Coverage for python/lsst/cp/pipe/utils.py: 11%

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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# 

22 

23__all__ = ['ddict2dict', 'CovFastFourierTransform'] 

24 

25 

26import galsim 

27import logging 

28import numpy as np 

29import itertools 

30import numpy.polynomial.polynomial as poly 

31 

32from scipy.optimize import leastsq 

33from scipy.stats import median_abs_deviation, norm 

34 

35from lsst.ip.isr import isrMock 

36import lsst.afw.image 

37import lsst.afw.math 

38 

39 

40def sigmaClipCorrection(nSigClip): 

41 """Correct measured sigma to account for clipping. 

42 

43 If we clip our input data and then measure sigma, then the 

44 measured sigma is smaller than the true value because real 

45 points beyond the clip threshold have been removed. This is a 

46 small (1.5% at nSigClip=3) effect when nSigClip >~ 3, but the 

47 default parameters for measure crosstalk use nSigClip=2.0. 

48 This causes the measured sigma to be about 15% smaller than 

49 real. This formula corrects the issue, for the symmetric case 

50 (upper clip threshold equal to lower clip threshold). 

51 

52 Parameters 

53 ---------- 

54 nSigClip : `float` 

55 Number of sigma the measurement was clipped by. 

56 

57 Returns 

58 ------- 

59 scaleFactor : `float` 

60 Scale factor to increase the measured sigma by. 

61 """ 

62 varFactor = 1.0 - (2 * nSigClip * norm.pdf(nSigClip)) / (norm.cdf(nSigClip) - norm.cdf(-nSigClip)) 

63 return 1.0 / np.sqrt(varFactor) 

64 

65 

66def calculateWeightedReducedChi2(measured, model, weightsMeasured, nData, nParsModel): 

67 """Calculate weighted reduced chi2. 

68 

69 Parameters 

70 ---------- 

71 measured : `list` 

72 List with measured data. 

73 model : `list` 

74 List with modeled data. 

75 weightsMeasured : `list` 

76 List with weights for the measured data. 

77 nData : `int` 

78 Number of data points. 

79 nParsModel : `int` 

80 Number of parameters in the model. 

81 

82 Returns 

83 ------- 

84 redWeightedChi2 : `float` 

85 Reduced weighted chi2. 

86 """ 

87 wRes = (measured - model)*weightsMeasured 

88 return ((wRes*wRes).sum())/(nData-nParsModel) 

89 

90 

91def makeMockFlats(expTime, gain=1.0, readNoiseElectrons=5, fluxElectrons=1000, 

92 randomSeedFlat1=1984, randomSeedFlat2=666, powerLawBfParams=[], 

93 expId1=0, expId2=1): 

94 """Create a pair or mock flats with isrMock. 

95 

96 Parameters 

97 ---------- 

98 expTime : `float` 

99 Exposure time of the flats. 

100 gain : `float`, optional 

101 Gain, in e/ADU. 

102 readNoiseElectrons : `float`, optional 

103 Read noise rms, in electrons. 

104 fluxElectrons : `float`, optional 

105 Flux of flats, in electrons per second. 

106 randomSeedFlat1 : `int`, optional 

107 Random seed for the normal distrubutions for the mean signal 

108 and noise (flat1). 

109 randomSeedFlat2 : `int`, optional 

110 Random seed for the normal distrubutions for the mean signal 

111 and noise (flat2). 

112 powerLawBfParams : `list`, optional 

113 Parameters for `galsim.cdmodel.PowerLawCD` to simulate the 

114 brightter-fatter effect. 

115 expId1 : `int`, optional 

116 Exposure ID for first flat. 

117 expId2 : `int`, optional 

118 Exposure ID for second flat. 

119 

120 Returns 

121 ------- 

122 flatExp1 : `lsst.afw.image.exposure.ExposureF` 

123 First exposure of flat field pair. 

124 flatExp2 : `lsst.afw.image.exposure.ExposureF` 

125 Second exposure of flat field pair. 

126 

127 Notes 

128 ----- 

129 The parameters of `galsim.cdmodel.PowerLawCD` are `n, r0, t0, rx, 

130 tx, r, t, alpha`. For more information about their meaning, see 

131 the Galsim documentation 

132 https://galsim-developers.github.io/GalSim/_build/html/_modules/galsim/cdmodel.html # noqa: W505 

133 and Gruen+15 (1501.02802). 

