psfMatch.py

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# This file is part of ip_diffim.
#
# Developed for the LSST Data Management System.
# This product includes software developed by the LSST Project
# (https://www.lsst.org).
# See the COPYRIGHT file at the top-level directory of this distribution
# for details of code ownership.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
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# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
 
__all__ = ["PsfMatchConfig", "PsfMatchConfigAL", "PsfMatchConfigDF", "PsfMatchTask"]
 
import abc
import time
 
import numpy as np
 
import lsst.afw.image as afwImage
import lsst.pex.config as pexConfig
import lsst.afw.math as afwMath
import lsst.afw.display as afwDisplay
import lsst.pipe.base as pipeBase
from lsst.meas.algorithms import SubtractBackgroundConfig
from lsst.utils.logging import getTraceLogger
from lsst.utils.timer import timeMethod
from . import utils as diutils
from . import diffimLib
 
 
class NoKernelCandidatesError(pipeBase.AlgorithmError):
    """Raised if there are too few candidates to compute the PSF matching
    kernel.
    """
 
    @property
    def metadata(self) -> dict:
        return {}
 
 
class PsfMatchConfig(pexConfig.Config):
    """Base configuration for Psf-matching
 
    The base configuration of the Psf-matching kernel, and of the warping, detection,
    and background modeling subTasks."""
 
    warpingConfig = pexConfig.ConfigField("Config for warping exposures to a common alignment",
                                          afwMath.WarperConfig)
    afwBackgroundConfig = pexConfig.ConfigField("Controlling the Afw background fitting",
                                                SubtractBackgroundConfig)
 
