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scripts/cstsdist.py
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| 1 | +#! /usr/bin/env python | ||
| 2 | +# ========================================================================== | ||
| 3 | +# This script generates the TS distribution for a particular model based | ||
| 4 | +# on Monte-Carlo simulations. | ||
| 5 | +# | ||
| 6 | +# Copyright (C) 2011 Jurgen Knodlseder | ||
| 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 GNU General Public License | ||
| 19 | +# along with this program. If not, see <http://www.gnu.org/licenses/>. | ||
| 20 | +# | ||
| 21 | +# ========================================================================== | ||
| 22 | +from ctatools import * | ||
| 23 | +from gammalib import * | ||
| 24 | +import obsutils | ||
| 25 | +import sys | ||
| 26 | +import csv | ||
| 27 | +import math | ||
| 28 | + | ||
| 29 | + | ||
| 30 | +# ============== # | ||
| 31 | +# cstsdist class # | ||
| 32 | +# ============== # | ||
| 33 | +class cstsdist(GApplication): | ||
| 34 | + """ | ||
| 35 | + This class implements the TS distribution generation script. It derives | ||
| 36 | + from the GammaLib::GApplication class which provides support for parameter | ||
| 37 | + files, command line arguments, and logging. In that way the Python | ||
| 38 | + script behaves just as a regular ctool. | ||
| 39 | + """ | ||
| 40 | + def __init__(self, *argv): | ||
| 41 | + """ | ||
| 42 | + Constructor. | ||
| 43 | + """ | ||
| 44 | + # Set name | ||
| 45 | + self.name = "cstsdist" | ||
| 46 | + self.version = "0.1.0" | ||
| 47 | + | ||
| 48 | + # Initialise some members | ||
| 49 | + self.obs = None | ||
| 50 | + self.bkg_model = None | ||
| 51 | + self.full_model = None | ||
| 52 | + | ||
| 53 | + # Make sure that parfile exists | ||
| 54 | + file = self.parfile() | ||
| 55 | + | ||
| 56 | + # Initialise application | ||
| 57 | + if len(argv) == 0: | ||
| 58 | + GApplication.__init__(self, self.name, self.version) | ||
| 59 | + elif len(argv) ==1: | ||
| 60 | + GApplication.__init__(self, self.name, self.version, *argv) | ||
| 61 | + else: | ||
| 62 | + raise TypeError("Invalid number of arguments given.") | ||
| 63 | + | ||
| 64 | + # Set logger properties | ||
| 65 | + self.log_header() | ||
| 66 | + self.log.date(True) | ||
| 67 | + | ||
| 68 | + # Return | ||
| 69 | + return | ||
| 70 | + | ||
| 71 | + def __del__(self): | ||
| 72 | + """ | ||
| 73 | + Destructor. | ||
| 74 | + """ | ||
| 75 | + # Write separator into logger | ||
| 76 | + if self.logTerse(): | ||
| 77 | + self.log("\n") | ||
| 78 | + | ||
| 79 | + # Return | ||
| 80 | + return | ||
| 81 | + | ||
| 82 | + def parfile(self): | ||
| 83 | + """ | ||
| 84 | + Check if parfile exists. If parfile does not exist then create a | ||
| 85 | + default parfile. This kluge avoids shipping the cscript with a parfile. | ||
| 86 | + """ | ||
| 87 | + # Set parfile name | ||
| 88 | + parfile = self.name+".par" | ||
| 89 | + | ||
| 90 | + try: | ||
| 91 | + pars = GPars(parfile) | ||
| 92 | + except: | ||
| 93 | + # Signal if parfile was not found | ||
| 94 | + print "Parfile "+parfile+" not found. Create default parfile." | ||
| 95 | + | ||
| 96 | + # Create default parfile | ||
| 97 | + pars = GPars() | ||
| 98 | + pars.append(GPar("outfile","f","h","ts.dat","","","Output file name")) | ||