134 

135 Example: galsim.cdmodel.PowerLawCD(8, 1.1e-7, 1.1e-7, 1.0e-8, 

136 1.0e-8, 1.0e-9, 1.0e-9, 2.0) 

137 """ 

138 flatFlux = fluxElectrons # e/s 

139 flatMean = flatFlux*expTime # e 

140 readNoise = readNoiseElectrons # e 

141 

142 mockImageConfig = isrMock.IsrMock.ConfigClass() 

143 

144 mockImageConfig.flatDrop = 0.99999 

145 mockImageConfig.isTrimmed = True 

146 

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

148 flatExp2 = flatExp1.clone() 

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

150 flatWidth = np.sqrt(flatMean) 

151 

152 rng1 = np.random.RandomState(randomSeedFlat1) 

153 flatData1 = rng1.normal(flatMean, flatWidth, (shapeX, shapeY)) + rng1.normal(0.0, readNoise, 

154 (shapeX, shapeY)) 

155 rng2 = np.random.RandomState(randomSeedFlat2) 

156 flatData2 = rng2.normal(flatMean, flatWidth, (shapeX, shapeY)) + rng2.normal(0.0, readNoise, 

157 (shapeX, shapeY)) 

158 # Simulate BF with power law model in galsim 

159 if len(powerLawBfParams): 

160 if not len(powerLawBfParams) == 8: 

161 raise RuntimeError("Wrong number of parameters for `galsim.cdmodel.PowerLawCD`. " 

162 f"Expected 8; passed {len(powerLawBfParams)}.") 

163 cd = galsim.cdmodel.PowerLawCD(*powerLawBfParams) 

164 tempFlatData1 = galsim.Image(flatData1) 

165 temp2FlatData1 = cd.applyForward(tempFlatData1) 

166 

167 tempFlatData2 = galsim.Image(flatData2) 

168 temp2FlatData2 = cd.applyForward(tempFlatData2) 

169 

170 flatExp1.image.array[:] = temp2FlatData1.array/gain # ADU 

171 flatExp2.image.array[:] = temp2FlatData2.array/gain # ADU 

172 else: 

173 flatExp1.image.array[:] = flatData1/gain # ADU 

174 flatExp2.image.array[:] = flatData2/gain # ADU 

175 

176 visitInfoExp1 = lsst.afw.image.VisitInfo(exposureTime=expTime) 

177 visitInfoExp2 = lsst.afw.image.VisitInfo(exposureTime=expTime) 

178 

179 flatExp1.info.id = expId1 

180 flatExp1.getInfo().setVisitInfo(visitInfoExp1) 

181 flatExp2.info.id = expId2 

182 flatExp2.getInfo().setVisitInfo(visitInfoExp2) 

183 

184 return flatExp1, flatExp2 

185 

186 

187def irlsFit(initialParams, dataX, dataY, function, weightsY=None, weightType='Cauchy', scaleResidual=True): 

188 """Iteratively reweighted least squares fit. 

189 

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

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

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

193 doi:10.1080/03610927708827533 

194 

195 Parameters 

196 ---------- 

197 initialParams : `list` [`float`] 

198 Starting parameters. 

199 dataX : `numpy.array`, (N,) 

200 Abscissa data. 

201 dataY : `numpy.array`, (N,) 

202 Ordinate data. 

203 function : callable 

204 Function to fit. 

205 weightsY : `numpy.array`, (N,) 

206 Weights to apply to the data. 

207 weightType : `str`, optional 

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

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

210 scaleResidual : `bool`, optional 

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

212 

213 Returns 

214 ------- 

215 polyFit : `list` [`float`] 

216 Final best fit parameters. 

217 polyFitErr : `list` [`float`] 

218 Final errors on fit parameters. 

219 chiSq : `float` 

220 Reduced chi squared. 

221 weightsY : `list` [`float`] 

222 Final weights used for each point. 

223 

224 Raises 

225 ------ 

226 RuntimeError : 

227 Raised if an unknown weightType string is passed. 

228 """ 

229 if not weightsY: 

230 weightsY = np.ones_like(dataX) 

231 

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

233 for iteration in range(10): 

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

235 if scaleResidual: 

236 resid = resid / np.sqrt(dataY) 

237 if weightType == 'Cauchy': 

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

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

240 Z = resid / 2.385 

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

242 elif weightType == 'Anderson': 

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

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

245 Z = resid / (1.339 * np.pi) 

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

247 elif weightType == 'bisquare': 

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

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

250 Z = resid / 4.685 

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

252 elif weightType == 'box': 

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

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

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

256 elif weightType == 'Welsch': 

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

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

259 Z = resid / 2.985 

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

261 elif weightType == 'Huber': 

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

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

264 Z = resid / 1.345 

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

266 elif weightType == 'logistic': 

267 # Logistic weighting. This is a soft weight. 

