loadReferenceObjects.py

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#
# LSST Data Management System
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# Copyright 2008-2017  AURA/LSST.
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__all__ = ["getRefFluxField", "getRefFluxKeys", "LoadReferenceObjectsTask", "LoadReferenceObjectsConfig",
           "ReferenceObjectLoader"]

import abc
import itertools

import astropy.time
import astropy.units
import numpy

import lsst.geom
import lsst.afw.table as afwTable
import lsst.pex.config as pexConfig
import lsst.pex.exceptions as pexExceptions
import lsst.pipe.base as pipeBase
import lsst.pex.exceptions as pexExcept
import lsst.log
from lsst import geom
from lsst import sphgeom
from lsst.daf.base import PropertyList


def isOldFluxField(name, units):
    """Return True if this name/units combination corresponds to an
    "old-style" reference catalog flux field.
    """
    unitsCheck = units != 'nJy'  # (units == 'Jy' or units == '' or units == '?')
    isFlux = name.endswith('_flux')
    isFluxSigma = name.endswith('_fluxSigma')
    isFluxErr = name.endswith('_fluxErr')
    return (isFlux or isFluxSigma or isFluxErr) and unitsCheck


def hasNanojanskyFluxUnits(schema):
    """Return True if the units of all flux and fluxErr are correct (nJy).
    """
    for field in schema:
        if isOldFluxField(field.field.getName(), field.field.getUnits()):
            return False
    return True


def getFormatVersionFromRefCat(refCat):
    """"Return the format version stored in a reference catalog header.

    Parameters
    ----------
    refCat : `lsst.afw.table.SimpleCatalog`
        Reference catalog to inspect.

    Returns
    -------
    version : `int` or `None`
        Format version integer, or `None` if the catalog has no metadata
        or the metadata does not include a "REFCAT_FORMAT_VERSION" key.
    """
    md = refCat.getMetadata()
    if md is None:
        return None
    try:
        return md.getScalar("REFCAT_FORMAT_VERSION")
    except KeyError:
        return None


def convertToNanojansky(catalog, log, doConvert=True):
    """Convert fluxes in a catalog from jansky to nanojansky.

    Parameters
    ----------
    catalog : `lsst.afw.table.SimpleCatalog`
        The catalog to convert.
    log : `lsst.log.Log`
        Log to send messages to.
    doConvert : `bool`, optional
        Return a converted catalog, or just identify the fields that need to be converted?
        This supports the "write=False" mode of `bin/convert_to_nJy.py`.

    Returns
    -------
    catalog : `lsst.afw.table.SimpleCatalog` or None
        The converted catalog, or None if ``doConvert`` is False.

    Notes
    -----
    Support for old units in reference catalogs will be removed after the
    release of late calendar year 2019.
    Use `meas_algorithms/bin/convert_to_nJy.py` to update your reference catalog.
    """
    # Do not share the AliasMap: for refcats, that gets created when the
    # catalog is read from disk and should not be propagated.
    mapper = lsst.afw.table.SchemaMapper(catalog.schema, shareAliasMap=False)
    mapper.addMinimalSchema(lsst.afw.table.SimpleTable.makeMinimalSchema())
    input_fields = []
    output_fields = []
    for field in catalog.schema:
        oldName = field.field.getName()
        oldUnits = field.field.getUnits()
        if isOldFluxField(oldName, oldUnits):
            units = 'nJy'
            # remap Sigma flux fields to Err, so we can drop the alias
            if oldName.endswith('_fluxSigma'):
                name = oldName.replace('_fluxSigma', '_fluxErr')
            else:
                name = oldName
            newField = lsst.afw.table.Field[field.dtype](name, field.field.getDoc(), units)
            mapper.addMapping(field.getKey(), newField)
            input_fields.append(field.field)
            output_fields.append(newField)
        else:
            mapper.addMapping(field.getKey())

    fluxFieldsStr = '; '.join("(%s, '%s')" % (field.getName(), field.getUnits()) for field in input_fields)

    if doConvert:
        newSchema = mapper.getOutputSchema()
        output = lsst.afw.table.SimpleCatalog(newSchema)
        output.extend(catalog, mapper=mapper)
        for field in output_fields:
            output[field.getName()] *= 1e9
        log.info(f"Converted refcat flux fields to nJy (name, units): {fluxFieldsStr}")
        return output
    else:
        log.info(f"Found old-style refcat flux fields (name, units): {fluxFieldsStr}")
        return None


class _FilterCatalog:
    """This is a private helper class which filters catalogs by
    row based on the row being inside the region used to initialize
    the class.

    Parameters
    ----------
    region : `lsst.sphgeom.Region`
        The spatial region which all objects should lie within
    """
    def __init__(self, region):
        self.region = region

    def __call__(self, refCat, catRegion):
        """This call method on an instance of this class takes in a reference
        catalog, and the region from which the catalog was generated.

        If the catalog region is entirely contained within the region used to
        initialize this class, then all the entries in the catalog must be
        within the region and so the whole catalog is returned.

        If the catalog region is not entirely contained, then the location for
        each record is tested against the region used to initialize the class.
        Records which fall inside this region are added to a new catalog, and
        this catalog is then returned.

        Parameters
        ---------
        refCat : `lsst.afw.table.SourceCatalog`
            SourceCatalog to be filtered.
        catRegion : `lsst.sphgeom.Region`
            Region in which the catalog was created
        """
        if catRegion.isWithin(self.region):
            # no filtering needed, region completely contains refcat
            return refCat

        filteredRefCat = type(refCat)(refCat.table)
        for record in refCat:
            if self.region.contains(record.getCoord().getVector()):
                filteredRefCat.append(record)
        return filteredRefCat


class ReferenceObjectLoader:
    """ This class facilitates loading reference catalogs with gen 3 middleware

    The middleware preflight solver will create a list of datarefs that may
    possibly overlap a given region. These datarefs are then used to construct
    and instance of this class. The class instance should then be passed into
    a task which needs reference catalogs. These tasks should then determine
    the exact region of the sky reference catalogs will be loaded for, and
    call a corresponding method to load the reference objects.
    """
    def __init__(self, dataIds, butler, config, log=None):
        """ Constructs an instance of ReferenceObjectLoader

        Parameters
        ----------
        dataIds : iterable of `lsst.daf.butler.DataIds`
            An iterable object of DataSetRefs which point to reference catalogs
            in a gen 3 repository
        bulter : `lsst.daf.bulter.Butler`
            A gen 3 butler instance
        log : `lsst.log.Log`
            Logger object used to write out messages. If `None` (default) the default
            lsst logger will be used

        """
        self.dataIds = dataIds
        self.butler = butler
        self.log = log or lsst.log.Log.getDefaultLogger()
        self.config = config

    @staticmethod
    def _makeBoxRegion(BBox, wcs, BBoxPadding):
        outerLocalBBox = geom.Box2D(BBox)
        innerLocalBBox = geom.Box2D(BBox)

