1 #-*-coding:iso-8859-1-*-
3 # Copyright (C) 2008-2015 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, "3DVAR")
31 self.defineRequiredParameter(
35 message = "Minimiseur utilisé",
36 listval = ["LBFGSB","TNC", "CG", "NCG", "BFGS"],
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 cout lors de l'arrêt",
51 self.defineRequiredParameter(
52 name = "ProjectedGradientTolerance",
55 message = "Maximum des composantes du gradient projeté lors de l'arrêt",
58 self.defineRequiredParameter(
59 name = "GradientNormTolerance",
62 message = "Maximum des composantes du gradient lors de l'arrêt",
64 self.defineRequiredParameter(
65 name = "StoreInternalVariables",
68 message = "Stockage des variables internes ou intermédiaires du calcul",
70 self.defineRequiredParameter(
71 name = "StoreSupplementaryCalculations",
74 message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
75 listval = ["APosterioriCovariance", "BMA", "OMA", "OMB", "CurrentState", "CostFunctionJ", "Innovation", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles", "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"]
77 self.defineRequiredParameter(
81 message = "Liste des valeurs de quantiles",
85 self.defineRequiredParameter(
87 typecast = numpy.random.seed,
88 message = "Graine fixée pour le générateur aléatoire",
90 self.defineRequiredParameter(
91 name = "NumberOfSamplesForQuantiles",
94 message = "Nombre d'échantillons simulés pour le calcul des quantiles",
97 self.defineRequiredParameter(
98 name = "SimulationForQuantiles",
101 message = "Type de simulation pour l'estimation des quantiles",
102 listval = ["Linear", "NonLinear"]
105 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
107 if logging.getLogger().level < logging.WARNING:
108 self.__iprint, self.__disp = 1, 1
109 self.__message = scipy.optimize.tnc.MSG_ALL
111 self.__iprint, self.__disp = -1, 0
112 self.__message = scipy.optimize.tnc.MSG_NONE
114 # Paramètres de pilotage
115 # ----------------------
116 self.setParameters(Parameters)
118 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):
119 Bounds = self._parameters["Bounds"]
120 logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
124 # Correction pour pallier a un bug de TNC sur le retour du Minimum
125 if self._parameters.has_key("Minimizer") == "TNC":
126 self.setParameterValue("StoreInternalVariables",True)
130 Hm = HO["Direct"].appliedTo
131 Ha = HO["Adjoint"].appliedInXTo
133 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
134 # ----------------------------------------------------
135 if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
136 HXb = HO["AppliedToX"]["HXb"]
139 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
141 # Calcul de l'innovation
142 # ----------------------
143 if Y.size != HXb.size:
144 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))
145 if max(Y.shape) != max(HXb.shape):
146 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))
149 # Précalcul des inversions de B et R
150 # ----------------------------------
154 # Définition de la fonction-coût
155 # ------------------------------
157 _X = numpy.asmatrix(numpy.ravel( x )).T
159 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
160 Jb = 0.5 * (_X - Xb).T * BI * (_X - Xb)
161 Jo = 0.5 * (Y - _HX).T * RI * (Y - _HX)
162 J = float( Jb ) + float( Jo )
163 if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
164 self.StoredVariables["CurrentState"].store( _X )
165 if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
166 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
167 self.StoredVariables["CostFunctionJb"].store( Jb )
168 self.StoredVariables["CostFunctionJo"].store( Jo )
169 self.StoredVariables["CostFunctionJ" ].store( J )
172 def GradientOfCostFunction(x):
173 _X = numpy.asmatrix(numpy.ravel( x )).T
175 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
176 GradJb = BI * (_X - Xb)
177 GradJo = - Ha( (_X, RI * (Y - _HX)) )
178 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
181 # Point de démarrage de l'optimisation : Xini = Xb
182 # ------------------------------------
183 if type(Xb) is type(numpy.matrix([])):
184 Xini = Xb.A1.tolist()
188 # Minimisation de la fonctionnelle
189 # --------------------------------
190 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
192 if self._parameters["Minimizer"] == "LBFGSB":
193 Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
196 fprime = GradientOfCostFunction,
199 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
200 factr = self._parameters["CostDecrementTolerance"]*1.e14,
201 pgtol = self._parameters["ProjectedGradientTolerance"],
202 iprint = self.__iprint,
204 nfeval = Informations['funcalls']
205 rc = Informations['warnflag']
206 elif self._parameters["Minimizer"] == "TNC":
207 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
210 fprime = GradientOfCostFunction,
213 maxfun = self._parameters["MaximumNumberOfSteps"],
