src/daComposant/daAlgorithms/Atoms/std3dvar.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2022 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 __doc__ = """
  24     3DVAR
  25 """
  26 __author__ = "Jean-Philippe ARGAUD"
  27
  28 import numpy, scipy, scipy.optimize, scipy.version
  29 from daCore.NumericObjects import HessienneEstimation, QuantilesEstimations
  30
  31 # ==============================================================================
  32 def std3dvar(selfA, Xb, Y, U, HO, CM, R, B, __storeState = False):
  33     """
  34     Correction
  35     """
  36     #
  37     # Initialisations
  38     # ---------------
  39     Hm = HO["Direct"].appliedTo
  40     Ha = HO["Adjoint"].appliedInXTo
  41     #
  42     if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
  43         HXb = numpy.asarray(Hm( Xb, HO["AppliedInX"]["HXb"] ))
  44     else:
  45         HXb = numpy.asarray(Hm( Xb ))
  46     HXb = HXb.reshape((-1,1))
  47     if Y.size != HXb.size:
  48         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))
  49     if max(Y.shape) != max(HXb.shape):
  50         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))
  51     #
  52     if selfA._toStore("JacobianMatrixAtBackground"):
  53         HtMb = HO["Tangent"].asMatrix(Xb)
  54         HtMb = HtMb.reshape(Y.size,Xb.size) # ADAO & check shape
  55         selfA.StoredVariables["JacobianMatrixAtBackground"].store( HtMb )
  56     #
  57     BI = B.getI()
  58     RI = R.getI()
  59     #
  60     Xini = selfA._parameters["InitializationPoint"]
  61     #
  62     # Définition de la fonction-coût
  63     # ------------------------------
  64     def CostFunction(x):
  65         _X  = numpy.asarray(x).reshape((-1,1))
  66         if selfA._parameters["StoreInternalVariables"] or \
  67             selfA._toStore("CurrentState") or \
  68             selfA._toStore("CurrentOptimum"):
  69             selfA.StoredVariables["CurrentState"].store( _X )
  70         _HX = numpy.asarray(Hm( _X )).reshape((-1,1))
  71         _Innovation = Y - _HX
  72         if selfA._toStore("SimulatedObservationAtCurrentState") or \
  73             selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  74             selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
  75         if selfA._toStore("InnovationAtCurrentState"):
  76             selfA.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
  77         #
  78         Jb  = float( 0.5 * (_X - Xb).T * (BI * (_X - Xb)) )
  79         Jo  = float( 0.5 * _Innovation.T * (RI * _Innovation) )
  80         J   = Jb + Jo
  81         #
  82         selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["CostFunctionJ"]) )
  83         selfA.StoredVariables["CostFunctionJb"].store( Jb )
  84         selfA.StoredVariables["CostFunctionJo"].store( Jo )
  85         selfA.StoredVariables["CostFunctionJ" ].store( J )
  86         if selfA._toStore("IndexOfOptimum") or \
  87             selfA._toStore("CurrentOptimum") or \
  88             selfA._toStore("CostFunctionJAtCurrentOptimum") or \
  89             selfA._toStore("CostFunctionJbAtCurrentOptimum") or \
  90             selfA._toStore("CostFunctionJoAtCurrentOptimum") or \
  91             selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  92             IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
  93         if selfA._toStore("IndexOfOptimum"):
  94             selfA.StoredVariables["IndexOfOptimum"].store( IndexMin )
  95         if selfA._toStore("CurrentOptimum"):
  96             selfA.StoredVariables["CurrentOptimum"].store( selfA.StoredVariables["CurrentState"][IndexMin] )
  97         if selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  98             selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
  99         if selfA._toStore("CostFunctionJbAtCurrentOptimum"):
 100             selfA.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJb"][IndexMin] )
 101         if selfA._toStore("CostFunctionJoAtCurrentOptimum"):
 102             selfA.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJo"][IndexMin] )
 103         if selfA._toStore("CostFunctionJAtCurrentOptimum"):
 104             selfA.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( selfA.StoredVariables["CostFunctionJ" ][IndexMin] )
 105         return J
 106     #
 107     def GradientOfCostFunction(x):
