"CurrentIterationNumber",
"CurrentOptimum",
"CurrentState",
+ "ForecastCovariance",
"ForecastState",
"IndexOfOptimum",
"InnovationAtCurrentAnalysis",
.. include:: snippets/CurrentState.rst
+.. include:: snippets/ForecastCovariance.rst
+
.. include:: snippets/ForecastState.rst
.. include:: snippets/IndexOfOptimum.rst
from adao import adaoBuilder
case = adaoBuilder.New('')
#
+case.setBackground (Vector = [0.])
+case.setBackgroundError (ScalarSparseMatrix = 1.)
+#
case.setObservationOperator(Matrix = [1.])
case.setObservationError (ScalarSparseMatrix = 0.1**2)
#
],
},
)
-case.setObserver(
- Info=" Analyzed state at current observation:",
- Template='ValuePrinter',
- Variable='Analysis',
- )
#
# Loop to obtain an analysis at each observation arrival
#
-XaStep, VaStep = 0., 1.
for i in range(1,len(Yobs)):
- case.setBackground (Vector = "%s"%float(XaStep))
- case.setBackgroundError (ScalarSparseMatrix = "%s"%float(VaStep))
- case.setObservation (Vector = Yobs[i])
+ case.setObservation(Vector = Yobs[i])
case.execute( nextStep = True )
- XaStep = case.get("Analysis")[-1]
- VaStep = case.get("APosterioriCovariance")[-1]
#
Xa = case.get("Analysis")
Pa = case.get("APosterioriCovariance")
#
+print(" Analyzed state at final observation:", Xa[-1])
print("")
-print(" Final a posteriori variance:",Pa[-1])
+print(" Final a posteriori variance:", Pa[-1])
print("")
#
#-------------------------------------------------------------------------------
----------------------------------------------
Noisy measurements acquired on 50 time steps
- Analyzed state at current observation: [0.]
- Analyzed state at current observation: [-0.41804504]
- Analyzed state at current observation: [-0.3114053]
- Analyzed state at current observation: [-0.31191336]
- Analyzed state at current observation: [-0.32761493]
- Analyzed state at current observation: [-0.33597167]
- Analyzed state at current observation: [-0.35629573]
- Analyzed state at current observation: [-0.36840289]
- Analyzed state at current observation: [-0.37392713]
- Analyzed state at current observation: [-0.36331937]
- Analyzed state at current observation: [-0.35750362]
- Analyzed state at current observation: [-0.37963052]
- Analyzed state at current observation: [-0.37117993]
- Analyzed state at current observation: [-0.36732985]
- Analyzed state at current observation: [-0.37148382]
- Analyzed state at current observation: [-0.36798059]
- Analyzed state at current observation: [-0.37371077]
- Analyzed state at current observation: [-0.3661228]
- Analyzed state at current observation: [-0.36777529]
- Analyzed state at current observation: [-0.37681677]
- Analyzed state at current observation: [-0.37007654]
- Analyzed state at current observation: [-0.37974517]
- Analyzed state at current observation: [-0.37964703]
- Analyzed state at current observation: [-0.37514278]
- Analyzed state at current observation: [-0.38143128]
- Analyzed state at current observation: [-0.38790654]
- Analyzed state at current observation: [-0.38880008]
- Analyzed state at current observation: [-0.38393577]
- Analyzed state at current observation: [-0.3831028]
- Analyzed state at current observation: [-0.37680097]
- Analyzed state at current observation: [-0.37891813]
- Analyzed state at current observation: [-0.38147782]
- Analyzed state at current observation: [-0.37981569]
- Analyzed state at current observation: [-0.38274266]
- Analyzed state at current observation: [-0.38418507]
- Analyzed state at current observation: [-0.38923054]
- Analyzed state at current observation: [-0.38400006]
- Analyzed state at current observation: [-0.38562502]
- Analyzed state at current observation: [-0.3840503]
- Analyzed state at current observation: [-0.38775222]
- Analyzed state at current observation: [-0.37700787]
- Analyzed state at current observation: [-0.37328191]
- Analyzed state at current observation: [-0.38024181]
- Analyzed state at current observation: [-0.3815806]
- Analyzed state at current observation: [-0.38392063]
- Analyzed state at current observation: [-0.38539266]
- Analyzed state at current observation: [-0.37856929]
- Analyzed state at current observation: [-0.37744505]
- Analyzed state at current observation: [-0.37154554]
- Analyzed state at current observation: [-0.37405773]
- Analyzed state at current observation: [-0.37725236]
+ Analyzed state at final observation: [-0.37725236]
Final a posteriori variance: [[0.00033921]]
iteratively. The keyword "*nextStep*", included in the execution order, allows
to not store the background in duplicate of the previous analysis.
