Coverage for python/lsst/cp/pipe/utils.py: 9%

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21#

23__all__ = ['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.

115

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.

122

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).

130

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

137

138 mockImageConfig = isrMock.IsrMock.ConfigClass()

139

140 mockImageConfig.flatDrop = 0.99999

141 mockImageConfig.isTrimmed = True

142

143 flatExp1 = isrMock.FlatMock(config=mockImageConfig).run()

144 flatExp2 = flatExp1.clone()

145 (shapeY, shapeX) = flatExp1.getDimensions()

146 flatWidth = np.sqrt(flatMean)

147

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)

162

163 tempFlatData2 = galsim.Image(flatData2)

164 temp2FlatData2 = cd.applyForward(tempFlatData2)

165

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

171

172 visitInfoExp1 = lsst.afw.image.VisitInfo(exposureId=expId1, exposureTime=expTime)

173 visitInfoExp2 = lsst.afw.image.VisitInfo(exposureId=expId2, exposureTime=expTime)

174

175 flatExp1.info.id = expId1

176 flatExp1.getInfo().setVisitInfo(visitInfoExp1)

177 flatExp2.info.id = expId2

178 flatExp2.getInfo().setVisitInfo(visitInfoExp2)

179

180 return flatExp1, flatExp2

181

182

183def irlsFit(initialParams, dataX, dataY, function, weightsY=None, weightType='Cauchy', scaleResidual=True):

184 """Iteratively reweighted least squares fit.

185

186 This uses the `lsst.cp.pipe.utils.fitLeastSq`, but applies weights

187 based on the Cauchy distribution by default. Other weight options

188 are implemented. See e.g. Holland and Welsch, 1977,

189 doi:10.1080/03610927708827533

190

191 Parameters

192 ----------

193 initialParams : `list` [`float`]

194 Starting parameters.

195 dataX : `numpy.array`, (N,)

196 Abscissa data.

197 dataY : `numpy.array`, (N,)

198 Ordinate data.

199 function : callable

200 Function to fit.

201 weightsY : `numpy.array`, (N,)

202 Weights to apply to the data.

203 weightType : `str`, optional

204 Type of weighting to use. One of Cauchy, Anderson, bisquare,

205 box, Welsch, Huber, logistic, or Fair.

206 scaleResidual : `bool`, optional

207 If true, the residual is scaled by the sqrt of the Y values.

208

209 Returns

210 -------

211 polyFit : `list` [`float`]

212 Final best fit parameters.

213 polyFitErr : `list` [`float`]

214 Final errors on fit parameters.

215 chiSq : `float`

216 Reduced chi squared.

217 weightsY : `list` [`float`]

218 Final weights used for each point.

219

220 Raises

221 ------

222 RuntimeError :

223 Raised if an unknown weightType string is passed.

224 """

225 if not weightsY:

226 weightsY = np.ones_like(dataX)

227

228 polyFit, polyFitErr, chiSq = fitLeastSq(initialParams, dataX, dataY, function, weightsY=weightsY)

229 for iteration in range(10):

230 resid = np.abs(dataY - function(polyFit, dataX))

231 if scaleResidual:

232 resid = resid / np.sqrt(dataY)

233 if weightType == 'Cauchy':

234 # Use Cauchy weighting. This is a soft weight.

235 # At [2, 3, 5, 10] sigma, weights are [.59, .39, .19, .05].

236 Z = resid / 2.385

237 weightsY = 1.0 / (1.0 + np.square(Z))

238 elif weightType == 'Anderson':

239 # Anderson+1972 weighting. This is a hard weight.

240 # At [2, 3, 5, 10] sigma, weights are [.67, .35, 0.0, 0.0].

241 Z = resid / (1.339 * np.pi)

242 weightsY = np.where(Z < 1.0, np.sinc(Z), 0.0)

243 elif weightType == 'bisquare':

244 # Beaton and Tukey (1974) biweight. This is a hard weight.

245 # At [2, 3, 5, 10] sigma, weights are [.81, .59, 0.0, 0.0].

