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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__ = ['PlotPhotonTransferCurveTask'] 

24 

25import numpy as np 

26import matplotlib.pyplot as plt 

27import matplotlib as mpl 

28from matplotlib import gridspec 

29import os 

30from matplotlib.backends.backend_pdf import PdfPages 

31 

32import lsst.ip.isr as isr 

33import lsst.pex.config as pexConfig 

34import lsst.pipe.base as pipeBase 

35import pickle 

36 

37from .utils import (funcAstier, funcPolynomial, NonexistentDatasetTaskDataIdContainer, 

38 calculateWeightedReducedChi2) 

39from matplotlib.ticker import MaxNLocator 

40 

41from .astierCovPtcFit import computeApproximateAcoeffs 

42 

43 

44class PlotPhotonTransferCurveTaskConfig(pexConfig.Config): 

45 """Config class for photon transfer curve measurement task""" 

46 datasetFileName = pexConfig.Field( 

47 dtype=str, 

48 doc="datasetPtc file name (pkl)", 

49 default="", 

50 ) 

51 linearizerFileName = pexConfig.Field( 

52 dtype=str, 

53 doc="linearizer file name (fits)", 

54 default="", 

55 ) 

56 ccdKey = pexConfig.Field( 

57 dtype=str, 

58 doc="The key by which to pull a detector from a dataId, e.g. 'ccd' or 'detector'.", 

59 default='detector', 

60 ) 

61 signalElectronsRelativeA = pexConfig.Field( 

62 dtype=float, 

63 doc="Signal value for relative systematic bias between different methods of estimating a_ij " 

64 "(Fig. 15 of Astier+19).", 

65 default=75000, 

66 ) 

67 plotNormalizedCovariancesNumberOfBins = pexConfig.Field( 

68 dtype=int, 

69 doc="Number of bins in `plotNormalizedCovariancesNumber` function " 

70 "(Fig. 8, 10., of Astier+19).", 

71 default=10, 

72 ) 

73 

74 

75class PlotPhotonTransferCurveTask(pipeBase.CmdLineTask): 

76 """A class to plot the dataset from MeasurePhotonTransferCurveTask. 

77 

78 Parameters 

79 ---------- 

80 

81 *args: `list` 

82 Positional arguments passed to the Task constructor. None used at this 

83 time. 

84 **kwargs: `dict` 

85 Keyword arguments passed on to the Task constructor. None used at this 

86 time. 

87 

88 """ 

89 

90 ConfigClass = PlotPhotonTransferCurveTaskConfig 

91 _DefaultName = "plotPhotonTransferCurve" 

92 

93 def __init__(self, *args, **kwargs): 

94 pipeBase.CmdLineTask.__init__(self, *args, **kwargs) 

95 plt.interactive(False) # stop windows popping up when plotting. When headless, use 'agg' backend too 

96 self.config.validate() 

97 self.config.freeze() 

98 

99 @classmethod 

100 def _makeArgumentParser(cls): 

101 """Augment argument parser for the MeasurePhotonTransferCurveTask.""" 

102 parser = pipeBase.ArgumentParser(name=cls._DefaultName) 

103 parser.add_id_argument("--id", datasetType="photonTransferCurveDataset", 

104 ContainerClass=NonexistentDatasetTaskDataIdContainer, 

105 help="The ccds to use, e.g. --id ccd=0..100") 

106 return parser 

107 

108 @pipeBase.timeMethod 

109 def runDataRef(self, dataRef): 

110 """Run the Photon Transfer Curve (PTC) plotting measurement task. 

111 

112 Parameters 

113 ---------- 

114 dataRef : list of lsst.daf.persistence.ButlerDataRef 

115 dataRef for the detector for the visits to be fit. 

116 """ 

117 

118 datasetFile = self.config.datasetFileName 

119 

120 with open(datasetFile, "rb") as f: 

121 datasetPtc = pickle.load(f) 

122 

123 dirname = dataRef.getUri(datasetType='cpPipePlotRoot', write=True) 

124 if not os.path.exists(dirname): 

125 os.makedirs(dirname) 

126 

127 detNum = dataRef.dataId[self.config.ccdKey] 

128 filename = f"PTC_det{detNum}.pdf" 

129 filenameFull = os.path.join(dirname, filename) 

130 

131 if self.config.linearizerFileName: 

132 linearizer = isr.linearize.Linearizer.readFits(self.config.linearizerFileName) 

133 else: 

134 linearizer = None 

135 self.run(filenameFull, datasetPtc, linearizer=linearizer, log=self.log) 

136 

137 return pipeBase.Struct(exitStatus=0) 

138 

139 def run(self, filenameFull, datasetPtc, linearizer=None, log=None): 

140 """Make the plots for the PTC task""" 

141 ptcFitType = datasetPtc.ptcFitType 

142 with PdfPages(filenameFull) as pdfPages: 

143 if ptcFitType in ["FULLCOVARIANCE", ]: 

144 self.covAstierMakeAllPlots(datasetPtc.covariancesFits, datasetPtc.covariancesFitsWithNoB, 

145 pdfPages, log=log) 

146 elif ptcFitType in ["EXPAPPROXIMATION", "POLYNOMIAL"]: 

147 self._plotStandardPtc(datasetPtc, ptcFitType, pdfPages) 

148 else: 

149 raise RuntimeError(f"The input dataset had an invalid dataset.ptcFitType: {ptcFitType}. \n" + 

150 "Options: 'FULLCOVARIANCE', EXPAPPROXIMATION, or 'POLYNOMIAL'.") 

151 if linearizer: 

152 self._plotLinearizer(datasetPtc, linearizer, pdfPages) 

153 

154 return 

155 

156 def covAstierMakeAllPlots(self, covFits, covFitsNoB, pdfPages, 

157 log=None): 

158 """Make plots for MeasurePhotonTransferCurve task when doCovariancesAstier=True. 