-In a completely similar way to the reanalysis, the estimate is made in
-displaying intermediate results during iterative filtering. Thanks to these
-intermediate information, one can also obtain the graphs illustrating the
-estimation of the state and the associated *a posteriori* error covariance.
+In an entirely similar way to the reanalysis (knowing that intermediate results
+can be displayed, which are omitted here for simplicity), estimation gives the
+same results during iterative filtering. Thanks to these intermediate
+information, one can also obtain the graphs illustrating the estimation of the
+state and the associated *a posteriori* error covariance.
"CurrentIterationNumber",
"CurrentOptimum",
"CurrentState",
+ "ForecastCovariance",
"ForecastState",
"IndexOfOptimum",
"InnovationAtCurrentAnalysis",
.. include:: snippets/CurrentState.rst
+.. include:: snippets/ForecastCovariance.rst
+
.. include:: snippets/ForecastState.rst
.. include:: snippets/IndexOfOptimum.rst
from adao import adaoBuilder
case = adaoBuilder.New('')
#
+case.setBackground (Vector = [0.])
+case.setBackgroundError (ScalarSparseMatrix = 1.)
+#
case.setObservationOperator(Matrix = [1.])
case.setObservationError (ScalarSparseMatrix = 0.1**2)
#
],
},
)
-case.setObserver(
- Info=" État analysé à l'observation courante :",
- Template='ValuePrinter',
- Variable='Analysis',
- )
#
# Boucle pour obtenir une analyse à l'arrivée de chaque observation
#
-XaStep, VaStep = 0., 1.
for i in range(1,len(Yobs)):
- case.setBackground (Vector = "%s"%float(XaStep))
- case.setBackgroundError (ScalarSparseMatrix = "%s"%float(VaStep))
- case.setObservation (Vector = Yobs[i])
+ case.setObservation(Vector = Yobs[i])
case.execute( nextStep = True )
- XaStep = case.get("Analysis")[-1]
- VaStep = case.get("APosterioriCovariance")[-1]
#
Xa = case.get("Analysis")
Pa = case.get("APosterioriCovariance")
#
+print(" État analysé à l'observation finale :", Xa[-1])
print("")
-print(" Variance a posteriori finale :",Pa[-1])
+print(" Variance a posteriori finale :", Pa[-1])
print("")
#
#-------------------------------------------------------------------------------
------------------------------------------------
Observations bruitées acquises sur 50 pas de temps
- État analysé à l'observation courante : [0.]
