src/daComposant/daAlgorithms/Atoms/van3dvar.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 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, vt, vfloat
  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))  # noqa: E501
  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))  # noqa: E501
  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
  72     def CostFunction(v):
  73         _V = numpy.asarray(v).reshape((-1, 1))
  74         _X = Xb + (B @ _V).reshape((-1, 1))
  75         if selfA._parameters["StoreInternalVariables"] or \
  76                 selfA._toStore("CurrentState") or \
  77                 selfA._toStore("CurrentOptimum"):
  78             selfA.StoredVariables["CurrentState"].store( _X )
  79         _HX = numpy.asarray(Hm( _X )).reshape((-1, 1))
  80         _Innovation = Y - _HX
  81         if selfA._toStore("SimulatedObservationAtCurrentState") or \
  82                 selfA._toStore("SimulatedObservationAtCurrentOptimum"):
  83             selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
  84         if selfA._toStore("InnovationAtCurrentState"):
  85             selfA.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
  86         #
  87         Jb  = vfloat( 0.5 * _V.T * (BT * _V) )
  88         Jo  = vfloat( 0.5 * _Innovation.T * (RI * _Innovation) )
  89         J   = Jb + Jo
  90         #
  91         selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["CostFunctionJ"]) )
  92         selfA.StoredVariables["CostFunctionJb"].store( Jb )
  93         selfA.StoredVariables["CostFunctionJo"].store( Jo )
  94         selfA.StoredVariables["CostFunctionJ" ].store( J )
  95         if selfA._toStore("IndexOfOptimum") or \
  96                 selfA._toStore("CurrentOptimum") or \
  97                 selfA._toStore("CostFunctionJAtCurrentOptimum") or \
  98                 selfA._toStore("CostFunctionJbAtCurrentOptimum") or \
  99                 selfA._toStore("CostFunctionJoAtCurrentOptimum") or \
 100                 selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 101             IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps  # noqa: E501
 102         if selfA._toStore("IndexOfOptimum"):
 103             selfA.StoredVariables["IndexOfOptimum"].store( IndexMin )
 104         if selfA._toStore("CurrentOptimum"):
 105             selfA.StoredVariables["CurrentOptimum"].store( selfA.StoredVariables["CurrentState"][IndexMin] )  # noqa: E501
 106         if selfA._toStore("SimulatedObservationAtCurrentOptimum"):
 107             selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( selfA.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )  # noqa: E501
 108         if selfA._toStore("CostFunctionJbAtCurrentOptimum"):
 109             selfA.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJb"][IndexMin] )  # noqa: E501
 110         if selfA._toStore("CostFunctionJoAtCurrentOptimum"):
 111             selfA.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJo"][IndexMin] )  # noqa: E501
 112         if selfA._toStore("CostFunctionJAtCurrentOptimum"):
 113             selfA.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( selfA.StoredVariables["CostFunctionJ" ][IndexMin] )  # noqa: E501
 114         return J
 115
 116     def GradientOfCostFunction(v):
 117         _V = numpy.asarray(v).reshape((-1, 1))
 118         _X = Xb + (B @ _V).reshape((-1, 1))
 119         _HX     = numpy.asarray(Hm( _X )).reshape((-1, 1))
 120         GradJb  = BT * _V
 121         GradJo  = - BT * Ha( (_X, RI * (Y - _HX)) )
 122         GradJ   = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
 123         return GradJ
 124     #
 125     # Minimisation de la fonctionnelle
 126     # --------------------------------
 127     nbPreviousSteps = selfA.StoredVariables["CostFunctionJ"].stepnumber()
 128     #
 129     if selfA._parameters["Minimizer"] == "LBFGSB":
 130         if vt("0.19")  <= vt(scipy.version.version) <= vt("1.4.99"):
 131             import daAlgorithms.Atoms.lbfgsb14hlt as optimiseur
 132         elif vt("1.5.0") <= vt(scipy.version.version) <= vt("1.7.99"):
 133             import daAlgorithms.Atoms.lbfgsb17hlt as optimiseur
 134         elif vt("1.8.0") <= vt(scipy.version.version) <= vt("1.8.99"):
 135             import daAlgorithms.Atoms.lbfgsb18hlt as optimiseur
 136         elif vt("1.9.0") <= vt(scipy.version.version) <= vt("1.10.99"):
 137             import daAlgorithms.Atoms.lbfgsb19hlt as optimiseur
 138         elif vt("1.11.0") <= vt(scipy.version.version) <= vt("1.11.99"):
 139             import daAlgorithms.Atoms.lbfgsb111hlt as optimiseur
 140         elif vt("1.12.0") <= vt(scipy.version.version) <= vt("1.12.99"):
 141             import daAlgorithms.Atoms.lbfgsb112hlt as optimiseur
 142         elif vt("1.13.0") <= vt(scipy.version.version) <= vt("1.13.99"):
 143             import daAlgorithms.Atoms.lbfgsb113hlt as optimiseur
 144         elif vt("1.14.0") <= vt(scipy.version.version) <= vt("1.14.99"):
 145             import daAlgorithms.Atoms.lbfgsb114hlt as optimiseur
 146         else:
 147             import scipy.optimize as optimiseur
 148         Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
 149             func        = CostFunction,
 150             x0          = Xini,
 151             fprime      = GradientOfCostFunction,
 152             args        = (),
 153             bounds      = RecentredBounds(selfA._parameters["Bounds"], Xb, BI),
 154             maxfun      = selfA._parameters["MaximumNumberOfIterations"] - 1,
 155             factr       = selfA._parameters["CostDecrementTolerance"] * 1.e14,
 156             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 157             iprint      = selfA._parameters["optiprint"],
