"""
Calcul de l'opérateur tangent comme la Jacobienne par différences finies,
c'est-à-dire le gradient de H en X. On utilise des différences finies
- directionnelles autour du point X. X est un numpy.matrix.
+ directionnelles autour du point X. X est un numpy.ndarray.
Différences finies centrées (approximation d'ordre 2):
1/ Pour chaque composante i de X, on ajoute et on enlève la perturbation
#
return OutputCovOrEns
+# ==============================================================================
+def HessienneEstimation(nb, HaM, HtM, BI, RI):
+ "Estimation de la Hessienne"
+ #
+ HessienneI = []
+ for i in range(int(nb)):
+ _ee = numpy.zeros((nb,1))
+ _ee[i] = 1.
+ _HtEE = numpy.dot(HtM,_ee).reshape((-1,1))
+ HessienneI.append( numpy.ravel( BI * _ee + HaM * (RI * _HtEE) ) )
+ #
+ A = numpy.linalg.inv(numpy.array( HessienneI ))
+ #
+ if min(A.shape) != max(A.shape):
+ raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(selfA._name,str(A.shape)))
+ if (numpy.diag(A) < 0).any():
+ raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(selfA._name,))
+ if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
+ try:
+ L = numpy.linalg.cholesky( A )
+ except:
+ raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(selfA._name,))
+ #
+ return A
+
# ==============================================================================
def QuantilesEstimations(selfA, A, Xa, HXa = None, Hm = None, HtM = None):
"Estimation des quantiles a posteriori (selfA est modifié)"
#
return __Vector
+# ==============================================================================
+def c2ukf(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
+ """
+ Constrained Unscented Kalman Filter
+ """
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ selfA._parameters["StoreInternalVariables"] = True
+ selfA._parameters["Bounds"] = ForceNumericBounds( selfA._parameters["Bounds"] )
+ #
+ L = Xb.size
+ Alpha = selfA._parameters["Alpha"]
+ Beta = selfA._parameters["Beta"]
+ if selfA._parameters["Kappa"] == 0:
+ if selfA._parameters["EstimationOf"] == "State":
+ Kappa = 0
+ elif selfA._parameters["EstimationOf"] == "Parameters":
+ Kappa = 3 - L
+ else:
+ Kappa = selfA._parameters["Kappa"]
+ Lambda = float( Alpha**2 ) * ( L + Kappa ) - L
+ Gamma = math.sqrt( L + Lambda )
+ #
+ Ww = []
+ Ww.append( 0. )
+ for i in range(2*L):
+ Ww.append( 1. / (2.*(L + Lambda)) )
+ #
+ Wm = numpy.array( Ww )
+ Wm[0] = Lambda / (L + Lambda)
+ Wc = numpy.array( Ww )
+ Wc[0] = Lambda / (L + Lambda) + (1. - Alpha**2 + Beta)
+ #
+ # Opérateurs
+ Hm = HO["Direct"].appliedControledFormTo
+ #
+ if selfA._parameters["EstimationOf"] == "State":
+ Mm = 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
+ #
+ # 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
+ if hasattr(B,"asfullmatrix"):
+ Pn = B.asfullmatrix(__n)
+ else:
+ Pn = B
+ selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
+ selfA.StoredVariables["Analysis"].store( Xb )
+ if selfA._toStore("APosterioriCovariance"):
+ selfA.StoredVariables["APosterioriCovariance"].store( Pn )
+ 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.ravel( U[step] ).reshape((-1,1))
+ elif hasattr(U,"store") and len(U)==1:
+ Un = numpy.ravel( U[0] ).reshape((-1,1))
+ else:
+ Un = numpy.ravel( U ).reshape((-1,1))
+ else:
+ Un = None
+ #
+ Pndemi = numpy.real(scipy.linalg.sqrtm(Pn))
+ Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
+ nbSpts = 2*Xn.size+1
+ #
+ if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
+ for point in range(nbSpts):
+ Xnp[:,point] = ApplyBounds( Xnp[:,point], selfA._parameters["Bounds"] )
+ #
+ XEtnnp = []
+ for point in range(nbSpts):
+ if selfA._parameters["EstimationOf"] == "State":
+ XEtnnpi = numpy.asmatrix(numpy.ravel( Mm( (Xnp[:,point], Un) ) )).T
+ 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
+ XEtnnpi = XEtnnpi + Cm * Un
