#-*-coding:iso-8859-1-*-
#
-# Copyright (C) 2008-2009 EDF R&D
+# Copyright (C) 2008-2014 EDF R&D
#
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
#
# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
#
-__doc__ = """
- Algorithme variationnel statique (3D-VAR)
-"""
-__author__ = "Jean-Philippe ARGAUD - Mars 2009"
+# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
-import sys ; sys.path.insert(0, "../daCore")
import logging
-from daCore import Persistence
-from daCore.BasicObjects import Algorithm
-from daCore import PlatformInfo ; m = PlatformInfo.SystemUsage()
-
-import numpy
-import scipy.optimize
-
-if logging.getLogger().level < 30:
- iprint = 1
- message = scipy.optimize.tnc.MSG_ALL
- disp = 1
-else:
- iprint = -1
- message = scipy.optimize.tnc.MSG_NONE
- disp = 0
+from daCore import BasicObjects, PlatformInfo
+m = PlatformInfo.SystemUsage()
+import numpy, scipy.optimize
# ==============================================================================
-class ElementaryAlgorithm(Algorithm):
+class ElementaryAlgorithm(BasicObjects.Algorithm):
def __init__(self):
- Algorithm.__init__(self)
- self._name = "3DVAR"
- logging.debug("%s Initialisation"%self._name)
+ BasicObjects.Algorithm.__init__(self, "3DVAR")
+ self.defineRequiredParameter(
+ name = "Minimizer",
+ default = "LBFGSB",
+ typecast = str,
+ message = "Minimiseur utilisé",
+ listval = ["LBFGSB","TNC", "CG", "NCG", "BFGS"],
+ )
+ self.defineRequiredParameter(
+ name = "MaximumNumberOfSteps",
+ default = 15000,
+ typecast = int,
+ message = "Nombre maximal de pas d'optimisation",
+ minval = -1,
+ )
+ self.defineRequiredParameter(
+ name = "CostDecrementTolerance",
+ default = 1.e-7,
+ typecast = float,
+ message = "Diminution relative minimale du cout lors de l'arrêt",
+ )
+ self.defineRequiredParameter(
+ name = "ProjectedGradientTolerance",
+ default = -1,
+ typecast = float,
+ message = "Maximum des composantes du gradient projeté lors de l'arrêt",
+ minval = -1,
+ )
+ self.defineRequiredParameter(
+ name = "GradientNormTolerance",
+ default = 1.e-05,
+ typecast = float,
+ message = "Maximum des composantes du gradient lors de l'arrêt",
+ )
+ self.defineRequiredParameter(
+ name = "StoreInternalVariables",
+ default = False,
+ typecast = bool,
+ message = "Stockage des variables internes ou intermédiaires du calcul",
+ )
+ self.defineRequiredParameter(
+ name = "StoreSupplementaryCalculations",
+ default = [],
+ typecast = tuple,
+ message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
+ listval = ["APosterioriCovariance", "BMA", "OMA", "OMB", "Innovation", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles"]
+ )
+ self.defineRequiredParameter(
+ name = "Quantiles",
+ default = [],
+ typecast = tuple,
+ message = "Liste des valeurs de quantiles",
+ )
+ self.defineRequiredParameter(
+ name = "SetSeed",
+ typecast = numpy.random.seed,
+ message = "Graine fixée pour le générateur aléatoire",
+ )
+ self.defineRequiredParameter(
+ name = "NumberOfSamplesForQuantiles",
+ default = 100,
+ typecast = int,
+ message = "Nombre d'échantillons simulés pour le calcul des quantiles",
+ minval = 1,
+ )
+ self.defineRequiredParameter(
+ name = "SimulationForQuantiles",
+ default = "Linear",
+ typecast = str,
+ message = "Type de simulation pour l'estimation des quantiles",
+ listval = ["Linear", "NonLinear"]
+ )
- def run(self, Xb=None, Y=None, H=None, M=None, R=None, B=None, Q=None, Par=None):
- """
- Calcul de l'estimateur 3D-VAR
- """
+ def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
+ if logging.getLogger().level < logging.WARNING:
+ self.__iprint, self.__disp = 1, 1
+ self.__message = scipy.optimize.tnc.MSG_ALL
+ else:
+ self.__iprint, self.__disp = -1, 0
+ self.__message = scipy.optimize.tnc.MSG_NONE
+ #
logging.debug("%s Lancement"%self._name)
- logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("Mo")))
+ logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
+ #
+ # Paramètres de pilotage
+ # ----------------------
+ self.setParameters(Parameters)
+ #
+ if self._parameters.has_key("Bounds") and (type(self._parameters["Bounds"]) is type([]) or type(self._parameters["Bounds"]) is type(())) and (len(self._parameters["Bounds"]) > 0):
+ Bounds = self._parameters["Bounds"]
+ logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
+ else:
+ Bounds = None
#
- Hm = H["Direct"].appliedTo
- Ht = H["Adjoint"].appliedInXTo
+ # Correction pour pallier a un bug de TNC sur le retour du Minimum
+ if self._parameters.has_key("Minimizer") == "TNC":
+ self.setParameterValue("StoreInternalVariables",True)
+ #
+ # Opérateur d'observation
+ # -----------------------
+ Hm = HO["Direct"].appliedTo
+ Ha = HO["Adjoint"].appliedInXTo
#
# Utilisation éventuelle d'un vecteur H(Xb) précalculé
# ----------------------------------------------------
- if H["AppliedToX"] is not None and H["AppliedToX"].has_key("HXb"):
- logging.debug("%s Utilisation de HXb"%self._name)
- HXb = H["AppliedToX"]["HXb"]
+ if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
+ HXb = HO["AppliedToX"]["HXb"]
else:
- logging.debug("%s Calcul de Hm(Xb)"%self._name)
HXb = Hm( Xb )
- #
- # Calcul du préconditionnement
- # ----------------------------
- # Bdemi = numpy.linalg.cholesky(B)
+ HXb = numpy.asmatrix(numpy.ravel( HXb )).T
#
# Calcul de l'innovation
# ----------------------
+ if Y.size != HXb.size:
+ raise ValueError("The size %i of observations Y and %i of observed calculation H(X) are different, they have to be identical."%(Y.size,HXb.size))
+ if max(Y.shape) != max(HXb.shape):
+ raise ValueError("The shapes %s of observations Y and %s of observed calculation H(X) are different, they have to be identical."%(Y.shape,HXb.shape))
d = Y - HXb
- logging.debug("%s Innovation d = %s"%(self._name, d))
#
- # Précalcul des inversion appellée dans les fonction-coût et gradient
- # -------------------------------------------------------------------
- BI = B.I
- RI = R.I
+ # Précalcul des inversions de B et R
+ # ----------------------------------
+ BI = B.getI()
+ RI = R.getI()
#
# Définition de la fonction-coût
# ------------------------------
def CostFunction(x):
- _X = numpy.asmatrix(x).flatten().T
- logging.info("%s CostFunction X = %s"%(self._name, numpy.asmatrix( _X ).flatten()))
+ _X = numpy.asmatrix(numpy.ravel( x )).T
_HX = Hm( _X )
- _HX = numpy.asmatrix(_HX).flatten().T
+ _HX = numpy.asmatrix(numpy.ravel( _HX )).T
Jb = 0.5 * (_X - Xb).T * BI * (_X - Xb)
Jo = 0.5 * (Y - _HX).T * RI * (Y - _HX)
J = float( Jb ) + float( Jo )
- logging.info("%s CostFunction Jb = %s"%(self._name, Jb))
- logging.info("%s CostFunction Jo = %s"%(self._name, Jo))
- logging.info("%s CostFunction J = %s"%(self._name, J))
+ if self._parameters["StoreInternalVariables"]:
+ self.StoredVariables["CurrentState"].store( _X.A1 )
self.StoredVariables["CostFunctionJb"].store( Jb )
self.StoredVariables["CostFunctionJo"].store( Jo )
self.StoredVariables["CostFunctionJ" ].store( J )
- return float( J )
+ return J
#
def GradientOfCostFunction(x):
- _X = numpy.asmatrix(x).flatten().T
- logging.info("%s GradientOfCostFunction X = %s"%(self._name, numpy.asmatrix( _X ).flatten()))
+ _X = numpy.asmatrix(numpy.ravel( x )).T
_HX = Hm( _X )
- _HX = numpy.asmatrix(_HX).flatten().T
+ _HX = numpy.asmatrix(numpy.ravel( _HX )).T
GradJb = BI * (_X - Xb)
- GradJo = - Ht( (_X, RI * (Y - _HX)) )
- GradJ = numpy.asmatrix( GradJb ).flatten().T + numpy.asmatrix( GradJo ).flatten().T
- logging.debug("%s GradientOfCostFunction GradJb = %s"%(self._name, numpy.asmatrix( GradJb ).flatten()))
- logging.debug("%s GradientOfCostFunction GradJo = %s"%(self._name, numpy.asmatrix( GradJo ).flatten()))
- logging.debug("%s GradientOfCostFunction GradJ = %s"%(self._name, numpy.asmatrix( GradJ ).flatten()))