    useAfwBackground = pexConfig.Field(
        dtype=bool,
        doc="Use afw background subtraction instead of ip_diffim",
        default=False,
    )
    fitForBackground = pexConfig.Field(
        dtype=bool,
        doc="Include terms (including kernel cross terms) for background in ip_diffim",
        default=False,
    )
    kernelBasisSet = pexConfig.ChoiceField(
        dtype=str,
        doc="Type of basis set for PSF matching kernel.",
        default="alard-lupton",
        allowed={
            "alard-lupton": """Alard-Lupton sum-of-gaussians basis set,
                           * The first term has no spatial variation
                           * The kernel sum is conserved
                           * You may want to turn off 'usePcaForSpatialKernel'""",
            "delta-function": """Delta-function kernel basis set,
                           * You may enable the option useRegularization
                           * You should seriously consider usePcaForSpatialKernel, which will also
                             enable kernel sum conservation for the delta function kernels"""
        }
    )
    kernelSize = pexConfig.Field(
        dtype=int,
        doc="""Number of rows/columns in the convolution kernel; should be odd-valued.
                 Modified by kernelSizeFwhmScaling if scaleByFwhm = true""",
        default=21,
    )
    scaleByFwhm = pexConfig.Field(
        dtype=bool,
        doc="Scale kernelSize, alardGaussians by input Fwhm",
        default=True,
    )
    kernelSizeFwhmScaling = pexConfig.Field(
        dtype=float,
        doc="Multiplier of the largest AL Gaussian basis sigma to get the kernel bbox (pixel) size.",
        default=6.0,
        check=lambda x: x >= 1.0
    )
    kernelSizeMin = pexConfig.Field(
        dtype=int,
        doc="Minimum kernel bbox (pixel) size.",
        default=21,
    )
    kernelSizeMax = pexConfig.Field(
        dtype=int,
        doc="Maximum kernel bbox (pixel) size.",
        default=35,
    )
    spatialModelType = pexConfig.ChoiceField(
        dtype=str,
        doc="Type of spatial functions for kernel and background",
        default="chebyshev1",
        allowed={
            "chebyshev1": "Chebyshev polynomial of the first kind",
            "polynomial": "Standard x,y polynomial",
        }
    )
    spatialKernelOrder = pexConfig.Field(
        dtype=int,
        doc="Spatial order of convolution kernel variation",
        default=2,
        check=lambda x: x >= 0
    )
    spatialBgOrder = pexConfig.Field(
        dtype=int,
        doc="Spatial order of differential background variation",
        default=1,
        check=lambda x: x >= 0
    )
    sizeCellX = pexConfig.Field(
        dtype=int,
        doc="Size (rows) in pixels of each SpatialCell for spatial modeling",
        default=128,
        check=lambda x: x >= 32
    )
    sizeCellY = pexConfig.Field(
        dtype=int,
        doc="Size (columns) in pixels of each SpatialCell for spatial modeling",
        default=128,
        check=lambda x: x >= 32
    )
    nStarPerCell = pexConfig.Field(
        dtype=int,
        doc="Maximum number of KernelCandidates in each SpatialCell to use in the spatial fitting. "
            "Set to -1 to use all candidates in each cell.",
        default=5,
    )
    maxSpatialIterations = pexConfig.Field(
        dtype=int,
        doc="Maximum number of iterations for rejecting bad KernelCandidates in spatial fitting",
        default=3,
        check=lambda x: x >= 1 and x <= 5
    )
    usePcaForSpatialKernel = pexConfig.Field(
        dtype=bool,
        doc="""Use Pca to reduce the dimensionality of the kernel basis sets.
                 This is particularly useful for delta-function kernels.
                 Functionally, after all Cells have their raw kernels determined, we run
                 a Pca on these Kernels, re-fit the Cells using the eigenKernels and then
                 fit those for spatial variation using the same technique as for Alard-Lupton kernels.
                 If this option is used, the first term will have no spatial variation and the
                 kernel sum will be conserved.""",
        default=False,
    )
    subtractMeanForPca = pexConfig.Field(
        dtype=bool,
        doc="Subtract off the mean feature before doing the Pca",
        default=True,
    )
    numPrincipalComponents = pexConfig.Field(
        dtype=int,
        doc="""Number of principal components to use for Pca basis, including the
                 mean kernel if requested.""",
        default=5,
        check=lambda x: x >= 3
    )
    singleKernelClipping = pexConfig.Field(
        dtype=bool,
        doc="Do sigma clipping on each raw kernel candidate",
        default=True,
    )
    kernelSumClipping = pexConfig.Field(
        dtype=bool,
        doc="Do sigma clipping on the ensemble of kernel sums",
        default=True,
    )
    spatialKernelClipping = pexConfig.Field(
        dtype=bool,
        doc="Do sigma clipping after building the spatial model",
        default=True,
    )
    checkConditionNumber = pexConfig.Field(
        dtype=bool,
        doc="""Test for maximum condition number when inverting a kernel matrix.
                 Anything above maxConditionNumber is not used and the candidate is set as BAD.
                 Also used to truncate inverse matrix in estimateBiasedRisk.  However,
                 if you are doing any deconvolution you will want to turn this off, or use
                 a large maxConditionNumber""",
        default=False,
    )
    badMaskPlanes = pexConfig.ListField(
        dtype=str,
        doc="""Mask planes to ignore when calculating diffim statistics
                 Options: NO_DATA EDGE SAT BAD CR INTRP""",
        default=("NO_DATA", "EDGE", "SAT")
    )
    candidateResidualMeanMax = pexConfig.Field(
        dtype=float,
        doc="""Rejects KernelCandidates yielding bad difference image quality.
                 Used by BuildSingleKernelVisitor, AssessSpatialKernelVisitor.
                 Represents average over pixels of (image/sqrt(variance)).""",
        default=0.25,
        check=lambda x: x >= 0.0
    )
    candidateResidualStdMax = pexConfig.Field(
        dtype=float,
        doc="""Rejects KernelCandidates yielding bad difference image quality.
                 Used by BuildSingleKernelVisitor, AssessSpatialKernelVisitor.
                 Represents stddev over pixels of (image/sqrt(variance)).""",
        default=1.50,
        check=lambda x: x >= 0.0
    )
    useCoreStats = pexConfig.Field(
        dtype=bool,
        doc="""Use the core of the footprint for the quality statistics, instead of the entire footprint.
                 WARNING: if there is deconvolution we probably will need to turn this off""",
        default=False,
    )
    candidateCoreRadius = pexConfig.Field(
        dtype=int,
        doc="""Radius for calculation of stats in 'core' of KernelCandidate diffim.
                 Total number of pixels used will be (2*radius)**2.
                 This is used both for 'core' diffim quality as well as ranking of
                 KernelCandidates by their total flux in this core""",
        default=3,
        check=lambda x: x >= 1
    )
    maxKsumSigma = pexConfig.Field(
        dtype=float,
        doc="""Maximum allowed sigma for outliers from kernel sum distribution.
                 Used to reject variable objects from the kernel model""",
        default=3.0,
        check=lambda x: x >= 0.0
    )
    maxConditionNumber = pexConfig.Field(
        dtype=float,
        doc="Maximum condition number for a well conditioned matrix",
        default=5.0e7,
        check=lambda x: x >= 0.0
    )
    conditionNumberType = pexConfig.ChoiceField(
        dtype=str,
        doc="Use singular values (SVD) or eigen values (EIGENVALUE) to determine condition number",
        default="EIGENVALUE",
        allowed={
            "SVD": "Use singular values",
            "EIGENVALUE": "Use eigen values (faster)",
        }
    )
    maxSpatialConditionNumber = pexConfig.Field(
        dtype=float,
        doc="Maximum condition number for a well conditioned spatial matrix",
        default=1.0e10,
        check=lambda x: x >= 0.0
    )
    iterateSingleKernel = pexConfig.Field(
        dtype=bool,
        doc="""Remake KernelCandidate using better variance estimate after first pass?
                 Primarily useful when convolving a single-depth image, otherwise not necessary.""",
        default=False,
    )
    constantVarianceWeighting = pexConfig.Field(
        dtype=bool,
        doc="""Use constant variance weighting in single kernel fitting?
                 In some cases this is better for bright star residuals.""",
        default=True,
    )
    calculateKernelUncertainty = pexConfig.Field(
        dtype=bool,
        doc="""Calculate kernel and background uncertainties for each kernel candidate?
                 This comes from the inverse of the covariance matrix.
                 Warning: regularization can cause problems for this step.""",
        default=False,
    )
    useBicForKernelBasis = pexConfig.Field(
        dtype=bool,
        doc="""Use Bayesian Information Criterion to select the number of bases going into the kernel""",
        default=False,
    )
 
