# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
import logging
-from daCore import BasicObjects, PlatformInfo
-import numpy, math
-mfp = PlatformInfo.PlatformInfo().MaximumPrecision()
+from daCore import BasicObjects, NumericObjects
+import numpy
# ==============================================================================
class ElementaryAlgorithm(BasicObjects.Algorithm):
def __init__(self):
BasicObjects.Algorithm.__init__(self, "ENSEMBLEKALMANFILTER")
+ self.defineRequiredParameter(
+ name = "Minimizer",
+ default = "StochasticEnKF",
+ typecast = str,
+ message = "Minimiseur utilisé",
+ listval = ["StochasticEnKF", "DeterministicEnKF", "ETKF"],
+ )
self.defineRequiredParameter(
name = "NumberOfMembers",
default = 100,
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
- # ----------
- H = HO["Direct"].appliedControledFormTo
- #
- if self._parameters["EstimationOf"] == "State":
- M = EM["Direct"].appliedControledFormTo
- #
- 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()
- __p = numpy.cumprod(Y.shape())[-1]
+ if self._parameters["Minimizer"] == "StochasticEnKF":
+ NumericObjects.senkf(self, Xb, Y, U, HO, EM, CM, R, B, Q)
+ elif self._parameters["Minimizer"] in ["DeterministicEnKF", "ETKF"]:
+ NumericObjects.etkf(self, Xb, Y, U, HO, EM, CM, R, B, Q)
else:
- duration = 2
- __p = numpy.array(Y).size
- #
- # 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()
- # BIdemi = B.choleskyI()
- # RIdemi = R.choleskyI()
- #
- # Initialisation
- # --------------
- __n = Xb.size
- __m = self._parameters["NumberOfMembers"]
- Xn = numpy.asmatrix(numpy.dot( Xb.reshape(__n,1), numpy.ones((1,__m)) ))
- if hasattr(B,"asfullmatrix"): Pn = B.asfullmatrix(__n)
- else: Pn = B
- if hasattr(R,"asfullmatrix"): Rn = R.asfullmatrix(__p)
- else: Rn = R
- if hasattr(Q,"asfullmatrix"): Qn = Q.asfullmatrix(__n)
- else: Qn = Q
- #
- if len(self.StoredVariables["Analysis"])==0 or not self._parameters["nextStep"]:
- self.StoredVariables["Analysis"].store( numpy.ravel(Xb) )
- if self._toStore("APosterioriCovariance"):
- self.StoredVariables["APosterioriCovariance"].store( Pn )
- covarianceXa = Pn
- #
- Xa = Xb
- XaMin = Xb
- previousJMinimum = numpy.finfo(float).max
- #
- # Predimensionnement
- Xn_predicted = numpy.asmatrix(numpy.zeros((__n,__m)))
- HX_predicted = numpy.asmatrix(numpy.zeros((__p,__m)))
- #
- 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":
- for i in range(__m):
- qi = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__n), Qn, (1,1,1))).T
- Xn_predicted[:,i] = numpy.asmatrix(numpy.ravel( M((Xn[:,i], Un)) )).T + qi
- HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
- 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
- elif self._parameters["EstimationOf"] == "Parameters":
- # --- > Par principe, M = Id, Q = 0
- Xn_predicted = Xn
- #
- Xfm = numpy.asmatrix(numpy.ravel(Xn_predicted.mean(axis=1, dtype=mfp).astype('float'))).T
- Hfm = numpy.asmatrix(numpy.ravel(HX_predicted.mean(axis=1, dtype=mfp).astype('float'))).T
- #
- PfHT, HPfHT = 0., 0.
