src/daComposant/daAlgorithms/Atoms/incr3dvar.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 incrémental
  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 incr3dvar(selfA, Xb, Y, U, HO, CM, R, B, __storeState = False):
  36     """
  37     Correction
  38     """
  39     #
  40     # Initialisations
  41     # ---------------
  42     Hm = HO["Direct"].appliedTo
  43     #
  44     if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
  45         HXb = numpy.asarray(Hm( Xb, HO["AppliedInX"]["HXb"] ))
  46     else:
  47         HXb = numpy.asarray(Hm( Xb ))
  48     HXb = HXb.reshape((-1,1))
  49     if Y.size != HXb.size:
  50         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))
  51     if max(Y.shape) != max(HXb.shape):
  52         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))
  53     #
  54     if selfA._toStore("JacobianMatrixAtBackground"):
  55         HtMb = HO["Tangent"].asMatrix(ValueForMethodForm = Xb)
  56         HtMb = HtMb.reshape(Y.size,Xb.size) # ADAO & check shape
  57         selfA.StoredVariables["JacobianMatrixAtBackground"].store( HtMb )
  58     #
  59     BI = B.getI()
  60     RI = R.getI()
  61     #
  62     Innovation = Y - HXb
  63     #
  64     # Outer Loop
  65     # ----------
  66     iOuter = 0
  67     J      = 1./mpr
  68     DeltaJ = 1./mpr
  69     Xr     = numpy.asarray(selfA._parameters["InitializationPoint"]).reshape((-1,1))
  70     while abs(DeltaJ) >= selfA._parameters["CostDecrementTolerance"] and iOuter <= selfA._parameters["MaximumNumberOfIterations"]:
  71         #
  72         # Inner Loop
  73         # ----------
  74         Ht = HO["Tangent"].asMatrix(Xr)
  75         Ht = Ht.reshape(Y.size,Xr.size) # ADAO & check shape
  76         #
  77         # Définition de la fonction-coût
  78         # ------------------------------
  79         def CostFunction(dx):
  80             _dX  = numpy.asarray(dx).reshape((-1,1))
  81             if selfA._parameters["StoreInternalVariables"] or \
  82                 selfA._toStore("CurrentState") or \
  83                 selfA._toStore("CurrentOptimum"):
  84                 selfA.StoredVariables["CurrentState"].store( Xb + _dX )
  85             _HdX = (Ht @ _dX).reshape((-1,1))
  86             _dInnovation = Innovation - _HdX
  87             if selfA._toStore("SimulatedObservationAtCurrentState") or \
  88                 selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  89                 selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( HXb + _HdX )
  90             if selfA._toStore("InnovationAtCurrentState"):
  91                 selfA.StoredVariables["InnovationAtCurrentState"].store( _dInnovation )
  92             #
  93             Jb  = float( 0.5 * _dX.T * (BI * _dX) )
  94             Jo  = float( 0.5 * _dInnovation.T * (RI * _dInnovation) )
  95             J   = Jb + Jo
  96             #
  97             selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["CostFunctionJ"]) )
  98             selfA.StoredVariables["CostFunctionJb"].store( Jb )
  99             selfA.StoredVariables["CostFunctionJo"].store( Jo )
 100             selfA.StoredVariables["CostFunctionJ" ].store( J )
 101             if selfA._toStore("IndexOfOptimum") or \
 102                 selfA._toStore("CurrentOptimum") or \
 103                 selfA._toStore("CostFunctionJAtCurrentOptimum") or \
 104                 selfA._toStore("CostFunctionJbAtCurrentOptimum") or \
 105                 selfA._toStore("CostFunctionJoAtCurrentOptimum") or \
 106                 selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 107                 IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 108             if selfA._toStore("IndexOfOptimum"):
 109                 selfA.StoredVariables["IndexOfOptimum"].store( IndexMin )
 110             if selfA._toStore("CurrentOptimum"):
 111                 selfA.StoredVariables["CurrentOptimum"].store( selfA.StoredVariables["CurrentState"][IndexMin] )
 112             if selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 113                 selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 114             if selfA._toStore("CostFunctionJbAtCurrentOptimum"):
 115                 selfA.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJb"][IndexMin] )
 116             if selfA._toStore("CostFunctionJoAtCurrentOptimum"):
 117                 selfA.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJo"][IndexMin] )
 118             if selfA._toStore("CostFunctionJAtCurrentOptimum"):
 119                 selfA.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( selfA.StoredVariables["CostFunctionJ" ][IndexMin] )
 120             return J
 121         #