 
class PsfMatchConfigAL(PsfMatchConfig):
    """The parameters specific to the "Alard-Lupton" (sum-of-Gaussian) Psf-matching basis"""
 
    def setDefaults(self):
        PsfMatchConfig.setDefaults(self)
        self.kernelBasisSet = "alard-lupton"
        self.maxConditionNumber = 5.0e7
 
    alardNGauss = pexConfig.Field(
        dtype=int,
        doc="Number of base Gaussians in alard-lupton kernel basis function generation.",
        default=3,
        check=lambda x: x >= 1
    )
    alardDegGauss = pexConfig.ListField(
        dtype=int,
        doc="Polynomial order of spatial modification of base Gaussians. "
            "List length must be `alardNGauss`.",
        default=(4, 2, 2),
    )
    alardSigGauss = pexConfig.ListField(
        dtype=float,
        doc="Default sigma values in pixels of base Gaussians. "
            "List length must be `alardNGauss`."
            "Only used if the template and science image PSFs have equal size.",
        default=(0.7, 1.5, 3.0),
    )
    alardGaussBeta = pexConfig.Field(
        dtype=float,
        doc="Used if `scaleByFwhm==True`, scaling multiplier of base "
            "Gaussian sigmas for automated sigma determination",
        default=2.0,
        check=lambda x: x >= 0.0,
    )
    alardMinSig = pexConfig.Field(
        dtype=float,
        doc="Used if `scaleByFwhm==True`, minimum sigma (pixels) for base Gaussians",
        default=0.7,
        check=lambda x: x >= 0.25
    )
    alardDegGaussDeconv = pexConfig.Field(
        dtype=int,
        doc="Used if `scaleByFwhm==True`, degree of spatial modification of ALL base Gaussians "
            "in AL basis during deconvolution",
        default=3,
        check=lambda x: x >= 1,
        deprecated="No longer used. Will be removed after v29"
    )
    alardMinSigDeconv = pexConfig.Field(
        dtype=float,
        doc="Used if `scaleByFwhm==True`, minimum sigma (pixels) for base Gaussians during deconvolution; "
            "make smaller than `alardMinSig` as this is only indirectly used",
        default=0.4,
        check=lambda x: x >= 0.25
    )
    alardNGaussDeconv = pexConfig.Field(
        dtype=int,
        doc="Used if `scaleByFwhm==True`, number of base Gaussians in AL basis during deconvolution",
        default=3,
        check=lambda x: x >= 1,
        deprecated="No longer used. Will be removed after v29"
    )
 
 
class PsfMatchConfigDF(PsfMatchConfig):
    """The parameters specific to the delta-function (one basis per-pixel) Psf-matching basis"""
 
    def setDefaults(self):
        PsfMatchConfig.setDefaults(self)
        self.kernelBasisSet = "delta-function"
        self.maxConditionNumber = 5.0e6
        self.usePcaForSpatialKernel = True
        self.subtractMeanForPca = True
        self.useBicForKernelBasis = False
 