| 99 | + pars.append(GPar("ntrials","i","a","10","","","Number of trials")) | ||
| 100 | + pars.append(GPar("caldb","s","a","$GAMMALIB/share/caldb/cta","","","Calibration database")) | ||
| 101 | + pars.append(GPar("irf","s","a","kb_E_50h_v3","","","Instrument response function")) | ||
| 102 | + pars.append(GPar("type","s","a","point","","","Source model type (point/gauss/shell/disk)")) | ||
| 103 | + pars.append(GPar("index","r","h","-2.48","","","Spectral index")) | ||
| 104 | + pars.append(GPar("offset","r","a","0.0","0.0","","Source offset angle (deg)")) | ||
| 105 | + pars.append(GPar("bkg","s","a","$GAMMALIB/share/models/bkg_kb_E_50h_v3.txt","","","Background model file function (none=power law for E)")) | ||
| 106 | + pars.append(GPar("emin","r","a","0.1","0.0","","Lower energy limit (TeV)")) | ||
| 107 | + pars.append(GPar("emax","r","a","100.0","0.0","","Upper energy limit (TeV)")) | ||
| 108 | + pars.append(GPar("enumbins","i","a","0","","","Number of energy bins (0=unbinned)")) | ||
| 109 | + pars.append(GPar("duration","r","a","180000.0","","","Effective exposure time (s)")) | ||
| 110 | + pars.append(GPar("rad","r","h","5.0","","","Radius of ROI (deg)")) | ||
| 111 | + pars.append(GPar("npix","i","h","200","","","Number of pixels for binned")) | ||
| 112 | + pars.append(GPar("binsz","r","h","0.05","","","Pixel size for binned (deg/pixel)")) | ||
| 113 | + pars.append_standard() | ||
| 114 | + pars.save(parfile) | ||
| 115 | + | ||
| 116 | + # Return | ||
| 117 | + return | ||
| 118 | + | ||
| 119 | + def get_parameters(self): | ||
| 120 | + """ | ||
| 121 | + Get parameters from parfile and setup the observation. | ||
| 122 | + """ | ||
| 123 | + # Get parameters | ||
| 124 | + self.m_outfile = self["outfile"].filename() | ||
| 125 | + self.m_ntrials = self["ntrials"].integer() | ||
| 126 | + self.m_caldb = self["caldb"].string() | ||
| 127 | + self.m_irf = self["irf"].string() | ||
| 128 | + self.m_type = self["type"].string() | ||
| 129 | + self.m_index = self["index"].real() | ||
| 130 | + self.m_offset = self["offset"].real() | ||
| 131 | + self.m_bkg = self["bkg"].string() | ||
| 132 | + self.m_emin = self["emin"].real() | ||
| 133 | + self.m_emax = self["emax"].real() | ||
| 134 | + self.m_enumbins = self["enumbins"].integer() | ||
| 135 | + self.m_duration = self["duration"].real() | ||
| 136 | + self.m_rad = self["rad"].real() | ||
| 137 | + self.m_npix = self["npix"].integer() | ||
| 138 | + self.m_binsz = self["binsz"].real() | ||
| 139 | + | ||
| 140 | + # Set some fixed parameters | ||
| 141 | + self.m_log = False # Logging in client tools | ||
| 142 | + self.m_debug = False # Debugging in client tools | ||
| 143 | + | ||
| 144 | + # Setup observation | ||
| 145 | + self.obs = self.set_obs(emin=self.m_emin, emax=self.m_emax) | ||
| 146 | + | ||
| 147 | + # Initialise models. Note that we centre the point source at the Galactic | ||
| 148 | + # center as our observation is also centred at the Galactic centre, so | ||
| 149 | + # we're onaxis. | ||
| 150 | + self.bkg_model = GModels() | ||
| 151 | + self.full_model = GModels() | ||
| 152 | + self.bkg_model.append(self.set_bkg_model()) | ||
| 153 | + self.full_model.append(self.set_bkg_model()) | ||
| 154 | + self.full_model.append(self.set_src_model(0.0, self.m_offset, \ | ||
