def testMakeBadKernels(self):
"""Attempt to make various invalid kernels; make sure the constructor shows an exception
"""
kWidth = 4
kHeight = 3
gaussFunc1 = afwMath.GaussianFunction1D(1.0)
gaussFunc2 = afwMath.GaussianFunction2D(1.0, 1.0, 0.0)
spFunc = afwMath.PolynomialFunction2D(1)
kernelList = []
kernelList.append(afwMath.FixedKernel(
afwImage.ImageD(lsst.geom.Extent2I(kWidth, kHeight), 0.1)))
kernelList.append(afwMath.FixedKernel(
afwImage.ImageD(lsst.geom.Extent2I(kWidth, kHeight), 0.2)))
for numKernelParams in (2, 4):
spFuncList = []
for ii in range(numKernelParams):
spFuncList.append(spFunc.clone())
try:
afwMath.AnalyticKernel(kWidth, kHeight, gaussFunc2, spFuncList)
self.fail("Should have failed with wrong # of spatial functions")
except pexExcept.Exception:
pass
for numKernelParams in (1, 3):
spFuncList = []
for ii in range(numKernelParams):
spFuncList.append(spFunc.clone())
try:
afwMath.LinearCombinationKernel(kernelList, spFuncList)
self.fail("Should have failed with wrong # of spatial functions")
except pexExcept.Exception:
pass
kParamList = [0.2]*numKernelParams
try:
afwMath.LinearCombinationKernel(kernelList, kParamList)
self.fail("Should have failed with wrong # of kernel parameters")
except pexExcept.Exception:
pass
try:
afwMath.SeparableKernel(
kWidth, kHeight, gaussFunc1, gaussFunc1, spFuncList)
self.fail("Should have failed with wrong # of spatial functions")
except pexExcept.Exception:
pass
for pointX in range(-1, kWidth+2):
for pointY in range(-1, kHeight+2):
if (0 <= pointX < kWidth) and (0 <= pointY < kHeight):
continue
try:
afwMath.DeltaFunctionKernel(
kWidth, kHeight, lsst.geom.Point2I(pointX, pointY))
self.fail("Should have failed with point not on kernel")
except pexExcept.Exception:
pass
def testRefactorDeltaLinearCombinationKernel(self):
"""Test LinearCombinationKernel.refactor with delta function basis kernels
"""
kWidth = 4
kHeight = 3
for spOrder in (0, 1, 2):
spFunc = afwMath.PolynomialFunction2D(spOrder)
numSpParams = spFunc.getNParameters()
basisKernelList = makeDeltaFunctionKernelList(kWidth, kHeight)
kernel = afwMath.LinearCombinationKernel(basisKernelList, spFunc)
numBasisKernels = kernel.getNKernelParameters()
maxVal = 1.01 + ((numSpParams - 1) * 0.1)
sParamList = [
numpy.arange(kInd + 1.0, kInd + maxVal, 0.1)
for kInd in range(numBasisKernels)
]
kernel.setSpatialParameters(sParamList)
refKernel = kernel.refactor()
self.assert_(refKernel)
errStr = self.compareKernels(kernel,
refKernel,
compareParams=False)
if errStr:
self.fail("failed with %s for spOrder=%s (numSpCoeff=%s)" %
(errStr, spOrder, numSpParams))
def testSpatiallyVaryingDeltaFunctionLinearCombination(self):
"""Test convolution with a spatially varying LinearCombinationKernel of delta function basis kernels.
"""
kWidth = 2
kHeight = 2
# create spatially model
sFunc = afwMath.PolynomialFunction2D(1)
# spatial parameters are a list of entries, one per kernel parameter;
# each entry is a list of spatial parameters
sParams = (
(1.0, -0.5 / self.width, -0.5 / self.height),
(0.0, 1.0 / self.width, 0.0 / self.height),
(0.0, 0.0 / self.width, 1.0 / self.height),
(0.5, 0.0, 0.0),
)
basisKernelList = makeDeltaFunctionKernelList(kWidth, kHeight)
kernel = afwMath.LinearCombinationKernel(basisKernelList, sFunc)
kernel.setSpatialParameters(sParams)
for maxInterpDist, rtol, methodStr in (
(0, 1.0e-5, "brute force"),
(10, 1.0e-3, "interpolation over 10 x 10 pixels"),
):
self.runStdTest(
kernel,
kernelDescr=
"Spatially varying LinearCombinationKernel of delta function kernels using %s"
% (methodStr, ),
maxInterpDist=maxInterpDist,
rtol=rtol)
def testLinearCombinationKernelDelta(self):
"""Test LinearCombinationKernel using a set of delta basis functions
"""
kWidth = 3
kHeight = 2
# create list of kernels
basisKernelList = makeDeltaFunctionKernelList(kWidth, kHeight)
basisImArrList = []
for basisKernel in basisKernelList:
basisImage = afwImage.ImageD(basisKernel.getDimensions())
basisKernel.computeImage(basisImage, True)
basisImArrList.append(basisImage.getArray())
kParams = [0.0] * len(basisKernelList)
kernel = afwMath.LinearCombinationKernel(basisKernelList, kParams)
self.assert_(kernel.isDeltaFunctionBasis())
self.basicTests(kernel, len(kParams))
for ii in range(len(basisKernelList)):
kParams = [0.0] * len(basisKernelList)
kParams[ii] = 1.0
kernel.setKernelParameters(kParams)
kIm = afwImage.ImageD(kernel.getDimensions())
kernel.computeImage(kIm, True)
kImArr = kIm.getArray()
if not numpy.allclose(kImArr, basisImArrList[ii]):
self.fail("%s = %s != %s for the %s'th basis kernel" % \
(kernel.__class__.__name__, kImArr, basisImArrList[ii], ii))
kernelClone = kernel.clone()
errStr = self.compareKernels(kernel, kernelClone)
if errStr:
self.fail(errStr)
self.verifyCache(kernel, hasCache=False)
def testRefactorGaussianLinearCombinationKernel(self):
"""Test LinearCombinationKernel.refactor with Gaussian basis kernels
"""
kWidth = 4
kHeight = 3
for spOrder in (0, 1, 2):
spFunc = afwMath.PolynomialFunction2D(spOrder)
numSpParams = spFunc.getNParameters()
gaussParamsList = [
(1.5, 1.5, 0.0),
(2.5, 1.5, 0.0),
(2.5, 1.5, math.pi / 2.0),
]
gaussBasisKernelList = makeGaussianKernelList(
kWidth, kHeight, gaussParamsList)
kernel = afwMath.LinearCombinationKernel(
gaussBasisKernelList, spFunc)
numBasisKernels = kernel.getNKernelParameters()
maxVal = 1.01 + ((numSpParams - 1) * 0.1)
sParamList = [np.arange(kInd + 1.0, kInd + maxVal, 0.1)
for kInd in range(numBasisKernels)]
kernel.setSpatialParameters(sParamList)
refKernel = kernel.refactor()
self.assertTrue(refKernel)
errStr = self.compareKernels(
kernel, refKernel, compareParams=False)
if errStr:
self.fail(f"failed with {errStr} for spOrder={spOrder}, numSpParams={numSpParams}")
def makeSpatialKernel(self, order):
basicGaussian1 = afwMath.GaussianFunction2D(2., 2., 0.)
basicKernel1 = afwMath.AnalyticKernel(self.ksize, self.ksize,
basicGaussian1)
basicGaussian2 = afwMath.GaussianFunction2D(5., 3., 0.5 * num.pi)
basicKernel2 = afwMath.AnalyticKernel(self.ksize, self.ksize,
basicGaussian2)
basisList = []
basisList.append(basicKernel1)
basisList.append(basicKernel2)
basisList = ipDiffim.renormalizeKernelList(basisList)
spatialKernelFunction = afwMath.PolynomialFunction2D(order)
spatialKernel = afwMath.LinearCombinationKernel(
basisList, spatialKernelFunction)
kCoeffs = [
[
0.0 for x in range(1,
spatialKernelFunction.getNParameters() + 1)
],
[
0.01 * x
for x in range(1,
spatialKernelFunction.getNParameters() + 1)
]
]
kCoeffs[0][
0] = 1.0 # it does not vary spatially; constant across image
spatialKernel.setSpatialParameters(kCoeffs)
return spatialKernel
def testLinearCombinationKernelAnalytic(self):
"""Test LinearCombinationKernel using analytic basis kernels.
The basis kernels are mutable so that we can verify that the
LinearCombinationKernel has private copies of the basis kernels.
