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1# This file is part of cp_pipe.
2#
3# Developed for the LSST Data Management System.
4# This product includes software developed by the LSST Project
5# (https://www.lsst.org).
6# See the COPYRIGHT file at the top-level directory of this distribution
7# for details of code ownership.
8#
9# This program is free software: you can redistribute it and/or modify
10# it under the terms of the GNU General Public License as published by
11# the Free Software Foundation, either version 3 of the License, or
12# (at your option) any later version.
13#
14# This program is distributed in the hope that it will be useful,
15# but WITHOUT ANY WARRANTY; without even the implied warranty of
16# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17# GNU General Public License for more details.
18#
19# You should have received a copy of the GNU General Public License
20# along with this program. If not, see <https://www.gnu.org/licenses/>.
21#
23__all__ = ['countMaskedPixels', 'ddict2dict', 'CovFastFourierTransform']
25import numpy as np
26from scipy.optimize import leastsq
27import numpy.polynomial.polynomial as poly
28from scipy.stats import norm
30from lsst.ip.isr import isrMock
31import lsst.afw.image
33import galsim
36def sigmaClipCorrection(nSigClip):
37 """Correct measured sigma to account for clipping.
39 If we clip our input data and then measure sigma, then the
40 measured sigma is smaller than the true value because real
41 points beyond the clip threshold have been removed. This is a
42 small (1.5% at nSigClip=3) effect when nSigClip >~ 3, but the
43 default parameters for measure crosstalk use nSigClip=2.0.
44 This causes the measured sigma to be about 15% smaller than
45 real. This formula corrects the issue, for the symmetric case
46 (upper clip threshold equal to lower clip threshold).
48 Parameters
49 ----------
50 nSigClip : `float`
51 Number of sigma the measurement was clipped by.
53 Returns
54 -------
55 scaleFactor : `float`
56 Scale factor to increase the measured sigma by.
57 """
58 varFactor = 1.0 - (2 * nSigClip * norm.pdf(nSigClip)) / (norm.cdf(nSigClip) - norm.cdf(-nSigClip))
59 return 1.0 / np.sqrt(varFactor)
62def calculateWeightedReducedChi2(measured, model, weightsMeasured, nData, nParsModel):
63 """Calculate weighted reduced chi2.
65 Parameters
66 ----------
67 measured : `list`
68 List with measured data.
69 model : `list`
70 List with modeled data.
71 weightsMeasured : `list`
72 List with weights for the measured data.
73 nData : `int`
74 Number of data points.
75 nParsModel : `int`
76 Number of parameters in the model.
78 Returns
79 -------
80 redWeightedChi2 : `float`
81 Reduced weighted chi2.
82 """
83 wRes = (measured - model)*weightsMeasured
84 return ((wRes*wRes).sum())/(nData-nParsModel)
87def makeMockFlats(expTime, gain=1.0, readNoiseElectrons=5, fluxElectrons=1000,
88 randomSeedFlat1=1984, randomSeedFlat2=666, powerLawBfParams=[],
89 expId1=0, expId2=1):
90 """Create a pair or mock flats with isrMock.
92 Parameters
93 ----------
94 expTime : `float`
95 Exposure time of the flats.
96 gain : `float`, optional
97 Gain, in e/ADU.
98 readNoiseElectrons : `float`, optional
99 Read noise rms, in electrons.
100 fluxElectrons : `float`, optional
101 Flux of flats, in electrons per second.
102 randomSeedFlat1 : `int`, optional
103 Random seed for the normal distrubutions for the mean signal
104 and noise (flat1).
105 randomSeedFlat2 : `int`, optional
106 Random seed for the normal distrubutions for the mean signal
107 and noise (flat2).
108 powerLawBfParams : `list`, optional
109 Parameters for `galsim.cdmodel.PowerLawCD` to simulate the
110 brightter-fatter effect.