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

269 Z = resid / 1.205 

270 weightsY = np.tanh(Z) / Z 

271 elif weightType == 'Fair': 

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

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

274 Z = resid / 1.4 

275 weightsY = (1.0 / (1.0 + (Z))) 

276 else: 

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

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

279 

280 return polyFit, polyFitErr, chiSq, weightsY 

281 

282 

283def fitLeastSq(initialParams, dataX, dataY, function, weightsY=None): 

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

285 scipy.optimize.leastq. 

286 

287 optimize.leastsq returns the fractional covariance matrix. To 

288 estimate the standard deviation of the fit parameters, multiply 

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

290 and take the square root of the diagonal elements. 

291 

292 Parameters 

293 ---------- 

294 initialParams : `list` [`float`] 

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

296 its length determines the degree of the polynomial. 

297 dataX : `numpy.array`, (N,) 

298 Data in the abscissa axis. 

299 dataY : `numpy.array`, (N,) 

300 Data in the ordinate axis. 

301 function : callable object (function) 

302 Function to fit the data with. 

303 weightsY : `numpy.array`, (N,) 

304 Weights of the data in the ordinate axis. 

305 

306 Return 

307 ------ 

308 pFitSingleLeastSquares : `list` [`float`] 

309 List with fitted parameters. 

310 pErrSingleLeastSquares : `list` [`float`] 

311 List with errors for fitted parameters. 

312 

313 reducedChiSqSingleLeastSquares : `float` 

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

315 """ 

316 if weightsY is None: 

317 weightsY = np.ones(len(dataX)) 

318 

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

320 if weightsY is None: 

321 weightsY = np.ones(len(x)) 

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

323 

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

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

326 epsfcn=0.0001) 

327 

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

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

330 len(initialParams)) 

331 pCov *= reducedChiSq 

332 else: 

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

334 pCov[:, :] = np.nan 

335 reducedChiSq = np.nan 

336 

337 errorVec = [] 

338 for i in range(len(pFit)): 

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

340 

341 pFitSingleLeastSquares = pFit 

342 pErrSingleLeastSquares = np.array(errorVec) 

343 

344 return pFitSingleLeastSquares, pErrSingleLeastSquares, reducedChiSq 

345 

346 

347def fitBootstrap(initialParams, dataX, dataY, function, weightsY=None, confidenceSigma=1.): 

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

349 

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

351 

352 Parameters 

353 ---------- 

354 initialParams : `list` [`float`] 

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

356 its length determines the degree of the polynomial. 

357 dataX : `numpy.array`, (N,) 

358 Data in the abscissa axis. 

359 dataY : `numpy.array`, (N,) 

360 Data in the ordinate axis. 

361 function : callable object (function) 

362 Function to fit the data with. 

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

364 Weights of the data in the ordinate axis. 

365 confidenceSigma : `float`, optional. 

366 Number of sigmas that determine confidence interval for the 

367 bootstrap errors. 

368 

369 Return 

370 ------ 

371 pFitBootstrap : `list` [`float`] 

372 List with fitted parameters. 

373 pErrBootstrap : `list` [`float`] 

374 List with errors for fitted parameters. 

375 reducedChiSqBootstrap : `float` 

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

377 """ 

378 if weightsY is None: 

379 weightsY = np.ones(len(dataX)) 

380 

381 def errFunc(p, x, y, weightsY): 

382 if weightsY is None: 

383 weightsY = np.ones(len(x)) 

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

385 

386 # Fit first time 

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

388 

389 # Get the stdev of the residuals 

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

391 # 100 random data sets are generated and fitted 

392 pars = [] 

393 for i in range(100): 

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

395 randomDataY = dataY + randomDelta 

396 randomFit, _ = leastsq(errFunc, initialParams, 

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

398 pars.append(randomFit) 

399 pars = np.array(pars) 

400 meanPfit = np.mean(pars, 0) 

401 

402 # confidence interval for parameter estimates 

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

404 pFitBootstrap = meanPfit 

405 pErrBootstrap = errPfit 

406 

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

408 len(initialParams)) 

409 return pFitBootstrap, pErrBootstrap, reducedChiSq 

410 

411 

412def funcPolynomial(pars, x): 

413 """Polynomial function definition 

414 Parameters 

415 ---------- 

416 params : `list` 

417 Polynomial coefficients. Its length determines the polynomial order. 

418 

419 x : `numpy.array`, (N,) 

420 Abscisa array. 

421 

422 Returns 

423 ------- 

424 y : `numpy.array`, (N,) 

425 Ordinate array after evaluating polynomial of order 

426 len(pars)-1 at `x`. 