"""
kWidth = 5
kHeight = 8
# create list of kernels
basisImArrList = []
basisKernelList = []
for basisKernelParams in [(1.2, 0.3, 1.570796), (1.0, 0.2, 0.0)]:
basisKernelFunction = afwMath.GaussianFunction2D(
*basisKernelParams)
basisKernel = afwMath.AnalyticKernel(
kWidth, kHeight, basisKernelFunction)
basisImage = afwImage.ImageD(basisKernel.getDimensions())
basisKernel.computeImage(basisImage, True)
basisImArrList.append(basisImage.getArray())
basisKernelList.append(basisKernel)
kParams = [0.0]*len(basisKernelList)
kernel = afwMath.LinearCombinationKernel(basisKernelList, kParams)
self.assertTrue(not kernel.isDeltaFunctionBasis())
self.basicTests(kernel, len(kParams))
kernelResized = self.verifyResized(kernel)
self.basicTests(kernelResized, len(kParams))
# make sure the linear combination kernel has private copies of its basis kernels
# by altering the local basis kernels and making sure the new images do
# NOT match
modBasisImArrList = []
for basisKernel in basisKernelList:
basisKernel.setKernelParameters((0.4, 0.5, 0.6))
modBasisImage = afwImage.ImageD(basisKernel.getDimensions())
basisKernel.computeImage(modBasisImage, True)
modBasisImArrList.append(modBasisImage.getArray())
for ii in range(len(basisKernelList)):
kParams = [0.0]*len(basisKernelList)
kParams[ii] = 1.0
kernel.setKernelParameters(kParams)
kIm = afwImage.ImageD(kernel.getDimensions())
kernel.computeImage(kIm, True)
kImArr = kIm.getArray()
if not np.allclose(kImArr, basisImArrList[ii]):
self.fail(f"{kernel.__class__.__name__} = {kImArr} != "
f"{basisImArrList[ii]} for the {ii}'th basis kernel")
if np.allclose(kImArr, modBasisImArrList[ii]):
self.fail(f"{kernel.__class__.__name__} = {kImArr} != "
f"{modBasisImArrList[ii]} for *modified* {ii}'th basis kernel")
kernelClone = kernel.clone()
errStr = self.compareKernels(kernel, kernelClone)
if errStr:
self.fail(errStr)
self.verifyCache(kernel, hasCache=False)
def _computeVaryingPsf(self):
"""Compute a varying PSF as a linear combination of PCA (== Karhunen-Loeve) basis functions
We simply desire a PSF that is not constant across the image, so the precise choice of
parameters (e.g., sigmas, setSpatialParameters) are not crucial.
"""
kernelSize = 31
sigma1 = 1.75
sigma2 = 2.0 * sigma1
basisKernelList = []
for sigma in (sigma1, sigma2):
basisKernel = afwMath.AnalyticKernel(
kernelSize, kernelSize,
afwMath.GaussianFunction2D(sigma, sigma))
basisImage = afwImage.ImageD(basisKernel.getDimensions())
basisKernel.computeImage(basisImage, True)
basisImage /= np.sum(basisImage.getArray())
if sigma == sigma1:
basisImage0 = basisImage
else:
basisImage -= basisImage0
basisKernelList.append(afwMath.FixedKernel(basisImage))
order = 1
spFunc = afwMath.PolynomialFunction2D(order)
exactKernel = afwMath.LinearCombinationKernel(basisKernelList, spFunc)
exactKernel.setSpatialParameters([[1.0, 0, 0], [0.0, 0.5E-2, 0.2E-2]])
exactPsf = measAlg.PcaPsf(exactKernel)
return exactPsf
def testSVLinearCombinationKernel(self):
"""Test a spatially varying LinearCombinationKernel
"""
kWidth = 3
kHeight = 2
# create image arrays for the basis kernels
basisImArrList = []
imArr = np.zeros((kWidth, kHeight), dtype=float)
imArr += 0.1
imArr[kWidth // 2, :] = 0.9
basisImArrList.append(imArr)
imArr = np.zeros((kWidth, kHeight), dtype=float)
imArr += 0.2
imArr[:, kHeight // 2] = 0.8
basisImArrList.append(imArr)
# create a list of basis kernels from the images
kVec = []
for basisImArr in basisImArrList:
basisImage = afwImage.makeImageFromArray(
basisImArr.transpose().copy())
kernel = afwMath.FixedKernel(basisImage)
kVec.append(kernel)
# create spatially varying linear combination kernel
spFunc = afwMath.PolynomialFunction2D(1)
# spatial parameters are a list of entries, one per kernel parameter;
# each entry is a list of spatial parameters
sParams = (
(0.0, 1.0, 0.0),
(0.0, 0.0, 1.0),
)
k = afwMath.LinearCombinationKernel(kVec, spFunc)
k.setSpatialParameters(sParams)
with lsst.utils.tests.getTempFilePath(".fits") as filename:
k.writeFits(filename)
k2 = afwMath.LinearCombinationKernel.readFits(filename)
self.kernelCheck(k, k2)
kImage = afwImage.ImageD(lsst.geom.Extent2I(kWidth, kHeight))
for colPos, rowPos, coeff0, coeff1 in [
(0.0, 0.0, 0.0, 0.0),
(1.0, 0.0, 1.0, 0.0),
(0.0, 1.0, 0.0, 1.0),
(1.0, 1.0, 1.0, 1.0),
(0.5, 0.5, 0.5, 0.5),
]:
k2.computeImage(kImage, False, colPos, rowPos)
kImArr = kImage.getArray().transpose()
refKImArr = (basisImArrList[0] * coeff0) + \
(basisImArrList[1] * coeff1)
if not np.allclose(kImArr, refKImArr):
self.fail(f"{k2.__class__.__name__} = {kImArr} != {refKImArr} "
f"at colPos={colPos}, rowPos={rowPos}")
def testLinearCombinationKernel(self):
"""Test LinearCombinationKernel using a set of delta basis functions
"""
kWidth = 3
kHeight = 2
pol = pexPolicy.Policy()
additionalData = dafBase.PropertySet()
loc = dafPersist.LogicalLocation(
os.path.join(testPath, "data", "kernel5.boost"))
persistence = dafPersist.Persistence.getPersistence(pol)
# create list of kernels
basisImArrList = []
kVec = afwMath.KernelList()
for row in range(kHeight):
for col in range(kWidth):
kernel = afwMath.DeltaFunctionKernel(kWidth, kHeight,
afwGeom.Point2I(col, row))
basisImage = afwImage.ImageD(kernel.getDimensions())
kernel.computeImage(basisImage, True)
basisImArrList.append(basisImage.getArray().transpose().copy())
kVec.append(kernel)
kParams = [0.0] * len(kVec)
k = afwMath.LinearCombinationKernel(kVec, kParams)
for ii in range(len(kVec)):
kParams = [0.0] * len(kVec)
kParams[ii] = 1.0
k.setKernelParameters(kParams)
storageList = dafPersist.StorageList()
storage = persistence.getPersistStorage("XmlStorage", loc)
storageList.append(storage)
persistence.persist(k, storageList, additionalData)
storageList2 = dafPersist.StorageList()
storage2 = persistence.getRetrieveStorage("XmlStorage", loc)
storageList2.append(storage2)
x = persistence.unsafeRetrieve("LinearCombinationKernel",
storageList2, additionalData)
k2 = afwMath.LinearCombinationKernel.swigConvert(x)
self.kernelCheck(k, k2)
kIm = afwImage.ImageD(k2.getDimensions())
k2.computeImage(kIm, True)
kImArr = kIm.getArray().transpose()
if not np.allclose(kImArr, basisImArrList[ii]):
self.fail(
"%s = %s != %s for the %s'th basis kernel" %
(k2.__class__.__name__, kImArr, basisImArrList[ii], ii))
def testTicket873(self):
"""Demonstrate ticket 873: convolution of a MaskedImage with a spatially varying
LinearCombinationKernel of basis kernels with low covariance gives incorrect variance.
"""
# create spatial model
sFunc = afwMath.PolynomialFunction2D(1)
# spatial parameters are a list of entries, one per kernel parameter;
# each entry is a list of spatial parameters
sParams = (
(1.0, -0.5/self.width, -0.5/self.height),
(0.0, 1.0/self.width, 0.0/self.height),
(0.0, 0.0/self.width, 1.0/self.height),
)
# create three kernels with some non-overlapping pixels
# (non-zero pixels in one kernel vs. zero pixels in other kernels);
# note: the extreme example of this is delta function kernels, but this
# is less extreme
basisKernelList = []
kImArr = numpy.zeros([5, 5], dtype=float)
kImArr[1:4, 1:4] = 0.5
kImArr[2, 2] = 1.0
kImage = afwImage.makeImageFromArray(kImArr)
basisKernelList.append(afwMath.FixedKernel(kImage))
kImArr[:, :] = 0.0
kImArr[0:2, 0:2] = 0.125
kImArr[3:5, 3:5] = 0.125
kImage = afwImage.makeImageFromArray(kImArr)
basisKernelList.append(afwMath.FixedKernel(kImage))
kImArr[:, :] = 0.0
kImArr[0:2, 3:5] = 0.125
kImArr[3:5, 0:2] = 0.125
kImage = afwImage.makeImageFromArray(kImArr)
basisKernelList.append(afwMath.FixedKernel(kImage))
kernel = afwMath.LinearCombinationKernel(basisKernelList, sFunc)
kernel.setSpatialParameters(sParams)
for maxInterpDist, rtol, methodStr in (
(0, 1.0e-5, "brute force"),
(10, 3.0e-3, "interpolation over 10 x 10 pixels"),
):
self.runStdTest(
kernel,
kernelDescr="Spatially varying LinearCombinationKernel of basis "
"kernels with low covariance, using %s" % (
methodStr,),
maxInterpDist=maxInterpDist,
rtol=rtol)
def getDeltaLinearCombinationKernel(kSize, imSize, spOrder):
"""Return a LinearCombinationKernel of delta functions
@param kSize: kernel size (scalar; height = width)
@param x, y imSize: image size
"""
kernelList = afwMath.KernelList()
for ctrX in range(kSize):
for ctrY in range(kSize):
kernelList.append(afwMath.DeltaFunctionKernel(kSize, kSize, afwGeom.Point2I(ctrX, ctrY)))
polyFunc = afwMath.PolynomialFunction2D(spOrder)
kernel = afwMath.LinearCombinationKernel(kernelList, polyFunc)
spParams = getSpatialParameters(len(kernelList), polyFunc)
kernel.setSpatialParameters(spParams);
return kernel
def testZeroWidthKernel(self):
"""Convolution by a 0x0 kernel should raise an exception.
