1 # -*- coding: utf-8 -*-
3 # Copyright (C) 2008-2020 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",
90 "InnovationAtCurrentState",
93 "SimulatedObservationAtBackground",
94 "SimulatedObservationAtCurrentOptimum",
95 "SimulatedObservationAtCurrentState",
96 "SimulatedObservationAtOptimum",
99 self.defineRequiredParameter( # Pas de type
101 message = "Liste des valeurs de bornes",
103 self.requireInputArguments(
104 mandatory= ("Xb", "Y", "HO", "R"),
106 self.setAttributes(tags=(
112 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
113 self._pre_run(Parameters, Xb, Y, R, B, Q)
115 # Correction pour pallier a un bug de TNC sur le retour du Minimum
116 if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
117 self.setParameterValue("StoreInternalVariables",True)
121 Hm = HO["Direct"].appliedTo
122 Ha = HO["Adjoint"].appliedInXTo
124 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
125 # ----------------------------------------------------
126 if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
127 HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
130 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
131 if Y.size != HXb.size:
132 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))
133 if max(Y.shape) != max(HXb.shape):
134 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))
136 # Précalcul des inversions de B et R
137 # ----------------------------------
139 if self._parameters["Minimizer"] == "LM":
140 RdemiI = R.choleskyI()
142 # Définition de la fonction-coût
143 # ------------------------------
145 _X = numpy.asmatrix(numpy.ravel( x )).T
146 if self._parameters["StoreInternalVariables"] or \
147 self._toStore("CurrentState") or \
148 self._toStore("CurrentOptimum"):
149 self.StoredVariables["CurrentState"].store( _X )
151 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
152 _Innovation = Y - _HX
153 if self._toStore("SimulatedObservationAtCurrentState") or \
154 self._toStore("SimulatedObservationAtCurrentOptimum"):
155 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
156 if self._toStore("InnovationAtCurrentState"):
157 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
160 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
163 self.StoredVariables["CostFunctionJb"].store( Jb )
164 self.StoredVariables["CostFunctionJo"].store( Jo )
165 self.StoredVariables["CostFunctionJ" ].store( J )
166 if self._toStore("IndexOfOptimum") or \
167 self._toStore("CurrentOptimum") or \
168 self._toStore("CostFunctionJAtCurrentOptimum") or \
169 self._toStore("CostFunctionJbAtCurrentOptimum") or \
170 self._toStore("CostFunctionJoAtCurrentOptimum") or \
171 self._toStore("SimulatedObservationAtCurrentOptimum"):
172 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
173 if self._toStore("IndexOfOptimum"):
174 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
175 if self._toStore("CurrentOptimum"):
176 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
177 if self._toStore("SimulatedObservationAtCurrentOptimum"):
178 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
179 if self._toStore("CostFunctionJbAtCurrentOptimum"):
180 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
181 if self._toStore("CostFunctionJoAtCurrentOptimum"):
182 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
183 if self._toStore("CostFunctionJAtCurrentOptimum"):
184 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
187 def GradientOfCostFunction(x):
188 _X = numpy.asmatrix(numpy.ravel( x )).T
190 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
192 GradJo = - Ha( (_X, RI * (Y - _HX)) )
193 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
196 def CostFunctionLM(x):
197 _X = numpy.asmatrix(numpy.ravel( x )).T
199 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
200 _Innovation = Y - _HX
202 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
204 if self._parameters["StoreInternalVariables"] or \
205 self._toStore("CurrentState"):
206 self.StoredVariables["CurrentState"].store( _X )
207 self.StoredVariables["CostFunctionJb"].store( Jb )
208 self.StoredVariables["CostFunctionJo"].store( Jo )
209 self.StoredVariables["CostFunctionJ" ].store( J )
211 return numpy.ravel( RdemiI*_Innovation )
213 def GradientOfCostFunctionLM(x):
214 _X = numpy.asmatrix(numpy.ravel( x )).T
216 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
218 GradJo = - Ha( (_X, RI * (Y - _HX)) )
219 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