427 """ 

428 return poly.polyval(x, [*pars]) 

429 

430 

431def funcAstier(pars, x): 

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

433 Astier+19. 

434 

435 Parameters 

436 ---------- 

437 params : `list` 

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

439 and noise (e^2). 

440 x : `numpy.array`, (N,) 

441 Signal mu (ADU). 

442 

443 Returns 

444 ------- 

445 y : `numpy.array`, (N,) 

446 C_00 (variance) in ADU^2. 

447 """ 

448 a00, gain, noise = pars 

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

450 

451 

452def arrangeFlatsByExpTime(exposureList, exposureIdList, log=None): 

453 """Arrange exposures by exposure time. 

454 

455 Parameters 

456 ---------- 

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

458 Input list of exposure references. 

459 exposureIdList : `list` [`int`] 

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

461 log : `lsst.utils.logging.LsstLogAdapter`, optional 

462 Log object. 

463 

464 Returns 

465 ------ 

466 flatsAtExpTime : `dict` [`float`, 

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

468 `int`)]] 

469 Dictionary that groups references to flat-field exposures 

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

471 """ 

472 flatsAtExpTime = {} 

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

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

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

476 if not np.isfinite(expTime) and log is not None: 

477 log.warning("Exposure %d has non-finite exposure time.", expId) 

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

479 listAtExpTime.append((expRef, expId)) 

480 

481 return flatsAtExpTime 

482 

483 

484def arrangeFlatsByExpFlux(exposureList, exposureIdList, fluxKeyword, log=None): 

485 """Arrange exposures by exposure flux. 

486 

487 Parameters 

488 ---------- 

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

490 Input list of exposure references. 

491 exposureIdList : `list` [`int`] 

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

493 fluxKeyword : `str` 

494 Header keyword that contains the flux per exposure. 

495 log : `lsst.utils.logging.LsstLogAdapter`, optional 

496 Log object. 

497 

498 Returns 

499 ------- 

500 flatsAtFlux : `dict` [`float`, 

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

502 `int`)]] 

503 Dictionary that groups references to flat-field exposures 

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

505 """ 

506 flatsAtExpFlux = {} 

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

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

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

510 try: 

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

512 except KeyError: 

513 # If it's missing from the header, continue; it will 

514 # be caught and rejected when pairing exposures. 

515 expFlux = None 

516 if expFlux is None: 

517 if log is not None: 

518 log.warning("Exposure %d does not have valid header keyword %s.", expId, fluxKeyword) 

519 expFlux = np.nan 

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

521 listAtExpFlux.append((expRef, expId)) 

522 

523 return flatsAtExpFlux 

524 

525 

526def arrangeFlatsByExpId(exposureList, exposureIdList): 

527 """Arrange exposures by exposure ID. 

528 

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

530 allows a sequence of flats that have different illumination 

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

532 

533 Parameters 

534 ---------- 

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

536 Input list of exposure references. 

537 exposureIdList : `list`[`int`] 

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

539 

540 Returns 

541 ------ 

542 flatsAtExpId : `dict` [`float`, 

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

544 `int`)]] 

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

546 IDs) sequentially by their exposure id. 

547 

548 Notes 

549 ----- 

550 

551 This algorithm sorts the input exposure references by their exposure 

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

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

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

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

556 populated pairs. 

557 """ 

558 flatsAtExpId = {} 

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

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

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

562 

563 for jPair, expTuple in enumerate(sortedExposures): 

564 if (jPair + 1) % 2: 

565 kPair = jPair // 2 

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

567 try: 

568 listAtExpId.append(expTuple) 

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

570 except IndexError: 

571 pass 

572 

573 return flatsAtExpId 

574 

575 

576class CovFastFourierTransform: 

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

578 

579 Implements appendix of Astier+19. 

580 

581 Parameters 

582 ---------- 

583 diff : `numpy.array` 

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

585 image of two flats). 

586 w : `numpy.array` 

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

588 0's (bad pixels). 

589 fftShape : `tuple` 

590 2d-tuple with the shape of the FFT 

591 maxRangeCov : `int` 

592 Maximum range for the covariances. 

593 """ 

594 

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

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

597 # is large enough for the required correlation range 

598 assert fftShape[0] > diff.shape[0]+maxRangeCov+1 

599 assert fftShape[1] > diff.shape[1]+maxRangeCov+1 

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

601 # the second dimension should be even, so 

602 if fftShape[1]%2 == 1: 

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

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

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

606 # sum of "squares" 

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

608 # sum of values 

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

610 # number of w!=0 pixels. 