The only way to produce a 0x0 kernel is to use the default constructor
(which exists only to support persistence; it does not produce a useful kernel).
"""
kernelList = [
afwMath.FixedKernel(),
afwMath.AnalyticKernel(),
afwMath.SeparableKernel(),
# afwMath.DeltaFunctionKernel(), # DeltaFunctionKernel has no default constructor
afwMath.LinearCombinationKernel(),
]
convolutionControl = afwMath.ConvolutionControl()
for kernel in kernelList:
self.assertRaises(Exception, afwMath.convolve, self.cnvMaskedImage,
self.maskedImage, kernel, convolutionControl)
def testBad(self):
ti = afwImage.MaskedImageF(geom.Extent2I(100, 100))
ti.getVariance().set(0.1)
ti[50, 50, afwImage.LOCAL] = (1., 0x0, 1.)
sKernel = self.makeSpatialKernel(2)
si = afwImage.MaskedImageF(ti.getDimensions())
convolutionControl = afwMath.ConvolutionControl()
convolutionControl.setDoNormalize(True)
afwMath.convolve(si, ti, sKernel, convolutionControl)
bbox = geom.Box2I(geom.Point2I(25, 25), geom.Point2I(75, 75))
si = afwImage.MaskedImageF(si, bbox, origin=afwImage.LOCAL)
ti = afwImage.MaskedImageF(ti, bbox, origin=afwImage.LOCAL)
kc = ipDiffim.KernelCandidateF(50., 50., ti, si, self.ps)
badGaussian = afwMath.GaussianFunction2D(1., 1., 0.)
badKernel = afwMath.AnalyticKernel(self.ksize, self.ksize, badGaussian)
basisList = []
basisList.append(badKernel)
badSpatialKernelFunction = afwMath.PolynomialFunction2D(0)
badSpatialKernel = afwMath.LinearCombinationKernel(
basisList, badSpatialKernelFunction)
badSpatialKernel.setSpatialParameters([[
1,
]])
sBg = afwMath.PolynomialFunction2D(1)
bgCoeffs = [10., 10., 10.]
sBg.setParameters(bgCoeffs)
# must be initialized
bskv = ipDiffim.BuildSingleKernelVisitorF(self.kList, self.ps)
bskv.processCandidate(kc)
self.assertEqual(kc.isInitialized(), True)
askv = ipDiffim.AssessSpatialKernelVisitorF(badSpatialKernel, sBg,
self.ps)
askv.processCandidate(kc)
self.assertEqual(askv.getNProcessed(), 1)
self.assertEqual(askv.getNRejected(), 1)
self.assertEqual(kc.getStatus(), afwMath.SpatialCellCandidate.BAD)
def testSpatiallyVaryingGaussianLinerCombination(self):
"""Test convolution with a spatially varying LinearCombinationKernel of two Gaussian basis kernels.
"""
kWidth = 5
kHeight = 5
# create spatial model
for nBasisKernels in (3, 4):
# at 3 the kernel will not be refactored, at 4 it will be
sFunc = afwMath.PolynomialFunction2D(1)
# spatial parameters are a list of entries, one per kernel parameter;
# each entry is a list of spatial parameters
sParams = (
(1.0, -0.01 / self.width, -0.01 / self.height),
(0.0, 0.01 / self.width, 0.0 / self.height),
(0.0, 0.0 / self.width, 0.01 / self.height),
(0.5, 0.005 / self.width, -0.005 / self.height),
)[:nBasisKernels]
gaussParamsList = (
(1.5, 1.5, 0.0),
(2.5, 1.5, 0.0),
(2.5, 1.5, math.pi / 2.0),
(2.5, 2.5, 0.0),
)[:nBasisKernels]
basisKernelList = makeGaussianKernelList(kWidth, kHeight,
gaussParamsList)
kernel = afwMath.LinearCombinationKernel(basisKernelList, sFunc)
kernel.setSpatialParameters(sParams)
for maxInterpDist, rtol, methodStr in (
(0, 1.0e-5, "brute force"),
(10, 1.0e-5, "interpolation over 10 x 10 pixels"),
):
self.runStdTest(
kernel,
kernelDescr="%s with %d basis kernels convolved using %s" %
("Spatially Varying Gaussian Analytic Kernel",
nBasisKernels, methodStr),
maxInterpDist=maxInterpDist,
rtol=rtol)
def testCast(self):
instances = []
kVec = makeGaussianKernelList(9, 9, [(2.0, 2.0, 0.0)])
kParams = [0.0] * len(kVec)
instances.append(afwMath.LinearCombinationKernel(kVec, kParams))
instances.append(
afwMath.AnalyticKernel(7, 7,
afwMath.GaussianFunction2D(2.0, 2.0, 0.0)))
instances.append(
afwMath.DeltaFunctionKernel(5, 5, afwGeom.Point2I(1, 1)))
instances.append(
afwMath.FixedKernel(afwImage.ImageD(afwGeom.Extent2I(7, 7))))
instances.append(
afwMath.SeparableKernel(3, 3, afwMath.PolynomialFunction1D(0),
afwMath.PolynomialFunction1D(0)))
for instance in instances:
Class = type(instance)
base = instance.clone()
self.assertEqual(type(base), afwMath.Kernel)
derived = Class.cast(base)
self.assertEqual(type(derived), Class)
def testComputeImageRaise(self):
"""Test Kernel.computeImage raises OverflowException iff doNormalize True and kernel sum exactly 0
"""
kWidth = 4
kHeight = 3
polyFunc1 = afwMath.PolynomialFunction1D(0)
polyFunc2 = afwMath.PolynomialFunction2D(0)
analKernel = afwMath.AnalyticKernel(kWidth, kHeight, polyFunc2)
kImage = afwImage.ImageD(analKernel.getDimensions())
for coeff in (-1, -1e-99, 0, 1e99, 1):
analKernel.setKernelParameters([coeff])
analKernel.computeImage(kImage, False)
fixedKernel = afwMath.FixedKernel(kImage)
sepKernel = afwMath.SeparableKernel(
kWidth, kHeight, polyFunc1, polyFunc1)
sepKernel.setKernelParameters([coeff, coeff])
kernelList = []
kernelList.append(analKernel)
lcKernel = afwMath.LinearCombinationKernel(kernelList, [1])
self.assertFalse(lcKernel.isDeltaFunctionBasis())
doRaise = (coeff == 0)
self.basicTestComputeImageRaise(
analKernel, doRaise, "AnalyticKernel")
self.basicTestComputeImageRaise(
fixedKernel, doRaise, "FixedKernel")
self.basicTestComputeImageRaise(
sepKernel, doRaise, "SeparableKernel")
self.basicTestComputeImageRaise(
lcKernel, doRaise, "LinearCombinationKernel")
lcKernel.setKernelParameters([0])
self.basicTestComputeImageRaise(
lcKernel, True, "LinearCombinationKernel")
def testLinearCombinationKernel(self):
"""Test LinearCombinationKernel using a set of delta basis functions
"""
kWidth = 3
kHeight = 2
# create list of kernels
basisImArrList = []
kVec = []
for row in range(kHeight):
for col in range(kWidth):
kernel = afwMath.DeltaFunctionKernel(
kWidth, kHeight, lsst.geom.Point2I(col, row))
basisImage = afwImage.ImageD(kernel.getDimensions())
kernel.computeImage(basisImage, True)
basisImArrList.append(basisImage.getArray().transpose().copy())
kVec.append(kernel)
kParams = [0.0] * len(kVec)
k = afwMath.LinearCombinationKernel(kVec, kParams)
for ii in range(len(kVec)):
kParams = [0.0] * len(kVec)
kParams[ii] = 1.0
k.setKernelParameters(kParams)
with lsst.utils.tests.getTempFilePath(".fits") as filename:
k.writeFits(filename)
k2 = afwMath.LinearCombinationKernel.readFits(filename)
self.kernelCheck(k, k2)
kIm = afwImage.ImageD(k2.getDimensions())
k2.computeImage(kIm, True)
kImArr = kIm.getArray().transpose()
if not np.allclose(kImArr, basisImArrList[ii]):
self.fail(
f"{k2.__class__.__name__} = {kImArr} != {basisImArrList[ii]} "
f"for the {ii}'th basis kernel")
def getGaussianLinearCombinationKernel(kSize, imSize, spOrder):
"""Return a LinearCombinationKernel with 5 bases, each a Gaussian
@param kSize: kernel size (scalar; height = width)
@param x, y imSize: image size
"""
kernelList = afwMath.KernelList()
for fwhmX, fwhmY, angle in (
(2.0, 2.0, 0.0),
(0.5, 4.0, 0.0),
(0.5, 4.0, math.pi / 4.0),
(0.5, 4.0, math.pi / 2.0),
(4.0, 4.0, 0.0),
):
gaussFunc = afwMath.GaussianFunction2D(fwhmX, fwhmY, angle)
kernelList.append(afwMath.AnalyticKernel(kSize, kSize, gaussFunc))
polyFunc = afwMath.PolynomialFunction2D(spOrder)
kernel = afwMath.LinearCombinationKernel(kernelList, polyFunc)
spParams = getSpatialParameters(len(kernelList), polyFunc)
kernel.setSpatialParameters(spParams);
return kernel
def testSVLinearCombinationKernel(self):
"""Test a spatially varying LinearCombinationKernel
"""
kWidth = 3
kHeight = 2
pol = pexPolicy.Policy()
additionalData = dafBase.PropertySet()
loc = dafPersist.LogicalLocation(
os.path.join(testPath, "data", "kernel6.boost"))
persistence = dafPersist.Persistence.getPersistence(pol)
# create image arrays for the basis kernels
basisImArrList = []
imArr = np.zeros((kWidth, kHeight), dtype=float)
imArr += 0.1
imArr[kWidth // 2, :] = 0.9
basisImArrList.append(imArr)
imArr = np.zeros((kWidth, kHeight), dtype=float)
imArr += 0.2
imArr[:, kHeight // 2] = 0.8
basisImArrList.append(imArr)
# create a list of basis kernels from the images
kVec = []
for basisImArr in basisImArrList:
basisImage = afwImage.makeImageFromArray(
basisImArr.transpose().copy())
kernel = afwMath.FixedKernel(basisImage)
kVec.append(kernel)
# create spatially varying linear combination kernel
spFunc = afwMath.PolynomialFunction2D(1)
# spatial parameters are a list of entries, one per kernel parameter;
# each entry is a list of spatial parameters
sParams = (
(0.0, 1.0, 0.0),
(0.0, 0.0, 1.0),
)
k = afwMath.LinearCombinationKernel(kVec, spFunc)
k.setSpatialParameters(sParams)
storageList = dafPersist.StorageList()
storage = persistence.getPersistStorage("XmlStorage", loc)
storageList.append(storage)
persistence.persist(k, storageList, additionalData)
storageList2 = dafPersist.StorageList()
storage2 = persistence.getRetrieveStorage("XmlStorage", loc)
storageList2.append(storage2)
k2 = persistence.unsafeRetrieve("LinearCombinationKernel",
storageList2, additionalData)
self.kernelCheck(k, k2)
kImage = afwImage.ImageD(afwGeom.Extent2I(kWidth, kHeight))
for colPos, rowPos, coeff0, coeff1 in [
(0.0, 0.0, 0.0, 0.0),
(1.0, 0.0, 1.0, 0.0),
(0.0, 1.0, 0.0, 1.0),
(1.0, 1.0, 1.0, 1.0),
(0.5, 0.5, 0.5, 0.5),
]:
k2.computeImage(kImage, False, colPos, rowPos)
kImArr = kImage.getArray().transpose()
refKImArr = (basisImArrList[0] * coeff0) + \
(basisImArrList[1] * coeff1)
if not np.allclose(kImArr, refKImArr):
self.fail(
"%s = %s != %s at colPos=%s, rowPos=%s" %
(k2.__class__.__name__, kImArr, refKImArr, colPos, rowPos))
def showPsfCandidates(exposure, psfCellSet, psf=None, frame=None, normalize=True, showBadCandidates=True,
variance=None, chi=None):
"""Display the PSF candidates.
