src/daComposant/daAlgorithms/3DVAR.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
  25 import numpy, scipy.optimize
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "3DVAR")
  31         self.defineRequiredParameter(
  32             name     = "Minimizer",
  33             default  = "LBFGSB",
  34             typecast = str,
  35             message  = "Minimiseur utilisé",
  36             listval  = ["LBFGSB","TNC", "CG", "NCG", "BFGS"],
  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     = "CostDecrementTolerance",
  47             default  = 1.e-7,
  48             typecast = float,
  49             message  = "Diminution relative minimale du cout lors de l'arrêt",
  50             )
  51         self.defineRequiredParameter(
  52             name     = "ProjectedGradientTolerance",
  53             default  = -1,
  54             typecast = float,
  55             message  = "Maximum des composantes du gradient projeté lors de l'arrêt",
  56             minval   = -1,
  57             )
  58         self.defineRequiredParameter(
  59             name     = "GradientNormTolerance",
  60             default  = 1.e-05,
  61             typecast = float,
  62             message  = "Maximum des composantes du gradient lors de l'arrêt",
  63             )
  64         self.defineRequiredParameter(
  65             name     = "StoreInternalVariables",
  66             default  = False,
  67             typecast = bool,
  68             message  = "Stockage des variables internes ou intermédiaires du calcul",
  69             )
  70         self.defineRequiredParameter(
  71             name     = "StoreSupplementaryCalculations",
  72             default  = [],
  73             typecast = tuple,
  74             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  75             listval  = [
  76                 "APosterioriCorrelations",
  77                 "APosterioriCovariance",
  78                 "APosterioriStandardDeviations",
  79                 "APosterioriVariances",
  80                 "BMA",
  81                 "OMA",
  82                 "OMB",
  83                 "CostFunctionJ",
  84                 "CostFunctionJb",
  85                 "CostFunctionJo",
  86                 "CurrentState",
  87                 "CurrentOptimum",
  88                 "IndexOfOptimum",
  89                 "Innovation",
  90                 "InnovationAtCurrentState",
  91                 "CostFunctionJAtCurrentOptimum",
  92                 "CostFunctionJbAtCurrentOptimum",
  93                 "CostFunctionJoAtCurrentOptimum",
  94                 "SigmaObs2",
  95                 "MahalanobisConsistency",
  96                 "SimulationQuantiles",
  97                 "SimulatedObservationAtBackground",
  98                 "SimulatedObservationAtCurrentState",
  99                 "SimulatedObservationAtOptimum",
 100                 "SimulatedObservationAtCurrentOptimum",
 101                 ]
 102             )
 103         self.defineRequiredParameter(
 104             name     = "Quantiles",
 105             default  = [],
 106             typecast = tuple,
 107             message  = "Liste des valeurs de quantiles",
 108             minval   = 0.,
 109             maxval   = 1.,
 110             )
 111         self.defineRequiredParameter(
 112             name     = "SetSeed",
 113             typecast = numpy.random.seed,
 114             message  = "Graine fixée pour le générateur aléatoire",
 115             )
 116         self.defineRequiredParameter(
 117             name     = "NumberOfSamplesForQuantiles",
 118             default  = 100,
 119             typecast = int,
 120             message  = "Nombre d'échantillons simulés pour le calcul des quantiles",
 121             minval   = 1,
 122             )
 123         self.defineRequiredParameter(
 124             name     = "SimulationForQuantiles",
 125             default  = "Linear",
 126             typecast = str,
 127             message  = "Type de simulation pour l'estimation des quantiles",
 128             listval  = ["Linear", "NonLinear"]
 129             )
 130         self.defineRequiredParameter( # Pas de type
 131             name     = "Bounds",
 132             message  = "Liste des valeurs de bornes",
 133             )
 134         self.requireInputArguments(
 135             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 136             )
 137
 138     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 139         self._pre_run(Parameters, Xb, Y, R, B, Q)
 140         #
 141         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 142         if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
 143             self.setParameterValue("StoreInternalVariables",True)
 144         #
 145         # Opérateurs
 146         # ----------
 147         Hm = HO["Direct"].appliedTo
 148         Ha = HO["Adjoint"].appliedInXTo
 149         #
 150         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 151         # ----------------------------------------------------
 152         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 153             HXb = Hm( Xb, HO["AppliedInX"]["HXb"])
 154         else:
 155             HXb = Hm( Xb )
 156         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 157         if Y.size != HXb.size:
 158             raise ValueError("The size %i of observations Y and %i of observed calculation H(X) are different, they have to be identical."%(Y.size,HXb.size))
 159         if max(Y.shape) != max(HXb.shape):
 160             raise ValueError("The shapes %s of observations Y and %s of observed calculation H(X) are different, they have to be identical."%(Y.shape,HXb.shape))
 161         #
 162         # Précalcul des inversions de B et R
 163         # ----------------------------------
 164         BI = B.getI()
 165         RI = R.getI()
 166         #
 167         # Définition de la fonction-coût
 168         # ------------------------------
 169         def CostFunction(x):
 170             _X  = numpy.asmatrix(numpy.ravel( x )).T
 171             if self._parameters["StoreInternalVariables"] or \
 172                 "CurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 173                 "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 174                 self.StoredVariables["CurrentState"].store( _X )