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

612 

613 def cov(self, dx, dy): 

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

615 

616 Implements appendix of Astier+19. 

617 

618 Parameters 

619 ---------- 

620 dx : `int` 

621 Lag in x 

622 dy : `int` 

623 Lag in y 

624 

625 Returns 

626 ------- 

627 0.5*(cov1+cov2) : `float` 

628 Covariance at (dx, dy) lag 

629 npix1+npix2 : `int` 

630 Number of pixels used in covariance calculation. 

631 

632 Raises 

633 ------ 

634 ValueError if number of pixels for a given lag is 0. 

635 """ 

636 # compensate rounding errors 

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

638 if nPix1 == 0: 

639 raise ValueError(f"Could not compute covariance term {dy}, {dx}, as there are no good pixels.") 

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

641 if (dx == 0 or dy == 0): 

642 return cov1, nPix1 

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

644 if nPix2 == 0: 

645 raise ValueError("Could not compute covariance term {dy}, {dx} as there are no good pixels.") 

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

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

648 

649 def reportCovFastFourierTransform(self, maxRange): 

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

651 

652 Implements appendix of Astier+19. 

653 

654 Parameters 

655 ---------- 

656 maxRange : `int` 

657 Maximum range of covariances. 

658 

659 Returns 

660 ------- 

661 tupleVec : `list` 

662 List with covariance tuples. 

663 """ 

664 tupleVec = [] 

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

666 for dy in range(maxRange+1): 

667 for dx in range(maxRange+1): 

668 cov, npix = self.cov(dx, dy) 

669 if (dx == 0 and dy == 0): 

670 var = cov 

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

672 return tupleVec 

673 

674 

675def getFitDataFromCovariances(i, j, mu, fullCov, fullCovModel, fullCovSqrtWeights, gain=1.0, 

676 divideByMu=False, returnMasked=False): 

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

678 covariance lag (i, j). 

679 

680 Parameters 

681 ---------- 

682 i : `int` 

683 Lag for covariance matrix. 

684 j : `int` 

685 Lag for covariance matrix. 

686 mu : `list` 

687 Mean signal values. 

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

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

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

691 List of square root of measured covariances at each mean 

692 signal level in mu. 

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

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

695 gain : `float`, optional 

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

697 quantities will be in electrons or powers of electrons. 

698 divideByMu : `bool`, optional 

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

700 signal mu? 

701 returnMasked : `bool`, optional 

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

703 covariance, and model)? 

704 

705 Returns 

706 ------- 

707 mu : `numpy.array` 

708 list of signal values at (i, j). 

709 covariance : `numpy.array` 

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

711 covarianceModel : `numpy.array` 

712 Covariance model at (i, j). 

713 weights : `numpy.array` 

714 Weights at (i, j). 

715 maskFromWeights : `numpy.array`, optional 

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

717 differ from 0. 

718 """ 

719 mu = np.array(mu) 

720 fullCov = np.array(fullCov) 

721 fullCovModel = np.array(fullCovModel) 

722 fullCovSqrtWeights = np.array(fullCovSqrtWeights) 

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

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

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

726 

727 maskFromWeights = weights != 0 

728 if returnMasked: 

729 weights = weights[maskFromWeights] 

730 covarianceModel = covarianceModel[maskFromWeights] 

731 mu = mu[maskFromWeights] 

732 covariance = covariance[maskFromWeights] 

733 

734 if divideByMu: 

735 covariance /= mu 

736 covarianceModel /= mu 

737 weights *= mu 

738 return mu, covariance, covarianceModel, weights, maskFromWeights 

739 

740 

741def symmetrize(inputArray): 

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

743 

744 Parameters 

745 ---------- 

746 inputarray : `numpy.array` 

747 Input array to symmetrize. 

748 

749 Returns 

750 ------- 

751 aSym : `numpy.array` 

752 Symmetrized array. 

753 """ 

754 targetShape = list(inputArray.shape) 

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

756 targetShape[-1] = 2*r1-1 

757 targetShape[-2] = 2*r2-1 

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

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

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

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

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

763 

764 return aSym 

765 

766 

767def ddict2dict(d): 

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

769 

770 This is needed to prevent yaml persistence issues. 

771 

772 Parameters 

773 ---------- 

774 d : `defaultdict` 

775 A possibly nested set of `defaultdict`. 

776 

777 Returns 

778 ------- 

779 dict : `dict` 

780 A possibly nested set of `dict`. 

781 """ 

782 for k, v in d.items(): 

783 if isinstance(v, dict): 

784 d[k] = ddict2dict(v) 

785 return dict(d) 

786 

787 

788class Pol2D: 

789 """2D Polynomial Regression. 

