#-*-coding:iso-8859-1-*-
#
-# Copyright (C) 2008-2012 EDF R&D
+# Copyright (C) 2008-2013 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
__doc__ = """
Définit les versions approximées des opérateurs tangents et adjoints.
"""
__author__ = "Jean-Philippe ARGAUD"
-import os, numpy, time
+import os, numpy, time, copy
import logging
-# logging.getLogger().setLevel(logging.DEBUG)
+# logging.getLogger().setLevel(logging.DEBUG)
# ==============================================================================
class FDApproximation:
"""
Cette classe sert d'interface pour définir les opérateurs approximés. A la
- création d'un objet, en fournissant une fonction "FunctionH", on obtient un
- objet qui dispose de 3 méthodes "FunctionH", "TangentH" et "AdjointH". On
- contrôle l'approximation DF avec l'incrément multiplicatif "increment"
- valant par défaut 1%, ou avec l'incrément fixe "dX" qui sera multiplié par
- "increment" (donc en %), et on effectue de DF centrées si le booléen
- "centeredDF" est vrai.
+ création d'un objet, en fournissant une fonction "Function", on obtient un
+ objet qui dispose de 3 méthodes "DirectOperator", "TangentOperator" et
+ "AdjointOperator". On contrôle l'approximation DF avec l'incrément
+ multiplicatif "increment" valant par défaut 1%, ou avec l'incrément fixe
+ "dX" qui sera multiplié par "increment" (donc en %), et on effectue de DF
+ centrées si le booléen "centeredDF" est vrai.
"""
- def __init__(self, FunctionH = None, centeredDF = False, increment = 0.01, dX = None):
- self.FunctionH = FunctionH
+ def __init__(self,
+ Function = None,
+ centeredDF = False,
+ increment = 0.01,
+ dX = None,
+ avoidingRedundancy = True,
+ toleranceInRedundancy = 1.e-18,
+ lenghtOfRedundancy = -1,
+ ):
+ self.__userFunction = Function
self.__centeredDF = bool(centeredDF)
+ if avoidingRedundancy:
+ self.__avoidRC = True
+ self.__tolerBP = float(toleranceInRedundancy)
+ self.__lenghtRH = int(lenghtOfRedundancy)
+ self.__lenghtRJ = int(lenghtOfRedundancy)
+ self.__listDPCP = [] # Direct Operator Previous Calculated Points
+ self.__listDPCR = [] # Direct Operator Previous Calculated Results
+ self.__listDPCN = [] # Direct Operator Previous Calculated Point Norms
+ self.__listJPCP = [] # Jacobian Previous Calculated Points
+ self.__listJPCI = [] # Jacobian Previous Calculated Increment
+ self.__listJPCR = [] # Jacobian Previous Calculated Results
+ self.__listJPPN = [] # Jacobian Previous Calculated Point Norms
+ self.__listJPIN = [] # Jacobian Previous Calculated Increment Norms
+ else:
+ self.__avoidRC = False
if float(increment) <> 0.:
self.__increment = float(increment)
else:
if dX is None:
self.__dX = None
else:
- self.__dX = numpy.asmatrix(dX).flatten().T
+ self.__dX = numpy.asmatrix(numpy.ravel( dX )).T
+ logging.debug("FDA Reduction des doublons de calcul : %s"%self.__avoidRC)
+ if self.__avoidRC:
+ logging.debug("FDA Tolerance de determination des doublons : %.2e"%self.__tolerBP)
+
+ # ---------------------------------------------------------
+ def __doublon__(self, e, l, n, v=""):
+ __ac, __iac = False, -1
+ for i in xrange(len(l)-1,-1,-1):
+ if numpy.linalg.norm(e - l[i]) < self.__tolerBP * n[i]:
+ __ac, __iac = True, i
+ if v is not None: logging.debug("FDA Cas%s déja calculé, récupération du doublon %i"%(v,__iac))
+ break
+ return __ac, __iac
# ---------------------------------------------------------
- def TangentHMatrix(self, X ):
+ def DirectOperator(self, X ):
+ """
+ Calcul du direct à l'aide de la fonction fournie.
