1 #-*-coding:iso-8859-1-*-
3 # Copyright (C) 2008-2012 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
23 from daCore import BasicObjects, PlatformInfo
24 m = PlatformInfo.SystemUsage()
28 # ==============================================================================
29 class ElementaryAlgorithm(BasicObjects.Algorithm):
31 BasicObjects.Algorithm.__init__(self, "GRADIENTTEST")
32 self.defineRequiredParameter(
33 name = "ResiduFormula",
36 message = "Formule de résidu utilisée",
37 listval = ["Norm", "Taylor"],
39 self.defineRequiredParameter(
40 name = "EpsilonMinimumExponent",
43 message = "Exposant minimal en puissance de 10 pour le multiplicateur d'incrément",
47 self.defineRequiredParameter(
48 name = "InitialDirection",
51 message = "Direction initiale de la dérivée directionnelle autour du point nominal",
53 self.defineRequiredParameter(
54 name = "AmplitudeOfInitialDirection",
57 message = "Amplitude de la direction initiale de la dérivée directionnelle autour du point nominal",
59 self.defineRequiredParameter(
61 typecast = numpy.random.seed,
62 message = "Graine fixée pour le générateur aléatoire",
64 self.defineRequiredParameter(
68 message = "Trace et sauve les résultats",
70 self.defineRequiredParameter(
74 message = "Nom de base (hors extension) des fichiers de sauvegarde des résultats",
76 self.defineRequiredParameter(
80 message = "Titre du tableau et de la figure",
82 self.defineRequiredParameter(
86 message = "Label de la courbe tracée dans la figure",
89 def run(self, Xb=None, Y=None, H=None, M=None, R=None, B=None, Q=None, Parameters=None):
90 logging.debug("%s Lancement"%self._name)
91 logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("Mo")))
93 # Paramètres de pilotage
94 # ----------------------
95 self.setParameters(Parameters)
97 # Opérateur d'observation
98 # -----------------------
99 Hm = H["Direct"].appliedTo
100 if self._parameters["ResiduFormula"] is "Taylor":
101 Ht = H["Tangent"].appliedInXTo
103 # Construction des perturbations
104 # ------------------------------
105 Perturbations = [ 10**i for i in xrange(self._parameters["EpsilonMinimumExponent"],1) ]
106 Perturbations.reverse()
108 # Calcul du point courant
109 # -----------------------
110 X = numpy.asmatrix(Xb).flatten().T
111 FX = numpy.asmatrix( Hm( X ) ).flatten().T
112 FX = numpy.asmatrix(FX).flatten().T
113 NormeX = numpy.linalg.norm( X )
114 NormeFX = numpy.linalg.norm( FX )
116 # Fabrication de la direction de l'incrément dX
117 # ----------------------------------------------
118 if len(self._parameters["InitialDirection"]) == 0:
122 dX0.append( numpy.random.normal(0.,abs(v)) )
124 dX0.append( numpy.random.normal(0.,X.mean()) )
126 dX0 = numpy.asmatrix(self._parameters["InitialDirection"]).flatten()
128 dX0 = float(self._parameters["AmplitudeOfInitialDirection"]) * numpy.matrix( dX0 ).T
130 # Calcul du gradient au point courant X pour l'incrément dX
131 # ---------------------------------------------------------
132 if self._parameters["ResiduFormula"] is "Taylor":
133 GradFxdX = Ht( (X, dX0) )
134 GradFxdX = numpy.asmatrix(GradFxdX).flatten().T
136 # Entete des resultats
137 # --------------------
138 if self._parameters["ResiduFormula"] is "Taylor":
140 On observe le residu issu du développement de Taylor de la fonction H :
142 R(Alpha) = || H(x+Alpha*dx) - H(x) - Alpha * TangentH_x(dx) ||
144 Ce résidu doit décroître en Alpha**2 selon Alpha.
145 On prend dX0 = Normal(0,X) et dX = Alpha*dX0. H est le code de calcul.
147 elif self._parameters["ResiduFormula"] is "Norm":
149 On observe le residu, qui est une approximation du gradient :
151 || H(X+Alpha*dX) - H(X) ||
152 R(Alpha) = ---------------------------
155 qui doit rester constant jusqu'à ce qu'on atteigne la précision du calcul.
