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                 "Analysis",
  79                 "APosterioriCorrelations",
  80                 "APosterioriCovariance",
  81                 "APosterioriStandardDeviations",
  82                 "APosterioriVariances",
  83                 "BMA",
  84                 "CostFunctionJ",
  85                 "CostFunctionJAtCurrentOptimum",
  86                 "CostFunctionJb",
  87                 "CostFunctionJbAtCurrentOptimum",
  88                 "CostFunctionJo",
  89                 "CostFunctionJoAtCurrentOptimum",
  90                 "CurrentOptimum",
  91                 "CurrentState",
  92                 "IndexOfOptimum",
  93                 "Innovation",
  94                 "InnovationAtCurrentState",
  95                 "JacobianMatrixAtBackground",
  96                 "JacobianMatrixAtOptimum",
  97                 "KalmanGainAtOptimum",
  98                 "MahalanobisConsistency",
  99                 "OMA",
 100                 "OMB",
 101                 "SigmaObs2",
 102                 "SimulatedObservationAtBackground",
 103                 "SimulatedObservationAtCurrentOptimum",
 104                 "SimulatedObservationAtCurrentState",
 105                 "SimulatedObservationAtOptimum",
 106                 "SimulationQuantiles",
 107                 ]
 108             )
 109         self.defineRequiredParameter(
 110             name     = "Quantiles",
 111             default  = [],
 112             typecast = tuple,
 113             message  = "Liste des valeurs de quantiles",
 114             minval   = 0.,
 115             maxval   = 1.,
 116             )
 117         self.defineRequiredParameter(
 118             name     = "SetSeed",
 119             typecast = numpy.random.seed,
 120             message  = "Graine fixée pour le générateur aléatoire",
 121             )
 122         self.defineRequiredParameter(
 123             name     = "NumberOfSamplesForQuantiles",
 124             default  = 100,
 125             typecast = int,
 126             message  = "Nombre d'échantillons simulés pour le calcul des quantiles",
 127             minval   = 1,
 128             )
 129         self.defineRequiredParameter(
 130             name     = "SimulationForQuantiles",
 131             default  = "Linear",
 132             typecast = str,
 133             message  = "Type de simulation pour l'estimation des quantiles",
 134             listval  = ["Linear", "NonLinear"]
 135             )
 136         self.defineRequiredParameter( # Pas de type
 137             name     = "Bounds",
 138             message  = "Liste des valeurs de bornes",
 139             )
 140         self.requireInputArguments(
 141             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 142             )
 143
 144     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 145         self._pre_run(Parameters, Xb, Y, R, B, Q)
 146         #
 147         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 148         if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
 149             self.setParameterValue("StoreInternalVariables",True)
 150         #
 151         # Opérateurs
 152         # ----------
 153         Hm = HO["Direct"].appliedTo
 154         Ha = HO["Adjoint"].appliedInXTo
 155         #
 156         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
 157         # ----------------------------------------------------
 158         if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
 159             HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
 160         else:
 161             HXb = Hm( Xb )
 162         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 163         if Y.size != HXb.size:
 164             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))
 165         if max(Y.shape) != max(HXb.shape):
 166             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))
 167         #
 168         if self._toStore("JacobianMatrixAtBackground"):
 169             HtMb = HO["Tangent"].asMatrix(ValueForMethodForm = Xb)
 170             HtMb = HtMb.reshape(Y.size,Xb.size) # ADAO & check shape
 171             self.StoredVariables["JacobianMatrixAtBackground"].store( HtMb )
 172         #
 173         # Précalcul des inversions de B et R
 174         # ----------------------------------
 175         BI = B.getI()
 176         RI = R.getI()
 177         #
 178         # Définition de la fonction-coût
 179         # ------------------------------
 180         def CostFunction(x):
 181             _X  = numpy.asmatrix(numpy.ravel( x )).T
 182             if self._parameters["StoreInternalVariables"] or \
 183                 self._toStore("CurrentState") or \
 184                 self._toStore("CurrentOptimum"):
 185                 self.StoredVariables["CurrentState"].store( _X )
 186             _HX = Hm( _X )
 187             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 188             _Innovation = Y - _HX
 189             if self._toStore("SimulatedObservationAtCurrentState") or \
 190                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 191                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 192             if self._toStore("InnovationAtCurrentState"):
 193                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 194             #
 195             Jb  = float( 0.5 * (_X - Xb).T * BI * (_X - Xb) )
 196             Jo  = float( 0.5 * _Innovation.T * RI * _Innovation )
 197             J   = Jb + Jo
 198             #
 199             self.StoredVariables["CostFunctionJb"].store( Jb )
 200             self.StoredVariables["CostFunctionJo"].store( Jo )
 201             self.StoredVariables["CostFunctionJ" ].store( J )
 202             if self._toStore("IndexOfOptimum") or \
 203                 self._toStore("CurrentOptimum") or \
 204                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 205                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 206                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 207                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 208                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 209             if self._toStore("IndexOfOptimum"):
 210                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 211             if self._toStore("CurrentOptimum"):
 212                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 213             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 214                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 215             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 216                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 217             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 218                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 219             if self._toStore("CostFunctionJAtCurrentOptimum"):
