kernelCandidateQa.py

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#
# LSST Data Management System
# Copyright 2008-2016 LSST Corporation.
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__all__ = ["KernelCandidateQa"]
 
import numpy as np
import numpy.ma as ma
 
import lsst.afw.image as afwImage
import lsst.afw.table as afwTable
import lsst.afw.math as afwMath
import lsst.geom as geom
from . import diffimLib
from .utils import calcCentroid, calcWidth
 
 
class KernelCandidateQa(object):
    """Quality Assessment class for Kernel Candidates"""
 
    def __init__(self, nKernelSpatial):
        """Class to undertake QA of KernelCandidates after modeling of
        the Psf-matching kernel.  Both directly--fitted diffim (LOCAL)
        and spatially--interpolated kernel diffim (SPATIAL) metrics
        are calculated, based on the distribution of residuals in the
        KernelCandidates stamp.
 
        Parameters
        ----------
        nKernelSpatial : `int`
            Number of terms in the spatial model; needed to initialize per-basis QA arrays
        """
        self.fields = []
        self.fields.append(afwTable.Field["PointD"](
            "RegisterRefPosition",
            "Position of reference object for registration (radians)."))
        # TODO check units of the following angles
        self.fields.append(afwTable.Field["Angle"]("RegisterResidualBearing",
                                                   "Angle of residual wrt declination parallel in radians"))
 
        self.fields.append(afwTable.Field["Angle"]("RegisterResidualDistance",
                                                   "Offset of residual in radians"))
        metricMap = self.makeMetricMap()
 
        for kType in ("LOCAL", "SPATIAL"):
            for k in metricMap:
                commentAndUnit = metricMap[k]['comment']
                self.fields.append(afwTable.Field[metricMap[k]['type']](k%(kType), *commentAndUnit))
 
        self.fields.append(afwTable.Field["I"]("KCKernelStatus_LOCAL",
                                               "Status of the KernelCandidate"))
 
        self.fields.append(afwTable.Field["ArrayD"]("KernelCoeffValues_LOCAL",
                                                    "Original basis coefficients",
                                                    nKernelSpatial))
 
        self.fields.append(afwTable.Field["F"]("BackgroundValue_LOCAL",
                                               "Evaluation of background model at this point"))
 
        self.fields.append(afwTable.Field["F"]("KCDiffimMseKernel_SPATIAL",
                                               "Mean squared error of spatial kernel estimate"))
 
    def makeMetricMap(self):
        nameList = ['KCDiffimMean_%s', 'KCDiffimMedian_%s', 'KCDiffimIQR_%s', 'KCDiffimStDev_%s',
                    'KCDiffimKSD_%s', 'KCDiffimKSProb_%s', 'KCDiffimADA2_%s', 'KCDiffimADCrit_%s',
                    'KCDiffimADSig_%s', 'KCDiffimChiSq_%s', 'KCDiffimMseResids_%s', 'KCKernelCentX_%s',
                    'KCKernelCentY_%s', 'KCKernelStdX_%s', 'KCKernelStdY_%s', 'KernelCandidateId_%s']
        typeList = ['F', 'F', 'F', 'F', 'F', 'F', 'F', 'ArrayD', 'ArrayD', 'F', 'F', 'F',
                    'F', 'F', 'F', 'I']
        commentList = [
            ("Mean of KernelCandidate diffim", "sigma"),
            ("Median of KernelCandidate diffim", "sigma"),
            ("Inner quartile range of KernelCandidate diffim", "sigma"),
            ("Standard deviation of KernelCandidate diffim", "sigma"),
            ("D from K-S test of diffim pixels relative to Normal", ),
            ("Prob from K-S test of diffim pixels relative to Normal", "likelihood"),
            ("Anderson-Darling test statistic of diffim pixels relative to Normal", ),
            ("Critical values for the significance levels in KCDiffimADSig.  If A2 is greater "
             "than this number, hypothesis that the distributions are similar can be rejected.", 5),
            ("Anderson-Darling significance levels for the Normal distribution", 5),
            ("Reduced chi^2 of the residual.", "likelihood"),
            ("Mean squared error in diffim : Variance + Bias**2",),
            ("Centroid in X for this Kernel", "pixel"),
            ("Centroid in Y for this Kernel", "pixel"),
            ("Standard deviation in X for this Kernel", "pixel"),
            ("Standard deviation in Y for this Kernel", "pixel"),
            ("Id for this KernelCandidate",),
        ]
        metricMap = {}
        for name, mtype, comment in zip(nameList, typeList, commentList):
            metricMap[name] = {'type': mtype, 'comment': comment}
 