+ """
+ _X = numpy.asmatrix(numpy.ravel( X )).T
+ #
+ __alreadyCalculated = False
+ if self.__avoidRC:
+ __alreadyCalculated, __i = self.__doublon__(_X, self.__listDPCP, self.__listDPCN, " H")
+ #
+ if __alreadyCalculated:
+ logging.debug("FDA Calcul DirectOperator (par récupération du doublon %i)"%__i)
+ _HX = self.__listDPCR[__i]
+ else:
+ logging.debug("FDA Calcul DirectOperator (explicite)")
+ _HX = numpy.ravel(self.__userFunction( _X ))
+ if self.__avoidRC:
+ if self.__lenghtRH < 0: self.__lenghtRH = 2 * _X.size
+ if len(self.__listDPCP) > self.__lenghtRH:
+ logging.debug("FDA Réduction de la liste de H à %i éléments"%self.__lenghtRH)
+ self.__listDPCP.pop(0)
+ self.__listDPCR.pop(0)
+ self.__listDPCN.pop(0)
+ self.__listDPCP.append( copy.copy(_X) )
+ self.__listDPCR.append( copy.copy(_HX) )
+ self.__listDPCN.append( numpy.linalg.norm(_X) )
+ #
+ return _HX
+
+ # ---------------------------------------------------------
+ def TangentMatrix(self, X ):
"""
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.
- Différences finies centrées :
+ Différences finies centrées (approximation d'ordre 2):
1/ Pour chaque composante i de X, on ajoute et on enlève la perturbation
dX[i] à la composante X[i], pour composer X_plus_dXi et X_moins_dXi, et
on calcule les réponses HX_plus_dXi = H( X_plus_dXi ) et HX_moins_dXi =
le pas 2*dXi
3/ Chaque résultat, par composante, devient une colonne de la Jacobienne
- Différences finies non centrées :
+ Différences finies non centrées (approximation d'ordre 1):
1/ Pour chaque composante i de X, on ajoute la perturbation dX[i] à la
composante X[i] pour composer X_plus_dXi, et on calcule la réponse
HX_plus_dXi = H( X_plus_dXi )
4/ Chaque résultat, par composante, devient une colonne de la Jacobienne
"""
- logging.debug(" == Calcul de la Jacobienne")
- logging.debug(" Incrément de............: %s*X"%float(self.__increment))
- logging.debug(" Approximation centrée...: %s"%(self.__centeredDF))
+ logging.debug("FDA Calcul de la Jacobienne")
+ logging.debug("FDA Incrément de............: %s*X"%float(self.__increment))
+ logging.debug("FDA Approximation centrée...: %s"%(self.__centeredDF))
+ #
+ if X is None or len(X)==0:
+ raise ValueError("Nominal point X for approximate derivatives can not be None or void.")
#
- _X = numpy.asmatrix(X).flatten().T
+ _X = numpy.asmatrix(numpy.ravel( X )).T
#
if self.__dX is None:
_dX = self.__increment * _X
else:
- _dX = numpy.asmatrix(self.__dX).flatten().T
- logging.debug(" Incrément non corrigé...: %s"%(_dX))
+ _dX = numpy.asmatrix(numpy.ravel( self.__dX )).T
#
if (_dX == 0.).any():
moyenne = _dX.mean()
_dX = numpy.where( _dX == 0., float(self.__increment), _dX )
else:
_dX = numpy.where( _dX == 0., moyenne, _dX )
- logging.debug(" Incrément dX............: %s"%(_dX))
#
- if self.__centeredDF:
- #
- # Boucle de calcul des colonnes de la Jacobienne
- # ----------------------------------------------
- Jacobienne = []
- for i in range( len(_dX) ):
- X_plus_dXi = numpy.array( _X.A1, dtype=float )
- X_plus_dXi[i] = _X[i] + _dX[i]
- X_moins_dXi = numpy.array( _X.A1, dtype=float )
- X_moins_dXi[i] = _X[i] - _dX[i]
- #
- HX_plus_dXi = self.FunctionH( X_plus_dXi )
- HX_moins_dXi = self.FunctionH( X_moins_dXi )