+ if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
+ XEtnnpi = ApplyBounds( XEtnnpi, selfA._parameters["Bounds"] )
+ elif selfA._parameters["EstimationOf"] == "Parameters":
+ # --- > Par principe, M = Id, Q = 0
+ XEtnnpi = Xnp[:,point]
+ XEtnnp.append( XEtnnpi )
+ XEtnnp = numpy.hstack( XEtnnp )
+ #
+ Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
+ #
+ if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
+ Xncm = ApplyBounds( Xncm, selfA._parameters["Bounds"] )
+ #
+ if selfA._parameters["EstimationOf"] == "State": Pnm = Q
+ elif selfA._parameters["EstimationOf"] == "Parameters": Pnm = 0.
+ for point in range(nbSpts):
+ Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
+ #
+ if selfA._parameters["EstimationOf"] == "Parameters" and selfA._parameters["Bounds"] is not None:
+ Pnmdemi = selfA._parameters["Reconditioner"] * numpy.real(scipy.linalg.sqrtm(Pnm))
+ else:
+ Pnmdemi = numpy.real(scipy.linalg.sqrtm(Pnm))
+ #
+ Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
+ #
+ if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
+ for point in range(nbSpts):
+ Xnnp[:,point] = ApplyBounds( Xnnp[:,point], selfA._parameters["Bounds"] )
+ #
+ Ynnp = []
+ for point in range(nbSpts):
+ if selfA._parameters["EstimationOf"] == "State":
+ Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], None) ) )).T
+ elif selfA._parameters["EstimationOf"] == "Parameters":
+ Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], Un) ) )).T
+ Ynnp.append( Ynnpi )
+ Ynnp = numpy.hstack( Ynnp )
+ #
+ Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
+ #
+ Pyyn = R
+ Pxyn = 0.
+ for point in range(nbSpts):
+ Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
+ Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
+ #
+ _Innovation = Ynpu - Yncm
+ if selfA._parameters["EstimationOf"] == "Parameters":
+ if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
+ _Innovation = _Innovation - Cm * Un
+ #
+ Kn = Pxyn * Pyyn.I
+ Xn = Xncm + Kn * _Innovation
+ Pn = Pnm - Kn * Pyyn * Kn.T
+ #
+ if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
+ Xn = ApplyBounds( Xn, selfA._parameters["Bounds"] )
+ #
+ 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( Hm((Xa, Un)) )
+ 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( Xncm )
+ if selfA._toStore("ForecastCovariance"):
+ selfA.StoredVariables["ForecastCovariance"].store( Pnm )
+ if selfA._toStore("BMA"):
+ selfA.StoredVariables["BMA"].store( Xncm - Xa )
+ if selfA._toStore("InnovationAtCurrentState"):
+ selfA.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
+ if selfA._toStore("SimulatedObservationAtCurrentState") \
+ or selfA._toStore("SimulatedObservationAtCurrentOptimum"):
+ selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( Yncm )
+ # ---> 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 cekf(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
"""
#
if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
- Minimum = numpy.asmatrix(numpy.ravel( Minimum )).T
else:
- Minimum = Xb + numpy.asmatrix(numpy.ravel( Minimum )).T
+ Minimum = Xb + Minimum.reshape((-1,1))
#
Xr = Minimum
DeltaJ = selfA.StoredVariables["CostFunctionJ" ][-1] - J
iOuter = selfA.StoredVariables["CurrentIterationNumber"][-1]
#
- # Obtention de l'analyse
- # ----------------------
Xa = Xr
+ #--------------------------
#
selfA.StoredVariables["Analysis"].store( Xa )
#
else:
HXa = Hm( Xa )
#
- # Calcul de la covariance d'analyse
- # ---------------------------------
if selfA._toStore("APosterioriCovariance") or \
selfA._toStore("SimulationQuantiles") or \
selfA._toStore("JacobianMatrixAtOptimum") or \
HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
if selfA._toStore("APosterioriCovariance") or \
selfA._toStore("SimulationQuantiles"):
- HessienneI = []
- nb = Xa.size
- for i in range(nb):
- _ee = numpy.matrix(numpy.zeros(nb)).T
- _ee[i] = 1.
