src/daComposant/daAlgorithms/3DVAR.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2019 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 coût lors de l'arrêt",
  50             minval   = 0.,
  51             )
  52         self.defineRequiredParameter(
  53             name     = "ProjectedGradientTolerance",
  54             default  = -1,
  55             typecast = float,
  56             message  = "Maximum des composantes du gradient projeté lors de l'arrêt",
  57             minval   = -1,
  58             )
  59         self.defineRequiredParameter(
  60             name     = "GradientNormTolerance",
  61             default  = 1.e-05,
  62             typecast = float,
  63             message  = "Maximum des composantes du gradient lors de l'arrêt",
  64             minval   = 0.,
  65             )
  66         self.defineRequiredParameter(
  67             name     = "StoreInternalVariables",
  68             default  = False,
  69             typecast = bool,
  70             message  = "Stockage des variables internes ou intermédiaires du calcul",
  71             )
  72         self.defineRequiredParameter(
  73             name     = "StoreSupplementaryCalculations",
  74             default  = [],
  75             typecast = tuple,
  76             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  77             listval  = [
  78                 "APosterioriCorrelations",
  79                 "APosterioriCovariance",
  80                 "APosterioriStandardDeviations",
  81                 "APosterioriVariances",
  82                 "BMA",
  83                 "CostFunctionJ",
  84                 "CostFunctionJAtCurrentOptimum",
  85                 "CostFunctionJb",
  86                 "CostFunctionJbAtCurrentOptimum",
  87                 "CostFunctionJo",
  88                 "CostFunctionJoAtCurrentOptimum",
  89                 "CurrentOptimum",
  90                 "CurrentState",
  91                 "IndexOfOptimum",
  92                 "Innovation",
  93                 "InnovationAtCurrentState",
  94                 "MahalanobisConsistency",
  95                 "OMA",
  96                 "OMB",
  97                 "SigmaObs2",
  98                 "SimulatedObservationAtBackground",
  99                 "SimulatedObservationAtCurrentOptimum",
 100                 "SimulatedObservationAtCurrentState",
 101                 "SimulatedObservationAtOptimum",
 102                 "SimulationQuantiles",
 103                 ]
 104             )
 105         self.defineRequiredParameter(
 106             name     = "Quantiles",
 107             default  = [],
 108             typecast = tuple,
 109             message  = "Liste des valeurs de quantiles",
 110             minval   = 0.,
 111             maxval   = 1.,
 112             )
 113         self.defineRequiredParameter(
 114             name     = "SetSeed",
 115             typecast = numpy.random.seed,
 116             message  = "Graine fixée pour le générateur aléatoire",
 117             )
 118         self.defineRequiredParameter(
 119             name     = "NumberOfSamplesForQuantiles",
 120             default  = 100,
 121             typecast = int,
 122             message  = "Nombre d'échantillons simulés pour le calcul des quantiles",
 123             minval   = 1,
 124             )
 125         self.defineRequiredParameter(
 126             name     = "SimulationForQuantiles",
 127             default  = "Linear",
 128             typecast = str,
 129             message  = "Type de simulation pour l'estimation des quantiles",
 130             listval  = ["Linear", "NonLinear"]
 131             )
 132         self.defineRequiredParameter( # Pas de type
 133             name     = "Bounds",
 134             message  = "Liste des valeurs de bornes",
 135             )
 136         self.requireInputArguments(
 137             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 138             )
 139
 140     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 141         self._pre_run(Parameters, Xb, Y, R, B, Q)
 142         #
 143         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 144         if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
 145             self.setParameterValue("StoreInternalVariables",True)
 146         #
 147         # Opérateurs
 148         # ----------
 149         Hm = HO["Direct"].appliedTo
 150         Ha = HO["Adjoint"].appliedInXTo
 151         #
 152         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 153         # ----------------------------------------------------
 154         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 155             HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
 156         else:
 157             HXb = Hm( Xb )
 158         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 159         if Y.size != HXb.size:
 160             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))
 161         if max(Y.shape) != max(HXb.shape):
 162             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))
 163         #
 164         # Précalcul des inversions de B et R
 165         # ----------------------------------
 166         BI = B.getI()
 167         RI = R.getI()
 168         #
 169         # Définition de la fonction-coût
 170         # ------------------------------
 171         def CostFunction(x):
 172             _X  = numpy.asmatrix(numpy.ravel( x )).T
 173             if self._parameters["StoreInternalVariables"] or \
 174                 self._toStore("CurrentState") or \
 175                 self._toStore("CurrentOptimum"):
 176                 self.StoredVariables["CurrentState"].store( _X )
 177             _HX = Hm( _X )
 178             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 179             _Innovation = Y - _HX
 180             if self._toStore("SimulatedObservationAtCurrentState") or \
