def testFromGrid(self):
outOrder = 8
inOrder = 2
toInvert = makeRandomScaledPolynomialTransform(inOrder)
bbox = lsst.afw.geom.Box2D(lsst.afw.geom.Point2D(432, -671), lsst.afw.geom.Point2D(527, -463))
fitter = ScaledPolynomialTransformFitter.fromGrid(outOrder, bbox, 50, 50, toInvert)
fitter.fit(outOrder)
fitter.updateModel()
data = fitter.getData()
result = fitter.getTransform()
inputKey = lsst.afw.table.Point2DKey(data.schema["input"])
outputKey = lsst.afw.table.Point2DKey(data.schema["output"])
for record in data:
self.assertFloatsAlmostEqual(np.array(record.get(inputKey)),
np.array(toInvert(record.get(outputKey))))
self.assertFloatsAlmostEqual(np.array(result(record.get(inputKey))),
np.array(record.get(outputKey)),
rtol=1E-2) # even at much higher order, inverse can't be perfect.
def testFromGrid(self):
outOrder = 8
inOrder = 2
toInvert = makeRandomScaledPolynomialTransform(inOrder)
bbox = lsst.geom.Box2D(lsst.geom.Point2D(432, -671), lsst.geom.Point2D(527, -463))
fitter = ScaledPolynomialTransformFitter.fromGrid(outOrder, bbox, 50, 50, toInvert)
fitter.fit(outOrder)
fitter.updateModel()
data = fitter.getData()
result = fitter.getTransform()
inputKey = lsst.afw.table.Point2DKey(data.schema["input"])
outputKey = lsst.afw.table.Point2DKey(data.schema["output"])
for record in data:
self.assertFloatsAlmostEqual(np.array(record.get(inputKey)),
np.array(toInvert(record.get(outputKey))))
self.assertFloatsAlmostEqual(np.array(result(record.get(inputKey))),
np.array(record.get(outputKey)),
rtol=1E-2) # even at much higher order, inverse can't be perfect.
def testFromMatches(self):
# Setup artifical matches that correspond to a known (random) PolynomialTransform.
order = 3
truePoly = makeRandomPolynomialTransform(order)
crval = lsst.afw.coord.IcrsCoord(lsst.afw.geom.Point2D(35.0, 10.0),
lsst.afw.geom.degrees)
crpix = lsst.afw.geom.Point2D(50, 50)
cd = lsst.afw.geom.LinearTransform.makeScaling(
(0.2 * lsst.afw.geom.arcseconds).asDegrees())
initialWcs = lsst.afw.image.makeWcs(crval, crpix, cd[cd.XX], cd[cd.XY],
cd[cd.YX], cd[cd.YY])
bbox = lsst.afw.geom.Box2D(
(lsst.afw.geom.Point2D(crval.getPosition(lsst.afw.geom.arcseconds))
- lsst.afw.geom.Extent2D(20, 20)),
(lsst.afw.geom.Point2D(crval.getPosition(lsst.afw.geom.arcseconds))
+ lsst.afw.geom.Extent2D(20, 20)))
srcSchema = lsst.afw.table.SourceTable.makeMinimalSchema()
srcPosKey = lsst.afw.table.Point2DKey.addFields(
srcSchema, "pos", "source position", "pix")
srcErrKey = lsst.afw.table.CovarianceMatrix2fKey.addFields(
srcSchema, "pos", ["x", "y"], ["pix", "pix"])
srcSchema.getAliasMap().set("slot_Centroid", "pos")
nPoints = 10
trueSrc = lsst.afw.table.SourceCatalog(srcSchema)
trueSrc.reserve(nPoints)
measSrc = lsst.afw.table.SourceCatalog(srcSchema)
measSrc.reserve(nPoints)
ref = lsst.afw.table.SimpleCatalog(
lsst.afw.table.SimpleTable.makeMinimalSchema())
ref.reserve(nPoints)
refCoordKey = ref.getCoordKey()
errScaling = 1E-14
matches = []
for i in range(nPoints):
refRec = ref.addNew()
skyPos = lsst.afw.geom.Point2D(
np.random.uniform(low=bbox.getMinX(), high=bbox.getMaxX()),
np.random.uniform(low=bbox.getMinY(), high=bbox.getMaxY()))
skyCoord = lsst.afw.coord.IcrsCoord(skyPos,
lsst.afw.geom.arcseconds)
refRec.set(refCoordKey, skyCoord)
trueRec = trueSrc.addNew()
truePos = truePoly(
initialWcs.skyToIntermediateWorldCoord(skyCoord))
trueRec.set(srcPosKey, truePos)
measRec = measSrc.addNew()
covSqrt = np.random.randn(3, 2)
cov = (errScaling * (np.dot(covSqrt.transpose(), covSqrt) +
np.diag([1.0, 1.0]))).astype(np.float32)
# We don't actually perturb positions according to noise level, as
# this makes it much harder to test that the result agrees with
# what we put in.
measPos = truePos
measRec.set(srcPosKey, measPos)
measRec.set(srcErrKey, cov)
match = lsst.afw.table.ReferenceMatch(
refRec, measRec, (measPos - truePos).computeNorm())
matches.append(match)