- _HtEE = numpy.dot(HtM,_ee)
- _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
- HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
- HessienneI = numpy.matrix( HessienneI )
- A = HessienneI.I
- if min(A.shape) != max(A.shape):
- raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(selfA._name,str(A.shape)))
- if (numpy.diag(A) < 0).any():
- raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(selfA._name,))
- if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
- try:
- L = numpy.linalg.cholesky( A )
- except:
- raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(selfA._name,))
+ A = HessienneEstimation(Xa.size, HaM, HtM, BI, RI)
if selfA._toStore("APosterioriCovariance"):
selfA.StoredVariables["APosterioriCovariance"].store( A )
if selfA._toStore("JacobianMatrixAtOptimum"):
selfA._toStore("OMB"):
d = Y - HXb
if selfA._toStore("Innovation"):
- selfA.StoredVariables["Innovation"].store( numpy.ravel(d) )
+ selfA.StoredVariables["Innovation"].store( d )
if selfA._toStore("BMA"):
selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
if selfA._toStore("OMA"):
selfA.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
if selfA._toStore("OMB"):
- selfA.StoredVariables["OMB"].store( numpy.ravel(d) )
+ selfA.StoredVariables["OMB"].store( d )
if selfA._toStore("SigmaObs2"):
TraceR = R.trace(Y.size)
- selfA.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
+ selfA.StoredVariables["SigmaObs2"].store( float( (d.T @ (numpy.ravel(Y)-numpy.ravel(HXa))) ) / TraceR )
if selfA._toStore("MahalanobisConsistency"):
selfA.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
if selfA._toStore("SimulationQuantiles"):
QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
if selfA._toStore("SimulatedObservationAtBackground"):
- selfA.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
+ selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
if selfA._toStore("SimulatedObservationAtOptimum"):
- selfA.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
+ selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
#
return 0
# Définition de la fonction-coût
# ------------------------------
def CostFunction(w):
- _W = numpy.asmatrix(numpy.ravel( w )).T
+ _W = w.reshape((-1,1))
if selfA._parameters["StoreInternalVariables"] or \
selfA._toStore("CurrentState") or \
selfA._toStore("CurrentOptimum"):
- selfA.StoredVariables["CurrentState"].store( Xb + BHT * _W )
+ selfA.StoredVariables["CurrentState"].store( Xb + BHT @ _W )
if selfA._toStore("SimulatedObservationAtCurrentState") or \
selfA._toStore("SimulatedObservationAtCurrentOptimum"):
- selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( Hm( Xb + BHT * _W ) )
+ selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( Hm( Xb + BHT @ _W ) )
if selfA._toStore("InnovationAtCurrentState"):
selfA.StoredVariables["InnovationAtCurrentState"].store( Innovation )
#
- Jb = float( 0.5 * _W.T * HBHTpR * _W )
- Jo = float( - _W.T * Innovation )
+ Jb = float( 0.5 * _W.T @ (HBHTpR @ _W) )
+ Jo = float( - _W.T @ Innovation )
J = Jb + Jo
#
selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["CostFunctionJ"]) )
return J
#
def GradientOfCostFunction(w):
- _W = numpy.asmatrix(numpy.ravel( w )).T
- GradJb = HBHTpR * _W
+ _W = w.reshape((-1,1))
+ GradJb = HBHTpR @ _W
GradJo = - Innovation
GradJ = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
return GradJ