159 

160 This function call other functions that mostly reproduce the plots in Astier+19. 

161 Most of the code is ported from Pierre Astier's repository https://github.com/PierreAstier/bfptc 

162 

163 Parameters 

164 ---------- 

165 covFits: `dict` 

166 Dictionary of CovFit objects, with amp names as keys. 

167 

168 covFitsNoB: `dict` 

169 Dictionary of CovFit objects, with amp names as keys (b=0 in Eq. 20 of Astier+19). 

170 

171 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

172 PDF file where the plots will be saved. 

173 

174 log : `lsst.log.Log`, optional 

175 Logger to handle messages 

176 """ 

177 self.plotCovariances(covFits, pdfPages) 

178 self.plotNormalizedCovariances(covFits, covFitsNoB, 0, 0, pdfPages, offset=0.01, topPlot=True, 

179 numberOfBins=self.config.plotNormalizedCovariancesNumberOfBins, 

180 log=log) 

181 self.plotNormalizedCovariances(covFits, covFitsNoB, 0, 1, pdfPages, 

182 numberOfBins=self.config.plotNormalizedCovariancesNumberOfBins, 

183 log=log) 

184 self.plotNormalizedCovariances(covFits, covFitsNoB, 1, 0, pdfPages, 

185 numberOfBins=self.config.plotNormalizedCovariancesNumberOfBins, 

186 log=log) 

187 self.plot_a_b(covFits, pdfPages) 

188 self.ab_vs_dist(covFits, pdfPages, bRange=4) 

189 self.plotAcoeffsSum(covFits, pdfPages) 

190 self.plotRelativeBiasACoeffs(covFits, covFitsNoB, self.config.signalElectronsRelativeA, pdfPages, 

191 maxr=4) 

192 

193 return 

194 

195 @staticmethod 

196 def plotCovariances(covFits, pdfPages): 

197 """Plot covariances and models: Cov00, Cov10, Cov01. 

198 

199 Figs. 6 and 7 of Astier+19 

200 

201 Parameters 

202 ---------- 

203 covFits: `dict` 

204 Dictionary of CovFit objects, with amp names as keys. 

205 

206 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

207 PDF file where the plots will be saved. 

208 """ 

209 

210 legendFontSize = 7 

211 labelFontSize = 7 

212 titleFontSize = 9 

213 supTitleFontSize = 18 

214 markerSize = 25 

215 

216 nAmps = len(covFits) 

217 if nAmps == 2: 

218 nRows, nCols = 2, 1 

219 nRows = np.sqrt(nAmps) 

220 mantissa, _ = np.modf(nRows) 

221 if mantissa > 0: 

222 nRows = int(nRows) + 1 

223 nCols = nRows 

224 else: 

225 nRows = int(nRows) 

226 nCols = nRows 

227 

228 f, ax = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

229 f2, ax2 = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

230 fResCov00, axResCov00 = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', 

231 figsize=(13, 10)) 

232 fCov01, axCov01 = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

233 fCov10, axCov10 = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

234 

235 for i, (fitPair, a, a2, aResVar, a3, a4) in enumerate(zip(covFits.items(), ax.flatten(), 

236 ax2.flatten(), axResCov00.flatten(), 

237 axCov01.flatten(), axCov10.flatten())): 

238 

239 amp = fitPair[0] 

240 fit = fitPair[1] 

241 

242 (meanVecOriginal, varVecOriginal, varVecModelOriginal, 

243 weightsOriginal, varMask) = fit.getFitData(0, 0) 

244 meanVecFinal, varVecFinal = meanVecOriginal[varMask], varVecOriginal[varMask] 

245 varVecModelFinal = varVecModelOriginal[varMask] 

246 meanVecOutliers = meanVecOriginal[np.invert(varMask)] 

247 varVecOutliers = varVecOriginal[np.invert(varMask)] 

248 varWeightsFinal = weightsOriginal[varMask] 

249 # Get weighted reduced chi2 

250 chi2FullModelVar = calculateWeightedReducedChi2(varVecFinal, varVecModelFinal, 

251 varWeightsFinal, len(meanVecFinal), 4) 

252 

253 (meanVecOrigCov01, varVecOrigCov01, varVecModelOrigCov01, 

254 _, maskCov01) = fit.getFitData(0, 1) 

255 meanVecFinalCov01, varVecFinalCov01 = meanVecOrigCov01[maskCov01], varVecOrigCov01[maskCov01] 

256 varVecModelFinalCov01 = varVecModelOrigCov01[maskCov01] 

257 meanVecOutliersCov01 = meanVecOrigCov01[np.invert(maskCov01)] 

258 varVecOutliersCov01 = varVecOrigCov01[np.invert(maskCov01)] 

259 

260 (meanVecOrigCov10, varVecOrigCov10, varVecModelOrigCov10, 

261 _, maskCov10) = fit.getFitData(1, 0) 

262 meanVecFinalCov10, varVecFinalCov10 = meanVecOrigCov10[maskCov10], varVecOrigCov10[maskCov10] 

263 varVecModelFinalCov10 = varVecModelOrigCov10[maskCov10] 

264 meanVecOutliersCov10 = meanVecOrigCov10[np.invert(maskCov10)] 

265 varVecOutliersCov10 = varVecOrigCov10[np.invert(maskCov10)] 

266 

267 # cuadratic fit for residuals below 

268 par2 = np.polyfit(meanVecFinal, varVecFinal, 2, w=varWeightsFinal) 

269 varModelFinalQuadratic = np.polyval(par2, meanVecFinal) 

270 chi2QuadModelVar = calculateWeightedReducedChi2(varVecFinal, varModelFinalQuadratic, 

271 varWeightsFinal, len(meanVecFinal), 3) 

272 

273 # fit with no 'b' coefficient (c = a*b in Eq. 20 of Astier+19) 

274 fitNoB = fit.copy() 

275 fitNoB.params['c'].fix(val=0) 

276 fitNoB.fitFullModel() 

277 (meanVecFinalNoB, varVecFinalNoB, varVecModelFinalNoB, 

278 varWeightsFinalNoB, maskNoB) = fitNoB.getFitData(0, 0, returnMasked=True) 

279 chi2FullModelNoBVar = calculateWeightedReducedChi2(varVecFinalNoB, varVecModelFinalNoB, 

280 varWeightsFinalNoB, len(meanVecFinalNoB), 3) 

281 

282 if len(meanVecFinal): # Empty if the whole amp is bad, for example. 