# Construct a fitter, and verify that the internal catalog it constructs is what we expect.
fitter = ScaledPolynomialTransformFitter.fromMatches(
order, matches, initialWcs, 0.0)
expected = lsst.meas.astrom.compose(
fitter.getOutputScaling(),
lsst.meas.astrom.compose(truePoly,
fitter.getInputScaling().invert()))
data = fitter.getData()
dataOutKey = lsst.afw.table.Point2DKey(data.schema["src"])
dataInKey = lsst.afw.table.Point2DKey(data.schema["intermediate"])
dataErrKey = lsst.afw.table.CovarianceMatrix2fKey(
data.schema["src"], ["x", "y"])
scaledInBBox = lsst.afw.geom.Box2D()
scaledOutBBox = lsst.afw.geom.Box2D()
vandermonde = np.zeros((nPoints, (order + 1) * (order + 2) // 2),
dtype=float)
for i, (match, dataRec,
trueRec) in enumerate(zip(matches, data, trueSrc)):
self.assertEqual(match.second.getX(), dataRec.get("src_x"))
self.assertEqual(match.second.getY(), dataRec.get("src_y"))
self.assertEqual(match.first.getId(), dataRec.get("ref_id"))
self.assertEqual(match.second.getId(), dataRec.get("src_id"))
refPos = initialWcs.skyToIntermediateWorldCoord(
match.first.getCoord())
self.assertEqual(refPos.getX(), dataRec.get("intermediate_x"))
self.assertEqual(refPos.getY(), dataRec.get("intermediate_y"))
self.assertFloatsAlmostEqual(match.second.get(srcErrKey),
dataRec.get(dataErrKey),
rtol=1E-7)
scaledIn = fitter.getInputScaling()(dataRec.get(dataInKey))
scaledOut = fitter.getOutputScaling()(dataRec.get(dataOutKey))
scaledInBBox.include(scaledIn)
scaledOutBBox.include(scaledOut)
self.assertFloatsAlmostEqual(np.array(expected(scaledIn)),
np.array(scaledOut),
rtol=1E-7)
j = 0
for n in range(order + 1):
for p in range(n + 1):
q = n - p
vandermonde[i, j] = scaledIn.getX()**p * scaledIn.getY()**q
j += 1
# Verify that scaling transforms move inputs and outputs into [-1, 1]
self.assertFloatsAlmostEqual(scaledInBBox.getMinX(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledInBBox.getMinY(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledInBBox.getMaxX(), 1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledInBBox.getMaxY(), 1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMinX(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMinY(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMaxX(), 1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMaxY(), 1.0, rtol=1E-12)
# Run the fitter, and check that we get out approximately what we put in.
fitter.fit(order)
fitter.updateModel()
# Check the transformed input points.
self.assertFloatsAlmostEqual(data.get("model_x"),
trueSrc.getX(),
rtol=1E-15)
self.assertFloatsAlmostEqual(data.get("model_y"),
trueSrc.getY(),
rtol=1E-15)
# Check the actual transform's coefficients (after composing in the scaling, which is
# a lot of the reason we lose a lot of precision here).
fittedPoly = lsst.meas.astrom.PolynomialTransform.convert(
fitter.getTransform())
self.assertFloatsAlmostEqual(fittedPoly.getXCoeffs(),
truePoly.getXCoeffs(),
rtol=1E-5,
atol=1E-5)
self.assertFloatsAlmostEqual(fittedPoly.getYCoeffs(),
truePoly.getYCoeffs(),
rtol=1E-5,
atol=1E-5)
def testFromMatches(self):
# Setup artifical matches that correspond to a known (random) PolynomialTransform.
order = 3
truePoly = makeRandomPolynomialTransform(order)
crval = lsst.afw.geom.SpherePoint(35.0, 10.0, lsst.afw.geom.degrees)
crpix = lsst.afw.geom.Point2D(50, 50)
cd = lsst.afw.geom.LinearTransform.makeScaling((0.2*lsst.afw.geom.arcseconds).asDegrees()).getMatrix()
initialWcs = lsst.afw.geom.makeSkyWcs(crpix=crpix, crval=crval, cdMatrix=cd)
bbox = lsst.afw.geom.Box2D(
crval.getPosition(lsst.afw.geom.arcseconds) - lsst.afw.geom.Extent2D(20, 20),
crval.getPosition(lsst.afw.geom.arcseconds) + lsst.afw.geom.Extent2D(20, 20),
)
srcSchema = lsst.afw.table.SourceTable.makeMinimalSchema()
srcPosKey = lsst.afw.table.Point2DKey.addFields(srcSchema, "pos", "source position", "pix")
srcErrKey = lsst.afw.table.CovarianceMatrix2fKey.addFields(srcSchema, "pos",
["x", "y"], ["pix", "pix"])
srcSchema.getAliasMap().set("slot_Centroid", "pos")
nPoints = 10
trueSrc = lsst.afw.table.SourceCatalog(srcSchema)
trueSrc.reserve(nPoints)
measSrc = lsst.afw.table.SourceCatalog(srcSchema)
measSrc.reserve(nPoints)
ref = lsst.afw.table.SimpleCatalog(lsst.afw.table.SimpleTable.makeMinimalSchema())
ref.reserve(nPoints)
refCoordKey = ref.getCoordKey()
errScaling = 1E-14
matches = []
initialIwcToSky = lsst.afw.geom.getIntermediateWorldCoordsToSky(initialWcs)
for i in range(nPoints):
refRec = ref.addNew()
raDeg, decDeg = (
np.random.uniform(low=bbox.getMinX(), high=bbox.getMaxX()),
np.random.uniform(low=bbox.getMinY(), high=bbox.getMaxY()),
)
skyCoord = lsst.afw.geom.SpherePoint(raDeg, decDeg, lsst.afw.geom.arcseconds)
refRec.set(refCoordKey, skyCoord)
trueRec = trueSrc.addNew()
truePos = truePoly(initialIwcToSky.applyInverse(skyCoord))
trueRec.set(srcPosKey, truePos)
measRec = measSrc.addNew()
covSqrt = np.random.randn(3, 2)
cov = (errScaling*(np.dot(covSqrt.transpose(), covSqrt) +
np.diag([1.0, 1.0]))).astype(np.float32)