        # Grow the bounding box to make sure the spherical geometry bbox will contain
        # the same region, as non-padded boxes may contain different regions because of optical distortion.
        # Also create an inner region that is sure to be inside the bbox
        outerLocalBBox.grow(BBoxPadding)
        innerLocalBBox.grow(-1*BBoxPadding)

        # Handle the fact that the inner bounding box shrunk to a zero sized region in at least one
        # dimension, in which case all reference catalogs must be checked fully against the input
        # bounding box
        if innerLocalBBox.getDimensions() == geom.Extent2D(0, 0):
            innerSkyRegion = sphgeom.Box()
        else:
            innerBoxCorners = innerLocalBBox.getCorners()
            innerSphCorners = [wcs.pixelToSky(corner).getVector() for corner in innerBoxCorners]

            innerSkyRegion = sphgeom.ConvexPolygon(innerSphCorners)

        # Convert the corners of the box to sky coordinates
        outerBoxCorners = outerLocalBBox.getCorners()
        outerSphCorners = [wcs.pixelToSky(corner).getVector() for corner in outerBoxCorners]

        outerSkyRegion = sphgeom.ConvexPolygon(outerSphCorners)

        return innerSkyRegion, outerSkyRegion, innerSphCorners, outerSphCorners

    def loadPixelBox(self, bbox, wcs, filterName=None, epoch=None, photoCalib=None, bboxPadding=100):
        """Load reference objects that are within a pixel-based rectangular region

        This algorithm works by creating a spherical box whose corners correspond
        to the WCS converted corners of the input bounding box (possibly padded).
        It then defines a filtering function which will look at a reference
        objects pixel position and accept objects that lie within the specified
        bounding box.

        The spherical box region and filtering function are passed to the generic
        loadRegion method which will load and filter the reference objects from
        the datastore and return a single catalog containing all reference objects

        Parameters
        ----------
        bbox : `lsst.geom.box2I`
            Box which bounds a region in pixel space
        wcs : `lsst.afw.geom.SkyWcs`
            Wcs object defining the pixel to sky (and inverse) transform for the space
            of pixels of the supplied bbox
        filterName : `str`
            Name of camera filter, or None or blank for the default filter
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.
        photoCalib : None
            Deprecated and ignored, only included for api compatibility
        bboxPadding : `int`
            Number describing how much to pad the input bbox by (in pixels), defaults
            to 100. This parameter is necessary because optical distortions in telescopes
            can cause a rectangular pixel grid to map into a non "rectangular" spherical
            region in sky coordinates. This padding is used to create a spherical
            "rectangle", which will for sure enclose the input box.  This padding is only
            used to determine if the reference catalog for a sky patch will be loaded from
            the data store, this function will filter out objects which lie within the
            padded region but fall outside the input bounding box region.

        Returns
        -------
        referenceCatalog : `lsst.afw.table.SimpleCatalog`
            Catalog containing reference objects inside the specified bounding box

        Raises
        ------
        `lsst.pex.exception.RuntimeError`
            Raised if no reference catalogs could be found for the specified region

        `lsst.pex.exception.TypeError`
            Raised if the loaded reference catalogs do not have matching schemas
        """
        innerSkyRegion, outerSkyRegion, _, _ = self._makeBoxRegion(bbox, wcs, bboxPadding)

        def _filterFunction(refCat, region):
            # Add columns to the reference catalog relating to center positions and use afwTable
            # to populate those columns
            refCat = self.remapReferenceCatalogSchema(refCat, position=True)
            afwTable.updateRefCentroids(wcs, refCat)
            # no need to filter the catalog if it is sure that it is entirely contained in the region
            # defined by given bbox
            if innerSkyRegion.contains(region):
                return refCat
            # Create a new reference catalog, and populate it with records which fall inside the bbox
            filteredRefCat = type(refCat)(refCat.table)
            centroidKey = afwTable.Point2DKey(refCat.schema['centroid'])
            for record in refCat:
                pixCoords = record[centroidKey]
                if bbox.contains(geom.Point2I(pixCoords)):
                    filteredRefCat.append(record)
            return filteredRefCat
        return self.loadRegion(outerSkyRegion, filtFunc=_filterFunction, epoch=epoch, filterName=filterName)

    def loadRegion(self, region, filtFunc=None, filterName=None, epoch=None):
        """ Load reference objects within a specified region

        This function loads the DataIds used to construct an instance of this class
        which intersect or are contained within the specified region. The reference
        catalogs which intersect but are not fully contained within the input region are
        further filtered by the specified filter function. This function will return a
        single source catalog containing all reference objects inside the specified region.

        Parameters
        ----------
        region : `lsst.sphgeom.Region`
            This can be any type that is derived from `lsst.sphgeom.region` and should
            define the spatial region for which reference objects are to be loaded.
        filtFunc : callable
            This optional parameter should be a callable object that takes a reference
            catalog and its corresponding region as parameters, filters the catalog by
            some criteria and returns the filtered reference catalog. If the value is
            left as the default (None) than an internal filter function is used which
            filters according to if a reference object falls within the input region.
        filterName : `str`
            Name of camera filter, or None or blank for the default filter
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.

        Returns
        -------
        referenceCatalog : `lsst.afw.table.SourceCatalog`
            Catalog containing reference objects which intersect the input region,
            filtered by the specified filter function

        Raises
        ------
        `lsst.pex.exception.RuntimeError`
            Raised if no reference catalogs could be found for the specified region

        `lsst.pex.exception.TypeError`
            Raised if the loaded reference catalogs do not have matching schemas

        """
        regionBounding = region.getBoundingBox()
        self.log.info("Loading reference objects from region bounded by {}, {} lat lon".format(
            regionBounding.getLat(), regionBounding.getLon()))
        if filtFunc is None:
            filtFunc = _FilterCatalog(region)
        # filter out all the regions supplied by the constructor that do not overlap
        overlapList = []
        for dataId in self.dataIds:
            # SphGeom supports some objects intersecting others, but is not symmetric,
            # try the intersect operation in both directions
            try:
                intersects = dataId.region.intersects(region)
            except TypeError:
                intersects = region.intersects(dataId.region)

            if intersects:
                overlapList.append(dataId)

        if len(overlapList) == 0:
            raise pexExceptions.RuntimeError("No reference tables could be found for input region")

        firstCat = self.butler.get('ref_cat', overlapList[0])
        refCat = filtFunc(firstCat, overlapList[0].region)
        trimmedAmount = len(firstCat) - len(refCat)

        # Load in the remaining catalogs
        for dataId in overlapList[1:]:
            tmpCat = self.butler.get('ref_cat', dataId)

            if tmpCat.schema != firstCat.schema:
                raise pexExceptions.TypeError("Reference catalogs have mismatching schemas")

            filteredCat = filtFunc(tmpCat, dataId.region)
            refCat.extend(filteredCat)
            trimmedAmount += len(tmpCat) - len(filteredCat)

        self.log.debug(f"Trimmed {trimmedAmount} out of region objects, leaving {len(refCat)}")
        self.log.info(f"Loaded {len(refCat)} reference objects")

        if epoch is not None and "pm_ra" in refCat.schema:
            # check for a catalog in a non-standard format
            if isinstance(refCat.schema["pm_ra"].asKey(), lsst.afw.table.KeyAngle):
                applyProperMotionsImpl(self.log, refCat, epoch)
            else:
                self.log.warn("Catalog pm_ra field is not an Angle; not applying proper motion")