283 stringLegend = (f"Gain: {fit.getGain():.4} e/DN \n" + 

284 f"Noise: {fit.getRon():.4} e \n" + 

285 r"$a_{00}$: %.3e 1/e"%fit.getA()[0, 0] + 

286 "\n" + r"$b_{00}$: %.3e 1/e"%fit.getB()[0, 0]) 

287 minMeanVecFinal = np.min(meanVecFinal) 

288 maxMeanVecFinal = np.max(meanVecFinal) 

289 deltaXlim = maxMeanVecFinal - minMeanVecFinal 

290 

291 a.set_xlabel(r'Mean signal ($\mu$, DN)', fontsize=labelFontSize) 

292 a.set_ylabel(r'Variance (DN$^2$)', fontsize=labelFontSize) 

293 a.tick_params(labelsize=11) 

294 a.set_xscale('linear', fontsize=labelFontSize) 

295 a.set_yscale('linear', fontsize=labelFontSize) 

296 a.scatter(meanVecFinal, varVecFinal, c='blue', marker='o', s=markerSize) 

297 a.scatter(meanVecOutliers, varVecOutliers, c='magenta', marker='s', s=markerSize) 

298 a.plot(meanVecFinal, varVecModelFinal, color='red', lineStyle='-') 

299 a.text(0.03, 0.7, stringLegend, transform=a.transAxes, fontsize=legendFontSize) 

300 a.set_title(amp, fontsize=titleFontSize) 

301 a.set_xlim([minMeanVecFinal - 0.2*deltaXlim, maxMeanVecFinal + 0.2*deltaXlim]) 

302 

303 # Same as above, but in log-scale 

304 a2.set_xlabel(r'Mean Signal ($\mu$, DN)', fontsize=labelFontSize) 

305 a2.set_ylabel(r'Variance (DN$^2$)', fontsize=labelFontSize) 

306 a2.tick_params(labelsize=11) 

307 a2.set_xscale('log') 

308 a2.set_yscale('log') 

309 a2.plot(meanVecFinal, varVecModelFinal, color='red', lineStyle='-') 

310 a2.scatter(meanVecFinal, varVecFinal, c='blue', marker='o', s=markerSize) 

311 a2.scatter(meanVecOutliers, varVecOutliers, c='magenta', marker='s', s=markerSize) 

312 a2.text(0.03, 0.7, stringLegend, transform=a2.transAxes, fontsize=legendFontSize) 

313 a2.set_title(amp, fontsize=titleFontSize) 

314 a2.set_xlim([minMeanVecFinal, maxMeanVecFinal]) 

315 

316 # Residuals var - model 

317 aResVar.set_xlabel(r'Mean signal ($\mu$, DN)', fontsize=labelFontSize) 

318 aResVar.set_ylabel(r'Residuals (DN$^2$)', fontsize=labelFontSize) 

319 aResVar.tick_params(labelsize=11) 

320 aResVar.set_xscale('linear', fontsize=labelFontSize) 

321 aResVar.set_yscale('linear', fontsize=labelFontSize) 

322 aResVar.plot(meanVecFinal, varVecFinal - varVecModelFinal, color='blue', lineStyle='-', 

323 label=r'Full fit ($\chi_{\rm{red}}^2$: %g)'%chi2FullModelVar) 

324 aResVar.plot(meanVecFinal, varVecFinal - varModelFinalQuadratic, color='red', lineStyle='-', 

325 label=r'Quadratic fit ($\chi_{\rm{red}}^2$: %g)'%chi2QuadModelVar) 

326 aResVar.plot(meanVecFinalNoB, varVecFinalNoB - varVecModelFinalNoB, color='green', 

327 lineStyle='-', 

328 label=r'Full fit (b=0) ($\chi_{\rm{red}}^2$: %g)'%chi2FullModelNoBVar) 

329 aResVar.axhline(color='black') 

330 aResVar.set_title(amp, fontsize=titleFontSize) 

331 aResVar.set_xlim([minMeanVecFinal - 0.2*deltaXlim, maxMeanVecFinal + 0.2*deltaXlim]) 

332 aResVar.legend(fontsize=7) 

333 

334 a3.set_xlabel(r'Mean signal ($\mu$, DN)', fontsize=labelFontSize) 

335 a3.set_ylabel(r'Cov01 (DN$^2$)', fontsize=labelFontSize) 

336 a3.tick_params(labelsize=11) 

337 a3.set_xscale('linear', fontsize=labelFontSize) 

338 a3.set_yscale('linear', fontsize=labelFontSize) 

339 a3.scatter(meanVecFinalCov01, varVecFinalCov01, c='blue', marker='o', s=markerSize) 

340 a3.scatter(meanVecOutliersCov01, varVecOutliersCov01, c='magenta', marker='s', s=markerSize) 

341 a3.plot(meanVecFinalCov01, varVecModelFinalCov01, color='red', lineStyle='-') 

342 a3.set_title(amp, fontsize=titleFontSize) 

343 a3.set_xlim([minMeanVecFinal - 0.2*deltaXlim, maxMeanVecFinal + 0.2*deltaXlim]) 

344 

345 a4.set_xlabel(r'Mean signal ($\mu$, DN)', fontsize=labelFontSize) 

346 a4.set_ylabel(r'Cov10 (DN$^2$)', fontsize=labelFontSize) 

347 a4.tick_params(labelsize=11) 

348 a4.set_xscale('linear', fontsize=labelFontSize) 

349 a4.set_yscale('linear', fontsize=labelFontSize) 

350 a4.scatter(meanVecFinalCov10, varVecFinalCov10, c='blue', marker='o', s=markerSize) 

351 a4.scatter(meanVecOutliersCov10, varVecOutliersCov10, c='magenta', marker='s', s=markerSize) 

352 a4.plot(meanVecFinalCov10, varVecModelFinalCov10, color='red', lineStyle='-') 

353 a4.set_title(amp, fontsize=titleFontSize) 

354 a4.set_xlim([minMeanVecFinal - 0.2*deltaXlim, maxMeanVecFinal + 0.2*deltaXlim]) 

355 

356 else: 

357 a.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

358 a2.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

359 a3.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

360 a4.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

361 

362 f.suptitle("PTC from covariances as in Astier+19 \n Fit: Eq. 20, Astier+19", 

363 fontsize=supTitleFontSize) 

364 pdfPages.savefig(f) 

365 f2.suptitle("PTC from covariances as in Astier+19 (log-log) \n Fit: Eq. 20, Astier+19", 

366 fontsize=supTitleFontSize) 

367 pdfPages.savefig(f2) 

368 fResCov00.suptitle("Residuals (data- model) for Cov00 (Var)", fontsize=supTitleFontSize) 

369 pdfPages.savefig(fResCov00) 

370 fCov01.suptitle("Cov01 as in Astier+19 (nearest parallel neighbor covariance) \n" + 

371 " Fit: Eq. 20, Astier+19", fontsize=supTitleFontSize) 

372 pdfPages.savefig(fCov01) 

373 fCov10.suptitle("Cov10 as in Astier+19 (nearest serial neighbor covariance) \n" + 

374 "Fit: Eq. 20, Astier+19", fontsize=supTitleFontSize) 

375 pdfPages.savefig(fCov10) 

376 

377 return 

378 

379 def plotNormalizedCovariances(self, covFits, covFitsNoB, i, j, pdfPages, offset=0.004, 

380 numberOfBins=10, plotData=True, topPlot=False, log=None): 

381 """Plot C_ij/mu vs mu. 

