1 # -*- coding: utf-8 -*-
3 # Copyright (C) 2008-2017 EDF R&D
5 # This library is free software; you can redistribute it and/or
6 # modify it under the terms of the GNU Lesser General Public
7 # License as published by the Free Software Foundation; either
8 # version 2.1 of the License.
10 # This library is distributed in the hope that it will be useful,
11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 # Lesser General Public License for more details.
15 # You should have received a copy of the GNU Lesser General Public
16 # License along with this library; if not, write to the Free Software
17 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
19 # See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
21 # Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
24 from daCore import BasicObjects, PlatformInfo
26 mpr = PlatformInfo.PlatformInfo().MachinePrecision()
27 if sys.version_info.major > 2:
30 # ==============================================================================
31 class ElementaryAlgorithm(BasicObjects.Algorithm):
33 BasicObjects.Algorithm.__init__(self, "TANGENTTEST")
34 self.defineRequiredParameter(
35 name = "ResiduFormula",
38 message = "Formule de résidu utilisée",
41 self.defineRequiredParameter(
42 name = "EpsilonMinimumExponent",
45 message = "Exposant minimal en puissance de 10 pour le multiplicateur d'incrément",
49 self.defineRequiredParameter(
50 name = "InitialDirection",
53 message = "Direction initiale de la dérivée directionnelle autour du point nominal",
55 self.defineRequiredParameter(
56 name = "AmplitudeOfInitialDirection",
59 message = "Amplitude de la direction initiale de la dérivée directionnelle autour du point nominal",
61 self.defineRequiredParameter(
62 name = "AmplitudeOfTangentPerturbation",
65 message = "Amplitude de la perturbation pour le calcul de la forme tangente",
69 self.defineRequiredParameter(
71 typecast = numpy.random.seed,
72 message = "Graine fixée pour le générateur aléatoire",
74 self.defineRequiredParameter(
78 message = "Titre du tableau et de la figure",
80 self.defineRequiredParameter(
81 name = "StoreSupplementaryCalculations",
84 message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
85 listval = ["CurrentState", "Residu", "SimulatedObservationAtCurrentState"]
87 self.requireInputArguments(
88 mandatory= ("Xb", "HO"),
91 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
92 self._pre_run(Parameters, Xb, Y, R, B, Q)
94 Hm = HO["Direct"].appliedTo
95 Ht = HO["Tangent"].appliedInXTo
97 # Construction des perturbations
98 # ------------------------------
99 Perturbations = [ 10**i for i in range(self._parameters["EpsilonMinimumExponent"],1) ]
100 Perturbations.reverse()
102 # Calcul du point courant
103 # -----------------------
104 Xn = numpy.asmatrix(numpy.ravel( Xb )).T
105 FX = numpy.asmatrix(numpy.ravel( Hm( Xn ) )).T
106 NormeX = numpy.linalg.norm( Xn )
107 NormeFX = numpy.linalg.norm( FX )
108 if "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
109 self.StoredVariables["CurrentState"].store( numpy.ravel(Xn) )
110 if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
111 self.StoredVariables["SimulatedObservationAtCurrentState"].store( numpy.ravel(FX) )
113 # Fabrication de la direction de l'increment dX
114 # ---------------------------------------------
115 if len(self._parameters["InitialDirection"]) == 0:
119 dX0.append( numpy.random.normal(0.,abs(v)) )
121 dX0.append( numpy.random.normal(0.,Xn.mean()) )
123 dX0 = numpy.ravel( self._parameters["InitialDirection"] )
125 dX0 = float(self._parameters["AmplitudeOfInitialDirection"]) * numpy.matrix( dX0 ).T
127 # Calcul du gradient au point courant X pour l'increment dX
128 # qui est le tangent en X multiplie par dX
129 # ---------------------------------------------------------
130 dX1 = float(self._parameters["AmplitudeOfTangentPerturbation"]) * dX0
131 GradFxdX = Ht( (Xn, dX1) )
132 GradFxdX = numpy.asmatrix(numpy.ravel( GradFxdX )).T
133 GradFxdX = float(1./self._parameters["AmplitudeOfTangentPerturbation"]) * GradFxdX
134 NormeGX = numpy.linalg.norm( GradFxdX )
136 # Entete des resultats
137 # --------------------
140 Remarque : les nombres inferieurs a %.0e (environ) representent un zero
141 a la precision machine.\n"""%mpr
142 if self._parameters["ResiduFormula"] == "Taylor":
143 __entete = u" i Alpha ||X|| ||F(X)|| | R(Alpha) |R-1|/Alpha"
145 On observe le residu provenant du rapport d'increments utilisant le
148 || F(X+Alpha*dX) - F(X) ||
149 R(Alpha) = -----------------------------
150 || Alpha * TangentF_X * dX ||
152 qui doit rester stable en 1+O(Alpha) jusqu'a ce que l'on atteigne la
155 Lorsque |R-1|/Alpha est inferieur ou egal a une valeur stable
156 lorsque Alpha varie, le tangent est valide, jusqu'a ce que l'on
157 atteigne la precision du calcul.
159 Si |R-1|/Alpha est tres faible, le code F est vraisemblablement
160 lineaire ou quasi-lineaire, et le tangent est valide jusqu'a ce que
161 l'on atteigne la precision du calcul.
163 On prend dX0 = Normal(0,X) et dX = Alpha*dX0. F est le code de calcul.\n""" + __precision
165 if len(self._parameters["ResultTitle"]) > 0:
166 __rt = unicode(self._parameters["ResultTitle"])
168 msgs += __marge + "====" + "="*len(__rt) + "====\n"
169 msgs += __marge + " " + __rt + "\n"
170 msgs += __marge + "====" + "="*len(__rt) + "====\n"
175 __nbtirets = len(__entete) + 2
176 msgs += "\n" + __marge + "-"*__nbtirets
177 msgs += "\n" + __marge + __entete
178 msgs += "\n" + __marge + "-"*__nbtirets
180 # Boucle sur les perturbations
181 # ----------------------------
182 for i,amplitude in enumerate(Perturbations):
185 if self._parameters["ResiduFormula"] == "Taylor":
186 FX_plus_dX = numpy.asmatrix(numpy.ravel( Hm( Xn + dX ) )).T
188 Residu = numpy.linalg.norm( FX_plus_dX - FX ) / (amplitude * NormeGX)
190 self.StoredVariables["Residu"].store( Residu )
191 msg = " %2i %5.0e %9.3e %9.3e | %11.5e %5.1e"%(i,amplitude,NormeX,NormeFX,Residu,abs(Residu-1.)/amplitude)
192 msgs += "\n" + __marge + msg
194 msgs += "\n" + __marge + "-"*__nbtirets
197 # Sorties eventuelles
198 # -------------------
199 print("\nResults of tangent check by \"%s\" formula:"%self._parameters["ResiduFormula"])
205 # ==============================================================================
206 if __name__ == "__main__":
207 print('\n AUTODIAGNOSTIC \n')