214 pgtol = self._parameters["ProjectedGradientTolerance"],
215 ftol = self._parameters["CostDecrementTolerance"],
216 messages = self.__message,
218 elif self._parameters["Minimizer"] == "CG":
219 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
222 fprime = GradientOfCostFunction,
224 maxiter = self._parameters["MaximumNumberOfSteps"],
225 gtol = self._parameters["GradientNormTolerance"],
229 elif self._parameters["Minimizer"] == "NCG":
230 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
233 fprime = GradientOfCostFunction,
235 maxiter = self._parameters["MaximumNumberOfSteps"],
236 avextol = self._parameters["CostDecrementTolerance"],
240 elif self._parameters["Minimizer"] == "BFGS":
241 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
244 fprime = GradientOfCostFunction,
246 maxiter = self._parameters["MaximumNumberOfSteps"],
247 gtol = self._parameters["GradientNormTolerance"],
252 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
254 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
255 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
257 # Correction pour pallier a un bug de TNC sur le retour du Minimum
258 # ----------------------------------------------------------------
259 if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
260 Minimum = self.StoredVariables["CurrentState"][IndexMin]
262 # Obtention de l'analyse
263 # ----------------------
264 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
266 self.StoredVariables["Analysis"].store( Xa.A1 )
268 if "OMA" in self._parameters["StoreSupplementaryCalculations"] or \
269 "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
270 "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
271 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
274 # Calcul de la covariance d'analyse
275 # ---------------------------------
276 if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
277 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
278 HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
279 HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
280 HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
281 HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
285 _ee = numpy.matrix(numpy.zeros(nb)).T
287 _HtEE = numpy.dot(HtM,_ee)
288 _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
289 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
290 HessienneI = numpy.matrix( HessienneI )
292 if min(A.shape) != max(A.shape):
293 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)))
294 if (numpy.diag(A) < 0).any():
295 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,))
296 if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
298 L = numpy.linalg.cholesky( A )
300 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,))
301 self.StoredVariables["APosterioriCovariance"].store( A )
303 # Calculs et/ou stockages supplémentaires
304 # ---------------------------------------
305 if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
306 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
307 if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
308 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
309 if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
310 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
311 if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
312 self.StoredVariables["OMB"].store( numpy.ravel(d) )
313 if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
314 TraceR = R.trace(Y.size)
315 self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
316 if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
317 self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
318 if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
319 Qtls = self._parameters["Quantiles"]
320 nech = self._parameters["NumberOfSamplesForQuantiles"]
321 HXa = numpy.matrix(numpy.ravel( HXa )).T
323 for i in range(nech):
324 if self._parameters["SimulationForQuantiles"] == "Linear":
325 dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
326 dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
328 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
329 Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
330 Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
334 YfQ = numpy.hstack((YfQ,Yr))
337 for quantile in Qtls:
338 if not (0. <= quantile <= 1.): continue
339 indice = int(nech * quantile - 1./nech)
340 if YQ is None: YQ = YfQ[:,indice]
341 else: YQ = numpy.hstack((YQ,YfQ[:,indice]))
342 self.StoredVariables["SimulationQuantiles"].store( YQ )
343 if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
344 self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
345 if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
346 self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
351 # ==============================================================================
352 if __name__ == "__main__":
353 print '\n AUTODIAGNOSTIC \n'