1 #-*-coding:iso-8859-1-*-
3 # Copyright (C) 2008-2014 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, PlatformInfo
25 m = PlatformInfo.SystemUsage()
26 import numpy, scipy.optimize
28 # ==============================================================================
29 class ElementaryAlgorithm(BasicObjects.Algorithm):
31 BasicObjects.Algorithm.__init__(self, "3DVAR")
32 self.defineRequiredParameter(
36 message = "Minimiseur utilisé",
37 listval = ["LBFGSB","TNC", "CG", "NCG", "BFGS"],
39 self.defineRequiredParameter(
40 name = "MaximumNumberOfSteps",
43 message = "Nombre maximal de pas d'optimisation",
46 self.defineRequiredParameter(
47 name = "CostDecrementTolerance",
50 message = "Diminution relative minimale du cout 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",
65 self.defineRequiredParameter(
66 name = "StoreInternalVariables",
69 message = "Stockage des variables internes ou intermédiaires du calcul",
71 self.defineRequiredParameter(
72 name = "StoreSupplementaryCalculations",
75 message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
76 listval = ["APosterioriCovariance", "BMA", "OMA", "OMB", "Innovation", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles"]
78 self.defineRequiredParameter(
82 message = "Liste des valeurs de quantiles",
84 self.defineRequiredParameter(
86 typecast = numpy.random.seed,
87 message = "Graine fixée pour le générateur aléatoire",
89 self.defineRequiredParameter(
90 name = "NumberOfSamplesForQuantiles",
93 message = "Nombre d'échantillons simulés pour le calcul des quantiles",
96 self.defineRequiredParameter(
97 name = "SimulationForQuantiles",
100 message = "Type de simulation pour l'estimation des quantiles",
101 listval = ["Linear", "NonLinear"]
104 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
105 if logging.getLogger().level < logging.WARNING:
106 self.__iprint, self.__disp = 1, 1
107 self.__message = scipy.optimize.tnc.MSG_ALL
109 self.__iprint, self.__disp = -1, 0
110 self.__message = scipy.optimize.tnc.MSG_NONE
112 logging.debug("%s Lancement"%self._name)
113 logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
115 # Paramètres de pilotage
116 # ----------------------
117 self.setParameters(Parameters)
119 if self._parameters.has_key("Bounds") and (type(self._parameters["Bounds"]) is type([]) or type(self._parameters["Bounds"]) is type(())) and (len(self._parameters["Bounds"]) > 0):
120 Bounds = self._parameters["Bounds"]
121 logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
125 # Correction pour pallier a un bug de TNC sur le retour du Minimum
126 if self._parameters.has_key("Minimizer") == "TNC":
127 self.setParameterValue("StoreInternalVariables",True)
129 # Opérateur d'observation
130 # -----------------------
131 Hm = HO["Direct"].appliedTo
132 Ha = HO["Adjoint"].appliedInXTo
134 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
135 # ----------------------------------------------------
136 if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
137 HXb = HO["AppliedToX"]["HXb"]
140 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
142 # Calcul de l'innovation
143 # ----------------------
144 if Y.size != HXb.size:
145 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))
146 if max(Y.shape) != max(HXb.shape):
147 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))
150 # Précalcul des inversions de B et R
151 # ----------------------------------
155 # Définition de la fonction-coût
156 # ------------------------------
158 _X = numpy.asmatrix(numpy.ravel( x )).T
160 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
161 Jb = 0.5 * (_X - Xb).T * BI * (_X - Xb)
162 Jo = 0.5 * (Y - _HX).T * RI * (Y - _HX)
163 J = float( Jb ) + float( Jo )
164 if self._parameters["StoreInternalVariables"]:
165 self.StoredVariables["CurrentState"].store( _X.A1 )
166 self.StoredVariables["CostFunctionJb"].store( Jb )
167 self.StoredVariables["CostFunctionJo"].store( Jo )
168 self.StoredVariables["CostFunctionJ" ].store( J )
171 def GradientOfCostFunction(x):
172 _X = numpy.asmatrix(numpy.ravel( x )).T
174 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
175 GradJb = BI * (_X - Xb)
176 GradJo = - Ha( (_X, RI * (Y - _HX)) )
177 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
180 # Point de démarrage de l'optimisation : Xini = Xb
181 # ------------------------------------
182 if type(Xb) is type(numpy.matrix([])):
183 Xini = Xb.A1.tolist()
187 # Minimisation de la fonctionnelle
188 # --------------------------------
189 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
191 if self._parameters["Minimizer"] == "LBFGSB":
192 Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
195 fprime = GradientOfCostFunction,
198 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
199 factr = self._parameters["CostDecrementTolerance"]*1.e14,
200 pgtol = self._parameters["ProjectedGradientTolerance"],
201 iprint = self.__iprint,
203 nfeval = Informations['funcalls']
204 rc = Informations['warnflag']
205 elif self._parameters["Minimizer"] == "TNC":
206 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
209 fprime = GradientOfCostFunction,
212 maxfun = self._parameters["MaximumNumberOfSteps"],
213 pgtol = self._parameters["ProjectedGradientTolerance"],