If psf is provided include PSF model and residuals; if normalize is true normalize the PSFs (and residuals)
If chi is True, generate a plot of residuals/sqrt(variance), i.e. chi
"""
if chi is None:
if variance is not None: # old name for chi
chi = variance
#
# Show us the ccandidates
#
mos = displayUtils.Mosaic()
#
candidateCenters = []
candidateCentersBad = []
candidateIndex = 0
for cell in psfCellSet.getCellList():
for cand in cell.begin(False): # include bad candidates
cand = algorithmsLib.cast_PsfCandidateF(cand)
rchi2 = cand.getChi2()
if rchi2 > 1e100:
rchi2 = numpy.nan
if not showBadCandidates and cand.isBad():
continue
if psf:
im_resid = displayUtils.Mosaic(gutter=0, background=-5, mode="x")
try:
im = cand.getMaskedImage() # copy of this object's image
xc, yc = cand.getXCenter(), cand.getYCenter()
margin = 0 if True else 5
w, h = im.getDimensions()
bbox = afwGeom.BoxI(afwGeom.PointI(margin, margin), im.getDimensions())
if margin > 0:
bim = im.Factory(w + 2*margin, h + 2*margin)
stdev = numpy.sqrt(afwMath.makeStatistics(im.getVariance(), afwMath.MEAN).getValue())
afwMath.randomGaussianImage(bim.getImage(), afwMath.Random())
bim *= stdev
var = bim.getVariance(); var.set(stdev**2); del var
sbim = im.Factory(bim, bbox)
sbim <<= im
del sbim
im = bim
xc += margin; yc += margin
im = im.Factory(im, True)
im.setXY0(cand.getMaskedImage().getXY0())
except:
continue
if not variance:
im_resid.append(im.Factory(im, True))
# residuals using spatial model
chi2 = algorithmsLib.subtractPsf(psf, im, xc, yc)
resid = im
if variance:
resid = resid.getImage()
var = im.getVariance()
var = var.Factory(var, True)
numpy.sqrt(var.getArray(), var.getArray()) # inplace sqrt
resid /= var
im_resid.append(resid)
# Fit the PSF components directly to the data (i.e. ignoring the spatial model)
im = cand.getMaskedImage()
im = im.Factory(im, True)
im.setXY0(cand.getMaskedImage().getXY0())
noSpatialKernel = afwMath.cast_LinearCombinationKernel(psf.getKernel())
candCenter = afwGeom.PointD(cand.getXCenter(), cand.getYCenter())
fit = algorithmsLib.fitKernelParamsToImage(noSpatialKernel, im, candCenter)
params = fit[0]
kernels = afwMath.KernelList(fit[1])
outputKernel = afwMath.LinearCombinationKernel(kernels, params)
outImage = afwImage.ImageD(outputKernel.getDimensions())
outputKernel.computeImage(outImage, False)
im -= outImage.convertF()
resid = im
if margin > 0:
bim = im.Factory(w + 2*margin, h + 2*margin)
afwMath.randomGaussianImage(bim.getImage(), afwMath.Random())
bim *= stdev
sbim = im.Factory(bim, bbox)
sbim <<= resid
del sbim
resid = bim
if variance:
resid = resid.getImage()
resid /= var
im_resid.append(resid)
im = im_resid.makeMosaic()
else:
im = cand.getMaskedImage()
if normalize:
im /= afwMath.makeStatistics(im, afwMath.MAX).getValue()
objId = splitId(cand.getSource().getId(), True)["objId"]
if psf:
lab = "%d chi^2 %.1f" % (objId, rchi2)
ctype = ds9.RED if cand.isBad() else ds9.GREEN
else:
lab = "%d flux %8.3g" % (objId, cand.getSource().getPsfFlux())
ctype = ds9.GREEN
mos.append(im, lab, ctype)
if False and numpy.isnan(rchi2):
ds9.mtv(cand.getMaskedImage().getImage(), title="candidate", frame=1)
print "amp", cand.getAmplitude()
im = cand.getMaskedImage()
center = (candidateIndex, xc - im.getX0(), yc - im.getY0())
candidateIndex += 1
if cand.isBad():
candidateCentersBad.append(center)
else:
candidateCenters.append(center)
if variance:
title = "chi(Psf fit)"
else:
title = "Stars & residuals"
mosaicImage = mos.makeMosaic(frame=frame, title=title)
with ds9.Buffering():
for centers, color in ((candidateCenters, ds9.GREEN), (candidateCentersBad, ds9.RED)):
for cen in centers:
bbox = mos.getBBox(cen[0])
ds9.dot("+", cen[1] + bbox.getMinX(), cen[2] + bbox.getMinY(), frame=frame, ctype=color)
return mosaicImage
def showPsfCandidates(exposure, psfCellSet, psf=None, display=None, normalize=True, showBadCandidates=True,
fitBasisComponents=False, variance=None, chi=None):
"""Display the PSF candidates.
