#-*-coding:iso-8859-1-*-
#
-# Copyright (C) 2008-2011 EDF R&D
+# Copyright (C) 2008-2012 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
#
+# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
import logging
from daCore import BasicObjects, PlatformInfo
import numpy
import scipy.optimize
-if logging.getLogger().level < 30:
+if logging.getLogger().level < logging.WARNING:
iprint = 1
message = scipy.optimize.tnc.MSG_ALL
disp = 1
# ==============================================================================
class ElementaryAlgorithm(BasicObjects.Algorithm):
def __init__(self):
- BasicObjects.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"]
+ )
def run(self, Xb=None, Y=None, H=None, M=None, R=None, B=None, Q=None, Parameters=None):
- """
- Calcul de l'estimateur 3D-VAR
- """
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
+ #
+ # Correction pour pallier a un bug de TNC sur le retour du Minimum
+ if self._parameters.has_key("Minimizer") is "TNC":
+ self.setParameterValue("StoreInternalVariables",True)
#
# Opérateur d'observation
# -----------------------
Hm = H["Direct"].appliedTo
- Ht = H["Adjoint"].appliedInXTo
+ Ha = H["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"]
else:
- logging.debug("%s Calcul de Hm(Xb)"%self._name)
HXb = Hm( Xb )
- HXb = numpy.asmatrix(HXb).flatten().T
+ HXb = numpy.asmatrix(numpy.ravel( HXb )).T
#
# Calcul de l'innovation
# ----------------------
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 inversions de B et R
# ----------------------------------
if B is not None:
BI = B.I
- elif Parameters["B_scalar"] is not None:
- BI = 1.0 / Parameters["B_scalar"]
+ elif self._parameters["B_scalar"] is not None:
+ BI = 1.0 / self._parameters["B_scalar"]
+ else:
+ raise ValueError("Background error covariance matrix has to be properly defined!")
#
if R is not None:
RI = R.I
- elif Parameters["R_scalar"] is not None:
- RI = 1.0 / Parameters["R_scalar"]
+ elif self._parameters["R_scalar"] is not None:
+ RI = 1.0 / self._parameters["R_scalar"]
+ else:
+ raise ValueError("Observation error covariance matrix has to be properly defined!")
#
# Définition de la fonction-coût
# ------------------------------
def CostFunction(x):
- _X = numpy.asmatrix(x).flatten().T
- logging.debug("%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.debug("%s CostFunction Jb = %s"%(self._name, Jb))
- logging.debug("%s CostFunction Jo = %s"%(self._name, Jo))
- logging.debug("%s CostFunction J = %s"%(self._name, J))
- self.StoredVariables["CurrentState"].store( _X.A1 )
+ 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.debug("%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()))
+ 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
- # ----------------------
- # Potentiels : "Bounds", "Minimizer", "MaximumNumberOfSteps", "ProjectedGradientTolerance", "GradientNormTolerance", "InnerMinimizer"
- if Parameters.has_key("Bounds") and (type(Parameters["Bounds"]) is type([]) or type(Parameters["Bounds"]) is type(())) and (len(Parameters["Bounds"]) > 0):
- Bounds = Parameters["Bounds"]
- else:
- Bounds = None
- MinimizerList = ["LBFGSB","TNC", "CG", "NCG", "BFGS"]
- if Parameters.has_key("Minimizer") and (Parameters["Minimizer"] in MinimizerList):
- Minimizer = str( Parameters["Minimizer"] )
- else:
- Minimizer = "LBFGSB"
- logging.warning("%s Unknown or undefined minimizer, replaced by the default one \"%s\""%(self._name,Minimizer))
- logging.debug("%s Minimiseur utilisé = %s"%(self._name, Minimizer))
- if Parameters.has_key("MaximumNumberOfSteps") and (Parameters["MaximumNumberOfSteps"] > -1):
- maxiter = int( Parameters["MaximumNumberOfSteps"] )
- else:
- maxiter = 15000
- logging.debug("%s Nombre maximal de pas d'optimisation = %s"%(self._name, str(maxiter)))
- if Parameters.has_key("CostDecrementTolerance") and (Parameters["CostDecrementTolerance"] > 0):
- ftol = float(Parameters["CostDecrementTolerance"])
- factr = ftol * 1.e14
- else:
- ftol = 1.e-7
- factr = ftol * 1.e14
- logging.debug("%s Diminution relative minimale du cout lors de l'arret = %s"%(self._name, str(1./factr)))
- if Parameters.has_key("ProjectedGradientTolerance") and (Parameters["ProjectedGradientTolerance"] > -1):
- pgtol = float(Parameters["ProjectedGradientTolerance"])
- else:
- pgtol = -1
- logging.debug("%s Maximum des composantes du gradient projete lors de l'arret = %s"%(self._name, str(pgtol)))
- if Parameters.has_key("GradientNormTolerance") and (Parameters["GradientNormTolerance"] > -1):
- gtol = float(Parameters["GradientNormTolerance"])
- else:
- gtol = 1.e-05
- logging.debug("%s Maximum des composantes du gradient lors de l'arret = %s"%(self._name, str(gtol)))
