eemiTauvc7LI6m9jsbaUBi\nByWS2U2JZPj2s9oojj8+aduoLoa8V7r3u8ceyY3g6pIXh04Bo1Mi6aBEMrspkRRJJE00dGctbb6N\nIutWsvr5j2fWtJGISPX23bf6bRaZvHGffarfb69f/ELdb2OnEolEJ/YSybx5ni5rrkSyZg1cemnr\ntXq6/A6PQz2mJp2qtjookcxusSeSUNVKrX002dg9qKF7993hqafq2a/UQ1VbIpG68MLqt7lmDWRV\nK2VNE3PuudXvvy3/nKMkIi0qkUh0YiuRbNsGhx2W/3pTpYHkFq/NVi+deCJ0DIzeZfFiePjh+vYr\n9VDVVgclktkttkSy117w+OP5r4dMJHV3vU3i6F+mn99kUtWWzCGVf89L7f+JJ3JWa9i8jF9r3UkE\nkhJZy6JFSiLST4lEpEfS5hHf2TIphTefZA87rN3t9tFHG9+9TABVbUl0smaehWavhEeZsLC+qq3e\nJd37XbRIJ3YZjdpIOiiRzH5NNyoP23+MiUQ/ARmV2khkTotllte8mznVIbnTYP7MtyKxUIlEotR7\nNd70x51X6uhdvnQp3Hdfc3G0POc58OCD9e1XZidVbXVQIpn9OhNJiI+6aCJ56KF67yWvmW+lSnUl\nkgVVb1CkCpNyoqwzieQZdDtikRDURiISsfXru5+bwc7mmmlEClHVlkiGolVb+hrKJFGvLRERiZIS\niUgBl1/ebNdfkUmiqi2RDLHcZlakSqraEonM5s2hIxCJgxKJSIYkSQwubrzudY2EIhI9VW2J5Ogf\nVa4eWzLZZl3Vlpm918xuM7Pvm9mfdCxfb2Z3mdntZnZSqPhERKSYICPbzexE4A3Ake4+Y2YHpMtX\nAm8GVgIHA980s+Xuru4yIiKRClUiOQP4mLvPALj7A+nyNcBX3H3G3bcBdwPHhQlRpJPqsUTyhEok\nLwb+m5ldZ2bTZnZsuvwgYHvHettJSiYiEdAkVyJZaqvaMrMtwIEZL52d7nc/d3+lmb0CuAR4Qc6m\nMi8FN23atOvx1NQUU1NTZcIVGUlyO16RuE1PTzM9PV37foL02jKzy4Hz3f3f0ud3A68E/geAu5+f\nLr8C2Oju1/e8X722pHbdvbbUY0sm32zrtXUp8FoAM1sOLHT3B4HLgLeY2UIzO5ykCuyGQDGKiEgB\noe5H8jngc2Z2K/A08DsA7r7VzC4BtgLPAOtU9JBwLOexiHTSgESRHINuIKWvn0yi2Va1JRK9iy8G\ndfsVGU4TxxaEAAAHe0lEQVQlEpEB+qdJgdWr4corw8QjUkZdJRIlEpEBshKJvnoyqVS1JRKEGtlF\nhlEiERGRUpRIRAZ42cu6n6taS6Sf2khEROYItZGIiEiUlEhERKQUJRIRESlFiUREREpRIhERkVKU\nSEREpBQlEhERKUWJRERESlEiERGRUpRIRESkFCUSEREpRYlERERKUSIREZFSlEhERKQUJRIRESkl\nSCIxs+PM7AYzu9HMvmNmr+h4bb2Z3WVmt5vZSSHiExGR4kKVSP4U+LC7vxz4SPocM1sJvBlYCZwM\nXGRmlcU4PT1d1aYapbibNYlxT2LMoLhni1CJ5KfA4vTxEuDe9PEa4CvuPuPu24C7geOq2umkfviK\nu1mTGPckxgyKe7ZYEGi/ZwHXmtnHSZLZq9LlBwHXday3HTi44dhERGQEtSUSM9sCHJjx0tnA+4D3\nufs/mdmpwOeA1Tmb0s3ZRUQiZu7Nn6fN7FF33zd9bMDD7r7YzM4CcPfz09euADa6+/U971dyEREZ\ng7tb1dsMVbV1t5m9xt3/DXgtcGe6/DLgy2b2CZIqrRcDN/S+uY4DISIi4wmVSH4XuNDMdgeeTJ/j\n7lvN7BJgK/AMsM5DFJlERKSwIFVbIiIye0zsyHYzm58OaPxa+vwoM/t3M7vFzC4zs0Xp8mVm9mS6\n7o1mdlHHNo4xs1vTAZB/3rF8dzP7u3T5dWZ2WEUxb0vju9HMbkiX7W9mW8zsTjO70syWdKyfOTgz\n5rhjOd45MZ9qZj8ws2fN7Oie9WM+1plxx3KsB8R9gZndZmY3m9lXzWxxx/oxH+/MuCfgeH80jfkm\nM7vKzA7tWL/e4+3uE/kHfAD4EnBZ+vw7wAnp43cB56aPlwG35mzjBuC49PFm4OT08TrgovTxm4G/\nrSjmHwL79yz7U+CP0scfAs5PH68EbgJ2S/8Pd9MuQcYcdxTHOyfmFcBy4Grg6I7lsR/rvLijONYD\n4l4NzEsfnz9B3+28uGM/3os6Hr8X+GxTx7v0fyjEH3AI8E3gROBr6bKHO14/FPjBoA8feB5wW8fz\ntwB/lT6+AliVPl4APFDhh/+cnmW3A0vTxwcCt6eP1wMf6ljvCuCVExB3FMc7K+aO13pPyFEf6wFx\nR3Gsh8Wdvv4m4IuTdLwz4p6k472edgKs/XhPatXWJ4EPAjs7lv3AzNakj08lSSYth6dFwGkze3W6\n7GCSAY8t99Ie/Hgw8GMAd38GeMTM9q8gbge+aWbfNbP3pMuWuvuO9PEOYGn6+KCe+FqDM3uXxxY3\nxHG8s2LOE/uxHiSGY10k7rUkV7wwWce7M26I/Hib2R+b2Y+AdwIfSxfXfrxD9doam5n9BnC/u99o\nZlMdL60FPmVmHybpRvx0uvwnwKHu/pAl9cuXmtlLGw267Xh3/6mZHQBsMbPbO190d7c4x8iMEncs\nx7svZne/JkAcoxol7liONQyI28zOBp529y8Him2QUeKO/ni7+9nA2ZaMyfszkmr+2k1iieRXgTeY\n2Q+BrwCvNbO/cfc73P3X3f1Y4G+B/wRw96fd/aH08X+ky19Mkn0P6djuIbSz873A8wHMbAGw2N1/\nVjZwd/9p+u8DwD+RzCO2w8wOTPf1POD+jhg6S1Wt+KKOO5bjnRNzntiPdd66URzrQXGb2TuBU4C3\ndawe/fHOinsSjneHLwOtWdVrP94Tl0jcfYO7H+ruh5PU6f2ru/9OmpmxZLbg/w38Zfr8l8xsfvr4\nBSQf/H+lH8SjZrbKzAx4B/DP6W4uA05PH/82cFXZuM1sL2v3JNsbOAm4tWdfpwOXdsTwFjNbaGaH\np3Hf4O73xRx3DMd7QMxdq3U8jv1YZ8Ydw7EeFLeZnUxSBb3G3Z/qeEvUxzsv7gk43i/qWG0NcGNH\nDPUe7yoafkL9Aa+h3WvrTOCO9O+8jnV+E/h+elC/B7y+47VjSH6odwOf6li+O3AJcBfJJJLLKoj1\ncJKeEzel8axPl+9P0nHgTuBKYEnHezaksd0O/PokxB3D8R4Q85tI6n2fBO4DLp+QY50ZN/BboY/1\nkLjvAu5J47uRtBfQBBzvzLgn4Hj/QxrDTcA/As9t6nhrQKKIiJQycVVbIiISFyUSEREpRYlERERK\nUSIREZFSlEhERKQUJRIRESlFiURkCDN7jrWnDv+pmW1PHz9mZn8ROj6R0DSORGQEZrYReMzdPxE6\nFpFYqEQiMjoDMLMpa99YbZOZfcHMvmXJTYd+08w+bsnNhy5P5ytq3Uho2pJZW69ozVcmMsmUSESq\nczjJPXLeAHwR2OLuR5JMbfJ6M9sN+DTwW55MLnox8MehghWpysRNIy8SKSeZA+tZM/s+yR32vpG+\ndivJTZGWAy8luY8EwHySqclFJpoSiUh1ngZw951mNtOxfCfJb81I7tz5qyGCE6mLqrZEqmHDV+EO\n4AAzeyWAme1mZivrDUukfkokIqPzjn+zHtPzGJIbSc6Q3NvhT8zsJpLpyF9VZ6AiTVD3XxERKUUl\nEhERKUWJRERESlEiERGRUpRIRESkFCUSEREpRYlERERKUSIREZFSlEhERKSU/w/niAQ+ySzhnQAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119a1d350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "obstimes = simdata['expMJD']\n",