- for i in range(__m):
- Exfi = Xn_predicted[:,i] - Xfm
- Eyfi = HX_predicted[:,i] - Hfm
- PfHT += Exfi * Eyfi.T
- HPfHT += Eyfi * Eyfi.T
- PfHT = (1./(__m-1)) * PfHT
- HPfHT = (1./(__m-1)) * HPfHT
- K = PfHT * ( R + HPfHT ).I
- del PfHT, HPfHT
- #
- for i in range(__m):
- ri = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__p), Rn, (1,1,1))).T
- Xn[:,i] = Xn_predicted[:,i] + K * (Ynpu + ri - HX_predicted[:,i])
- #
- Xa = Xn.mean(axis=1, dtype=mfp).astype('float')
- #
- if self._parameters["StoreInternalVariables"] \
- or self._toStore("CostFunctionJ") \
- or self._toStore("CostFunctionJb") \
- or self._toStore("CostFunctionJo") \
- or self._toStore("APosterioriCovariance") \
- or self._toStore("InnovationAtCurrentAnalysis") \
- or self._toStore("SimulatedObservationAtCurrentAnalysis") \
- or self._toStore("SimulatedObservationAtCurrentOptimum"):
- _HXa = numpy.asmatrix(numpy.ravel( H((Xa, Un)) )).T
- _Innovation = Ynpu - _HXa
- #
- self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["Analysis"]) )
- # ---> avec analysis
- self.StoredVariables["Analysis"].store( Xa )
- if self._toStore("SimulatedObservationAtCurrentAnalysis"):
- self.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( _HXa )
- 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( - HX_predicted + Ynpu )
- if self._toStore("SimulatedObservationAtCurrentState") \
- or self._toStore("SimulatedObservationAtCurrentOptimum"):
- self.StoredVariables["SimulatedObservationAtCurrentState"].store( HX_predicted )
- # ---> 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"):
- Pn = 0.
- for i in range(__m):
- Eai = Xn[:,i] - Xa
- Pn += Eai * Eai.T
- Pn = (1./(__m-1)) * Pn
- 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) )
+ raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
#
self._post_run(HO)
return 0
#
return variables, Ecart, [n,p,iteration,increment,0]
+# ==============================================================================
+def senkf(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
+ """
+ Stochastic EnKF (Envensen 1994, Burgers 1998)
+
+ selfA est identique au "self" d'algorithme appelant et contient les
+ valeurs.
+ """
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ selfA._parameters["StoreInternalVariables"] = True
+ #
+ # Opérateurs
+ # ----------
+ H = HO["Direct"].appliedControledFormTo
+ #
+ if selfA._parameters["EstimationOf"] == "State":
+ M = EM["Direct"].appliedControledFormTo
+ #
+ 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()
+ __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()
+ #
+ # Initialisation
+ # --------------
+ __n = Xb.size
+ __m = selfA._parameters["NumberOfMembers"]
+ Xn = numpy.asmatrix(numpy.dot( Xb.reshape(__n,1), numpy.ones((1,__m)) ))
+ if hasattr(B,"asfullmatrix"): Pn = B.asfullmatrix(__n)
+ else: Pn = B
+ if hasattr(R,"asfullmatrix"): Rn = R.asfullmatrix(__p)
+ else: Rn = R
+ if hasattr(Q,"asfullmatrix"): Qn = Q.asfullmatrix(__n)
+ else: Qn = Q
+ #
+ if len(selfA.StoredVariables["Analysis"])==0 or not selfA._parameters["nextStep"]:
+ selfA.StoredVariables["Analysis"].store( numpy.ravel(Xb) )
+ if selfA._toStore("APosterioriCovariance"):
+ selfA.StoredVariables["APosterioriCovariance"].store( Pn )
+ covarianceXa = Pn
+ #
+ previousJMinimum = numpy.finfo(float).max
+ #
+ # Predimensionnement
+ Xn_predicted = numpy.asmatrix(numpy.zeros((__n,__m)))
+ HX_predicted = numpy.asmatrix(numpy.zeros((__p,__m)))
+ #
+ 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 selfA._parameters["EstimationOf"] == "State": # Forecast + Q and observation of forecast
+ for i in range(__m):
+ qi = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__n), Qn, (1,1,1))).T
+ Xn_predicted[:,i] = numpy.asmatrix(numpy.ravel( M((Xn[:,i], Un)) )).T + qi
+ HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
+ 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
+ elif selfA._parameters["EstimationOf"] == "Parameters": # Observation of forecast
+ # --- > Par principe, M = Id, Q = 0
+ Xn_predicted = Xn
+ for i in range(__m):
+ HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
+ #
+ # Mean of forecast and observation of forecast
+ Xfm = numpy.asmatrix(numpy.ravel(Xn_predicted.mean(axis=1, dtype=mfp).astype('float'))).T
+ Hfm = numpy.asmatrix(numpy.ravel(HX_predicted.mean(axis=1, dtype=mfp).astype('float'))).T
+ #
+ PfHT, HPfHT = 0., 0.