| 155 | + flux=0.010, \ | ||
| 156 | + type=self.m_type, \ | ||
| 157 | + index=self.m_index)) | ||
| 158 | + | ||
| 159 | + # Attach background model to observation container | ||
| 160 | + self.obs.models(self.bkg_model) | ||
| 161 | + | ||
| 162 | + # Return | ||
| 163 | + return | ||
| 164 | + | ||
| 165 | + def models(self, models): | ||
| 166 | + """ | ||
| 167 | + Set model. | ||
| 168 | + """ | ||
| 169 | + # Copy models | ||
| 170 | + self.model = models.copy() | ||
| 171 | + | ||
| 172 | + # Return | ||
| 173 | + return | ||
| 174 | + | ||
| 175 | + def execute(self): | ||
| 176 | + """ | ||
| 177 | + Execute the script. | ||
| 178 | + """ | ||
| 179 | + # Run the script | ||
| 180 | + self.run() | ||
| 181 | + | ||
| 182 | + # Return | ||
| 183 | + return | ||
| 184 | + | ||
| 185 | + def run(self): | ||
| 186 | + """ | ||
| 187 | + Run the script. | ||
| 188 | + """ | ||
| 189 | + # Switch screen logging on in debug mode | ||
| 190 | + if self.logDebug(): | ||
| 191 | + self.log.cout(True) | ||
| 192 | + | ||
| 193 | + # Get parameters | ||
| 194 | + self.get_parameters() | ||
| 195 | + | ||
| 196 | + # Write input parameters into logger | ||
| 197 | + if self.logTerse(): | ||
| 198 | + self.log_parameters() | ||
| 199 | + self.log("\n") | ||
| 200 | + | ||
| 201 | + # Write observation into logger | ||
| 202 | + if self.logTerse(): | ||
| 203 | + self.log("\n") | ||
| 204 | + self.log.header1("Observation") | ||
| 205 | + self.log(str(self.obs)) | ||
| 206 | + self.log("\n") | ||
| 207 | + | ||
| 208 | + # Write models into logger | ||
| 209 | + if self.logTerse(): | ||
| 210 | + self.log("\n") | ||
| 211 | + self.log.header1("Test model") | ||
| 212 | + self.log(str(self.full_model)) | ||
| 213 | + self.log("\n") | ||
| 214 | + | ||
| 215 | + # Write header | ||
| 216 | + if self.logTerse(): | ||
| 217 | + self.log("\n") | ||
| 218 | + self.log.header1("Generate TS distribution") | ||
| 219 | + | ||
| 220 | + # Loop over trials | ||
| 221 | + for seed in range(self.m_ntrials): | ||
| 222 | + | ||
| 223 | + # Make a trial | ||
| 224 | + result = self.trial(seed) | ||
| 225 | + | ||
| 226 | + # Write out result immediately | ||
| 227 | + if seed == 0: | ||
| 228 | + file = open(self.m_outfile, 'w') | ||
| 229 | + writer = csv.DictWriter(file, result['colnames']) | ||
| 230 | + writer.writerow(dict((_,_) for _ in result['colnames'])) | ||
| 231 | + else: | ||
| 232 | + file = open(self.m_outfile, 'a') | ||
| 233 | + writer = csv.DictWriter(file, result['colnames']) | ||
| 234 | + writer.writerow(result['values']) | ||
| 235 | + file.close() | ||
| 236 | + | ||
| 237 | + # Return | ||
| 238 | + return | ||
| 239 | + | ||
| 240 | + def set_obs(self, lpnt=0.0, bpnt=0.0, emin=0.1, emax=100.0): | ||
| 241 | + """ | ||
| 242 | + Returns an observation container with a single CTA observation. | ||
| 243 | + | ||
| 244 | + Keywords: | ||
| 245 | + lpnt - Galactic longitude of pointing [deg] (default: 0.0) | ||
| 246 | + bpnt - Galactic latitude of pointing [deg] (default: 0.0) | ||
| 247 | + emin - Minimum energy [TeV] (default: 0.1) | ||
| 248 | + emax - Maximum energy [TeV] (default: 100.0) | ||
| 249 | + """ | ||
| 250 | + # Allocate observation container | ||
| 251 | + obs = GObservations() | ||
| 252 | + | ||
| 253 | + # Set single pointing | ||
| 254 | + pntdir = GSkyDir() | ||