If psf is provided include PSF model and residuals; if normalize is true normalize the PSFs
(and residuals)
If chi is True, generate a plot of residuals/sqrt(variance), i.e. chi
If fitBasisComponents is true, also find the best linear combination of the PSF's components
(if they exist)
"""
if not display:
display = afwDisplay.Display()
if chi is None:
if variance is not None: # old name for chi
chi = variance
#
# Show us the ccandidates
#
mos = displayUtils.Mosaic()
#
candidateCenters = []
candidateCentersBad = []
candidateIndex = 0
for cell in psfCellSet.getCellList():
for cand in cell.begin(False): # include bad candidates
rchi2 = cand.getChi2()
if rchi2 > 1e100:
rchi2 = numpy.nan
if not showBadCandidates and cand.isBad():
continue
if psf:
im_resid = displayUtils.Mosaic(gutter=0, background=-5, mode="x")
try:
im = cand.getMaskedImage() # copy of this object's image
xc, yc = cand.getXCenter(), cand.getYCenter()
margin = 0 if True else 5
w, h = im.getDimensions()
bbox = lsst.geom.BoxI(lsst.geom.PointI(margin, margin), im.getDimensions())
if margin > 0:
bim = im.Factory(w + 2*margin, h + 2*margin)
stdev = numpy.sqrt(afwMath.makeStatistics(im.getVariance(), afwMath.MEAN).getValue())
afwMath.randomGaussianImage(bim.getImage(), afwMath.Random())
bim.getVariance().set(stdev**2)
bim.assign(im, bbox)
im = bim
xc += margin
yc += margin
im = im.Factory(im, True)
im.setXY0(cand.getMaskedImage().getXY0())
except Exception:
continue
if not variance:
im_resid.append(im.Factory(im, True))
if True: # tweak up centroids
mi = im
psfIm = mi.getImage()
config = measBase.SingleFrameMeasurementTask.ConfigClass()
config.slots.centroid = "base_SdssCentroid"
schema = afwTable.SourceTable.makeMinimalSchema()
measureSources = measBase.SingleFrameMeasurementTask(schema, config=config)
catalog = afwTable.SourceCatalog(schema)
extra = 10 # enough margin to run the sdss centroider
miBig = mi.Factory(im.getWidth() + 2*extra, im.getHeight() + 2*extra)
miBig[extra:-extra, extra:-extra, afwImage.LOCAL] = mi
miBig.setXY0(mi.getX0() - extra, mi.getY0() - extra)
mi = miBig
del miBig
exp = afwImage.makeExposure(mi)
exp.setPsf(psf)
footprintSet = afwDet.FootprintSet(mi,
afwDet.Threshold(0.5*numpy.max(psfIm.getArray())),
"DETECTED")
footprintSet.makeSources(catalog)
if len(catalog) == 0:
raise RuntimeError("Failed to detect any objects")
measureSources.run(catalog, exp)
if len(catalog) == 1:
source = catalog[0]
else: # more than one source; find the once closest to (xc, yc)
dmin = None # an invalid value to catch logic errors
for i, s in enumerate(catalog):
d = numpy.hypot(xc - s.getX(), yc - s.getY())
if i == 0 or d < dmin:
source, dmin = s, d
xc, yc = source.getCentroid()
# residuals using spatial model
try:
subtractPsf(psf, im, xc, yc)
except Exception:
continue
resid = im
if variance:
resid = resid.getImage()
var = im.getVariance()
var = var.Factory(var, True)
numpy.sqrt(var.getArray(), var.getArray()) # inplace sqrt
resid /= var
im_resid.append(resid)
# Fit the PSF components directly to the data (i.e. ignoring the spatial model)
if fitBasisComponents:
im = cand.getMaskedImage()
im = im.Factory(im, True)
im.setXY0(cand.getMaskedImage().getXY0())
try:
noSpatialKernel = psf.getKernel()
except Exception:
noSpatialKernel = None
if noSpatialKernel:
candCenter = lsst.geom.PointD(cand.getXCenter(), cand.getYCenter())
fit = fitKernelParamsToImage(noSpatialKernel, im, candCenter)
params = fit[0]
kernels = afwMath.KernelList(fit[1])
outputKernel = afwMath.LinearCombinationKernel(kernels, params)
outImage = afwImage.ImageD(outputKernel.getDimensions())
outputKernel.computeImage(outImage, False)
im -= outImage.convertF()
resid = im
if margin > 0:
bim = im.Factory(w + 2*margin, h + 2*margin)
afwMath.randomGaussianImage(bim.getImage(), afwMath.Random())
bim *= stdev
bim.assign(resid, bbox)
resid = bim
if variance:
resid = resid.getImage()
resid /= var
im_resid.append(resid)
im = im_resid.makeMosaic()
else:
im = cand.getMaskedImage()
if normalize:
im /= afwMath.makeStatistics(im, afwMath.MAX).getValue()
objId = splitId(cand.getSource().getId(), True)["objId"]
if psf:
lab = "%d chi^2 %.1f" % (objId, rchi2)
ctype = afwDisplay.RED if cand.isBad() else afwDisplay.GREEN
else:
lab = "%d flux %8.3g" % (objId, cand.getSource().getPsfInstFlux())
ctype = afwDisplay.GREEN
mos.append(im, lab, ctype)
if False and numpy.isnan(rchi2):
display.mtv(cand.getMaskedImage().getImage(), title="showPsfCandidates: candidate")
print("amp", cand.getAmplitude())
im = cand.getMaskedImage()
center = (candidateIndex, xc - im.getX0(), yc - im.getY0())
candidateIndex += 1
if cand.isBad():
candidateCentersBad.append(center)
else:
candidateCenters.append(center)
if variance:
title = "chi(Psf fit)"
else:
title = "Stars & residuals"
mosaicImage = mos.makeMosaic(display=display, title=title)
with display.Buffering():
for centers, color in ((candidateCenters, afwDisplay.GREEN), (candidateCentersBad, afwDisplay.RED)):
for cen in centers:
bbox = mos.getBBox(cen[0])
display.dot("+", cen[1] + bbox.getMinX(), cen[2] + bbox.getMinY(), ctype=color)
return mosaicImage
def setUp(self):
self.schema = afwTable.SourceTable.makeMinimalSchema()
config = measBase.SingleFrameMeasurementConfig()
config.algorithms.names = [
"base_PixelFlags",
"base_SdssCentroid",
"base_GaussianFlux",
"base_SdssShape",
"base_CircularApertureFlux",
"base_PsfFlux",
]
config.algorithms["base_CircularApertureFlux"].radii = [3.0]
config.slots.centroid = "base_SdssCentroid"
config.slots.psfFlux = "base_PsfFlux"
config.slots.apFlux = "base_CircularApertureFlux_3_0"
config.slots.modelFlux = None
config.slots.instFlux = None
config.slots.calibFlux = None
config.slots.shape = "base_SdssShape"
self.measureTask = measBase.SingleFrameMeasurementTask(self.schema,
config=config)
width, height = 110, 301
self.mi = afwImage.MaskedImageF(afwGeom.ExtentI(width, height))
self.mi.set(0)
sd = 3 # standard deviation of image
self.mi.getVariance().set(sd * sd)
self.mi.getMask().addMaskPlane("DETECTED")
self.FWHM = 5
self.ksize = 31 # size of desired kernel
sigma1 = 1.75
sigma2 = 2 * sigma1
self.exposure = afwImage.makeExposure(self.mi)
self.exposure.setPsf(
measAlg.DoubleGaussianPsf(self.ksize, self.ksize, 1.5 * sigma1, 1,
0.1))
self.exposure.setDetector(DetectorWrapper().detector)
#
# Make a kernel with the exactly correct basis functions. Useful for debugging
#
basisKernelList = []
for sigma in (sigma1, sigma2):
basisKernel = afwMath.AnalyticKernel(
self.ksize, self.ksize,
afwMath.GaussianFunction2D(sigma, sigma))
basisImage = afwImage.ImageD(basisKernel.getDimensions())
basisKernel.computeImage(basisImage, True)
basisImage /= np.sum(basisImage.getArray())
if sigma == sigma1:
basisImage0 = basisImage
else:
basisImage -= basisImage0
basisKernelList.append(afwMath.FixedKernel(basisImage))
order = 1 # 1 => up to linear
spFunc = afwMath.PolynomialFunction2D(order)
exactKernel = afwMath.LinearCombinationKernel(basisKernelList, spFunc)
exactKernel.setSpatialParameters([[1.0, 0, 0],
[0.0, 0.5 * 1e-2, 0.2e-2]])
self.exactPsf = measAlg.PcaPsf(exactKernel)
rand = afwMath.Random() # make these tests repeatable by setting seed
addNoise = True
if addNoise:
im = self.mi.getImage()
afwMath.randomGaussianImage(im, rand) # N(0, 1)
im *= sd # N(0, sd^2)
del im
xarr, yarr = [], []
for x, y in [
(20, 20),
(60, 20),
(30, 35),
(50, 50),
(20, 90),
(70, 160),
(25, 265),
(75, 275),
(85, 30),
(50, 120),
(70, 80),
(60, 210),
(20, 210),
]:
xarr.append(x)
yarr.append(y)
for x, y in zip(xarr, yarr):
dx = rand.uniform() - 0.5 # random (centered) offsets
dy = rand.uniform() - 0.5
k = exactKernel.getSpatialFunction(1)(
x, y) # functional variation of Kernel ...
b = (k * sigma1**2 / ((1 - k) * sigma2**2)
) # ... converted double Gaussian's "b"
# flux = 80000 - 20*x - 10*(y/float(height))**2
flux = 80000 * (1 + 0.1 * (rand.uniform() - 0.5))
I0 = flux * (1 + b) / (2 * np.pi * (sigma1**2 + b * sigma2**2))
for iy in range(y - self.ksize // 2, y + self.ksize // 2 + 1):
if iy < 0 or iy >= self.mi.getHeight():
continue
for ix in range(x - self.ksize // 2, x + self.ksize // 2 + 1):
if ix < 0 or ix >= self.mi.getWidth():
continue
intensity = I0 * psfVal(ix, iy, x + dx, y + dy, sigma1,
sigma2, b)
Isample = rand.poisson(
intensity) if addNoise else intensity
self.mi.getImage().set(
ix, iy,
self.mi.getImage().get(ix, iy) + Isample)
self.mi.getVariance().set(
ix, iy,
self.mi.getVariance().get(ix, iy) + intensity)
#
bbox = afwGeom.BoxI(afwGeom.PointI(0, 0),
afwGeom.ExtentI(width, height))
self.cellSet = afwMath.SpatialCellSet(bbox, 100)
self.footprintSet = afwDetection.FootprintSet(
self.mi, afwDetection.Threshold(100), "DETECTED")
self.catalog = self.measure(self.footprintSet, self.exposure)
for source in self.catalog:
try:
cand = measAlg.makePsfCandidate(source, self.exposure)
self.cellSet.insertCandidate(cand)
except Exception as e:
print(e)
continue
def convertpsField(infile, filt, trim=True, rcscale=0.001, MAX_ORDER_B=5, LSST_ORDER=4):
if filt not in filtToHdu:
print("INVALID FILTER", filt)
sys.exit(1)
buff = open(infile, "rb")
pstruct = fits.getdata(buff, ext=filtToHdu[filt])
spaParList = [[]]*len(pstruct)
kernelList = []
for i in range(len(pstruct)):
nrow_b = pstruct[i][0] # ny
ncol_b = pstruct[i][1] # nx
cmat = pstruct[i][2].reshape((MAX_ORDER_B, MAX_ORDER_B))
krow = pstruct[i][4] # RNROW
kcol = pstruct[i][5] # RNCOL
# This is *not* transposed
karr = pstruct[i][7].reshape((krow, kcol)).astype(num.float64)
if trim:
karr = karr[10:41, 10:41]
kim = afwImage.ImageD(karr)
kern = afwMath.FixedKernel(kim)
kernelList.append(kern)
