#-*-coding:iso-8859-1-*-
#
-# Copyright (C) 2008-2012 EDF R&D
+# Copyright (C) 2008-2017 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
-# License as published by the Free Software Foundation; either
-# version 2.1 of the License.
+# This library is free software; you can redistribute it and/or
+# modify it under the terms of the GNU Lesser General Public
+# License as published by the Free Software Foundation; either
+# version 2.1 of the License.
#
-# This library is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
-# Lesser General Public License for more details.
+# This library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+# Lesser General Public License for more details.
#
-# You should have received a copy of the GNU Lesser General Public
-# License along with this library; if not, write to the Free Software
-# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+# You should have received a copy of the GNU Lesser General Public
+# License along with this library; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
-# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
+# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
#
-# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
+# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
import logging
-from daCore import BasicObjects, PlatformInfo
-m = PlatformInfo.SystemUsage()
-
-import numpy
-import scipy.optimize
-
-if logging.getLogger().level < logging.WARNING:
- 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
+import numpy, scipy.optimize
# ==============================================================================
class ElementaryAlgorithm(BasicObjects.Algorithm):
default = [],
typecast = tuple,
message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
- listval = ["APosterioriCovariance", "BMA", "OMA", "OMB", "Innovation", "SigmaObs2"]
+ listval = ["APosterioriCorrelations", "APosterioriCovariance", "APosterioriStandardDeviations", "APosterioriVariances", "BMA", "OMA", "OMB", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "CurrentState", "CurrentOptimum", "IndexOfOptimum", "Innovation", "InnovationAtCurrentState", "CostFunctionJAtCurrentOptimum", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles", "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum", "SimulatedObservationAtCurrentOptimum"]
+ )
+ self.defineRequiredParameter(
+ name = "Quantiles",
+ default = [],
+ typecast = tuple,
+ message = "Liste des valeurs de quantiles",
+ minval = 0.,
+ maxval = 1.,
+ )
+ 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"]
+ )
+ self.defineRequiredParameter( # Pas de type
+ name = "Bounds",
+ message = "Liste des valeurs de bornes",
)
- def run(self, Xb=None, Y=None, H=None, M=None, R=None, B=None, Q=None, Parameters=None):
- logging.debug("%s Lancement"%self._name)
- 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
+ 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)
#
# Correction pour pallier a un bug de TNC sur le retour du Minimum
- if self._parameters.has_key("Minimizer") is "TNC":
+ if self._parameters.has_key("Minimizer") == "TNC":
self.setParameterValue("StoreInternalVariables",True)
#
- # Opérateur d'observation
- # -----------------------
- Hm = H["Direct"].appliedTo
- Ha = H["Adjoint"].appliedInXTo
+ # Opérateurs
+ # ----------
+ 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"):
- HXb = H["AppliedToX"]["HXb"]
+ # Utilisation éventuelle d'un vecteur H(Xb) précalculé (sans cout)
+ # ----------------------------------------------------------------
+ if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
+ HXb = Hm( Xb, HO["AppliedToX"]["HXb"])
else:
HXb = Hm( Xb )
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
#
# Précalcul des inversions de B et R
# ----------------------------------
- if B is not None:
- BI = B.I
- 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 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!")
