__init__.py 22 KB
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 Yannick Roehlly committed Feb 18, 2014 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 ``````# -*- coding: utf-8 -*- # Copyright (C) 2013 Centre de données Astrophysiques de Marseille # Copyright (C) 2013-2014 Yannick Roehlly # Licensed under the CeCILL-v2 licence - see Licence_CeCILL_V2-en.txt # Author: Yannick Roehlly """ Probability Density Function analysis module ============================================ This module builds the probability density functions (PDF) of the SED parameters to compute their moments. The models corresponding to all possible combinations of parameters are computed and their fluxes in the same filters as the observations are integrated. These fluxes are compared to the observed ones to compute the χ² value of the fitting. This χ² give a probability that is associated with the model values for the parameters. At the end, for each parameter, the probability-weighted mean and standard deviation are computed and the best fitting model (the one with the least reduced χ²) is given for each observation. """ import os import numpy as np `````` Yannick Roehlly committed Feb 19, 2014 28 ``````import matplotlib `````` Yannick Roehlly committed Feb 18, 2014 29 30 31 32 ``````from numpy import newaxis from collections import OrderedDict from datetime import datetime from progressbar import ProgressBar `````` Yannick Roehlly committed Feb 19, 2014 33 ``````from matplotlib import pyplot as plt `````` Yannick Roehlly committed Feb 18, 2014 34 35 36 37 ``````from astropy.table import Table, Column from ...utils import read_table from .. import AnalysisModule, complete_obs_table from ...creation_modules import get_module as get_creation_module `````` Yannick Roehlly committed Feb 19, 2014 38 ``````from .utils import gen_compute_fluxes_at_redshift, gen_pdf, gen_best_sed_fig `````` Yannick Roehlly committed Feb 18, 2014 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 ``````from ...warehouse import SedWarehouse from ...data import Database # Tolerance threshold under which any flux or error is considered as 0. TOLERANCE = 1.e-12 # Probability threshold: models with a lower probability are excluded from # the moments computation. MIN_PROBABILITY = 1.e-20 # Name of the file containing the analysis results RESULT_FILE = "analysis_results.fits" # Name of the file containing the best models information BEST_MODEL_FILE = "best_models.fits" # Directory where the output files are stored OUT_DIR = "out/" # Wavelength limits (restframe) when plotting the best SED. PLOT_L_MIN = 91 PLOT_L_MAX = 1e6 `````` Yannick Roehlly committed Feb 19, 2014 56 57 ``````# Number of points in the PDF PDF_NB_POINTS = 1000 `````` Yannick Roehlly committed Feb 18, 2014 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 `````` class PdfAnalysis(AnalysisModule): """PDF analysis module""" parameter_list = OrderedDict([ ("analysed_variables", ( "array of strings", "List of the variables (in the SEDs info dictionaries) for which " "the statistical analysis will be done.", ["sfr", "average_sfr"] )), ("use_observation_redshift", ( "boolean", "If true, the redshift of each observation will be taken from the " "redshift column in the observation table (default) and you must " "not use a redshifting module. Set to false if you want to use a " "redshifting module to test various redshifts.", True )), ("save_best_sed", ( "boolean", "If true, save the best SED for each observation to a file.", False )), ("plot_best_sed", ( "boolean", "If true, for each observation save a plot of the best SED " "and the observed fluxes.", False )), ("plot_chi2_distribution", ( "boolean", "If true, for each observation and each analysed variable " "plot the value vs reduced chi-square distribution.", False )), ("save_pdf", ( "boolean", "If true, for each observation and each analysed variable " "save the probability density function.", False )), ("plot_pdf", ( "boolean", "If true, for each observation and each analysed variable " "plot