156 On prend dX0 = Normal(0,X) et dX = Alpha*dX0. H est le code de calcul.
161 msgs = " ====" + "="*len(self._parameters["ResultTitle"]) + "====\n"
162 msgs += " " + self._parameters["ResultTitle"] + "\n"
163 msgs += " ====" + "="*len(self._parameters["ResultTitle"]) + "====\n"
166 msg = " i Alpha ||X|| ||H(X)|| ||H(X+dX)|| ||dX|| ||H(X+dX)-H(X)|| ||H(X+dX)-H(X)||/||dX|| R(Alpha) "
168 msgs += "\n" + "-"*nbtirets
170 msgs += "\n" + "-"*nbtirets
180 # Boucle sur les perturbations
181 # ----------------------------
182 for i,amplitude in enumerate(Perturbations):
183 logging.debug("%s Etape de calcul numéro %i, avec la perturbation %8.3e"%(self._name, i, amplitude))
187 FX_plus_dX = Hm( X + dX )
188 FX_plus_dX = numpy.asmatrix(FX_plus_dX).flatten().T
190 NormedX = numpy.linalg.norm( dX )
191 NormeFXdX = numpy.linalg.norm( FX_plus_dX )
192 NormedFX = numpy.linalg.norm( FX_plus_dX - FX )
193 NormedFXsdX = NormedFX/NormedX
195 if self._parameters["ResiduFormula"] is "Taylor":
196 NormedFXGdX = numpy.linalg.norm( FX_plus_dX - FX - amplitude * GradFxdX )
198 NormedFXsAm = NormedFX/amplitude
200 # if numpy.abs(NormedFX) < 1.e-20:
203 NormesdX.append( NormedX )
204 NormesFXdX.append( NormeFXdX )
205 NormesdFX.append( NormedFX )
206 if self._parameters["ResiduFormula"] is "Taylor":
207 NormesdFXGdX.append( NormedFXGdX )
208 NormesdFXsdX.append( NormedFXsdX )
209 NormesdFXsAm.append( NormedFXsAm )
211 if self._parameters["ResiduFormula"] is "Taylor":
213 elif self._parameters["ResiduFormula"] is "Norm":
215 if Normalisation < 0 : Normalisation = Residu
217 msg = " %2i %5.0e %8.3e %8.3e %8.3e %8.3e %8.3e | %8.3e | %8.3e"%(i,amplitude,NormeX,NormeFX,NormeFXdX,NormedX,NormedFX,NormedFXsdX,Residu)
220 self.StoredVariables["CostFunctionJ"].store( Residu )
221 msgs += "\n" + "-"*nbtirets
224 # Sorties eventuelles
225 # -------------------
226 logging.debug("%s Résultats :\n%s"%(self._name, msgs))
228 print "Results of gradient stability check:"
231 if self._parameters["PlotAndSave"]:
232 f = open(str(self._parameters["ResultFile"])+".txt",'a')
236 Residus = self.StoredVariables["CostFunctionJ"].valueserie()[-len(Perturbations):]
237 if self._parameters["ResiduFormula"] is "Taylor":
238 PerturbationsCarre = [ 10**(2*i) for i in xrange(-len(NormesdFXGdX)+1,1) ]
239 PerturbationsCarre.reverse()
243 titre = self._parameters["ResultTitle"],
244 label = self._parameters["ResultLabel"],
247 filename = str(self._parameters["ResultFile"])+".ps",
248 YRef = PerturbationsCarre,
249 normdY0 = numpy.log10( NormesdFX[0] ),
251 elif self._parameters["ResiduFormula"] is "Norm":
255 titre = self._parameters["ResultTitle"],
256 label = self._parameters["ResultLabel"],
259 filename = str(self._parameters["ResultFile"])+".ps",
262 logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("Mo")))
263 logging.debug("%s Terminé"%self._name)
267 # ==============================================================================
278 YRef = None, # Vecteur de reference a comparer a Y
279 recalYRef = True, # Decalage du point 0 de YRef à Y[0]
280 normdY0 = 0., # Norme de DeltaY[0]
284 __g = __gnuplot.Gnuplot(persist=1) # persist=1
285 # __g('set terminal '+__gnuplot.GnuplotOpts.default_term)
286 __g('set style data lines')
289 __g('set title "'+titre+'"')
290 # __g('set xrange [] reverse')
291 # __g('set yrange [0:2]')
294 steps = numpy.log10( X )
295 __g('set xlabel "Facteur multiplicatif de dX, en echelle log10"')
298 __g('set xlabel "Facteur multiplicatif de dX"')
301 values = numpy.log10( Y )
302 __g('set ylabel "Amplitude du residu, en echelle log10"')
305 __g('set ylabel "Amplitude du residu"')
307 __g.plot( __gnuplot.Data( steps, values, title=label, with_='lines lw 3' ) )
310 valuesRef = numpy.log10( YRef )
313 if recalYRef and not numpy.all(values < -8):
314 valuesRef = valuesRef + values[0]
315 elif recalYRef and numpy.all(values < -8):
316 valuesRef = valuesRef + normdY0
319 __g.replot( __gnuplot.Data( steps, valuesRef, title="Reference", with_='lines lw 1' ) )
321 if filename is not "":
322 __g.hardcopy( filename, color=1)
324 raw_input('Please press return to continue...\n')
326 # ==============================================================================
327 if __name__ == "__main__":
328 print '\n AUTODIAGNOSTIC \n'