# ----------------------------------------------------------------
if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
- Minimum = numpy.asmatrix(numpy.ravel( Minimum )).T
else:
- Minimum = Xb + BHT * numpy.asmatrix(numpy.ravel( Minimum )).T
+ Minimum = Xb + BHT @ Minimum.reshape((-1,1))
#
- # Obtention de l'analyse
- # ----------------------
Xa = Minimum
+ #--------------------------
#
selfA.StoredVariables["Analysis"].store( Xa )
#
else:
HXa = Hm( Xa )
#
- # Calcul de la covariance d'analyse
- # ---------------------------------
if selfA._toStore("APosterioriCovariance") or \
selfA._toStore("SimulationQuantiles") or \
selfA._toStore("JacobianMatrixAtOptimum") or \
selfA._toStore("SimulationQuantiles"):
BI = B.getI()
RI = R.getI()
- HessienneI = []
- nb = Xa.size
- for i in range(nb):
- _ee = numpy.matrix(numpy.zeros(nb)).T
- _ee[i] = 1.
- _HtEE = numpy.dot(HtM,_ee)
- _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
- HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
- HessienneI = numpy.matrix( HessienneI )
- A = HessienneI.I
- if min(A.shape) != max(A.shape):
- raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(selfA._name,str(A.shape)))
- if (numpy.diag(A) < 0).any():
- raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(selfA._name,))
- if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
- try:
- L = numpy.linalg.cholesky( A )
- except:
- raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(selfA._name,))
+ A = HessienneEstimation(Xa.size, HaM, HtM, BI, RI)
if selfA._toStore("APosterioriCovariance"):
selfA.StoredVariables["APosterioriCovariance"].store( A )
if selfA._toStore("JacobianMatrixAtOptimum"):
selfA._toStore("OMB"):
d = Y - HXb
if selfA._toStore("Innovation"):
- selfA.StoredVariables["Innovation"].store( numpy.ravel(d) )
+ selfA.StoredVariables["Innovation"].store( d )
if selfA._toStore("BMA"):
selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
if selfA._toStore("OMA"):
selfA.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
if selfA._toStore("OMB"):
- selfA.StoredVariables["OMB"].store( numpy.ravel(d) )
+ selfA.StoredVariables["OMB"].store( d )
if selfA._toStore("SigmaObs2"):
TraceR = R.trace(Y.size)
- selfA.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
+ selfA.StoredVariables["SigmaObs2"].store( float( (d.T @ (numpy.ravel(Y)-numpy.ravel(HXa))) ) / TraceR )
if selfA._toStore("MahalanobisConsistency"):
selfA.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
if selfA._toStore("SimulationQuantiles"):
QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
if selfA._toStore("SimulatedObservationAtBackground"):
- selfA.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
+ selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
if selfA._toStore("SimulatedObservationAtOptimum"):
- selfA.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
+ selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
#
return 0
return J
#
def GradientOfCostFunction(x):
- _X = numpy.ravel( x ).reshape((-1,1))
- _HX = Hm( _X )
- _HX = numpy.ravel( _HX ).reshape((-1,1))
+ _X = x.reshape((-1,1))
+ _HX = Hm( _X ).reshape((-1,1))
GradJb = BI * (_X - Xb)
GradJo = - Ha( (_X, RI * (Y - _HX)) )
GradJ = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
if selfA._toStore("APosterioriCovariance") or \
selfA._toStore("SimulationQuantiles"):
- HessienneI = []
- nb = Xa.size
- for i in range(nb):
- _ee = numpy.zeros(nb)
- _ee[i] = 1.