790 

791 Parameters 

792 ---------- 

793 x : numpy.ndarray 

794 Input array for the x-coordinate. 

795 y : numpy.ndarray 

796 Input array for the y-coordinate. 

797 z : numpy.ndarray 

798 Input array for the dependent variable. 

799 order : int 

800 Order of the polynomial. 

801 w : numpy.ndarray, optional 

802 Weight array for weighted regression. Default is None. 

803 

804 Notes 

805 ----- 

806 Ported from by https://gitlab.in2p3.fr/astier/bfptc P. Astier. 

807 

808 Example: 

809 >>> x = np.array([1, 2, 3]) 

810 >>> y = np.array([4, 5, 6]) 

811 >>> z = np.array([7, 8, 9]) 

812 >>> order = 2 

813 >>> poly_reg = Pol2D(x, y, z, order) 

814 >>> result = poly_reg.eval(2.5, 5.5) 

815 """ 

816 def __init__(self, x, y, z, order, w=None): 

817 """ 

818 orderx : `int` 

819 Effective order in the x-direction. 

820 ordery : `int` 

821 Effective order in the y-direction. 

822 coeff : `numpy.ndarray` 

823 Coefficients of the polynomial regression. 

824 """ 

825 self.orderx = min(order, x.shape[0] - 1) 

826 self.ordery = min(order, x.shape[1] - 1) 

827 G = self.monomials(x.ravel(), y.ravel()) 

828 if w is None: 

829 self.coeff, _, rank, _ = np.linalg.lstsq(G, z.ravel(), rcond=None) 

830 else: 

831 self.coeff, _, rank, _ = np.linalg.lstsq((w.ravel() * G.T).T, z.ravel() * w.ravel(), rcond=None) 

832 

833 def monomials(self, x, y): 

834 """ 

835 Generate the monomials matrix for the given x and y. 

836 

837 Parameters 

838 ---------- 

839 x : numpy.ndarray 

840 Input array for the x-coordinate. 

841 y : numpy.ndarray 

842 Input array for the y-coordinate. 

843 

844 Returns 

845 ------- 

846 G : numpy.ndarray 

847 Monomials matrix. 

848 """ 

849 ncols = (self.orderx + 1) * (self.ordery + 1) 

850 G = np.zeros(x.shape + (ncols,)) 

851 ij = itertools.product(range(self.orderx + 1), range(self.ordery + 1)) 

852 for k, (i, j) in enumerate(ij): 

853 G[..., k] = x**i * y**j 

854 return G 

855 

856 def eval(self, x, y): 

857 """ 

858 Evaluate the polynomial at the given x and y coordinates. 

859 

860 Parameters 

861 ---------- 

862 x : `float` 

863 x-coordinate for evaluation. 

864 y : `float` 

865 y-coordinate for evaluation. 

866 

867 Returns 

868 ------- 

869 result : `float` 

870 Result of the polynomial evaluation. 

871 """ 

872 G = self.monomials(x, y) 

873 return np.dot(G, self.coeff) 

874 

875 

876class AstierSplineLinearityFitter: 

877 """Class to fit the Astier spline linearity model. 

878 

879 This is a spline fit with photodiode data based on a model 

880 from Pierre Astier, referenced in June 2023 from 

881 https://me.lsst.eu/astier/bot/7224D/model_nonlin.py 

882 

883 This model fits a spline with (optional) nuisance parameters 

884 to allow for different linearity coefficients with different 

885 photodiode settings. The minimization is a least-squares 

886 fit with the residual of 

887 Sum[(S(mu_i) + mu_i)/(k_j * D_i) - 1]**2, where S(mu_i) is 

888 an Akima Spline function of mu_i, the observed flat-pair 

889 mean; D_j is the photo-diode measurement corresponding to 

890 that flat-pair; and k_j is a constant of proportionality 

891 which is over index j as it is allowed to 

892 be different based on different photodiode settings (e.g. 

893 CCOBCURR). 

894 

895 The fit has additional constraints to ensure that the spline 

896 goes through the (0, 0) point, as well as a normalization 

897 condition so that the average of the spline over the full 

898 range is 0. The normalization ensures that the spline only 

899 fits deviations from linearity, rather than the linear 

900 function itself which is degenerate with the gain. 

