src/daComposant/daAlgorithms/Atoms/van3dvar.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 variational analysis with no inversion of B
  25 """
  26 __author__ = "Jean-Philippe ARGAUD"
  27
  28 import numpy, scipy, scipy.optimize, scipy.version
  29 from daCore.NumericObjects import HessienneEstimation, QuantilesEstimations
  30 from daCore.NumericObjects import RecentredBounds
  31 from daCore.PlatformInfo import PlatformInfo
  32 mpr = PlatformInfo().MachinePrecision()
  33
  34 # ==============================================================================
  35 def van3dvar(selfA, Xb, Y, U, HO, CM, R, B, __storeState = False):
  36     """
  37     Correction
  38     """
  39     #
  40     # Initialisations
  41     # ---------------
  42     Hm = HO["Direct"].appliedTo
  43     Ha = HO["Adjoint"].appliedInXTo
  44     #
  45     if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
  46         HXb = numpy.asarray(Hm( Xb, HO["AppliedInX"]["HXb"] ))
  47     else:
  48         HXb = numpy.asarray(Hm( Xb ))
  49     HXb = HXb.reshape((-1,1))
  50     if Y.size != HXb.size:
  51         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))
  52     if max(Y.shape) != max(HXb.shape):
  53         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))
  54     #
  55     if selfA._toStore("JacobianMatrixAtBackground"):
  56         HtMb = HO["Tangent"].asMatrix(ValueForMethodForm = Xb)
  57         HtMb = HtMb.reshape(Y.size,Xb.size) # ADAO & check shape
  58         selfA.StoredVariables["JacobianMatrixAtBackground"].store( HtMb )
  59     #
  60     BT = B.getT()
  61     RI = R.getI()
  62     if ("Bounds" in selfA._parameters) and selfA._parameters["Bounds"] is not None:
  63         BI = B.getI()
  64     else:
  65         BI = None
  66     #
  67     Xini = numpy.zeros(Xb.size)
  68     #
  69     # Définition de la fonction-coût
  70     # ------------------------------
  71     def CostFunction(v):
  72         _V = numpy.asarray(v).reshape((-1,1))
  73         _X = Xb + (B @ _V).reshape((-1,1))
  74         if selfA._parameters["StoreInternalVariables"] or \
  75             selfA._toStore("CurrentState") or \
  76             selfA._toStore("CurrentOptimum"):
  77             selfA.StoredVariables["CurrentState"].store( _X )
  78         _HX = numpy.asarray(Hm( _X )).reshape((-1,1))
  79         _Innovation = Y - _HX
  80         if selfA._toStore("SimulatedObservationAtCurrentState") or \
  81             selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  82             selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
  83         if selfA._toStore("InnovationAtCurrentState"):
  84             selfA.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
  85         #
  86         Jb  = float( 0.5 * _V.T * (BT * _V) )
  87         Jo  = float( 0.5 * _Innovation.T * (RI * _Innovation) )
  88         J   = Jb + Jo
  89         #
  90         selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["CostFunctionJ"]) )
  91         selfA.StoredVariables["CostFunctionJb"].store( Jb )
  92         selfA.StoredVariables["CostFunctionJo"].store( Jo )
  93         selfA.StoredVariables["CostFunctionJ" ].store( J )
  94         if selfA._toStore("IndexOfOptimum") or \
  95             selfA._toStore("CurrentOptimum") or \
  96             selfA._toStore("CostFunctionJAtCurrentOptimum") or \
  97             selfA._toStore("CostFunctionJbAtCurrentOptimum") or \
  98             selfA._toStore("CostFunctionJoAtCurrentOptimum") or \
  99             selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 100             IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 101         if selfA._toStore("IndexOfOptimum"):
 102             selfA.StoredVariables["IndexOfOptimum"].store( IndexMin )
 103         if selfA._toStore("CurrentOptimum"):
 104             selfA.StoredVariables["CurrentOptimum"].store( selfA.StoredVariables["CurrentState"][IndexMin] )
 105         if selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 106             selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 107         if selfA._toStore("CostFunctionJbAtCurrentOptimum"):
 108             selfA.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJb"][IndexMin] )
 109         if selfA._toStore("CostFunctionJoAtCurrentOptimum"):
 110             selfA.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJo"][IndexMin] )
 111         if selfA._toStore("CostFunctionJAtCurrentOptimum"):
 112             selfA.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( selfA.StoredVariables["CostFunctionJ" ][IndexMin] )