111 expId1 : `int`, optional
112 Exposure ID for first flat.
113 expId2 : `int`, optional
114 Exposure ID for second flat.
116 Returns
117 -------
118 flatExp1 : `lsst.afw.image.exposure.ExposureF`
119 First exposure of flat field pair.
120 flatExp2 : `lsst.afw.image.exposure.ExposureF`
121 Second exposure of flat field pair.
123 Notes
124 -----
125 The parameters of `galsim.cdmodel.PowerLawCD` are `n, r0, t0, rx,
126 tx, r, t, alpha`. For more information about their meaning, see
127 the Galsim documentation
128 https://galsim-developers.github.io/GalSim/_build/html/_modules/galsim/cdmodel.html # noqa: W505
129 and Gruen+15 (1501.02802).
131 Example: galsim.cdmodel.PowerLawCD(8, 1.1e-7, 1.1e-7, 1.0e-8,
132 1.0e-8, 1.0e-9, 1.0e-9, 2.0)
133 """
134 flatFlux = fluxElectrons # e/s
135 flatMean = flatFlux*expTime # e
136 readNoise = readNoiseElectrons # e
138 mockImageConfig = isrMock.IsrMock.ConfigClass()
140 mockImageConfig.flatDrop = 0.99999
141 mockImageConfig.isTrimmed = True
143 flatExp1 = isrMock.FlatMock(config=mockImageConfig).run()
144 flatExp2 = flatExp1.clone()
145 (shapeY, shapeX) = flatExp1.getDimensions()
146 flatWidth = np.sqrt(flatMean)
148 rng1 = np.random.RandomState(randomSeedFlat1)
149 flatData1 = rng1.normal(flatMean, flatWidth, (shapeX, shapeY)) + rng1.normal(0.0, readNoise,
150 (shapeX, shapeY))
151 rng2 = np.random.RandomState(randomSeedFlat2)
152 flatData2 = rng2.normal(flatMean, flatWidth, (shapeX, shapeY)) + rng2.normal(0.0, readNoise,
153 (shapeX, shapeY))
154 # Simulate BF with power law model in galsim
155 if len(powerLawBfParams):
156 if not len(powerLawBfParams) == 8:
157 raise RuntimeError("Wrong number of parameters for `galsim.cdmodel.PowerLawCD`. "
158 f"Expected 8; passed {len(powerLawBfParams)}.")
159 cd = galsim.cdmodel.PowerLawCD(*powerLawBfParams)
160 tempFlatData1 = galsim.Image(flatData1)
161 temp2FlatData1 = cd.applyForward(tempFlatData1)
163 tempFlatData2 = galsim.Image(flatData2)
164 temp2FlatData2 = cd.applyForward(tempFlatData2)
166 flatExp1.image.array[:] = temp2FlatData1.array/gain # ADU
167 flatExp2.image.array[:] = temp2FlatData2.array/gain # ADU
168 else:
169 flatExp1.image.array[:] = flatData1/gain # ADU
170 flatExp2.image.array[:] = flatData2/gain # ADU
172 visitInfoExp1 = lsst.afw.image.VisitInfo(exposureId=expId1, exposureTime=expTime)
173 visitInfoExp2 = lsst.afw.image.VisitInfo(exposureId=expId2, exposureTime=expTime)
175 flatExp1.info.id = expId1
176 flatExp1.getInfo().setVisitInfo(visitInfoExp1)
177 flatExp2.info.id = expId2
178 flatExp2.getInfo().setVisitInfo(visitInfoExp2)
180 return flatExp1, flatExp2
183def countMaskedPixels(maskedIm, maskPlane):
184 """Count the number of pixels in a given mask plane.
186 Parameters
187 ----------
188 maskedIm : `~lsst.afw.image.MaskedImage`
189 Masked image to examine.
190 maskPlane : `str`
191 Name of the mask plane to examine.
193 Returns
194 -------
195 nPix : `int`
196 Number of pixels in the requested mask plane.
197 """
198 maskBit = maskedIm.mask.getPlaneBitMask(maskPlane)
199 nPix = np.where(np.bitwise_and(maskedIm.mask.array, maskBit))[0].flatten().size
200 return nPix
203def irlsFit(initialParams, dataX, dataY, function, weightsY=None, weightType='Cauchy', scaleResidual=True):
204 """Iteratively reweighted least squares fit.