246 Z = resid / 4.685

247 weightsY = np.where(Z < 1.0, 1.0 - np.square(Z), 0.0)

248 elif weightType == 'box':

249 # Hinich and Talwar (1975). This is a hard weight.

250 # At [2, 3, 5, 10] sigma, weights are [1.0, 0.0, 0.0, 0.0].

251 weightsY = np.where(resid < 2.795, 1.0, 0.0)

252 elif weightType == 'Welsch':

253 # Dennis and Welsch (1976). This is a hard weight.

254 # At [2, 3, 5, 10] sigma, weights are [.64, .36, .06, 1e-5].

255 Z = resid / 2.985

256 weightsY = np.exp(-1.0 * np.square(Z))

257 elif weightType == 'Huber':

258 # Huber (1964) weighting. This is a soft weight.

259 # At [2, 3, 5, 10] sigma, weights are [.67, .45, .27, .13].

260 Z = resid / 1.345

261 weightsY = np.where(Z < 1.0, 1.0, 1 / Z)

262 elif weightType == 'logistic':

263 # Logistic weighting. This is a soft weight.

264 # At [2, 3, 5, 10] sigma, weights are [.56, .40, .24, .12].

265 Z = resid / 1.205

266 weightsY = np.tanh(Z) / Z

267 elif weightType == 'Fair':

268 # Fair (1974) weighting. This is a soft weight.

269 # At [2, 3, 5, 10] sigma, weights are [.41, .32, .22, .12].

270 Z = resid / 1.4

271 weightsY = (1.0 / (1.0 + (Z)))

272 else:

273 raise RuntimeError(f"Unknown weighting type: {weightType}")

274 polyFit, polyFitErr, chiSq = fitLeastSq(initialParams, dataX, dataY, function, weightsY=weightsY)

275

276 return polyFit, polyFitErr, chiSq, weightsY

277

278

279def fitLeastSq(initialParams, dataX, dataY, function, weightsY=None):

280 """Do a fit and estimate the parameter errors using using

281 scipy.optimize.leastq.

282

283 optimize.leastsq returns the fractional covariance matrix. To

284 estimate the standard deviation of the fit parameters, multiply

285 the entries of this matrix by the unweighted reduced chi squared

286 and take the square root of the diagonal elements.

287

288 Parameters

289 ----------

290 initialParams : `list` [`float`]

291 initial values for fit parameters. For ptcFitType=POLYNOMIAL,

292 its length determines the degree of the polynomial.

293 dataX : `numpy.array`, (N,)

294 Data in the abscissa axis.

295 dataY : `numpy.array`, (N,)

296 Data in the ordinate axis.

297 function : callable object (function)

298 Function to fit the data with.

299 weightsY : `numpy.array`, (N,)

300 Weights of the data in the ordinate axis.

301

302 Return

303 ------

304 pFitSingleLeastSquares : `list` [`float`]

305 List with fitted parameters.

306 pErrSingleLeastSquares : `list` [`float`]

307 List with errors for fitted parameters.

308

309 reducedChiSqSingleLeastSquares : `float`

310 Reduced chi squared, unweighted if weightsY is not provided.

311 """

312 if weightsY is None:

313 weightsY = np.ones(len(dataX))

314

315 def errFunc(p, x, y, weightsY=None):

316 if weightsY is None:

317 weightsY = np.ones(len(x))

318 return (function(p, x) - y)*weightsY

319

320 pFit, pCov, infoDict, errMessage, success = leastsq(errFunc, initialParams,

321 args=(dataX, dataY, weightsY), full_output=1,

322 epsfcn=0.0001)

323

324 if (len(dataY) > len(initialParams)) and pCov is not None:

325 reducedChiSq = calculateWeightedReducedChi2(dataY, function(pFit, dataX), weightsY, len(dataY),

326 len(initialParams))

327 pCov *= reducedChiSq

328 else:

329 pCov = np.zeros((len(initialParams), len(initialParams)))

330 pCov[:, :] = np.nan

331 reducedChiSq = np.nan

332

333 errorVec = []

334 for i in range(len(pFit)):

335 errorVec.append(np.fabs(pCov[i][i])**0.5)

336

337 pFitSingleLeastSquares = pFit

338 pErrSingleLeastSquares = np.array(errorVec)

339

340 return pFitSingleLeastSquares, pErrSingleLeastSquares, reducedChiSq

341

342

343def fitBootstrap(initialParams, dataX, dataY, function, weightsY=None, confidenceSigma=1.):

344 """Do a fit using least squares and bootstrap to estimate parameter errors.