 181                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 182                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 183             if self._toStore("InnovationAtCurrentState"):
 184                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 185             #
 186             Jb  = float( 0.5 * (_X - Xb).T * BI * (_X - Xb) )
 187             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 188             J   = Jb + Jo
 189             #
 190             self.StoredVariables["CostFunctionJb"].store( Jb )
 191             self.StoredVariables["CostFunctionJo"].store( Jo )
 192             self.StoredVariables["CostFunctionJ" ].store( J )
 193             if self._toStore("IndexOfOptimum") or \
 194                 self._toStore("CurrentOptimum") or \
 195                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 196                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 197                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 198                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 199                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 200             if self._toStore("IndexOfOptimum"):
 201                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 202             if self._toStore("CurrentOptimum"):
 203                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 204             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 205                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 206             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 207                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 208             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 209                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 210             if self._toStore("CostFunctionJAtCurrentOptimum"):
 211                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 212             return J
 213         #
 214         def GradientOfCostFunction(x):
 215             _X      = numpy.asmatrix(numpy.ravel( x )).T
 216             _HX     = Hm( _X )
 217             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 218             GradJb  = BI * (_X - Xb)
 219             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 220             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 221             return GradJ.A1
 222         #
 223         # Point de démarrage de l'optimisation : Xini = Xb
 224         # ------------------------------------
 225         Xini = numpy.ravel(Xb)
 226         #
 227         # Minimisation de la fonctionnelle
 228         # --------------------------------
 229         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 230         #
 231         if self._parameters["Minimizer"] == "LBFGSB":
 232             # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 233             import lbfgsbhlt
 234             Minimum, J_optimal, Informations = lbfgsbhlt.fmin_l_bfgs_b(
 235                 func        = CostFunction,
 236                 x0          = Xini,
 237                 fprime      = GradientOfCostFunction,
 238                 args        = (),
 239                 bounds      = self._parameters["Bounds"],
 240                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 241                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 242                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 243                 iprint      = self._parameters["optiprint"],
 244                 )
 245             nfeval = Informations['funcalls']
 246             rc     = Informations['warnflag']
 247         elif self._parameters["Minimizer"] == "TNC":
 248             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 249                 func        = CostFunction,
 250                 x0          = Xini,
 251                 fprime      = GradientOfCostFunction,
 252                 args        = (),
 253                 bounds      = self._parameters["Bounds"],
 254                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 255                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 256                 ftol        = self._parameters["CostDecrementTolerance"],
 257                 messages    = self._parameters["optmessages"],
 258                 )
 259         elif self._parameters["Minimizer"] == "CG":
 260             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 261                 f           = CostFunction,
 262                 x0          = Xini,
 263                 fprime      = GradientOfCostFunction,
 264                 args        = (),
 265                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 266                 gtol        = self._parameters["GradientNormTolerance"],
 267                 disp        = self._parameters["optdisp"],
 268                 full_output = True,
 269                 )
 270         elif self._parameters["Minimizer"] == "NCG":
 271             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 272                 f           = CostFunction,
 273                 x0          = Xini,
 274                 fprime      = GradientOfCostFunction,
 275                 args        = (),
 276                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 277                 avextol     = self._parameters["CostDecrementTolerance"],
 278                 disp        = self._parameters["optdisp"],
 279                 full_output = True,
 280                 )
 281         elif self._parameters["Minimizer"] == "BFGS":
 282             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 283                 f           = CostFunction,
 284                 x0          = Xini,
 285                 fprime      = GradientOfCostFunction,
 286                 args        = (),
 287                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 288                 gtol        = self._parameters["GradientNormTolerance"],