- _HtEE = numpy.dot(HtM,_ee)
- HessienneI.append( numpy.ravel( BI * _ee.reshape((-1,1)) + HaM * (RI * _HtEE.reshape((-1,1))) ) )
- A = numpy.linalg.inv(numpy.array( HessienneI ))
- if min(A.shape) != max(A.shape):
- raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(selfA._name,str(A.shape)))
- if (numpy.diag(A) < 0).any():
- raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(selfA._name,))
- if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
- try:
- L = numpy.linalg.cholesky( A )
- except:
- raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(selfA._name,))
+ A = HessienneEstimation(Xa.size, HaM, HtM, BI, RI)
if selfA._toStore("APosterioriCovariance"):
selfA.StoredVariables["APosterioriCovariance"].store( A )
if selfA._toStore("JacobianMatrixAtOptimum"):
elif (Y.size > Xb.size): KG = (BI + numpy.dot(HaM, RI * HtM)).I * HaM * RI
selfA.StoredVariables["KalmanGainAtOptimum"].store( KG )
#
+ # Calculs et/ou stockages supplémentaires
+ # ---------------------------------------
if selfA._toStore("Innovation") or \
selfA._toStore("SigmaObs2") or \
selfA._toStore("MahalanobisConsistency") or \
#
return 0
-# ==============================================================================
-def uckf(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
- """
- Constrained Unscented Kalman Filter
- """
- if selfA._parameters["EstimationOf"] == "Parameters":
- selfA._parameters["StoreInternalVariables"] = True
- selfA._parameters["Bounds"] = ForceNumericBounds( selfA._parameters["Bounds"] )
- #
- L = Xb.size
- Alpha = selfA._parameters["Alpha"]
- Beta = selfA._parameters["Beta"]
- if selfA._parameters["Kappa"] == 0:
- if selfA._parameters["EstimationOf"] == "State":
- Kappa = 0
- elif selfA._parameters["EstimationOf"] == "Parameters":
- Kappa = 3 - L
- else:
- Kappa = selfA._parameters["Kappa"]
- Lambda = float( Alpha**2 ) * ( L + Kappa ) - L
- Gamma = math.sqrt( L + Lambda )
- #
- Ww = []
- Ww.append( 0. )
- for i in range(2*L):
- Ww.append( 1. / (2.*(L + Lambda)) )
- #
- Wm = numpy.array( Ww )
- Wm[0] = Lambda / (L + Lambda)
- Wc = numpy.array( Ww )
- Wc[0] = Lambda / (L + Lambda) + (1. - Alpha**2 + Beta)
- #
- # Opérateurs
- Hm = HO["Direct"].appliedControledFormTo
- #
- if selfA._parameters["EstimationOf"] == "State":
- Mm = 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
- #
- # 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
- if hasattr(B,"asfullmatrix"):
- Pn = B.asfullmatrix(__n)
- else:
- Pn = B
- selfA.StoredVariables["CurrentIterationNumber"].store( len(selfA.StoredVariables["Analysis"]) )
- selfA.StoredVariables["Analysis"].store( Xb )
- if selfA._toStore("APosterioriCovariance"):
- selfA.StoredVariables["APosterioriCovariance"].store( Pn )
- 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.ravel( U[step] ).reshape((-1,1))
- elif hasattr(U,"store") and len(U)==1:
- Un = numpy.ravel( U[0] ).reshape((-1,1))
- else:
- Un = numpy.ravel( U ).reshape((-1,1))
- else:
- Un = None
- #
- Pndemi = numpy.linalg.cholesky(Pn)
- Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
- nbSpts = 2*Xn.size+1
- #
- if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
- for point in range(nbSpts):
- Xnp[:,point] = ApplyBounds( Xnp[:,point], selfA._parameters["Bounds"] )
- #
- XEtnnp = []
- for point in range(nbSpts):
- if selfA._parameters["EstimationOf"] == "State":
- XEtnnpi = numpy.asmatrix(numpy.ravel( Mm( (Xnp[:,point], Un) ) )).T
- 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
- XEtnnpi = XEtnnpi + Cm * Un
- if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
- XEtnnpi = ApplyBounds( XEtnnpi, selfA._parameters["Bounds"] )
- elif selfA._parameters["EstimationOf"] == "Parameters":
- # --- > Par principe, M = Id, Q = 0
- XEtnnpi = Xnp[:,point]
- XEtnnp.append( XEtnnpi )
- XEtnnp = numpy.hstack( XEtnnp )
- #
- Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
- #
- if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
- Xncm = ApplyBounds( Xncm, selfA._parameters["Bounds"] )
- #
- if selfA._parameters["EstimationOf"] == "State": Pnm = Q
- elif selfA._parameters["EstimationOf"] == "Parameters": Pnm = 0.