    useRegularization = pexConfig.Field(
        dtype=bool,
        doc="Use regularization to smooth the delta function kernels",
        default=True,
    )
    regularizationType = pexConfig.ChoiceField(
        dtype=str,
        doc="Type of regularization.",
        default="centralDifference",
        allowed={
            "centralDifference": "Penalize second derivative using 2-D stencil of central finite difference",
            "forwardDifference": "Penalize first, second, third derivatives using forward finite differeces"
        }
    )
    centralRegularizationStencil = pexConfig.ChoiceField(
        dtype=int,
        doc="Type of stencil to approximate central derivative (for centralDifference only)",
        default=9,
        allowed={
            5: "5-point stencil including only adjacent-in-x,y elements",
            9: "9-point stencil including diagonal elements"
        }
    )
    forwardRegularizationOrders = pexConfig.ListField(
        dtype=int,
        doc="Array showing which order derivatives to penalize (for forwardDifference only)",
        default=(1, 2),
        itemCheck=lambda x: (x > 0) and (x < 4)
    )
    regularizationBorderPenalty = pexConfig.Field(
        dtype=float,
        doc="Value of the penalty for kernel border pixels",
        default=3.0,
        check=lambda x: x >= 0.0
    )
    lambdaType = pexConfig.ChoiceField(
        dtype=str,
        doc="How to choose the value of the regularization strength",
        default="absolute",
        allowed={
            "absolute": "Use lambdaValue as the value of regularization strength",
            "relative": "Use lambdaValue as fraction of the default regularization strength (N.R. 18.5.8)",
            "minimizeBiasedRisk": "Minimize biased risk estimate",
            "minimizeUnbiasedRisk": "Minimize unbiased risk estimate",
        }
    )
    lambdaValue = pexConfig.Field(
        dtype=float,
        doc="Value used for absolute determinations of regularization strength",
        default=0.2,
    )
    lambdaScaling = pexConfig.Field(
        dtype=float,
        doc="Fraction of the default lambda strength (N.R. 18.5.8) to use.  1e-4 or 1e-5",
        default=1e-4,
    )
    lambdaStepType = pexConfig.ChoiceField(
        dtype=str,
        doc="""If a scan through lambda is needed (minimizeBiasedRisk, minimizeUnbiasedRisk),
                 use log or linear steps""",
        default="log",
        allowed={
            "log": "Step in log intervals; e.g. lambdaMin, lambdaMax, lambdaStep = -1.0, 2.0, 0.1",
            "linear": "Step in linear intervals; e.g. lambdaMin, lambdaMax, lambdaStep = 0.1, 100, 0.1",
        }
    )
    lambdaMin = pexConfig.Field(
        dtype=float,
        doc="""If scan through lambda needed (minimizeBiasedRisk, minimizeUnbiasedRisk),
                 start at this value.  If lambdaStepType = log:linear, suggest -1:0.1""",
        default=-1.0,
    )
    lambdaMax = pexConfig.Field(
        dtype=float,
        doc="""If scan through lambda needed (minimizeBiasedRisk, minimizeUnbiasedRisk),
                 stop at this value.  If lambdaStepType = log:linear, suggest 2:100""",
        default=2.0,
    )
    lambdaStep = pexConfig.Field(
        dtype=float,
        doc="""If scan through lambda needed (minimizeBiasedRisk, minimizeUnbiasedRisk),
                 step in these increments.  If lambdaStepType = log:linear, suggest 0.1:0.1""",
        default=0.1,
    )
 
 
class PsfMatchTask(pipeBase.Task, abc.ABC):
    """Base class for Psf Matching; should not be called directly
 
    Notes
    -----
    PsfMatchTask is a base class that implements the core functionality for matching the
    Psfs of two images using a spatially varying Psf-matching `lsst.afw.math.LinearCombinationKernel`.
    The Task requires the user to provide an instance of an `lsst.afw.math.SpatialCellSet`,
    filled with `lsst.ip.diffim.KernelCandidate` instances, and a list of `lsst.afw.math.Kernels`
    of basis shapes that will be used for the decomposition.  If requested, the Task
    also performs background matching and returns the differential background model as an
    `lsst.afw.math.Kernel.SpatialFunction`.
 
    The initialization sets the Psf-matching kernel configuration using the
    value of self.config.kernel.active.  If the kernel is requested with
    regularization to moderate the bias/variance tradeoff, currently only used
    when a delta function kernel basis is provided, it creates a
    regularization matrix stored as member variable self.hMat.
 
    **Invoking the Task**
 
    As a base class, this Task is not directly invoked.  However, ``run()`` methods that are
    implemented on derived classes will make use of the core ``_solve()`` functionality,
    which defines a sequence of `lsst.afw.math.CandidateVisitor` classes that iterate
    through the KernelCandidates, first building up a per-candidate solution and then
    building up a spatial model from the ensemble of candidates.  Sigma clipping is
    performed using the mean and standard deviation of all kernel sums (to reject
    variable objects), on the per-candidate substamp diffim residuals
    (to indicate a bad choice of kernel basis shapes for that particular object),
    and on the substamp diffim residuals using the spatial kernel fit (to indicate a bad
    choice of spatial kernel order, or poor constraints on the spatial model).  The
    ``_diagnostic()`` method logs information on the quality of the spatial fit, and also
    modifies the Task metadata.
 
    .. list-table:: Quantities set in Metadata
       :header-rows: 1
 
       * - Parameter
         - Description
       * - ``spatialConditionNum``
         - Condition number of the spatial kernel fit
       * - ``spatialKernelSum``
         - Kernel sum (10^{-0.4 * ``Delta``; zeropoint}) of the spatial Psf-matching kernel
       * - ``ALBasisNGauss``
         - If using sum-of-Gaussian basis, the number of gaussians used
       * - ``ALBasisDegGauss``
         - If using sum-of-Gaussian basis, the deg of spatial variation of the Gaussians
       * - ``ALBasisSigGauss``
         - If using sum-of-Gaussian basis, the widths (sigma) of the Gaussians
       * - ``ALKernelSize``
         - If using sum-of-Gaussian basis, the kernel size
       * - ``NFalsePositivesTotal``
         - Total number of diaSources
       * - ``NFalsePositivesRefAssociated``
         - Number of diaSources that associate with the reference catalog
       * - ``NFalsePositivesRefAssociated``
         - Number of diaSources that associate with the source catalog
       * - ``NFalsePositivesUnassociated``
         - Number of diaSources that are orphans
       * - ``metric_MEAN``
         - Mean value of substamp diffim quality metrics across all KernelCandidates,
           for both the per-candidate (LOCAL) and SPATIAL residuals
       * - ``metric_MEDIAN``
         - Median value of substamp diffim quality metrics across all KernelCandidates,
           for both the per-candidate (LOCAL) and SPATIAL residuals
       * - ``metric_STDEV``
         - Standard deviation of substamp diffim quality metrics across all KernelCandidates,
           for both the per-candidate (LOCAL) and SPATIAL residuals
 