 108         _X      = numpy.asarray(x).reshape((-1,1))
 109         _HX     = numpy.asarray(Hm( _X )).reshape((-1,1))
 110         GradJb  = BI * (_X - Xb)
 111         GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 112         GradJ   = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
 113         return GradJ
 114     #
 115     # Minimisation de la fonctionnelle
 116     # --------------------------------
 117     nbPreviousSteps = selfA.StoredVariables["CostFunctionJ"].stepnumber()
 118     #
 119     if selfA._parameters["Minimizer"] == "LBFGSB":
 120         if "0.19" <= scipy.version.version <= "1.4.99":
 121             import daAlgorithms.Atoms.lbfgsb14hlt as optimiseur
 122         elif "1.5.0" <= scipy.version.version <= "1.7.99":
 123             import daAlgorithms.Atoms.lbfgsb17hlt as optimiseur
 124         elif "1.8.0" <= scipy.version.version <= "1.8.99":
 125             import daAlgorithms.Atoms.lbfgsb18hlt as optimiseur
 126         elif "1.9.0" <= scipy.version.version <= "1.9.99":
 127             import daAlgorithms.Atoms.lbfgsb19hlt as optimiseur
 128         else:
 129             import scipy.optimize as optimiseur
 130         Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 131             func        = CostFunction,
 132             x0          = Xini,
 133             fprime      = GradientOfCostFunction,
 134             args        = (),
 135             bounds      = selfA._parameters["Bounds"],
 136             maxfun      = selfA._parameters["MaximumNumberOfIterations"]-1,
 137             factr       = selfA._parameters["CostDecrementTolerance"]*1.e14,
 138             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 139             iprint      = selfA._parameters["optiprint"],
 140             )
 141         # nfeval = Informations['funcalls']
 142         # rc     = Informations['warnflag']
 143     elif selfA._parameters["Minimizer"] == "TNC":
 144         Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 145             func        = CostFunction,
 146             x0          = Xini,
 147             fprime      = GradientOfCostFunction,
 148             args        = (),
 149             bounds      = selfA._parameters["Bounds"],
 150             maxfun      = selfA._parameters["MaximumNumberOfIterations"],
 151             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 152             ftol        = selfA._parameters["CostDecrementTolerance"],
 153             messages    = selfA._parameters["optmessages"],
 154             )
 155     elif selfA._parameters["Minimizer"] == "CG":
 156         Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 157             f           = CostFunction,
 158             x0          = Xini,
 159             fprime      = GradientOfCostFunction,
 160             args        = (),
 161             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 162             gtol        = selfA._parameters["GradientNormTolerance"],
 163             disp        = selfA._parameters["optdisp"],
 164             full_output = True,
 165             )
 166     elif selfA._parameters["Minimizer"] == "NCG":
 167         Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 168             f           = CostFunction,
 169             x0          = Xini,
 170             fprime      = GradientOfCostFunction,
 171             args        = (),
 172             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 173             avextol     = selfA._parameters["CostDecrementTolerance"],
 174             disp        = selfA._parameters["optdisp"],
 175             full_output = True,
 176             )
 177     elif selfA._parameters["Minimizer"] == "BFGS":
 178         Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 179             f           = CostFunction,
 180             x0          = Xini,
 181             fprime      = GradientOfCostFunction,
 182             args        = (),
 183             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 184             gtol        = selfA._parameters["GradientNormTolerance"],
 185             disp        = selfA._parameters["optdisp"],
 186             full_output = True,
 187             )
 188     else:
 189         raise ValueError("Error in minimizer name: %s is unkown"%selfA._parameters["Minimizer"])
 190     #