 113         return J
 114     #
 115     def GradientOfCostFunction(v):
 116         _V = numpy.asarray(v).reshape((-1,1))
 117         _X = Xb + (B @ _V).reshape((-1,1))
 118         _HX     = numpy.asarray(Hm( _X )).reshape((-1,1))
 119         GradJb  = BT * _V
 120         GradJo  = - BT * Ha( (_X, RI * (Y - _HX)) )
 121         GradJ   = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
 122         return GradJ
 123     #
 124     # Minimisation de la fonctionnelle
 125     # --------------------------------
 126     nbPreviousSteps = selfA.StoredVariables["CostFunctionJ"].stepnumber()
 127     #
 128     if selfA._parameters["Minimizer"] == "LBFGSB":
 129         if "0.19" <= scipy.version.version <= "1.4.99":
 130             import daAlgorithms.Atoms.lbfgsb14hlt as optimiseur
 131         elif "1.5.0" <= scipy.version.version <= "1.7.99":
 132             import daAlgorithms.Atoms.lbfgsb17hlt as optimiseur
 133         elif "1.8.0" <= scipy.version.version <= "1.8.99":
 134             import daAlgorithms.Atoms.lbfgsb18hlt as optimiseur
 135         elif "1.9.0" <= scipy.version.version <= "1.9.99":
 136             import daAlgorithms.Atoms.lbfgsb19hlt as optimiseur
 137         else:
 138             import scipy.optimize as optimiseur
 139         Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 140             func        = CostFunction,
 141             x0          = Xini,
 142             fprime      = GradientOfCostFunction,
 143             args        = (),
 144             bounds      = RecentredBounds(selfA._parameters["Bounds"], Xb, BI),
 145             maxfun      = selfA._parameters["MaximumNumberOfIterations"]-1,
 146             factr       = selfA._parameters["CostDecrementTolerance"]*1.e14,
 147             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 148             iprint      = selfA._parameters["optiprint"],
 149             )
 150         # nfeval = Informations['funcalls']
 151         # rc     = Informations['warnflag']
 152     elif selfA._parameters["Minimizer"] == "TNC":
 153         Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 154             func        = CostFunction,
 155             x0          = Xini,
 156             fprime      = GradientOfCostFunction,
 157             args        = (),
 158             bounds      = RecentredBounds(selfA._parameters["Bounds"], Xb, BI),
 159             maxfun      = selfA._parameters["MaximumNumberOfIterations"],
 160             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 161             ftol        = selfA._parameters["CostDecrementTolerance"],
 162             messages    = selfA._parameters["optmessages"],
 163             )
 164     elif selfA._parameters["Minimizer"] == "CG":
 165         Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 166             f           = CostFunction,
 167             x0          = Xini,
 168             fprime      = GradientOfCostFunction,
 169             args        = (),
 170             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 171             gtol        = selfA._parameters["GradientNormTolerance"],
 172             disp        = selfA._parameters["optdisp"],
 173             full_output = True,
 174             )
 175     elif selfA._parameters["Minimizer"] == "NCG":
 176         Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 177             f           = CostFunction,
 178             x0          = Xini,
 179             fprime      = GradientOfCostFunction,
 180             args        = (),
 181             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 182             avextol     = selfA._parameters["CostDecrementTolerance"],
 183             disp        = selfA._parameters["optdisp"],
 184             full_output = True,
 185             )
 186     elif selfA._parameters["Minimizer"] == "BFGS":
 187         Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 188             f           = CostFunction,
 189             x0          = Xini,
 190             fprime      = GradientOfCostFunction,
 191             args        = (),
 192             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 193             gtol        = selfA._parameters["GradientNormTolerance"],
 194             disp        = selfA._parameters["optdisp"],
 195             full_output = True,
 196             )
 197     else:
 198         raise ValueError("Error in minimizer name: %s is unkown"%selfA._parameters["Minimizer"])
 199     #