+ for i in range(__m):
+ Exfi = Xn_predicted[:,i] - Xfm
+ Eyfi = HX_predicted[:,i] - Hfm
+ PfHT += Exfi * Eyfi.T
+ HPfHT += Eyfi * Eyfi.T
+ PfHT = (1./(__m-1)) * PfHT
+ HPfHT = (1./(__m-1)) * HPfHT
+ K = PfHT * ( R + HPfHT ).I
+ del PfHT, HPfHT
+ #
+ for i in range(__m):
+ ri = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__p), Rn, (1,1,1))).T
+ Xn[:,i] = Xn_predicted[:,i] + K * (Ynpu + ri - HX_predicted[:,i])
+ #
+ Xa = Xn.mean(axis=1, dtype=mfp).astype('float')
+ #
+ 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
+ _Innovation = Ynpu - _HXa
+ #
+ selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
+ # ---> avec analysis
+ selfA.StoredVariables["Analysis"].store( Xa )
+ if selfA._toStore("SimulatedObservationAtCurrentAnalysis"):
+ selfA.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( _HXa )
+ 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("BMA"):
+ selfA.StoredVariables["BMA"].store( Xn_predicted - Xa )
+ if selfA._toStore("InnovationAtCurrentState"):
+ selfA.StoredVariables["InnovationAtCurrentState"].store( - HX_predicted + Ynpu )
+ 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"):
+ Eai = (1/numpy.sqrt(__m-1)) * (Xn - Xa.reshape((__n,-1))) # Anomalies
+ Pn = Eai @ Eai.T
+ Pn = 0.5 * (Pn + Pn.T)
+ selfA.StoredVariables["APosterioriCovariance"].store( Pn )
+ if selfA._parameters["EstimationOf"] == "Parameters" \
+ and J < previousJMinimum:
+ previousJMinimum = J
+ XaMin = Xa
+ if selfA._toStore("APosterioriCovariance"):
+ covarianceXaMin = Pn
+ #
+ # 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 etkf(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
+ """
+ Ensemble-Transform EnKF (ETKF or Deterministic EnKF: Bishop 2001, Hunt 2007)
+
+ selfA est identique au "self" d'algorithme appelant et contient les
+ valeurs.