- État analysé à l'observation courante : [-0.41804504]
- État analysé à l'observation courante : [-0.3114053]
- État analysé à l'observation courante : [-0.31191336]
- État analysé à l'observation courante : [-0.32761493]
- État analysé à l'observation courante : [-0.33597167]
- État analysé à l'observation courante : [-0.35629573]
- État analysé à l'observation courante : [-0.36840289]
- État analysé à l'observation courante : [-0.37392713]
- État analysé à l'observation courante : [-0.36331937]
- État analysé à l'observation courante : [-0.35750362]
- État analysé à l'observation courante : [-0.37963052]
- État analysé à l'observation courante : [-0.37117993]
- État analysé à l'observation courante : [-0.36732985]
- État analysé à l'observation courante : [-0.37148382]
- État analysé à l'observation courante : [-0.36798059]
- État analysé à l'observation courante : [-0.37371077]
- État analysé à l'observation courante : [-0.3661228]
- État analysé à l'observation courante : [-0.36777529]
- État analysé à l'observation courante : [-0.37681677]
- État analysé à l'observation courante : [-0.37007654]
- État analysé à l'observation courante : [-0.37974517]
- État analysé à l'observation courante : [-0.37964703]
- État analysé à l'observation courante : [-0.37514278]
- État analysé à l'observation courante : [-0.38143128]
- État analysé à l'observation courante : [-0.38790654]
- État analysé à l'observation courante : [-0.38880008]
- État analysé à l'observation courante : [-0.38393577]
- État analysé à l'observation courante : [-0.3831028]
- État analysé à l'observation courante : [-0.37680097]
- État analysé à l'observation courante : [-0.37891813]
- État analysé à l'observation courante : [-0.38147782]
- État analysé à l'observation courante : [-0.37981569]
- État analysé à l'observation courante : [-0.38274266]
- État analysé à l'observation courante : [-0.38418507]
- État analysé à l'observation courante : [-0.38923054]
- État analysé à l'observation courante : [-0.38400006]
- État analysé à l'observation courante : [-0.38562502]
- État analysé à l'observation courante : [-0.3840503]
- État analysé à l'observation courante : [-0.38775222]
- État analysé à l'observation courante : [-0.37700787]
- État analysé à l'observation courante : [-0.37328191]
- État analysé à l'observation courante : [-0.38024181]
- État analysé à l'observation courante : [-0.3815806]
- État analysé à l'observation courante : [-0.38392063]
- État analysé à l'observation courante : [-0.38539266]
- État analysé à l'observation courante : [-0.37856929]
- État analysé à l'observation courante : [-0.37744505]
- État analysé à l'observation courante : [-0.37154554]
- État analysé à l'observation courante : [-0.37405773]
- État analysé à l'observation courante : [-0.37725236]
+ État analysé à l'observation finale : [-0.37725236]
Variance a posteriori finale : [[0.00033921]]
itérativement. Le mot-clé "*nextStep*", inclut dans l'ordre d'exécution, permet
de ne pas stocker l'ébauche en double de l'analyse précédente.
-De manière entièrement similaire à la réanalyse, l'estimation s'effectue en
-affichant des résultats intermédiaires lors du filtrage itératif. Grâce à ces
-informations intermédiaires, on peut aussi obtenir les graphiques illustrant
-l'estimation de l'état et de la covariance d'erreur *a posteriori* associée.
+De manière entièrement similaire à la réanalyse (sachant que l'on peut afficher
+des résultats intermédiaires qui sont ici omis par simplicité), l'estimation
+donne les mêmes résultats lors du filtrage itératif. Grâce à ces informations
+intermédiaires, on peut aussi obtenir les graphiques illustrant l'estimation de
+l'état et de la covariance d'erreur *a posteriori* associée.
# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
import logging
-from daCore import BasicObjects
+from daCore import BasicObjects, NumericObjects
import numpy