 122         def GradientOfCostFunction(dx):
 123             _dX          = numpy.ravel( dx )
 124             _HdX         = (Ht @ _dX).reshape((-1,1))
 125             _dInnovation = Innovation - _HdX
 126             GradJb       = BI @ _dX
 127             GradJo       = - Ht.T @ (RI * _dInnovation)
 128             GradJ        = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
 129             return GradJ
 130         #
 131         # Minimisation de la fonctionnelle
 132         # --------------------------------
 133         nbPreviousSteps = selfA.StoredVariables["CostFunctionJ"].stepnumber()
 134         #
 135         if selfA._parameters["Minimizer"] == "LBFGSB":
 136             # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 137             if "0.19" <= scipy.version.version <= "1.4.99":
 138                 import daAlgorithms.Atoms.lbfgsb14hlt as optimiseur
 139             elif "1.5.0" <= scipy.version.version <= "1.7.99":
 140                 import daAlgorithms.Atoms.lbfgsb17hlt as optimiseur
 141             elif "1.8.0" <= scipy.version.version <= "1.8.99":
 142                 import daAlgorithms.Atoms.lbfgsb18hlt as optimiseur
 143             elif "1.9.0" <= scipy.version.version <= "1.9.99":
 144                 import daAlgorithms.Atoms.lbfgsb19hlt as optimiseur
 145             else:
 146                 import scipy.optimize as optimiseur
 147             Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 148                 func        = CostFunction,
 149                 x0          = numpy.zeros(Xb.size),
 150                 fprime      = GradientOfCostFunction,
 151                 args        = (),
 152                 bounds      = RecentredBounds(selfA._parameters["Bounds"], Xb),
 153                 maxfun      = selfA._parameters["MaximumNumberOfIterations"]-1,
 154                 factr       = selfA._parameters["CostDecrementTolerance"]*1.e14,
 155                 pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 156                 iprint      = selfA._parameters["optiprint"],
 157                 )
 158             # nfeval = Informations['funcalls']
 159             # rc     = Informations['warnflag']
 160         elif selfA._parameters["Minimizer"] == "TNC":
 161             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 162                 func        = CostFunction,
 163                 x0          = numpy.zeros(Xb.size),
 164                 fprime      = GradientOfCostFunction,
 165                 args        = (),
 166                 bounds      = RecentredBounds(selfA._parameters["Bounds"], Xb),
 167                 maxfun      = selfA._parameters["MaximumNumberOfIterations"],
 168                 pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 169                 ftol        = selfA._parameters["CostDecrementTolerance"],
 170                 messages    = selfA._parameters["optmessages"],
 171                 )
 172         elif selfA._parameters["Minimizer"] == "CG":
 173             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 174                 f           = CostFunction,
 175                 x0          = numpy.zeros(Xb.size),
 176                 fprime      = GradientOfCostFunction,
 177                 args        = (),
 178                 maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 179                 gtol        = selfA._parameters["GradientNormTolerance"],
 180                 disp        = selfA._parameters["optdisp"],
 181                 full_output = True,
 182                 )
 183         elif selfA._parameters["Minimizer"] == "NCG":
 184             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 185                 f           = CostFunction,
 186                 x0          = numpy.zeros(Xb.size),
 187                 fprime      = GradientOfCostFunction,
 188                 args        = (),
 189                 maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 190                 avextol     = selfA._parameters["CostDecrementTolerance"],
 191                 disp        = selfA._parameters["optdisp"],
 192                 full_output = True,
 193                 )
 194         elif selfA._parameters["Minimizer"] == "BFGS":
 195             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 196                 f           = CostFunction,
 197                 x0          = numpy.zeros(Xb.size),
 198                 fprime      = GradientOfCostFunction,
 199                 args        = (),
 200                 maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 201                 gtol        = selfA._parameters["GradientNormTolerance"],
 202                 disp        = selfA._parameters["optdisp"],
 203                 full_output = True,
