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1# 

2# LSST Data Management System 

3# Copyright 2008-2016 LSST Corporation. 

4# 

5# This product includes software developed by the 

6# LSST Project (http://www.lsst.org/). 

7# 

8# This program is free software: you can redistribute it and/or modify 

9# it under the terms of the GNU General Public License as published by 

10# the Free Software Foundation, either version 3 of the License, or 

11# (at your option) any later version. 

12# 

13# This program is distributed in the hope that it will be useful, 

14# but WITHOUT ANY WARRANTY; without even the implied warranty of 

15# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 

16# GNU General Public License for more details. 

17# 

18# You should have received a copy of the LSST License Statement and 

19# the GNU General Public License along with this program. If not, 

20# see <http://www.lsstcorp.org/LegalNotices/>. 

21# 

22 

23__all__ = ["makeKernelBasisList", "generateAlardLuptonBasisList"] 

24 

25from . import diffimLib 

26from lsst.log import Log 

27import numpy as np 

28 

29sigma2fwhm = 2. * np.sqrt(2. * np.log(2.)) 

30 

31 

32def makeKernelBasisList(config, targetFwhmPix=None, referenceFwhmPix=None, 

33 basisDegGauss=None, metadata=None): 

34 """Generate the delta function or Alard-Lupton kernel bases depending on the Config. 

35 Wrapper to call either `lsst.ip.diffim.makeDeltaFunctionBasisList` or 

36 `lsst.ip.diffim.generateAlardLuptonBasisList`. 

37 

38 Parameters 

39 ---------- 

40 config : `lsst.ip.diffim.PsfMatchConfigAL` 

41 Configuration object. 

42 targetFwhmPix : `float`, optional 

43 Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`. 

44 Not used for delta function basis sets. 

45 referenceFwhmPix : `float`, optional 

46 Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`. 

47 Not used for delta function basis sets. 

48 basisDegGauss : `list` of `int`, optional 

49 Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`. 

50 Not used for delta function basis sets. 

51 metadata : `lsst.daf.base.PropertySet`, optional 

52 Passed on to `lsst.ip.diffim.generateAlardLuptonBasisList`. 

53 Not used for delta function basis sets. 

54 

55 Returns 

56 ------- 

57 basisList: `list` of `lsst.afw.math.kernel.FixedKernel` 

58 List of basis kernels. 

59 

60 Notes 

61 ----- 

62 See `lsst.ip.diffim.generateAlardLuptonBasisList` and 

63 `lsst.ip.diffim.makeDeltaFunctionBasisList` for more information. 

64 

65 Raises 

66 ------ 

67 ValueError 

68 If ``config.kernelBasisSet`` has an invalid value (not "alard-lupton" or "delta-function"). 

69 """ 

70 if config.kernelBasisSet == "alard-lupton": 

71 return generateAlardLuptonBasisList(config, targetFwhmPix=targetFwhmPix, 

72 referenceFwhmPix=referenceFwhmPix, 

73 basisDegGauss=basisDegGauss, 

74 metadata=metadata) 

75 elif config.kernelBasisSet == "delta-function": 

76 kernelSize = config.kernelSize 

77 return diffimLib.makeDeltaFunctionBasisList(kernelSize, kernelSize) 

78 else: 

79 raise ValueError("Cannot generate %s basis set" % (config.kernelBasisSet)) 

80 

81 

82def generateAlardLuptonBasisList(config, targetFwhmPix=None, referenceFwhmPix=None, 

83 basisDegGauss=None, metadata=None): 

84 """Generate an Alard-Lupton kernel basis list based upon the Config and 

85 the input FWHM of the science and template images. 