    "for sso in orbits[0:1]:\n",
    "    oorbelems = packOorbElem(sso)\n",
    "    oorbephems, err = oo.pyoorb.oorb_ephemeris(in_orbits = oorbelems, in_obscode=807, in_date_ephems=ephTimes)\n",
    "    ephs = unpackEphs(oorbephems)\n",
    "    interpfuncs = interpolateEphs(ephs)\n",
    "    # Have a look.\n",
    "    for n in interpfuncs:\n",
    "        plt.figure()\n",
    "        plt.plot(obstimes, interpfuncs[n](obstimes), 'r-')\n",
    "        plt.plot(ephs['time'][0], ephs[n][0], 'b.')\n",
    "        plt.xlim(obstimes[0], obstimes[-1])\n",
    "        plt.xlabel('Time')\n",
    "        plt.ylabel(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loops, best of 3: 8.17 s per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "# Check the timing\n",
    "for sso in orbits[0:1]:\n",
    "    oorbelems = packOorbElem(sso)\n",
    "    oorbephems, err = oo.pyoorb.oorb_ephemeris(in_orbits = oorbelems, in_obscode=807, in_date_ephems=ephTimes)\n",
    "    ephs = unpackEphs(oorbephems)\n",
    "    interpfuncs = interpolateEphs(ephs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Awesome. Still about 8s per object with the interpolation. (This would not be true if we did higher order than linear interpolation). <br>\n",
    "Let's add the step of checking the positions against the opsim pointings, to determine when the object might actually have been seen.\n",
    "\n",
    "Simple circular FOV:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ssoInFov(interpfuncs, simdata, rFov=np.radians(1.75), raCol='fieldRA', decCol='fieldDec'):\n",
    "    \"\"\"\n",
    "    Return the indexes of the observations where the object could be seen.\n",
    "    \"\"\"\n",
    "    raSso = np.radians(interpfuncs['ra'](simdata['expMJD']))\n",
    "    decSso = np.radians(interpfuncs['dec'](simdata['expMJD']))\n",
    "    sep = haversine(raSso, decSso, simdata[raCol], simdata[decCol])\n",
    "    idxObs = np.where(sep<rFov)[0]\n",
    "    return idxObs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Actual camera chipgaps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# For the footprint generation and conversion between galactic/equatorial coordinates.\n",
    "from lsst.obs.lsstSim import LsstSimMapper\n",
    "from lsst.sims.coordUtils import findChipName, observedFromICRS\n",
    "from lsst.sims.catalogs.generation.db.ObservationMetaData import ObservationMetaData\n",
    "\n",
    "mapper = LsstSimMapper()\n",
    "camera = mapper.camera\n",
    "epoch = 2000.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def ssoInFovChip(interpfuncs, simdata, rFov=np.radians(1.75), raCol='fieldRA', decCol='fieldDec'):\n",
    "    \"\"\"\n",
    "    Return the indexes of the observations where the object could be seen.\n",
    "    \"\"\"\n",
    "    raSso = np.radians(interpfuncs['ra'](simdata['expMJD']))\n",
    "    decSso = np.radians(interpfuncs['dec'](simdata['expMJD']))\n",
    "    sep = haversine(raSso, decSso, simdata[raCol], simdata[decCol])\n",
    "    idxObsRough = np.where(sep<rFov)[0]\n",
    "    idxObs = []\n",
    "    for idx in idxObsRough:\n",
    "        mjd = simdata[idx]['expMJD']\n",
    "        obs_metadata = ObservationMetaData(unrefractedRA=np.degrees(simdata[idx][raCol]),\n",
    "                                           unrefractedDec=np.degrees(simdata[idx][decCol]),\n",
    "                                           rotSkyPos=np.degrees(simdata[idx]['rotSkyPos']),\n",
    "                                           mjd=simdata[idx]['expMJD'])\n",
    "        raObj = np.radians(np.array([interpfuncs['ra'](simdata[idx]['expMJD'])]))\n",
