1 # -*- coding: utf-8 -*-
3 # Copyright (C) 2008-2021 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
25 import numpy, scipy.optimize, scipy.version
27 # ==============================================================================
28 class ElementaryAlgorithm(BasicObjects.Algorithm):
30 BasicObjects.Algorithm.__init__(self, "NONLINEARLEASTSQUARES")
31 self.defineRequiredParameter(
35 message = "Minimiseur utilisé",
36 listval = ["LBFGSB","TNC", "CG", "NCG", "BFGS", "LM"],
38 self.defineRequiredParameter(
39 name = "MaximumNumberOfSteps",
42 message = "Nombre maximal de pas d'optimisation",
45 self.defineRequiredParameter(
46 name = "CostDecrementTolerance",
49 message = "Diminution relative minimale du coût lors de l'arrêt",
52 self.defineRequiredParameter(
53 name = "ProjectedGradientTolerance",
56 message = "Maximum des composantes du gradient projeté lors de l'arrêt",
59 self.defineRequiredParameter(
60 name = "GradientNormTolerance",
63 message = "Maximum des composantes du gradient lors de l'arrêt",
66 self.defineRequiredParameter(
67 name = "StoreInternalVariables",
70 message = "Stockage des variables internes ou intermédiaires du calcul",
72 self.defineRequiredParameter(
73 name = "StoreSupplementaryCalculations",
76 message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
81 "CostFunctionJAtCurrentOptimum",
83 "CostFunctionJbAtCurrentOptimum",
85 "CostFunctionJoAtCurrentOptimum",
86 "CurrentIterationNumber",
91 "InnovationAtCurrentState",
94 "SimulatedObservationAtBackground",
95 "SimulatedObservationAtCurrentOptimum",
96 "SimulatedObservationAtCurrentState",
97 "SimulatedObservationAtOptimum",
100 self.defineRequiredParameter( # Pas de type
102 message = "Liste des valeurs de bornes",
104 self.defineRequiredParameter(
105 name = "InitializationPoint",
106 typecast = numpy.ravel,
107 message = "État initial imposé (par défaut, c'est l'ébauche si None)",
109 self.requireInputArguments(
110 mandatory= ("Xb", "Y", "HO", "R"),
112 self.setAttributes(tags=(
118 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
119 self._pre_run(Parameters, Xb, Y, U, HO, EM, CM, R, B, Q)
123 Hm = HO["Direct"].appliedTo
124 Ha = HO["Adjoint"].appliedInXTo
126 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
127 # ----------------------------------------------------
128 if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
129 HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
132 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
133 if Y.size != HXb.size:
134 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))
135 if max(Y.shape) != max(HXb.shape):
136 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))
138 # Précalcul des inversions de B et R
139 # ----------------------------------
141 if self._parameters["Minimizer"] == "LM":
142 RdemiI = R.choleskyI()
144 # Définition de la fonction-coût
145 # ------------------------------
147 _X = numpy.asmatrix(numpy.ravel( x )).T
148 if self._parameters["StoreInternalVariables"] or \
149 self._toStore("CurrentState") or \
150 self._toStore("CurrentOptimum"):
151 self.StoredVariables["CurrentState"].store( _X )
153 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
154 _Innovation = Y - _HX
155 if self._toStore("SimulatedObservationAtCurrentState") or \
156 self._toStore("SimulatedObservationAtCurrentOptimum"):
157 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
158 if self._toStore("InnovationAtCurrentState"):
159 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
162 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
165 self.StoredVariables["CurrentIterationNumber"].store( len(self.StoredVariables["CostFunctionJ"]) )
166 self.StoredVariables["CostFunctionJb"].store( Jb )
167 self.StoredVariables["CostFunctionJo"].store( Jo )
168 self.StoredVariables["CostFunctionJ" ].store( J )
169 if self._toStore("IndexOfOptimum") or \
170 self._toStore("CurrentOptimum") or \
171 self._toStore("CostFunctionJAtCurrentOptimum") or \
172 self._toStore("CostFunctionJbAtCurrentOptimum") or \
173 self._toStore("CostFunctionJoAtCurrentOptimum") or \
174 self._toStore("SimulatedObservationAtCurrentOptimum"):
175 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
176 if self._toStore("IndexOfOptimum"):
177 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
178 if self._toStore("CurrentOptimum"):
179 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
180 if self._toStore("SimulatedObservationAtCurrentOptimum"):
181 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
182 if self._toStore("CostFunctionJbAtCurrentOptimum"):
183 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
184 if self._toStore("CostFunctionJoAtCurrentOptimum"):
185 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
186 if self._toStore("CostFunctionJAtCurrentOptimum"):
187 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
190 def GradientOfCostFunction(x):
191 _X = numpy.asmatrix(numpy.ravel( x )).T
193 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
195 GradJo = - Ha( (_X, RI * (Y - _HX)) )
196 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
199 def CostFunctionLM(x):
200 _X = numpy.asmatrix(numpy.ravel( x )).T
