1 #-*-coding:iso-8859-1-*-
3 # Copyright (C) 2008-2017 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 = ["APosterioriCorrelations", "APosterioriCovariance", "APosterioriStandardDeviations", "APosterioriVariances", "BMA", "OMA", "OMB", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "CurrentState", "CurrentOptimum", "IndexOfOptimum", "Innovation", "InnovationAtCurrentState", "CostFunctionJAtCurrentOptimum", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles", "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum", "SimulatedObservationAtCurrentOptimum"]
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"]
104 self.defineRequiredParameter( # Pas de type
106 message = "Liste des valeurs de bornes",
109 def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
110 self._pre_run(Parameters)
112 # Correction pour pallier a un bug de TNC sur le retour du Minimum
113 if "Minimizer" in self._parameters and self._parameters["Minimizer"] == "TNC":
114 self.setParameterValue("StoreInternalVariables",True)
118 Hm = HO["Direct"].appliedTo
119 Ha = HO["Adjoint"].appliedInXTo
121 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
122 # ----------------------------------------------------
123 if HO["AppliedToX"] is not None and "HXb" in HO["AppliedToX"]:
124 HXb = Hm( Xb, HO["AppliedToX"]["HXb"])
127 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
128 if Y.size != HXb.size:
129 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))
130 if max(Y.shape) != max(HXb.shape):
131 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))
133 # Précalcul des inversions de B et R
134 # ----------------------------------
138 # Définition de la fonction-coût
139 # ------------------------------
141 _X = numpy.asmatrix(numpy.ravel( x )).T
142 if self._parameters["StoreInternalVariables"] or \
143 "CurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
144 "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
145 self.StoredVariables["CurrentState"].store( _X )
147 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
148 _Innovation = Y - _HX
149 if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"] or \
150 "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
151 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
152 if "InnovationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
153 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
155 Jb = float( 0.5 * (_X - Xb).T * BI * (_X - Xb) )
156 Jo = float( 0.5 * _Innovation.T * RI * _Innovation )
159 self.StoredVariables["CostFunctionJb"].store( Jb )
160 self.StoredVariables["CostFunctionJo"].store( Jo )
161 self.StoredVariables["CostFunctionJ" ].store( J )
162 if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
163 "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
164 "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"] or \
165 "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
166 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
167 if "IndexOfOptimum" in self._parameters["StoreSupplementaryCalculations"]:
168 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
169 if "CurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
170 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
171 if "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
172 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
173 if "CostFunctionJAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
174 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
175 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
176 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
179 def GradientOfCostFunction(x):
180 _X = numpy.asmatrix(numpy.ravel( x )).T
182 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
183 GradJb = BI * (_X - Xb)
184 GradJo = - Ha( (_X, RI * (Y - _HX)) )
185 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
188 # Point de démarrage de l'optimisation : Xini = Xb
189 # ------------------------------------
190 Xini = numpy.ravel(Xb)
192 # Minimisation de la fonctionnelle
193 # --------------------------------
194 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
196 if self._parameters["Minimizer"] == "LBFGSB":
197 Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
200 fprime = GradientOfCostFunction,
202 bounds = self._parameters["Bounds"],
203 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
204 factr = self._parameters["CostDecrementTolerance"]*1.e14,
205 pgtol = self._parameters["ProjectedGradientTolerance"],
206 iprint = self._parameters["optiprint"],
208 nfeval = Informations['funcalls']
209 rc = Informations['warnflag']
210 elif self._parameters["Minimizer"] == "TNC":
211 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
214 fprime = GradientOfCostFunction,
216 bounds = self._parameters["Bounds"],
217 maxfun = self._parameters["MaximumNumberOfSteps"],
218 pgtol = self._parameters["ProjectedGradientTolerance"],
219 ftol = self._parameters["CostDecrementTolerance"],
220 messages = self._parameters["optmessages"],
222 elif self._parameters["Minimizer"] == "CG":
223 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
226 fprime = GradientOfCostFunction,
228 maxiter = self._parameters["MaximumNumberOfSteps"],
229 gtol = self._parameters["GradientNormTolerance"],
230 disp = self._parameters["optdisp"],
233 elif self._parameters["Minimizer"] == "NCG":
234 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
237 fprime = GradientOfCostFunction,
239 maxiter = self._parameters["MaximumNumberOfSteps"],
240 avextol = self._parameters["CostDecrementTolerance"],
241 disp = self._parameters["optdisp"],
244 elif self._parameters["Minimizer"] == "BFGS":
245 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
248 fprime = GradientOfCostFunction,
250 maxiter = self._parameters["MaximumNumberOfSteps"],
251 gtol = self._parameters["GradientNormTolerance"],
252 disp = self._parameters["optdisp"],
256 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
258 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
259 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
261 # Correction pour pallier a un bug de TNC sur le retour du Minimum
262 # ----------------------------------------------------------------
263 if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
264 Minimum = self.StoredVariables["CurrentState"][IndexMin]
266 # Obtention de l'analyse
267 # ----------------------
268 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
270 self.StoredVariables["Analysis"].store( Xa.A1 )
272 if "OMA" in self._parameters["StoreSupplementaryCalculations"] or \
273 "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
274 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"] or \
275 "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
276 if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
277 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
278 elif "SimulatedObservationAtCurrentOptimum" in self._parameters["StoreSupplementaryCalculations"]:
279 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
283 # Calcul de la covariance d'analyse
284 # ---------------------------------
285 if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
286 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
287 HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
288 HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
289 HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
290 HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
294 _ee = numpy.matrix(numpy.zeros(nb)).T
296 _HtEE = numpy.dot(HtM,_ee)
297 _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
298 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
299 HessienneI = numpy.matrix( HessienneI )
301 if min(A.shape) != max(A.shape):
302 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)))
303 if (numpy.diag(A) < 0).any():
304 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,))
305 if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
307 L = numpy.linalg.cholesky( A )
309 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,))
310 self.StoredVariables["APosterioriCovariance"].store( A )
312 # Calculs et/ou stockages supplémentaires
313 # ---------------------------------------
314 if "Innovation" in self._parameters["StoreSupplementaryCalculations"] or \
315 "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
316 "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"] or \
317 "OMB" in self._parameters["StoreSupplementaryCalculations"]:
319 if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
320 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
321 if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
322 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
323 if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
324 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
325 if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
326 self.StoredVariables["OMB"].store( numpy.ravel(d) )
327 if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
328 TraceR = R.trace(Y.size)
329 self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
330 if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
331 self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
332 if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
333 Qtls = map(float, self._parameters["Quantiles"])
334 nech = self._parameters["NumberOfSamplesForQuantiles"]
335 HXa = numpy.matrix(numpy.ravel( HXa )).T
337 for i in range(nech):
338 if self._parameters["SimulationForQuantiles"] == "Linear":
339 dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
340 dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
342 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
343 Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
344 Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
348 YfQ = numpy.hstack((YfQ,Yr))
351 for quantile in Qtls:
352 if not (0. <= quantile <= 1.): continue
353 indice = int(nech * quantile - 1./nech)
354 if YQ is None: YQ = YfQ[:,indice]
355 else: YQ = numpy.hstack((YQ,YfQ[:,indice]))
356 self.StoredVariables["SimulationQuantiles"].store( YQ )
357 if "SimulatedObservationAtBackground" in self._parameters["StoreSupplementaryCalculations"]:
358 self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(HXb) )
359 if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
360 self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
365 # ==============================================================================
366 if __name__ == "__main__":
367 print('\n AUTODIAGNOSTIC \n')