86 

87 Parameters 

88 ---------- 

89 config : `lsst.ip.diffim.PsfMatchConfigAL` 

90 Configuration object for the Alard-Lupton algorithm. 

91 targetFwhmPix : `float`, optional 

92 Fwhm width (pixel) of the template exposure characteristic psf. 

93 This is the _target_ that will be matched to the science exposure. 

94 referenceFwhmPix : `float`, optional 

95 Fwhm width (pixel) of the science exposure characteristic psf. 

96 basisDegGauss : `list` of `int`, optional 

97 Polynomial degree of each Gaussian (sigma) basis. If None, defaults to `config.alardDegGauss`. 

98 metadata : `lsst.daf.base.PropertySet`, optional 

99 If specified, object to collect metadata fields about the kernel basis list. 

100 

101 Returns 

102 ------- 

103 basisList : `list` of `lsst.afw.math.kernel.FixedKernel` 

104 List of basis kernels. For each degree value ``n`` in ``config.basisDegGauss`` (n+2)(n+1)/2 kernels 

105 are generated and appended to the list in the order of the polynomial parameter number. 

106 See `lsst.afw.math.polynomialFunction2D` documentation for more details. 

107 

108 Raises 

109 ------ 

110 RuntimeError 

111 - if ``config.kernelBasisSet`` is not equal to "alard-lupton" 

112 ValueError 

113 - if ``config.kernelSize`` is even 

114 - if the number of Gaussians and the number of given 

115 sigma values are not equal or 

116 - if the number of Gaussians and the number of given 

117 polynomial degree values are not equal 

118 

119 Notes 

120 ----- 

121 The polynomial functions (``f``) are always evaluated in the -1.0, +1.0 range in both x, y directions, 

122 edge to edge, with ``f(0,0)`` evaluated at the kernel center pixel, ``f(-1.0,-1.0)`` at the kernel 

123 ``(0,0)`` pixel. They are not scaled by the sigmas of the Gaussians. 

124 

125 Base Gaussian widths (sigmas in pixels) of the kernels are determined as: 

126 - If not all fwhm parameters are provided or ``config.scaleByFwhm==False`` 

127 then ``config.alardNGauss`` and ``config.alardSigGauss`` are used. 

128 - If ``targetFwhmPix<referenceFwhmPix`` (normal convolution): 

129 First sigma ``Sig_K`` is determined to satisfy: ``Sig_reference**2 = Sig_target**2 + Sig_K**2``. 

130 If it's larger than ``config.alardMinSig * config.alardGaussBeta``, make it the 

131 second kernel. Else make it the smallest kernel, unless only 1 kernel is asked for. 

132 - If ``referenceFwhmPix < targetFwhmPix`` (deconvolution): 

133 Define the progression of Gaussians using a 

134 method to derive a deconvolution sum-of-Gaussians from it's 

135 convolution counterpart. [1]_ Only use 3 since the algorithm 

136 assumes 3 components. 

137 

138 **Metadata fields** 

139 

140 ALBasisNGauss : `int` 

141 The number of base Gaussians in the AL basis functions. 

142 ALBasisDegGauss : `list` of `int` 

143 Polynomial order of spatial modification of the base Gaussian functions. 

144 ALBasisSigGauss : `list` of `float` 

145 Sigmas in pixels of the base Gaussians. 

146 ALKernelSize : `int` 

147 Kernel stamp size is (ALKernelSize pix, ALKernelSize pix). 

148 ALBasisMode : `str`, either of ``config``, ``convolution``, ``deconvolution`` 

149 Indicates whether the config file values, the convolution or deconvolution algorithm 

150 was used to determine the base Gaussian sigmas and the kernel stamp size. 