214 ftol = self._parameters["CostDecrementTolerance"],
215 messages = self.__message,
217 elif self._parameters["Minimizer"] == "CG":
218 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
221 fprime = GradientOfCostFunction,
223 maxiter = self._parameters["MaximumNumberOfSteps"],
224 gtol = self._parameters["GradientNormTolerance"],
228 elif self._parameters["Minimizer"] == "NCG":
229 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
232 fprime = GradientOfCostFunction,
234 maxiter = self._parameters["MaximumNumberOfSteps"],
235 avextol = self._parameters["CostDecrementTolerance"],
239 elif self._parameters["Minimizer"] == "BFGS":
240 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
243 fprime = GradientOfCostFunction,
245 maxiter = self._parameters["MaximumNumberOfSteps"],
246 gtol = self._parameters["GradientNormTolerance"],
251 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
253 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
254 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
256 # Correction pour pallier a un bug de TNC sur le retour du Minimum
257 # ----------------------------------------------------------------
258 if self._parameters["StoreInternalVariables"]:
259 Minimum = self.StoredVariables["CurrentState"][IndexMin]
261 # Obtention de l'analyse
262 # ----------------------
263 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
265 self.StoredVariables["Analysis"].store( Xa.A1 )
267 if "OMA" in self._parameters["StoreSupplementaryCalculations"] or \
268 "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
269 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
272 # Calcul de la covariance d'analyse
273 # ---------------------------------
274 if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
275 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
276 HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
277 HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
278 HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
279 HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
283 _ee = numpy.matrix(numpy.zeros(nb)).T
285 _HtEE = numpy.dot(HtM,_ee)
286 _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
287 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
288 HessienneI = numpy.matrix( HessienneI )
290 if min(A.shape) != max(A.shape):
291 raise ValueError("The %s a posteriori covariance matrix A is of shape %s, despites it has to be a squared matrix. There is an error in the observation operator, please check it."%(self._name,str(A.shape)))
292 if (numpy.diag(A) < 0).any():
293 raise ValueError("The %s a posteriori covariance matrix A has at least one negative value on its diagonal. There is an error in the observation operator, please check it."%(self._name,))
294 if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
296 L = numpy.linalg.cholesky( A )
298 raise ValueError("The %s a posteriori covariance matrix A is not symmetric positive-definite. Please check your a priori covariances and your observation operator."%(self._name,))
299 self.StoredVariables["APosterioriCovariance"].store( A )
301 # Calculs et/ou stockages supplémentaires
302 # ---------------------------------------
303 if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
304 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
305 if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
306 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
307 if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
308 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
309 if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
310 self.StoredVariables["OMB"].store( numpy.ravel(d) )
311 if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
312 TraceR = R.trace(Y.size)
313 self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
314 if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
315 self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
316 if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
317 Qtls = self._parameters["Quantiles"]
318 nech = self._parameters["NumberOfSamplesForQuantiles"]
319 HXa = numpy.matrix(numpy.ravel( HXa )).T
321 for i in range(nech):
322 if self._parameters["SimulationForQuantiles"] == "Linear":
323 dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
324 dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
326 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
327 Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
328 Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
332 YfQ = numpy.hstack((YfQ,Yr))
335 for quantile in Qtls:
336 if not (0. <= quantile <= 1.): continue
337 indice = int(nech * quantile - 1./nech)
338 if YQ is None: YQ = YfQ[:,indice]
339 else: YQ = numpy.hstack((YQ,YfQ[:,indice]))
340 self.StoredVariables["SimulationQuantiles"].store( YQ )
342 logging.debug("%s Nombre d'évaluation(s) de l'opérateur d'observation direct/tangent/adjoint : %i/%i/%i"%(self._name, HO["Direct"].nbcalls()[0],HO["Tangent"].nbcalls()[0],HO["Adjoint"].nbcalls()[0]))
343 logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
344 logging.debug("%s Terminé"%self._name)
348 # ==============================================================================
349 if __name__ == "__main__":
350 print '\n AUTODIAGNOSTIC \n'