| 255 | + pntdir.lb_deg(lpnt, bpnt) | ||
| 256 | + | ||
| 257 | + # Create CTA observation | ||
| 258 | + run = obsutils.set(pntdir, caldb=self.m_caldb, irf=self.m_irf, \ | ||
| 259 | + duration=self.m_duration, \ | ||
| 260 | + emin=emin, emax=emax, rad=self.m_rad) | ||
| 261 | + | ||
| 262 | + # Append observation to container | ||
| 263 | + obs.append(run) | ||
| 264 | + | ||
| 265 | + # Return observation container | ||
| 266 | + return obs | ||
| 267 | + | ||
| 268 | + def set_bkg_model(self): | ||
| 269 | + """ | ||
| 270 | + Setup CTA background model. | ||
| 271 | + """ | ||
| 272 | + # Define radial component | ||
| 273 | + radial = GCTAModelRadialGauss(3.0) | ||
| 274 | + | ||
| 275 | + # Define spectral component | ||
| 276 | + spectrum = GModelSpectralFunc(self.m_bkg) | ||
| 277 | + | ||
| 278 | + # Create background model | ||
| 279 | + model = GCTAModelRadialAcceptance(radial, spectrum) | ||
| 280 | + model.name("Background") | ||
| 281 | + model.instruments("CTA") | ||
| 282 | + | ||
| 283 | + # Return background model | ||
| 284 | + return model | ||
| 285 | + | ||
| 286 | + def set_src_model(self, l, b, flux=1.0, index=-2.48, \ | ||
| 287 | + type="point", sigma=1.0, radius=1.0, width=0.1, \ | ||
| 288 | + fitpos=False, fitidx=False): | ||
| 289 | + """ | ||
| 290 | + Returns a single source with Crab-like spectrum. The source flux | ||
| 291 | + can be scaled in Crab units. The Crab spectrum is based on MAGIC | ||
| 292 | + observations (Albert et al. 2008, ApJ, 674, 1037). | ||
| 293 | + | ||
| 294 | + Parameters: | ||
| 295 | + l - Galactic longitude of source location [deg] | ||
| 296 | + b - Galactic latitude of source location [deg] | ||
| 297 | + Keywords: | ||
| 298 | + flux - Source flux [Crabs] | ||
| 299 | + index - Spectral index | ||
| 300 | + type - Source type ("point", "gauss", "disk", "shell") | ||
| 301 | + sigma - Gaussian sigma (for type="gauss") | ||
| 302 | + radius - Disk or shell inner radius [deg] (for type="disk" and type="shell") | ||
| 303 | + width - Shell width [deg] (for type="shell") | ||
| 304 | + fitpos - Fit position? (default: True) | ||
| 305 | + fitidx - Fit index? (default: True) | ||
| 306 | + """ | ||
| 307 | + # Set source location | ||
| 308 | + location = GSkyDir() | ||
| 309 | + location.lb_deg(l, b) | ||
| 310 | + | ||
| 311 | + # Set source spectrum | ||
| 312 | + spectrum = GModelSpectralPlaw(flux, index) | ||
| 313 | + spectrum["Prefactor"].scale(5.7e-16) | ||
| 314 | + spectrum["PivotEnergy"].value(0.3) | ||
| 315 | + spectrum["PivotEnergy"].scale(1.0e6) | ||
| 316 | + if fitidx: | ||
| 317 | + spectrum["Index"].free() | ||
| 318 | + else: | ||
| 319 | + spectrum["Index"].fix() | ||
| 320 | + | ||
| 321 | + # Set source | ||
| 322 | + if type == "point": | ||
| 323 | + spatial = GModelSpatialPtsrc(location) | ||
| 324 | + if fitpos: | ||
| 325 | + spatial[0].free() | ||
| 326 | + spatial[1].free() | ||
| 327 | + source = GModelPointSource(spatial, spectrum) | ||
| 328 | + elif type == "gauss": | ||
| 329 | + radial = GModelRadialGauss(location, sigma) | ||
| 330 | + if fitpos: | ||
| 331 | + radial[0].free() | ||
| 332 | + radial[1].free() | ||
| 333 | + source = GModelExtendedSource(radial, spectrum) | ||
| 334 | + elif type == "disk": | ||
| 335 | + radial = GModelRadialDisk(location, radius) | ||
| 336 | + if fitpos: | ||