202 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
203 _Innovation = Y - _HX
205 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
207 if self._parameters["StoreInternalVariables"] or \
208 self._toStore("CurrentState"):
209 self.StoredVariables["CurrentState"].store( _X )
210 self.StoredVariables["CostFunctionJb"].store( Jb )
211 self.StoredVariables["CostFunctionJo"].store( Jo )
212 self.StoredVariables["CostFunctionJ" ].store( J )
214 return numpy.ravel( RdemiI*_Innovation )
216 def GradientOfCostFunctionLM(x):
217 _X = numpy.asmatrix(numpy.ravel( x )).T
219 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
221 GradJo = - Ha( (_X, RI * (Y - _HX)) )
222 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
223 return - RdemiI*HO["Tangent"].asMatrix( _X )
225 # Point de démarrage de l'optimisation : Xini = Xb
226 # ------------------------------------
227 Xini = self._parameters["InitializationPoint"]
229 # Minimisation de la fonctionnelle
230 # --------------------------------
231 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
233 if self._parameters["Minimizer"] == "LBFGSB":
234 # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
235 if "0.19" <= scipy.version.version <= "1.1.0":
236 import lbfgsbhlt as optimiseur
238 import scipy.optimize as optimiseur
239 Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
242 fprime = GradientOfCostFunction,
244 bounds = self._parameters["Bounds"],
245 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
246 factr = self._parameters["CostDecrementTolerance"]*1.e14,
247 pgtol = self._parameters["ProjectedGradientTolerance"],
248 iprint = self._parameters["optiprint"],
250 nfeval = Informations['funcalls']
251 rc = Informations['warnflag']
252 elif self._parameters["Minimizer"] == "TNC":
253 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
256 fprime = GradientOfCostFunction,
258 bounds = self._parameters["Bounds"],
259 maxfun = self._parameters["MaximumNumberOfSteps"],
260 pgtol = self._parameters["ProjectedGradientTolerance"],
261 ftol = self._parameters["CostDecrementTolerance"],
262 messages = self._parameters["optmessages"],
264 elif self._parameters["Minimizer"] == "CG":
265 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
268 fprime = GradientOfCostFunction,
270 maxiter = self._parameters["MaximumNumberOfSteps"],
271 gtol = self._parameters["GradientNormTolerance"],
272 disp = self._parameters["optdisp"],
275 elif self._parameters["Minimizer"] == "NCG":
276 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
279 fprime = GradientOfCostFunction,
281 maxiter = self._parameters["MaximumNumberOfSteps"],
282 avextol = self._parameters["CostDecrementTolerance"],
283 disp = self._parameters["optdisp"],
286 elif self._parameters["Minimizer"] == "BFGS":
287 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
290 fprime = GradientOfCostFunction,
292 maxiter = self._parameters["MaximumNumberOfSteps"],
293 gtol = self._parameters["GradientNormTolerance"],
294 disp = self._parameters["optdisp"],
297 elif self._parameters["Minimizer"] == "LM":
298 Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
299 func = CostFunctionLM,
301 Dfun = GradientOfCostFunctionLM,
303 ftol = self._parameters["CostDecrementTolerance"],
304 maxfev = self._parameters["MaximumNumberOfSteps"],
305 gtol = self._parameters["GradientNormTolerance"],
308 nfeval = infodict['nfev']
310 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
312 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
313 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
315 # Correction pour pallier a un bug de TNC sur le retour du Minimum
316 # ----------------------------------------------------------------
317 if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
318 Minimum = self.StoredVariables["CurrentState"][IndexMin]
320 # Obtention de l'analyse
321 # ----------------------
322 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
324 self.StoredVariables["Analysis"].store( Xa.A1 )
326 if self._toStore("OMA") or \
327 self._toStore("SimulatedObservationAtOptimum"):
328 if self._toStore("SimulatedObservationAtCurrentState"):
329 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
330 elif self._toStore("SimulatedObservationAtCurrentOptimum"):
331 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
336 # Calculs et/ou stockages supplémentaires
337 # ---------------------------------------
338 if self._toStore("Innovation") or \
339 self._toStore("OMB"):
341 if self._toStore("Innovation"):
342 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
343 if self._toStore("BMA"):
344 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
345 if self._toStore("OMA"):
346 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
347 if self._toStore("OMB"):
348 self.StoredVariables["OMB"].store( numpy.ravel(d) )
349 if self._toStore("SimulatedObservationAtBackground"):
350 self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
351 if self._toStore("SimulatedObservationAtOptimum"):
352 self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
357 # ==============================================================================
358 if __name__ == "__main__":
359 print('\n AUTODIAGNOSTIC\n')