382 

383 Figs. 8, 10, and 11 of Astier+19 

384 

385 Parameters 

386 ---------- 

387 covFits: `dict` 

388 Dictionary of CovFit objects, with amp names as keys. 

389 

390 covFitsNoB: `dict` 

391 Dictionary of CovFit objects, with amp names as keys (b=0 in Eq. 20 of Astier+19). 

392 

393 i : `int` 

394 Covariane lag 

395 

396 j : `int 

397 Covariance lag 

398 

399 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

400 PDF file where the plots will be saved. 

401 

402 offset : `float`, optional 

403 Constant offset factor to plot covariances in same panel (so they don't overlap). 

404 

405 numberOfBins : `int`, optional 

406 Number of bins for top and bottom plot. 

407 

408 plotData : `bool`, optional 

409 Plot the data points? 

410 

411 topPlot : `bool`, optional 

412 Plot the top plot with the covariances, and the bottom plot with the model residuals? 

413 

414 log : `lsst.log.Log`, optional 

415 Logger to handle messages. 

416 """ 

417 

418 lchi2, la, lb, lcov = [], [], [], [] 

419 

420 if (not topPlot): 

421 fig = plt.figure(figsize=(8, 10)) 

422 gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1]) 

423 gs.update(hspace=0) 

424 ax0 = plt.subplot(gs[0]) 

425 plt.setp(ax0.get_xticklabels(), visible=False) 

426 else: 

427 fig = plt.figure(figsize=(8, 8)) 

428 ax0 = plt.subplot(111) 

429 ax0.ticklabel_format(style='sci', axis='x', scilimits=(0, 0)) 

430 ax0.tick_params(axis='both', labelsize='x-large') 

431 mue, rese, wce = [], [], [] 

432 mueNoB, reseNoB, wceNoB = [], [], [] 

433 for counter, (amp, fit) in enumerate(covFits.items()): 

434 mu, cov, model, weightCov, _ = fit.getFitData(i, j, divideByMu=True, returnMasked=True) 

435 wres = (cov-model)*weightCov 

436 chi2 = ((wres*wres).sum())/(len(mu)-3) 

437 chi2bin = 0 

438 mue += list(mu) 

439 rese += list(cov - model) 

440 wce += list(weightCov) 

441 

442 fitNoB = covFitsNoB[amp] 

443 (muNoB, covNoB, modelNoB, 

444 weightCovNoB, _) = fitNoB.getFitData(i, j, divideByMu=True, returnMasked=True) 

445 mueNoB += list(muNoB) 

446 reseNoB += list(covNoB - modelNoB) 

447 wceNoB += list(weightCovNoB) 

448 

449 # the corresponding fit 

450 fit_curve, = plt.plot(mu, model + counter*offset, '-', linewidth=4.0) 

451 # bin plot. len(mu) = no binning 

452 gind = self.indexForBins(mu, numberOfBins) 

453 

454 xb, yb, wyb, sigyb = self.binData(mu, cov, gind, weightCov) 

455 chi2bin = (sigyb*wyb).mean() # chi2 of enforcing the same value in each bin 

456 plt.errorbar(xb, yb+counter*offset, yerr=sigyb, marker='o', linestyle='none', markersize=6.5, 

457 color=fit_curve.get_color(), label=f"{amp} (N: {len(mu)})") 

458 # plot the data 

459 if plotData: 

460 points, = plt.plot(mu, cov + counter*offset, '.', color=fit_curve.get_color()) 

461 plt.legend(loc='upper right', fontsize=8) 

462 aij = fit.getA()[i, j] 

463 bij = fit.getB()[i, j] 

464 la.append(aij) 

465 lb.append(bij) 

466 if fit.getACov() is not None: 

467 lcov.append(fit.getACov()[i, j, i, j]) 

468 else: 

469 lcov.append(np.nan) 

470 lchi2.append(chi2) 

471 log.info('Cov%d%d %s: slope %g b %g chi2 %f chi2bin %f'%(i, j, amp, aij, bij, chi2, chi2bin)) 

472 # end loop on amps 

473 la = np.array(la) 

474 lb = np.array(lb) 

475 lcov = np.array(lcov) 

476 lchi2 = np.array(lchi2) 

477 mue = np.array(mue) 

478 rese = np.array(rese) 

479 wce = np.array(wce) 

480 mueNoB = np.array(mueNoB) 

481 reseNoB = np.array(reseNoB) 

482 wceNoB = np.array(wceNoB) 

483 

484 plt.xlabel(r"$\mu (el)$", fontsize='x-large') 

485 plt.ylabel(r"$Cov{%d%d}/\mu + Cst (el)$"%(i, j), fontsize='x-large') 

486 if (not topPlot): 

487 gind = self.indexForBins(mue, numberOfBins) 

488 xb, yb, wyb, sigyb = self.binData(mue, rese, gind, wce) 

489 

490 ax1 = plt.subplot(gs[1], sharex=ax0) 

491 ax1.errorbar(xb, yb, yerr=sigyb, marker='o', linestyle='none', label='Full fit') 

492 gindNoB = self.indexForBins(mueNoB, numberOfBins) 

493 xb2, yb2, wyb2, sigyb2 = self.binData(mueNoB, reseNoB, gindNoB, wceNoB) 

494 

495 ax1.errorbar(xb2, yb2, yerr=sigyb2, marker='o', linestyle='none', label='b = 0') 

496 ax1.tick_params(axis='both', labelsize='x-large') 

497 plt.legend(loc='upper left', fontsize='large') 

498 # horizontal line at zero 

499 plt.plot(xb, [0]*len(xb), '--', color='k') 

500 plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0)) 

501 plt.ticklabel_format(style='sci', axis='y', scilimits=(0, 0)) 

