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",
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"),
107 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
108 self._pre_run(Parameters, Xb, Y, R, B, Q)
110 # Correction pour pallier a un bug de TNC sur le retour du Minimum
111 if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
112 self.setParameterValue("StoreInternalVariables",True)
116 Hm = HO["Direct"].appliedTo
117 Ha = HO["Adjoint"].appliedInXTo
119 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
120 # ----------------------------------------------------
121 if HO["AppliedInX"] is not None and "HXb" in HO["AppliedInX"]:
122 HXb = Hm( Xb, HO["AppliedInX"]["HXb"] )
125 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
126 if Y.size != HXb.size:
127 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))
128 if max(Y.shape) != max(HXb.shape):
129 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))
131 # Précalcul des inversions de B et R
132 # ----------------------------------
134 if self._parameters["Minimizer"] == "LM":
135 RdemiI = R.choleskyI()
137 # Définition de la fonction-coût
138 # ------------------------------
140 _X = numpy.asmatrix(numpy.ravel( x )).T
141 if self._parameters["StoreInternalVariables"] or \
142 self._toStore("CurrentState") or \
143 self._toStore("CurrentOptimum"):
144 self.StoredVariables["CurrentState"].store( _X )
146 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
147 _Innovation = Y - _HX
148 if self._toStore("SimulatedObservationAtCurrentState") or \
149 self._toStore("SimulatedObservationAtCurrentOptimum"):
150 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
151 if self._toStore("InnovationAtCurrentState"):
152 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
155 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
158 self.StoredVariables["CostFunctionJb"].store( Jb )
159 self.StoredVariables["CostFunctionJo"].store( Jo )
160 self.StoredVariables["CostFunctionJ" ].store( J )
161 if self._toStore("IndexOfOptimum") or \
162 self._toStore("CurrentOptimum") or \
163 self._toStore("CostFunctionJAtCurrentOptimum") or \
164 self._toStore("CostFunctionJbAtCurrentOptimum") or \
165 self._toStore("CostFunctionJoAtCurrentOptimum") or \
166 self._toStore("SimulatedObservationAtCurrentOptimum"):
167 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
168 if self._toStore("IndexOfOptimum"):
169 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
170 if self._toStore("CurrentOptimum"):
171 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
172 if self._toStore("SimulatedObservationAtCurrentOptimum"):
173 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
174 if self._toStore("CostFunctionJbAtCurrentOptimum"):
175 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
176 if self._toStore("CostFunctionJoAtCurrentOptimum"):
177 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
178 if self._toStore("CostFunctionJAtCurrentOptimum"):
179 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
182 def GradientOfCostFunction(x):
183 _X = numpy.asmatrix(numpy.ravel( x )).T
185 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
187 GradJo = - Ha( (_X, RI * (Y - _HX)) )
188 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
191 def CostFunctionLM(x):
192 _X = numpy.asmatrix(numpy.ravel( x )).T
194 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
195 _Innovation = Y - _HX
197 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
199 if self._parameters["StoreInternalVariables"] or \
200 self._toStore("CurrentState"):
201 self.StoredVariables["CurrentState"].store( _X )
202 self.StoredVariables["CostFunctionJb"].store( Jb )
203 self.StoredVariables["CostFunctionJo"].store( Jo )
204 self.StoredVariables["CostFunctionJ" ].store( J )
206 return numpy.ravel( RdemiI*_Innovation )
208 def GradientOfCostFunctionLM(x):
209 _X = numpy.asmatrix(numpy.ravel( x )).T
211 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
213 GradJo = - Ha( (_X, RI * (Y - _HX)) )
214 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
215 return - RdemiI*HO["Tangent"].asMatrix( _X )
217 # Point de démarrage de l'optimisation : Xini = Xb
218 # ------------------------------------
219 Xini = numpy.ravel(Xb)
221 # Minimisation de la fonctionnelle
222 # --------------------------------
223 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
225 if self._parameters["Minimizer"] == "LBFGSB":
226 # Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
228 Minimum, J_optimal, Informations = lbfgsbhlt.fmin_l_bfgs_b(
231 fprime = GradientOfCostFunction,
233 bounds = self._parameters["Bounds"],
234 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
235 factr = self._parameters["CostDecrementTolerance"]*1.e14,
236 pgtol = self._parameters["ProjectedGradientTolerance"],
237 iprint = self._parameters["optiprint"],
239 nfeval = Informations['funcalls']
240 rc = Informations['warnflag']
241 elif self._parameters["Minimizer"] == "TNC":
242 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
245 fprime = GradientOfCostFunction,
247 bounds = self._parameters["Bounds"],
248 maxfun = self._parameters["MaximumNumberOfSteps"],
249 pgtol = self._parameters["ProjectedGradientTolerance"],
250 ftol = self._parameters["CostDecrementTolerance"],
251 messages = self._parameters["optmessages"],
253 elif self._parameters["Minimizer"] == "CG":
254 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
257 fprime = GradientOfCostFunction,
259 maxiter = self._parameters["MaximumNumberOfSteps"],
260 gtol = self._parameters["GradientNormTolerance"],
261 disp = self._parameters["optdisp"],
264 elif self._parameters["Minimizer"] == "NCG":
265 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
268 fprime = GradientOfCostFunction,
270 maxiter = self._parameters["MaximumNumberOfSteps"],
271 avextol = self._parameters["CostDecrementTolerance"],
272 disp = self._parameters["optdisp"],
275 elif self._parameters["Minimizer"] == "BFGS":
276 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
279 fprime = GradientOfCostFunction,
281 maxiter = self._parameters["MaximumNumberOfSteps"],
282 gtol = self._parameters["GradientNormTolerance"],
283 disp = self._parameters["optdisp"],
286 elif self._parameters["Minimizer"] == "LM":
287 Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
288 func = CostFunctionLM,
290 Dfun = GradientOfCostFunctionLM,
292 ftol = self._parameters["CostDecrementTolerance"],
293 maxfev = self._parameters["MaximumNumberOfSteps"],
294 gtol = self._parameters["GradientNormTolerance"],
297 nfeval = infodict['nfev']
299 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
301 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
302 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
304 # Correction pour pallier a un bug de TNC sur le retour du Minimum
305 # ----------------------------------------------------------------
306 if self._parameters["StoreInternalVariables"] or self._toStore("CurrentState"):
307 Minimum = self.StoredVariables["CurrentState"][IndexMin]
309 # Obtention de l'analyse
310 # ----------------------
311 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
313 self.StoredVariables["Analysis"].store( Xa.A1 )
315 if self._toStore("OMA") or \
316 self._toStore("SimulatedObservationAtOptimum"):
317 if self._toStore("SimulatedObservationAtCurrentState"):
318 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
319 elif self._toStore("SimulatedObservationAtCurrentOptimum"):
320 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
325 # Calculs et/ou stockages supplémentaires
326 # ---------------------------------------
327 if self._toStore("Innovation") or \
328 self._toStore("OMB"):
330 if self._toStore("Innovation"):
331 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
332 if self._toStore("BMA"):
333 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
334 if self._toStore("OMA"):
335 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
336 if self._toStore("OMB"):
337 self.StoredVariables["OMB"].store( numpy.ravel(d) )
338 if self._toStore("SimulatedObservationAtBackground"):
339 self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
340 if self._toStore("SimulatedObservationAtOptimum"):
341 self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
346 # ==============================================================================
347 if __name__ == "__main__":
348 print('\n AUTODIAGNOSTIC \n')