# NOTES:
# Afw has the polynomial terms like:
#
# * f(x,y) = c0 (0th order)
# * + c1 x + c2 y (1st order)
# * + c3 x^2 + c4 x y + c5 y^2 (2nd order)
# * + c6 x^3 + c7 x^2 y + c8 x y^2 + c9 y^3 (3rd order)
# * + c10 x^4 + c11 x^3 y + c12 x^2 y^2 + c13 x y^3 + c14 y^4 (4th order)
#
# So, ordered: x^0,y^0 x^1,y^0 x^0,y^1 x^2,y^0 x^1,y^1 x^0,y^2
# SDSS has the terms ordered like, after reshape():
#
# x^0,y^0 x^0,y^1 x^0,y^2
# x^1,y^0 x^1,y^1 x^1,y^2
# x^2,y^0 x^2,y^1 x^2,y^2
#
# So, it technically goes up to fourth order in LSST-speak. OK, that is the trick.
#
# Mapping:
# cmat[0][0] = c0 x^0y^0
# cmat[1][0] = c2 x^0y^1
# cmat[2][0] = c5 x^0y^2
# cmat[0][1] = c1 x^1y^0
# cmat[1][1] = c4 x^1y^1
# cmat[2][1] = c8 x^1y^2
# cmat[0][2] = c3 x^2y^0
# cmat[1][2] = c7 x^2y^1
# cmat[2][2] = c12 x^2y^2
#
# This is quantified in skMatrixPos2TriSeqPosT
spaParamsTri = num.zeros(MAX_ORDER_B * MAX_ORDER_B)
for k in range(nrow_b * ncol_b):
row = k % nrow_b
col = k // nrow_b
coeff = cmat[row, col]
scale = pow(rcscale, row) * pow(rcscale, col)
scaledCoeff = coeff * scale
# Was originally written like this, but the SDSS code
# takes inputs as y,x instead of x,y meaning it was
# originally transposed
#
# idx = row * MAX_ORDER_B + col
idx = col * MAX_ORDER_B + row
spaParamsTri[skMatrixPos2TriSeqPosT[idx]] = scaledCoeff
# print "%d y=%d x=%d %10.3e %2d %2d %10.3e" % \
# (i, row, col, cmat[row,col], idx, skMatrixPos2TriSeqPosT[idx], scaledCoeff)
# print spaParamsTri
nTerms = (LSST_ORDER + 1) * (LSST_ORDER + 2) // 2
spaParamsTri = spaParamsTri[:nTerms]
spaParList[i] = spaParamsTri
buff.close()
spaFun = afwMath.PolynomialFunction2D(LSST_ORDER)
spatialKernel = afwMath.LinearCombinationKernel(kernelList, spaFun)
spatialKernel.setSpatialParameters(spaParList)
spatialPsf = measAlg.PcaPsf(spatialKernel)
return spatialPsf
def setUp(self):
config = SingleFrameMeasurementTask.ConfigClass()
config.slots.apFlux = 'base_CircularApertureFlux_12_0'
self.schema = afwTable.SourceTable.makeMinimalSchema()
self.measureSources = SingleFrameMeasurementTask(self.schema,
config=config)
width, height = 110, 301
self.mi = afwImage.MaskedImageF(geom.ExtentI(width, height))
self.mi.set(0)
sd = 3 # standard deviation of image
self.mi.getVariance().set(sd * sd)
self.mi.getMask().addMaskPlane("DETECTED")
self.ksize = 31 # size of desired kernel
sigma1 = 1.75
sigma2 = 2 * sigma1
self.exposure = afwImage.makeExposure(self.mi)
self.exposure.setPsf(
measAlg.DoubleGaussianPsf(self.ksize, self.ksize, 1.5 * sigma1, 1,
0.1))
cdMatrix = np.array([1.0, 0.0, 0.0, 1.0])
cdMatrix.shape = (2, 2)
wcs = afwGeom.makeSkyWcs(crpix=geom.PointD(0, 0),
crval=geom.SpherePoint(
0.0, 0.0, geom.degrees),
cdMatrix=cdMatrix)
self.exposure.setWcs(wcs)
#
# Make a kernel with the exactly correct basis functions.
# Useful for debugging
#
basisKernelList = []
for sigma in (sigma1, sigma2):
basisKernel = afwMath.AnalyticKernel(
self.ksize, self.ksize,
afwMath.GaussianFunction2D(sigma, sigma))
basisImage = afwImage.ImageD(basisKernel.getDimensions())
basisKernel.computeImage(basisImage, True)
basisImage /= np.sum(basisImage.getArray())
if sigma == sigma1:
basisImage0 = basisImage
else:
basisImage -= basisImage0
basisKernelList.append(afwMath.FixedKernel(basisImage))
order = 1 # 1 => up to linear
spFunc = afwMath.PolynomialFunction2D(order)
exactKernel = afwMath.LinearCombinationKernel(basisKernelList, spFunc)
exactKernel.setSpatialParameters([[1.0, 0, 0],
[0.0, 0.5 * 1e-2, 0.2e-2]])
rand = afwMath.Random() # make these tests repeatable by setting seed
addNoise = True
if addNoise:
im = self.mi.getImage()
afwMath.randomGaussianImage(im, rand) # N(0, 1)
im *= sd # N(0, sd^2)
del im
xarr, yarr = [], []
for x, y in [
(20, 20),
(60, 20),
(30, 35),
(50, 50),
(20, 90),
(70, 160),
(25, 265),
(75, 275),
(85, 30),
(50, 120),
(70, 80),
(60, 210),
(20, 210),
]:
xarr.append(x)
yarr.append(y)
for x, y in zip(xarr, yarr):
dx = rand.uniform() - 0.5 # random (centered) offsets
dy = rand.uniform() - 0.5
k = exactKernel.getSpatialFunction(1)(
x, y) # functional variation of Kernel ...
b = (k * sigma1**2 / ((1 - k) * sigma2**2)
) # ... converted double Gaussian's "b"
# flux = 80000 - 20*x - 10*(y/float(height))**2
flux = 80000 * (1 + 0.1 * (rand.uniform() - 0.5))
I0 = flux * (1 + b) / (2 * np.pi * (sigma1**2 + b * sigma2**2))
for iy in range(y - self.ksize // 2, y + self.ksize // 2 + 1):
if iy < 0 or iy >= self.mi.getHeight():
continue
for ix in range(x - self.ksize // 2, x + self.ksize // 2 + 1):
if ix < 0 or ix >= self.mi.getWidth():
continue
II = I0 * psfVal(ix, iy, x + dx, y + dy, sigma1, sigma2, b)
Isample = rand.poisson(II) if addNoise else II
self.mi.image[ix, iy, afwImage.LOCAL] += Isample
self.mi.variance[ix, iy, afwImage.LOCAL] += II
bbox = geom.BoxI(geom.PointI(0, 0), geom.ExtentI(width, height))
self.cellSet = afwMath.SpatialCellSet(bbox, 100)
self.footprintSet = afwDetection.FootprintSet(
self.mi, afwDetection.Threshold(100), "DETECTED")
self.catalog = self.measure(self.footprintSet, self.exposure)
for source in self.catalog:
try:
cand = measAlg.makePsfCandidate(source, self.exposure)
self.cellSet.insertCandidate(cand)
except Exception as e:
print(e)
continue
def testAutoCorrelation(orderMake, orderFit, inMi=None, display=False):
config = ipDiffim.ImagePsfMatchTask.ConfigClass()
config.kernel.name = "AL"
subconfig = config.kernel.active
subconfig.fitForBackground = True
stride = 100
if inMi == None:
width = 512
height = 2048
inMi = afwImage.MaskedImageF(afwGeom.Extent2I(width, height))
for j in num.arange(stride // 2, height, stride):
j = int(j)
for i in num.arange(stride // 2, width, stride):
i = int(i)
inMi.set(i - 1, j - 1, (100., 0x0, 1.))
inMi.set(i - 1, j + 0, (100., 0x0, 1.))
inMi.set(i - 1, j + 1, (100., 0x0, 1.))
inMi.set(i + 0, j - 1, (100., 0x0, 1.))
inMi.set(i + 0, j + 0, (100., 0x0, 1.))
inMi.set(i + 0, j + 1, (100., 0x0, 1.))
inMi.set(i + 1, j - 1, (100., 0x0, 1.))
inMi.set(i + 1, j + 0, (100., 0x0, 1.))
inMi.set(i + 1, j + 1, (100., 0x0, 1.))
addNoise(inMi)
kSize = subconfig.kernelSize
basicGaussian1 = afwMath.GaussianFunction2D(2., 2., 0.)