502 plt.xlabel(r'$\mu (el)$', fontsize='x-large') 

503 plt.ylabel(r'$Cov{%d%d}/\mu$ -model (el)'%(i, j), fontsize='x-large') 

504 plt.tight_layout() 

505 plt.suptitle(f"Nbins: {numberOfBins}") 

506 # overlapping y labels: 

507 fig.canvas.draw() 

508 labels0 = [item.get_text() for item in ax0.get_yticklabels()] 

509 labels0[0] = u'' 

510 ax0.set_yticklabels(labels0) 

511 pdfPages.savefig(fig) 

512 

513 return 

514 

515 @staticmethod 

516 def plot_a_b(covFits, pdfPages, bRange=3): 

517 """Fig. 12 of Astier+19 

518 

519 Color display of a and b arrays fits, averaged over channels. 

520 

521 Parameters 

522 ---------- 

523 covFits: `dict` 

524 Dictionary of CovFit objects, with amp names as keys. 

525 

526 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

527 PDF file where the plots will be saved. 

528 

529 bRange : `int` 

530 Maximum lag for b arrays. 

531 """ 

532 a, b = [], [] 

533 for amp, fit in covFits.items(): 

534 a.append(fit.getA()) 

535 b.append(fit.getB()) 

536 a = np.array(a).mean(axis=0) 

537 b = np.array(b).mean(axis=0) 

538 fig = plt.figure(figsize=(7, 11)) 

539 ax0 = fig.add_subplot(2, 1, 1) 

540 im0 = ax0.imshow(np.abs(a.transpose()), origin='lower', norm=mpl.colors.LogNorm()) 

541 ax0.tick_params(axis='both', labelsize='x-large') 

542 ax0.set_title(r'$|a|$', fontsize='x-large') 

543 ax0.xaxis.set_ticks_position('bottom') 

544 cb0 = plt.colorbar(im0) 

545 cb0.ax.tick_params(labelsize='x-large') 

546 

547 ax1 = fig.add_subplot(2, 1, 2) 

548 ax1.tick_params(axis='both', labelsize='x-large') 

549 ax1.yaxis.set_major_locator(MaxNLocator(integer=True)) 

550 ax1.xaxis.set_major_locator(MaxNLocator(integer=True)) 

551 im1 = ax1.imshow(1e6*b[:bRange, :bRange].transpose(), origin='lower') 

552 cb1 = plt.colorbar(im1) 

553 cb1.ax.tick_params(labelsize='x-large') 

554 ax1.set_title(r'$b \times 10^6$', fontsize='x-large') 

555 ax1.xaxis.set_ticks_position('bottom') 

556 plt.tight_layout() 

557 pdfPages.savefig(fig) 

558 

559 return 

560 

561 @staticmethod 

562 def ab_vs_dist(covFits, pdfPages, bRange=4): 

563 """Fig. 13 of Astier+19. 

564 

565 Values of a and b arrays fits, averaged over amplifiers, as a function of distance. 

566 

567 Parameters 

568 ---------- 

569 covFits: `dict` 

570 Dictionary of CovFit objects, with amp names as keys. 

571 

572 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

573 PDF file where the plots will be saved. 

574 

575 bRange : `int` 

576 Maximum lag for b arrays. 

577 """ 

578 a = np.array([f.getA() for f in covFits.values()]) 

579 y = a.mean(axis=0) 

580 sy = a.std(axis=0)/np.sqrt(len(covFits)) 

581 i, j = np.indices(y.shape) 

582 upper = (i >= j).ravel() 

583 r = np.sqrt(i**2 + j**2).ravel() 

584 y = y.ravel() 

585 sy = sy.ravel() 

586 fig = plt.figure(figsize=(6, 9)) 

587 ax = fig.add_subplot(211) 

588 ax.set_xlim([0.5, r.max()+1]) 

589 ax.errorbar(r[upper], y[upper], yerr=sy[upper], marker='o', linestyle='none', color='b', 

590 label='$i>=j$') 

591 ax.errorbar(r[~upper], y[~upper], yerr=sy[~upper], marker='o', linestyle='none', color='r', 

592 label='$i<j$') 

593 ax.legend(loc='upper center', fontsize='x-large') 

594 ax.set_xlabel(r'$\sqrt{i^2+j^2}$', fontsize='x-large') 

595 ax.set_ylabel(r'$a_{ij}$', fontsize='x-large') 

596 ax.set_yscale('log') 

597 ax.tick_params(axis='both', labelsize='x-large') 

598 

599 # 

600 axb = fig.add_subplot(212) 

601 b = np.array([f.getB() for f in covFits.values()]) 

602 yb = b.mean(axis=0) 

603 syb = b.std(axis=0)/np.sqrt(len(covFits)) 

604 ib, jb = np.indices(yb.shape) 

605 upper = (ib > jb).ravel() 

606 rb = np.sqrt(i**2 + j**2).ravel() 

607 yb = yb.ravel() 

608 syb = syb.ravel() 

609 xmin = -0.2 

610 xmax = bRange 

611 axb.set_xlim([xmin, xmax+0.2]) 

612 cutu = (r > xmin) & (r < xmax) & (upper) 

613 cutl = (r > xmin) & (r < xmax) & (~upper) 

614 axb.errorbar(rb[cutu], yb[cutu], yerr=syb[cutu], marker='o', linestyle='none', color='b', 

615 label='$i>=j$') 

616 axb.errorbar(rb[cutl], yb[cutl], yerr=syb[cutl], marker='o', linestyle='none', color='r', 

617 label='$i<j$') 

618 plt.legend(loc='upper center', fontsize='x-large') 

619 axb.set_xlabel(r'$\sqrt{i^2+j^2}$', fontsize='x-large') 

620 axb.set_ylabel(r'$b_{ij}$', fontsize='x-large') 

621 axb.ticklabel_format(style='sci', axis='y', scilimits=(0, 0)) 

622 axb.tick_params(axis='both', labelsize='x-large') 

623 plt.tight_layout() 

624 pdfPages.savefig(fig) 

625 

626 return 

627 

628 @staticmethod 

629 def plotAcoeffsSum(covFits, pdfPages): 

630 """Fig. 14. of Astier+19 

631 

632 Cumulative sum of a_ij as a function of maximum separation. This plot displays the average over 

633 channels. 