    **Debug variables**
 
    The ``pipetask`` command line interface supports a
    flag --debug to import @b debug.py from your PYTHONPATH.  The relevant contents of debug.py
    for this Task include:
 
    .. code-block:: py
 
        import sys
        import lsstDebug
        def DebugInfo(name):
            di = lsstDebug.getInfo(name)
            if name == "lsst.ip.diffim.psfMatch":
                # enable debug output
                di.display = True
                # display mask transparency
                di.maskTransparency = 80
                # show all the candidates and residuals
                di.displayCandidates = True
                # show kernel basis functions
                di.displayKernelBasis = False
                # show kernel realized across the image
                di.displayKernelMosaic = True
                # show coefficients of spatial model
                di.plotKernelSpatialModel = False
                # show fixed and spatial coefficients and coefficient histograms
                di.plotKernelCoefficients = True
                # show the bad candidates (red) along with good (green)
                di.showBadCandidates = True
            return di
        lsstDebug.Info = DebugInfo
        lsstDebug.frame = 1
 
    Note that if you want additional logging info, you may add to your scripts:
 
    .. code-block:: py
 
        import lsst.utils.logging as logUtils
        logUtils.trace_set_at("lsst.ip.diffim", 4)
    """
    ConfigClass = PsfMatchConfig
    _DefaultName = "psfMatch"
 
    def __init__(self, *args, **kwargs):
        pipeBase.Task.__init__(self, *args, **kwargs)
        self.kConfig = self.config.kernel.active
 
        if 'useRegularization' in self.kConfig:
            self.useRegularization = self.kConfig.useRegularization
        else:
            self.useRegularization = False
 
        if self.useRegularization:
            self.hMat = diffimLib.makeRegularizationMatrix(pexConfig.makePropertySet(self.kConfig))
 
    def _diagnostic(self, kernelCellSet, spatialSolution, spatialKernel, spatialBg):
        """Provide logging diagnostics on quality of spatial kernel fit
 
        Parameters
        ----------
        kernelCellSet : `lsst.afw.math.SpatialCellSet`
            Cellset that contains the KernelCandidates used in the fitting
        spatialSolution : `lsst.ip.diffim.SpatialKernelSolution`
            KernelSolution of best-fit
        spatialKernel : `lsst.afw.math.LinearCombinationKernel`
            Best-fit spatial Kernel model
        spatialBg : `lsst.afw.math.Function2D`
            Best-fit spatial background model
        """
        # What is the final kernel sum
        kImage = afwImage.ImageD(spatialKernel.getDimensions())
        # Evaluate the kernel at the cell-set center, not at the world origin.
        xcen, ycen = kernelCellSet.getBBox().getCenter()
        kSum = spatialKernel.computeImage(kImage, doNormalize=False, x=xcen, y=ycen)
        self.log.info("Final spatial kernel sum %.3f", kSum)
 
        # Look at how well conditioned the matrix is
        conditionNum = spatialSolution.getConditionNumber(
            getattr(diffimLib.KernelSolution, self.kConfig.conditionNumberType))
        self.log.info("Spatial model condition number %.3e", conditionNum)
 
        if conditionNum < 0.0:
            self.log.warning("Condition number is negative (%.3e)", conditionNum)
        if conditionNum > self.kConfig.maxSpatialConditionNumber:
            self.log.warning("Spatial solution exceeds max condition number (%.3e > %.3e)",
                             conditionNum, self.kConfig.maxSpatialConditionNumber)
 
        self.metadata["spatialConditionNum"] = conditionNum
        self.metadata["spatialKernelSum"] = kSum
 
        # Look at how well the solution is constrained
        nBasisKernels = spatialKernel.getNBasisKernels()
        nKernelTerms = spatialKernel.getNSpatialParameters()
        if nKernelTerms == 0:  # order 0
            nKernelTerms = 1
 
        # Not fit for
        nBgTerms = spatialBg.getNParameters()
        if nBgTerms == 1:
            if spatialBg.getParameters()[0] == 0.0:
                nBgTerms = 0
 
        nGood = 0
        nBad = 0
        nTot = 0
        for cell in kernelCellSet.getCellList():
            for cand in cell.begin(False):  # False = include bad candidates
                nTot += 1
                if cand.getStatus() == afwMath.SpatialCellCandidate.GOOD:
                    nGood += 1
                if cand.getStatus() == afwMath.SpatialCellCandidate.BAD:
                    nBad += 1
 
        self.log.info("Doing stats of kernel candidates used in the spatial fit.")
 