basicKernel1 = afwMath.AnalyticKernel(kSize, kSize, basicGaussian1)
basicGaussian2 = afwMath.GaussianFunction2D(5., 3., 0.5 * num.pi)
basicKernel2 = afwMath.AnalyticKernel(kSize, kSize, basicGaussian2)
basisList = []
basisList.append(basicKernel1)
basisList.append(basicKernel2)
spatialKernelFunction = afwMath.PolynomialFunction2D(orderMake)
spatialKernel = afwMath.LinearCombinationKernel(basisList,
spatialKernelFunction)
kCoeffs = [[
1.0 for x in range(1,
spatialKernelFunction.getNParameters() + 1)
], [
0.01 * x for x in range(1,
spatialKernelFunction.getNParameters() + 1)
]]
spatialKernel.setSpatialParameters(kCoeffs)
cMi = afwImage.MaskedImageF(inMi.getDimensions())
afwMath.convolve(cMi, inMi, spatialKernel, True)
if display:
ds9.mtv(inMi.getImage(), frame=1)
ds9.mtv(inMi.getVariance(), frame=2)
ds9.mtv(cMi.getImage(), frame=3)
ds9.mtv(cMi.getVariance(), frame=4)
subconfig.spatialKernelOrder = orderFit
subconfig.sizeCellX = stride
subconfig.sizeCellY = stride
psfmatch = ipDiffim.ImagePsfMatchTask(config=config)
result = psfmatch.run(inMi, cMi, "subtractMaskedImages")
differenceMaskedImage = result.subtractedImage
spatialKernel = result.psfMatchingKernel
spatialBg = result.backgroundModel
kernelCellSet = result.kernelCellSet
makeAutoCorrelation(kernelCellSet, spatialKernel, makePlot=True)
def testAutoCorrelation(orderMake, orderFit, inMi=None, display=False):
config = ipDiffim.ImagePsfMatchTask.ConfigClass()
config.kernel.name = "AL"
subconfig = config.kernel.active
subconfig.fitForBackground = True
stride = 100
if inMi is None:
width = 512
height = 2048
inMi = afwImage.MaskedImageF(afwGeom.Extent2I(width, height))
for j in num.arange(stride // 2, height, stride):
j = int(j)
for i in num.arange(stride // 2, width, stride):
i = int(i)
inMi._set((i - 1, j - 1), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i - 1, j + 0), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i - 1, j + 1), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i + 0, j - 1), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i + 0, j + 0), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i + 0, j + 1), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i + 1, j - 1), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i + 1, j + 0), (100., 0x0, 1.), afwImage.LOCAL)
inMi._set((i + 1, j + 1), (100., 0x0, 1.), afwImage.LOCAL)
addNoise(inMi)
kSize = subconfig.kernelSize
basicGaussian1 = afwMath.GaussianFunction2D(2., 2., 0.)
basicKernel1 = afwMath.AnalyticKernel(kSize, kSize, basicGaussian1)
basicGaussian2 = afwMath.GaussianFunction2D(5., 3., 0.5 * num.pi)
basicKernel2 = afwMath.AnalyticKernel(kSize, kSize, basicGaussian2)
basisList = []
basisList.append(basicKernel1)
basisList.append(basicKernel2)
spatialKernelFunction = afwMath.PolynomialFunction2D(orderMake)
spatialKernel = afwMath.LinearCombinationKernel(basisList,
spatialKernelFunction)
kCoeffs = [[
1.0 for x in range(1,
spatialKernelFunction.getNParameters() + 1)
], [
0.01 * x for x in range(1,
spatialKernelFunction.getNParameters() + 1)
]]
spatialKernel.setSpatialParameters(kCoeffs)
cMi = afwImage.MaskedImageF(inMi.getDimensions())
convolutionControl = afwMath.ConvolutionControl()
convolutionControl.setDoNormalize(True)
afwMath.convolve(cMi, inMi, spatialKernel, convolutionControl)
if display:
afwDisplay.Display(frame=1).mtv(inMi.getImage())
afwDisplay.Display(frame=2).mtv(inMi.getVariance())
afwDisplay.Display(frame=3).mtv(cMi.getImage())
afwDisplay.Display(frame=4).mtv(cMi.getVariance())
subconfig.spatialKernelOrder = orderFit
subconfig.sizeCellX = stride
subconfig.sizeCellY = stride
psfmatch = ipDiffim.ImagePsfMatchTask(config=config)
candList = psfmatch.makeCandidateList(afwImage.ExposureF(inMi),
afwImage.ExposureF(cMi), kSize)
result = psfmatch.subtractMaskedImages(inMi, cMi, candList)
spatialKernel = result.psfMatchingKernel
kernelCellSet = result.kernelCellSet
makeAutoCorrelation(kernelCellSet, spatialKernel, makePlot=True)
def setUp(self):
width, height = 110, 301
self.mi = afwImage.MaskedImageF(afwGeom.ExtentI(width, height))
self.mi.set(0)
sd = 3 # standard deviation of image
self.mi.getVariance().set(sd*sd)
self.mi.getMask().addMaskPlane("DETECTED")
self.FWHM = 5
self.ksize = 31 # size of desired kernel
sigma1 = 1.75
sigma2 = 2*sigma1
self.exposure = afwImage.makeExposure(self.mi)
self.exposure.setPsf(measAlg.DoubleGaussianPsf(self.ksize, self.ksize,
1.5*sigma1, 1, 0.1))
crval = afwCoord.makeCoord(afwCoord.ICRS, 0.0*afwGeom.degrees, 0.0*afwGeom.degrees)
wcs = afwImage.makeWcs(crval, afwGeom.PointD(0, 0), 1.0, 0, 0, 1.0)
self.exposure.setWcs(wcs)
ccd = cameraGeom.Ccd(cameraGeom.Id(1))
ccd.addAmp(cameraGeom.Amp(cameraGeom.Id(0),
afwGeom.BoxI(afwGeom.PointI(0,0), self.exposure.getDimensions()),
afwGeom.BoxI(afwGeom.PointI(0,0), afwGeom.ExtentI(0,0)),
afwGeom.BoxI(afwGeom.PointI(0,0), self.exposure.getDimensions()),
cameraGeom.ElectronicParams(1.0, 100.0, 65535)))
self.exposure.setDetector(ccd)
self.exposure.getDetector().setDistortion(None)
#
# Make a kernel with the exactly correct basis functions. Useful for debugging
#
basisKernelList = afwMath.KernelList()
for sigma in (sigma1, sigma2):
basisKernel = afwMath.AnalyticKernel(self.ksize, self.ksize,
afwMath.GaussianFunction2D(sigma, sigma))
basisImage = afwImage.ImageD(basisKernel.getDimensions())
basisKernel.computeImage(basisImage, True)
basisImage /= np.sum(basisImage.getArray())
if sigma == sigma1:
basisImage0 = basisImage
else:
basisImage -= basisImage0
basisKernelList.append(afwMath.FixedKernel(basisImage))
order = 1 # 1 => up to linear
spFunc = afwMath.PolynomialFunction2D(order)
exactKernel = afwMath.LinearCombinationKernel(basisKernelList, spFunc)
exactKernel.setSpatialParameters([[1.0, 0, 0],
[0.0, 0.5*1e-2, 0.2e-2]])
rand = afwMath.Random() # make these tests repeatable by setting seed
addNoise = True
if addNoise:
im = self.mi.getImage()
afwMath.randomGaussianImage(im, rand) # N(0, 1)
im *= sd # N(0, sd^2)
del im
xarr, yarr = [], []
for x, y in [(20, 20), (60, 20),
(30, 35),
(50, 50),
(20, 90), (70, 160), (25, 265), (75, 275), (85, 30),
(50, 120), (70, 80),
(60, 210), (20, 210),
]:
xarr.append(x)
yarr.append(y)
for x, y in zip(xarr, yarr):
dx = rand.uniform() - 0.5 # random (centered) offsets
dy = rand.uniform() - 0.5
k = exactKernel.getSpatialFunction(1)(x, y) # functional variation of Kernel ...