        # Verify the schema is in the correct units and has the correct version; automatically convert
        # it with a warning if this is not the case.
        if not hasNanojanskyFluxUnits(refCat.schema) or not getFormatVersionFromRefCat(refCat) >= 1:
            self.log.warn("Found version 0 reference catalog with old style units in schema.")
            self.log.warn("run `meas_algorithms/bin/convert_refcat_to_nJy.py` to convert fluxes to nJy.")
            self.log.warn("See RFC-575 for more details.")
            refCat = convertToNanojansky(refCat, self.log)

        expandedCat = self.remapReferenceCatalogSchema(refCat, position=True)

        # Add flux aliases
        self.addFluxAliases(expandedCat, self.config.defaultFilter, self.config.filterMap)

        # Ensure that the returned reference catalog is continuous in memory
        if not expandedCat.isContiguous():
            expandedCat = refCat.copy(deep=True)

        fluxField = getRefFluxField(schema=expandedCat.schema, filterName=filterName)
        return pipeBase.Struct(refCat=expandedCat, fluxField=fluxField)

    def loadSkyCircle(self, ctrCoord, radius, filterName=None, epoch=None):
        """Load reference objects that lie within a circular region on the sky

        This method constructs a circular region from an input center and angular radius,
        loads reference catalogs which are contained in or intersect the circle, and
        filters reference catalogs which intersect down to objects which lie within
        the defined circle.

        Parameters
        ----------
        ctrCoord : `lsst.geom.SpherePoint`
            Point defining the center of the circular region
        radius : `lsst.geom.Angle`
            Defines the angular radius of the circular region
        filterName : `str`
            Name of camera filter, or None or blank for the default filter
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.

        Returns
        -------
        referenceCatalog : `lsst.afw.table.SourceCatalog`
            Catalog containing reference objects inside the specified bounding box

        Raises
        ------
        `lsst.pex.exception.RuntimeError`
            Raised if no reference catalogs could be found for the specified region

        `lsst.pex.exception.TypeError`
            Raised if the loaded reference catalogs do not have matching schemas

        """
        centerVector = ctrCoord.getVector()
        sphRadius = sphgeom.Angle(radius.asRadians())
        circularRegion = sphgeom.Circle(centerVector, sphRadius)
        return self.loadRegion(circularRegion, filterName=filterName, epoch=None)

    def joinMatchListWithCatalog(self, matchCat, sourceCat):
        """Relink an unpersisted match list to sources and reference
        objects.

        A match list is persisted and unpersisted as a catalog of IDs
        produced by afw.table.packMatches(), with match metadata
        (as returned by the astrometry tasks) in the catalog's metadata
        attribute. This method converts such a match catalog into a match
        list, with links to source records and reference object records.

        Parameters
        ----------
        matchCat : `lsst.afw.table.BaseCatalog`
            Unpersisted packed match list.
            ``matchCat.table.getMetadata()`` must contain match metadata,
            as returned by the astrometry tasks.
        sourceCat : `lsst.afw.table.SourceCatalog`
            Source catalog. As a side effect, the catalog will be sorted
            by ID.

        Returns
        -------
        matchList : `lsst.afw.table.ReferenceMatchVector`
            Match list.
        """
        return joinMatchListWithCatalogImpl(self, matchCat, sourceCat)

    @classmethod
    def getMetadataBox(cls, bbox, wcs, filterName=None, photoCalib=None, epoch=None, bboxPadding=100):
        """Return metadata about the load

        This metadata is used for reloading the catalog (e.g., for
        reconstituting a normalised match list.)

        Parameters
        ----------
        bbox : `lsst.geom.Box2I`
            Bounding bos for the pixels
        wcs : `lsst.afw.geom.SkyWcs
            WCS object
        filterName : `str` or None
            filterName of the camera filter, or None or blank for the default filter
        photoCalib : None
            Deprecated, only included for api compatibility
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.
        bboxPadding : `int`
            Number describing how much to pad the input bbox by (in pixels), defaults
            to 100. This parameter is necessary because optical distortions in telescopes
            can cause a rectangular pixel grid to map into a non "rectangular" spherical
            region in sky coordinates. This padding is used to create a spherical
            "rectangle", which will for sure enclose the input box.  This padding is only
            used to determine if the reference catalog for a sky patch will be loaded from
            the data store, this function will filter out objects which lie within the
            padded region but fall outside the input bounding box region.
        Returns
        -------
        md : `lsst.daf.base.PropertyList`
        """
        _, _, innerCorners, outerCorners = cls._makeBoxRegion(bbox, wcs, bboxPadding)
        md = PropertyList()
        for box, corners in zip(("INNER", "OUTER"), (innerCorners, outerCorners)):
            for (name, corner) in zip(("UPPER_LEFT", "UPPER_RIGHT", "LOWER_LEFT", "LOWER_RIGHT"),
                                      corners):
                md.add(f"{box}_{name}_RA", geom.SpherePoint(corner).getRa().asDegrees(), f"{box}_corner")
                md.add(f"{box}_{name}_DEC", geom.SpherePoint(corner).getDec().asDegrees(), f"{box}_corner")
        md.add("SMATCHV", 1, 'SourceMatchVector version number')
        filterName = "UNKNOWN" if filterName is None else str(filterName)
        md.add('FILTER', filterName, 'filter name for photometric data')
        # Calling str on the epoch is a workaround for code that never worked anyway and was not used
        # see DM-17438
        md.add('EPOCH', "NONE" if epoch is None else str(epoch), 'Epoch (TAI MJD) for catalog')
        return md

    @staticmethod
    def getMetadataCircle(coord, radius, filterName, photoCalib=None, epoch=None):
        """Return metadata about the load

        This metadata is used for reloading the catalog (e.g. for reconstituting
        a normalized match list.)

        Parameters
        ----------
        coord : `lsst.geom.SpherePoint`
            ICRS center of a circle
        radius : `lsst.geom.angle`
            radius of a circle
        filterName : `str` or None
            filterName of the camera filter, or None or blank for the default filter
        photoCalib : None
            Deprecated, only included for api compatibility
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.

        Returns
        -------
        md : `lsst.daf.base.PropertyList`
        """
        md = PropertyList()
        md.add('RA', coord.getRa().asDegrees(), 'field center in degrees')
        md.add('DEC', coord.getDec().asDegrees(), 'field center in degrees')
        md.add('RADIUS', radius.asDegrees(), 'field radius in degrees, minimum')
        md.add('SMATCHV', 1, 'SourceMatchVector version number')
        filterName = "UNKNOWN" if filterName is None else str(filterName)
        md.add('FILTER', filterName, 'filter name for photometric data')
        md.add('EPOCH', "NONE" if epoch is None else epoch, 'Epoch (TAI MJD) for catalog')
        return md

    @staticmethod
    def addFluxAliases(refCat, defaultFilter, filterReferenceMap):
        """This function creates a new catalog containing the information of the input refCat
        as well as added flux columns and aliases between camera and reference flux.