- for point in range(nbSpts):
- Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
- #
- if selfA._parameters["EstimationOf"] == "Parameters" and selfA._parameters["Bounds"] is not None:
- Pnmdemi = selfA._parameters["Reconditioner"] * numpy.linalg.cholesky(Pnm)
- else:
- Pnmdemi = numpy.linalg.cholesky(Pnm)
- #
- Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
- #
- if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
- for point in range(nbSpts):
- Xnnp[:,point] = ApplyBounds( Xnnp[:,point], selfA._parameters["Bounds"] )
- #
- Ynnp = []
- for point in range(nbSpts):
- if selfA._parameters["EstimationOf"] == "State":
- Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], None) ) )).T
- elif selfA._parameters["EstimationOf"] == "Parameters":
- Ynnpi = numpy.asmatrix(numpy.ravel( Hm( (Xnnp[:,point], Un) ) )).T
- Ynnp.append( Ynnpi )
- Ynnp = numpy.hstack( Ynnp )
- #
- Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
- #
- Pyyn = R
- Pxyn = 0.
- for point in range(nbSpts):
- Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
- Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
- #
- _Innovation = Ynpu - Yncm
- if selfA._parameters["EstimationOf"] == "Parameters":
- if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
- _Innovation = _Innovation - Cm * Un
- #
- Kn = Pxyn * Pyyn.I
- Xn = Xncm + Kn * _Innovation
- Pn = Pnm - Kn * Pyyn * Kn.T
- #
- if selfA._parameters["Bounds"] is not None and selfA._parameters["ConstrainedBy"] == "EstimateProjection":
- Xn = ApplyBounds( Xn, selfA._parameters["Bounds"] )
- #
- 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( Hm((Xa, Un)) )
- 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( Xncm )
- if selfA._toStore("ForecastCovariance"):
- selfA.StoredVariables["ForecastCovariance"].store( Pnm )
- if selfA._toStore("BMA"):
- selfA.StoredVariables["BMA"].store( Xncm - Xa )
- if selfA._toStore("InnovationAtCurrentState"):
- selfA.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
- if selfA._toStore("SimulatedObservationAtCurrentState") \
- or selfA._toStore("SimulatedObservationAtCurrentOptimum"):
- selfA.StoredVariables["SimulatedObservationAtCurrentState"].store( Yncm )
- # ---> 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 uskf(selfA, Xb, Y, U, HO, EM, CM, R, B, Q):
"""
else:
Un = None
#
- Pndemi = numpy.linalg.cholesky(Pn)
+ Pndemi = numpy.real(scipy.linalg.sqrtm(Pn))
Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
nbSpts = 2*Xn.size+1
#
for point in range(nbSpts):
Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
#
- Pnmdemi = numpy.linalg.cholesky(Pnm)
+ Pnmdemi = numpy.real(scipy.linalg.sqrtm(Pnm))
#
Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
#
return J
#
def GradientOfCostFunction(v):
- _V = numpy.asmatrix(numpy.ravel( v )).T
- _X = Xb + B * _V
- _HX = Hm( _X )
- _HX = numpy.asmatrix(numpy.ravel( _HX )).T
+ _V = v.reshape((-1,1))
+ _X = Xb + (B @ _V).reshape((-1,1))
+ _HX = Hm( _X ).reshape((-1,1))
GradJb = BT * _V
GradJo = - Ha( (_X, RI * (Y - _HX)) )
GradJ = numpy.ravel( GradJb ) + numpy.ravel( GradJo )