206 This uses the `lsst.cp.pipe.utils.fitLeastSq`, but applies weights
207 based on the Cauchy distribution by default. Other weight options
208 are implemented. See e.g. Holland and Welsch, 1977,
209 doi:10.1080/03610927708827533
211 Parameters
212 ----------
213 initialParams : `list` [`float`]
214 Starting parameters.
215 dataX : `numpy.array`, (N,)
216 Abscissa data.
217 dataY : `numpy.array`, (N,)
218 Ordinate data.
219 function : callable
220 Function to fit.
221 weightsY : `numpy.array`, (N,)
222 Weights to apply to the data.
223 weightType : `str`, optional
224 Type of weighting to use. One of Cauchy, Anderson, bisquare,
225 box, Welsch, Huber, logistic, or Fair.
226 scaleResidual : `bool`, optional
227 If true, the residual is scaled by the sqrt of the Y values.
229 Returns
230 -------
231 polyFit : `list` [`float`]
232 Final best fit parameters.
233 polyFitErr : `list` [`float`]
234 Final errors on fit parameters.
235 chiSq : `float`
236 Reduced chi squared.
237 weightsY : `list` [`float`]
238 Final weights used for each point.
240 Raises
241 ------
242 RuntimeError :
243 Raised if an unknown weightType string is passed.
244 """
245 if not weightsY:
246 weightsY = np.ones_like(dataX)
248 polyFit, polyFitErr, chiSq = fitLeastSq(initialParams, dataX, dataY, function, weightsY=weightsY)
249 for iteration in range(10):
250 resid = np.abs(dataY - function(polyFit, dataX))
251 if scaleResidual:
252 resid = resid / np.sqrt(dataY)
253 if weightType == 'Cauchy':
254 # Use Cauchy weighting. This is a soft weight.
255 # At [2, 3, 5, 10] sigma, weights are [.59, .39, .19, .05].
256 Z = resid / 2.385
257 weightsY = 1.0 / (1.0 + np.square(Z))
258 elif weightType == 'Anderson':
259 # Anderson+1972 weighting. This is a hard weight.
260 # At [2, 3, 5, 10] sigma, weights are [.67, .35, 0.0, 0.0].
261 Z = resid / (1.339 * np.pi)
262 weightsY = np.where(Z < 1.0, np.sinc(Z), 0.0)
263 elif weightType == 'bisquare':
264 # Beaton and Tukey (1974) biweight. This is a hard weight.
265 # At [2, 3, 5, 10] sigma, weights are [.81, .59, 0.0, 0.0].
266 Z = resid / 4.685
267 weightsY = np.where(Z < 1.0, 1.0 - np.square(Z), 0.0)
268 elif weightType == 'box':
269 # Hinich and Talwar (1975). This is a hard weight.
270 # At [2, 3, 5, 10] sigma, weights are [1.0, 0.0, 0.0, 0.0].
271 weightsY = np.where(resid < 2.795, 1.0, 0.0)
272 elif weightType == 'Welsch':
273 # Dennis and Welsch (1976). This is a hard weight.
274 # At [2, 3, 5, 10] sigma, weights are [.64, .36, .06, 1e-5].
275 Z = resid / 2.985
276 weightsY = np.exp(-1.0 * np.square(Z))
277 elif weightType == 'Huber':
278 # Huber (1964) weighting. This is a soft weight.
279 # At [2, 3, 5, 10] sigma, weights are [.67, .45, .27, .13].
280 Z = resid / 1.345
281 weightsY = np.where(Z < 1.0, 1.0, 1 / Z)
282 elif weightType == 'logistic':
283 # Logistic weighting. This is a soft weight.
284 # At [2, 3, 5, 10] sigma, weights are [.56, .40, .24, .12].
285 Z = resid / 1.205
286 weightsY = np.tanh(Z) / Z
287 elif weightType == 'Fair':
288 # Fair (1974) weighting. This is a soft weight.
289 # At [2, 3, 5, 10] sigma, weights are [.41, .32, .22, .12].
290 Z = resid / 1.4
291 weightsY = (1.0 / (1.0 + (Z)))
292 else:
293 raise RuntimeError(f"Unknown weighting type: {weightType}")
294 polyFit, polyFitErr, chiSq = fitLeastSq(initialParams, dataX, dataY, function, weightsY=weightsY)
296 return polyFit, polyFitErr, chiSq, weightsY
299def fitLeastSq(initialParams, dataX, dataY, function, weightsY=None):
300 """Do a fit and estimate the parameter errors using using
301 scipy.optimize.leastq.