345

346 The bootstrap error bars are calculated by fitting 100 random data sets.

347

348 Parameters

349 ----------

350 initialParams : `list` [`float`]

351 initial values for fit parameters. For ptcFitType=POLYNOMIAL,

352 its length determines the degree of the polynomial.

353 dataX : `numpy.array`, (N,)

354 Data in the abscissa axis.

355 dataY : `numpy.array`, (N,)

356 Data in the ordinate axis.

357 function : callable object (function)

358 Function to fit the data with.

359 weightsY : `numpy.array`, (N,), optional.

360 Weights of the data in the ordinate axis.

361 confidenceSigma : `float`, optional.

362 Number of sigmas that determine confidence interval for the

363 bootstrap errors.

364

365 Return

366 ------

367 pFitBootstrap : `list` [`float`]

368 List with fitted parameters.

369 pErrBootstrap : `list` [`float`]

370 List with errors for fitted parameters.

371 reducedChiSqBootstrap : `float`

372 Reduced chi squared, unweighted if weightsY is not provided.

373 """

374 if weightsY is None:

375 weightsY = np.ones(len(dataX))

376

377 def errFunc(p, x, y, weightsY):

378 if weightsY is None:

379 weightsY = np.ones(len(x))

380 return (function(p, x) - y)*weightsY

381

382 # Fit first time

383 pFit, _ = leastsq(errFunc, initialParams, args=(dataX, dataY, weightsY), full_output=0)

384

385 # Get the stdev of the residuals

386 residuals = errFunc(pFit, dataX, dataY, weightsY)

387 # 100 random data sets are generated and fitted

388 pars = []

389 for i in range(100):

390 randomDelta = np.random.normal(0., np.fabs(residuals), len(dataY))

391 randomDataY = dataY + randomDelta

392 randomFit, _ = leastsq(errFunc, initialParams,

393 args=(dataX, randomDataY, weightsY), full_output=0)

394 pars.append(randomFit)

395 pars = np.array(pars)

396 meanPfit = np.mean(pars, 0)

397

398 # confidence interval for parameter estimates

399 errPfit = confidenceSigma*np.std(pars, 0)

400 pFitBootstrap = meanPfit

401 pErrBootstrap = errPfit

402

403 reducedChiSq = calculateWeightedReducedChi2(dataY, function(pFitBootstrap, dataX), weightsY, len(dataY),

404 len(initialParams))

405 return pFitBootstrap, pErrBootstrap, reducedChiSq

406

407

408def funcPolynomial(pars, x):

409 """Polynomial function definition

410 Parameters

411 ----------

412 params : `list`

413 Polynomial coefficients. Its length determines the polynomial order.

414

415 x : `numpy.array`, (N,)

416 Abscisa array.

417

418 Returns

419 -------

420 y : `numpy.array`, (N,)

421 Ordinate array after evaluating polynomial of order

422 len(pars)-1 at `x`.

423 """

424 return poly.polyval(x, [*pars])

425

426

427def funcAstier(pars, x):

428 """Single brighter-fatter parameter model for PTC; Equation 16 of

429 Astier+19.

430

431 Parameters

432 ----------

433 params : `list`

434 Parameters of the model: a00 (brightter-fatter), gain (e/ADU),

435 and noise (e^2).