634 

635 Parameters 

636 ---------- 

637 covFits: `dict` 

638 Dictionary of CovFit objects, with amp names as keys. 

639 

640 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

641 PDF file where the plots will be saved. 

642 """ 

643 a, b = [], [] 

644 for amp, fit in covFits.items(): 

645 a.append(fit.getA()) 

646 b.append(fit.getB()) 

647 a = np.array(a).mean(axis=0) 

648 b = np.array(b).mean(axis=0) 

649 fig = plt.figure(figsize=(7, 6)) 

650 w = 4*np.ones_like(a) 

651 w[0, 1:] = 2 

652 w[1:, 0] = 2 

653 w[0, 0] = 1 

654 wa = w*a 

655 indices = range(1, a.shape[0]+1) 

656 sums = [wa[0:n, 0:n].sum() for n in indices] 

657 ax = plt.subplot(111) 

658 ax.plot(indices, sums/sums[0], 'o', color='b') 

659 ax.set_yscale('log') 

660 ax.set_xlim(indices[0]-0.5, indices[-1]+0.5) 

661 ax.set_ylim(None, 1.2) 

662 ax.set_ylabel(r'$[\sum_{|i|<n\ &\ |j|<n} a_{ij}] / |a_{00}|$', fontsize='x-large') 

663 ax.set_xlabel('n', fontsize='x-large') 

664 ax.tick_params(axis='both', labelsize='x-large') 

665 plt.tight_layout() 

666 pdfPages.savefig(fig) 

667 

668 return 

669 

670 @staticmethod 

671 def plotRelativeBiasACoeffs(covFits, covFitsNoB, signalElectrons, pdfPages, maxr=None): 

672 """Fig. 15 in Astier+19. 

673 

674 Illustrates systematic bias from estimating 'a' 

675 coefficients from the slope of correlations as opposed to the 

676 full model in Astier+19. 

677 

678 Parameters 

679 ---------- 

680 covFits : `dict` 

681 Dictionary of CovFit objects, with amp names as keys. 

682 

683 covFitsNoB : `dict` 

684 Dictionary of CovFit objects, with amp names as keys (b=0 in Eq. 20 of Astier+19). 

685 

686 signalElectrons : `float` 

687 Signal at which to evaluate the a_ij coefficients. 

688 

689 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

690 PDF file where the plots will be saved. 

691 

692 maxr : `int`, optional 

693 Maximum lag. 

694 """ 

695 

696 fig = plt.figure(figsize=(7, 11)) 

697 title = [f"'a' relative bias at {signalElectrons} e", "'a' relative bias (b=0)"] 

698 data = [covFits, covFitsNoB] 

699 

700 for k in range(2): 

701 diffs = [] 

702 amean = [] 

703 for fit in data[k].values(): 

704 if fit is None: 

705 continue 

706 aOld = computeApproximateAcoeffs(fit, signalElectrons) 

707 a = fit.getA() 

708 amean.append(a) 

709 diffs.append((aOld-a)) 

710 amean = np.array(amean).mean(axis=0) 

711 diff = np.array(diffs).mean(axis=0) 

712 diff = diff/amean 

713 # The difference should be close to zero 

714 diff[0, 0] = 0 

715 if maxr is None: 

716 maxr = diff.shape[0] 

717 diff = diff[:maxr, :maxr] 

718 ax0 = fig.add_subplot(2, 1, k+1) 

719 im0 = ax0.imshow(diff.transpose(), origin='lower') 

720 ax0.yaxis.set_major_locator(MaxNLocator(integer=True)) 

721 ax0.xaxis.set_major_locator(MaxNLocator(integer=True)) 

722 ax0.tick_params(axis='both', labelsize='x-large') 

723 plt.colorbar(im0) 

724 ax0.set_title(title[k]) 

725 

726 plt.tight_layout() 

727 pdfPages.savefig(fig) 

728 

729 return 

730 

731 def _plotStandardPtc(self, dataset, ptcFitType, pdfPages): 

732 """Plot PTC, linearity, and linearity residual per amplifier 

733 

734 Parameters 

735 ---------- 

736 dataset : `lsst.cp.pipe.ptc.PhotonTransferCurveDataset` 

737 The dataset containing the means, variances, exposure times, and mask. 

738 

739 ptcFitType : `str` 

740 Type of the model fit to the PTC. Options: 'FULLCOVARIANCE', EXPAPPROXIMATION, or 'POLYNOMIAL'. 

741 

742 pdfPages: `matplotlib.backends.backend_pdf.PdfPages` 

743 PDF file where the plots will be saved. 

744 """ 

745 

746 if ptcFitType == 'EXPAPPROXIMATION': 

747 ptcFunc = funcAstier 

748 stringTitle = (r"Var = $\frac{1}{2g^2a_{00}}(\exp (2a_{00} \mu g) - 1) + \frac{n_{00}}{g^2}$ ") 

749 elif ptcFitType == 'POLYNOMIAL': 

750 ptcFunc = funcPolynomial 

751 for key in dataset.ptcFitPars: 

752 deg = len(dataset.ptcFitPars[key]) - 1 

753 break 

754 stringTitle = r"Polynomial (degree: %g)" % (deg) 

755 else: 

756 raise RuntimeError(f"The input dataset had an invalid dataset.ptcFitType: {ptcFitType}. \n" + 

757 "Options: 'FULLCOVARIANCE', EXPAPPROXIMATION, or 'POLYNOMIAL'.") 

758 

759 legendFontSize = 7 

760 labelFontSize = 7 

761 titleFontSize = 9 

762 supTitleFontSize = 18 

763 markerSize = 25 

764 

765 # General determination of the size of the plot grid 

766 nAmps = len(dataset.ampNames) 

767 if nAmps == 2: 

768 nRows, nCols = 2, 1 

769 nRows = np.sqrt(nAmps) 

770 mantissa, _ = np.modf(nRows) 

771 if mantissa > 0: 

772 nRows = int(nRows) + 1 

773 nCols = nRows 

774 else: 

775 nRows = int(nRows) 

776 nCols = nRows 

777 

778 f, ax = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

779 f2, ax2 = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

780 

781 for i, (amp, a, a2) in enumerate(zip(dataset.ampNames, ax.flatten(), ax2.flatten())): 

782 meanVecOriginal = np.array(dataset.rawMeans[amp]) 

783 varVecOriginal = np.array(dataset.rawVars[amp]) 

784 mask = dataset.visitMask[amp] 