the probability density function.", False )), ("storage_type", ( "string", "Type of storage used to cache the generate SED.", "memory" )) ]) def process(self, data_file, column_list, creation_modules, creation_modules_params, parameters): """Process with the psum analysis. The analysis is done in two nested loops: over each observation and over each theoretical SEDs. We first loop over the SEDs to limit the number of time the SEDs are created. Parameters ---------- data_file: string Name of the file containing the observations to fit. column_list: list of strings Name of the columns from the data file to use for the analysis. creation_modules: list of strings List of the module names (in the right order) to use for creating the SEDs. creation_modules_params: list of dictionaries List of the parameter dictionaries for each module. parameters: dictionary Dictionary containing the parameters. """ `````` Yannick Roehlly committed Feb 19, 2014 138 139 140 `````` # To be sure matplotlib will not display the interactive window. matplotlib.interactive(0) `````` Yannick Roehlly committed Feb 18, 2014 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 `````` # Rename the output directory if it exists if os.path.exists(OUT_DIR): new_name = datetime.now().strftime("%Y%m%d%H%M") + "_" + OUT_DIR os.rename(OUT_DIR, new_name) print("The existing {} directory was renamed to {}".format( OUT_DIR, new_name )) os.mkdir(OUT_DIR) # Get the parameters analysed_variables = parameters["analysed_variables"] use_observation_redshift = (parameters["use_observation_redshift"] .lower() == "true") save_best_sed = (parameters["save_best_sed"].lower() == "true") plot_best_sed = (parameters["plot_best_sed"].lower() == "true") plot_chi2_distribution = ( parameters["plot_chi2_distribution"].lower() == "true") save_pdf = (parameters["save_pdf"].lower() == "true") plot_pdf = (parameters["plot_pdf"].lower() == "true") # Get the needed filters in the pcigale database. We use an ordered # dictionary because we need the keys to always be returned in the # same order. with Database() as base: filters = OrderedDict([(name, base.get_filter(name)) for name in column_list if not name.endswith('_err')]) # If needed, get the redshifting and IGM attenuation modules (we set # redshift=0 but the redshift value is adapted later). redshifting_module = None igm_module = None if use_observation_redshift: redshifting_module = get_creation_module("redshifting", redshift=0) igm_module = get_creation_module("igm_attenuation") # Read the observation table and complete it by adding error where # none is provided and by adding the systematic deviation. obs_table = complete_obs_table( read_table(data_file), column_list, filters, TOLERANCE ) ################################################################## # Model computation # ################################################################## print("Computing the models fluxes...") # First, we compute for all the possible theoretical models (one for # each parameter set in sed_module_parameters) the fluxes in all the # filters at the redshift of each observed galaxy. These fluxes are # stored in: # model_fluxes: # - axis 0: model index # - axis 1: observation index # - axis 2: filter index # We use a numpy masked array to mask the fluxes of models that would # be older than the age of the Universe at the considered redshift # The values for the analysed variables are stored in: # model_variables: # - axis 0: the model index in sed_module_params # - axis 1: the variable index in analysed_variables model_fluxes = np.ma.zeros((len(creation_modules_params), len(obs_table), len(filters))) model_variables = np.ma.zeros((len(creation_modules_params), len(analysed_variables))) # We keep the information (i.e. the content of the sed.info # dictionary) for each model. model_info = [] progress_bar = ProgressBar(maxval=len(creation_modules_params)).start() # The SED warehouse is used to retrieve SED corresponding to some # modules and parameters. with SedWarehouse(cache_type=parameters["storage_type"]) as \ sed_warehouse: `````` Yannick Roehlly committed Feb 19, 2014 229 230 `````` for model_index, model_params in enumerate( creation_modules_params): `````` Yannick Roehlly committed Feb 18, 2014 231 `````` `````` Yannick Roehlly committed Feb 19, 2014 232 `````` sed = sed_warehouse.get_sed(creation_modules, model_params) `````` Yannick Roehlly committed Feb 18, 2014 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 `````` # Cached function to compute the SED fluxes at a redshift gen_fluxes = gen_compute_fluxes_at_redshift( sed, filters.values(), redshifting_module, igm_module) for obs_index, redshift in enumerate(obs_table["redshift"]): model_fluxes[model_index, obs_index] = gen_fluxes(redshift) model_variables[model_index] = np.array( [sed.info[name] for name in analysed_variables] ) model_info.append(sed.info.values()) progress_bar.update(model_index + 1) # Mask the invalid fluxes `````` Yannick Roehlly committed Feb 19, 2014 250 `````` model_fluxes = np.ma.masked_less(model_fluxes, -90) `````` Yannick Roehlly committed Feb 18, 2014 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 `````` progress_bar.finish() ################################################################## # Observations to models comparison # ################################################################## print("Comparing the observations to the models...") # To accelerate the computations, we put observations fluxes and # errors in multi-dimensional numpy array: # - axis 0: the observation index # - axis 1: the filter index obs_fluxes = np.array([ obs_table[name] for name in filters] ).transpose() obs_errors = np.array([ obs_table[name + "_err"] for name in filters] ).transpose() # Some observations may not have flux value in some filters, in that # case the user is asked to put -9999 as value. We mask these values. # Note, we must mask obs_fluxes after obs_errors. obs_errors = np.ma.masked_where(obs_fluxes < -9990., obs_errors) obs_fluxes = np.ma.masked_less(obs_fluxes, -9990.) # Normalisation factor to be applied to a model fluxes to best fit an # observation fluxes. Normalised flux of the models. χ² and # likelihood of the fitting. Reduced χ² (divided by the number of # filters to do the fit). # axis 0: model index # axis 1: observation index normalisation_factors = ( np.sum( model_fluxes * obs_fluxes[newaxis, :, :] / ( obs_errors * obs_errors)[newaxis, :, :], axis=2 ) / np.sum( model_fluxes * model_fluxes / ( obs_errors * obs_errors)[newaxis, :, :], axis=2) ) norm_model_fluxes = model_fluxes * normalisation_factors[:, :, newaxis] # χ² of the comparison of each model to each observation. The # chi_squares array is: # axis 0: model index # axis 1: observation index chi_squares = np.sum( np.square( (obs_fluxes[newaxis, :, :] - norm_model_fluxes) / obs_errors[newaxis, :, :] ), axis=2 ) # We define the reduced χ² as the χ² divided by the number of fluxes # used for the fitting. reduced_chi_squares = chi_squares / obs_fluxes.count(1)[newaxis, :] # We use the exponential probability associated with the χ² as # likelihood function. The likelihood array is: # axis 0: model index # axis 1: observation index likelihood = np.exp(-chi_squares/2) # For the analysis, we consider that the computed models explain each # observation. We normalise the likelihood function to have a # total likelihood of 1 for each observation. likelihood /= np.sum(likelihood, axis=0)[newaxis, :] # We don't want to take into account the models with a probability # less that the threshold. likelihood = np.ma.masked_less(likelihood, MIN_PROBABILITY) # We re-normalise the likelihood. likelihood /= np.sum(likelihood, axis=0)[newaxis, :] # Some model variables depend on the galaxy mass (the normalisation # factor) so we expand the model_variables array to have a new axis # corresponding to the observation and multiply (when needed) the # value of the variables by the normalisation factor of the fitting # for each observation. # The new array will have be: # axis 0: model index # axis 1: observation index # axis 