+ __alreadyCalculated = False
+ if self.__avoidRC:
+ __bidon, __alreadyCalculatedP = self.__doublon__(_X, self.__listJPCP, self.__listJPPN, None)
+ __bidon, __alreadyCalculatedI = self.__doublon__(_dX, self.__listJPCI, self.__listJPIN, None)
+ if __alreadyCalculatedP == __alreadyCalculatedI > -1:
+ __alreadyCalculated, __i = True, __alreadyCalculatedP
+ logging.debug("FDA Cas J déja calculé, récupération du doublon %i"%__i)
+ #
+ if __alreadyCalculated:
+ logging.debug("FDA Calcul Jacobienne (par récupération du doublon %i)"%__i)
+ _Jacobienne = self.__listJPCR[__i]
+ else:
+ logging.debug("FDA Calcul Jacobienne (explicite)")
+ if self.__centeredDF:
#
- HX_Diff = ( HX_plus_dXi - HX_moins_dXi ) / (2.*_dX[i])
+ _Jacobienne = []
+ for i in range( _dX.size ):
+ _dXi = _dX[i]
+ _X_plus_dXi = numpy.array( _X.A1, dtype=float )
+ _X_plus_dXi[i] = _X[i] + _dXi
+ _X_moins_dXi = numpy.array( _X.A1, dtype=float )
+ _X_moins_dXi[i] = _X[i] - _dXi
+ #
+ _HX_plus_dXi = self.DirectOperator( _X_plus_dXi )
+ _HX_moins_dXi = self.DirectOperator( _X_moins_dXi )
+ #
+ _Jacobienne.append( numpy.ravel( _HX_plus_dXi - _HX_moins_dXi ) / (2.*_dXi) )
#
- Jacobienne.append( HX_Diff )
- #
- else:
- #
- # Boucle de calcul des colonnes de la Jacobienne
- # ----------------------------------------------
- HX_plus_dX = []
- for i in range( len(_dX) ):
- X_plus_dXi = numpy.array( _X.A1, dtype=float )
- X_plus_dXi[i] = _X[i] + _dX[i]
+ else:
#
- HX_plus_dXi = self.FunctionH( X_plus_dXi )
+ _Jacobienne = []
+ _HX = self.DirectOperator( _X )
+ for i in range( _dX.size ):
+ _dXi = _dX[i]
+ _X_plus_dXi = numpy.array( _X.A1, dtype=float )
+ _X_plus_dXi[i] = _X[i] + _dXi
+ #
+ _HX_plus_dXi = self.DirectOperator( _X_plus_dXi )
+ #
+ _Jacobienne.append( numpy.ravel(( _HX_plus_dXi - _HX ) / _dXi) )
#
- HX_plus_dX.append( HX_plus_dXi )
#
- # Calcul de la valeur centrale
- # ----------------------------
- HX = self.FunctionH( _X )
- #
- # Calcul effectif de la Jacobienne par différences finies
- # -------------------------------------------------------
- Jacobienne = []
- for i in range( len(_dX) ):
- Jacobienne.append( numpy.asmatrix(( HX_plus_dX[i] - HX ) / _dX[i]).flatten().A1 )
+ _Jacobienne = numpy.matrix( numpy.vstack( _Jacobienne ) ).T
+ if self.__avoidRC:
+ if self.__lenghtRJ < 0: self.__lenghtRJ = 2 * _X.size
+ if len(self.__listJPCP) > self.__lenghtRJ:
+ logging.debug("FDA Réduction de la liste de J à %i éléments"%self.__lenghtRJ)
+ self.__listJPCP.pop(0)
+ self.__listJPCI.pop(0)
+ self.__listJPCR.pop(0)
+ self.__listJPPN.pop(0)
+ self.__listJPIN.pop(0)
+ self.__listJPCP.append( copy.copy(_X) )
+ self.__listJPCI.append( copy.copy(_dX) )
+ self.__listJPCR.append( copy.copy(_Jacobienne) )
+ self.__listJPPN.append( numpy.linalg.norm(_X) )
+ self.__listJPIN.append( numpy.linalg.norm(_Jacobienne) )
#
- Jacobienne = numpy.matrix( numpy.vstack( Jacobienne ) ).T
- logging.debug(" == Fin du calcul de la Jacobienne")
+ logging.debug("FDA Fin du calcul de la Jacobienne")
#
- return Jacobienne
+ return _Jacobienne
# ---------------------------------------------------------
- def TangentH(self, (X, dX) ):
+ def TangentOperator(self, (X, dX) ):
"""
Calcul du tangent à l'aide de la Jacobienne.