901 

902 Parameters 

903 ---------- 

904 nodes : `np.ndarray` (N,) 

905 Array of spline node locations. 

906 grouping_values : `np.ndarray` (M,) 

907 Array of values to group values for different proportionality 

908 constants (e.g. CCOBCURR). 

909 pd : `np.ndarray` (M,) 

910 Array of photodiode measurements. 

911 mu : `np.ndarray` (M,) 

912 Array of flat mean values. 

913 mask : `np.ndarray` (M,), optional 

914 Input mask (True is good point, False is bad point). 

915 log : `logging.logger`, optional 

916 Logger object to use for logging. 

917 """ 

918 def __init__(self, nodes, grouping_values, pd, mu, mask=None, log=None): 

919 self._pd = pd 

920 self._mu = mu 

921 self._grouping_values = grouping_values 

922 self.log = log if log else logging.getLogger(__name__) 

923 

924 self._nodes = nodes 

925 if nodes[0] != 0.0: 

926 raise ValueError("First node must be 0.0") 

927 if not np.all(np.diff(nodes) > 0): 

928 raise ValueError("Nodes must be sorted with no repeats.") 

929 

930 # Check if sorted (raise otherwise) 

931 if not np.all(np.diff(self._grouping_values) >= 0): 

932 raise ValueError("Grouping values must be sorted.") 

933 

934 _, uindex, ucounts = np.unique(self._grouping_values, return_index=True, return_counts=True) 

935 self.ngroup = len(uindex) 

936 

937 self.group_indices = [] 

938 for i in range(self.ngroup): 

939 self.group_indices.append(np.arange(uindex[i], uindex[i] + ucounts[i])) 

940 

941 # Outlier weight values. Will be 1 (in) or 0 (out). 

942 self._w = np.ones(len(self._pd)) 

943 

944 if mask is not None: 

945 self._w[~mask] = 0.0 

946 

947 # Values to regularize spline fit. 

948 self._x_regularize = np.linspace(0.0, self._mu[self.mask].max(), 100) 

949 

950 def estimate_p0(self): 

951 """Estimate initial fit parameters. 

952 

953 Returns 

954 ------- 

955 p0 : `np.ndarray` 

956 Parameter array, with spline values (one for each node) followed 

957 by proportionality constants (one for each group). 

958 """ 

959 npt = len(self._nodes) + self.ngroup 

960 p0 = np.zeros(npt) 

961 

962 # Do a simple linear fit and set all the constants to this. 

963 linfit = np.polyfit(self._pd[self.mask], self._mu[self.mask], 1) 

964 p0[-self.ngroup:] = linfit[0] 

965 

966 # Look at the residuals... 

967 ratio_model = self.compute_ratio_model( 

968 self._nodes, 

969 self.group_indices, 

970 p0, 

971 self._pd, 

972 self._mu, 

973 ) 

974 # ...and adjust the linear parameters accordingly. 

975 p0[-self.ngroup:] *= np.median(ratio_model[self.mask]) 

976 

977 # Re-compute the residuals. 

978 ratio_model2 = self.compute_ratio_model( 

979 self._nodes, 

980 self.group_indices, 

981 p0, 

982 self._pd, 

983 self._mu, 

984 ) 

985 

986 # And compute a first guess of the spline nodes. 

987 bins = np.searchsorted(self._nodes, self._mu[self.mask]) 

988 tot_arr = np.zeros(len(self._nodes)) 

989 n_arr = np.zeros(len(self._nodes), dtype=int) 

990 np.add.at(tot_arr, bins, ratio_model2[self.mask]) 

991 np.add.at(n_arr, bins, 1) 

992 

993 ratio = np.ones(len(self._nodes)) 

994 ratio[n_arr > 0] = tot_arr[n_arr > 0]/n_arr[n_arr > 0] 

995 ratio[0] = 1.0 

996 p0[0: len(self._nodes)] = (ratio - 1) * self._nodes 

997 

998 return p0 

999 

1000 @staticmethod 

1001 def compute_ratio_model(nodes, group_indices, pars, pd, mu, return_spline=False): 

1002 """Compute the ratio model values. 

1003 

1004 Parameters 

1005 ---------- 

1006 nodes : `np.ndarray` (M,) 

1007 Array of node positions. 

1008 group_indices : `list` [`np.ndarray`] 

1009 List of group indices, one array for each group. 

1010 pars : `np.ndarray` 

1011 Parameter array, with spline values (one for each node) followed 

1012 by proportionality constants (one for each group.) 