        return metricMap
 
    def addToSchema(self, inSourceCatalog):
        """Add the to-be-generated QA keys to the Source schema"""
        schema = inSourceCatalog.getSchema()
        inKeys = []
        psfDef = inSourceCatalog.schema.getAliasMap().get("slot_PsfFlux")
        centroidDef = inSourceCatalog.getCentroidDefinition()
        shapeDef = inSourceCatalog.getShapeDefinition()
        for n in schema.getNames():
            inKeys.append(schema[n].asKey())
 
        for field in self.fields:
            schema.addField(field)
        outSourceCatalog = afwTable.SourceCatalog(schema)
        for source in inSourceCatalog:
            rec = outSourceCatalog.addNew()
            for k in inKeys:
                if k.getTypeString() == 'Coord':
                    rec.setCoord(source.getCoord())
                else:
                    setter = getattr(rec, "set"+k.getTypeString())
                    getter = getattr(source, "get"+k.getTypeString())
                    setter(k, getter(k))
        outSourceCatalog.definePsfFlux(psfDef)
        outSourceCatalog.defineCentroid(centroidDef)
        outSourceCatalog.defineShape(shapeDef)
        return outSourceCatalog
 
    @staticmethod
    def _calculateStats(di, dof=0.):
        """Calculate the core QA statistics on a difference image"""
        mask = di.getMask()
        maskArr = di.getMask().getArray()
 
        # Create a mask using BAD, SAT, NO_DATA, EDGE bits.  Keep detections
        maskArr &= mask.getPlaneBitMask(["BAD", "SAT", "NO_DATA", "EDGE"])
 
        # Mask out values based on maskArr
        diArr = ma.array(di.getImage().getArray(), mask=maskArr)
        varArr = ma.array(di.getVariance().getArray(), mask=maskArr)
 
        # Normalize by sqrt variance, units are in sigma
        diArr /= np.sqrt(varArr)
        mean = diArr.mean()
 
        # This is the maximum-likelihood extimate of the variance stdev**2
        stdev = diArr.std()
        median = ma.extras.median(diArr)
 
        # Compute IQR of just un-masked data
        data = ma.getdata(diArr[~diArr.mask])
        iqr = np.percentile(data, 75.) - np.percentile(data, 25.)
 
        # Calculte chisquare of the residual
        chisq = np.sum(np.power(data, 2.))
 
        # Mean squared error: variance + bias**2
        # Bias = |data - model| = mean of diffim
        # Variance = |(data - model)**2| = mean of diffim**2
        bias = mean
        variance = np.power(data, 2.).mean()
        mseResids = bias**2 + variance
 
        # If scipy is not set up, return zero for the stats
        try:
            # In try block because of risk of divide by zero
            rchisq = chisq/(len(data) - 1 - dof)
            # K-S test on the diffim to a Normal distribution
            import scipy.stats
            D, prob = scipy.stats.kstest(data, 'norm')
 
            A2, crit, sig = scipy.stats.anderson(data, 'norm')
            # Anderson Darling statistic cand be inf for really non-Gaussian distributions.
            if np.isinf(A2) or np.isnan(A2):
                A2 = 9999.
        except ZeroDivisionError:
            D = 0.
            prob = 0.
            A2 = 0.
            crit = np.zeros(5)
            sig = np.zeros(5)
            rchisq = 0
 
        return {"mean": mean, "stdev": stdev, "median": median, "iqr": iqr,
                "D": D, "prob": prob, "A2": A2, "crit": crit, "sig": sig,
                "rchisq": rchisq, "mseResids": mseResids}
 
