-#-*-coding:iso-8859-1-*-
+# -*- coding: utf-8 -*-
#
-# Copyright (C) 2008-2017 EDF R&D
+# Copyright (C) 2008-2023 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
#
# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
-import logging
-from daCore import BasicObjects, PlatformInfo
-import numpy, math
+import numpy
+from daCore import BasicObjects, NumericObjects, PlatformInfo
mpr = PlatformInfo.PlatformInfo().MachinePrecision()
+mfp = PlatformInfo.PlatformInfo().MaximumPrecision()
# ==============================================================================
class ElementaryAlgorithm(BasicObjects.Algorithm):
name = "ResiduFormula",
default = "Taylor",
typecast = str,
- message = "Formule de résidu utilisée",
+ message = "Formule de résidu utilisée",
listval = ["Taylor"],
)
self.defineRequiredParameter(
name = "EpsilonMinimumExponent",
default = -8,
typecast = int,
- message = "Exposant minimal en puissance de 10 pour le multiplicateur d'incrément",
+ message = "Exposant minimal en puissance de 10 pour le multiplicateur d'incrément",
minval = -20,
maxval = 0,
)
name = "InitialDirection",
default = [],
typecast = list,
- message = "Direction initiale de la dérivée directionnelle autour du point nominal",
+ message = "Direction initiale de la dérivée directionnelle autour du point nominal",
)
self.defineRequiredParameter(
name = "AmplitudeOfInitialDirection",
default = 1.,
typecast = float,
- message = "Amplitude de la direction initiale de la dérivée directionnelle autour du point nominal",
+ message = "Amplitude de la direction initiale de la dérivée directionnelle autour du point nominal",
)
self.defineRequiredParameter(
name = "AmplitudeOfTangentPerturbation",
self.defineRequiredParameter(
name = "SetSeed",
typecast = numpy.random.seed,
- message = "Graine fixée pour le générateur aléatoire",
+ message = "Graine fixée pour le générateur aléatoire",
+ )
+ self.defineRequiredParameter(
+ name = "NumberOfPrintedDigits",
+ default = 5,
+ typecast = int,
+ message = "Nombre de chiffres affichés pour les impressions de réels",
+ minval = 0,
)
self.defineRequiredParameter(
name = "ResultTitle",
name = "StoreSupplementaryCalculations",
default = [],
typecast = tuple,
- message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
- listval = ["CurrentState", "Residu", "SimulatedObservationAtCurrentState"]
+ message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
+ listval = [
+ "CurrentState",
+ "Residu",
+ "SimulatedObservationAtCurrentState",
+ ]
)
+ self.requireInputArguments(
+ mandatory= ("Xb", "HO"),
+ )
+ self.setAttributes(tags=(
+ "Checking",
+ ))
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)
+ self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
#
Hm = HO["Direct"].appliedTo
Ht = HO["Tangent"].appliedInXTo
#
- # Construction des perturbations
- # ------------------------------
+ X0 = numpy.ravel( Xb ).reshape((-1,1))
+ #
+ # ----------
+ __p = self._parameters["NumberOfPrintedDigits"]
+ #
+ __marge = 5*u" "
+ __flech = 3*"="+"> "
+ msgs = ("\n") # 1
+ if len(self._parameters["ResultTitle"]) > 0:
+ __rt = str(self._parameters["ResultTitle"])
+ msgs += (__marge + "====" + "="*len(__rt) + "====\n")
+ msgs += (__marge + " " + __rt + "\n")
+ msgs += (__marge + "====" + "="*len(__rt) + "====\n")
+ else:
+ msgs += (__marge + "%s\n"%self._name)
+ msgs += (__marge + "%s\n"%("="*len(self._name),))
+ #
+ msgs += ("\n")
+ msgs += (__marge + "This test allows to analyze the numerical stability of the tangent of some\n")
+ msgs += (__marge + "given simulation operator F, applied to one single vector argument x.\n")
+ msgs += (__marge + "The output shows simple statistics related to its stability for various\n")
+ msgs += (__marge + "increments, around an input checking point X.\n")
+ msgs += ("\n")
+ msgs += (__flech + "Information before launching:\n")
+ msgs += (__marge + "-----------------------------\n")
+ msgs += ("\n")
+ msgs += (__marge + "Characteristics of input vector X, internally converted:\n")
+ msgs += (__marge + " Type...............: %s\n")%type( X0 )
+ msgs += (__marge + " Length of vector...: %i\n")%max(numpy.ravel( X0 ).shape)
+ msgs += (__marge + " Minimum value......: %."+str(__p)+"e\n")%numpy.min( X0 )
+ msgs += (__marge + " Maximum value......: %."+str(__p)+"e\n")%numpy.max( X0 )
+ msgs += (__marge + " Mean of vector.....: %."+str(__p)+"e\n")%numpy.mean( X0, dtype=mfp )
+ msgs += (__marge + " Standard error.....: %."+str(__p)+"e\n")%numpy.std( X0, dtype=mfp )