 220                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 221             return J
 222         #
 223         def GradientOfCostFunction(x):
 224             _X      = numpy.asmatrix(numpy.ravel( x )).T
 225             _HX     = Hm( _X )
 226             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 227             GradJb  = BI * (_X - Xb)
 228             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 229             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 230             return GradJ.A1
 231         #
 232         # Point de démarrage de l'optimisation : Xini = Xb
 233         # ------------------------------------
 234         Xini = numpy.ravel(Xb)
 235         #
 236         # Minimisation de la fonctionnelle
 237         # --------------------------------
 238         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 239         #
 240         if self._parameters["Minimizer"] == "LBFGSB":
 241             # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 242             import lbfgsbhlt
 243             Minimum, J_optimal, Informations = lbfgsbhlt.fmin_l_bfgs_b(
 244                 func        = CostFunction,
 245                 x0          = Xini,
 246                 fprime      = GradientOfCostFunction,
 247                 args        = (),
 248                 bounds      = self._parameters["Bounds"],
 249                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 250                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 251                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 252                 iprint      = self._parameters["optiprint"],
 253                 )
 254             nfeval = Informations['funcalls']
 255             rc     = Informations['warnflag']
 256         elif self._parameters["Minimizer"] == "TNC":
 257             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 258                 func        = CostFunction,
 259                 x0          = Xini,
 260                 fprime      = GradientOfCostFunction,
 261                 args        = (),
 262                 bounds      = self._parameters["Bounds"],
 263                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 264                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 265                 ftol        = self._parameters["CostDecrementTolerance"],
 266                 messages    = self._parameters["optmessages"],
 267                 )
 268         elif self._parameters["Minimizer"] == "CG":
 269             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 270                 f           = CostFunction,
 271                 x0          = Xini,
 272                 fprime      = GradientOfCostFunction,
 273                 args        = (),
 274                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 275                 gtol        = self._parameters["GradientNormTolerance"],
 276                 disp        = self._parameters["optdisp"],
 277                 full_output = True,
 278                 )
 279         elif self._parameters["Minimizer"] == "NCG":
 280             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 281                 f           = CostFunction,
 282                 x0          = Xini,
 283                 fprime      = GradientOfCostFunction,
 284                 args        = (),
 285                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 286                 avextol     = self._parameters["CostDecrementTolerance"],
 287                 disp        = self._parameters["optdisp"],
 288                 full_output = True,
 289                 )
 290         elif self._parameters["Minimizer"] == "BFGS":
 291             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 292                 f           = CostFunction,
 293                 x0          = Xini,
 294                 fprime      = GradientOfCostFunction,
 295                 args        = (),
 296                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 297                 gtol        = self._parameters["GradientNormTolerance"],
 298                 disp        = self._parameters["optdisp"],
 299                 full_output = True,
 300                 )
 301         else:
 302             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 303         #
 304         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 305         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 306         #
 307         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 308         # ----------------------------------------------------------------
 309         if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
 310             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 311         #
 312         # Obtention de l'analyse
 313         # ----------------------
 314         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 315         #
 316         self.StoredVariables["Analysis"].store( Xa.A1 )
 317         #
 318         if self._toStore("OMA") or \
 319             self._toStore("SigmaObs2") or \
 320             self._toStore("SimulationQuantiles") or \
 321             self._toStore("SimulatedObservationAtOptimum"):
 322             if self._toStore("SimulatedObservationAtCurrentState"):
 323                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 324             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 325                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 326             else:
 327                 HXa = Hm( Xa )
 328         #
 329         # Calcul de la covariance d'analyse
 330         # ---------------------------------
 331         if self._toStore("APosterioriCovariance") or \
 332             self._toStore("SimulationQuantiles") or \
 333             self._toStore("JacobianMatrixAtOptimum") or \
 334             self._toStore("KalmanGainAtOptimum"):
 335             HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 336             HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 337         if self._toStore("APosterioriCovariance") or \
 338             self._toStore("SimulationQuantiles") or \
 339             self._toStore("KalmanGainAtOptimum"):
 340             HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 341             HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 342         if self._toStore("APosterioriCovariance") or \
 343             self._toStore("SimulationQuantiles"):
 344             HessienneI = []
 345             nb = Xa.size
 346             for i in range(nb):
 347                 _ee    = numpy.matrix(numpy.zeros(nb)).T
 348                 _ee[i] = 1.