 191     IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 192     MinJ     = selfA.StoredVariables["CostFunctionJ"][IndexMin]
 193     #
 194     # Correction pour pallier a un bug de TNC sur le retour du Minimum
 195     # ----------------------------------------------------------------
 196     if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
 197         Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
 198     #
 199     Xa = Minimum
 200     if __storeState: selfA._setInternalState("Xn", Xa)
 201     #--------------------------
 202     #
 203     selfA.StoredVariables["Analysis"].store( Xa )
 204     #
 205     if selfA._toStore("OMA") or \
 206         selfA._toStore("InnovationAtCurrentAnalysis") or \
 207         selfA._toStore("SigmaObs2") or \
 208         selfA._toStore("SimulationQuantiles") or \
 209         selfA._toStore("SimulatedObservationAtOptimum"):
 210         if selfA._toStore("SimulatedObservationAtCurrentState"):
 211             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 212         elif selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 213             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 214         else:
 215             HXa = Hm( Xa )
 216         oma = Y - HXa.reshape((-1,1))
 217     #
 218     if selfA._toStore("APosterioriCovariance") or \
 219         selfA._toStore("SimulationQuantiles") or \
 220         selfA._toStore("JacobianMatrixAtOptimum") or \
 221         selfA._toStore("KalmanGainAtOptimum"):
 222         HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 223         HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 224     if selfA._toStore("APosterioriCovariance") or \
 225         selfA._toStore("SimulationQuantiles") or \
 226         selfA._toStore("KalmanGainAtOptimum"):
 227         HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 228         HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 229     if selfA._toStore("APosterioriCovariance") or \
 230         selfA._toStore("SimulationQuantiles"):
 231         A = HessienneEstimation(selfA, Xa.size, HaM, HtM, BI, RI)
 232     if selfA._toStore("APosterioriCovariance"):
 233         selfA.StoredVariables["APosterioriCovariance"].store( A )
 234     if selfA._toStore("JacobianMatrixAtOptimum"):
 235         selfA.StoredVariables["JacobianMatrixAtOptimum"].store( HtM )
 236     if selfA._toStore("KalmanGainAtOptimum"):
 237         if   (Y.size <= Xb.size): KG  = B * HaM * (R + numpy.dot(HtM, B * HaM)).I
 238         elif (Y.size >  Xb.size): KG = (BI + numpy.dot(HaM, RI * HtM)).I * HaM * RI
 239         selfA.StoredVariables["KalmanGainAtOptimum"].store( KG )
 240     #
 241     # Calculs et/ou stockages supplémentaires
 242     # ---------------------------------------
 243     if selfA._toStore("Innovation") or \
 244         selfA._toStore("SigmaObs2") or \
 245         selfA._toStore("MahalanobisConsistency") or \
 246         selfA._toStore("OMB"):
 247         Innovation  = Y - HXb
 248     if selfA._toStore("Innovation"):
 249         selfA.StoredVariables["Innovation"].store( Innovation )
 250     if selfA._toStore("BMA"):
 251         selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 252     if selfA._toStore("OMA"):
 253         selfA.StoredVariables["OMA"].store( oma )
 254     if selfA._toStore("InnovationAtCurrentAnalysis"):
 255         selfA.StoredVariables["InnovationAtCurrentAnalysis"].store( oma )
 256     if selfA._toStore("OMB"):
 257         selfA.StoredVariables["OMB"].store( Innovation )
 258     if selfA._toStore("SigmaObs2"):
 259         TraceR = R.trace(Y.size)
 260         selfA.StoredVariables["SigmaObs2"].store( float( (Innovation.T @ oma) ) / TraceR )
 261     if selfA._toStore("MahalanobisConsistency"):
 262         selfA.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/Innovation.size ) )
 263     if selfA._toStore("SimulationQuantiles"):
 264         QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
 265     if selfA._toStore("SimulatedObservationAtBackground"):
 266         selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
 267     if selfA._toStore("SimulatedObservationAtOptimum"):
 268         selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
 269     #
 270     return 0
 271
 272 # ==============================================================================
 273 if __name__ == "__main__":
 274     print('\n AUTODIAGNOSTIC\n')