+ msgs += (__marge + " L2 norm of vector..: %."+str(__p)+"e\n")%numpy.linalg.norm( X0 )
+ msgs += ("\n")
+ msgs += (__marge + "%s\n\n"%("-"*75,))
+ msgs += (__flech + "Numerical quality indicators:\n")
+ msgs += (__marge + "-----------------------------\n")
+ msgs += ("\n")
+ msgs += (__marge + "Using the \"%s\" formula, one observes the residue R which is the\n"%self._parameters["ResiduFormula"])
+ msgs += (__marge + "ratio of increments using the tangent linear:\n")
+ msgs += ("\n")
+ #
+ if self._parameters["ResiduFormula"] == "Taylor":
+ msgs += (__marge + " || F(X+Alpha*dX) - F(X) ||\n")
+ msgs += (__marge + " R(Alpha) = -----------------------------\n")
+ msgs += (__marge + " || Alpha * TangentF_X * dX ||\n")
+ msgs += ("\n")
+ msgs += (__marge + "which must remain stable in 1+O(Alpha) until the accuracy of the\n")
+ msgs += (__marge + "calculation is reached.\n")
+ msgs += ("\n")
+ msgs += (__marge + "When |R-1|/Alpha is less than or equal to a stable value when Alpha varies,\n")
+ msgs += (__marge + "the tangent is valid, until the accuracy of the calculation is reached.\n")
+ msgs += ("\n")
+ msgs += (__marge + "If |R-1|/Alpha is very small, the code F is likely linear or quasi-linear,\n")
+ msgs += (__marge + "and the tangent is valid until computational accuracy is reached.\n")
+ #
+ __entete = u" i Alpha ||X|| ||F(X)|| | R(Alpha) |R-1|/Alpha"
+ #
+ msgs += ("\n")
+ msgs += (__marge + "We take dX0 = Normal(0,X) and dX = Alpha*dX0. F is the calculation code.\n")
+ msgs += ("\n")
+ msgs += (__marge + "(Remark: numbers that are (about) under %.0e represent 0 to machine precision)\n"%mpr)
+ print(msgs) # 1
+ #
Perturbations = [ 10**i for i in range(self._parameters["EpsilonMinimumExponent"],1) ]
Perturbations.reverse()
#
- # Calcul du point courant
- # -----------------------
- Xn = numpy.asmatrix(numpy.ravel( Xb )).T
- FX = numpy.asmatrix(numpy.ravel( Hm( Xn ) )).T
- NormeX = numpy.linalg.norm( Xn )
+ FX = numpy.ravel( Hm( X0 ) ).reshape((-1,1))
+ NormeX = numpy.linalg.norm( X0 )
NormeFX = numpy.linalg.norm( FX )
- if "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
- self.StoredVariables["CurrentState"].store( numpy.ravel(Xn) )
- if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
- self.StoredVariables["SimulatedObservationAtCurrentState"].store( numpy.ravel(FX) )
- #
- # Fabrication de la direction de l'incrément dX
- # ----------------------------------------------
- if len(self._parameters["InitialDirection"]) == 0:
- dX0 = []
- for v in Xn.A1:
- if abs(v) > 1.e-8:
- dX0.append( numpy.random.normal(0.,abs(v)) )
- else:
- dX0.append( numpy.random.normal(0.,Xn.mean()) )
- else:
- dX0 = numpy.ravel( self._parameters["InitialDirection"] )
+ if NormeFX < mpr: NormeFX = mpr
+ if self._toStore("CurrentState"):
+ self.StoredVariables["CurrentState"].store( X0 )
+ if self._toStore("SimulatedObservationAtCurrentState"):
+ self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX )
#
- dX0 = float(self._parameters["AmplitudeOfInitialDirection"]) * numpy.matrix( dX0 ).T
+ dX0 = NumericObjects.SetInitialDirection(
+ self._parameters["InitialDirection"],
+ self._parameters["AmplitudeOfInitialDirection"],
+ X0,
+ )
#
- # Calcul du gradient au point courant X pour l'incrément dX
- # qui est le tangent en X multiplié par dX
+ # Calcul du gradient au point courant X pour l'incrément dX
+ # qui est le tangent en X multiplie par dX
# ---------------------------------------------------------
dX1 = float(self._parameters["AmplitudeOfTangentPerturbation"]) * dX0
- GradFxdX = Ht( (Xn, dX1) )
- GradFxdX = numpy.asmatrix(numpy.ravel( GradFxdX )).T
+ GradFxdX = Ht( (X0, dX1) )
+ GradFxdX = numpy.ravel( GradFxdX ).reshape((-1,1))
GradFxdX = float(1./self._parameters["AmplitudeOfTangentPerturbation"]) * GradFxdX
NormeGX = numpy.linalg.norm( GradFxdX )
+ if NormeGX < mpr: NormeGX = mpr
#
- # Entete des resultats
- # --------------------
- __marge = 12*" "
- __precision = """
- Remarque : les nombres inferieurs a %.0e (environ) representent un zero
- a la precision machine.\n"""%mpr
- if self._parameters["ResiduFormula"] == "Taylor":
- __entete = " i Alpha ||X|| ||F(X)|| | R(Alpha) |R-1|/Alpha "
- __msgdoc = """
- On observe le résidu provenant du rapport d'incréments utilisant le
- linéaire tangent :
-
- || F(X+Alpha*dX) - F(X) ||
- R(Alpha) = -----------------------------
- || Alpha * TangentF_X * dX ||
-
- qui doit rester stable en 1+O(Alpha) jusqu'à ce que l'on atteigne la
- précision du calcul.