| 337 | + radial[0].free() | ||
| 338 | + radial[1].free() | ||
| 339 | + source = GModelExtendedSource(radial, spectrum) | ||
| 340 | + elif type == "shell": | ||
| 341 | + radial = GModelRadialShell(location, radius, width) | ||
| 342 | + if fitpos: | ||
| 343 | + radial[0].free() | ||
| 344 | + radial[1].free() | ||
| 345 | + source = GModelExtendedSource(radial, spectrum) | ||
| 346 | + else: | ||
| 347 | + self.log("ERROR: Unknown source type '"+type+"'.\n") | ||
| 348 | + return None | ||
| 349 | + | ||
| 350 | + # Set source name | ||
| 351 | + source.name("Test") | ||
| 352 | + | ||
| 353 | + # Return source | ||
| 354 | + return source | ||
| 355 | + | ||
| 356 | + def trial(self, seed): | ||
| 357 | + """ | ||
| 358 | + Create the TS for a single trial. | ||
| 359 | + | ||
| 360 | + Parameters: | ||
| 361 | + seed - Random number generator seed | ||
| 362 | + """ | ||
| 363 | + # Write header | ||
| 364 | + if self.logExplicit(): | ||
| 365 | + self.log.header2("Trial "+str(seed+1)) | ||
| 366 | + | ||
| 367 | + # Simulate events | ||
| 368 | + sim = obsutils.sim(self.obs, \ | ||
| 369 | + nbins=self.m_enumbins, \ | ||
| 370 | + seed=seed, \ | ||
| 371 | + binsz=self.m_binsz, \ | ||
| 372 | + npix=self.m_npix, \ | ||
| 373 | + log=self.m_log, debug=self.m_debug) | ||
| 374 | + | ||
| 375 | + # Determine number of events in simulation | ||
| 376 | + nevents = 0.0 | ||
| 377 | + for run in sim: | ||
| 378 | + nevents += run.events().number() | ||
| 379 | + | ||
| 380 | + # Write simulation results | ||
| 381 | + if self.logExplicit(): | ||
| 382 | + self.log.header3("Simulation") | ||
| 383 | + self.log.parformat("Number of simulated events") | ||
| 384 | + self.log(nevents) | ||
| 385 | + self.log("\n") | ||
| 386 | + | ||
| 387 | + # Fit background only | ||
| 388 | + sim.models(self.bkg_model) | ||
| 389 | + like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug) | ||
| 390 | + result_bgm = like.obs().models().copy() | ||
| 391 | + LogL_bgm = like.opt().value() | ||
| 392 | + npred_bgm = like.obs().npred() | ||
| 393 | + | ||
| 394 | + # Write background fit results | ||
| 395 | + if self.logExplicit(): | ||
| 396 | + self.log.header3("Background model fit") | ||
| 397 | + self.log.parformat("log likelihood") | ||
| 398 | + self.log(LogL_bgm) | ||
| 399 | + self.log("\n") | ||
| 400 | + self.log.parformat("Number of predicted events") | ||
| 401 | + self.log(npred_bgm) | ||
| 402 | + self.log("\n") | ||
| 403 | + for model in result_bgm: | ||
| 404 | + self.log.parformat("Model") | ||
| 405 | + self.log(model.name()) | ||
| 406 | + self.log("\n") | ||
| 407 | + for par in model: | ||
| 408 | + self.log(str(par)+"\n") | ||
| 409 | + | ||
| 410 | + # Fit background and test source | ||
| 411 | + sim.models(self.full_model) | ||
| 412 | + like = obsutils.fit(sim, log=self.m_log, debug=self.m_debug) | ||
| 413 | + result_all = like.obs().models().copy() | ||
| 414 | + LogL_all = like.opt().value() | ||
| 415 | + npred_all = like.obs().npred() | ||
| 416 | + ts = 2.0*(LogL_bgm-LogL_all) | ||
| 417 | + | ||
| 418 | + # Write background and test source fit results | ||
| 419 | + if self.logExplicit(): | ||
| 420 | + self.log.header3("Background and test source model fit") | ||
| 421 | + self.log.parformat("Test statistics") | ||
| 422 | + self.log(ts) | ||
