src/daComposant/daAlgorithms/Atoms/psas3dvar.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2024 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 from daCore.PlatformInfo import vt, vfloat
  31
  32 # ==============================================================================
  33 def psas3dvar(selfA, Xb, Y, U, HO, CM, R, B, __storeState = False):
  34     """
  35     Correction
  36     """
  37     #
  38     # Initialisations
  39     # ---------------
  40     Hm = HO["Direct"].appliedTo
  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))  # noqa: E501
  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))  # noqa: E501
  51     #
  52     Ht = HO["Tangent"].asMatrix(Xb)
  53     Ht = Ht.reshape(Y.size, Xb.size)  # ADAO & check shape
  54     BHT = B * Ht.T
  55     HBHTpR = R + Ht * BHT
  56     Innovation = Y - HXb
  57     #
  58     if selfA._toStore("JacobianMatrixAtBackground"):
  59         selfA.StoredVariables["JacobianMatrixAtBackground"].store( Ht )
  60     #
  61     Xini = numpy.zeros(Y.size)
  62     #
  63     # Définition de la fonction-coût
  64     # ------------------------------
  65
  66     def CostFunction(w):
  67         _W = numpy.asarray(w).reshape((-1, 1))
  68         if selfA._parameters["StoreInternalVariables"] or \
  69                 selfA._toStore("CurrentState") or \
  70                 selfA._toStore("CurrentOptimum"):
  71             selfA.StoredVariables["CurrentState"].store( Xb + BHT @ _W )
  72         if selfA._toStore("SimulatedObservationAtCurrentState") or \
  73                 selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  74             selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( Hm( Xb + BHT @ _W ) )
  75         if selfA._toStore("InnovationAtCurrentState"):
  76             selfA.StoredVariables["InnovationAtCurrentState"].store( Innovation )
  77         #
  78         Jb  = vfloat( 0.5 * _W.T @ (HBHTpR @ _W) )
  79         Jo  = vfloat( - _W.T @ 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] )  # noqa: E501
  99         if selfA._toStore("CostFunctionJbAtCurrentOptimum"):
 100             selfA.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJb"][IndexMin] )  # noqa: E501
 101         if selfA._toStore("CostFunctionJoAtCurrentOptimum"):
 102             selfA.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJo"][IndexMin] )  # noqa: E501
 103         if selfA._toStore("CostFunctionJAtCurrentOptimum"):
 104             selfA.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( selfA.StoredVariables["CostFunctionJ" ][IndexMin] )  # noqa: E501
 105         return J
 106
 107     def GradientOfCostFunction(w):
 108         _W = numpy.asarray(w).reshape((-1, 1))
 109         GradJb  = HBHTpR @ _W
 110         GradJo  = - Innovation
 111         GradJ   = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
 112         return GradJ
 113     #
 114     # Minimisation de la fonctionnelle
 115     # --------------------------------
 116     nbPreviousSteps = selfA.StoredVariables["CostFunctionJ"].stepnumber()
 117     #
 118     if selfA._parameters["Minimizer"] == "LBFGSB":
 119         if vt("0.19")  <= vt(scipy.version.version) <= vt("1.4.99"):
 120             import daAlgorithms.Atoms.lbfgsb14hlt as optimiseur
 121         elif vt("1.5.0") <= vt(scipy.version.version) <= vt("1.7.99"):
 122             import daAlgorithms.Atoms.lbfgsb17hlt as optimiseur
 123         elif vt("1.8.0") <= vt(scipy.version.version) <= vt("1.8.99"):
 124             import daAlgorithms.Atoms.lbfgsb18hlt as optimiseur
 125         elif vt("1.9.0") <= vt(scipy.version.version) <= vt("1.10.99"):
 126             import daAlgorithms.Atoms.lbfgsb19hlt as optimiseur
 127         elif vt("1.11.0") <= vt(scipy.version.version) <= vt("1.11.99"):
 128             import daAlgorithms.Atoms.lbfgsb111hlt as optimiseur
 129         elif vt("1.12.0") <= vt(scipy.version.version) <= vt("1.12.99"):
 130             import daAlgorithms.Atoms.lbfgsb112hlt as optimiseur
 131         elif vt("1.13.0") <= vt(scipy.version.version) <= vt("1.13.99"):
 132             import daAlgorithms.Atoms.lbfgsb113hlt as optimiseur
 133         elif vt("1.14.0") <= vt(scipy.version.version) <= vt("1.14.99"):
 134             import daAlgorithms.Atoms.lbfgsb114hlt as optimiseur
 135         else:
 136             import scipy.optimize as optimiseur
 137         Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 138             func        = CostFunction,
 139             x0          = Xini,
 140             fprime      = GradientOfCostFunction,
 141             args        = (),
 142             maxfun      = selfA._parameters["MaximumNumberOfIterations"] - 1,
 143             factr       = selfA._parameters["CostDecrementTolerance"] * 1.e14,
 144             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 145             iprint      = selfA._parameters["optiprint"],
 146         )
 147         # nfeval = Informations['funcalls']
 148         # rc     = Informations['warnflag']
 149     elif selfA._parameters["Minimizer"] == "TNC":
 150         Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 151             func        = CostFunction,