785 meanVecFinal = meanVecOriginal[mask] 

786 varVecFinal = varVecOriginal[mask] 

787 meanVecOutliers = meanVecOriginal[np.invert(mask)] 

788 varVecOutliers = varVecOriginal[np.invert(mask)] 

789 pars, parsErr = dataset.ptcFitPars[amp], dataset.ptcFitParsError[amp] 

790 if ptcFitType == 'EXPAPPROXIMATION': 

791 if len(meanVecFinal): 

792 ptcA00, ptcA00error = pars[0], parsErr[0] 

793 ptcGain, ptcGainError = pars[1], parsErr[1] 

794 ptcNoise = np.sqrt((pars[2])) 

795 ptcNoiseError = 0.5*(parsErr[2]/np.fabs(pars[2]))*np.sqrt(np.fabs(pars[2])) 

796 stringLegend = (f"a00: {ptcA00:.2e}+/-{ptcA00error:.2e} 1/e" 

797 f"\n Gain: {ptcGain:.4}+/-{ptcGainError:.2e} e/DN" 

798 f"\n Noise: {ptcNoise:.4}+/-{ptcNoiseError:.2e} e \n") 

799 

800 if ptcFitType == 'POLYNOMIAL': 

801 if len(meanVecFinal): 

802 ptcGain, ptcGainError = 1./pars[1], np.fabs(1./pars[1])*(parsErr[1]/pars[1]) 

803 ptcNoise = np.sqrt((pars[0]))*ptcGain 

804 ptcNoiseError = (0.5*(parsErr[0]/np.fabs(pars[0]))*(np.sqrt(np.fabs(pars[0]))))*ptcGain 

805 stringLegend = (f"Gain: {ptcGain:.4}+/-{ptcGainError:.2e} e/DN \n" 

806 f"Noise: {ptcNoise:.4}+/-{ptcNoiseError:.2e} e \n") 

807 

808 a.set_xlabel(r'Mean signal ($\mu$, DN)', fontsize=labelFontSize) 

809 a.set_ylabel(r'Variance (DN$^2$)', fontsize=labelFontSize) 

810 a.tick_params(labelsize=11) 

811 a.set_xscale('linear', fontsize=labelFontSize) 

812 a.set_yscale('linear', fontsize=labelFontSize) 

813 

814 a2.set_xlabel(r'Mean Signal ($\mu$, DN)', fontsize=labelFontSize) 

815 a2.set_ylabel(r'Variance (DN$^2$)', fontsize=labelFontSize) 

816 a2.tick_params(labelsize=11) 

817 a2.set_xscale('log') 

818 a2.set_yscale('log') 

819 

820 if len(meanVecFinal): # Empty if the whole amp is bad, for example. 

821 minMeanVecFinal = np.min(meanVecFinal) 

822 maxMeanVecFinal = np.max(meanVecFinal) 

823 meanVecFit = np.linspace(minMeanVecFinal, maxMeanVecFinal, 100*len(meanVecFinal)) 

824 minMeanVecOriginal = np.min(meanVecOriginal) 

825 maxMeanVecOriginal = np.max(meanVecOriginal) 

826 deltaXlim = maxMeanVecOriginal - minMeanVecOriginal 

827 

828 a.plot(meanVecFit, ptcFunc(pars, meanVecFit), color='red') 

829 a.plot(meanVecFinal, pars[0] + pars[1]*meanVecFinal, color='green', linestyle='--') 

830 a.scatter(meanVecFinal, varVecFinal, c='blue', marker='o', s=markerSize) 

831 a.scatter(meanVecOutliers, varVecOutliers, c='magenta', marker='s', s=markerSize) 

832 a.text(0.03, 0.7, stringLegend, transform=a.transAxes, fontsize=legendFontSize) 

833 a.set_title(amp, fontsize=titleFontSize) 

834 a.set_xlim([minMeanVecOriginal - 0.2*deltaXlim, maxMeanVecOriginal + 0.2*deltaXlim]) 

835 

836 # Same, but in log-scale 

837 a2.plot(meanVecFit, ptcFunc(pars, meanVecFit), color='red') 

838 a2.scatter(meanVecFinal, varVecFinal, c='blue', marker='o', s=markerSize) 

839 a2.scatter(meanVecOutliers, varVecOutliers, c='magenta', marker='s', s=markerSize) 

840 a2.text(0.03, 0.7, stringLegend, transform=a2.transAxes, fontsize=legendFontSize) 

841 a2.set_title(amp, fontsize=titleFontSize) 

842 a2.set_xlim([minMeanVecOriginal, maxMeanVecOriginal]) 

843 else: 

844 a.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

845 a2.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

846 

847 f.suptitle("PTC \n Fit: " + stringTitle, fontsize=supTitleFontSize) 

848 pdfPages.savefig(f) 

849 f2.suptitle("PTC (log-log)", fontsize=supTitleFontSize) 

850 pdfPages.savefig(f2) 

851 

852 return 

853 

854 def _plotLinearizer(self, dataset, linearizer, pdfPages): 

855 """Plot linearity and linearity residual per amplifier 

856 

857 Parameters 

858 ---------- 

859 dataset : `lsst.cp.pipe.ptc.PhotonTransferCurveDataset` 

860 The dataset containing the means, variances, exposure times, and mask. 

861 

862 linearizer : `lsst.ip.isr.Linearizer` 

863 Linearizer object 

864 """ 

865 legendFontSize = 7 

866 labelFontSize = 7 

867 titleFontSize = 9 

868 supTitleFontSize = 18 

869 

870 # General determination of the size of the plot grid 

871 nAmps = len(dataset.ampNames) 

872 if nAmps == 2: 

873 nRows, nCols = 2, 1 

874 nRows = np.sqrt(nAmps) 

875 mantissa, _ = np.modf(nRows) 

876 if mantissa > 0: 

877 nRows = int(nRows) + 1 

878 nCols = nRows 

879 else: 

880 nRows = int(nRows) 

881 nCols = nRows 

882 

883 # Plot mean vs time (f1), and fractional residuals (f2) 

884 f, ax = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

885 f2, ax2 = plt.subplots(nrows=nRows, ncols=nCols, sharex='col', sharey='row', figsize=(13, 10)) 

886 for i, (amp, a, a2) in enumerate(zip(dataset.ampNames, ax.flatten(), ax2.flatten())): 