| 423 | + self.log("\n") | ||
| 424 | + self.log.parformat("log likelihood") | ||
| 425 | + self.log(LogL_all) | ||
| 426 | + self.log("\n") | ||
| 427 | + self.log.parformat("Number of predicted events") | ||
| 428 | + self.log(npred_all) | ||
| 429 | + self.log("\n") | ||
| 430 | + for model in result_all: | ||
| 431 | + self.log.parformat("Model") | ||
| 432 | + self.log(model.name()) | ||
| 433 | + self.log("\n") | ||
| 434 | + for par in model: | ||
| 435 | + self.log(str(par)+"\n") | ||
| 436 | + | ||
| 437 | + # Write result | ||
| 438 | + elif self.logTerse(): | ||
| 439 | + self.log.parformat("Trial "+str(seed)) | ||
| 440 | + self.log("TS=") | ||
| 441 | + self.log(ts) | ||
| 442 | + self.log(" Prefactor=") | ||
| 443 | + self.log(result_all["Test"]["Prefactor"].value()) | ||
| 444 | + self.log("+/-") | ||
| 445 | + self.log(result_all["Test"]["Prefactor"].error()) | ||
| 446 | + self.log("\n") | ||
| 447 | + | ||
| 448 | + # Initialise results | ||
| 449 | + colnames = [] | ||
| 450 | + values = {} | ||
| 451 | + | ||
| 452 | + # Set TS value | ||
| 453 | + colnames.append("TS") | ||
| 454 | + values["TS"] = ts | ||
| 455 | + | ||
| 456 | + # Set logL for background fit | ||
| 457 | + colnames.append("LogL_bgm") | ||
| 458 | + values["LogL_bgm"] = LogL_bgm | ||
| 459 | + | ||
| 460 | + # Set logL for full fit | ||
| 461 | + colnames.append("LogL_all") | ||
| 462 | + values["LogL_all"] = LogL_all | ||
| 463 | + | ||
| 464 | + # Set Nevents | ||
| 465 | + colnames.append("Nevents") | ||
| 466 | + values["Nevents"] = nevents | ||
| 467 | + | ||
| 468 | + # Set Npred for background fit | ||
| 469 | + colnames.append("Npred_bkg") | ||
| 470 | + values["Npred_bkg"] = npred_bgm | ||
| 471 | + | ||
| 472 | + # Set Npred for full fit | ||
| 473 | + colnames.append("Npred_all") | ||
| 474 | + values["Npred_all"] = npred_all | ||
| 475 | + | ||
| 476 | + # Gather free full fit parameters | ||
| 477 | + for i in range(result_all.size()): | ||
| 478 | + model = result_all[i] | ||
| 479 | + model_name = model.name() | ||
| 480 | + for k in range(model.size()): | ||
| 481 | + par = model[k] | ||
| 482 | + if par.isfree(): | ||
| 483 | + | ||
| 484 | + # Set parameter name | ||
| 485 | + name = model_name+"_"+par.name() | ||
| 486 | + | ||
| 487 | + # Append value | ||
| 488 | + colnames.append(name) | ||
| 489 | + values[name] = par.value() | ||
| 490 | + | ||
| 491 | + # Append error | ||
| 492 | + name = "Unc_"+name | ||
| 493 | + colnames.append(name) | ||
| 494 | + values[name] = par.error() | ||
| 495 | + | ||
| 496 | + # Bundle together results | ||
| 497 | + result = {'colnames': colnames, 'values': values} | ||
| 498 | + | ||
| 499 | + # Return | ||
| 500 | + return result | ||
| 501 | + | ||
| 502 | + | ||
| 503 | +# ======================== # | ||
| 504 | +# Main routine entry point # | ||
| 505 | +# ======================== # | ||
| 506 | +if __name__ == '__main__': | ||
| 507 | + """ | ||
| 508 | + Generates TS distribution. | ||
| 509 | + """ | ||
| 510 | + # Create instance of application | ||
| 511 | + app = cstsdist(sys.argv) | ||
| 512 | + | ||
| 513 | + # Open logfile | ||
| 514 | + app.logFileOpen() | ||
| 515 | + | ||
| 516 | + # Execute application | ||
| 517 | + app.execute() | ||
| 518 | + | ||
| 0 | \ No newline at end of file | 519 | \ No newline at end of file |