    "        decObj = np.radians(np.array([interpfuncs['dec'](simdata[idx]['expMJD'])]))\n",
    "        raObj, decObj = observedFromICRS(raObj, decObj, obs_metadata=obs_metadata, epoch=epoch)\n",
    "        chipNames = findChipName(ra=raObj,dec=decObj, epoch=epoch, camera=camera, obs_metadata=obs_metadata)\n",
    "        if chipNames != [None]:\n",
    "            idxObs.append(idx)\n",
    "    idxObs = np.array(idxObs)\n",
    "    return idxObs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So let's test adding in the check if the object is in the FOV and finding the properties of the object at those times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "501\n"
     ]
    }
   ],
   "source": [
    "for sso in orbits[0:1]:\n",
    "    oorbelems = packOorbElem(sso)\n",
    "    oorbephems, err = oo.pyoorb.oorb_ephemeris(in_orbits = oorbelems, in_obscode=807, in_date_ephems=ephTimes)\n",
    "    ephs = unpackEphs(oorbephems)\n",
    "    interpfuncs = interpolateEphs(ephs)\n",
    "    idxObs = ssoInFov(interpfuncs, simdata)\n",
    "    #idxObs = ssoInFovChip(interpfuncs, simdata)\n",
    "    tvis = simdata['expMJD'][idxObs]\n",
    "    obs = np.recarray([len(tvis)], dtype=ephs.dtype)\n",
    "    for n in interpfuncs:\n",
    "        obs[n] = interpfuncs[n](tvis)\n",
    "    obs['time'] = tvis        \n",
    "    print len(idxObs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "448 with the chipgaps; 501 with the circular aperture for the first PHA. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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kvzXPxzQqccMM/bC7du3SRCKh8XhcE4lEVQ+CmzSmYRcLAO3p6fE9FhMGoE1iyhgPVYZJ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\nXGPSICIi1/4/NvZDTgaxtrQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12128cb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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f+973ePjhhzUVi0gdUHVWnajVqUU6Ojp45ZVXipbv3r07gYhEJqe4qrOUROpE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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12160b590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8CWsEZCu2kVCgenp6ICLTj56enkC/32uKDRNTbySTSQwNDRWsIb9y5Uq89dZb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\nyv8HXWXYQEDYAKsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1212cc7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lcoyMjHi27927d14/S7OeJNWSsDmM1LYbbphVSSiwPSqnT5/2bE/SNsJKFBKJ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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1216a04d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ivgB8AUDSHOC/RMQfS2qNiN2STgL+jPLEASS1AG9GxGFJHwBmAD+OiF9I2idp\nFtAFXAPclr7mCeBaYD1wFfB0P7nU/AIoMzMbnDxvmRPp52JJPTPWHomIe1J7NvBlSYconxP6k4j4\nRVq2FLgHaAZWRUTPLQXuBu6XtBnYAyzKdhPMzOxEjYhb5piZWf1ouDsX1MsFqYPMfWvKc4OkrhSb\nJGmtpJclrZF0WkX/G1MumyTNHcr8B5J7A+37hZJelHRY0oW9+tfNvh9o/g20/78l6UeSfijp7yRN\nrOjfCPu/z/wbaP9/JeX+vKSnJZ1d0T/b/Z/V5IIMJy38KfAA8ER6//+AP0jt/wB8ObXPATb28xld\nwMWpvQq4LLWXAnem9tXA39Q4958Ak3rFvkn5glqA/wp8I7XPA54HTk7b8grvjlBzz3+AuTfKvv8Q\n5QkuzwAXVsTrat8PIv9G2f//Djgptb9Rr3/3B5F/o+z/8RXt5cBf5bX/G2rEozq6IPUE9J7oUPmd\n91bksgB4MCIORcRWyn/4s4Y4/2pz73vlOtv3EbEpIl7uo1897nuoPv++V66//NdGRM81fj8A3p/a\njbL/+8u/75XrL/9fVrw9FfhZame+/xuq8FBHF6QOUgBPSXpO0nUpdkZEvJHabwBnpPb7euW5I+XX\nO55X/gPJHRpj3/en3vY9DCx/aLz9/ynK/4OGxtz/lflDg+x/SV+TtB34JPDnKZz5/m+YB8Gp4oJU\nSYWKRZ8CbpP0RcrTq3tfkPqmyse/H5M0M9ek3+uSiNgpqRVYK2lT5cKICEn1OttjILk3xL6vGCk3\ngoHk31D7X9JNwNsRUc9XcA8k/4bZ/xFxE3CTpM8Df0H5dEXmGmnE83vA5ZJ+AjwI/FtJ90XEP0dE\nW0T8K+BvgC0AEfF2RLyZ2v+Y4jMoV+nKIfH7ebeKvwZMAZDUBEyMiJ/XagMiYmf6uZvyDVIvBt6Q\n9BvpO88EdlXkUjl668lzSPIfSO4NtO/7U1f7HgaWfyPtf0mfpHz4/BMV3Rtm//eVfyPt/worgN+p\nyCXT/d8whScivhARZ0fENMrX63w30gWpAOrjglRJo1K78oLUncA+SbMkifIFqY+nr+m5IBWOcUHq\nYEgap3dn3J0CzAU29vrOa4HHKnJZJGm0pGkp/66IeD3v/AeaewPt+6O6VbTrZt8PJv9G2f8q32X+\ns8CCiKh8XklD7P/+8m+g/f+bFd0WABsqcsl2/x9r5kG9voA5vDur7dPAP6fX1yv6