    @classmethod
    def apply(cls, candidateList, spatialKernel, spatialBackground, dof=0):
        """Evaluate the QA metrics for all KernelCandidates in the
        candidateList; set the values of the metrics in their
        associated Sources"""
        for kernelCandidate in candidateList:
            source = kernelCandidate.getSource()
            schema = source.schema
 
            # Calculate ORIG stats (original basis fit)
            if kernelCandidate.getStatus() != afwMath.SpatialCellCandidate.UNKNOWN:
                kType = getattr(diffimLib.KernelCandidateF, "ORIG")
                di = kernelCandidate.getDifferenceImage(kType)
                kernelValues = kernelCandidate.getKernel(kType).getKernelParameters()
                kernelValues = np.asarray(kernelValues)
 
                lkim = kernelCandidate.getKernelImage(kType)
                centx, centy = calcCentroid(lkim.getArray())
                stdx, stdy = calcWidth(lkim.getArray(), centx, centy)
                # NOTE
                # What is the difference between kernelValues and solution?
 
                localResults = cls._calculateStats(di, dof=dof)
 
                metrics = {"KCDiffimMean_LOCAL": localResults["mean"],
                           "KCDiffimMedian_LOCAL": localResults["median"],
                           "KCDiffimIQR_LOCAL": localResults["iqr"],
                           "KCDiffimStDev_LOCAL": localResults["stdev"],
                           "KCDiffimKSD_LOCAL": localResults["D"],
                           "KCDiffimKSProb_LOCAL": localResults["prob"],
                           "KCDiffimADA2_LOCAL": localResults["A2"],
                           "KCDiffimADCrit_LOCAL": localResults["crit"],
                           "KCDiffimADSig_LOCAL": localResults["sig"],
                           "KCDiffimChiSq_LOCAL": localResults["rchisq"],
                           "KCDiffimMseResids_LOCAL": localResults["mseResids"],
                           "KCKernelCentX_LOCAL": centx,
                           "KCKernelCentY_LOCAL": centy,
                           "KCKernelStdX_LOCAL": stdx,
                           "KCKernelStdY_LOCAL": stdy,
                           "KernelCandidateId_LOCAL": kernelCandidate.getId(),
                           "KernelCoeffValues_LOCAL": kernelValues}
                for k in metrics:
                    key = schema[k].asKey()
                    setter = getattr(source, "set"+key.getTypeString())
                    setter(key, metrics[k])
            else:
                try:
                    kType = getattr(diffimLib.KernelCandidateF, "ORIG")
                    lkim = kernelCandidate.getKernelImage(kType)
                except Exception:
                    lkim = None
 
            # Calculate spatial model evaluated at each position, for
            # all candidates
            skim = afwImage.ImageD(spatialKernel.getDimensions())
            spatialKernel.computeImage(skim, False, kernelCandidate.getXCenter(),
                                       kernelCandidate.getYCenter())
            centx, centy = calcCentroid(skim.getArray())
            stdx, stdy = calcWidth(skim.getArray(), centx, centy)
 
            sk = afwMath.FixedKernel(skim)
            sbg = spatialBackground(kernelCandidate.getXCenter(), kernelCandidate.getYCenter())
            di = kernelCandidate.getDifferenceImage(sk, sbg)
            spatialResults = cls._calculateStats(di, dof=dof)
 