        Parameters
        ----------
        refCat : `lsst.afw.table.SimpleCatalog`
            Catalog of reference objects
        defaultFilter : `str`
            Name of the default reference filter
        filterReferenceMap : `dict` of `str`
            Dictionary with keys corresponding to a filter name, and values which
            correspond to the name of the reference filter.

        Returns
        -------
        refCat : `lsst.afw.table.SimpleCatalog`
            Reference catalog with columns added to track reference filters

        Raises
        ------
        `RuntimeError`
            If specified reference filter name is not a filter specifed as a key in the
            reference filter map.
        """
        refCat = ReferenceObjectLoader.remapReferenceCatalogSchema(refCat,
                                                                   filterNameList=filterReferenceMap.keys())
        aliasMap = refCat.schema.getAliasMap()

        if filterReferenceMap is None:
            filterReferenceMap = {}
        for filterName, refFilterName in itertools.chain([(None, defaultFilter)],
                                                         filterReferenceMap.items()):
            if refFilterName:
                camFluxName = filterName + "_camFlux" if filterName is not None else "camFlux"
                refFluxName = refFilterName + "_flux"
                if refFluxName not in refCat.schema:
                    raise RuntimeError("Unknown reference filter %s" % (refFluxName,))
                aliasMap.set(camFluxName, refFluxName)

                refFluxErrName = refFluxName + "Err"
                camFluxErrName = camFluxName + "Err"
                aliasMap.set(camFluxErrName, refFluxErrName)

        return refCat

    @staticmethod
    def remapReferenceCatalogSchema(refCat, *, filterNameList=None, position=False, photometric=False):
        """This function takes in a reference catalog and creates a new catalog with additional
        columns defined the remaining function arguments.

        Parameters
        ----------
        refCat : `lsst.afw.table.SimpleCatalog`
            Reference catalog to map to new catalog

        Returns
        -------
        expandedCat : `lsst.afw.table.SimpleCatalog`
            Deep copy of input reference catalog with additional columns added
        """
        mapper = afwTable.SchemaMapper(refCat.schema, True)
        mapper.addMinimalSchema(refCat.schema, True)
        mapper.editOutputSchema().disconnectAliases()
        if filterNameList:
            for filterName in filterNameList:
                mapper.editOutputSchema().addField(f"{filterName}_flux",
                                                   type=numpy.float64,
                                                   doc=f"flux in filter {filterName}",
                                                   units="Jy"
                                                   )
                mapper.editOutputSchema().addField(f"{filterName}_fluxErr",
                                                   type=numpy.float64,
                                                   doc=f"flux uncertanty in filter {filterName}",
                                                   units="Jy"
                                                   )

        if position:
            mapper.editOutputSchema().addField("centroid_x", type=float, doReplace=True)
            mapper.editOutputSchema().addField("centroid_y", type=float, doReplace=True)
            mapper.editOutputSchema().addField("hasCentroid", type="Flag", doReplace=True)
            mapper.editOutputSchema().getAliasMap().set("slot_Centroid", "centroid")

        if photometric:
            mapper.editOutputSchema().addField("photometric",
                                               type="Flag",
                                               doc="set if the object can be used for photometric" +
                                                   "calibration",
                                               )
            mapper.editOutputSchema().addField("resolved",
                                               type="Flag",
                                               doc="set if the object is spatially resolved"
                                               )
            mapper.editOutputSchema().addField("variable",
                                               type="Flag",
                                               doc="set if the object has variable brightness"
                                               )

        expandedCat = afwTable.SimpleCatalog(mapper.getOutputSchema())
        expandedCat.setMetadata(refCat.getMetadata())
        expandedCat.extend(refCat, mapper=mapper)

        return expandedCat


def getRefFluxField(schema, filterName=None):
    """Get the name of a flux field from a schema.

    if filterName is specified:
        return *filterName*_camFlux if present
        else return *filterName*_flux if present (camera filter name matches reference filter name)
        else throw RuntimeError
    else:
        return camFlux, if present,
        else throw RuntimeError

    Parameters
    ----------
    schema : `lsst.afw.table.Schema`
        Reference catalog schema.
    filterName : `str`
        Name of camera filter.

    Returns
    -------
    fluxFieldName : `str`
        Name of flux field.

    Raises
    ------
    RuntimeError
        If an appropriate field is not found.
    """
    if not isinstance(schema, afwTable.Schema):
        raise RuntimeError("schema=%s is not a schema" % (schema,))
    if filterName:
        fluxFieldList = [filterName + "_camFlux", filterName + "_flux"]
    else:
        fluxFieldList = ["camFlux"]
    for fluxField in fluxFieldList:
        if fluxField in schema:
            return fluxField

    raise RuntimeError("Could not find flux field(s) %s" % (", ".join(fluxFieldList)))


def getRefFluxKeys(schema, filterName=None):
    """Return keys for flux and flux error.

    Parameters
    ----------
    schema : `lsst.afw.table.Schema`
        Reference catalog schema.
    filterName : `str`
        Name of camera filter.

    Returns
    -------
    keys : `tuple` of (`lsst.afw.table.Key`, `lsst.afw.table.Key`)
        Two keys:

        - flux key
        - flux error key, if present, else None

    Raises
    ------
    RuntimeError
        If flux field not found.
    """
    fluxField = getRefFluxField(schema, filterName)
    fluxErrField = fluxField + "Err"
    fluxKey = schema[fluxField].asKey()
    try:
        fluxErrKey = schema[fluxErrField].asKey()
    except Exception:
        fluxErrKey = None
    return (fluxKey, fluxErrKey)


class LoadReferenceObjectsConfig(pexConfig.Config):
    pixelMargin = pexConfig.RangeField(
        doc="Padding to add to 4 all edges of the bounding box (pixels)",
        dtype=int,
        default=300,
        min=0,
    )
    defaultFilter = pexConfig.Field(
        doc="Default reference catalog filter to use if filter not specified in exposure; "
        "if blank then filter must be specified in exposure",
        dtype=str,
        default="",
    )
    filterMap = pexConfig.DictField(
        doc="Mapping of camera filter name: reference catalog filter name; "
        "each reference filter must exist",
        keytype=str,
        itemtype=str,
        default={},
    )
    requireProperMotion = pexConfig.Field(
        doc="Require that the fields needed to correct proper motion "
            "(epoch, pm_ra and pm_dec) are present?",
        dtype=bool,
        default=False,
    )

# The following comment block adds a link to this task from the Task Documentation page.



class LoadReferenceObjectsTask(pipeBase.Task, metaclass=abc.ABCMeta):
    r"""!Abstract base class to load objects from reference catalogs

    @anchor LoadReferenceObjectsTask_

    @section meas_algorithms_loadReferenceObjects_Contents Contents

     - @ref meas_algorithms_loadReferenceObjects_Purpose
     - @ref meas_algorithms_loadReferenceObjects_Initialize
     - @ref meas_algorithms_loadReferenceObjects_IO
     - @ref meas_algorithms_loadReferenceObjects_Schema
     - @ref meas_algorithms_loadReferenceObjects_Config

    @section meas_algorithms_loadReferenceObjects_Purpose  Description

    Abstract base class for tasks that load objects from a reference catalog
    in a particular region of the sky.