- # self.StoredVariables["GradientOfCostFunctionJb"].store( Jb )
- # self.StoredVariables["GradientOfCostFunctionJo"].store( Jo )
- # self.StoredVariables["GradientOfCostFunctionJ" ].store( J )
+ GradJo = - Ha( (_X, RI * (Y - _HX)) )
+ GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
return GradJ.A1
#
# Point de démarrage de l'optimisation : Xini = Xb
Xini = Xb.A1.tolist()
else:
Xini = list(Xb)
- logging.debug("%s Point de démarrage Xini = %s"%(self._name, Xini))
- #
- # Paramètres de pilotage
- # ----------------------
- if Par.has_key("Bounds") and (type(Par["Bounds"]) is type([]) or type(Par["Bounds"]) is type(())) and (len(Par["Bounds"]) > 0):
- Bounds = Par["Bounds"]
- else:
- Bounds = None
- MinimizerList = ["LBFGSB","TNC", "CG", "BFGS"]
- if Par.has_key("Minimizer") and (Par["Minimizer"] in MinimizerList):
- Minimizer = str( Par["Minimizer"] )
- else:
- Minimizer = "LBFGSB"
- logging.debug("%s Minimiseur utilisé = %s"%(self._name, Minimizer))
- if Par.has_key("MaximumNumberOfSteps") and (Par["MaximumNumberOfSteps"] > -1):
- maxiter = int( Par["MaximumNumberOfSteps"] )
- else:
- maxiter = 15000
- logging.debug("%s Nombre maximal de pas d'optimisation = %s"%(self._name, maxiter))
#
# Minimisation de la fonctionnelle
# --------------------------------
- if Minimizer == "LBFGSB":
+ nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
+ #
+ if self._parameters["Minimizer"] == "LBFGSB":
Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
func = CostFunction,
x0 = Xini,
fprime = GradientOfCostFunction,
args = (),
bounds = Bounds,
- maxfun = maxiter,
- iprint = iprint,
+ maxfun = self._parameters["MaximumNumberOfSteps"]-1,
+ factr = self._parameters["CostDecrementTolerance"]*1.e14,
+ pgtol = self._parameters["ProjectedGradientTolerance"],
+ iprint = self.__iprint,
)
- logging.debug("%s %s Minimum = %s"%(self._name, Minimizer, Minimum))
- logging.debug("%s %s Nb of F = %s"%(self._name, Minimizer, Informations['funcalls']))
- logging.debug("%s %s RetCode = %s"%(self._name, Minimizer, Informations['warnflag']))
- elif Minimizer == "TNC":
+ nfeval = Informations['funcalls']
+ rc = Informations['warnflag']
+ elif self._parameters["Minimizer"] == "TNC":
Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
func = CostFunction,
x0 = Xini,
fprime = GradientOfCostFunction,
args = (),
bounds = Bounds,
- maxfun = maxiter,
- messages = message,
+ maxfun = self._parameters["MaximumNumberOfSteps"],
+ pgtol = self._parameters["ProjectedGradientTolerance"],
+ ftol = self._parameters["CostDecrementTolerance"],
+ messages = self.__message,
)
- logging.debug("%s %s Minimum = %s"%(self._name, Minimizer, Minimum))
- logging.debug("%s %s Nb of F = %s"%(self._name, Minimizer, nfeval))
- logging.debug("%s %s RetCode = %s"%(self._name, Minimizer, rc))
- elif Minimizer == "CG":
+ elif self._parameters["Minimizer"] == "CG":
Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
f = CostFunction,
x0 = Xini,
fprime = GradientOfCostFunction,
args = (),
- maxiter = maxiter,
- disp = disp,
+ maxiter = self._parameters["MaximumNumberOfSteps"],
+ gtol = self._parameters["GradientNormTolerance"],
+ disp = self.__disp,
+ full_output = True,
+ )
+ elif self._parameters["Minimizer"] == "NCG":
+ Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
+ f = CostFunction,
+ x0 = Xini,
+ fprime = GradientOfCostFunction,
+ args = (),
+ maxiter = self._parameters["MaximumNumberOfSteps"],
+ avextol = self._parameters["CostDecrementTolerance"],
+ disp = self.__disp,
full_output = True,
)
- logging.debug("%s %s Minimum = %s"%(self._name, Minimizer, Minimum))
- logging.debug("%s %s Nb of F = %s"%(self._name, Minimizer, nfeval))
- logging.debug("%s %s RetCode = %s"%(self._name, Minimizer, rc))
- elif Minimizer == "BFGS":
+ elif self._parameters["Minimizer"] == "BFGS":
Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
f = CostFunction,
x0 = Xini,
fprime = GradientOfCostFunction,