303 optimize.leastsq returns the fractional covariance matrix. To
304 estimate the standard deviation of the fit parameters, multiply
305 the entries of this matrix by the unweighted reduced chi squared
306 and take the square root of the diagonal elements.
308 Parameters
309 ----------
310 initialParams : `list` [`float`]
311 initial values for fit parameters. For ptcFitType=POLYNOMIAL,
312 its length determines the degree of the polynomial.
313 dataX : `numpy.array`, (N,)
314 Data in the abscissa axis.
315 dataY : `numpy.array`, (N,)
316 Data in the ordinate axis.
317 function : callable object (function)
318 Function to fit the data with.
319 weightsY : `numpy.array`, (N,)
320 Weights of the data in the ordinate axis.
322 Return
323 ------
324 pFitSingleLeastSquares : `list` [`float`]
325 List with fitted parameters.
326 pErrSingleLeastSquares : `list` [`float`]
327 List with errors for fitted parameters.
329 reducedChiSqSingleLeastSquares : `float`
330 Reduced chi squared, unweighted if weightsY is not provided.
331 """
332 if weightsY is None:
333 weightsY = np.ones(len(dataX))
335 def errFunc(p, x, y, weightsY=None):
336 if weightsY is None:
337 weightsY = np.ones(len(x))
338 return (function(p, x) - y)*weightsY
340 pFit, pCov, infoDict, errMessage, success = leastsq(errFunc, initialParams,
341 args=(dataX, dataY, weightsY), full_output=1,
342 epsfcn=0.0001)
344 if (len(dataY) > len(initialParams)) and pCov is not None:
345 reducedChiSq = calculateWeightedReducedChi2(dataY, function(pFit, dataX), weightsY, len(dataY),
346 len(initialParams))
347 pCov *= reducedChiSq
348 else:
349 pCov = np.zeros((len(initialParams), len(initialParams)))
350 pCov[:, :] = np.nan
351 reducedChiSq = np.nan
353 errorVec = []
354 for i in range(len(pFit)):
355 errorVec.append(np.fabs(pCov[i][i])**0.5)
357 pFitSingleLeastSquares = pFit
358 pErrSingleLeastSquares = np.array(errorVec)
360 return pFitSingleLeastSquares, pErrSingleLeastSquares, reducedChiSq
363def fitBootstrap(initialParams, dataX, dataY, function, weightsY=None, confidenceSigma=1.):
364 """Do a fit using least squares and bootstrap to estimate parameter errors.
366 The bootstrap error bars are calculated by fitting 100 random data sets.
368 Parameters
369 ----------
370 initialParams : `list` [`float`]
371 initial values for fit parameters. For ptcFitType=POLYNOMIAL,
372 its length determines the degree of the polynomial.
373 dataX : `numpy.array`, (N,)
374 Data in the abscissa axis.
375 dataY : `numpy.array`, (N,)
376 Data in the ordinate axis.
377 function : callable object (function)
378 Function to fit the data with.
379 weightsY : `numpy.array`, (N,), optional.
380 Weights of the data in the ordinate axis.
381 confidenceSigma : `float`, optional.
382 Number of sigmas that determine confidence interval for the
383 bootstrap errors.
385 Return
386 ------
387 pFitBootstrap : `list` [`float`]
388 List with fitted parameters.
389 pErrBootstrap : `list` [`float`]