    Implementations must subclass this class, override the loadSkyCircle method,
    and will typically override the value of ConfigClass with a task-specific config class.

    @section meas_algorithms_loadReferenceObjects_Initialize   Task initialisation

    @copydoc \_\_init\_\_

    @section meas_algorithms_loadReferenceObjects_IO       Invoking the Task

    @copydoc loadPixelBox

    @section meas_algorithms_loadReferenceObjects_Schema       Schema of the reference object catalog

    Reference object catalogs are instances of lsst.afw.table.SimpleCatalog with the following schema
    (other fields may also be present).
    The units use astropy quantity conventions, so a 2 suffix means squared.
    See also makeMinimalSchema.
    - coord: ICRS position of star on sky (an lsst.geom.SpherePoint)
    - centroid: position of star on an exposure, if relevant (an lsst.afw.Point2D)
    - hasCentroid: is centroid usable? (a Flag)
    - *referenceFilterName*_flux: brightness in the specified reference catalog filter (nJy)
        Note: you can use astropy.units to convert from AB Magnitude to nJy:
            `u.Magnitude(value, u.ABmag).to_value(u.nJy)`
    - *referenceFilterName*_fluxErr (optional): brightness standard deviation (nJy);
        omitted if no data is available; possibly nan if data is available for some objects but not others
    - camFlux: brightness in default camera filter (nJy); omitted if defaultFilter not specified
    - camFluxErr: brightness standard deviation for default camera filter;
        omitted if defaultFilter not specified or standard deviation not available that filter
    - *cameraFilterName*_camFlux: brightness in specified camera filter (nJy)
    - *cameraFilterName*_camFluxErr (optional): brightness standard deviation
        in specified camera filter (nJy); omitted if no data is available;
        possibly nan if data is available for some objects but not others
    - photometric (optional): is the object usable for photometric calibration? (a Flag)
    - resolved (optional): is the object spatially resolved? (a Flag)
    - variable (optional): does the object have variable brightness? (a Flag)
    - coord_raErr: uncertainty in `coord` along the direction of right ascension (radian, an Angle)
                    = uncertainty in ra * cos(dec); nan if unknown
    - coord_decErr: uncertainty in `coord` along the direction of declination (radian, an Angle);
        nan if unknown

    The following are optional; fields should only be present if the
    information is available for at least some objects.
    Numeric values are `nan` if unknown:
    - epoch: date of observation as TAI MJD (day)

    - pm_ra: proper motion along the direction of right ascension (rad/year, an Angle) = dra/dt * cos(dec)
    - pm_dec: proper motion along the direction of declination (rad/year, and Angle)
    - pm_raErr: uncertainty in `pm_ra` (rad/year)
    - pm_decErr: uncertainty in `pm_dec` (rad/year)
    - pm_ra_dec_Cov: covariance between pm_ra and pm_dec (rad2/year2)
    - pm_flag: set if proper motion, error or covariance is bad

    - parallax: parallax (rad, an Angle)
    - parallaxErr: uncertainty in `parallax` (rad)
    - parallax_flag: set if parallax value or parallaxErr is bad

    - coord_ra_pm_ra_Cov: covariance between coord_ra and pm_ra (rad2/year)
    - coord_ra_pm_dec_Cov: covariance between coord_ra and pm_dec (rad2/year)
    - coord_ra_parallax_Cov: covariance between coord_ra and parallax (rad2/year)
    - coord_dec_pm_ra_Cov: covariance between coord_dec and pm_ra (rad2/year)
    - coord_dec_pm_dec_Cov: covariance between coord_dec and pm_dec (rad2/year)
    - coord_dec_parallax_Cov: covariance between coord_dec and parallax (rad2/year)
    - pm_ra_parallax_Cov: covariance between pm_ra and parallax (rad2/year)
    - pm_dec_parallax_Cov: covariance between pm_dec and parallax (rad2/year)

    @section meas_algorithms_loadReferenceObjects_Config       Configuration parameters

    See @ref LoadReferenceObjectsConfig for a base set of configuration parameters.
    Most subclasses will add configuration variables.
    """
    ConfigClass = LoadReferenceObjectsConfig
    _DefaultName = "LoadReferenceObjects"

    def __init__(self, butler=None, *args, **kwargs):
        """Construct a LoadReferenceObjectsTask

        Parameters
        ----------
        butler : `lsst.daf.persistence.Butler`
            Data butler, for access reference catalogs.
        """
        pipeBase.Task.__init__(self, *args, **kwargs)
        self.butler = butler

    @pipeBase.timeMethod
    def loadPixelBox(self, bbox, wcs, filterName=None, photoCalib=None, epoch=None):
        """Load reference objects that overlap a rectangular pixel region.

        Parameters
        ----------
        bbox : `lsst.geom.Box2I` or `lsst.geom.Box2D`
            Bounding box for pixels.
        wcs : `lsst.afw.geom.SkyWcs`
            WCS; used to convert pixel positions to sky coordinates
            and vice-versa.
        filterName : `str`
            Name of filter, or `None` or `""` for the default filter.
            This is used for flux values in case we have flux limits
            (which are not yet implemented).
        photoCalib : `lsst.afw.image.PhotoCalib` (optional)
            Calibration, or `None` if unknown.
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.

        Returns
        -------
        results : `lsst.pipe.base.Struct`
            A Struct containing the following fields:
            refCat : `lsst.afw.catalog.SimpleCatalog`
                A catalog of reference objects with the standard
                schema, as documented in the main doc string for
                `LoadReferenceObjects`.
                The catalog is guaranteed to be contiguous.
            fluxField : `str`
                Name of flux field for specified `filterName`.

        Notes
        -----
        The search algorithm works by searching in a region in sky
        coordinates whose center is the center of the bbox and radius
        is large enough to just include all 4 corners of the bbox.
        Stars that lie outside the bbox are then trimmed from the list.
        """
        circle = self._calculateCircle(bbox, wcs)

        # find objects in circle
        self.log.info("Loading reference objects using center %s and radius %s deg" %
                      (circle.coord, circle.radius.asDegrees()))
        loadRes = self.loadSkyCircle(circle.coord, circle.radius, filterName)
        refCat = loadRes.refCat
        numFound = len(refCat)

        # trim objects outside bbox
        refCat = self._trimToBBox(refCat=refCat, bbox=circle.bbox, wcs=wcs)
        numTrimmed = numFound - len(refCat)
        self.log.debug("trimmed %d out-of-bbox objects, leaving %d", numTrimmed, len(refCat))
        self.log.info("Loaded %d reference objects", len(refCat))

        # make sure catalog is contiguous
        if not refCat.isContiguous():
            loadRes.refCat = refCat.copy(deep=True)

        return loadRes

    @abc.abstractmethod
    def loadSkyCircle(self, ctrCoord, radius, filterName=None, epoch=None):
        """Load reference objects that overlap a circular sky region.