fBz4p7Qz/wGY\nV7HsIsozR2RzAAAB2UlEQVS/uK8At1XExwAPA5sp3w3hnBrmPI3yTJHnU143pvgkypMiXgbWAKdV\nrPOFlOMmoG2o8h9o7g2076+kfFz6APA68Pf1tu8Hkz/lCTaNsP83A9tSnhtIs6IaaP/3mX8D7f+/\nTbk8T3lCwOS89r8vIDUzs1w1zKE2MzMbHlx4zMwsVy48ZmaWKxceMzPLlQuPmZnlyoXHzMxy5cJj\nVkOSTte7t8PfKWlHav9S0h1DnZ9ZPfB1PGYZkdQB/DIi/sdQ52JWTzziMcuWACQV9O7DC4uS7pW0\nTuUHdH1c0n9X+UFdf5/uddXz0K1Ole8ovLrnvnhmjc6Fx2xoTAP+DeXnmPxPYG1EfJjy7W/mSToZ\nuB34wyjfAPevga8NVbJmtdQwj0UwG0aC8n3VDkv6J8pPsfzfadlGyk99/CAwk/IzVABGUb7dvlnD\nc+ExGxpvA0TEEUmHKuJHKP9eCngxIn5vKJIzy5IPtZnlr/cjxPvyz0CrpN8FkHSypPOyTcssHy48\nZtmKip99tenVhvIDXQ9Rfq7JzZKep3yL/X+dZaJmefF0ajMzy5VHPGZmlisXHjMzy5ULj5mZ5cqF\nx8zMcuXCY2ZmuXLhMTOzXLnwmJlZrlx4zMwsV/8fjWz4/hQUFkUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1216d1350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VfUMq93f/XkS6w46zjn+jqj8WkasBPCYih2t3qqpKfOeMNBJ7Is69qv6z4Zga\n0Uj8iTr/koyJt43En5jzr6rDAIZF5M8AfBGV2/qhi+IK4/0AfltEXgawG8BviMhXVPVFVS2o6q8A\n+CqAIwCgqudV9Q17+xm7/V+gkhVra069E5ey5o8AdAGAiFgAOlT1FAKiqj+2/30dwNcA3ADgJyKy\n0X7OdwA4XhNL7dVSNU4j8TcSe4LOvZtYnXugsfiTdP6lMvH2wwD+Y83hiTn/TvEn6fzX2AXgV2ti\nCfX8h54wVPXTqnqtqm5G5d7ZP6nqH9gZEyLSAuDPAfyV/XWniKTs7Xeh8oL9P/vEvSkivyYiAuD3\nAfyD/TQPA/hDe/s/APhmUPGLyFq5NILrbQC2Aji45Dn/EMDf18TyMRFpFZHNdvxPquqxqONvNPYE\nnftFh9Vsx+bcryT+pJx/uTTx9iO6eOJtIs6/W/wJOv+/UHPYRwA8WxNLuOc/yA6aeg8AOVwaJbUd\nwIv2496aY34XwHP2SXgaQG/Nvl9G5Q/u+wDGatrTAP4PgJcAPAFgU4Axb0Zl5MEBO64ddvsGVDry\nv4dKufb1Nd/zaTvGwwAKpuJvNPYEnftbULnveg7AMQCPxu3cryR+AL+XkPP/EoBX7DifhT3KJkHn\n3zH+BJ3/v7VjOQDg7wBcE9X558Q9IiLyJQ7lzYmIKAGYMIiIyBcmDCIi8oUJg4iIfGHCICIiX5gw\niIjIFyYMIgAikpFLZa1/LCI/tLffEpEJ0/ERxQHnYRAtISIjAN5S1f9hOhaiOOEVBpEzAQARycul\nRb+KIvJlEZmWysI2vysi/10qC9w8atfiqS5WU5ZKhdGpat0uoqRjwiBqzGZU1nX5bQAPAHhMVf81\nKmU+ekVkDYBxAL+nlcKaXwIwaipYoiCFXt6cqIkoKnWfLorIc6is2vYNe99BVBbgeTeAblTWMACA\nFCpls4kSjwmDqDHnAUBV50XkQk37PCp/T4LK6pHvNxEcUZh4S4rIP6l/CF4EcLWI3AgAIrJGRN4T\nblhE0WDCIHKmNf86bWPJNlBZwPACKusKfE5EDqBSKvumMAMligqH1RIRkS+8wiAiIl+YMIiIyBcm\nDCIi8oUJg4iIfGHCICIiX5gwiIjIFyYMIiLyhQmDiIh8+f+MPK/EI/Ra6AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1218cb590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x121a5b750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Od74z6Wtr9SWdyWRCG//jmHI8SSabgHBoaIiTJ0/S0tLCmjVrlDwSqLE/wZIa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\nEREpS4lCRETK+v8Puieg4BFYnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121acb650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LL7zgW75v3z7Wrl3reyyovB588pOfrKi8EcRtQqOpgTCqNWHd8Kr/Qe3ts2/G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\nPynX/63ASuDfgHcUlSfl+gf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      "text/plain": [
       "<matplotlib.figure.Figure at 0x121c5c810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rLH7e9lpp2Iqurq6yw434dety6TwXhVtay90SPH/+fF/iiLpq3jfFi1/zcsTR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121cce150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in obs.dtype.names:\n",
    "    plt.figure()\n",
    "    plt.plot(obs['time'], obs[n], 'ko')\n",
    "    plt.xlabel('Time')\n",
    "    plt.ylabel(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "So we now can generate all of the observations of the object, including whether they're in the FOV with or without chipgaps. \n",
    "\n",
    "We still need to pull out the opsim data at each observation, and this is easiest when we still have the 'idxObs' list for each object. \n",
    "\n",
    "In order to get all of the info we need at each observation, we need to calculate the colors of all objects (to generate offsets between the standard magV and the filter used in each observation). \n",
    "We also have to calculate trailing losses and detection losses (see [Trailing Loss notebook](./Trailing%20Losses.ipynb)). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calcColors(sedname='C.dat'):\n",
    "    # Calculate SSO colors. \n",