 152             x0          = Xini,
 153             fprime      = GradientOfCostFunction,
 154             args        = (),
 155             maxfun      = selfA._parameters["MaximumNumberOfIterations"],
 156             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 157             ftol        = selfA._parameters["CostDecrementTolerance"],
 158             messages    = selfA._parameters["optmessages"],
 159         )
 160     elif selfA._parameters["Minimizer"] == "CG":
 161         Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 162             f           = CostFunction,
 163             x0          = Xini,
 164             fprime      = GradientOfCostFunction,
 165             args        = (),
 166             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 167             gtol        = selfA._parameters["GradientNormTolerance"],
 168             disp        = selfA._parameters["optdisp"],
 169             full_output = True,
 170         )
 171     elif selfA._parameters["Minimizer"] == "NCG":
 172         Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 173             f           = CostFunction,
 174             x0          = Xini,
 175             fprime      = GradientOfCostFunction,
 176             args        = (),
 177             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 178             avextol     = selfA._parameters["CostDecrementTolerance"],
 179             disp        = selfA._parameters["optdisp"],
 180             full_output = True,
 181         )
 182     elif selfA._parameters["Minimizer"] == "BFGS":
 183         Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 184             f           = CostFunction,
 185             x0          = Xini,
 186             fprime      = GradientOfCostFunction,
 187             args        = (),
 188             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 189             gtol        = selfA._parameters["GradientNormTolerance"],
 190             disp        = selfA._parameters["optdisp"],
 191             full_output = True,
 192         )
 193     else:
 194         raise ValueError("Error in minimizer name: %s is unkown"%selfA._parameters["Minimizer"])
 195     #
 196     IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 197     MinJ     = selfA.StoredVariables["CostFunctionJ"][IndexMin]
 198     #
 199     # Correction pour pallier a un bug de TNC sur le retour du Minimum
 200     # ----------------------------------------------------------------
 201     if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
 202         Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
 203     else:
 204         Minimum = Xb + BHT @ Minimum.reshape((-1, 1))
 205     #
 206     Xa = Minimum
 207     if __storeState:
 208         selfA._setInternalState("Xn", Xa)
 209     # --------------------------
 210     #
 211     selfA.StoredVariables["Analysis"].store( Xa )
 212     #
 213     if selfA._toStore("OMA") or \
 214             selfA._toStore("InnovationAtCurrentAnalysis") or \
 215             selfA._toStore("SigmaObs2") or \
 216             selfA._toStore("SimulationQuantiles") or \
 217             selfA._toStore("SimulatedObservationAtOptimum"):
 218         if selfA._toStore("SimulatedObservationAtCurrentState"):
 219             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 220         elif selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 221             HXa = selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 222         else:
 223             HXa = Hm( Xa )
 224         oma = Y - numpy.asarray(HXa).reshape((-1, 1))
 225     #
 226     if selfA._toStore("APosterioriCovariance") or \
 227             selfA._toStore("SimulationQuantiles") or \
 228             selfA._toStore("JacobianMatrixAtOptimum") or \
 229             selfA._toStore("KalmanGainAtOptimum"):
 230         HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
 231         HtM = HtM.reshape(Y.size, Xa.size)  # ADAO & check shape
 232     if selfA._toStore("APosterioriCovariance") or \
 233             selfA._toStore("SimulationQuantiles") or \
 234             selfA._toStore("KalmanGainAtOptimum"):
 235         HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
 236         HaM = HaM.reshape(Xa.size, Y.size)  # ADAO & check shape
 237     if selfA._toStore("APosterioriCovariance") or \
 238             selfA._toStore("SimulationQuantiles"):
 239         BI = B.getI()
 240         RI = R.getI()
 241         A = HessienneEstimation(selfA, Xa.size, HaM, HtM, BI, RI)
 242     if selfA._toStore("APosterioriCovariance"):
 243         selfA.StoredVariables["APosterioriCovariance"].store( A )
 244     if selfA._toStore("JacobianMatrixAtOptimum"):
 245         selfA.StoredVariables["JacobianMatrixAtOptimum"].store( HtM )
 246     if selfA._toStore("KalmanGainAtOptimum"):
 247         if (Y.size <= Xb.size):
 248             KG  = B * HaM * (R + numpy.dot(HtM, B * HaM)).I
 249         elif (Y.size > Xb.size):
 250             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( vfloat( (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')