# ==============================================================================
"CurrentIterationNumber",
"CurrentOptimum",
"CurrentState",
+ "ForecastCovariance",
"ForecastState",
"IndexOfOptimum",
"InnovationAtCurrentAnalysis",
def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
#
- if self._parameters["EstimationOf"] == "Parameters":
- self._parameters["StoreInternalVariables"] = True
- #
- # Opérateurs
- # ----------
- Ht = HO["Tangent"].asMatrix(Xb)
- Ha = HO["Adjoint"].asMatrix(Xb)
- #
- if self._parameters["EstimationOf"] == "State":
- Mt = EM["Tangent"].asMatrix(Xb)
- Ma = EM["Adjoint"].asMatrix(Xb)
- #
- if CM is not None and "Tangent" in CM and U is not None:
- Cm = CM["Tangent"].asMatrix(Xb)
- else:
- Cm = None
- #
- # Nombre de pas identique au nombre de pas d'observations
- # -------------------------------------------------------
- if hasattr(Y,"stepnumber"):
- duration = Y.stepnumber()
- else:
- duration = 2
- #
- # Précalcul des inversions de B et R
- # ----------------------------------
- if self._parameters["StoreInternalVariables"] \
- or self._toStore("CostFunctionJ") \
- or self._toStore("CostFunctionJb") \
- or self._toStore("CostFunctionJo") \
- or self._toStore("CurrentOptimum") \
- or self._toStore("APosterioriCovariance"):
- BI = B.getI()
- RI = R.getI()
- #
- # Initialisation
- # --------------
- Xn = Xb
- Pn = B
- #
- if len(self.StoredVariables["Analysis"])==0 or not self._parameters["nextStep"]:
- self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["Analysis"]) )
- self.StoredVariables["Analysis"].store( numpy.ravel(Xn) )
- if self._toStore("APosterioriCovariance"):
- self.StoredVariables["APosterioriCovariance"].store( Pn.asfullmatrix(Xn.size) )
- covarianceXa = Pn
- if self._parameters["EstimationOf"] == "Parameters":
- covarianceXaMin = Pn
- #
- if self._parameters["EstimationOf"] == "Parameters":
- XaMin = Xn
- previousJMinimum = numpy.finfo(float).max
- #
- for step in range(duration-1):
- if hasattr(Y,"store"):
- Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
- else:
- Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
- #
- if U is not None:
- if hasattr(U,"store") and len(U)>1:
- Un = numpy.asmatrix(numpy.ravel( U[step] )).T
- elif hasattr(U,"store") and len(U)==1:
- Un = numpy.asmatrix(numpy.ravel( U[0] )).T
- else:
- Un = numpy.asmatrix(numpy.ravel( U )).T
- else:
- Un = None
- #
- if self._parameters["EstimationOf"] == "State":
- Xn_predicted = Mt * Xn
- if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
- Cm = Cm.reshape(Xn.size,Un.size) # ADAO & check shape
- Xn_predicted = Xn_predicted + Cm * Un
- Pn_predicted = Q + Mt * Pn * Ma
- elif self._parameters["EstimationOf"] == "Parameters":
- # --- > Par principe, M = Id, Q = 0
- Xn_predicted = Xn
- Pn_predicted = Pn
- #
- if self._parameters["EstimationOf"] == "State":
- _HX = Ht * Xn_predicted
- _Innovation = Ynpu - _HX
- elif self._parameters["EstimationOf"] == "Parameters":
- _HX = Ht * Xn_predicted
- _Innovation = Ynpu - _HX
- if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
- _Innovation = _Innovation - Cm * Un
- #
- Kn = Pn_predicted * Ha * numpy.linalg.inv(R + numpy.dot(Ht, Pn_predicted * Ha))
- Xn = Xn_predicted + Kn * _Innovation
- Pn = Pn_predicted - Kn * Ht * Pn_predicted
- Xa = Xn # Pointeurs
- #
- self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["Analysis"]) )
- # ---> avec analysis
- self.StoredVariables["Analysis"].store( Xa )
- if self._toStore("SimulatedObservationAtCurrentAnalysis"):
- self.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( Ht * Xn )
- if self._toStore("InnovationAtCurrentAnalysis"):
- self.StoredVariables["InnovationAtCurrentAnalysis"].store( _Innovation )
- # ---> avec current state
- if self._parameters["StoreInternalVariables"] \
- or self._toStore("CurrentState"):
- self.StoredVariables["CurrentState"].store( Xn )
- if self._toStore("ForecastState"):
- self.StoredVariables["ForecastState"].store( Xn_predicted )