+ """
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ selfA._parameters["StoreInternalVariables"] = True
+ #
+ # Opérateurs
+ # ----------
+ H = HO["Direct"].appliedControledFormTo
+ #
+ if selfA._parameters["EstimationOf"] == "State":
+ M = EM["Direct"].appliedControledFormTo
+ #
+ 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()
+ __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()
+ RIdemi = R.choleskyI()
+ #
+ # Initialisation
+ # --------------
+ __n = Xb.size
+ __m = selfA._parameters["NumberOfMembers"]
+ Xn = numpy.asmatrix(numpy.dot( Xb.reshape(__n,1), numpy.ones((1,__m)) ))
+ if hasattr(B,"asfullmatrix"): Pn = B.asfullmatrix(__n)
+ else: Pn = B
+ if hasattr(R,"asfullmatrix"): Rn = R.asfullmatrix(__p)
+ else: Rn = R
+ if hasattr(Q,"asfullmatrix"): Qn = Q.asfullmatrix(__n)
+ else: Qn = Q
+ #
+ if len(selfA.StoredVariables["Analysis"])==0 or not selfA._parameters["nextStep"]:
+ selfA.StoredVariables["Analysis"].store( numpy.ravel(Xb) )
+ if selfA._toStore("APosterioriCovariance"):
+ selfA.StoredVariables["APosterioriCovariance"].store( Pn )
+ covarianceXa = Pn
+ #
+ previousJMinimum = numpy.finfo(float).max
+ #
+ # Predimensionnement
+ Xn_predicted = numpy.asmatrix(numpy.zeros((__n,__m)))
+ HX_predicted = numpy.asmatrix(numpy.zeros((__p,__m)))
+ #
+ 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 selfA._parameters["EstimationOf"] == "State": # Forecast + Q and observation of forecast
+ for i in range(__m):
+ qi = numpy.asmatrix(numpy.random.multivariate_normal(numpy.zeros(__n), Qn, (1,1,1))).T
+ Xn_predicted[:,i] = numpy.asmatrix(numpy.ravel( M((Xn[:,i], Un)) )).T + qi
+ HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
+ 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
+ elif selfA._parameters["EstimationOf"] == "Parameters": # Observation of forecast
+ # --- > Par principe, M = Id, Q = 0
+ Xn_predicted = Xn
+ for i in range(__m):
+ HX_predicted[:,i] = numpy.asmatrix(numpy.ravel( H((Xn_predicted[:,i], Un)) )).T
+ #
+ # Mean of forecast and observation of forecast
+ Xfm = Xn_predicted.mean(axis=1, dtype=mfp).astype('float')
+ Hfm = HX_predicted.mean(axis=1, dtype=mfp).astype('float')
+ #
+ EaX = (Xn_predicted - Xfm.reshape((__n,-1))) / numpy.sqrt(__m-1)
+ EaHX = (HX_predicted - Hfm.reshape((__p,-1))) / numpy.sqrt(__m-1)
+ #
+ mS = RIdemi * EaHX
+ delta = RIdemi * ( Ynpu.reshape((__p,-1)) - Hfm.reshape((__p,-1)) )
+ mT = numpy.linalg.inv( numpy.eye(__m) + mS.T @ mS )
+ vw = mT @ mS.transpose() @ delta
+ #
+ Tdemi = numpy.linalg.cholesky(mT)
+ mU = numpy.eye(__m)
+ #
+ Xn = Xfm.reshape((__n,-1)) + EaX @ ( vw.reshape((__m,-1)) + numpy.sqrt(__m-1) * Tdemi @ mU )
+ #
+ Xa = Xn.mean(axis=1, dtype=mfp).astype('float')
+ #
+ 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
+ _Innovation = Ynpu - _HXa
+ #
+ selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
+ # ---> avec analysis
+ selfA.StoredVariables["Analysis"].store( Xa )
+ if selfA._toStore("SimulatedObservationAtCurrentAnalysis"):
+ selfA.StoredVariables["SimulatedObservationAtCurrentAnalysis"].store( _HXa )
+ 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("BMA"):
+ selfA.StoredVariables["BMA"].store( Xn_predicted - Xa )
+ if selfA._toStore("InnovationAtCurrentState"):
+ selfA.StoredVariables["InnovationAtCurrentState"].store( - HX_predicted + Ynpu )
+ 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"):
+ Eai = (1/numpy.sqrt(__m-1)) * (Xn - Xa.reshape((__n,-1))) # Anomalies
+ Pn = Eai @ Eai.T
+ Pn = 0.5 * (Pn + Pn.T)
+ selfA.StoredVariables["APosterioriCovariance"].store( Pn )
+ if selfA._parameters["EstimationOf"] == "Parameters" \
+ and J < previousJMinimum:
+ previousJMinimum = J
+ XaMin = Xa
+ if selfA._toStore("APosterioriCovariance"):
+ covarianceXaMin = Pn
+ #
+ # 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
+
# ==============================================================================
if __name__ == "__main__":
print('\n AUTODIAGNOSTIC\n')