    "    filterdir = os.getenv('LSST_THROUGHPUTS_BASELINE')\n",
    "    filterlist = ('u', 'g', 'r', 'i', 'z', 'y')\n",
    "    lsst ={}\n",
    "    for f in filterlist:\n",
    "        lsst[f] = Bandpass()\n",
    "        lsst[f].readThroughput(os.path.join(filterdir, 'total_'+f+'.dat'))\n",
    "    vband = Bandpass()\n",
    "    vband.readThroughput('harris_V.dat')\n",
    "    csed = Sed()\n",
    "    csed.readSED_flambda(sedname)\n",
    "    vmag = csed.calcMag(vband)\n",
    "    dmags = {}\n",
    "    for f in filterlist:\n",
    "        dmags[f] = csed.calcMag(lsst[f]) - vmag\n",
    "    return dmags"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u 1.6144033523\n",
      "g 0.302320621737\n",
      "r -0.172306859497\n",
      "i -0.291351785733\n",
      "z -0.298075537869\n",
      "y -0.30256349639\n",
      "---\n",
      "u 21.6144033523\n",
      "g 20.3023206217\n",
      "r 19.8276931405\n",
      "i 19.7086482143\n",
      "z 19.7019244621\n",
      "y 19.6974365036\n"
     ]
    }
   ],
   "source": [
    "filterlist = ('u', 'g', 'r', 'i', 'z', 'y')\n",
    "dmags = calcColors()\n",
    "for f in filterlist:\n",
    "    print f, dmags[f]\n",
    "# Example:\n",
    "print '---'\n",
    "v = 20\n",
    "for f in filterlist:\n",
    "    print f, v+dmags[f]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the additional things we must write out to add to the simdata, and write these + the opsim and object ephemeride data out for each observation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def joinObs(ephs, simdata, idxObs, sedname='C.dat', tol=1e-8, outfileName='out.txt', \n",
    "            seeingcol='finSeeing', expTime='visitExpTime'):\n",
    "    \"\"\"\n",
    "    Call for each object; write out the observations of each object.\n",
    "    \"\"\"\n",
    "    # calculate extra values (color, trailing loss, and detection loss terms)\n",
    "    # Calculate color term. \n",
    "    dmagColor = np.zeros(len(idxObs), float)\n",
    "    dmagDict = calcColors(sedname)\n",
    "    filterlist = np.unique(simdata[idxObs]['filter'])\n",
    "    for f in filterlist:\n",
    "        if f not in dmagDict:\n",
    "            raise UserWarning('Could not find filter %s in calculated colors!' %(f))\n",
    "        match = np.where(simdata[idxObs]['filter'] == f)[0]\n",
    "        dmagColor[match] = dmagDict[f]\n",
    "    # Calculate trailing and detection loses. \n",
    "    pm_LHS = np.array([  4.04959668e-04,   1.54946862e-03,  -7.32311940e-02,\n",
    "                         4.13138884e-01,  -2.13021674e-01,   1.03493047e+00], float)\n",
    "    pt_LHS = np.array([ -4.65513418e-04,   8.86629066e-03,  -6.20199786e-02,\n",
    "                        1.81920172e-01, 1.86156205e-02,   9.97466212e-01], float)\n",
    "    x = ephs['velocity'] * simdata['visitExpTime'][idxObs] / simdata['finSeeing'][idxObs] / 24.0\n",
    "    trail = 2.5*np.log10(np.polyval(pt_LHS, x))\n",
    "    detect = 2.5*np.log10(np.polyval(pm_LHS, x))\n",
    "    dmagTrailing = np.where(trail<0, 0, trail)\n",
    "    dmagDetect = np.where(detect<0, 0, detect)\n",
    "    \n",
    "    # Turn into a recarray so it's easier below.\n",
    "    dmags = np.rec.fromarrays([dmagColor, dmagTrailing, dmagDetect], \n",
    "                              names=['dmagColor', 'dmagTrailing', 'dmagDetect'])\n",
    "    \n",
    "    outCols = list(ephs.dtype.names) + list(simdata.dtype.names) + list(dmags.dtype.names)\n",
    "    if not os.path.isfile(outfileName):\n",
    "        outfile = open(outfileName, 'w')\n",
    "        writestring = '#'\n",
    "        for col in outCols:\n",
    "            writestring += '%s ' %(col)\n",
    "        print >> outfile, writestring\n",
    "    else:\n",
    "        outfile = open(outfileName, 'a')\n",
    "    \n",