        # Counting statistics
        if nBad > 2*nGood:
            self.log.warning("Many more candidates rejected than accepted; %d total, %d rejected, %d used",
                             nTot, nBad, nGood)
        else:
            self.log.info("%d candidates total, %d rejected, %d used", nTot, nBad, nGood)
 
        # Some judgements on the quality of the spatial models
        if nGood < nKernelTerms:
            self.log.warning("Spatial kernel model underconstrained; %d candidates, %d terms, %d bases",
                             nGood, nKernelTerms, nBasisKernels)
            self.log.warning("Consider lowering the spatial order")
        elif nGood <= 2*nKernelTerms:
            self.log.warning("Spatial kernel model poorly constrained; %d candidates, %d terms, %d bases",
                             nGood, nKernelTerms, nBasisKernels)
            self.log.warning("Consider lowering the spatial order")
        else:
            self.log.info("Spatial kernel model well constrained; %d candidates, %d terms, %d bases",
                          nGood, nKernelTerms, nBasisKernels)
 
        if nGood < nBgTerms:
            self.log.warning("Spatial background model underconstrained; %d candidates, %d terms",
                             nGood, nBgTerms)
            self.log.warning("Consider lowering the spatial order")
        elif nGood <= 2*nBgTerms:
            self.log.warning("Spatial background model poorly constrained; %d candidates, %d terms",
                             nGood, nBgTerms)
            self.log.warning("Consider lowering the spatial order")
        else:
            self.log.info("Spatial background model appears well constrained; %d candidates, %d terms",
                          nGood, nBgTerms)
 
    def _displayDebug(self, kernelCellSet, spatialKernel, spatialBackground):
        """Provide visualization of the inputs and ouputs to the Psf-matching code
 
        Parameters
        ----------
        kernelCellSet : `lsst.afw.math.SpatialCellSet`
            The SpatialCellSet used in determining the matching kernel and background
        spatialKernel : `lsst.afw.math.LinearCombinationKernel`
            Spatially varying Psf-matching kernel
        spatialBackground : `lsst.afw.math.Function2D`
            Spatially varying background-matching function
        """
        import lsstDebug
        displayCandidates = lsstDebug.Info(__name__).displayCandidates
        displayKernelBasis = lsstDebug.Info(__name__).displayKernelBasis
        displayKernelMosaic = lsstDebug.Info(__name__).displayKernelMosaic
        plotKernelSpatialModel = lsstDebug.Info(__name__).plotKernelSpatialModel
        plotKernelCoefficients = lsstDebug.Info(__name__).plotKernelCoefficients
        showBadCandidates = lsstDebug.Info(__name__).showBadCandidates
        maskTransparency = lsstDebug.Info(__name__).maskTransparency
        if not maskTransparency:
            maskTransparency = 0
        afwDisplay.setDefaultMaskTransparency(maskTransparency)
 
        if displayCandidates:
            diutils.showKernelCandidates(kernelCellSet, kernel=spatialKernel, background=spatialBackground,
                                         frame=lsstDebug.frame,
                                         showBadCandidates=showBadCandidates)
            lsstDebug.frame += 1
            diutils.showKernelCandidates(kernelCellSet, kernel=spatialKernel, background=spatialBackground,
                                         frame=lsstDebug.frame,
                                         showBadCandidates=showBadCandidates,
                                         kernels=True)
            lsstDebug.frame += 1
            diutils.showKernelCandidates(kernelCellSet, kernel=spatialKernel, background=spatialBackground,
                                         frame=lsstDebug.frame,
                                         showBadCandidates=showBadCandidates,
                                         resids=True)
            lsstDebug.frame += 1
 
        if displayKernelBasis:
            diutils.showKernelBasis(spatialKernel, frame=lsstDebug.frame)
            lsstDebug.frame += 1
 
        if displayKernelMosaic:
            diutils.showKernelMosaic(kernelCellSet.getBBox(), spatialKernel, frame=lsstDebug.frame)
            lsstDebug.frame += 1
 
        if plotKernelSpatialModel:
            diutils.plotKernelSpatialModel(spatialKernel, kernelCellSet, showBadCandidates=showBadCandidates)
 
        if plotKernelCoefficients:
            diutils.plotKernelCoefficients(spatialKernel, kernelCellSet)
 
    def _createPcaBasis(self, kernelCellSet, nStarPerCell, ps):
        """Create Principal Component basis
 
        If a principal component analysis is requested, typically when using a delta function basis,
        perform the PCA here and return a new basis list containing the new principal components.
 