151 

152 References 

153 ---------- 

154 .. [1] Ulmer, W.: Inverse problem of linear combinations of Gaussian convolution kernels 

155 (deconvolution) and some applications to proton/photon dosimetry and image 

156 processing. http://iopscience.iop.org/0266-5611/26/8/085002 Equation 40 

157 """ 

158 

159 if config.kernelBasisSet != "alard-lupton": 

160 raise RuntimeError("Cannot generate %s basis within generateAlardLuptonBasisList" % 

161 config.kernelBasisSet) 

162 

163 kernelSize = config.kernelSize 

164 fwhmScaling = config.kernelSizeFwhmScaling 

165 basisNGauss = config.alardNGauss 

166 basisSigmaGauss = config.alardSigGauss 

167 basisGaussBeta = config.alardGaussBeta 

168 basisMinSigma = config.alardMinSig 

169 if basisDegGauss is None: 

170 basisDegGauss = config.alardDegGauss 

171 

172 if len(basisDegGauss) != basisNGauss: 

173 raise ValueError("len(basisDegGauss) != basisNGauss : %d vs %d" % (len(basisDegGauss), basisNGauss)) 

174 if len(basisSigmaGauss) != basisNGauss: 

175 raise ValueError("len(basisSigmaGauss) != basisNGauss : %d vs %d" % 

176 (len(basisSigmaGauss), basisNGauss)) 

177 if (kernelSize % 2) != 1: 

178 raise ValueError("Only odd-sized Alard-Lupton bases allowed") 

179 

180 logger = Log.getLogger("ip.diffim.generateAlardLuptonBasisList") 

181 if (targetFwhmPix is None) or (referenceFwhmPix is None) or (not config.scaleByFwhm): 

182 logger.info("PSF sigmas are not available or scaling by fwhm disabled, " 

183 "falling back to config values") 

184 if metadata is not None: 

185 metadata.add("ALBasisNGauss", basisNGauss) 

186 metadata.add("ALBasisDegGauss", basisDegGauss) 

187 metadata.add("ALBasisSigGauss", basisSigmaGauss) 

188 metadata.add("ALKernelSize", kernelSize) 

189 metadata.add("ALBasisMode", "config") 

190 

191 return diffimLib.makeAlardLuptonBasisList(kernelSize//2, basisNGauss, basisSigmaGauss, basisDegGauss) 

192 

193 targetSigma = targetFwhmPix / sigma2fwhm 

194 referenceSigma = referenceFwhmPix / sigma2fwhm 

195 logger.debug("Generating matching bases for sigma %.2f pix -> %.2f pix", targetSigma, referenceSigma) 

196 

197 # Modify the size of Alard Lupton kernels based upon the images FWHM 

198 # 

199 # Note the operation is : template.x.kernel = science 

200 # 

201 # Assuming the template and science image Psfs are Gaussians with 

202 # the Fwhm above, Fwhm_T **2 + Fwhm_K **2 = Fwhm_S **2 

203 # 

204 if targetSigma == referenceSigma: 

205 # Leave defaults as-is 

206 logger.info("Target and reference psf fwhms are equal, falling back to config values") 

207 basisMode = "config" 

208 elif referenceSigma > targetSigma: 

209 # Normal convolution 

210 

211 # First Gaussian has the sigma that comes from the convolution 

212 # of two Gaussians : Sig_S**2 = Sig_T**2 + Sig_K**2 

213 # 

214 # If it's larger than basisMinSigma * basisGaussBeta, make it the 

215 # second kernel. Else make it the smallest kernel. Unless 

216 # only 1 kernel is asked for. 

217 logger.info("Reference psf fwhm is the greater, normal convolution mode") 

218 basisMode = "convolution" 

219 kernelSigma = np.sqrt(referenceSigma**2 - targetSigma**2) 

220 if kernelSigma < basisMinSigma: 

221 kernelSigma = basisMinSigma 

222 

223 basisSigmaGauss = [] 

224 if basisNGauss == 1: 

225 basisSigmaGauss.append(kernelSigma) 

226 nAppended = 1 

227 else: 

228 if (kernelSigma/basisGaussBeta) > basisMinSigma: 

229 basisSigmaGauss.append(kernelSigma/basisGaussBeta) 

230 basisSigmaGauss.append(kernelSigma) 

231 nAppended = 2 

232 else: 

233 basisSigmaGauss.append(kernelSigma) 