    "    # Write results.\n",
    "    for eph, simdat, dm in zip(ephs, simdata[idxObs], dmags):\n",
    "        writestring = ''\n",
    "        for col in ephs.dtype.names:\n",
    "            writestring += '%s ' %(eph[col])\n",
    "        for col in simdat.dtype.names:\n",
    "            writestring += '%s ' %(simdat[col])\n",
    "        for col in dm.dtype.names:\n",
    "            writestring += '%s ' %(dm[col])\n",
    "        print >> outfile, writestring\n",
    "    outfile.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%%timeit\n",
    "for sso in orbits[0:3]:\n",
    "    oorbelems = packOorbElem(sso)\n",
    "    oorbephems, err = oo.pyoorb.oorb_ephemeris(in_orbits = oorbelems, in_obscode=807, in_date_ephems=ephTimes)\n",
    "    ephs = unpackEphs(oorbephems)\n",
    "    interpfuncs = interpolateEphs(ephs)\n",
    "    #idxObs = ssoInFov(interpfuncs, simdata)\n",
    "    idxObs = ssoInFovChip(interpfuncs, simdata)\n",
    "    tvis = simdata['expMJD'][idxObs]\n",
    "    obs = np.recarray([len(tvis)], dtype=ephs.dtype)\n",
    "    for n in interpfuncs:\n",
    "        obs[n] = interpfuncs[n](tvis)\n",
    "    obs['time'] = tvis        \n",
    "    joinObs(obs, simdata, idxObs, outfileName='test.txt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This required about 9 seconds for one object, 27s for 3 objects. Not too bad, especially as this gets us all the way to a complete output file. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>#delta</th>\n",
       "      <th>ra</th>\n",
       "      <th>dec</th>\n",
       "      <th>magV</th>\n",
       "      <th>time</th>\n",
       "      <th>dradt</th>\n",
       "      <th>ddecdt</th>\n",
       "      <th>phase</th>\n",
       "      <th>solarelon</th>\n",
       "      <th>velocity</th>\n",
       "      <th>...</th>\n",
       "      <th>fieldRA</th>\n",
       "      <th>fieldDec</th>\n",
       "      <th>rotSkyPos</th>\n",
       "      <th>filter</th>\n",
       "      <th>finSeeing</th>\n",
       "      <th>fiveSigmaDepth</th>\n",
       "      <th>visitExpTime</th>\n",
       "      <th>dmagColor</th>\n",
       "      <th>dmagTrailing</th>\n",
       "      <th>dmagDetect</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.407790</td>\n",
       "      <td>178.554054</td>\n",
       "      <td>7.853689</td>\n",
       "      <td>20.969449</td>\n",
       "      <td>49540.020904</td>\n",
       "      <td>2.528608</td>\n",
       "      <td>-1.748578</td>\n",
       "      <td>85.525555</td>\n",
       "      <td>70.905501</td>\n",
       "      <td>3.074311</td>\n",
       "      <td>...</td>\n",
       "      <td>3.141593</td>\n",
       "      <td>0.128524</td>\n",
       "      <td>4.063771</td>\n",
       "      <td>i</td>\n",
       "      <td>1.030507</td>\n",
       "      <td>23.394825</td>\n",
       "      <td>30</td>\n",
       "      <td>-0.291352</td>\n",
       "      <td>0.613400</td>\n",
       "      <td>1.110046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.407800</td>\n",
       "      <td>178.557465</td>\n",
       "      <td>7.851354</td>\n",
       "      <td>20.969423</td>\n",
       "      <td>49540.022240</td>\n",
       "      <td>2.528674</td>\n",
       "      <td>-1.748536</td>\n",
       "      <td>85.522353</td>\n",
       "      <td>70.908223</td>\n",
       "      <td>3.074342</td>\n",
       "      <td>...</td>\n",
       "      <td>3.087533</td>\n",
       "      <td>0.127822</td>\n",
       "      <td>4.095892</td>\n",
       "      <td>i</td>\n",
       "      <td>0.955558</td>\n",
       "      <td>23.445884</td>\n",
       "      <td>30</td>\n",
       "      <td>-0.291352</td>\n",
       "      <td>0.644290</td>\n",
       "      <td>1.166517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.535783</td>\n",
       "      <td>200.570397</td>\n",
