1 # -*- coding: utf-8 -*-
3 # Copyright (C) 2008-2019 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
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",
80 "CostFunctionJAtCurrentOptimum",
82 "CostFunctionJbAtCurrentOptimum",
84 "CostFunctionJoAtCurrentOptimum",
89 "InnovationAtCurrentState",
92 "SimulatedObservationAtBackground",
93 "SimulatedObservationAtCurrentOptimum",
94 "SimulatedObservationAtCurrentState",
95 "SimulatedObservationAtOptimum",
98 self.defineRequiredParameter( # Pas de type
100 message = "Liste des valeurs de bornes",
102 self.requireInputArguments(
103 mandatory= ("Xb", "Y", "HO", "R"),
106 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
107 self._pre_run(Parameters, Xb, Y, R, B, Q)
109 # Correction pour pallier a un bug de TNC sur le retour du Minimum
110 if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
111 self.setParameterValue("StoreInternalVariables",True)
115 Hm = HO["Direct"].appliedTo
116 Ha = HO["Adjoint"].appliedInXTo
118 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
119 # ----------------------------------------------------
120 if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
121 HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
124 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
125 if Y.size != HXb.size:
126 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))
127 if max(Y.shape) != max(HXb.shape):
128 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))
130 # Précalcul des inversions de B et R
131 # ----------------------------------
133 if self._parameters["Minimizer"] == "LM":
134 RdemiI = R.choleskyI()
136 # Définition de la fonction-coût
137 # ------------------------------
139 _X = numpy.asmatrix(numpy.ravel( x )).T
140 if self._parameters["StoreInternalVariables"] or \
141 self._toStore("CurrentState") or \
142 self._toStore("CurrentOptimum"):
143 self.StoredVariables["CurrentState"].store( _X )
145 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
146 _Innovation = Y - _HX
147 if self._toStore("SimulatedObservationAtCurrentState") or \
148 self._toStore("SimulatedObservationAtCurrentOptimum"):
149 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
150 if self._toStore("InnovationAtCurrentState"):
151 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
154 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
157 self.StoredVariables["CostFunctionJb"].store( Jb )
158 self.StoredVariables["CostFunctionJo"].store( Jo )
159 self.StoredVariables["CostFunctionJ" ].store( J )
160 if self._toStore("IndexOfOptimum") or \
161 self._toStore("CurrentOptimum") or \
162 self._toStore("CostFunctionJAtCurrentOptimum") or \
163 self._toStore("CostFunctionJbAtCurrentOptimum") or \
164 self._toStore("CostFunctionJoAtCurrentOptimum") or \
165 self._toStore("SimulatedObservationAtCurrentOptimum"):
166 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
167 if self._toStore("IndexOfOptimum"):
168 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
169 if self._toStore("CurrentOptimum"):
170 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
171 if self._toStore("SimulatedObservationAtCurrentOptimum"):
172 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
173 if self._toStore("CostFunctionJbAtCurrentOptimum"):
174 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
175 if self._toStore("CostFunctionJoAtCurrentOptimum"):
176 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
177 if self._toStore("CostFunctionJAtCurrentOptimum"):
178 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
181 def GradientOfCostFunction(x):
182 _X = numpy.asmatrix(numpy.ravel( x )).T
184 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
186 GradJo = - Ha( (_X, RI * (Y - _HX)) )
187 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
190 def CostFunctionLM(x):
191 _X = numpy.asmatrix(numpy.ravel( x )).T
193 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
194 _Innovation = Y - _HX
196 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
198 if self._parameters["StoreInternalVariables"] or \
199 self._toStore("CurrentState"):
200 self.StoredVariables["CurrentState"].store( _X )
201 self.StoredVariables["CostFunctionJb"].store( Jb )
202 self.StoredVariables["CostFunctionJo"].store( Jo )
203 self.StoredVariables["CostFunctionJ" ].store( J )
205 return numpy.ravel( RdemiI*_Innovation )
207 def GradientOfCostFunctionLM(x):
208 _X = numpy.asmatrix(numpy.ravel( x )).T
210 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