1013 pd : `np.ndarray` (N,) 

1014 Array of photodiode measurements. 

1015 mu : `np.ndarray` (N,) 

1016 Array of flat means. 

1017 return_spline : `bool`, optional 

1018 Return the spline interpolation as well as the model ratios? 

1019 

1020 Returns 

1021 ------- 

1022 ratio_models : `np.ndarray` (N,) 

1023 Model ratio, (mu_i - S(mu_i))/(k_j * D_i) 

1024 spl : `lsst.afw.math.thing` 

1025 Spline interpolator (returned if return_spline=True). 

1026 """ 

1027 spl = lsst.afw.math.makeInterpolate( 

1028 nodes, 

1029 pars[0: len(nodes)], 

1030 lsst.afw.math.stringToInterpStyle("AKIMA_SPLINE"), 

1031 ) 

1032 

1033 numerator = mu - spl.interpolate(mu) 

1034 denominator = pd.copy() 

1035 ngroup = len(group_indices) 

1036 kj = pars[-ngroup:] 

1037 for j in range(ngroup): 

1038 denominator[group_indices[j]] *= kj[j] 

1039 

1040 if return_spline: 

1041 return numerator / denominator, spl 

1042 else: 

1043 return numerator / denominator 

1044 

1045 def fit(self, p0, min_iter=3, max_iter=20, max_rejection_per_iteration=5, n_sigma_clip=5.0): 

1046 """ 

1047 Perform iterative fit for linear + spline model with offsets. 

1048 

1049 Parameters 

1050 ---------- 

1051 p0 : `np.ndarray` 

1052 Initial fit parameters (one for each knot, followed by one for 

1053 each grouping). 

1054 min_iter : `int`, optional 

1055 Minimum number of fit iterations. 

1056 max_iter : `int`, optional 

1057 Maximum number of fit iterations. 

1058 max_rejection_per_iteration : `int`, optional 

1059 Maximum number of points to reject per iteration. 

1060 n_sigma_clip : `float`, optional 

1061 Number of sigma to do clipping in each iteration. 

1062 """ 

1063 init_params = p0 

1064 for k in range(max_iter): 

1065 params, cov_params, _, msg, ierr = leastsq( 

1066 self, 

1067 init_params, 

1068 full_output=True, 

1069 ftol=1e-5, 

1070 maxfev=12000, 

1071 ) 

1072 init_params = params.copy() 

1073 

1074 # We need to cut off the constraints at the end (there are more 

1075 # residuals than data points.) 

1076 res = self(params)[: len(self._w)] 

1077 std_res = median_abs_deviation(res[self.good_points], scale="normal") 

1078 sample = len(self.good_points) 

1079 

1080 # We don't want to reject too many outliers at once. 

1081 if sample > max_rejection_per_iteration: 

1082 sres = np.sort(np.abs(res)) 

1083 cut = max(sres[-max_rejection_per_iteration], std_res*n_sigma_clip) 

1084 else: 

1085 cut = std_res*n_sigma_clip 

1086 

1087 outliers = np.abs(res) > cut 

1088 self._w[outliers] = 0 

1089 if outliers.sum() != 0: 

1090 self.log.info( 

1091 "After iteration %d there are %d outliers (of %d).", 

1092 k, 

1093 outliers.sum(), 

1094 sample, 

1095 ) 

1096 elif k >= min_iter: 

1097 self.log.info("After iteration %d there are no more outliers.", k) 

1098 break 

1099 

1100 return params 

1101 

1102 @property 

1103 def mask(self): 

1104 return (self._w > 0) 

1105 

1106 @property 

1107 def good_points(self): 

1108 return self.mask.nonzero()[0] 

1109 

1110 def __call__(self, pars): 

1111 

1112 ratio_model, spl = self.compute_ratio_model( 

1113 self._nodes, 

1114 self.group_indices, 

1115 pars, 

1116 self._pd, 

1117 self._mu, 

1118 return_spline=True, 

1119 ) 

1120 

1121 resid = self._w*(ratio_model - 1.0) 

1122 # Ensure masked points have 0 residual. 

1123 resid[~self.mask] = 0.0 

1124 

1125 constraint = [1e3 * np.mean(spl.interpolate(self._x_regularize))] 

1126 # 0 should transform to 0 

1127 constraint.append(spl.interpolate(0)*1e10) 

1128 

1129 return np.hstack([resid, constraint])