src/daComposant/daAlgorithms/Atoms/psas3dvar.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 PSAS
  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 psas3dvar(selfA, Xb, Y, U, HO, CM, R, B, __storeState = False):
  33     """
  34     Correction
  35     """
  36     #
  37     # Initialisations
  38     # ---------------
  39     Hm = HO["Direct"].appliedTo
  40     #
  41     if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
  42         HXb = numpy.asarray(Hm( Xb, HO["AppliedInX"]["HXb"] ))
  43     else:
  44         HXb = numpy.asarray(Hm( Xb ))
  45     HXb = HXb.reshape((-1,1))
  46     if Y.size != HXb.size:
  47         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))
  48     if max(Y.shape) != max(HXb.shape):
  49         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))
  50     #
  51     Ht = HO["Tangent"].asMatrix(Xb)
  52     Ht = Ht.reshape(Y.size,Xb.size) # ADAO & check shape
  53     BHT = B * Ht.T
  54     HBHTpR = R + Ht * BHT
  55     Innovation = Y - HXb
  56     #
  57     if selfA._toStore("JacobianMatrixAtBackground"):
  58         selfA.StoredVariables["JacobianMatrixAtBackground"].store( Ht )
  59     #
  60     Xini = numpy.zeros(Y.size)
  61     #
  62     # Définition de la fonction-coût
  63     # ------------------------------
  64     def CostFunction(w):
  65         _W = numpy.asarray(w).reshape((-1,1))
  66         if selfA._parameters["StoreInternalVariables"] or \
  67             selfA._toStore("CurrentState") or \
  68             selfA._toStore("CurrentOptimum"):
  69             selfA.StoredVariables["CurrentState"].store( Xb + BHT @ _W )
  70         if selfA._toStore("SimulatedObservationAtCurrentState") or \
  71             selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  72             selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( Hm( Xb + BHT @ _W ) )
  73         if selfA._toStore("InnovationAtCurrentState"):
  74             selfA.StoredVariables["InnovationAtCurrentState"].store( Innovation )
  75         #
  76         Jb  = float( 0.5 * _W.T @ (HBHTpR @ _W) )
  77         Jo  = float( - _W.T @ Innovation )
  78         J   = Jb + Jo
  79         #
  80         selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["CostFunctionJ"]) )
  81         selfA.StoredVariables["CostFunctionJb"].store( Jb )
  82         selfA.StoredVariables["CostFunctionJo"].store( Jo )
  83         selfA.StoredVariables["CostFunctionJ" ].store( J )
  84         if selfA._toStore("IndexOfOptimum") or \
  85             selfA._toStore("CurrentOptimum") or \
  86             selfA._toStore("CostFunctionJAtCurrentOptimum") or \
  87             selfA._toStore("CostFunctionJbAtCurrentOptimum") or \
  88             selfA._toStore("CostFunctionJoAtCurrentOptimum") or \
  89             selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  90             IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
  91         if selfA._toStore("IndexOfOptimum"):
  92             selfA.StoredVariables["IndexOfOptimum"].store( IndexMin )
  93         if selfA._toStore("CurrentOptimum"):
  94             selfA.StoredVariables["CurrentOptimum"].store( selfA.StoredVariables["CurrentState"][IndexMin] )
  95         if selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  96             selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
  97         if selfA._toStore("CostFunctionJbAtCurrentOptimum"):
  98             selfA.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJb"][IndexMin] )
  99         if selfA._toStore("CostFunctionJoAtCurrentOptimum"):
 100             selfA.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJo"][IndexMin] )
 101         if selfA._toStore("CostFunctionJAtCurrentOptimum"):
 102             selfA.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( selfA.StoredVariables["CostFunctionJ" ][IndexMin] )
 103         return J
 104     #
 105     def GradientOfCostFunction(w):
 106         _W = numpy.asarray(w).reshape((-1,1))
 107         GradJb  = HBHTpR @ _W
 108         GradJo  = - Innovation
 109         GradJ   = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
 110         return GradJ
 111     #
 112     # Minimisation de la fonctionnelle
 113     # --------------------------------
 114     nbPreviousSteps = selfA.StoredVariables["CostFunctionJ"].stepnumber()
 115     #
 116     if selfA._parameters["Minimizer"] == "LBFGSB":
 117         if "0.19" <= scipy.version.version <= "1.4.99":
 118             import daAlgorithms.Atoms.lbfgsb14hlt as optimiseur
 119         elif "1.5.0" <= scipy.version.version <= "1.7.99":
 120             import daAlgorithms.Atoms.lbfgsb17hlt as optimiseur
 121         elif "1.8.0" <= scipy.version.version <= "1.8.99":
 122             import daAlgorithms.Atoms.lbfgsb18hlt as optimiseur
 123         elif "1.9.0" <= scipy.version.version <= "1.9.99":
 124             import daAlgorithms.Atoms.lbfgsb19hlt as optimiseur
 125         else:
 126             import scipy.optimize as optimiseur
 127         Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 128             func        = CostFunction,
 129             x0          = Xini,
 130             fprime      = GradientOfCostFunction,
 131             args        = (),
 132             maxfun      = selfA._parameters["MaximumNumberOfIterations"]-1,
 133             factr       = selfA._parameters["CostDecrementTolerance"]*1.e14,
 134             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 135             iprint      = selfA._parameters["optiprint"],
 136             )
 137         # nfeval = Informations['funcalls']
 138         # rc     = Informations['warnflag']
 139     elif selfA._parameters["Minimizer"] == "TNC":
 140         Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 141             func        = CostFunction,
 142             x0          = Xini,
 143             fprime      = GradientOfCostFunction,
 144             args        = (),
 145             maxfun      = selfA._parameters["MaximumNumberOfIterations"],
 146             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 147             ftol        = selfA._parameters["CostDecrementTolerance"],