        Parameters
        ----------
        ctrCoord : `lsst.geom.SpherePoint`
            ICRS center of search region.
        radius : `lsst.geom.Angle`
            Radius of search region.
        filterName : `str` (optional)
            Name of filter, or `None` or `""` for the default filter.
            This is used for flux values in case we have flux limits
            (which are not yet implemented).
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.

        Returns
        -------
        results : `lsst.pipe.base.Struct`
            A Struct containing the following fields:
            refCat : `lsst.afw.catalog.SimpleCatalog`
                A catalog of reference objects with the standard
                schema, as documented in the main doc string for
                `LoadReferenceObjects`.
                The catalog is guaranteed to be contiguous.
            fluxField : `str`
                Name of flux field for specified `filterName`.

        Notes
        -----
        Note that subclasses are responsible for performing the proper motion
        correction, since this is the lowest-level interface for retrieving
        the catalog.
        """
        return

    @staticmethod
    def _trimToBBox(refCat, bbox, wcs):
        """Remove objects outside a given pixel bounding box and set
        centroid and hasCentroid fields.

        Parameters
        ----------
        refCat : `lsst.afw.table.SimpleCatalog`
            A catalog of objects. The schema must include fields
            "coord", "centroid" and "hasCentroid".
            The "coord" field is read.
            The "centroid" and "hasCentroid" fields are set.
        bbox : `lsst.geom.Box2D`
            Pixel region
        wcs : `lsst.afw.geom.SkyWcs`
            WCS; used to convert sky coordinates to pixel positions.

        @return a catalog of reference objects in bbox, with centroid and hasCentroid fields set
        """
        afwTable.updateRefCentroids(wcs, refCat)
        centroidKey = afwTable.Point2DKey(refCat.schema["centroid"])
        retStarCat = type(refCat)(refCat.table)
        for star in refCat:
            point = star.get(centroidKey)
            if bbox.contains(point):
                retStarCat.append(star)
        return retStarCat

    def _addFluxAliases(self, schema):
        """Add aliases for camera filter fluxes to the schema.

        If self.config.defaultFilter then adds these aliases:
            camFlux:      <defaultFilter>_flux
            camFluxErr: <defaultFilter>_fluxErr, if the latter exists

        For each camFilter: refFilter in self.config.filterMap adds these aliases:
            <camFilter>_camFlux:      <refFilter>_flux
            <camFilter>_camFluxErr: <refFilter>_fluxErr, if the latter exists

        Parameters
        ----------
        schema : `lsst.afw.table.Schema`
            Schema for reference catalog.

        Throws
        ------
        RuntimeError
            If any reference flux field is missing from the schema.
        """
        aliasMap = schema.getAliasMap()

        def addAliasesForOneFilter(filterName, refFilterName):
            """Add aliases for a single filter

            Parameters
            ----------
            filterName : `str` (optional)
                Camera filter name. The resulting alias name is
                <filterName>_camFlux, or simply "camFlux" if `filterName`
                is `None` or `""`.
            refFilterName : `str`
                Reference catalog filter name; the field
                <refFilterName>_flux must exist.
            """
            camFluxName = filterName + "_camFlux" if filterName is not None else "camFlux"
            refFluxName = refFilterName + "_flux"
            if refFluxName not in schema:
                raise RuntimeError("Unknown reference filter %s" % (refFluxName,))
            aliasMap.set(camFluxName, refFluxName)
            refFluxErrName = refFluxName + "Err"
            if refFluxErrName in schema:
                camFluxErrName = camFluxName + "Err"
                aliasMap.set(camFluxErrName, refFluxErrName)

        if self.config.defaultFilter:
            addAliasesForOneFilter(None, self.config.defaultFilter)

        for filterName, refFilterName in self.config.filterMap.items():
            addAliasesForOneFilter(filterName, refFilterName)

    @staticmethod
    def makeMinimalSchema(filterNameList, *, addCentroid=True,
                          addIsPhotometric=False, addIsResolved=False,
                          addIsVariable=False, coordErrDim=2,
                          addProperMotion=False, properMotionErrDim=2,
                          addParallax=False, addParallaxErr=True):
        """Make a standard schema for reference object catalogs.

        Parameters
        ----------
        filterNameList : `list` of `str`
            List of filter names. Used to create <filterName>_flux fields.
        addIsPhotometric : `bool`
            If True then add field "photometric".
        addIsResolved : `bool`
            If True then add field "resolved".
        addIsVariable : `bool`
            If True then add field "variable".
        coordErrDim : `int`
            Number of coord error fields; must be one of 0, 2, 3:

            - If 2 or 3: add fields "coord_raErr" and "coord_decErr".
            - If 3: also add field "coord_radecErr".
        addProperMotion : `bool`
            If True add fields "epoch", "pm_ra", "pm_dec" and "pm_flag".
        properMotionErrDim : `int`
            Number of proper motion error fields; must be one of 0, 2, 3;
            ignored if addProperMotion false:
            - If 2 or 3: add fields "pm_raErr" and "pm_decErr".
            - If 3: also add field "pm_radecErr".
        addParallax : `bool`
            If True add fields "epoch", "parallax", "parallaxErr"
            and "parallax_flag".
        addParallaxErr : `bool`
            If True add field "parallaxErr"; ignored if addParallax false.

        Returns
        -------
        schema : `lsst.afw.table.Schema`
            Schema for reference catalog, an
            `lsst.afw.table.SimpleCatalog`.

        Notes
        -----
        Reference catalogs support additional covariances, such as
        covariance between RA and proper motion in declination,
        that are not supported by this method, but can be added after
        calling this method.
        """
        schema = afwTable.SimpleTable.makeMinimalSchema()
        if addCentroid:
            afwTable.Point2DKey.addFields(
                schema,
                "centroid",
                "centroid on an exposure, if relevant",
                "pixel",
            )
            schema.addField(
                field="hasCentroid",
                type="Flag",
                doc="is position known?",
            )
        for filterName in filterNameList:
            schema.addField(
                field="%s_flux" % (filterName,),
                type=numpy.float64,
                doc="flux in filter %s" % (filterName,),
                units="nJy",
            )
        for filterName in filterNameList:
            schema.addField(
                field="%s_fluxErr" % (filterName,),
                type=numpy.float64,
                doc="flux uncertainty in filter %s" % (filterName,),
                units="nJy",
            )
        if addIsPhotometric:
            schema.addField(
                field="photometric",
                type="Flag",
                doc="set if the object can be used for photometric calibration",
            )
        if addIsResolved:
            schema.addField(
                field="resolved",
                type="Flag",
                doc="set if the object is spatially resolved",
            )
        if addIsVariable:
            schema.addField(
                field="variable",
                type="Flag",
                doc="set if the object has variable brightness",
            )
        if coordErrDim not in (0, 2, 3):
            raise ValueError("coordErrDim={}; must be (0, 2, 3)".format(coordErrDim))
        if coordErrDim > 0:
            afwTable.CovarianceMatrix2fKey.addFields(
                schema=schema,
                prefix="coord",
                names=["ra", "dec"],
                units=["rad", "rad"],
                diagonalOnly=(coordErrDim == 2),
            )