 204                 )
 205         else:
 206             raise ValueError("Error in minimizer name: %s is unkown"%selfA._parameters["Minimizer"])
 207         #
 208         IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 209         MinJ     = selfA.StoredVariables["CostFunctionJ"][IndexMin]
 210         #
 211         if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
 212             Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
 213         else:
 214             Minimum = Xb + Minimum.reshape((-1,1))
 215         #
 216         Xr     = Minimum
 217         DeltaJ = selfA.StoredVariables["CostFunctionJ" ][-1] - J
 218         iOuter = selfA.StoredVariables["CurrentIterationNumber"][-1]
 219     #
 220     Xa = Xr
 221     if __storeState: selfA._setInternalState("Xn", Xa)
 222     #--------------------------
 223     #
 224     selfA.StoredVariables["Analysis"].store( Xa )
 225     #
 226     if selfA._toStore("OMA") or \
 227         selfA._toStore("InnovationAtCurrentAnalysis") or \
 228         selfA._toStore("SigmaObs2") or \
 229         selfA._toStore("SimulationQuantiles") or \
 230         selfA._toStore("SimulatedObservationAtOptimum"):
 231         if selfA._toStore("SimulatedObservationAtCurrentState"):
 232             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 233         elif selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 234             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 235         else:
 236             HXa = Hm( Xa )
 237         oma = Y - HXa.reshape((-1,1))
 238     #
 239     if selfA._toStore("APosterioriCovariance") or \
 240         selfA._toStore("SimulationQuantiles") or \
 241         selfA._toStore("JacobianMatrixAtOptimum") or \
 242         selfA._toStore("KalmanGainAtOptimum"):
 243         HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 244         HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 245     if selfA._toStore("APosterioriCovariance") or \
 246         selfA._toStore("SimulationQuantiles") or \
 247         selfA._toStore("KalmanGainAtOptimum"):
 248         HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 249         HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 250     if selfA._toStore("APosterioriCovariance") or \
 251         selfA._toStore("SimulationQuantiles"):
 252         A = HessienneEstimation(selfA, Xa.size, HaM, HtM, BI, RI)
 253     if selfA._toStore("APosterioriCovariance"):
 254         selfA.StoredVariables["APosterioriCovariance"].store( A )
 255     if selfA._toStore("JacobianMatrixAtOptimum"):
 256         selfA.StoredVariables["JacobianMatrixAtOptimum"].store( HtM )
 257     if selfA._toStore("KalmanGainAtOptimum"):
 258         if   (Y.size <= Xb.size): KG  = B * HaM * (R + numpy.dot(HtM, B * HaM)).I
 259         elif (Y.size >  Xb.size): KG = (BI + numpy.dot(HaM, RI * HtM)).I * HaM * RI
 260         selfA.StoredVariables["KalmanGainAtOptimum"].store( KG )
 261     #
 262     # Calculs et/ou stockages supplémentaires
 263     # ---------------------------------------
 264     if selfA._toStore("Innovation") or \
 265         selfA._toStore("SigmaObs2") or \
 266         selfA._toStore("MahalanobisConsistency") or \
 267         selfA._toStore("OMB"):
 268         Innovation  = Y - HXb
 269     if selfA._toStore("Innovation"):
 270         selfA.StoredVariables["Innovation"].store( Innovation )
 271     if selfA._toStore("BMA"):
 272         selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 273     if selfA._toStore("OMA"):
 274         selfA.StoredVariables["OMA"].store( oma )
 275     if selfA._toStore("InnovationAtCurrentAnalysis"):
 276         selfA.StoredVariables["InnovationAtCurrentAnalysis"].store( oma )
 277     if selfA._toStore("OMB"):
 278         selfA.StoredVariables["OMB"].store( Innovation )
 279     if selfA._toStore("SigmaObs2"):
 280         TraceR = R.trace(Y.size)
 281         selfA.StoredVariables["SigmaObs2"].store( float( (Innovation.T @ oma) ) / TraceR )
 282     if selfA._toStore("MahalanobisConsistency"):
 283         selfA.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/Innovation.size ) )
 284     if selfA._toStore("SimulationQuantiles"):
 285         QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
 286     if selfA._toStore("SimulatedObservationAtBackground"):
 287         selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
 288     if selfA._toStore("SimulatedObservationAtOptimum"):
 289         selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
 290     #
 291     return 0
 292
 293 # ==============================================================================
 294 if __name__ == "__main__":
 295     print('\n AUTODIAGNOSTIC\n')