b = (k*sigma1**2/((1 - k)*sigma2**2)) # ... converted double Gaussian's "b"
#flux = 80000 - 20*x - 10*(y/float(height))**2
flux = 80000*(1 + 0.1*(rand.uniform() - 0.5))
I0 = flux*(1 + b)/(2*np.pi*(sigma1**2 + b*sigma2**2))
for iy in range(y - self.ksize//2, y + self.ksize//2 + 1):
if iy < 0 or iy >= self.mi.getHeight():
continue
for ix in range(x - self.ksize//2, x + self.ksize//2 + 1):
if ix < 0 or ix >= self.mi.getWidth():
continue
I = I0*psfVal(ix, iy, x + dx, y + dy, sigma1, sigma2, b)
Isample = rand.poisson(I) if addNoise else I
self.mi.getImage().set(ix, iy, self.mi.getImage().get(ix, iy) + Isample)
self.mi.getVariance().set(ix, iy, self.mi.getVariance().get(ix, iy) + I)
#
bbox = afwGeom.BoxI(afwGeom.PointI(0,0), afwGeom.ExtentI(width, height))
self.cellSet = afwMath.SpatialCellSet(bbox, 100)
self.footprintSet = afwDetection.FootprintSet(self.mi, afwDetection.Threshold(100), "DETECTED")
self.catalog = SpatialModelPsfTestCase.measure(self.footprintSet, self.exposure)
for source in self.catalog:
try:
cand = measAlg.makePsfCandidate(source, self.exposure)
self.cellSet.insertCandidate(cand)
except Exception, e:
print e
continue
def testSVLinearCombinationKernelFixed(self):
"""Test a spatially varying LinearCombinationKernel whose bases are FixedKernels"""
kWidth = 3
kHeight = 2
# create image arrays for the basis kernels
basisImArrList = []
imArr = np.zeros((kWidth, kHeight), dtype=float)
imArr += 0.1
imArr[kWidth//2, :] = 0.9
basisImArrList.append(imArr)
imArr = np.zeros((kWidth, kHeight), dtype=float)
imArr += 0.2
imArr[:, kHeight//2] = 0.8
basisImArrList.append(imArr)
# create a list of basis kernels from the images
basisKernelList = []
for basisImArr in basisImArrList:
basisImage = afwImage.makeImageFromArray(
basisImArr.transpose().copy())
kernel = afwMath.FixedKernel(basisImage)
basisKernelList.append(kernel)
# create spatially varying linear combination kernel
spFunc = afwMath.PolynomialFunction2D(1)
# spatial parameters are a list of entries, one per kernel parameter;
# each entry is a list of spatial parameters
sParams = (
(0.0, 1.0, 0.0),
(0.0, 0.0, 1.0),
)
kernel = afwMath.LinearCombinationKernel(basisKernelList, spFunc)
self.assertFalse(kernel.isDeltaFunctionBasis())
self.basicTests(kernel, 2, nSpatialParams=3)
kernel.setSpatialParameters(sParams)
kImage = afwImage.ImageD(lsst.geom.Extent2I(kWidth, kHeight))
for colPos, rowPos, coeff0, coeff1 in [
(0.0, 0.0, 0.0, 0.0),
(1.0, 0.0, 1.0, 0.0),
(0.0, 1.0, 0.0, 1.0),
(1.0, 1.0, 1.0, 1.0),
(0.5, 0.5, 0.5, 0.5),
]:
kernel.computeImage(kImage, False, colPos, rowPos)
kImArr = kImage.getArray().transpose()
refKImArr = (basisImArrList[0] * coeff0) + \
(basisImArrList[1] * coeff1)
if not np.allclose(kImArr, refKImArr):
self.fail(f"{kernel.__class__.__name__} = {kImArr} != "
f"{refKImArr} at colPos={colPos}, rowPos={rowPos}")
sParams = (
(0.1, 1.0, 0.0),
(0.1, 0.0, 1.0),
)
kernel.setSpatialParameters(sParams)
kernelClone = kernel.clone()
errStr = self.compareKernels(kernel, kernelClone)
if errStr:
self.fail(errStr)
newSParams = (
(0.1, 0.2, 0.5),
(0.1, 0.5, 0.2),
)
kernel.setSpatialParameters(newSParams)
errStr = self.compareKernels(kernel, kernelClone)
if not errStr:
self.fail(
"Clone was modified by changing original's spatial parameters")
def makeFakeKernelSet(sizeCell=128,
nCell=3,
deltaFunctionCounts=1.e4,
tGaussianWidth=1.0,
addNoise=True,
bgValue=100.,
display=False):
"""Generate test template and science images with sources.
Parameters
----------
sizeCell : `int`, optional
Size of the square spatial cells in pixels.
nCell : `int`, optional
Number of adjacent spatial cells in both direction in both images.
deltaFunctionCounts : `float`, optional
Flux value for the template image sources.
tGaussianWidth : `float`, optional
Sigma of the generated Gaussian PSF sources in the template image.
addNoise : `bool`, optional
If `True`, Poisson noise is added to both the generated template
and science images.
bgValue : `float`, optional
Background level to be added to the generated science image.
display : `bool`, optional
If `True` displays the generated template and science images by
`lsst.afw.display.Display`.
Notes
-----
- The generated images consist of adjacent ``nCell x nCell`` cells, each
of pixel size ``sizeCell x sizeCell``.
- The sources in the science image are generated by convolving the
template by ``sKernel``. ``sKernel`` is a spatial `LinearCombinationKernel`
of hard wired kernel bases functions. The linear combination has first
order polynomial spatial dependence with polynomial parameters from ``fakeCoeffs()``.
- The template image sources are generated in the center of each spatial
cell from one pixel, set to `deltaFunctionCounts` counts, then convolved
by a 2D Gaussian with sigma of `tGaussianWidth` along each axis.
- The sources are also returned in ``kernelCellSet`` each source is "detected"
exactly at the center of a cell.
Returns
-------
tMi : `lsst.afw.image.MaskedImage`
Generated template image.
sMi : `lsst.afw.image.MaskedImage`
Generated science image.
sKernel : `lsst.afw.math.LinearCombinationKernel`
The spatial kernel used to generate the sources in the science image.
kernelCellSet : `lsst.afw.math.SpatialCellSet`
Cell grid of `lsst.afw.math.SpatialCell` instances, containing
`lsst.ip.diffim.KernelCandidate` instances around all the generated sources
in the science image.
configFake : `lsst.ip.diffim.ImagePsfMatchConfig`
Config instance used in the image generation.
"""
from . import imagePsfMatch
configFake = imagePsfMatch.ImagePsfMatchConfig()
configFake.kernel.name = "AL"
subconfigFake = configFake.kernel.active
subconfigFake.alardNGauss = 1
subconfigFake.alardSigGauss = [
2.5,
]
subconfigFake.alardDegGauss = [
2,
]
subconfigFake.sizeCellX = sizeCell
subconfigFake.sizeCellY = sizeCell
subconfigFake.spatialKernelOrder = 1
subconfigFake.spatialModelType = "polynomial"
subconfigFake.singleKernelClipping = False # variance is a hack
subconfigFake.spatialKernelClipping = False # variance is a hack
if bgValue > 0.0:
subconfigFake.fitForBackground = True
psFake = pexConfig.makePropertySet(subconfigFake)
basisList = makeKernelBasisList(subconfigFake)
kSize = subconfigFake.kernelSize
# This sets the final extent of each convolved delta function
gaussKernelWidth = sizeCell // 2
# This sets the scale over which pixels are correlated in the
# spatial convolution; should be at least as big as the kernel you
# are trying to fit for
spatialKernelWidth = kSize
# Number of bad pixels due to convolutions
border = (gaussKernelWidth + spatialKernelWidth) // 2
# Make a fake image with a matrix of delta functions
totalSize = nCell * sizeCell + 2 * border
tim = afwImage.ImageF(geom.Extent2I(totalSize, totalSize))
for x in range(nCell):
for y in range(nCell):
tim[x * sizeCell + sizeCell // 2 + border - 1,
y * sizeCell + sizeCell // 2 + border - 1,
afwImage.LOCAL] = deltaFunctionCounts
# Turn this into stars with a narrow width; conserve counts
gaussFunction = afwMath.GaussianFunction2D(tGaussianWidth, tGaussianWidth)
gaussKernel = afwMath.AnalyticKernel(gaussKernelWidth, gaussKernelWidth,
gaussFunction)
cim = afwImage.ImageF(tim.getDimensions())
convolutionControl = afwMath.ConvolutionControl()
convolutionControl.setDoNormalize(True)
afwMath.convolve(cim, tim, gaussKernel, convolutionControl)
tim = cim
# Trim off border pixels
bbox = gaussKernel.shrinkBBox(tim.getBBox(afwImage.LOCAL))
tim = afwImage.ImageF(tim, bbox, afwImage.LOCAL)
# Now make a science image which is this convolved with some
# spatial function. Use input basis list.
polyFunc = afwMath.PolynomialFunction2D(1)
kCoeffs = fakeCoeffs()
nToUse = min(len(kCoeffs), len(basisList))
# Make the full convolved science image
sKernel = afwMath.LinearCombinationKernel(basisList[:nToUse], polyFunc)
sKernel.setSpatialParameters(kCoeffs[:nToUse])
sim = afwImage.ImageF(tim.getDimensions())
convolutionControl = afwMath.ConvolutionControl()
convolutionControl.setDoNormalize(True)
afwMath.convolve(sim, tim, sKernel, convolutionControl)
# Get the good subregion
bbox = sKernel.shrinkBBox(sim.getBBox(afwImage.LOCAL))
# Add background
sim += bgValue
# Watch out for negative values
tim += 2 * np.abs(np.min(tim.getArray()))
# Add noise?
if addNoise:
sim = makePoissonNoiseImage(sim)
tim = makePoissonNoiseImage(tim)
# And turn into MaskedImages
sim = afwImage.ImageF(sim, bbox, afwImage.LOCAL)
svar = afwImage.ImageF(sim, True)
smask = afwImage.Mask(sim.getDimensions())
smask.set(0x0)
sMi = afwImage.MaskedImageF(sim, smask, svar)
tim = afwImage.ImageF(tim, bbox, afwImage.LOCAL)
tvar = afwImage.ImageF(tim, True)
tmask = afwImage.Mask(tim.getDimensions())
tmask.set(0x0)
tMi = afwImage.MaskedImageF(tim, tmask, tvar)
if display:
import lsst.afw.display as afwDisplay
afwDisplay.Display(frame=1).mtv(tMi)
afwDisplay.Display(frame=2).mtv(sMi)
# Finally, make a kernelSet from these 2 images
kernelCellSet = afwMath.SpatialCellSet(
geom.Box2I(geom.Point2I(0, 0),
geom.Extent2I(sizeCell * nCell, sizeCell * nCell)),
sizeCell, sizeCell)
stampHalfWidth = 2 * kSize
for x in range(nCell):
for y in range(nCell):
xCoord = x * sizeCell + sizeCell // 2
yCoord = y * sizeCell + sizeCell // 2
p0 = geom.Point2I(xCoord - stampHalfWidth, yCoord - stampHalfWidth)
p1 = geom.Point2I(xCoord + stampHalfWidth, yCoord + stampHalfWidth)
bbox = geom.Box2I(p0, p1)
tsi = afwImage.MaskedImageF(tMi, bbox, origin=afwImage.LOCAL)
ssi = afwImage.MaskedImageF(sMi, bbox, origin=afwImage.LOCAL)
kc = diffimLib.makeKernelCandidate(xCoord, yCoord, tsi, ssi,
psFake)
kernelCellSet.insertCandidate(kc)
tMi.setXY0(0, 0)
sMi.setXY0(0, 0)
return tMi, sMi, sKernel, kernelCellSet, configFake