        if addProperMotion or addParallax:
            schema.addField(
                field="epoch",
                type=numpy.float64,
                doc="date of observation (TAI, MJD)",
                units="day",
            )

        if addProperMotion:
            schema.addField(
                field="pm_ra",
                type="Angle",
                doc="proper motion in the right ascension direction = dra/dt * cos(dec)",
                units="rad/year",
            )
            schema.addField(
                field="pm_dec",
                type="Angle",
                doc="proper motion in the declination direction",
                units="rad/year",
            )
            if properMotionErrDim not in (0, 2, 3):
                raise ValueError("properMotionErrDim={}; must be (0, 2, 3)".format(properMotionErrDim))
            if properMotionErrDim > 0:
                afwTable.CovarianceMatrix2fKey.addFields(
                    schema=schema,
                    prefix="pm",
                    names=["ra", "dec"],
                    units=["rad/year", "rad/year"],
                    diagonalOnly=(properMotionErrDim == 2),
                )
            schema.addField(
                field="pm_flag",
                type="Flag",
                doc="Set if proper motion or proper motion error is bad",
            )

        if addParallax:
            schema.addField(
                field="parallax",
                type=numpy.float64,
                doc="parallax",
                units="rad",
            )
            if addParallaxErr:
                schema.addField(
                    field="parallaxErr",
                    type=numpy.float64,
                    doc="uncertainty in parallax",
                    units="rad",
                )
            schema.addField(
                field="parallax_flag",
                type="Flag",
                doc="Set if parallax or parallax error is bad",
            )
        return schema

    def _calculateCircle(self, bbox, wcs):
        """Compute on-sky center and radius of search region.

        Parameters
        ----------
        bbox : `lsst.geom.Box2I` or `lsst.geom.Box2D`
            Pixel bounding box.
        wcs : `lsst.afw.geom.SkyWcs`
            WCS; used to convert pixel positions to sky coordinates.

        Returns
        -------
        results : `lsst.pipe.base.Struct`
            A Struct containing:

            - coord : `lsst.geom.SpherePoint`
                ICRS center of the search region.
            - radius : `lsst.geom.Angle`
                Radius of the search region.
            - bbox : `lsst.geom.Box2D`
                Bounding box used to compute the circle.
        """
        bbox = lsst.geom.Box2D(bbox)  # make sure bbox is double and that we have a copy
        bbox.grow(self.config.pixelMargin)
        coord = wcs.pixelToSky(bbox.getCenter())
        radius = max(coord.separation(wcs.pixelToSky(pp)) for pp in bbox.getCorners())
        return pipeBase.Struct(coord=coord, radius=radius, bbox=bbox)

    def getMetadataBox(self, bbox, wcs, filterName=None, photoCalib=None, epoch=None):
        """Return metadata about the load.

        This metadata is used for reloading the catalog (e.g., for
        reconstituting a normalised match list.

        Parameters
        ----------
        bbox : `lsst.geom.Box2I` or `lsst.geom.Box2D`
            Pixel bounding box.
        wcs : `lsst.afw.geom.SkyWcs`
            WCS; used to convert pixel positions to sky coordinates.
        filterName : `str`
            Name of camera filter, or `None` or `""` for the default
            filter.
        photoCalib : `lsst.afw.image.PhotoCalib` (optional)
            Calibration, or `None` if unknown.
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.

        Returns
        -------
        metadata : lsst.daf.base.PropertyList
            Metadata about the load.
        """
        circle = self._calculateCircle(bbox, wcs)
        return self.getMetadataCircle(circle.coord, circle.radius, filterName, photoCalib)

    def getMetadataCircle(self, coord, radius, filterName, photoCalib=None, epoch=None):
        """Return metadata about the load.

        This metadata is used for reloading the catalog (e.g., for
        reconstituting a normalised match list.

        Parameters
        ----------
        coord : `lsst.geom.SpherePoint`
            ICRS center of the search region.
        radius : `lsst.geom.Angle`
            Radius of the search region.
        filterName : `str`
            Name of camera filter, or `None` or `""` for the default
            filter.
        photoCalib : `lsst.afw.image.PhotoCalib` (optional)
            Calibration, or `None` if unknown.
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.

        Returns
        -------
        metadata : lsst.daf.base.PropertyList
            Metadata about the load
        """
        md = PropertyList()
        md.add('RA', coord.getRa().asDegrees(), 'field center in degrees')
        md.add('DEC', coord.getDec().asDegrees(), 'field center in degrees')
        md.add('RADIUS', radius.asDegrees(), 'field radius in degrees, minimum')
        md.add('SMATCHV', 1, 'SourceMatchVector version number')
        filterName = "UNKNOWN" if filterName is None else str(filterName)
        md.add('FILTER', filterName, 'filter name for photometric data')
        md.add('EPOCH', "NONE" if epoch is None else epoch, 'Epoch (TAI MJD) for catalog')
        return md

    def joinMatchListWithCatalog(self, matchCat, sourceCat):
        """Relink an unpersisted match list to sources and reference
        objects.

        A match list is persisted and unpersisted as a catalog of IDs
        produced by afw.table.packMatches(), with match metadata
        (as returned by the astrometry tasks) in the catalog's metadata
        attribute. This method converts such a match catalog into a match
        list, with links to source records and reference object records.

        Parameters
        ----------
        matchCat : `lsst.afw.table.BaseCatalog`
            Unperisted packed match list.
            ``matchCat.table.getMetadata()`` must contain match metadata,
            as returned by the astrometry tasks.
        sourceCat : `lsst.afw.table.SourceCatalog`
            Source catalog. As a side effect, the catalog will be sorted
            by ID.

        Returns
        -------
        matchList : `lsst.afw.table.ReferenceMatchVector`
            Match list.
        """
        return joinMatchListWithCatalogImpl(self, matchCat, sourceCat)

    def applyProperMotions(self, catalog, epoch):
        """Apply proper motion correction to a reference catalog.

        Adjust position and position error in the ``catalog``
        for proper motion to the specified ``epoch``,
        modifying the catalong in place.