- InnerMinimizerList = ["CG", "NCG", "BFGS"]
- if Parameters.has_key("InnerMinimizer") and (Parameters["InnerMinimizer"] in InnerMinimizerList):
- InnerMinimizer = str( Parameters["InnerMinimizer"] )
- else:
- InnerMinimizer = "BFGS"
- logging.debug("%s Minimiseur interne utilisé = %s"%(self._name, InnerMinimizer))
#
# Minimisation de la fonctionnelle
# --------------------------------
- if Minimizer == "LBFGSB":
+ 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-1,
- factr = factr,
- pgtol = pgtol,
+ maxfun = self._parameters["MaximumNumberOfSteps"]-1,
+ factr = self._parameters["CostDecrementTolerance"]*1.e14,
+ pgtol = self._parameters["ProjectedGradientTolerance"],
iprint = iprint,
)
nfeval = Informations['funcalls']
rc = Informations['warnflag']
- elif Minimizer == "TNC":
+ elif self._parameters["Minimizer"] == "TNC":
Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
func = CostFunction,
x0 = Xini,
fprime = GradientOfCostFunction,
args = (),
bounds = Bounds,
- maxfun = maxiter,
- pgtol = pgtol,
- ftol = ftol,
+ maxfun = self._parameters["MaximumNumberOfSteps"],
+ pgtol = self._parameters["ProjectedGradientTolerance"],
+ ftol = self._parameters["CostDecrementTolerance"],
messages = message,
)
- 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,
- gtol = gtol,
+ maxiter = self._parameters["MaximumNumberOfSteps"],
+ gtol = self._parameters["GradientNormTolerance"],
disp = disp,
full_output = True,
)
- elif Minimizer == "NCG":
+ elif self._parameters["Minimizer"] == "NCG":
Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
f = CostFunction,
x0 = Xini,
fprime = GradientOfCostFunction,
args = (),
- maxiter = maxiter,
- avextol = ftol,
+ maxiter = self._parameters["MaximumNumberOfSteps"],
+ avextol = self._parameters["CostDecrementTolerance"],
disp = disp,
full_output = True,
)
- 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,
- gtol = gtol,
+ maxiter = self._parameters["MaximumNumberOfSteps"],
+ gtol = self._parameters["GradientNormTolerance"],
disp = disp,
full_output = True,
)
else:
- raise ValueError("Error in Minimizer name: %s"%Minimizer)
+ raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
#
- # Correction pour pallier a un bug de TNC sur le retour du Minimum
- # ----------------------------------------------------------------
StepMin = numpy.argmin( self.StoredVariables["CostFunctionJ"].valueserie() )
MinJ = self.StoredVariables["CostFunctionJ"].valueserie(step = StepMin)
- Minimum = self.StoredVariables["CurrentState"].valueserie(step = StepMin)
#
- logging.debug("%s %s Step of min cost = %s"%(self._name, Minimizer, StepMin))
- logging.debug("%s %s Minimum cost = %s"%(self._name, Minimizer, MinJ))
- logging.debug("%s %s Minimum state = %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))
+ # Correction pour pallier a un bug de TNC sur le retour du Minimum
+ # ----------------------------------------------------------------
+ if self._parameters["StoreInternalVariables"]:
+ Minimum = self.StoredVariables["CurrentState"].valueserie(step = StepMin)
#
- # 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")))
+ # Calcul de la covariance d'analyse
+ # ---------------------------------
+ if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
+ Ht = H["Tangent"].asMatrix(ValueForMethodForm = Xa)
+ Ht = Ht.reshape(-1,len(Xa.A1)) # ADAO
+ HessienneI = []
+ nb = len(Xa.A1)
+ for i in range(nb):
+ _ee = numpy.matrix(numpy.zeros(nb)).T
+ _ee[i] = 1.
+ _HtEE = Ht * _ee
+ _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
+ HessienneI.append( ( BI*_ee + Ha((Xa,RI*_HtEE)) ).A1 )
+ HessienneI = numpy.matrix( HessienneI )
+ A = HessienneI.I
+ if min(A.shape) != max(A.shape):
+ raise ValueError("The 3DVAR 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."%str(A.shape))
+ if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
+ try:
+ L = numpy.linalg.cholesky( A )
+ except:
+ raise ValueError("The 3DVAR a posteriori covariance matrix A is not symmetric positive-definite. Check your B and R a priori covariances.")
+ 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 - Xa) )
+ if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["OMA"].store( numpy.ravel(Y - Hm(Xa)) )
+ if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["OMB"].store( numpy.ravel(d) )
+ if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["SigmaObs2"].store( float( (d.T * (Y-Hm(Xa))) / R.trace() ) )
+ if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/len(d) ) )
+ #
+ logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
logging.debug("%s Terminé"%self._name)
#
return 0