# ----------------------------------------------------------------
if selfA._parameters["StoreInternalVariables"] or selfA._toStore("CurrentState"):
Minimum = selfA.StoredVariables["CurrentState"][IndexMin]
- Minimum = numpy.asmatrix(numpy.ravel( Minimum )).T
else:
- Minimum = Xb + B * numpy.asmatrix(numpy.ravel( Minimum )).T
+ Minimum = Xb + B * Minimum.reshape((-1,1)) # Pas @
#
- # Obtention de l'analyse
- # ----------------------
Xa = Minimum
+ #--------------------------
#
selfA.StoredVariables["Analysis"].store( Xa )
#
else:
HXa = Hm( Xa )
#
- # Calcul de la covariance d'analyse
- # ---------------------------------
if selfA._toStore("APosterioriCovariance") or \
selfA._toStore("SimulationQuantiles") or \
selfA._toStore("JacobianMatrixAtOptimum") or \
if selfA._toStore("APosterioriCovariance") or \
selfA._toStore("SimulationQuantiles"):
BI = B.getI()
- HessienneI = []
- nb = Xa.size
- for i in range(nb):
- _ee = numpy.matrix(numpy.zeros(nb)).T
- _ee[i] = 1.
- _HtEE = numpy.dot(HtM,_ee)
- _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
- HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
- HessienneI = numpy.matrix( HessienneI )
- A = HessienneI.I
- if min(A.shape) != max(A.shape):
- raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(selfA._name,str(A.shape)))
- if (numpy.diag(A) < 0).any():
- raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(selfA._name,))
- if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
- try:
- L = numpy.linalg.cholesky( A )
- except:
- raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(selfA._name,))
+ A = HessienneEstimation(Xa.size, HaM, HtM, BI, RI)
if selfA._toStore("APosterioriCovariance"):
selfA.StoredVariables["APosterioriCovariance"].store( A )
if selfA._toStore("JacobianMatrixAtOptimum"):
selfA._toStore("OMB"):
d = Y - HXb
if selfA._toStore("Innovation"):
- selfA.StoredVariables["Innovation"].store( numpy.ravel(d) )
+ selfA.StoredVariables["Innovation"].store( d )
if selfA._toStore("BMA"):
selfA.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
if selfA._toStore("OMA"):
selfA.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
if selfA._toStore("OMB"):
- selfA.StoredVariables["OMB"].store( numpy.ravel(d) )
+ selfA.StoredVariables["OMB"].store( d )
if selfA._toStore("SigmaObs2"):
TraceR = R.trace(Y.size)
- selfA.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
+ selfA.StoredVariables["SigmaObs2"].store( float( (d.T @ (numpy.ravel(Y)-numpy.ravel(HXa))) ) / TraceR )
if selfA._toStore("MahalanobisConsistency"):
selfA.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
if selfA._toStore("SimulationQuantiles"):
QuantilesEstimations(selfA, A, Xa, HXa, Hm, HtM)
if selfA._toStore("SimulatedObservationAtBackground"):
- selfA.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
+ selfA.StoredVariables["SimulatedObservationAtBackground"].store( HXb )
if selfA._toStore("SimulatedObservationAtOptimum"):
- selfA.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
+ selfA.StoredVariables["SimulatedObservationAtOptimum"].store( HXa )
#
return 0