args = (),
- maxiter = maxiter,
- disp = disp,
+ maxiter = self._parameters["MaximumNumberOfSteps"],
+ gtol = self._parameters["GradientNormTolerance"],
+ disp = self.__disp,
full_output = True,
)
- logging.debug("%s %s Minimum = %s"%(self._name, Minimizer, Minimum))
- logging.debug("%s %s Nb of F = %s"%(self._name, Minimizer, nfeval))
- logging.debug("%s %s RetCode = %s"%(self._name, Minimizer, rc))
else:
- raise ValueError("Error in Minimizer name: %s"%Minimizer)
+ raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
+ #
+ IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
+ MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
+ #
+ # Correction pour pallier a un bug de TNC sur le retour du Minimum
+ # ----------------------------------------------------------------
+ if self._parameters["StoreInternalVariables"]:
+ Minimum = self.StoredVariables["CurrentState"][IndexMin]
#
- # Calcul de l'analyse
- # --------------------
- Xa = numpy.asmatrix(Minimum).T
- logging.debug("%s Analyse Xa = %s"%(self._name, Xa))
+ # Obtention de l'analyse
+ # ----------------------
+ Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
#
self.StoredVariables["Analysis"].store( Xa.A1 )
- self.StoredVariables["Innovation"].store( d.A1 )
#
- logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("MB")))
+ if "OMA" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
+ HXa = Hm(Xa)
+ #
+ # Calcul de la covariance d'analyse
+ # ---------------------------------
+ if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
+ HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
+ HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
+ HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
+ HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
+ 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."%(self._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."%(self._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."%(self._name,))
+ self.StoredVariables["APosterioriCovariance"].store( A )
+ #
+ # Calculs et/ou stockages supplémentaires
+ # ---------------------------------------
+ if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["Innovation"].store( numpy.ravel(d) )
+ if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
+ if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
+ if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["OMB"].store( numpy.ravel(d) )
+ if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
+ TraceR = R.trace(Y.size)
+ self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
+ if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
+ if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
+ Qtls = self._parameters["Quantiles"]
+ nech = self._parameters["NumberOfSamplesForQuantiles"]
+ HXa = numpy.matrix(numpy.ravel( HXa )).T
+ YfQ = None
+ for i in range(nech):
+ if self._parameters["SimulationForQuantiles"] == "Linear":
+ dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
+ dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
+ Yr = HXa + dYr
+ elif self._parameters["SimulationForQuantiles"] == "NonLinear":
+ Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
+ Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
+ if YfQ is None:
+ YfQ = Yr
+ else:
+ YfQ = numpy.hstack((YfQ,Yr))
+ YfQ.sort(axis=-1)
+ YQ = None
+ for quantile in Qtls:
+ if not (0. <= quantile <= 1.): continue
+ indice = int(nech * quantile - 1./nech)
+ if YQ is None: YQ = YfQ[:,indice]
+ else: YQ = numpy.hstack((YQ,YfQ[:,indice]))
+ self.StoredVariables["SimulationQuantiles"].store( YQ )
+ #
+ logging.debug("%s Nombre d'évaluation(s) de l'opérateur d'observation direct/tangent/adjoint : %i/%i/%i"%(self._name, HO["Direct"].nbcalls()[0],HO["Tangent"].nbcalls()[0],HO["Adjoint"].nbcalls()[0]))
+ logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
logging.debug("%s Terminé"%self._name)
#
return 0