 175             _HX = Hm( _X )
 176             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 177             _Innovation = Y - _HX
 178             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
 179                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 180                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 181             if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 182                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 183             #
 184             Jb  = float( 0.5 * (_X - Xb).T * BI * (_X - Xb) )
 185             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 186             J   = Jb + Jo
 187             #
 188             self.StoredVariables["CostFunctionJb"].store( Jb )
 189             self.StoredVariables["CostFunctionJo"].store( Jo )
 190             self.StoredVariables["CostFunctionJ" ].store( J )
 191             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 192                "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 193                "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 194                "CostFunctionJbAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 195                "CostFunctionJoAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
 196                "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 197                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 198             if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 199                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 200             if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 201                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 202             if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 203                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 204             if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 205                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 206             if "CostFunctionJbAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 207                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 208             if "CostFunctionJoAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 209                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 210             return J
 211         #
 212         def GradientOfCostFunction(x):
 213             _X      = numpy.asmatrix(numpy.ravel( x )).T
 214             _HX     = Hm( _X )
 215             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 216             GradJb  = BI * (_X - Xb)
 217             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 218             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 219             return GradJ.A1
 220         #
 221         # Point de démarrage de l'optimisation : Xini = Xb
 222         # ------------------------------------
 223         Xini = numpy.ravel(Xb)
 224         #
 225         # Minimisation de la fonctionnelle
 226         # --------------------------------
 227         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 228         #
 229         if self._parameters["Minimizer"] == "LBFGSB":
 230             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 231                 func        = CostFunction,
 232                 x0          = Xini,
 233                 fprime      = GradientOfCostFunction,
 234                 args        = (),
 235                 bounds      = self._parameters["Bounds"],
 236                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 237                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 238                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 239                 iprint      = self._parameters["optiprint"],
 240                 )
 241             nfeval = Informations['funcalls']
 242             rc     = Informations['warnflag']
 243         elif self._parameters["Minimizer"] == "TNC":
 244             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 245                 func        = CostFunction,
 246                 x0          = Xini,
 247                 fprime      = GradientOfCostFunction,
 248                 args        = (),
 249                 bounds      = self._parameters["Bounds"],
 250                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 251                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 252                 ftol        = self._parameters["CostDecrementTolerance"],
 253                 messages    = self._parameters["optmessages"],
 254                 )
 255         elif self._parameters["Minimizer"] == "CG":
 256             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 257                 f           = CostFunction,
 258                 x0          = Xini,
 259                 fprime      = GradientOfCostFunction,
 260                 args        = (),
 261                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 262                 gtol        = self._parameters["GradientNormTolerance"],
 263                 disp        = self._parameters["optdisp"],
 264                 full_output = True,
 265                 )
 266         elif self._parameters["Minimizer"] == "NCG":
 267             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 268                 f           = CostFunction,
 269                 x0          = Xini,
 270                 fprime      = GradientOfCostFunction,
 271                 args        = (),
 272                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 273                 avextol     = self._parameters["CostDecrementTolerance"],
 274                 disp        = self._parameters["optdisp"],
 275                 full_output = True,
 276                 )
 277         elif self._parameters["Minimizer"] == "BFGS":
 278             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 279                 f           = CostFunction,
 280                 x0          = Xini,
 281                 fprime      = GradientOfCostFunction,
 282                 args        = (),
 283                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 284                 gtol        = self._parameters["GradientNormTolerance"],
 285                 disp        = self._parameters["optdisp"],