 200     IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 201     MinJ     = selfA.StoredVariables["CostFunctionJ"][IndexMin]
 202     #
 203     # Correction pour pallier a un bug de TNC sur le retour du Minimum
 204     # ----------------------------------------------------------------
 205     if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
 206         Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
 207     else:
 208         Minimum = Xb + B * Minimum.reshape((-1,1)) # Pas @
 209     #
 210     Xa = Minimum
 211     if __storeState: selfA._setInternalState("Xn", Xa)
 212     #--------------------------
 213     #
 214     selfA.StoredVariables["Analysis"].store( Xa )
 215     #
 216     if selfA._toStore("OMA") or \
 217         selfA._toStore("InnovationAtCurrentAnalysis") or \
 218         selfA._toStore("SigmaObs2") or \
 219         selfA._toStore("SimulationQuantiles") or \
 220         selfA._toStore("SimulatedObservationAtOptimum"):
 221         if selfA._toStore("SimulatedObservationAtCurrentState"):
 222             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 223         elif selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 224             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 225         else:
 226             HXa = Hm( Xa )
 227         oma = Y - HXa.reshape((-1,1))
 228     #
 229     if selfA._toStore("APosterioriCovariance") or \
 230         selfA._toStore("SimulationQuantiles") or \
 231         selfA._toStore("JacobianMatrixAtOptimum") or \
 232         selfA._toStore("KalmanGainAtOptimum"):
 233         HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 234         HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 235     if selfA._toStore("APosterioriCovariance") or \
 236         selfA._toStore("SimulationQuantiles") or \
 237         selfA._toStore("KalmanGainAtOptimum"):
 238         HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 239         HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 240     if selfA._toStore("APosterioriCovariance") or \
 241         selfA._toStore("SimulationQuantiles"):
 242         BI = B.getI()
 243         A = HessienneEstimation(selfA, Xa.size, HaM, HtM, BI, RI)
 244     if selfA._toStore("APosterioriCovariance"):
 245         selfA.StoredVariables["APosterioriCovariance"].store( A )
 246     if selfA._toStore("JacobianMatrixAtOptimum"):
 247         selfA.StoredVariables["JacobianMatrixAtOptimum"].store( HtM )
 248     if selfA._toStore("KalmanGainAtOptimum"):
 249         if   (Y.size <= Xb.size): KG  = B * HaM * (R + numpy.dot(HtM, B * HaM)).I
 250         elif (Y.size >  Xb.size): KG = (BI + numpy.dot(HaM, RI * HtM)).I * HaM * RI
 251         selfA.StoredVariables["KalmanGainAtOptimum"].store( KG )
 252     #
 253     # Calculs et/ou stockages supplémentaires
 254     # ---------------------------------------
 255     if selfA._toStore("Innovation") or \
 256         selfA._toStore("SigmaObs2") or \
 257         selfA._toStore("MahalanobisConsistency") or \
 258         selfA._toStore("OMB"):
 259         Innovation  = Y - HXb
 260     if selfA._toStore("Innovation"):
 261         selfA.StoredVariables["Innovation"].store( Innovation )
 262     if selfA._toStore("BMA"):
 263         selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 264     if selfA._toStore("OMA"):
 265         selfA.StoredVariables["OMA"].store( oma )
 266     if selfA._toStore("InnovationAtCurrentAnalysis"):
 267         selfA.StoredVariables["InnovationAtCurrentAnalysis"].store( oma )
 268     if selfA._toStore("OMB"):
 269         selfA.StoredVariables["OMB"].store( Innovation )
 270     if selfA._toStore("SigmaObs2"):
 271         TraceR = R.trace(Y.size)
 272         selfA.StoredVariables["SigmaObs2"].store( float( (Innovation.T @ oma) ) / TraceR )
 273     if selfA._toStore("MahalanobisConsistency"):
 274         selfA.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/Innovation.size ) )
 275     if selfA._toStore("SimulationQuantiles"):
 276         QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
 277     if selfA._toStore("SimulatedObservationAtBackground"):
 278         selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
 279     if selfA._toStore("SimulatedObservationAtOptimum"):
 280         selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
 281     #
 282     return 0
 283
 284 # ==============================================================================
 285 if __name__ == "__main__":
 286     print('\n AUTODIAGNOSTIC\n')