2: variable index model_variables = model_variables[:, newaxis, :].repeat(len(obs_table), axis=1) # We take the mass-dependent variable list from the last computed sed. for index, variable in enumerate(analysed_variables): if variable in sed.mass_proportional_info: model_variables[:, :, index] *= normalisation_factors # We also add the galaxy mass to the analysed variables analysed_variables.insert(0, "galaxy_mass") model_variables = np.dstack((normalisation_factors, model_variables)) ################################################################## # Variable analysis # ################################################################## `````` Yannick Roehlly committed Feb 19, 2014 347 348 `````` print("Analysing the variables...") `````` Yannick Roehlly committed Feb 18, 2014 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 `````` # We compute the weighted average and standard deviation using the # likelihood as weight. We first build the weight array by expanding # the likelihood along a new axis corresponding to the analysed # variable. weights = likelihood[:, :, newaxis].repeat(len(analysed_variables), axis=2) # Analysed variables average and standard devisation arrays. # axis 0: observation index # axis 1: variable index analysed_averages = np.ma.average(model_variables, axis=0, weights=weights) analysed_variances = np.ma.average( (model_variables - analysed_averages[newaxis, :, :])**2, axis=0, weights=weights) analysed_std = np.ma.sqrt(analysed_variances) # Create and save the result table. result_table = Table() result_table.add_column(Column( obs_table["id"].data, name="observation_id" )) for index, variable in enumerate(analysed_variables): result_table.add_column(Column( analysed_averages[:, index], name=variable )) result_table.add_column(Column( analysed_std[:, index], name=variable+"_err" )) result_table.write(OUT_DIR + RESULT_FILE) ################################################################## # Best models # ################################################################## `````` Yannick Roehlly committed Feb 19, 2014 391 392 `````` print("Analysing the best models...") `````` Yannick Roehlly committed Feb 18, 2014 393 394 `````` # We define the best fitting model for each observation as the one # with the least χ². `````` Yannick Roehlly committed Feb 19, 2014 395 `````` best_model_index = list(chi_squares.argmin(axis=0)) `````` Yannick Roehlly committed Feb 18, 2014 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 `````` # We take the list of information added to the SEDs from the last # computed one. model_info_names = sed.info.keys() best_model_table = Table() best_model_table.add_column(Column( obs_table["id"].data, name="observation_id" )) best_model_table.add_column(Column( chi_squares[best_model_index, range(len(best_model_index))], name="chi_square" )) best_model_table.add_column(Column( reduced_chi_squares[best_model_index, range(len(best_model_index))], name="reduced_chi_square" )) best_model_table.add_column(Column( normalisation_factors[best_model_index, range(len(best_model_index))], name="galaxy_mass", unit="Msun" )) for index, name in enumerate(model_info_names): best_model_table.add_column(Column( [model_info[model_idx][index] for model_idx in best_model_index], name=name )) best_model_table.write(OUT_DIR + BEST_MODEL_FILE) `````` Yannick Roehlly committed Feb 19, 2014 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 `````` if plot_best_sed or save_best_sed: print("Plotting/saving the best models...") with SedWarehouse(cache_type=parameters["storage_type"]) as \ sed_warehouse: for obs_index, obs_name in enumerate(obs_table["id"]): obs_redshift = obs_table["redshift"][obs_index] best_index = best_model_index[obs_index] sed = sed_warehouse.get_sed( creation_modules, creation_modules_params[best_index] ) if use_observation_redshift: redshifting_module.parameters["redshift"] = \ obs_redshift redshifting_module.process(sed) igm_module.process(sed) best_lambda = sed.wavelength_grid best_fnu = sed.fnu * normalisation_factors[best_index, obs_index] if save_best_sed: table = Table(( Column(best_lambda, name="Wavelength", unit="nm"), Column(best_fnu, name="Fnu density", unit="mJy") )) table.write(OUT_DIR + "{}_best_model.fits".format( obs_name)) if plot_best_sed: plot_mask = ( (best_lambda >= PLOT_L_MIN * (1 + obs_redshift)) & (best_lambda <= PLOT_L_MAX * (1 + obs_redshift)) ) figure = gen_best_sed_fig( best_lambda[plot_mask], best_fnu[plot_mask], [f.effective_wavelength for f in filters.values()], norm_model_fluxes[best_index, obs_index, :], [obs_table[f][obs_index] for f in filters] ) if figure is None: print("Can not plot best model for observation " "{}!".format(obs_name)) else: figure.suptitle( u"Best model for {} - red-chi² = {}".format( obs_name, reduced_chi_squares[best_index, obs_index] ) ) figure.savefig(OUT_DIR + "{}_best_model.pdf".format( obs_name)) plt.close(figure) `````` Yannick Roehlly committed Feb 19, 2014 496 497 498 `````` ################################################################## # Probability Density Functions # ################################################################## `````` Yannick Roehlly committed Feb 18, 2014 499 `````` `````` Yannick Roehlly committed Feb 19, 2014 500 501 502 503 `````` # We estimate the probability density functions (PDF) of the # parameters using a weighted kernel density estimation. This part # should definitely be improved as we simulate the weigth by adding # as many value as their probability * 100. `````` Yannick Roehlly committed Feb 18, 2014 504 `````` `````` Yannick Roehlly committed Feb 19, 2014 505 `````` if save_pdf or plot_pdf: `````` Yannick Roehlly committed Feb 18, 2014 506 `````` `````` Yannick Roehlly committed Feb 19, 2014 507 `````` print("Computing the probability density functions...") `````` Yannick Roehlly committed Feb 18, 2014 508 `````` `````` Yannick Roehlly committed Feb 19, 2014 509 `````` for obs_index, obs_name in enumerate(obs_table["id"]): `````` Yannick Roehlly committed Feb 18, 2014 510 `````` `````` Yannick Roehlly committed Feb 19, 2014 511 `````` probabilities = likelihood[:, obs_index] `````` Yannick Roehlly committed Feb 18, 2014 512 `````` `````` Yannick Roehlly committed Feb 19, 2014 513 `````` for var_index, var_name in enumerate(analysed_variables): `````` Yannick Roehlly committed Feb 18, 2014 514 `````` `````` Yannick Roehlly committed Feb 19, 2014 515 `````` values = model_variables[:, obs_index, var_index] `````` Yannick Roehlly committed Feb 18, 2014 516 `````` `````` Yannick Roehlly committed Feb 19, 2014 517 518 519 `````` pdf_grid = np.linspace(values.min(), values.max(), PDF_NB_POINTS) pdf_prob = gen_pdf(values, probabilities, pdf_grid) `````` Yannick Roehlly committed Feb 18, 2014 520 `````` `````` Yannick Roehlly committed Feb 19, 2014 521 522 523 524 `````` if pdf_prob is None: # TODO: use logging print("Can not compute PDF for observation <{}> and " "variable <{}>.".format(obs_name, var_name)) `````` Yannick Roehlly committed Feb 18, 2014 525 `````` `````` Yannick Roehlly committed Feb 19, 2014 526 527 528 `````` if save_pdf and pdf_prob is not None: table = Table(( Column(pdf_grid, name=var_name), `````` Yannick Roehlly committed Feb 19, 2014 529 `````` Column(pdf_prob, name="probability density") `````` Yannick Roehlly committed Feb 19, 2014 530 531 532 `````` )) table.write(OUT_DIR + "{}_{}_pdf.fits".format( obs_name, var_name)) `````` Yannick Roehlly committed Feb 18, 2014 533 `````` `````` Yannick Roehlly committed Feb 19, 2014 534 535 536 537 538 `````` if plot_pdf and pdf_prob is not None: figure = plt.figure() ax = figure.add_subplot(111) ax.plot(pdf_grid, pdf_prob) ax.set_xlabel(var_name) `````` Yannick Roehlly committed Feb 19, 2014 539 `````` ax.set_ylabel("Probability density") `````` Yannick Roehlly committed Feb 19, 2014 540 541 542 `````` figure.savefig(OUT_DIR + "{}_{}_pdf.pdf".format( obs_name, var_name)) plt.close(figure) `````` Yannick Roehlly committed Feb 18, 2014 543 544 545 `````` # AnalysisModule to be returned by get_module Module = PdfAnalysis``````