 349                 _HtEE  = numpy.dot(HtM,_ee)
 350                 _HtEE  = numpy.asmatrix(numpy.ravel( _HtEE )).T
 351                 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
 352             HessienneI = numpy.matrix( HessienneI )
 353             A = HessienneI.I
 354             if min(A.shape) != max(A.shape):
 355                 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)))
 356             if (numpy.diag(A) < 0).any():
 357                 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,))
 358             if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
 359                 try:
 360                     L = numpy.linalg.cholesky( A )
 361                 except:
 362                     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,))
 363         if self._toStore("APosterioriCovariance"):
 364             self.StoredVariables["APosterioriCovariance"].store( A )
 365         if self._toStore("JacobianMatrixAtOptimum"):
 366             self.StoredVariables["JacobianMatrixAtOptimum"].store( HtM )
 367         if self._toStore("KalmanGainAtOptimum"):
 368             if   (Y.size <= Xb.size): KG  = B * HaM * (R + numpy.dot(HtM, B * HaM)).I
 369             elif (Y.size >  Xb.size): KG = (BI + numpy.dot(HaM, RI * HtM)).I * HaM * RI
 370             self.StoredVariables["KalmanGainAtOptimum"].store( KG )
 371         #
 372         # Calculs et/ou stockages supplémentaires
 373         # ---------------------------------------
 374         if self._toStore("Innovation") or \
 375             self._toStore("SigmaObs2") or \
 376             self._toStore("MahalanobisConsistency") or \
 377             self._toStore("OMB"):
 378             d  = Y - HXb
 379         if self._toStore("Innovation"):
 380             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 381         if self._toStore("BMA"):
 382             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 383         if self._toStore("OMA"):
 384             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 385         if self._toStore("OMB"):
 386             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 387         if self._toStore("SigmaObs2"):
 388             TraceR = R.trace(Y.size)
 389             self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
 390         if self._toStore("MahalanobisConsistency"):
 391             self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
 392         if self._toStore("SimulationQuantiles"):
 393             nech = self._parameters["NumberOfSamplesForQuantiles"]
 394             HXa  = numpy.matrix(numpy.ravel( HXa )).T
 395             YfQ  = None
 396             for i in range(nech):
 397                 if self._parameters["SimulationForQuantiles"] == "Linear":
 398                     dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
 399                     dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
 400                     Yr = HXa + dYr
 401                 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
 402                     Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
 403                     Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
 404                 if YfQ is None:
 405                     YfQ = Yr
 406                 else:
 407                     YfQ = numpy.hstack((YfQ,Yr))
 408             YfQ.sort(axis=-1)
 409             YQ = None
 410             for quantile in self._parameters["Quantiles"]:
 411                 if not (0. <= float(quantile) <= 1.): continue
 412                 indice = int(nech * float(quantile) - 1./nech)
 413                 if YQ is None: YQ = YfQ[:,indice]
 414                 else:          YQ = numpy.hstack((YQ,YfQ[:,indice]))
 415             self.StoredVariables["SimulationQuantiles"].store( YQ )
 416         if self._toStore("SimulatedObservationAtBackground"):
 417             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
 418         if self._toStore("SimulatedObservationAtOptimum"):
 419             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 420         #
 421         self._post_run(HO)
 422         return 0
 423
 424 # ==============================================================================
 425 if __name__ == "__main__":
 426     print('\n AUTODIAGNOSTIC \n')