"""
- Jacobienne = self.TangentHMatrix( X )
+ _Jacobienne = self.TangentMatrix( X )
if dX is None or len(dX) == 0:
#
# Calcul de la forme matricielle si le second argument est None
# -------------------------------------------------------------
- return Jacobienne
+ return _Jacobienne
else:
#
# Calcul de la valeur linéarisée de H en X appliqué à dX
# ------------------------------------------------------
- _dX = numpy.asmatrix(dX).flatten().T
- HtX = numpy.dot(Jacobienne, _dX)
- return HtX.A1
+ _dX = numpy.asmatrix(numpy.ravel( dX )).T
+ _HtX = numpy.dot(_Jacobienne, _dX)
+ return _HtX.A1
# ---------------------------------------------------------
- def AdjointH(self, (X, Y) ):
+ def AdjointOperator(self, (X, Y) ):
"""
Calcul de l'adjoint à l'aide de la Jacobienne.
"""
- JacobienneT = self.TangentHMatrix( X ).T
+ _JacobienneT = self.TangentMatrix( X ).T
if Y is None or len(Y) == 0:
#
# Calcul de la forme matricielle si le second argument est None
# -------------------------------------------------------------
- return JacobienneT
+ return _JacobienneT
else:
#
# Calcul de la valeur de l'adjoint en X appliqué à Y
# --------------------------------------------------
- _Y = numpy.asmatrix(Y).flatten().T
- HaY = numpy.dot(JacobienneT, _Y)
- return HaY.A1
-
-# ==============================================================================
-#
-def test1FunctionH( XX ):
- """ Direct non-linear simulation operator """
- #
- # NEED TO BE COMPLETED
- # NEED TO BE COMPLETED
- # NEED TO BE COMPLETED
- #
- # --------------------------------------> # EXAMPLE TO BE REMOVED
- # Example of Identity operator # EXAMPLE TO BE REMOVED
- if type(XX) is type(numpy.matrix([])): # EXAMPLE TO BE REMOVED
- HX = XX.A1.tolist() # EXAMPLE TO BE REMOVED
- elif type(XX) is type(numpy.array([])): # EXAMPLE TO BE REMOVED
- HX = numpy.matrix(XX).A1.tolist() # EXAMPLE TO BE REMOVED
- else: # EXAMPLE TO BE REMOVED
- HX = XX # EXAMPLE TO BE REMOVED
- # # EXAMPLE TO BE REMOVED
- HHX = [] # EXAMPLE TO BE REMOVED
- HHX.extend( HX ) # EXAMPLE TO BE REMOVED
- HHX.extend( HX ) # EXAMPLE TO BE REMOVED
- # --------------------------------------> # EXAMPLE TO BE REMOVED
- #
- return numpy.array( HHX )
+ _Y = numpy.asmatrix(numpy.ravel( Y )).T
+ _HaY = numpy.dot(_JacobienneT, _Y)
+ return _HaY.A1
# ==============================================================================
if __name__ == "__main__":
-
- print
- print "AUTODIAGNOSTIC"
- print "=============="
-
- X0 = [1, 2, 3]
-
- FDA = FDApproximation( test1FunctionH )
- print "H(X) =", FDA.FunctionH( X0 )
- print "Tg matrice =\n", FDA.TangentHMatrix( X0 )
- print "Tg(X) =", FDA.TangentH( (X0, X0) )
- print "Ad((X,Y)) =", FDA.AdjointH( (X0,range(3,3+2*len(X0))) )
- print
- del FDA
-
- FDA = FDApproximation( test1FunctionH, centeredDF=True )
- print "H(X) =", FDA.FunctionH( X0 )
- print "Tg matrice =\n", FDA.TangentHMatrix( X0 )
- print "Tg(X) =", FDA.TangentH( (X0, X0) )
- print "Ad((X,Y)) =", FDA.AdjointH( (X0,range(3,3+2*len(X0))) )
- print
- del FDA
-
- X0 = range(5)
-
- FDA = FDApproximation( test1FunctionH )
- print "H(X) =", FDA.FunctionH( X0 )
- print "Tg matrice =\n", FDA.TangentHMatrix( X0 )
- print "Tg(X) =", FDA.TangentH( (X0, X0) )
- print "Ad((X,Y)) =", FDA.AdjointH( (X0,range(7,7+2*len(X0))) )
- print
- del FDA
+ print '\n AUTODIAGNOSTIC \n'