220 return - RdemiI*HO["Tangent"].asMatrix( _X )
222 # Point de démarrage de l'optimisation : Xini = Xb
223 # ------------------------------------
224 Xini = numpy.ravel(Xb)
226 # Minimisation de la fonctionnelle
227 # --------------------------------
228 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
230 if self._parameters["Minimizer"] == "LBFGSB":
231 # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
232 if "0.19" <= scipy.version.version <= "1.1.0":
233 import lbfgsbhlt as optimiseur
235 import scipy.optimize as optimiseur
236 Minimum, J_optimal, Informations = optimiseur.fmin_l_bfgs_b(
239 fprime = GradientOfCostFunction,
241 bounds = self._parameters["Bounds"],
242 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
243 factr = self._parameters["CostDecrementTolerance"]*1.e14,
244 pgtol = self._parameters["ProjectedGradientTolerance"],
245 iprint = self._parameters["optiprint"],
247 nfeval = Informations['funcalls']
248 rc = Informations['warnflag']
249 elif self._parameters["Minimizer"] == "TNC":
250 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
253 fprime = GradientOfCostFunction,
255 bounds = self._parameters["Bounds"],
256 maxfun = self._parameters["MaximumNumberOfSteps"],
257 pgtol = self._parameters["ProjectedGradientTolerance"],
258 ftol = self._parameters["CostDecrementTolerance"],
259 messages = self._parameters["optmessages"],
261 elif self._parameters["Minimizer"] == "CG":
262 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
265 fprime = GradientOfCostFunction,
267 maxiter = self._parameters["MaximumNumberOfSteps"],
268 gtol = self._parameters["GradientNormTolerance"],
269 disp = self._parameters["optdisp"],
272 elif self._parameters["Minimizer"] == "NCG":
273 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
276 fprime = GradientOfCostFunction,
278 maxiter = self._parameters["MaximumNumberOfSteps"],
279 avextol = self._parameters["CostDecrementTolerance"],
280 disp = self._parameters["optdisp"],
283 elif self._parameters["Minimizer"] == "BFGS":
284 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
287 fprime = GradientOfCostFunction,
289 maxiter = self._parameters["MaximumNumberOfSteps"],
290 gtol = self._parameters["GradientNormTolerance"],
291 disp = self._parameters["optdisp"],
294 elif self._parameters["Minimizer"] == "LM":
295 Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
296 func = CostFunctionLM,
298 Dfun = GradientOfCostFunctionLM,
300 ftol = self._parameters["CostDecrementTolerance"],
301 maxfev = self._parameters["MaximumNumberOfSteps"],
302 gtol = self._parameters["GradientNormTolerance"],
305 nfeval = infodict['nfev']
307 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
309 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
310 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
312 # Correction pour pallier a un bug de TNC sur le retour du Minimum
313 # ----------------------------------------------------------------
314 if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
315 Minimum = self.StoredVariables["CurrentState"][IndexMin]
317 # Obtention de l'analyse
318 # ----------------------
319 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
321 self.StoredVariables["Analysis"].store( Xa.A1 )
323 if self._toStore("OMA") or \
324 self._toStore("SimulatedObservationAtOptimum"):
325 if self._toStore("SimulatedObservationAtCurrentState"):
326 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
327 elif self._toStore("SimulatedObservationAtCurrentOptimum"):
328 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
333 # Calculs et/ou stockages supplémentaires
334 # ---------------------------------------
335 if self._toStore("Innovation") or \
336 self._toStore("OMB"):
338 if self._toStore("Innovation"):
339 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
340 if self._toStore("BMA"):
341 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
342 if self._toStore("OMA"):
343 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
344 if self._toStore("OMB"):
345 self.StoredVariables["OMB"].store( numpy.ravel(d) )
346 if self._toStore("SimulatedObservationAtBackground"):
347 self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
348 if self._toStore("SimulatedObservationAtOptimum"):
349 self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
354 # ==============================================================================
355 if __name__ == "__main__":
356 print('\n AUTODIAGNOSTIC\n')