- if self._toStore("BMA"):
- self.StoredVariables["BMA"].store( Xn_predicted - Xa )
- if self._toStore("InnovationAtCurrentState"):
- self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
- if self._toStore("SimulatedObservationAtCurrentState") \
- or self._toStore("SimulatedObservationAtCurrentOptimum"):
- self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
- # ---> autres
- if self._parameters["StoreInternalVariables"] \
- or self._toStore("CostFunctionJ") \
- or self._toStore("CostFunctionJb") \
- or self._toStore("CostFunctionJo") \
- or self._toStore("CurrentOptimum") \
- or self._toStore("APosterioriCovariance"):
- Jb = float( 0.5 * (Xa - Xb).T * BI * (Xa - Xb) )
- Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
- J = Jb + Jo
- self.StoredVariables["CostFunctionJb"].store( Jb )
- self.StoredVariables["CostFunctionJo"].store( Jo )
- self.StoredVariables["CostFunctionJ" ].store( J )
- #
- if self._toStore("IndexOfOptimum") \
- or self._toStore("CurrentOptimum") \
- or self._toStore("CostFunctionJAtCurrentOptimum") \
- or self._toStore("CostFunctionJbAtCurrentOptimum") \
- or self._toStore("CostFunctionJoAtCurrentOptimum") \
- or self._toStore("SimulatedObservationAtCurrentOptimum"):
- IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
- if self._toStore("IndexOfOptimum"):
- self.StoredVariables["IndexOfOptimum"].store( IndexMin )
- if self._toStore("CurrentOptimum"):
- self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["Analysis"][IndexMin] )
- if self._toStore("SimulatedObservationAtCurrentOptimum"):
- self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentAnalysis"][IndexMin] )
- if self._toStore("CostFunctionJbAtCurrentOptimum"):
- self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
- if self._toStore("CostFunctionJoAtCurrentOptimum"):
- self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
- if self._toStore("CostFunctionJAtCurrentOptimum"):
- self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
- if self._toStore("APosterioriCovariance"):
- self.StoredVariables["APosterioriCovariance"].store( Pn )
- if self._parameters["EstimationOf"] == "Parameters" \
- and J < previousJMinimum:
- previousJMinimum = J
- XaMin = Xa
- if self._toStore("APosterioriCovariance"):
- covarianceXaMin = Pn
- #
- # Stockage final supplémentaire de l'optimum en estimation de paramètres
- # ----------------------------------------------------------------------
- if self._parameters["EstimationOf"] == "Parameters":
- self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["Analysis"]) )
- self.StoredVariables["Analysis"].store( XaMin )
- if self._toStore("APosterioriCovariance"):
- self.StoredVariables["APosterioriCovariance"].store( covarianceXaMin )
- if self._toStore("BMA"):
- self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(XaMin) )
+ #--------------------------
+ NumericObjects.stdkf(self, Xb, Y, U, HO, EM, CM, R, B, Q)
+ #--------------------------
#
self._post_run(HO)
return 0
Xn = selfA._getInternalState("Xn")
Pn = selfA._getInternalState("Pn")
#
- previousJMinimum = numpy.finfo(float).max
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ XaMin = Xn
+ previousJMinimum = numpy.finfo(float).max
#
for step in range(duration-1):
if hasattr(Y,"store"):
selfA._setInternalState("Pn", Pn)
#--------------------------
#
- if selfA._parameters["StoreInternalVariables"] \
- or selfA._toStore("CostFunctionJ") \
- or selfA._toStore("CostFunctionJb") \
- or selfA._toStore("CostFunctionJo") \
- or selfA._toStore("APosterioriCovariance") \
- or selfA._toStore("InnovationAtCurrentAnalysis") \
- or selfA._toStore("SimulatedObservationAtCurrentAnalysis") \
- or selfA._toStore("SimulatedObservationAtCurrentOptimum"):
- _HXa = numpy.asmatrix(numpy.ravel( H((Xa, Un)) )).T
- #
selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
# ---> avec analysis
selfA.StoredVariables["Analysis"].store( Xa )