390 List with errors for fitted parameters.
391 reducedChiSqBootstrap : `float`
392 Reduced chi squared, unweighted if weightsY is not provided.
393 """
394 if weightsY is None:
395 weightsY = np.ones(len(dataX))
397 def errFunc(p, x, y, weightsY):
398 if weightsY is None:
399 weightsY = np.ones(len(x))
400 return (function(p, x) - y)*weightsY
402 # Fit first time
403 pFit, _ = leastsq(errFunc, initialParams, args=(dataX, dataY, weightsY), full_output=0)
405 # Get the stdev of the residuals
406 residuals = errFunc(pFit, dataX, dataY, weightsY)
407 # 100 random data sets are generated and fitted
408 pars = []
409 for i in range(100):
410 randomDelta = np.random.normal(0., np.fabs(residuals), len(dataY))
411 randomDataY = dataY + randomDelta
412 randomFit, _ = leastsq(errFunc, initialParams,
413 args=(dataX, randomDataY, weightsY), full_output=0)
414 pars.append(randomFit)
415 pars = np.array(pars)
416 meanPfit = np.mean(pars, 0)
418 # confidence interval for parameter estimates
419 errPfit = confidenceSigma*np.std(pars, 0)
420 pFitBootstrap = meanPfit
421 pErrBootstrap = errPfit
423 reducedChiSq = calculateWeightedReducedChi2(dataY, function(pFitBootstrap, dataX), weightsY, len(dataY),
424 len(initialParams))
425 return pFitBootstrap, pErrBootstrap, reducedChiSq
428def funcPolynomial(pars, x):
429 """Polynomial function definition
430 Parameters
431 ----------
432 params : `list`
433 Polynomial coefficients. Its length determines the polynomial order.
435 x : `numpy.array`, (N,)
436 Abscisa array.
438 Returns
439 -------
440 y : `numpy.array`, (N,)
441 Ordinate array after evaluating polynomial of order
442 len(pars)-1 at `x`.
443 """
444 return poly.polyval(x, [*pars])
447def funcAstier(pars, x):
448 """Single brighter-fatter parameter model for PTC; Equation 16 of
449 Astier+19.
451 Parameters
452 ----------
453 params : `list`
454 Parameters of the model: a00 (brightter-fatter), gain (e/ADU),
455 and noise (e^2).
456 x : `numpy.array`, (N,)
457 Signal mu (ADU).
459 Returns
460 -------
461 y : `numpy.array`, (N,)
462 C_00 (variance) in ADU^2.
463 """
464 a00, gain, noise = pars
465 return 0.5/(a00*gain*gain)*(np.exp(2*a00*x*gain)-1) + noise/(gain*gain) # C_00
468def arrangeFlatsByExpTime(exposureList, exposureIdList):
469 """Arrange exposures by exposure time.
471 Parameters
472 ----------
473 exposureList : `list` [`lsst.pipe.base.connections.DeferredDatasetRef`]
474 Input list of exposure references.
475 exposureIdList : `list` [`int`]
476 List of exposure ids as obtained by dataId[`exposure`].
478 Returns
479 ------
480 flatsAtExpTime : `dict` [`float`,
481 `list`[(`lsst.pipe.base.connections.DeferredDatasetRef`,
482 `int`)]]
483 Dictionary that groups references to flat-field exposures
484 (and their IDs) that have the same exposure time (seconds).
485 """
486 flatsAtExpTime = {}
487 assert len(exposureList) == len(exposureIdList), "Different lengths for exp. list and exp. ID lists"
488 for expRef, expId in zip(exposureList, exposureIdList):
489 expTime = expRef.get(component='visitInfo').exposureTime
490 listAtExpTime = flatsAtExpTime.setdefault(expTime, [])
491 listAtExpTime.append((expRef, expId))
493 return flatsAtExpTime
496def arrangeFlatsByExpId(exposureList, exposureIdList):
497 """Arrange exposures by exposure ID.
499 There is no guarantee that this will properly group exposures, but
500 allows a sequence of flats that have different illumination
501 (despite having the same exposure time) to be processed.
503 Parameters
504 ----------
505 exposureList : `list`[`lsst.pipe.base.connections.DeferredDatasetRef`]
506 Input list of exposure references.
507 exposureIdList : `list`[`int`]
508 List of exposure ids as obtained by dataId[`exposure`].
510 Returns
511 ------
512 flatsAtExpId : `dict` [`float`,
513 `list`[(`lsst.pipe.base.connections.DeferredDatasetRef`,
514 `int`)]]
515 Dictionary that groups references to flat-field exposures (and their
516 IDs) sequentially by their exposure id.
518 Notes
519 -----
521 This algorithm sorts the input exposure references by their exposure
522 id, and then assigns each pair of exposure references (exp_j, exp_{j+1})
523 to pair k, such that 2*k = j, where j is the python index of one of the
524 exposure references (starting from zero). By checking for the IndexError
525 while appending, we can ensure that there will only ever be fully
526 populated pairs.