# We don't actually perturb positions according to noise level, as
# this makes it much harder to test that the result agrees with
# what we put in.
measPos = truePos
measRec.set(srcPosKey, measPos)
measRec.set(srcErrKey, cov)
match = lsst.afw.table.ReferenceMatch(refRec, measRec, (measPos - truePos).computeNorm())
matches.append(match)
# Construct a fitter, and verify that the internal catalog it constructs is what we expect.
fitter = ScaledPolynomialTransformFitter.fromMatches(order, matches, initialWcs, 0.0)
expected = lsst.meas.astrom.compose(
fitter.getOutputScaling(),
lsst.meas.astrom.compose(truePoly, fitter.getInputScaling().inverted())
)
data = fitter.getData()
dataOutKey = lsst.afw.table.Point2DKey(data.schema["src"])
dataInKey = lsst.afw.table.Point2DKey(data.schema["intermediate"])
dataErrKey = lsst.afw.table.CovarianceMatrix2fKey(data.schema["src"], ["x", "y"])
scaledInBBox = lsst.afw.geom.Box2D()
scaledOutBBox = lsst.afw.geom.Box2D()
vandermonde = np.zeros((nPoints, (order + 1)*(order + 2)//2), dtype=float)
for i, (match, dataRec, trueRec) in enumerate(zip(matches, data, trueSrc)):
self.assertEqual(match.second.getX(), dataRec.get("src_x"))
self.assertEqual(match.second.getY(), dataRec.get("src_y"))
self.assertEqual(match.first.getId(), dataRec.get("ref_id"))
self.assertEqual(match.second.getId(), dataRec.get("src_id"))
refPos = initialIwcToSky.applyInverse(match.first.getCoord())
self.assertEqual(refPos.getX(), dataRec.get("intermediate_x"))
self.assertEqual(refPos.getY(), dataRec.get("intermediate_y"))
self.assertFloatsAlmostEqual(match.second.get(srcErrKey), dataRec.get(dataErrKey), rtol=1E-7)
scaledIn = fitter.getInputScaling()(dataRec.get(dataInKey))
scaledOut = fitter.getOutputScaling()(dataRec.get(dataOutKey))
scaledInBBox.include(scaledIn)
scaledOutBBox.include(scaledOut)
self.assertFloatsAlmostEqual(np.array(expected(scaledIn)), np.array(scaledOut), rtol=1E-7)
j = 0
for n in range(order + 1):
for p in range(n + 1):
q = n - p
vandermonde[i, j] = scaledIn.getX()**p * scaledIn.getY()**q
j += 1
# Verify that scaling transforms move inputs and outputs into [-1, 1]
self.assertFloatsAlmostEqual(scaledInBBox.getMinX(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledInBBox.getMinY(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledInBBox.getMaxX(), 1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledInBBox.getMaxY(), 1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMinX(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMinY(), -1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMaxX(), 1.0, rtol=1E-12)
self.assertFloatsAlmostEqual(scaledOutBBox.getMaxY(), 1.0, rtol=1E-12)
# Run the fitter, and check that we get out approximately what we put in.
fitter.fit(order)
fitter.updateModel()
# Check the transformed input points.
self.assertFloatsAlmostEqual(data.get("model_x"), trueSrc.getX(), rtol=1E-15)
self.assertFloatsAlmostEqual(data.get("model_y"), trueSrc.getY(), rtol=1E-15)
# Check the actual transform's coefficients (after composing in the scaling, which is
# a lot of the reason we lose a lot of precision here).
fittedPoly = lsst.meas.astrom.PolynomialTransform.convert(fitter.getTransform())
self.assertFloatsAlmostEqual(fittedPoly.getXCoeffs(), truePoly.getXCoeffs(), rtol=1E-5, atol=1E-5)
self.assertFloatsAlmostEqual(fittedPoly.getYCoeffs(), truePoly.getYCoeffs(), rtol=1E-5, atol=1E-5)