        Parameters
        ----------
        kernelCellSet : `lsst.afw.math.SpatialCellSet`
            a SpatialCellSet containing KernelCandidates, from which components are derived
        nStarPerCell : `int`
            the number of stars per cell to visit when doing the PCA
        ps : `lsst.daf.base.PropertySet`
            input property set controlling the single kernel visitor
 
        Returns
        -------
        nRejectedPca : `int`
            number of KernelCandidates rejected during PCA loop
        spatialBasisList : `list` of `lsst.afw.math.kernel.FixedKernel`
            basis list containing the principal shapes as Kernels
 
        Raises
        ------
        RuntimeError
            If the Eigenvalues sum to zero.
        """
        nComponents = self.kConfig.numPrincipalComponents
        imagePca = diffimLib.KernelPcaD()
        importStarVisitor = diffimLib.KernelPcaVisitorF(imagePca)
        kernelCellSet.visitCandidates(importStarVisitor, nStarPerCell)
        if self.kConfig.subtractMeanForPca:
            importStarVisitor.subtractMean()
        imagePca.analyze()
 
        eigenValues = imagePca.getEigenValues()
        pcaBasisList = importStarVisitor.getEigenKernels()
 
        eSum = np.sum(eigenValues)
        if eSum == 0.0:
            raise RuntimeError("Eigenvalues sum to zero")
        trace_logger = getTraceLogger(self.log.getChild("_solve"), 5)
        for j in range(len(eigenValues)):
            trace_logger.debug("Eigenvalue %d : %f (%f)", j, eigenValues[j], eigenValues[j]/eSum)
 
        nToUse = min(nComponents, len(eigenValues))
        trimBasisList = []
        for j in range(nToUse):
            # Check for NaNs?
            kimage = afwImage.ImageD(pcaBasisList[j].getDimensions())
            pcaBasisList[j].computeImage(kimage, doNormalize=False)
            if not (True in np.isnan(kimage.array)):
                trimBasisList.append(pcaBasisList[j])
 
        # Put all the power in the first kernel, which will not vary spatially
        spatialBasisList = diffimLib.renormalizeKernelList(trimBasisList)
 
        # New Kernel visitor for this new basis list (no regularization explicitly)
        singlekvPca = diffimLib.BuildSingleKernelVisitorF(spatialBasisList, ps)
        singlekvPca.setSkipBuilt(False)
        kernelCellSet.visitCandidates(singlekvPca, nStarPerCell)
        singlekvPca.setSkipBuilt(True)
        nRejectedPca = singlekvPca.getNRejected()
 
        return nRejectedPca, spatialBasisList
 
    @abc.abstractmethod
    def _buildCellSet(self, *args):
        """Fill a SpatialCellSet with KernelCandidates for the Psf-matching process;
        override in derived classes"""
        return
 
    @timeMethod
    def _solve(self, kernelCellSet, basisList):
        """Solve for the PSF matching kernel
 
        Parameters
        ----------
        kernelCellSet : `lsst.afw.math.SpatialCellSet`
            a SpatialCellSet to use in determining the matching kernel
             (typically as provided by _buildCellSet)
        basisList : `list` of `lsst.afw.math.kernel.FixedKernel`
            list of Kernels to be used in the decomposition of the spatially varying kernel
            (typically as provided by makeKernelBasisList)
 
        Returns
        -------
        psfMatchingKernel : `lsst.afw.math.LinearCombinationKernel`
            Spatially varying Psf-matching kernel
        backgroundModel : `lsst.afw.math.Function2D`
            Spatially varying background-matching function
 
        Raises
        ------
        NoKernelCandidatesError :
            If there are no useable kernel candidates.
        """
 
        import lsstDebug
        display = lsstDebug.Info(__name__).display
 
        maxSpatialIterations = self.kConfig.maxSpatialIterations
        nStarPerCell = self.kConfig.nStarPerCell
        usePcaForSpatialKernel = self.kConfig.usePcaForSpatialKernel
 
        # Visitor for the single kernel fit
        ps = pexConfig.makePropertySet(self.kConfig)
        if self.useRegularization:
            singlekv = diffimLib.BuildSingleKernelVisitorF(basisList, ps, self.hMat)
        else:
            singlekv = diffimLib.BuildSingleKernelVisitorF(basisList, ps)
 
        # Visitor for the kernel sum rejection
        ksv = diffimLib.KernelSumVisitorF(ps)
 
        # Main loop
        trace_loggers = [getTraceLogger(self.log.getChild("_solve"), i) for i in range(5)]
        t0 = time.time()
        totalIterations = 0
        thisIteration = 0
        while (thisIteration < maxSpatialIterations):
 
            # Make sure there are no uninitialized candidates as active occupants of Cell
            nRejectedSkf = -1
            while (nRejectedSkf != 0):
                trace_loggers[1].debug("Building single kernels...")
                kernelCellSet.visitCandidates(singlekv, nStarPerCell, ignoreExceptions=True)
                nRejectedSkf = singlekv.getNRejected()
                trace_loggers[1].debug(
                    "Iteration %d, rejected %d candidates due to initial kernel fit",
                    thisIteration, nRejectedSkf
                )
 