436 x : `numpy.array`, (N,)

437 Signal mu (ADU).

438

439 Returns

440 -------

441 y : `numpy.array`, (N,)

442 C_00 (variance) in ADU^2.

443 """

444 a00, gain, noise = pars

445 return 0.5/(a00*gain*gain)*(np.exp(2*a00*x*gain)-1) + noise/(gain*gain) # C_00

446

447

448def arrangeFlatsByExpTime(exposureList, exposureIdList):

449 """Arrange exposures by exposure time.

450

451 Parameters

452 ----------

453 exposureList : `list` [`lsst.pipe.base.connections.DeferredDatasetRef`]

454 Input list of exposure references.

455 exposureIdList : `list` [`int`]

456 List of exposure ids as obtained by dataId[`exposure`].

457

458 Returns

459 ------

460 flatsAtExpTime : `dict` [`float`,

461 `list`[(`lsst.pipe.base.connections.DeferredDatasetRef`,

462 `int`)]]

463 Dictionary that groups references to flat-field exposures

464 (and their IDs) that have the same exposure time (seconds).

465 """

466 flatsAtExpTime = {}

467 assert len(exposureList) == len(exposureIdList), "Different lengths for exp. list and exp. ID lists"

468 for expRef, expId in zip(exposureList, exposureIdList):

469 expTime = expRef.get(component='visitInfo').exposureTime

470 listAtExpTime = flatsAtExpTime.setdefault(expTime, [])

471 listAtExpTime.append((expRef, expId))

472

473 return flatsAtExpTime

474

475

476def arrangeFlatsByExpFlux(exposureList, exposureIdList, fluxKeyword):

477 """Arrange exposures by exposure flux.

478

479 Parameters

480 ----------

481 exposureList : `list` [`lsst.pipe.base.connections.DeferredDatasetRef`]

482 Input list of exposure references.

483 exposureIdList : `list` [`int`]

484 List of exposure ids as obtained by dataId[`exposure`].

485 fluxKeyword : `str`

486 Header keyword that contains the flux per exposure.

487

488 Returns

489 -------

490 flatsAtFlux : `dict` [`float`,

491 `list`[(`lsst.pipe.base.connections.DeferredDatasetRef`,

492 `int`)]]

493 Dictionary that groups references to flat-field exposures

494 (and their IDs) that have the same flux.

495 """

496 flatsAtExpFlux = {}

497 assert len(exposureList) == len(exposureIdList), "Different lengths for exp. list and exp. ID lists"

498 for expRef, expId in zip(exposureList, exposureIdList):

499 # Get flux from header, assuming it is in the metadata.

500 expFlux = expRef.get().getMetadata()[fluxKeyword]

501 listAtExpFlux = flatsAtExpFlux.setdefault(expFlux, [])

502 listAtExpFlux.append((expRef, expId))

503

504 return flatsAtExpFlux

505

506

507def arrangeFlatsByExpId(exposureList, exposureIdList):

508 """Arrange exposures by exposure ID.

509

510 There is no guarantee that this will properly group exposures, but

511 allows a sequence of flats that have different illumination

512 (despite having the same exposure time) to be processed.

513

514 Parameters

515 ----------

516 exposureList : `list`[`lsst.pipe.base.connections.DeferredDatasetRef`]

517 Input list of exposure references.

518 exposureIdList : `list`[`int`]

519 List of exposure ids as obtained by dataId[`exposure`].

520

521 Returns

522 ------

523 flatsAtExpId : `dict` [`float`,

524 `list`[(`lsst.pipe.base.connections.DeferredDatasetRef`,

525 `int`)]]

526 Dictionary that groups references to flat-field exposures (and their

527 IDs) sequentially by their exposure id.

528

529 Notes

530 -----

531

532 This algorithm sorts the input exposure references by their exposure

533 id, and then assigns each pair of exposure references (exp_j, exp_{j+1})

534 to pair k, such that 2*k = j, where j is the python index of one of the

535 exposure references (starting from zero). By checking for the IndexError

536 while appending, we can ensure that there will only ever be fully

537 populated pairs.

538 """

539 flatsAtExpId = {}

540 assert len(exposureList) == len(exposureIdList), "Different lengths for exp. list and exp. ID lists"

541 # Sort exposures by expIds, which are in the second list `exposureIdList`.