887 meanVecFinal = np.array(dataset.rawMeans[amp])[dataset.visitMask[amp]] 

888 timeVecFinal = np.array(dataset.rawExpTimes[amp])[dataset.visitMask[amp]] 

889 

890 a.set_xlabel('Time (sec)', fontsize=labelFontSize) 

891 a.set_ylabel(r'Mean signal ($\mu$, DN)', fontsize=labelFontSize) 

892 a.tick_params(labelsize=labelFontSize) 

893 a.set_xscale('linear', fontsize=labelFontSize) 

894 a.set_yscale('linear', fontsize=labelFontSize) 

895 

896 a2.axhline(y=0, color='k') 

897 a2.axvline(x=0, color='k', linestyle='-') 

898 a2.set_xlabel(r'Mean signal ($\mu$, DN)', fontsize=labelFontSize) 

899 a2.set_ylabel('Fractional nonlinearity (%)', fontsize=labelFontSize) 

900 a2.tick_params(labelsize=labelFontSize) 

901 a2.set_xscale('linear', fontsize=labelFontSize) 

902 a2.set_yscale('linear', fontsize=labelFontSize) 

903 

904 if len(meanVecFinal): 

905 pars, parsErr = linearizer.fitParams[amp], linearizer.fitParamsErr[amp] 

906 k0, k0Error = pars[0], parsErr[0] 

907 k1, k1Error = pars[1], parsErr[1] 

908 k2, k2Error = pars[2], parsErr[2] 

909 stringLegend = (f"k0: {k0:.4}+/-{k0Error:.2e} DN\n k1: {k1:.4}+/-{k1Error:.2e} DN/t" 

910 f"\n k2: {k2:.2e}+/-{k2Error:.2e} DN/t^2 \n") 

911 a.scatter(timeVecFinal, meanVecFinal) 

912 a.plot(timeVecFinal, funcPolynomial(pars, timeVecFinal), color='red') 

913 a.text(0.03, 0.75, stringLegend, transform=a.transAxes, fontsize=legendFontSize) 

914 a.set_title(f"{amp}", fontsize=titleFontSize) 

915 

916 linearPart = k0 + k1*timeVecFinal 

917 fracLinRes = 100*(linearPart - meanVecFinal)/linearPart 

918 a2.plot(meanVecFinal, fracLinRes, c='g') 

919 a2.set_title(f"{amp}", fontsize=titleFontSize) 

920 else: 

921 a.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

922 a2.set_title(f"{amp} (BAD)", fontsize=titleFontSize) 

923 

924 f.suptitle("Linearity \n Fit: Polynomial (degree: %g)" 

925 % (len(pars)-1), 

926 fontsize=supTitleFontSize) 

927 f2.suptitle(r"Fractional NL residual" + "\n" + 

928 r"$100\times \frac{(k_0 + k_1*Time-\mu)}{k_0+k_1*Time}$", 

929 fontsize=supTitleFontSize) 

930 pdfPages.savefig(f) 

931 pdfPages.savefig(f2) 

932 

933 @staticmethod 

934 def findGroups(x, maxDiff): 

935 """Group data into bins, with at most maxDiff distance between bins. 

936 

937 Parameters 

938 ---------- 

939 x: `list` 

940 Data to bin. 

941 

942 maxDiff: `int` 

943 Maximum distance between bins. 

944 

945 Returns 

946 ------- 

947 index: `list` 

948 Bin indices. 

949 """ 

950 ix = np.argsort(x) 

951 xsort = np.sort(x) 

952 index = np.zeros_like(x, dtype=np.int32) 

953 xc = xsort[0] 

954 group = 0 

955 ng = 1 

956 

957 for i in range(1, len(ix)): 

958 xval = xsort[i] 

959 if (xval - xc < maxDiff): 

960 xc = (ng*xc + xval)/(ng+1) 

961 ng += 1 

962 index[ix[i]] = group 

963 else: 

964 group += 1 

965 ng = 1 

966 index[ix[i]] = group 

967 xc = xval 

968 

969 return index 

970 

971 @staticmethod 

972 def indexForBins(x, nBins): 

973 """Builds an index with regular binning. The result can be fed into binData. 

974 

975 Parameters 

976 ---------- 

977 x: `numpy.array` 

978 Data to bin. 

979 nBins: `int` 

980 Number of bin. 

981 

982 Returns 

983 ------- 

984 np.digitize(x, bins): `numpy.array` 

985 Bin indices. 

986 """ 

987 

988 bins = np.linspace(x.min(), x.max() + abs(x.max() * 1e-7), nBins + 1) 

989 return np.digitize(x, bins) 

990 

991 @staticmethod 

992 def binData(x, y, binIndex, wy=None): 

993 """Bin data (usually for display purposes). 

994 

995 Patrameters 

996 ----------- 

997 x: `numpy.array` 

998 Data to bin. 

999 

1000 y: `numpy.array` 

1001 Data to bin. 

1002 

1003 binIdex: `list` 

1004 Bin number of each datum. 

1005 

1006 wy: `numpy.array` 

1007 Inverse rms of each datum to use when averaging (the actual weight is wy**2). 

1008 

1009 Returns: 

1010 ------- 

1011 

1012 xbin: `numpy.array` 

1013 Binned data in x. 

1014 

1015 ybin: `numpy.array` 

1016 Binned data in y. 

1017 

1018 wybin: `numpy.array` 

1019 Binned weights in y, computed from wy's in each bin. 

1020 

1021 sybin: `numpy.array` 

1022 Uncertainty on the bin average, considering actual scatter, and ignoring weights. 

1023 """ 

1024 

1025 if wy is None: 

1026 wy = np.ones_like(x) 

1027 binIndexSet = set(binIndex) 

1028 w2 = wy*wy 

1029 xw2 = x*(w2) 

1030 xbin = np.array([xw2[binIndex == i].sum()/w2[binIndex == i].sum() for i in binIndexSet]) 

1031 

1032 yw2 = y*w2 

1033 ybin = np.array([yw2[binIndex == i].sum()/w2[binIndex == i].sum() for i in binIndexSet]) 

1034 

1035 wybin = np.sqrt(np.array([w2[binIndex == i].sum() for i in binIndexSet])) 

1036 sybin = np.array([y[binIndex == i].std()/np.sqrt(np.array([binIndex == i]).sum()) 

1037 for i in binIndexSet]) 

1038 

1039 return xbin, ybin, wybin, sybin