       "      <td>-7.461039</td>\n",
       "      <td>21.186844</td>\n",
       "      <td>49551.046682</td>\n",
       "      <td>1.480196</td>\n",
       "      <td>-1.019487</td>\n",
       "      <td>64.953147</td>\n",
       "      <td>86.517550</td>\n",
       "      <td>1.797316</td>\n",
       "      <td>...</td>\n",
       "      <td>3.499825</td>\n",
       "      <td>-0.114112</td>\n",
       "      <td>4.460240</td>\n",
       "      <td>z</td>\n",
       "      <td>1.015369</td>\n",
       "      <td>22.018934</td>\n",
       "      <td>30</td>\n",
       "      <td>-0.298076</td>\n",
       "      <td>0.399883</td>\n",
       "      <td>0.668842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.664376</td>\n",
       "      <td>210.695185</td>\n",
       "      <td>-13.963565</td>\n",
       "      <td>21.584802</td>\n",
       "      <td>49558.967844</td>\n",
       "      <td>1.033271</td>\n",
       "      <td>-0.651569</td>\n",
       "      <td>56.410782</td>\n",
       "      <td>90.570445</td>\n",
       "      <td>1.221554</td>\n",
       "      <td>...</td>\n",
       "      <td>3.690123</td>\n",
       "      <td>-0.263957</td>\n",
       "      <td>3.592248</td>\n",
       "      <td>y</td>\n",
       "      <td>1.502535</td>\n",
       "      <td>20.617902</td>\n",
       "      <td>30</td>\n",
       "      <td>-0.302563</td>\n",
       "      <td>0.149971</td>\n",
       "      <td>0.170791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.093462</td>\n",
       "      <td>228.996794</td>\n",
       "      <td>-23.126167</td>\n",
       "      <td>22.704031</td>\n",
       "      <td>49582.055036</td>\n",
       "      <td>0.558375</td>\n",
       "      <td>-0.236947</td>\n",
       "      <td>43.816952</td>\n",
       "      <td>87.775357</td>\n",
       "      <td>0.606572</td>\n",
       "      <td>...</td>\n",
       "      <td>3.984755</td>\n",
       "      <td>-0.396222</td>\n",
       "      <td>4.936402</td>\n",
       "      <td>z</td>\n",
       "      <td>0.628552</td>\n",
       "      <td>22.636733</td>\n",
       "      <td>30</td>\n",
       "      <td>-0.298076</td>\n",
       "      <td>0.191929</td>\n",
       "      <td>0.246530</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 23 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     #delta          ra        dec       magV          time     dradt  \\\n",
       "0  0.407790  178.554054   7.853689  20.969449  49540.020904  2.528608   \n",
       "1  0.407800  178.557465   7.851354  20.969423  49540.022240  2.528674   \n",
       "2  0.535783  200.570397  -7.461039  21.186844  49551.046682  1.480196   \n",
       "3  0.664376  210.695185 -13.963565  21.584802  49558.967844  1.033271   \n",
       "4  1.093462  228.996794 -23.126167  22.704031  49582.055036  0.558375   \n",
       "\n",
       "     ddecdt      phase  solarelon  velocity     ...       fieldRA  fieldDec  \\\n",
       "0 -1.748578  85.525555  70.905501  3.074311     ...      3.141593  0.128524   \n",
       "1 -1.748536  85.522353  70.908223  3.074342     ...      3.087533  0.127822   \n",
       "2 -1.019487  64.953147  86.517550  1.797316     ...      3.499825 -0.114112   \n",
       "3 -0.651569  56.410782  90.570445  1.221554     ...      3.690123 -0.263957   \n",
       "4 -0.236947  43.816952  87.775357  0.606572     ...      3.984755 -0.396222   \n",
       "\n",
       "   rotSkyPos  filter  finSeeing  fiveSigmaDepth visitExpTime  dmagColor  \\\n",
       "0   4.063771       i   1.030507       23.394825           30  -0.291352   \n",
       "1   4.095892       i   0.955558       23.445884           30  -0.291352   \n",
       "2   4.460240       z   1.015369       22.018934           30  -0.298076   \n",
       "3   3.592248       y   1.502535       20.617902           30  -0.302563   \n",
       "4   4.936402       z   0.628552       22.636733           30  -0.298076   \n",