if selfA._toStore("SimulatedObservationAtCurrentAnalysis"):
- selfA.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( _HXa )
+ selfA.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( H((Xa, Un)) )
if selfA._toStore("InnovationAtCurrentAnalysis"):
selfA.StoredVariables["InnovationAtCurrentAnalysis"].store( _Innovation )
# ---> avec current state
#
return 0
+# ==============================================================================
+def stdkf(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
+ """
+ Standard Kalman Filter
+ """
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ selfA._parameters["StoreInternalVariables"] = True
+ #
+ # Opérateurs
+ # ----------
+ Ht = HO["Tangent"].asMatrix(Xb)
+ Ha = HO["Adjoint"].asMatrix(Xb)
+ #
+ if selfA._parameters["EstimationOf"] == "State":
+ Mt = EM["Tangent"].asMatrix(Xb)
+ Ma = EM["Adjoint"].asMatrix(Xb)
+ #
+ if CM is not None and "Tangent" in CM and U is not None:
+ Cm = CM["Tangent"].asMatrix(Xb)
+ else:
+ Cm = None
+ #
+ # Durée d'observation et tailles
+ if hasattr(Y,"stepnumber"):
+ duration = Y.stepnumber()
+ __p = numpy.cumprod(Y.shape())[-1]
+ else:
+ duration = 2
+ __p = numpy.array(Y).size
+ #
+ # Précalcul des inversions de B et R
+ if selfA._parameters["StoreInternalVariables"] \
+ or selfA._toStore("CostFunctionJ") \
+ or selfA._toStore("CostFunctionJb") \
+ or selfA._toStore("CostFunctionJo") \
+ or selfA._toStore("CurrentOptimum") \
+ or selfA._toStore("APosterioriCovariance"):
+ BI = B.getI()
+ RI = R.getI()
+ #
+ __n = Xb.size
+ #
+ if len(selfA.StoredVariables["Analysis"])==0 or not selfA._parameters["nextStep"]:
+ Xn = Xb
+ Pn = B
+ selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
+ selfA.StoredVariables["Analysis"].store( Xb )
+ if selfA._toStore("APosterioriCovariance"):
+ if hasattr(B,"asfullmatrix"):
+ selfA.StoredVariables["APosterioriCovariance"].store( B.asfullmatrix(__n) )
+ else:
+ selfA.StoredVariables["APosterioriCovariance"].store( B )
+ selfA._setInternalState("seed", numpy.random.get_state())
+ elif selfA._parameters["nextStep"]:
+ Xn = selfA._getInternalState("Xn")
+ Pn = selfA._getInternalState("Pn")
+ #
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ XaMin = Xn
+ previousJMinimum = numpy.finfo(float).max
+ #
+ for step in range(duration-1):
+ if hasattr(Y,"store"):
+ Ynpu = numpy.ravel( Y[step+1] ).reshape((__p,1))
+ else:
+ Ynpu = numpy.ravel( Y ).reshape((__p,1))
+ #
+ if U is not None:
+ if hasattr(U,"store") and len(U)>1:
+ Un = numpy.asmatrix(numpy.ravel( U[step] )).T
+ elif hasattr(U,"store") and len(U)==1:
+ Un = numpy.asmatrix(numpy.ravel( U[0] )).T
+ else:
+ Un = numpy.asmatrix(numpy.ravel( U )).T
+ else:
+ Un = None
+ #
+ if selfA._parameters["EstimationOf"] == "State": # Forecast + Q and observation of forecast
+ Xn_predicted = Mt * Xn
+ if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
+ Cm = Cm.reshape(__n,Un.size) # ADAO & check shape
+ Xn_predicted = Xn_predicted + Cm * Un
+ Pn_predicted = Q + Mt * Pn * Ma
+ elif selfA._parameters["EstimationOf"] == "Parameters": # Observation of forecast
+ # --- > Par principe, M = Id, Q = 0
+ Xn_predicted = Xn
+ Pn_predicted = Pn
+ #
+ if selfA._parameters["EstimationOf"] == "State":
+ HX_predicted = Ht * Xn_predicted
+ _Innovation = Ynpu - HX_predicted
+ elif selfA._parameters["EstimationOf"] == "Parameters":
+ HX_predicted = Ht * Xn_predicted
+ _Innovation = Ynpu - HX_predicted
+ if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
+ _Innovation = _Innovation - Cm * Un
+ #
+ Kn = Pn_predicted * Ha * numpy.linalg.inv(R + numpy.dot(Ht, Pn_predicted * Ha))
+ Xn = Xn_predicted + Kn * _Innovation
+ Pn = Pn_predicted - Kn * Ht * Pn_predicted
+ #
+ Xa = Xn # Pointeurs
+ #--------------------------
+ selfA._setInternalState("Xn", Xn)
+ selfA._setInternalState("Pn", Pn)
+ #--------------------------
+ #
+ selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
+ # ---> avec analysis