542 sortedExposures = sorted(zip(exposureList, exposureIdList), key=lambda pair: pair[1])

543

544 for jPair, expTuple in enumerate(sortedExposures):

545 if (jPair + 1) % 2:

546 kPair = jPair // 2

547 listAtExpId = flatsAtExpId.setdefault(kPair, [])

548 try:

549 listAtExpId.append(expTuple)

550 listAtExpId.append(sortedExposures[jPair + 1])

551 except IndexError:

552 pass

553

554 return flatsAtExpId

555

556

557class CovFastFourierTransform:

558 """A class to compute (via FFT) the nearby pixels correlation function.

559

560 Implements appendix of Astier+19.

561

562 Parameters

563 ----------

564 diff : `numpy.array`

565 Image where to calculate the covariances (e.g., the difference

566 image of two flats).

567 w : `numpy.array`

568 Weight image (mask): it should consist of 1's (good pixel) and

569 0's (bad pixels).

570 fftShape : `tuple`

571 2d-tuple with the shape of the FFT

572 maxRangeCov : `int`

573 Maximum range for the covariances.

574 """

575

576 def __init__(self, diff, w, fftShape, maxRangeCov):

577 # check that the zero padding implied by "fft_shape"

578 # is large enough for the required correlation range

579 assert(fftShape[0] > diff.shape[0]+maxRangeCov+1)

580 assert(fftShape[1] > diff.shape[1]+maxRangeCov+1)

581 # for some reason related to numpy.fft.rfftn,

582 # the second dimension should be even, so

583 if fftShape[1]%2 == 1:

584 fftShape = (fftShape[0], fftShape[1]+1)

585 tIm = np.fft.rfft2(diff*w, fftShape)

586 tMask = np.fft.rfft2(w, fftShape)

587 # sum of "squares"

588 self.pCov = np.fft.irfft2(tIm*tIm.conjugate())

589 # sum of values

590 self.pMean = np.fft.irfft2(tIm*tMask.conjugate())

591 # number of w!=0 pixels.

592 self.pCount = np.fft.irfft2(tMask*tMask.conjugate())

593

594 def cov(self, dx, dy):

595 """Covariance for dx,dy averaged with dx,-dy if both non zero.

596

597 Implements appendix of Astier+19.

598

599 Parameters

600 ----------

601 dx : `int`

602 Lag in x

603 dy : `int`

604 Lag in y

605

606 Returns

607 -------

608 0.5*(cov1+cov2) : `float`

609 Covariance at (dx, dy) lag

610 npix1+npix2 : `int`

611 Number of pixels used in covariance calculation.

612 """

613 # compensate rounding errors

614 nPix1 = int(round(self.pCount[dy, dx]))

615 cov1 = self.pCov[dy, dx]/nPix1-self.pMean[dy, dx]*self.pMean[-dy, -dx]/(nPix1*nPix1)

616 if (dx == 0 or dy == 0):

617 return cov1, nPix1

618 nPix2 = int(round(self.pCount[-dy, dx]))

619 cov2 = self.pCov[-dy, dx]/nPix2-self.pMean[-dy, dx]*self.pMean[dy, -dx]/(nPix2*nPix2)

620 return 0.5*(cov1+cov2), nPix1+nPix2

621

622 def reportCovFastFourierTransform(self, maxRange):

623 """Produce a list of tuples with covariances.

624

625 Implements appendix of Astier+19.

626

627 Parameters

628 ----------

629 maxRange : `int`

630 Maximum range of covariances.

631

632 Returns

633 -------

634 tupleVec : `list`

635 List with covariance tuples.

636 """

637 tupleVec = []

638 # (dy,dx) = (0,0) has to be first

639 for dy in range(maxRange+1):

640 for dx in range(maxRange+1):

641 cov, npix = self.cov(dx, dy)

642 if (dx == 0 and dy == 0):

643 var = cov

644 tupleVec.append((dx, dy, var, cov, npix))

645 return tupleVec

646

647

648def getFitDataFromCovariances(i, j, mu, fullCov, fullCovModel, fullCovSqrtWeights, gain=1.0,

649 divideByMu=False, returnMasked=False):

650 """Get measured signal and covariance, cov model, weigths, and mask at

651 covariance lag (i, j).