       "\n",
       "   dmagTrailing  dmagDetect  \n",
       "0      0.613400    1.110046  \n",
       "1      0.644290    1.166517  \n",
       "2      0.399883    0.668842  \n",
       "3      0.149971    0.170791  \n",
       "4      0.191929    0.246530  \n",
       "\n",
       "[5 rows x 23 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read the output file (ephemerides + opsim data + trailing/etc losses, for each observation) back in.\n",
    "ssoObs = pd.read_table('test.txt', sep='\\s*', engine='python')\n",
    "ssoObs.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From here, please hop to the [Prototype SSO Metrics notebook](./Prototype%20SSO%20Metrics.ipynb) to see what to do with this output! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--- \n",
    "Just checking on the footprint code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# For the footprint generation and conversion between galactic/equatorial coordinates.\n",
    "from lsst.obs.lsstSim import LsstSimMapper\n",
    "from lsst.sims.coordUtils import findChipName, observedFromICRS\n",
    "from lsst.sims.catalogs.generation.db.ObservationMetaData import ObservationMetaData\n",
    "\n",
    "mapper = LsstSimMapper()\n",
    "camera = mapper.camera\n",
    "epoch = 2000.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lynnej/anaconda/lib/python2.7/site-packages/sqlalchemy/sql/elements.py:3758: SAWarning: Textual SQL expression 'night=1' should be explicitly declared as text('night=1') (this warning may be suppressed after 10 occurrences)\n",
      "  {\"expr\": util.ellipses_string(element)})\n"
     ]
    }
   ],
   "source": [
    "import lsst.sims.maf.db as db\n",
    "opsdb = db.OpsimDatabase('enigma_1189_sqlite.db')\n",
    "simdata = opsdb.fetchMetricData(['expMJD', 'fieldRA', 'fieldDec', 'rotSkyPos'], 'night=1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import itertools\n",
    "fieldra = 0.0\n",
    "fielddec = 0.0\n",
    "rotskypos = np.radians(45.0)\n",
    "obs_metadata = ObservationMetaData(unrefractedRA = np.degrees(fieldra),\n",
    "                                   unrefractedDec = np.degrees(fielddec),\n",
    "                                   rotSkyPos = np.degrees(rotskypos),\n",
    "                                   mjd = simdata[0]['expMJD'])\n",
    "rai = np.arange(fieldra - np.radians(2), \n",
    "                fieldra + np.radians(2), np.radians(0.02))\n",
    "deci = np.arange(fielddec - np.radians(2.5), \n",
    "                 fielddec + np.radians(2.5), np.radians(0.02))\n",
    "ra = []\n",
    "dec = []\n",
    "for i in itertools.product(rai, deci):\n",
    "    ra.append(i[0])\n",
    "    dec.append(i[1])\n",
    "ra = np.array(ra)\n",
    "dec = np.array(dec)\n",
    "ra, dec = observedFromICRS(ra, dec, obs_metadata=obs_metadata, epoch=epoch)\n",
    "chipNames = findChipName(ra=ra, dec=dec, epoch=epoch, camera=camera, obs_metadata=obs_metadata)\n",
    "vis = np.zeros(len(chipNames))\n",
    "for i, chip in enumerate(chipNames):\n",
    "    if chip is not None:\n",
    "        vis[i] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2e46fd8d0>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3Y8/rbvLbOUseZZObbFK0W+n9ReY/iCJlpSTuozxSTRpXTdq9lVzJTaadQRdfbPHwA2TK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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x306e07e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "condition = np.where(vis == 1)[0]\n",
    "plt.plot((np.degrees(ra)+10)%360, np.degrees(dec), 'g.', markersize=0.2)\n",
    "plt.plot((np.degrees(ra[condition])+10)%360, np.degrees(dec[condition]), 'b.', markersize=0.3)\n",
    "plt.plot(np.degrees(fieldra)+10, np.degrees(fielddec), 'r.')\n",
    "plt.xlabel('RA')\n",
    "plt.ylabel('Dec')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}