            # Reject outliers in kernel sum
            ksv.resetKernelSum()
            ksv.setMode(diffimLib.KernelSumVisitorF.AGGREGATE)
            kernelCellSet.visitCandidates(ksv, nStarPerCell, ignoreExceptions=True)
 
            allCellsEmpty = True
            for cell in kernelCellSet.getCellList():
                if not cell.empty():
                    allCellsEmpty = False
                    break
            if allCellsEmpty:
                raise NoKernelCandidatesError("All spatial cells are empty of candidates")
 
            try:
                ksv.processKsumDistribution()
            except RuntimeError as e:
                raise NoKernelCandidatesError("Unable to calculate the kernel sum") from e
 
            ksv.setMode(diffimLib.KernelSumVisitorF.REJECT)
            kernelCellSet.visitCandidates(ksv, nStarPerCell, ignoreExceptions=True)
 
            nRejectedKsum = ksv.getNRejected()
            trace_loggers[1].debug(
                "Iteration %d, rejected %d candidates due to kernel sum",
                thisIteration, nRejectedKsum
            )
 
            # Do we jump back to the top without incrementing thisIteration?
            if nRejectedKsum > 0:
                totalIterations += 1
                continue
 
            # At this stage we can either apply the spatial fit to
            # the kernels, or we run a PCA, use these as a *new*
            # basis set with lower dimensionality, and then apply
            # the spatial fit to these kernels
 
            if (usePcaForSpatialKernel):
                trace_loggers[0].debug("Building Pca basis")
 
                nRejectedPca, spatialBasisList = self._createPcaBasis(kernelCellSet, nStarPerCell, ps)
                trace_loggers[1].debug(
                    "Iteration %d, rejected %d candidates due to Pca kernel fit",
                    thisIteration, nRejectedPca
                )
 
                # We don't want to continue on (yet) with the
                # spatial modeling, because we have bad objects
                # contributing to the Pca basis.  We basically
                # need to restart from the beginning of this loop,
                # since the cell-mates of those objects that were
                # rejected need their original Kernels built by
                # singleKernelFitter.
 
                # Don't count against thisIteration
                if (nRejectedPca > 0):
                    totalIterations += 1
                    continue
            else:
                spatialBasisList = basisList
 
            # We have gotten on to the spatial modeling part
            regionBBox = kernelCellSet.getBBox()
            spatialkv = diffimLib.BuildSpatialKernelVisitorF(spatialBasisList, regionBBox, ps)
            kernelCellSet.visitCandidates(spatialkv, nStarPerCell)
            spatialkv.solveLinearEquation()
            trace_loggers[2].debug("Spatial kernel built with %d candidates", spatialkv.getNCandidates())
            spatialKernel, spatialBackground = spatialkv.getSolutionPair()
 
            # Check the quality of the spatial fit (look at residuals)
            assesskv = diffimLib.AssessSpatialKernelVisitorF(spatialKernel, spatialBackground, ps)
            kernelCellSet.visitCandidates(assesskv, nStarPerCell)
            nRejectedSpatial = assesskv.getNRejected()
            nGoodSpatial = assesskv.getNGood()
            trace_loggers[1].debug(
                "Iteration %d, rejected %d candidates due to spatial kernel fit",
                thisIteration, nRejectedSpatial
            )
            trace_loggers[1].debug("%d candidates used in fit", nGoodSpatial)
 
            # If only nGoodSpatial == 0, might be other candidates in the cells
            if nGoodSpatial == 0 and nRejectedSpatial == 0:
                raise NoKernelCandidatesError("No kernel candidates for spatial fit")
 
            if nRejectedSpatial == 0:
                # Nothing rejected, finished with spatial fit
                break
 
            # Otherwise, iterate on...
            thisIteration += 1
 
        # Final fit if above did not converge
        if (nRejectedSpatial > 0) and (thisIteration == maxSpatialIterations):
            trace_loggers[1].debug("Final spatial fit")
            if (usePcaForSpatialKernel):
                nRejectedPca, spatialBasisList = self._createPcaBasis(kernelCellSet, nStarPerCell, ps)
            regionBBox = kernelCellSet.getBBox()
            spatialkv = diffimLib.BuildSpatialKernelVisitorF(spatialBasisList, regionBBox, ps)
            kernelCellSet.visitCandidates(spatialkv, nStarPerCell)
            spatialkv.solveLinearEquation()
            trace_loggers[2].debug("Spatial kernel built with %d candidates", spatialkv.getNCandidates())
            spatialKernel, spatialBackground = spatialkv.getSolutionPair()
 
        # Run after the final fit to use the updated kernel visitor `spatialkv`
        if spatialkv.getNCandidates() < 1:
            raise NoKernelCandidatesError("No kernel candidates remain after max iterations")
 
        spatialSolution = spatialkv.getKernelSolution()
 
        t1 = time.time()
        trace_loggers[0].debug("Total time to compute the spatial kernel : %.2f s", (t1 - t0))
 
        if display:
            self._displayDebug(kernelCellSet, spatialKernel, spatialBackground)
 
        self._diagnostic(kernelCellSet, spatialSolution, spatialKernel, spatialBackground)
 
        return spatialSolution, spatialKernel, spatialBackground
 
 
PsfMatch = PsfMatchTask