src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2018 EDF R&D
   4 #
   5 # This library is free software; you can redistribute it and/or
   6 # modify it under the terms of the GNU Lesser General Public
   7 # License as published by the Free Software Foundation; either
   8 # version 2.1 of the License.
   9 #
  10 # This library is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13 # Lesser General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU Lesser General Public
  16 # License along with this library; if not, write to the Free Software
  17 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
  18 #
  19 # See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  20 #
  21 # Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  22
  23 import logging
  24 from daCore import BasicObjects, PlatformInfo
  25 import numpy, scipy.optimize
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "DERIVATIVEFREEOPTIMIZATION")
  31         self.defineRequiredParameter(
  32             name     = "Minimizer",
  33             default  = "BOBYQA",
  34             typecast = str,
  35             message  = "Minimiseur utilisé",
  36             listval  = ["BOBYQA", "COBYLA", "NEWUOA", "POWELL", "SIMPLEX", "SUBPLEX"],
  37             )
  38         self.defineRequiredParameter(
  39             name     = "MaximumNumberOfSteps",
  40             default  = 15000,
  41             typecast = int,
  42             message  = "Nombre maximal de pas d'optimisation",
  43             minval   = -1,
  44             )
  45         self.defineRequiredParameter(
  46             name     = "MaximumNumberOfFunctionEvaluations",
  47             default  = 15000,
  48             typecast = int,
  49             message  = "Nombre maximal d'évaluations de la fonction",
  50             minval   = -1,
  51             )
  52         self.defineRequiredParameter(
  53             name     = "StateVariationTolerance",
  54             default  = 1.e-4,
  55             typecast = float,
  56             message  = "Variation relative maximale de l'état lors de l'arrêt",
  57             )
  58         self.defineRequiredParameter(
  59             name     = "CostDecrementTolerance",
  60             default  = 1.e-7,
  61             typecast = float,
  62             message  = "Diminution relative minimale du cout lors de l'arrêt",
  63             )
  64         self.defineRequiredParameter(
  65             name     = "QualityCriterion",
  66             default  = "AugmentedWeightedLeastSquares",
  67             typecast = str,
  68             message  = "Critère de qualité utilisé",
  69             listval  = ["AugmentedWeightedLeastSquares","AWLS","DA",
  70                         "WeightedLeastSquares","WLS",
  71                         "LeastSquares","LS","L2",
  72                         "AbsoluteValue","L1",
  73                         "MaximumError","ME"],
  74             )
  75         self.defineRequiredParameter(
  76             name     = "StoreInternalVariables",
  77             default  = False,
  78             typecast = bool,
  79             message  = "Stockage des variables internes ou intermédiaires du calcul",
  80             )
  81         self.defineRequiredParameter(
  82             name     = "StoreSupplementaryCalculations",
  83             default  = [],
  84             typecast = tuple,
  85             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  86             listval  = [
  87                 "CurrentState",
  88                 "CostFunctionJ",
  89                 "CostFunctionJb",
  90                 "CostFunctionJo",
  91                 "CostFunctionJAtCurrentOptimum",
  92                 "CostFunctionJbAtCurrentOptimum",
  93                 "CostFunctionJoAtCurrentOptimum",
  94                 "CurrentOptimum",
  95                 "IndexOfOptimum",
  96                 "InnovationAtCurrentState",
  97                 "BMA",
  98                 "OMA",
  99                 "OMB",
 100                 "SimulatedObservationAtBackground",
 101                 "SimulatedObservationAtCurrentOptimum",
 102                 "SimulatedObservationAtCurrentState",
 103                 "SimulatedObservationAtOptimum",
 104                 ]
 105             )
 106         self.defineRequiredParameter( # Pas de type
 107             name     = "Bounds",
 108             message  = "Liste des valeurs de bornes",
 109             )
 110         self.requireInputArguments(
 111             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 112             )
 113
 114     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 115         self._pre_run(Parameters, Xb, Y, R, B, Q)
 116         #
 117         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
 118             logging.debug("%s Absence de NLopt, utilisation forcee du minimiseur SIMPLEX"%(self._name,))
 119             self._parameters["Minimizer"] = "SIMPLEX"
 120         #
 121         # Opérateurs
 122         # ----------
 123         Hm = HO["Direct"].appliedTo
 124         #
 125         # Précalcul des inversions de B et R
 126         # ----------------------------------
 127         BI = B.getI()
 128         RI = R.getI()
 129         #
 130         # Définition de la fonction-coût
 131         # ------------------------------
 132         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 133             _X  = numpy.asmatrix(numpy.ravel( x )).T
 134             self.StoredVariables["CurrentState"].store( _X )
 135             _HX = Hm( _X )
 136             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 137             _Innovation = Y - _HX
 138             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 139                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 140                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 141             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 142                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 143             #
 144             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 145                 if BI is None or RI is None:
 146                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 147                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 148                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 149             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 150                 if RI is None:
 151                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 152                 Jb  = 0.