 289                 disp        = self._parameters["optdisp"],
 290                 full_output = True,
 291                 )
 292         else:
 293             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 294         #
 295         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 296         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 297         #
 298         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 299         # ----------------------------------------------------------------
 300         if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
 301             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 302         #
 303         # Obtention de l'analyse
 304         # ----------------------
 305         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 306         #
 307         self.StoredVariables["Analysis"].store( Xa.A1 )
 308         #
 309         if self._toStore("OMA") or \
 310             self._toStore("SigmaObs2") or \
 311             self._toStore("SimulationQuantiles") or \
 312             self._toStore("SimulatedObservationAtOptimum"):
 313             if self._toStore("SimulatedObservationAtCurrentState"):
 314                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 315             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 316                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 317             else:
 318                 HXa = Hm( Xa )
 319         #
 320         # Calcul de la covariance d'analyse
 321         # ---------------------------------
 322         if self._toStore("APosterioriCovariance") or \
 323            self._toStore("SimulationQuantiles"):
 324             HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 325             HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 326             HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 327             HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 328             HessienneI = []
 329             nb = Xa.size
 330             for i in range(nb):
 331                 _ee    = numpy.matrix(numpy.zeros(nb)).T
 332                 _ee[i] = 1.
 333                 _HtEE  = numpy.dot(HtM,_ee)
 334                 _HtEE  = numpy.asmatrix(numpy.ravel( _HtEE )).T
 335                 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
 336             HessienneI = numpy.matrix( HessienneI )
 337             A = HessienneI.I
 338             if min(A.shape) != max(A.shape):
 339                 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)))
 340             if (numpy.diag(A) < 0).any():
 341                 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,))
 342             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 343                 try:
 344                     L = numpy.linalg.cholesky( A )
 345                 except:
 346                     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,))
 347         if self._toStore("APosterioriCovariance"):
 348             self.StoredVariables["APosterioriCovariance"].store( A )
 349         #
 350         # Calculs et/ou stockages supplémentaires
 351         # ---------------------------------------
 352         if self._toStore("Innovation") or \
 353             self._toStore("SigmaObs2") or \
 354             self._toStore("MahalanobisConsistency") or \
 355             self._toStore("OMB"):
 356             d  = Y - HXb
 357         if self._toStore("Innovation"):
 358             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 359         if self._toStore("BMA"):
 360             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 361         if self._toStore("OMA"):
 362             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 363         if self._toStore("OMB"):
 364             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 365         if self._toStore("SigmaObs2"):
 366             TraceR = R.trace(Y.size)
 367             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
 368         if self._toStore("MahalanobisConsistency"):
 369             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
 370         if self._toStore("SimulationQuantiles"):
 371             nech = self._parameters["NumberOfSamplesForQuantiles"]
 372             HXa  = numpy.matrix(numpy.ravel( HXa )).T
 373             YfQ  = None
 374             for i in range(nech):
 375                 if self._parameters["SimulationForQuantiles"] == "Linear":
 376                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 377                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 378                     Yr = HXa + dYr
 379                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 380                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 381                     Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
 382                 if YfQ is None:
 383                     YfQ = Yr
 384                 else:
 385                     YfQ = numpy.hstack((YfQ,Yr))
 386             YfQ.sort(axis=-1)
 387             YQ = None
 388             for quantile in self._parameters["Quantiles"]:
 389                 if not (0. <= float(quantile) <= 1.): continue
 390                 indice = int(nech * float(quantile) - 1./nech)
 391                 if YQ is None: YQ = YfQ[:,indice]
 392                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 393             self.StoredVariables["SimulationQuantiles"].store( YQ )
 394         if self._toStore("SimulatedObservationAtBackground"):
 395             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 396         if self._toStore("SimulatedObservationAtOptimum"):
 397             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 398         #
 399         self._post_run(HO)
 400         return 0
 401
 402 # ==============================================================================
 403 if __name__ == "__main__":
 404     print('\n AUTODIAGNOSTIC \n')