527 """
528 flatsAtExpId = {}
529 assert len(exposureList) == len(exposureIdList), "Different lengths for exp. list and exp. ID lists"
530 # Sort exposures by expIds, which are in the second list `exposureIdList`.
531 sortedExposures = sorted(zip(exposureList, exposureIdList), key=lambda pair: pair[1])
533 for jPair, expTuple in enumerate(sortedExposures):
534 if (jPair + 1) % 2:
535 kPair = jPair // 2
536 listAtExpId = flatsAtExpId.setdefault(kPair, [])
537 try:
538 listAtExpId.append(expTuple)
539 listAtExpId.append(sortedExposures[jPair + 1])
540 except IndexError:
541 pass
543 return flatsAtExpId
546class CovFastFourierTransform:
547 """A class to compute (via FFT) the nearby pixels correlation function.
549 Implements appendix of Astier+19.
551 Parameters
552 ----------
553 diff : `numpy.array`
554 Image where to calculate the covariances (e.g., the difference
555 image of two flats).
556 w : `numpy.array`
557 Weight image (mask): it should consist of 1's (good pixel) and
558 0's (bad pixels).
559 fftShape : `tuple`
560 2d-tuple with the shape of the FFT
561 maxRangeCov : `int`
562 Maximum range for the covariances.
563 """
565 def __init__(self, diff, w, fftShape, maxRangeCov):
566 # check that the zero padding implied by "fft_shape"
567 # is large enough for the required correlation range
568 assert(fftShape[0] > diff.shape[0]+maxRangeCov+1)
569 assert(fftShape[1] > diff.shape[1]+maxRangeCov+1)
570 # for some reason related to numpy.fft.rfftn,
571 # the second dimension should be even, so
572 if fftShape[1]%2 == 1:
573 fftShape = (fftShape[0], fftShape[1]+1)
574 tIm = np.fft.rfft2(diff*w, fftShape)
575 tMask = np.fft.rfft2(w, fftShape)
576 # sum of "squares"
577 self.pCov = np.fft.irfft2(tIm*tIm.conjugate())
578 # sum of values
579 self.pMean = np.fft.irfft2(tIm*tMask.conjugate())
580 # number of w!=0 pixels.
581 self.pCount = np.fft.irfft2(tMask*tMask.conjugate())
583 def cov(self, dx, dy):
584 """Covariance for dx,dy averaged with dx,-dy if both non zero.
586 Implements appendix of Astier+19.
588 Parameters
589 ----------
590 dx : `int`
591 Lag in x
592 dy : `int
593 Lag in y
595 Returns
596 -------
597 0.5*(cov1+cov2) : `float`
598 Covariance at (dx, dy) lag
599 npix1+npix2 : `int`
600 Number of pixels used in covariance calculation.
601 """
602 # compensate rounding errors
603 nPix1 = int(round(self.pCount[dy, dx]))
604 cov1 = self.pCov[dy, dx]/nPix1-self.pMean[dy, dx]*self.pMean[-dy, -dx]/(nPix1*nPix1)
605 if (dx == 0 or dy == 0):
606 return cov1, nPix1
607 nPix2 = int(round(self.pCount[-dy, dx]))
608 cov2 = self.pCov[-dy, dx]/nPix2-self.pMean[-dy, dx]*self.pMean[dy, -dx]/(nPix2*nPix2)
609 return 0.5*(cov1+cov2), nPix1+nPix2
611 def reportCovFastFourierTransform(self, maxRange):
612 """Produce a list of tuples with covariances.