 153                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 154             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 155                 Jb  = 0.
 156                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 157             elif QualityMeasure in ["AbsoluteValue","L1"]:
 158                 Jb  = 0.
 159                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 160             elif QualityMeasure in ["MaximumError","ME"]:
 161                 Jb  = 0.
 162                 Jo  = numpy.max( numpy.abs(_Innovation) )
 163             #
 164             J   = float( Jb ) + float( Jo )
 165             #
 166             self.StoredVariables["CostFunctionJb"].store( Jb )
 167             self.StoredVariables["CostFunctionJo"].store( Jo )
 168             self.StoredVariables["CostFunctionJ" ].store( J )
 169             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 170                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 171                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 172                "CostFunctionJbAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 173                "CostFunctionJoAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 174                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 175                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 176             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 177                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 178             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 179                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 180             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 181                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 182             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 183                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 184             if "CostFunctionJbAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 185                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 186             if "CostFunctionJoAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 187                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 188             return J
 189         #
 190         # Point de démarrage de l'optimisation : Xini = Xb
 191         # ------------------------------------
 192         Xini = numpy.ravel(Xb)
 193         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 194             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 195         #
 196         # Minimisation de la fonctionnelle
 197         # --------------------------------
 198         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 199         #
 200         if self._parameters["Minimizer"] == "POWELL":
 201             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 202                 func        = CostFunction,
 203                 x0          = Xini,
 204                 args        = (self._parameters["QualityCriterion"],),
 205                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 206                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 207                 xtol        = self._parameters["StateVariationTolerance"],
 208                 ftol        = self._parameters["CostDecrementTolerance"],
 209                 full_output = True,
 210                 disp        = self._parameters["optdisp"],
 211                 )
 212         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 213             def make_constraints(bounds):
 214                 constraints = []
 215                 for (i,(a,b)) in enumerate(bounds):
 216                     lower = lambda x: x[i] - a
 217                     upper = lambda x: b - x[i]
 218                     constraints = constraints + [lower] + [upper]
 219                 return constraints
 220             if self._parameters["Bounds"] is None:
 221                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 222             Minimum = scipy.optimize.fmin_cobyla(
 223                 func        = CostFunction,
 224                 x0          = Xini,
 225                 cons        = make_constraints( self._parameters["Bounds"] ),
 226                 args        = (self._parameters["QualityCriterion"],),
 227                 consargs    = (), # To avoid extra-args
 228                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 229                 rhobeg      = 1.0,
 230                 rhoend      = self._parameters["StateVariationTolerance"],
 231                 catol       = 2.*self._parameters["StateVariationTolerance"],
 232                 disp        = self._parameters["optdisp"],
 233                 )
 234         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 235             import nlopt
 236             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 237             def _f(_Xx, Grad):
 238                 # DFO, so no gradient
 239                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 240             opt.set_min_objective(_f)
 241             if self._parameters["Bounds"] is not None:
 242                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 243                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 244                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 245                 if self._parameters["optdisp"]:
 246                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 247                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 248                 opt.set_upper_bounds(ub)
 249                 opt.set_lower_bounds(lb)
 250             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 251             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 252             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 253             Minimum = opt.optimize( Xini )
 254             if self._parameters["optdisp"]:
 255                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 256                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 257                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 258         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 259             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 260                 func        = CostFunction,
 261                 x0          = Xini,
 262                 args        = (self._parameters["QualityCriterion"],),
 263                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 264                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 265                 xtol        = self._parameters["StateVariationTolerance"],
 266                 ftol        = self._parameters["CostDecrementTolerance"],
 267                 full_output = True,
 268                 disp        = self._parameters["optdisp"],
 269                 )
 270         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 271             import nlopt
 272             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 273             def _f(_Xx, Grad):
 274                 # DFO, so no gradient
 275                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 276             opt.set_min_objective(_f)
 277             if self._parameters["Bounds"] is not None:
 278                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 279                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 280                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 281                 if self._parameters["optdisp"]:
 282                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 283                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 284                 opt.set_upper_bounds(ub)
 285                 opt.set_lower_bounds(lb)
 286             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 287             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 288             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 289             Minimum = opt.optimize( Xini )
 290             if self._parameters["optdisp"]:
 291                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 292                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 293                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 294         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 295             import nlopt
 296             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 297             def _f(_Xx, Grad):
 298                 # DFO, so no gradient
 299                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 300             opt.set_min_objective(_f)
 301             if self._parameters["Bounds"] is not None:
 302                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 303                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 304                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 305                 if self._parameters["optdisp"]:
 306                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 307                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 308                 opt.set_upper_bounds(ub)
 309                 opt.set_lower_bounds(lb)
 310             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 311             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 312             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 313             Minimum = opt.optimize( Xini )
 314             if self._parameters["optdisp"]:
 315                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 316                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 317                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 318         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 319             import nlopt
 320             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 321             def _f(_Xx, Grad):
 322                 # DFO, so no gradient
 323                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 324             opt.set_min_objective(_f)
 325             if self._parameters["Bounds"] is not None:
 326                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 327                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 328                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 329                 if self._parameters["optdisp"]:
 330                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 331                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 332                 opt.set_upper_bounds(ub)
 333                 opt.set_lower_bounds(lb)
 334             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 335             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 336             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 337             Minimum = opt.optimize( Xini )
 338             if self._parameters["optdisp"]:
 339                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 340                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 341                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 342         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 343             import nlopt
 344             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 345             def _f(_Xx, Grad):
 346                 # DFO, so no gradient
 347                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 348             opt.set_min_objective(_f)
 349             if self._parameters["Bounds"] is not None:
 350                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 351                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 352                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 353                 if self._parameters["optdisp"]:
 354                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 355                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 356                 opt.set_upper_bounds(ub)
 357                 opt.set_lower_bounds(lb)
 358             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 359             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 360             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 361             Minimum = opt.optimize( Xini )
 362             if self._parameters["optdisp"]:
 363                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 364                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 365                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 366         else:
 367             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 368         #
 369         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 370         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 371         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 372         #
 373         # Obtention de l'analyse
 374         # ----------------------
 375         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 376         #
 377         self.StoredVariables["Analysis"].store( Xa.A1 )
 378         #
 379         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 380            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 381             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 382                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 383             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 384                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 385             else:
 386                 HXa = Hm(Xa)
 387         #
 388         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 389             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 390         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 391             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 392         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 393             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 394         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 395             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 396         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 397             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 398         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 399             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 400         #
 401         self._post_run()
 402         return 0
 403
 404 # ==============================================================================
 405 if __name__ == "__main__":
 406     print('\n AUTODIAGNOSTIC \n')