212 GradJo = - Ha( (_X, RI * (Y - _HX)) )
213 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
214 return - RdemiI*HO["Tangent"].asMatrix( _X )
216 # Point de démarrage de l'optimisation : Xini = Xb
217 # ------------------------------------
218 Xini = numpy.ravel(Xb)
220 # Minimisation de la fonctionnelle
221 # --------------------------------
222 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
224 if self._parameters["Minimizer"] == "LBFGSB":
225 # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
227 Minimum, J_optimal, Informations = lbfgsbhlt.fmin_l_bfgs_b(
230 fprime = GradientOfCostFunction,
232 bounds = self._parameters["Bounds"],
233 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
234 factr = self._parameters["CostDecrementTolerance"]*1.e14,
235 pgtol = self._parameters["ProjectedGradientTolerance"],
236 iprint = self._parameters["optiprint"],
238 nfeval = Informations['funcalls']
239 rc = Informations['warnflag']
240 elif self._parameters["Minimizer"] == "TNC":
241 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
244 fprime = GradientOfCostFunction,
246 bounds = self._parameters["Bounds"],
247 maxfun = self._parameters["MaximumNumberOfSteps"],
248 pgtol = self._parameters["ProjectedGradientTolerance"],
249 ftol = self._parameters["CostDecrementTolerance"],
250 messages = self._parameters["optmessages"],
252 elif self._parameters["Minimizer"] == "CG":
253 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
256 fprime = GradientOfCostFunction,
258 maxiter = self._parameters["MaximumNumberOfSteps"],
259 gtol = self._parameters["GradientNormTolerance"],
260 disp = self._parameters["optdisp"],
263 elif self._parameters["Minimizer"] == "NCG":
264 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
267 fprime = GradientOfCostFunction,
269 maxiter = self._parameters["MaximumNumberOfSteps"],
270 avextol = self._parameters["CostDecrementTolerance"],
271 disp = self._parameters["optdisp"],
274 elif self._parameters["Minimizer"] == "BFGS":
275 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
278 fprime = GradientOfCostFunction,
280 maxiter = self._parameters["MaximumNumberOfSteps"],
281 gtol = self._parameters["GradientNormTolerance"],
282 disp = self._parameters["optdisp"],
285 elif self._parameters["Minimizer"] == "LM":
286 Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
287 func = CostFunctionLM,
289 Dfun = GradientOfCostFunctionLM,
291 ftol = self._parameters["CostDecrementTolerance"],
292 maxfev = self._parameters["MaximumNumberOfSteps"],
293 gtol = self._parameters["GradientNormTolerance"],
296 nfeval = infodict['nfev']
298 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
300 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
301 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
303 # Correction pour pallier a un bug de TNC sur le retour du Minimum
304 # ----------------------------------------------------------------
305 if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
306 Minimum = self.StoredVariables["CurrentState"][IndexMin]
308 # Obtention de l'analyse
309 # ----------------------
310 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
312 self.StoredVariables["Analysis"].store( Xa.A1 )
314 if self._toStore("OMA") or \
315 self._toStore("SimulatedObservationAtOptimum"):
316 if self._toStore("SimulatedObservationAtCurrentState"):
317 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
318 elif self._toStore("SimulatedObservationAtCurrentOptimum"):
319 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
324 # Calculs et/ou stockages supplémentaires
325 # ---------------------------------------
326 if self._toStore("Innovation") or \
327 self._toStore("OMB"):
329 if self._toStore("Innovation"):
330 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
331 if self._toStore("BMA"):
332 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
333 if self._toStore("OMA"):
334 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
335 if self._toStore("OMB"):
336 self.StoredVariables["OMB"].store( numpy.ravel(d) )
337 if self._toStore("SimulatedObservationAtBackground"):
338 self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
339 if self._toStore("SimulatedObservationAtOptimum"):
340 self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
345 # ==============================================================================
346 if __name__ == "__main__":
347 print('\n AUTODIAGNOSTIC \n')