 158         )
 159         # nfeval = Informations['funcalls']
 160         # rc     = Informations['warnflag']
 161     elif selfA._parameters["Minimizer"] == "TNC":
 162         Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 163             func        = CostFunction,
 164             x0          = Xini,
 165             fprime      = GradientOfCostFunction,
 166             args        = (),
 167             bounds      = RecentredBounds(selfA._parameters["Bounds"], Xb, BI),
 168             maxfun      = selfA._parameters["MaximumNumberOfIterations"],
 169             pgtol       = selfA._parameters["ProjectedGradientTolerance"],
 170             ftol        = selfA._parameters["CostDecrementTolerance"],
 171             messages    = selfA._parameters["optmessages"],
 172         )
 173     elif selfA._parameters["Minimizer"] == "CG":
 174         Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 175             f           = CostFunction,
 176             x0          = Xini,
 177             fprime      = GradientOfCostFunction,
 178             args        = (),
 179             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 180             gtol        = selfA._parameters["GradientNormTolerance"],
 181             disp        = selfA._parameters["optdisp"],
 182             full_output = True,
 183         )
 184     elif selfA._parameters["Minimizer"] == "NCG":
 185         Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 186             f           = CostFunction,
 187             x0          = Xini,
 188             fprime      = GradientOfCostFunction,
 189             args        = (),
 190             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 191             avextol     = selfA._parameters["CostDecrementTolerance"],
 192             disp        = selfA._parameters["optdisp"],
 193             full_output = True,
 194         )
 195     elif selfA._parameters["Minimizer"] == "BFGS":
 196         Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 197             f           = CostFunction,
 198             x0          = Xini,
 199             fprime      = GradientOfCostFunction,
 200             args        = (),
 201             maxiter     = selfA._parameters["MaximumNumberOfIterations"],
 202             gtol        = selfA._parameters["GradientNormTolerance"],
 203             disp        = selfA._parameters["optdisp"],
 204             full_output = True,
 205         )
 206     else:
 207         raise ValueError("Error in minimizer name: %s is unkown"%selfA._parameters["Minimizer"])
 208     #
 209     IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 210     MinJ     = selfA.StoredVariables["CostFunctionJ"][IndexMin]
 211     #
 212     # Correction pour pallier a un bug de TNC sur le retour du Minimum
 213     # ----------------------------------------------------------------
 214     if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
 215         Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
 216     else:
 217         Minimum = Xb + B * Minimum.reshape((-1, 1))  # Pas de @
 218     #
 219     Xa = Minimum
 220     if __storeState:
 221         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 - numpy.asarray(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         BI = B.getI()
 253         A = HessienneEstimation(selfA, Xa.size, HaM, HtM, BI, RI)
 254     if selfA._toStore("APosterioriCovariance"):
 255         selfA.StoredVariables["APosterioriCovariance"].store( A )
 256     if selfA._toStore("JacobianMatrixAtOptimum"):
 257         selfA.StoredVariables["JacobianMatrixAtOptimum"].store( HtM )
 258     if selfA._toStore("KalmanGainAtOptimum"):
 259         if (Y.size <= Xb.size):
 260             KG  = B * HaM * (R + numpy.dot(HtM, B * HaM)).I
 261         elif (Y.size > Xb.size):
 262             KG = (BI + numpy.dot(HaM, RI * HtM)).I * HaM * RI
 263         selfA.StoredVariables["KalmanGainAtOptimum"].store( KG )
 264     #
 265     # Calculs et/ou stockages supplémentaires
 266     # ---------------------------------------
 267     if selfA._toStore("Innovation") or \
 268             selfA._toStore("SigmaObs2") or \
 269             selfA._toStore("MahalanobisConsistency") or \
 270             selfA._toStore("OMB"):
 271         Innovation  = Y - HXb
 272     if selfA._toStore("Innovation"):
 273         selfA.StoredVariables["Innovation"].store( Innovation )
 274     if selfA._toStore("BMA"):
 275         selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 276     if selfA._toStore("OMA"):
 277         selfA.StoredVariables["OMA"].store( oma )
 278     if selfA._toStore("InnovationAtCurrentAnalysis"):
 279         selfA.StoredVariables["InnovationAtCurrentAnalysis"].store( oma )
 280     if selfA._toStore("OMB"):
 281         selfA.StoredVariables["OMB"].store( Innovation )
 282     if selfA._toStore("SigmaObs2"):
 283         TraceR = R.trace(Y.size)
 284         selfA.StoredVariables["SigmaObs2"].store( vfloat( (Innovation.T @ oma) ) / TraceR )
 285     if selfA._toStore("MahalanobisConsistency"):
 286         selfA.StoredVariables["MahalanobisConsistency"].store( float( 2. * MinJ / Innovation.size ) )
 287     if selfA._toStore("SimulationQuantiles"):
 288         QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
 289     if selfA._toStore("SimulatedObservationAtBackground"):
 290         selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
 291     if selfA._toStore("SimulatedObservationAtOptimum"):
 292         selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
 293     #
 294     return 0
 295
 296 # ==============================================================================
 297 if __name__ == "__main__":
 298     print('\n AUTODIAGNOSTIC\n')