+ selfA.StoredVariables["Analysis"].store( Xa )
+ if selfA._toStore("SimulatedObservationAtCurrentAnalysis"):
+ selfA.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( Ht * Xa )
+ if selfA._toStore("InnovationAtCurrentAnalysis"):
+ selfA.StoredVariables["InnovationAtCurrentAnalysis"].store( _Innovation )
+ # ---> avec current state
+ if selfA._parameters["StoreInternalVariables"] \
+ or selfA._toStore("CurrentState"):
+ selfA.StoredVariables["CurrentState"].store( Xn )
+ if selfA._toStore("ForecastState"):
+ selfA.StoredVariables["ForecastState"].store( Xn_predicted )
+ if selfA._toStore("ForecastCovariance"):
+ selfA.StoredVariables["ForecastCovariance"].store( Pn_predicted )
+ if selfA._toStore("BMA"):
+ selfA.StoredVariables["BMA"].store( Xn_predicted - Xa )
+ if selfA._toStore("InnovationAtCurrentState"):
+ selfA.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
+ if selfA._toStore("SimulatedObservationAtCurrentState") \
+ or selfA._toStore("SimulatedObservationAtCurrentOptimum"):
+ selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( HX_predicted )
+ # ---> autres
+ if selfA._parameters["StoreInternalVariables"] \
+ or selfA._toStore("CostFunctionJ") \
+ or selfA._toStore("CostFunctionJb") \
+ or selfA._toStore("CostFunctionJo") \
+ or selfA._toStore("CurrentOptimum") \
+ or selfA._toStore("APosterioriCovariance"):
+ Jb = float( 0.5 * (Xa - Xb).T * BI * (Xa - Xb) )
+ Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
+ J = Jb + Jo
+ selfA.StoredVariables["CostFunctionJb"].store( Jb )
+ selfA.StoredVariables["CostFunctionJo"].store( Jo )
+ selfA.StoredVariables["CostFunctionJ" ].store( J )
+ #
+ if selfA._toStore("IndexOfOptimum") \
+ or selfA._toStore("CurrentOptimum") \
+ or selfA._toStore("CostFunctionJAtCurrentOptimum") \
+ or selfA._toStore("CostFunctionJbAtCurrentOptimum") \
+ or selfA._toStore("CostFunctionJoAtCurrentOptimum") \
+ or selfA._toStore("SimulatedObservationAtCurrentOptimum"):
+ IndexMin = numpy.argmin( selfA.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
+ if selfA._toStore("IndexOfOptimum"):
+ selfA.StoredVariables["IndexOfOptimum"].store( IndexMin )
+ if selfA._toStore("CurrentOptimum"):
+ selfA.StoredVariables["CurrentOptimum"].store( selfA.StoredVariables["Analysis"][IndexMin] )
+ if selfA._toStore("SimulatedObservationAtCurrentOptimum"):
+ selfA.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( selfA.StoredVariables["SimulatedObservationAtCurrentAnalysis"][IndexMin] )
+ if selfA._toStore("CostFunctionJbAtCurrentOptimum"):
+ selfA.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJb"][IndexMin] )
+ if selfA._toStore("CostFunctionJoAtCurrentOptimum"):
+ selfA.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( selfA.StoredVariables["CostFunctionJo"][IndexMin] )
+ if selfA._toStore("CostFunctionJAtCurrentOptimum"):
+ selfA.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( selfA.StoredVariables["CostFunctionJ" ][IndexMin] )
+ if selfA._toStore("APosterioriCovariance"):
+ selfA.StoredVariables["APosterioriCovariance"].store( Pn )
+ if selfA._parameters["EstimationOf"] == "Parameters" \
+ and J < previousJMinimum:
+ previousJMinimum = J
+ XaMin = Xa
+ if selfA._toStore("APosterioriCovariance"):
+ covarianceXaMin = selfA.StoredVariables["APosterioriCovariance"][-1]
+ #
+ # Stockage final supplémentaire de l'optimum en estimation de paramètres
+ # ----------------------------------------------------------------------
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
+ selfA.StoredVariables["Analysis"].store( XaMin )
+ if selfA._toStore("APosterioriCovariance"):
+ selfA.StoredVariables["APosterioriCovariance"].store( covarianceXaMin )
+ if selfA._toStore("BMA"):
+ selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(XaMin) )
+ #
+ return 0
+
# ==============================================================================
def std3dvar(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
"""