-
- Lorsque |R-1|/Alpha est inférieur ou égal à une valeur stable
- lorsque Alpha varie, le tangent est valide, jusqu'à ce que l'on
- atteigne la précision du calcul.
-
- Si |R-1|/Alpha est très faible, le code F est vraisemblablement
- linéaire ou quasi-linéaire, et le tangent est valide jusqu'à ce que
- l'on atteigne la précision du calcul.
-
- On prend dX0 = Normal(0,X) et dX = Alpha*dX0. F est le code de calcul.
- """ + __precision
- #
- if len(self._parameters["ResultTitle"]) > 0:
- msgs = "\n"
- msgs += __marge + "====" + "="*len(self._parameters["ResultTitle"]) + "====\n"
- msgs += __marge + " " + self._parameters["ResultTitle"] + "\n"
- msgs += __marge + "====" + "="*len(self._parameters["ResultTitle"]) + "====\n"
- else:
- msgs = ""
- msgs += __msgdoc
- #
- __nbtirets = len(__entete)
+ # Boucle sur les perturbations
+ # ----------------------------
+ __nbtirets = len(__entete) + 2
+ msgs = ("") # 2
msgs += "\n" + __marge + "-"*__nbtirets
msgs += "\n" + __marge + __entete
msgs += "\n" + __marge + "-"*__nbtirets
- #
- # Boucle sur les perturbations
- # ----------------------------
+ msgs += ("\n")
for i,amplitude in enumerate(Perturbations):
- dX = amplitude * dX0
+ dX = amplitude * dX0.reshape((-1,1))
#
if self._parameters["ResiduFormula"] == "Taylor":
- FX_plus_dX = numpy.asmatrix(numpy.ravel( Hm( Xn + dX ) )).T
+ FX_plus_dX = numpy.ravel( Hm( X0 + dX ) ).reshape((-1,1))
#
Residu = numpy.linalg.norm( FX_plus_dX - FX ) / (amplitude * NormeGX)
- #
- self.StoredVariables["Residu"].store( Residu )
- msg = " %2i %5.0e %9.3e %9.3e | %11.5e %5.1e"%(i,amplitude,NormeX,NormeFX,Residu,abs(Residu-1.)/amplitude)
- msgs += "\n" + __marge + msg
- #
- msgs += "\n" + __marge + "-"*__nbtirets
- msgs += "\n"
+ #
+ self.StoredVariables["Residu"].store( Residu )
+ ttsep = " %2i %5.0e %9.3e %9.3e | %11.5e %5.1e\n"%(i,amplitude,NormeX,NormeFX,Residu,abs(Residu-1.)/amplitude)
+ msgs += __marge + ttsep
#
- # Sorties eventuelles
- # -------------------
- print("\nResults of tangent check by \"%s\" formula:"%self._parameters["ResiduFormula"])
- print(msgs)
+ msgs += (__marge + "-"*__nbtirets + "\n\n")
+ msgs += (__marge + "End of the \"%s\" verification by the \"%s\" formula.\n\n"%(self._name,self._parameters["ResiduFormula"]))
+ msgs += (__marge + "%s\n"%("-"*75,))
+ print(msgs) # 2
#
self._post_run(HO)
return 0
# ==============================================================================
if __name__ == "__main__":
- print('\n AUTODIAGNOSTIC \n')
+ print("\n AUTODIAGNOSTIC\n")