            # Kernel mse
            if lkim is not None:
                skim -= lkim
                bias = np.mean(skim.getArray())
                variance = np.mean(np.power(skim.getArray(), 2.))
                mseKernel = bias**2 + variance
            else:
                mseKernel = -99.999
 
            metrics = {"KCDiffimMean_SPATIAL": spatialResults["mean"],
                       "KCDiffimMedian_SPATIAL": spatialResults["median"],
                       "KCDiffimIQR_SPATIAL": spatialResults["iqr"],
                       "KCDiffimStDev_SPATIAL": spatialResults["stdev"],
                       "KCDiffimKSD_SPATIAL": spatialResults["D"],
                       "KCDiffimKSProb_SPATIAL": spatialResults["prob"],
                       "KCDiffimADA2_SPATIAL": spatialResults["A2"],
                       "KCDiffimADCrit_SPATIAL": spatialResults["crit"],
                       "KCDiffimADSig_SPATIAL": spatialResults["sig"],
                       "KCDiffimChiSq_SPATIAL": spatialResults["rchisq"],
                       "KCDiffimMseResids_SPATIAL": spatialResults["mseResids"],
                       "KCDiffimMseKernel_SPATIAL": mseKernel,
                       "KCKernelCentX_SPATIAL": centx,
                       "KCKernelCentY_SPATIAL": centy,
                       "KCKernelStdX_SPATIAL": stdx,
                       "KCKernelStdY_SPATIAL": stdy,
                       "KernelCandidateId_SPATIAL": kernelCandidate.getId()}
            for k in metrics:
                key = schema[k].asKey()
                setter = getattr(source, "set"+key.getTypeString())
                setter(key, metrics[k])
 
    @staticmethod
    def aggregate(sourceCatalog, metadata, wcsresids, diaSources=None):
        """Generate aggregate metrics (e.g. total numbers of false
        positives) from all the Sources in the sourceCatalog"""
        for source in sourceCatalog:
            sourceId = source.getId()
            if sourceId in wcsresids:
                # Note that the residuals are not delta RA, delta Dec
                # From the source code "bearing (angle wrt a declination parallel) and distance
                coord, resids = wcsresids[sourceId]
                key = source.schema["RegisterResidualBearing"].asKey()
                setter = getattr(source, "set"+key.getTypeString())
                setter(key, resids[0])
                key = source.schema["RegisterResidualDistance"].asKey()
                setter = getattr(source, "set"+key.getTypeString())
                setter(key, resids[1])
                key = source.schema["RegisterRefPosition"].asKey()
                setter = getattr(source, "set"+key.getTypeString())
                setter(key, geom.Point2D(coord.getRa().asRadians(),
                                         coord.getDec().asRadians()))
        if diaSources:
            metadata.add("NFalsePositivesTotal", len(diaSources))
            nRefMatch = 0
            nSrcMatch = 0
            nunmatched = 0
            for source in diaSources:
                refId = source.get("refMatchId")
                srcId = source.get("srcMatchId")
                if refId > 0:
                    nRefMatch += 1
                if srcId > 0:
                    nSrcMatch += 1
                if refId == 0 and srcId == 0:
                    nunmatched += 1
            metadata.add("NFalsePositivesRefAssociated", nRefMatch)
            metadata.add("NFalsePositivesSrcAssociated", nSrcMatch)
            metadata.add("NFalsePositivesUnassociated", nunmatched)
        for kType in ("LOCAL", "SPATIAL"):
            for sName in ("KCDiffimMean", "KCDiffimMedian", "KCDiffimIQR", "KCDiffimStDev",
                          "KCDiffimKSProb", "KCDiffimADSig", "KCDiffimChiSq",
                          "KCDiffimMseResids", "KCDiffimMseKernel"):
                if sName == "KCDiffimMseKernel" and kType == "LOCAL":
                    continue
                kName = "%s_%s" % (sName, kType)
                vals = np.array([s.get(kName) for s in sourceCatalog])
                idx = np.isfinite(vals)
                metadata.add("%s_MEAN" % (kName), np.mean(vals[idx]))
                metadata.add("%s_MEDIAN" % (kName), np.median(vals[idx]))
                metadata.add("%s_STDEV" % (kName), np.std(vals[idx]))