        Parameters
        ----------
        catalog : `lsst.afw.table.SimpleCatalog`
            Catalog of positions, containing:

            - Coordinates, retrieved by the table's coordinate key.
            - ``coord_raErr`` : Error in Right Ascension (rad).
            - ``coord_decErr`` : Error in Declination (rad).
            - ``pm_ra`` : Proper motion in Right Ascension (rad/yr,
                East positive)
            - ``pm_raErr`` : Error in ``pm_ra`` (rad/yr), optional.
            - ``pm_dec`` : Proper motion in Declination (rad/yr,
                North positive)
            - ``pm_decErr`` : Error in ``pm_dec`` (rad/yr), optional.
            - ``epoch`` : Mean epoch of object (an astropy.time.Time)
        epoch : `astropy.time.Time` (optional)
            Epoch to which to correct proper motion and parallax,
            or None to not apply such corrections.
        """
        if ("epoch" not in catalog.schema or "pm_ra" not in catalog.schema or "pm_dec" not in catalog.schema):
            if self.config.requireProperMotion:
                raise RuntimeError("Proper motion correction required but not available from catalog")
            self.log.warn("Proper motion correction not available from catalog")
            return
        applyProperMotionsImpl(self.log, catalog, epoch)


def joinMatchListWithCatalogImpl(refObjLoader, matchCat, sourceCat):
    """Relink an unpersisted match list to sources and reference
    objects.

    A match list is persisted and unpersisted as a catalog of IDs
    produced by afw.table.packMatches(), with match metadata
    (as returned by the astrometry tasks) in the catalog's metadata
    attribute. This method converts such a match catalog into a match
    list, with links to source records and reference object records.

    Parameters
    ----------
    refObjLoader
        Reference object loader to use in getting reference objects
    matchCat : `lsst.afw.table.BaseCatalog`
        Unperisted packed match list.
        ``matchCat.table.getMetadata()`` must contain match metadata,
        as returned by the astrometry tasks.
    sourceCat : `lsst.afw.table.SourceCatalog`
        Source catalog. As a side effect, the catalog will be sorted
        by ID.

    Returns
    -------
    matchList : `lsst.afw.table.ReferenceMatchVector`
        Match list.
    """
    matchmeta = matchCat.table.getMetadata()
    version = matchmeta.getInt('SMATCHV')
    if version != 1:
        raise ValueError('SourceMatchVector version number is %i, not 1.' % version)
    filterName = matchmeta.getString('FILTER').strip()
    try:
        epoch = matchmeta.getDouble('EPOCH')
    except (pexExcept.NotFoundError, pexExcept.TypeError):
        epoch = None  # Not present, or not correct type means it's not set
    if 'RADIUS' in matchmeta:
        # This is a circle style metadata, call loadSkyCircle
        ctrCoord = lsst.geom.SpherePoint(matchmeta.getDouble('RA'),
                                         matchmeta.getDouble('DEC'), lsst.geom.degrees)
        rad = matchmeta.getDouble('RADIUS') * lsst.geom.degrees
        refCat = refObjLoader.loadSkyCircle(ctrCoord, rad, filterName, epoch=epoch).refCat
    elif "INNER_UPPER_LEFT_RA" in matchmeta:
        # This is the sky box type (only triggers in the LoadReferenceObject class, not task)
        # Only the outer box is required to be loaded to get the maximum region, all filtering
        # will be done by the unpackMatches function, and no spatial filtering needs to be done
        # by the refObjLoader
        box = []
        for place in ("UPPER_LEFT", "UPPER_RIGHT", "LOWER_LEFT", "LOWER_RIGHT"):
            coord = lsst.geom.SpherePoint(matchmeta.getDouble(f"OUTER_{place}_RA"),
                                          matchmeta.getDouble(f"OUTER_{place}_DEC"),
                                          lsst.geom.degrees).getVector()
            box.append(coord)
        outerBox = sphgeom.ConvexPolygon(box)
        refCat = refObjLoader.loadRegion(outerBox, filterName=filterName, epoch=epoch).refCat

    refCat.sort()
    sourceCat.sort()
    return afwTable.unpackMatches(matchCat, refCat, sourceCat)


def applyProperMotionsImpl(log, catalog, epoch):
    """Apply proper motion correction to a reference catalog.

    Adjust position and position error in the ``catalog``
    for proper motion to the specified ``epoch``,
    modifying the catalong in place.

    Parameters
    ----------
    log : `lsst.log.log`
        log object to write to
    catalog : `lsst.afw.table.SimpleCatalog`
        Catalog of positions, containing:

        - Coordinates, retrieved by the table's coordinate key.
        - ``coord_raErr`` : Error in Right Ascension (rad).
        - ``coord_decErr`` : Error in Declination (rad).
        - ``pm_ra`` : Proper motion in Right Ascension (rad/yr,
            East positive)
        - ``pm_raErr`` : Error in ``pm_ra`` (rad/yr), optional.
        - ``pm_dec`` : Proper motion in Declination (rad/yr,
            North positive)
        - ``pm_decErr`` : Error in ``pm_dec`` (rad/yr), optional.
        - ``epoch`` : Mean epoch of object (an astropy.time.Time)
    epoch : `astropy.time.Time` (optional)
        Epoch to which to correct proper motion and parallax,
        or None to not apply such corrections.
    """
    if "epoch" not in catalog.schema or "pm_ra" not in catalog.schema or "pm_dec" not in catalog.schema:
        log.warn("Proper motion correction not available from catalog")
        return
    if not catalog.isContiguous():
        raise RuntimeError("Catalog must be contiguous")
    catEpoch = astropy.time.Time(catalog["epoch"], scale="tai", format="mjd")
    log.debug("Correcting reference catalog for proper motion to %r", epoch)
    # Use `epoch.tai` to make sure the time difference is in TAI
    timeDiffsYears = (epoch.tai - catEpoch).to(astropy.units.yr).value
    coordKey = catalog.table.getCoordKey()
    # Compute the offset of each object due to proper motion
    # as components of the arc of a great circle along RA and Dec
    pmRaRad = catalog["pm_ra"]
    pmDecRad = catalog["pm_dec"]
    offsetsRaRad = pmRaRad*timeDiffsYears
    offsetsDecRad = pmDecRad*timeDiffsYears
    # Compute the corresponding bearing and arc length of each offset
    # due to proper motion, and apply the offset
    # The factor of 1e6 for computing bearing is intended as
    # a reasonable scale for typical values of proper motion
    # in order to avoid large errors for small values of proper motion;
    # using the offsets is another option, but it can give
    # needlessly large errors for short duration
    offsetBearingsRad = numpy.arctan2(pmDecRad*1e6, pmRaRad*1e6)
    offsetAmountsRad = numpy.hypot(offsetsRaRad, offsetsDecRad)
    for record, bearingRad, amountRad in zip(catalog, offsetBearingsRad, offsetAmountsRad):
        record.set(coordKey,
                   record.get(coordKey).offset(bearing=bearingRad*lsst.geom.radians,
                                               amount=amountRad*lsst.geom.radians))
    # Increase error in RA and Dec based on error in proper motion
    if "coord_raErr" in catalog.schema:
        catalog["coord_raErr"] = numpy.hypot(catalog["coord_raErr"],
                                             catalog["pm_raErr"]*timeDiffsYears)
    if "coord_decErr" in catalog.schema:
        catalog["coord_decErr"] = numpy.hypot(catalog["coord_decErr"],
                                              catalog["pm_decErr"]*timeDiffsYears)