+ BI = B.getI()
+ RI = R.getI()
#
# Définition de la fonction-coût
# ------------------------------
def CostFunction(x):
_X = numpy.asmatrix(numpy.ravel( x )).T
+ if self._parameters["StoreInternalVariables"] or \
+ "CurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
+ "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["CurrentState"].store( _X )
_HX = Hm( _X )
_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 )
- if self._parameters["StoreInternalVariables"]:
- self.StoredVariables["CurrentState"].store( _X.A1 )
+ _Innovation = Y - _HX
+ if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
+ if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
+ #
+ Jb = float( 0.5 * (_X - Xb).T * BI * (_X - 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 "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
+ "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
+ "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
+ if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["IndexOfOptimum"].store( IndexMin )
+ if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
+ if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
+ if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
+ self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
+ self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
return J
#
def GradientOfCostFunction(x):
#
# Point de démarrage de l'optimisation : Xini = Xb
# ------------------------------------
- if type(Xb) is type(numpy.matrix([])):
- Xini = Xb.A1.tolist()
- else:
- Xini = list(Xb)
+ Xini = numpy.ravel(Xb)
#
# Minimisation de la fonctionnelle
# --------------------------------
+ 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,
+ bounds = self._parameters["Bounds"],
maxfun = self._parameters["MaximumNumberOfSteps"]-1,
factr = self._parameters["CostDecrementTolerance"]*1.e14,
pgtol = self._parameters["ProjectedGradientTolerance"],
- iprint = iprint,
+ iprint = self._parameters["optiprint"],
)
nfeval = Informations['funcalls']
rc = Informations['warnflag']
x0 = Xini,
fprime = GradientOfCostFunction,
args = (),
- bounds = Bounds,
+ bounds = self._parameters["Bounds"],
maxfun = self._parameters["MaximumNumberOfSteps"],
pgtol = self._parameters["ProjectedGradientTolerance"],
ftol = self._parameters["CostDecrementTolerance"],
- messages = message,
+ messages = self._parameters["optmessages"],
)
elif self._parameters["Minimizer"] == "CG":
Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
args = (),
maxiter = self._parameters["MaximumNumberOfSteps"],
gtol = self._parameters["GradientNormTolerance"],
- disp = disp,
+ disp = self._parameters["optdisp"],
full_output = True,
)
elif self._parameters["Minimizer"] == "NCG":
args = (),
maxiter = self._parameters["MaximumNumberOfSteps"],
avextol = self._parameters["CostDecrementTolerance"],
- disp = disp,
+ disp = self._parameters["optdisp"],
full_output = True,
)
elif self._parameters["Minimizer"] == "BFGS":
args = (),
maxiter = self._parameters["MaximumNumberOfSteps"],
gtol = self._parameters["GradientNormTolerance"],
- disp = disp,
+ disp = self._parameters["optdisp"],
full_output = True,
)
else:
raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
#
- StepMin = numpy.argmin( self.StoredVariables["CostFunctionJ"].valueserie() )
- MinJ = self.StoredVariables["CostFunctionJ"].valueserie(step = StepMin)
+ 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"].valueserie(step = StepMin)
+ if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
+ Minimum = self.StoredVariables["CurrentState"][IndexMin]
#
# Obtention de l'analyse
# ----------------------
#
self.StoredVariables["Analysis"].store( Xa.A1 )
#
+ if "OMA" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
+ if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
+ HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
+ elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
+ else:
+ HXa = Hm(Xa)
+ #
# 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
+ 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 = len(Xini)
+ nb = Xa.size
for i in range(nb):
_ee = numpy.matrix(numpy.zeros(nb)).T
_ee[i] = 1.
- _HtEE = Ht * _ee
+ _HtEE = numpy.dot(HtM,_ee)
_HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
- HessienneI.append( ( BI*_ee + Ha((Xa,RI*_HtEE)) ).A1 )
+ HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
HessienneI = numpy.matrix( HessienneI )
- if numpy.alltrue(numpy.isfinite( HessienneI )):
- A = HessienneI.I
- else:
- raise ValueError("The 3DVAR a posteriori covariance matrix A can not be calculated. Your problem is perhaps too non-linear?")
+ 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 3DVAR a posteriori covariance matrix A is not symmetric positive-definite. Check your B and R a priori covariances.")
+ 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"] or \
+ "OMB" in self._parameters["StoreSupplementaryCalculations"] or \
+ "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
+ "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
+ d = Y - HXb
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) )
+ self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
- self.StoredVariables["OMA"].store( numpy.ravel(Y - Hm(Xa)) )
+ 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"]:
- self.StoredVariables["SigmaObs2"].store( float( (d.T * (Y-Hm(Xa))) / R.trace() ) )
- #
- logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
- logging.debug("%s Terminé"%self._name)
+ 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 = map(float, 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 )
+ if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
+ if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
+ self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
#
+ self._post_run(HO)
return 0
# ==============================================================================