614 Implements appendix of Astier+19.
616 Parameters
617 ----------
618 maxRange : `int`
619 Maximum range of covariances.
621 Returns
622 -------
623 tupleVec : `list`
624 List with covariance tuples.
625 """
626 tupleVec = []
627 # (dy,dx) = (0,0) has to be first
628 for dy in range(maxRange+1):
629 for dx in range(maxRange+1):
630 cov, npix = self.cov(dx, dy)
631 if (dx == 0 and dy == 0):
632 var = cov
633 tupleVec.append((dx, dy, var, cov, npix))
634 return tupleVec
637def getFitDataFromCovariances(i, j, mu, fullCov, fullCovModel, fullCovSqrtWeights, gain=1.0,
638 divideByMu=False, returnMasked=False):
639 """Get measured signal and covariance, cov model, weigths, and mask at
640 covariance lag (i, j).
642 Parameters
643 ----------
644 i : `int`
645 Lag for covariance matrix.
646 j : `int`
647 Lag for covariance matrix.
648 mu : `list`
649 Mean signal values.
650 fullCov : `list` of `numpy.array`
651 Measured covariance matrices at each mean signal level in mu.
652 fullCovSqrtWeights : `list` of `numpy.array`
653 List of square root of measured covariances at each mean
654 signal level in mu.
655 fullCovModel : `list` of `numpy.array`
656 List of modeled covariances at each mean signal level in mu.
657 gain : `float`, optional
658 Gain, in e-/ADU. If other than 1.0 (default), the returned
659 quantities will be in electrons or powers of electrons.
660 divideByMu : `bool`, optional
661 Divide returned covariance, model, and weights by the mean
662 signal mu?
663 returnMasked : `bool`, optional
664 Use mask (based on weights) in returned arrays (mu,
665 covariance, and model)?
667 Returns
668 -------
669 mu : `numpy.array`
670 list of signal values at (i, j).
671 covariance : `numpy.array`
672 Covariance at (i, j) at each mean signal mu value (fullCov[:, i, j]).
673 covarianceModel : `numpy.array`
674 Covariance model at (i, j).
675 weights : `numpy.array`
676 Weights at (i, j).
677 maskFromWeights : `numpy.array`, optional
678 Boolean mask of the covariance at (i,j), where the weights
679 differ from 0.
680 """
681 mu = np.array(mu)
682 fullCov = np.array(fullCov)
683 fullCovModel = np.array(fullCovModel)
684 fullCovSqrtWeights = np.array(fullCovSqrtWeights)
685 covariance = fullCov[:, i, j]*(gain**2)
686 covarianceModel = fullCovModel[:, i, j]*(gain**2)
687 weights = fullCovSqrtWeights[:, i, j]/(gain**2)
689 maskFromWeights = weights != 0
690 if returnMasked:
691 weights = weights[maskFromWeights]
692 covarianceModel = covarianceModel[maskFromWeights]
693 mu = mu[maskFromWeights]
694 covariance = covariance[maskFromWeights]
696 if divideByMu:
697 covariance /= mu
698 covarianceModel /= mu
699 weights *= mu
700 return mu, covariance, covarianceModel, weights, maskFromWeights
703def symmetrize(inputArray):
704 """ Copy array over 4 quadrants prior to convolution.
706 Parameters
707 ----------
708 inputarray : `numpy.array`
709 Input array to symmetrize.
711 Returns
712 -------
713 aSym : `numpy.array`
714 Symmetrized array.
715 """
716 targetShape = list(inputArray.shape)
717 r1, r2 = inputArray.shape[-1], inputArray.shape[-2]
718 targetShape[-1] = 2*r1-1
719 targetShape[-2] = 2*r2-1
720 aSym = np.ndarray(tuple(targetShape))
721 aSym[..., r2-1:, r1-1:] = inputArray
722 aSym[..., r2-1:, r1-1::-1] = inputArray
723 aSym[..., r2-1::-1, r1-1::-1] = inputArray
724 aSym[..., r2-1::-1, r1-1:] = inputArray
726 return aSym
729def ddict2dict(d):
730 """Convert nested default dictionaries to regular dictionaries.
732 This is needed to prevent yaml persistence issues.
734 Parameters
735 ----------
736 d : `defaultdict`
737 A possibly nested set of `defaultdict`.
739 Returns
740 -------
741 dict : `dict`
742 A possibly nested set of `dict`.
743 """
744 for k, v in d.items():
745 if isinstance(v, dict):
746 d[k] = ddict2dict(v)
747 return dict(d)