234 nAppended = 1 

235 

236 # Any other Gaussians above basisNGauss=1 come from a scaling 

237 # relationship: Sig_i+1 / Sig_i = basisGaussBeta 

238 for i in range(nAppended, basisNGauss): 

239 basisSigmaGauss.append(basisSigmaGauss[-1]*basisGaussBeta) 

240 

241 kernelSize = int(fwhmScaling * basisSigmaGauss[-1]) 

242 kernelSize += 0 if kernelSize%2 else 1 # Make sure it's odd 

243 kernelSize = min(config.kernelSizeMax, max(kernelSize, config.kernelSizeMin)) 

244 

245 else: 

246 # Deconvolution; Define the progression of Gaussians using a 

247 # method to derive a deconvolution sum-of-Gaussians from it's 

248 # convolution counterpart. Only use 3 since the algorithm 

249 # assumes 3 components. 

250 # 

251 # http://iopscience.iop.org/0266-5611/26/8/085002 Equation 40 

252 

253 # Use specializations for deconvolution 

254 logger.info("Target psf fwhm is the greater, deconvolution mode") 

255 basisMode = "deconvolution" 

256 basisNGauss = config.alardNGaussDeconv 

257 basisMinSigma = config.alardMinSigDeconv 

258 

259 kernelSigma = np.sqrt(targetSigma**2 - referenceSigma**2) 

260 if kernelSigma < basisMinSigma: 

261 kernelSigma = basisMinSigma 

262 

263 basisSigmaGauss = [] 

264 if (kernelSigma/basisGaussBeta) > basisMinSigma: 

265 basisSigmaGauss.append(kernelSigma/basisGaussBeta) 

266 basisSigmaGauss.append(kernelSigma) 

267 nAppended = 2 

268 else: 

269 basisSigmaGauss.append(kernelSigma) 

270 nAppended = 1 

271 

272 for i in range(nAppended, basisNGauss): 

273 basisSigmaGauss.append(basisSigmaGauss[-1]*basisGaussBeta) 

274 

275 kernelSize = int(fwhmScaling * basisSigmaGauss[-1]) 

276 kernelSize += 0 if kernelSize%2 else 1 # Make sure it's odd 

277 kernelSize = min(config.kernelSizeMax, max(kernelSize, config.kernelSizeMin)) 

278 

279 # Now build a deconvolution set from these sigmas 

280 sig0 = basisSigmaGauss[0] 

281 sig1 = basisSigmaGauss[1] 

282 sig2 = basisSigmaGauss[2] 

283 basisSigmaGauss = [] 

284 for n in range(1, 3): 

285 for j in range(n): 

286 sigma2jn = (n - j)*sig1**2 

287 sigma2jn += j * sig2**2 

288 sigma2jn -= (n + 1)*sig0**2 

289 sigmajn = np.sqrt(sigma2jn) 

290 basisSigmaGauss.append(sigmajn) 

291 

292 basisSigmaGauss.sort() 

293 basisNGauss = len(basisSigmaGauss) 

294 basisDegGauss = [config.alardDegGaussDeconv for x in basisSigmaGauss] 

295 

296 if metadata is not None: 

297 metadata.add("ALBasisNGauss", basisNGauss) 

298 metadata.add("ALBasisDegGauss", basisDegGauss) 

299 metadata.add("ALBasisSigGauss", basisSigmaGauss) 

300 metadata.add("ALKernelSize", kernelSize) 

301 metadata.add("ALBasisMode", basisMode) 

302 

303 logger.debug("basisSigmaGauss: %s basisDegGauss: %s", 

304 ','.join(['{:.1f}'.format(v) for v in basisSigmaGauss]), 

305 ','.join(['{:d}'.format(v) for v in basisDegGauss])) 

306 

307 return diffimLib.makeAlardLuptonBasisList(kernelSize//2, basisNGauss, basisSigmaGauss, basisDegGauss)