 148             messages    = selfA._parameters["optmessages"],
 149             )
 150     elif selfA._parameters["Minimizer"] == "CG":
 151         Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 152             f           = CostFunction,
 153             x0          = Xini,
 154             fprime      = GradientOfCostFunction,
 155             args        = (),
 156             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 157             gtol        = selfA._parameters["GradientNormTolerance"],
 158             disp        = selfA._parameters["optdisp"],
 159             full_output = True,
 160             )
 161     elif selfA._parameters["Minimizer"] == "NCG":
 162         Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 163             f           = CostFunction,
 164             x0          = Xini,
 165             fprime      = GradientOfCostFunction,
 166             args        = (),
 167             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 168             avextol     = selfA._parameters["CostDecrementTolerance"],
 169             disp        = selfA._parameters["optdisp"],
 170             full_output = True,
 171             )
 172     elif selfA._parameters["Minimizer"] == "BFGS":
 173         Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 174             f           = CostFunction,
 175             x0          = Xini,
 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     else:
 184         raise ValueError("Error in minimizer name: %s is unkown"%selfA._parameters["Minimizer"])
 185     #
 186     IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 187     MinJ     = selfA.StoredVariables["CostFunctionJ"][IndexMin]
 188     #
 189     # Correction pour pallier a un bug de TNC sur le retour du Minimum
 190     # ----------------------------------------------------------------
 191     if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
 192         Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
 193     else:
 194         Minimum = Xb + BHT @ Minimum.reshape((-1,1))
 195     #
 196     Xa = Minimum
 197     if __storeState: selfA._setInternalState("Xn", Xa)
 198     #--------------------------
 199     #
 200     selfA.StoredVariables["Analysis"].store( Xa )
 201     #
 202     if selfA._toStore("OMA") or \
 203         selfA._toStore("InnovationAtCurrentAnalysis") or \
 204         selfA._toStore("SigmaObs2") or \
 205         selfA._toStore("SimulationQuantiles") or \
 206         selfA._toStore("SimulatedObservationAtOptimum"):
 207         if selfA._toStore("SimulatedObservationAtCurrentState"):
 208             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 209         elif selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 210             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 211         else:
 212             HXa = Hm( Xa )
 213         oma = Y - HXa.reshape((-1,1))
 214     #
 215     if selfA._toStore("APosterioriCovariance") or \
 216         selfA._toStore("SimulationQuantiles") or \
 217         selfA._toStore("JacobianMatrixAtOptimum") or \
 218         selfA._toStore("KalmanGainAtOptimum"):
 219         HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 220         HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
 221     if selfA._toStore("APosterioriCovariance") or \
 222         selfA._toStore("SimulationQuantiles") or \
 223         selfA._toStore("KalmanGainAtOptimum"):
 224         HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 225         HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
 226     if selfA._toStore("APosterioriCovariance") or \
 227         selfA._toStore("SimulationQuantiles"):
 228         BI = B.getI()
 229         RI = R.getI()
 230         A = HessienneEstimation(selfA, Xa.size, HaM, HtM, BI, RI)
 231     if selfA._toStore("APosterioriCovariance"):
 232         selfA.StoredVariables["APosterioriCovariance"].store( A )
 233     if selfA._toStore("JacobianMatrixAtOptimum"):
 234         selfA.StoredVariables["JacobianMatrixAtOptimum"].store( HtM )
 235     if selfA._toStore("KalmanGainAtOptimum"):
 236         if   (Y.size <= Xb.size): KG  = B * HaM * (R + numpy.dot(HtM, B * HaM)).I
 237         elif (Y.size >  Xb.size): KG = (BI + numpy.dot(HaM, RI * HtM)).I * HaM * RI
 238         selfA.StoredVariables["KalmanGainAtOptimum"].store( KG )
 239     #
 240     # Calculs et/ou stockages supplémentaires
 241     # ---------------------------------------
 242     if selfA._toStore("Innovation") or \
 243         selfA._toStore("SigmaObs2") or \
 244         selfA._toStore("MahalanobisConsistency") or \
 245         selfA._toStore("OMB"):
 246         Innovation  = Y - HXb
 247     if selfA._toStore("Innovation"):
 248         selfA.StoredVariables["Innovation"].store( Innovation )
 249     if selfA._toStore("BMA"):
 250         selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 251     if selfA._toStore("OMA"):
 252         selfA.StoredVariables["OMA"].store( oma )
 253     if selfA._toStore("InnovationAtCurrentAnalysis"):
 254         selfA.StoredVariables["InnovationAtCurrentAnalysis"].store( oma )
 255     if selfA._toStore("OMB"):
 256         selfA.StoredVariables["OMB"].store( Innovation )
 257     if selfA._toStore("SigmaObs2"):
 258         TraceR = R.trace(Y.size)
 259         selfA.StoredVariables["SigmaObs2"].store( float( (Innovation.T @ oma) ) / TraceR )
 260     if selfA._toStore("MahalanobisConsistency"):
 261         selfA.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/Innovation.size ) )
 262     if selfA._toStore("SimulationQuantiles"):
 263         QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
 264     if selfA._toStore("SimulatedObservationAtBackground"):
 265         selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
 266     if selfA._toStore("SimulatedObservationAtOptimum"):
 267         selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
 268     #
 269     return 0
 270
 271 # ==============================================================================
 272 if __name__ == "__main__":
 273     print('\n AUTODIAGNOSTIC\n')