652

653 Parameters

654 ----------

655 i : `int`

656 Lag for covariance matrix.

657 j : `int`

658 Lag for covariance matrix.

659 mu : `list`

660 Mean signal values.

661 fullCov : `list` of `numpy.array`

662 Measured covariance matrices at each mean signal level in mu.

663 fullCovSqrtWeights : `list` of `numpy.array`

664 List of square root of measured covariances at each mean

665 signal level in mu.

666 fullCovModel : `list` of `numpy.array`

667 List of modeled covariances at each mean signal level in mu.

668 gain : `float`, optional

669 Gain, in e-/ADU. If other than 1.0 (default), the returned

670 quantities will be in electrons or powers of electrons.

671 divideByMu : `bool`, optional

672 Divide returned covariance, model, and weights by the mean

673 signal mu?

674 returnMasked : `bool`, optional

675 Use mask (based on weights) in returned arrays (mu,

676 covariance, and model)?

677

678 Returns

679 -------

680 mu : `numpy.array`

681 list of signal values at (i, j).

682 covariance : `numpy.array`

683 Covariance at (i, j) at each mean signal mu value (fullCov[:, i, j]).

684 covarianceModel : `numpy.array`

685 Covariance model at (i, j).

686 weights : `numpy.array`

687 Weights at (i, j).

688 maskFromWeights : `numpy.array`, optional

689 Boolean mask of the covariance at (i,j), where the weights

690 differ from 0.

691 """

692 mu = np.array(mu)

693 fullCov = np.array(fullCov)

694 fullCovModel = np.array(fullCovModel)

695 fullCovSqrtWeights = np.array(fullCovSqrtWeights)

696 covariance = fullCov[:, i, j]*(gain**2)

697 covarianceModel = fullCovModel[:, i, j]*(gain**2)

698 weights = fullCovSqrtWeights[:, i, j]/(gain**2)

699

700 maskFromWeights = weights != 0

701 if returnMasked:

702 weights = weights[maskFromWeights]

703 covarianceModel = covarianceModel[maskFromWeights]

704 mu = mu[maskFromWeights]

705 covariance = covariance[maskFromWeights]

706

707 if divideByMu:

708 covariance /= mu

709 covarianceModel /= mu

710 weights *= mu

711 return mu, covariance, covarianceModel, weights, maskFromWeights

712

713

714def symmetrize(inputArray):

715 """ Copy array over 4 quadrants prior to convolution.

716

717 Parameters

718 ----------

719 inputarray : `numpy.array`

720 Input array to symmetrize.

721

722 Returns

723 -------

724 aSym : `numpy.array`

725 Symmetrized array.

726 """

727 targetShape = list(inputArray.shape)

728 r1, r2 = inputArray.shape[-1], inputArray.shape[-2]

729 targetShape[-1] = 2*r1-1

730 targetShape[-2] = 2*r2-1

731 aSym = np.ndarray(tuple(targetShape))

732 aSym[..., r2-1:, r1-1:] = inputArray

733 aSym[..., r2-1:, r1-1::-1] = inputArray

734 aSym[..., r2-1::-1, r1-1::-1] = inputArray

735 aSym[..., r2-1::-1, r1-1:] = inputArray

736

737 return aSym

738

739

740def ddict2dict(d):

741 """Convert nested default dictionaries to regular dictionaries.

742

743 This is needed to prevent yaml persistence issues.

744

745 Parameters

746 ----------

747 d : `defaultdict`

748 A possibly nested set of `defaultdict`.

749

750 Returns

751 -------

752 dict : `dict`

753 A possibly nested set of `dict`.

754 """

755 for k, v in d.items():

756 if isinstance(v, dict):

757 d[k] = ddict2dict(v)

758 return dict(d)