 286                 full_output = True,
 287                 )
 288         else:
 289             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 290         #
 291         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 292         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 293         #
 294         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 295         # ----------------------------------------------------------------
 296         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 297             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 298         #
 299         # Obtention de l'analyse
 300         # ----------------------
 301         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 302         #
 303         self.StoredVariables["Analysis"].store( Xa.A1 )
 304         #
 305         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 306            "SigmaObs2"                     in self._parameters["StoreSupplementaryCalculations"] or \
 307            "SimulationQuantiles"           in self._parameters["StoreSupplementaryCalculations"] or \
 308            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 309             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 310                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 311             elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 312                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 313             else:
 314                 HXa = Hm(Xa)
 315         #
 316         # Calcul de la covariance d'analyse
 317         # ---------------------------------
 318         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
 319            "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 320             HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 321             HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 322             HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 323             HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 324             HessienneI = []
 325             nb = Xa.size
 326             for i in range(nb):
 327                 _ee    = numpy.matrix(numpy.zeros(nb)).T
 328                 _ee[i] = 1.
 329                 _HtEE  = numpy.dot(HtM,_ee)
 330                 _HtEE  = numpy.asmatrix(numpy.ravel( _HtEE )).T
 331                 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
 332             HessienneI = numpy.matrix( HessienneI )
 333             A = HessienneI.I
 334             if min(A.shape) != max(A.shape):
 335                 raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(self._name,str(A.shape)))
 336             if (numpy.diag(A) < 0).any():
 337                 raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(self._name,))
 338             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 339                 try:
 340                     L = numpy.linalg.cholesky( A )
 341                 except:
 342                     raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(self._name,))
 343             self.StoredVariables["APosterioriCovariance"].store( A )
 344         #
 345         # Calculs et/ou stockages supplémentaires
 346         # ---------------------------------------
 347         if "Innovation" in self._parameters["StoreSupplementaryCalculations"] or \
 348             "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
 349             "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"] or \
 350             "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 351             d  = Y - HXb
 352         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 353             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 354         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 355             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 356         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 357             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 358         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 359             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 360         if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
 361             TraceR = R.trace(Y.size)
 362             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
 363         if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
 364             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
 365         if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
 366             nech = self._parameters["NumberOfSamplesForQuantiles"]
 367             HXa  = numpy.matrix(numpy.ravel( HXa )).T
 368             YfQ  = None
 369             for i in range(nech):
 370                 if self._parameters["SimulationForQuantiles"] == "Linear":
 371                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 372                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 373                     Yr = HXa + dYr
 374                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 375                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 376                     Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
 377                 if YfQ is None:
 378                     YfQ = Yr
 379                 else:
 380                     YfQ = numpy.hstack((YfQ,Yr))
 381             YfQ.sort(axis=-1)
 382             YQ = None
 383             for quantile in self._parameters["Quantiles"]:
 384                 if not (0. <= float(quantile) <= 1.): continue
 385                 indice = int(nech * float(quantile) - 1./nech)
 386                 if YQ is None: YQ = YfQ[:,indice]
 387                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 388             self.StoredVariables["SimulationQuantiles"].store( YQ )
 389         if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
 390             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 391         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 392             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 393         #
 394         self._post_run(HO)
 395         return 0
 396
 397 # ==============================================================================
 398 if __name__ == "__main__":
 399     print('\n AUTODIAGNOSTIC \n')