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
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", "Innovation", "SigmaObs2", "MahalanobisConsistency", "SimulationQuantiles"]
77 self.defineRequiredParameter(
81 message = "Liste des valeurs de quantiles",
83 self.defineRequiredParameter(
85 typecast = numpy.random.seed,
86 message = "Graine fixée pour le générateur aléatoire",
88 self.defineRequiredParameter(
89 name = "NumberOfSamplesForQuantiles",
92 message = "Nombre d'échantillons simulés pour le calcul des quantiles",
95 self.defineRequiredParameter(
96 name = "SimulationForQuantiles",
99 message = "Type de simulation pour l'estimation des quantiles",
100 listval = ["Linear", "NonLinear"]
103 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 # Paramètres de pilotage
113 # ----------------------
114 self.setParameters(Parameters)
116 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):
117 Bounds = self._parameters["Bounds"]
118 logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
122 # Correction pour pallier a un bug de TNC sur le retour du Minimum
123 if self._parameters.has_key("Minimizer") == "TNC":
124 self.setParameterValue("StoreInternalVariables",True)
126 # Opérateur d'observation
127 # -----------------------
128 Hm = HO["Direct"].appliedTo
129 Ha = HO["Adjoint"].appliedInXTo
131 # Utilisation éventuelle d'un vecteur H(Xb) précalculé
132 # ----------------------------------------------------
133 if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
134 HXb = HO["AppliedToX"]["HXb"]
137 HXb = numpy.asmatrix(numpy.ravel( HXb )).T
139 # Calcul de l'innovation
140 # ----------------------
141 if Y.size != HXb.size:
142 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))
143 if max(Y.shape) != max(HXb.shape):
144 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))
147 # Précalcul des inversions de B et R
148 # ----------------------------------
152 # Définition de la fonction-coût
153 # ------------------------------
155 _X = numpy.asmatrix(numpy.ravel( x )).T
157 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
158 Jb = 0.5 * (_X - Xb).T * BI * (_X - Xb)
159 Jo = 0.5 * (Y - _HX).T * RI * (Y - _HX)
160 J = float( Jb ) + float( Jo )
161 if self._parameters["StoreInternalVariables"]:
162 self.StoredVariables["CurrentState"].store( _X )
163 self.StoredVariables["CostFunctionJb"].store( Jb )
164 self.StoredVariables["CostFunctionJo"].store( Jo )
165 self.StoredVariables["CostFunctionJ" ].store( J )
168 def GradientOfCostFunction(x):
169 _X = numpy.asmatrix(numpy.ravel( x )).T
171 _HX = numpy.asmatrix(numpy.ravel( _HX )).T
172 GradJb = BI * (_X - Xb)
173 GradJo = - Ha( (_X, RI * (Y - _HX)) )
174 GradJ = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
177 # Point de démarrage de l'optimisation : Xini = Xb
178 # ------------------------------------
179 if type(Xb) is type(numpy.matrix([])):
180 Xini = Xb.A1.tolist()
184 # Minimisation de la fonctionnelle
185 # --------------------------------
186 nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
188 if self._parameters["Minimizer"] == "LBFGSB":
189 Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
192 fprime = GradientOfCostFunction,
195 maxfun = self._parameters["MaximumNumberOfSteps"]-1,
196 factr = self._parameters["CostDecrementTolerance"]*1.e14,
197 pgtol = self._parameters["ProjectedGradientTolerance"],
198 iprint = self.__iprint,
200 nfeval = Informations['funcalls']
201 rc = Informations['warnflag']
202 elif self._parameters["Minimizer"] == "TNC":
203 Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
206 fprime = GradientOfCostFunction,
209 maxfun = self._parameters["MaximumNumberOfSteps"],
210 pgtol = self._parameters["ProjectedGradientTolerance"],
211 ftol = self._parameters["CostDecrementTolerance"],
212 messages = self.__message,
214 elif self._parameters["Minimizer"] == "CG":
215 Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
218 fprime = GradientOfCostFunction,
220 maxiter = self._parameters["MaximumNumberOfSteps"],
221 gtol = self._parameters["GradientNormTolerance"],
225 elif self._parameters["Minimizer"] == "NCG":
226 Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
229 fprime = GradientOfCostFunction,
231 maxiter = self._parameters["MaximumNumberOfSteps"],
232 avextol = self._parameters["CostDecrementTolerance"],
236 elif self._parameters["Minimizer"] == "BFGS":
237 Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
240 fprime = GradientOfCostFunction,
242 maxiter = self._parameters["MaximumNumberOfSteps"],
243 gtol = self._parameters["GradientNormTolerance"],
248 raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
250 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
251 MinJ = self.StoredVariables["CostFunctionJ"][IndexMin]
253 # Correction pour pallier a un bug de TNC sur le retour du Minimum
254 # ----------------------------------------------------------------
255 if self._parameters["StoreInternalVariables"]:
256 Minimum = self.StoredVariables["CurrentState"][IndexMin]
258 # Obtention de l'analyse
259 # ----------------------
260 Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
262 self.StoredVariables["Analysis"].store( Xa.A1 )
264 if "OMA" in self._parameters["StoreSupplementaryCalculations"] or \
265 "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"] or \
266 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
269 # Calcul de la covariance d'analyse
270 # ---------------------------------
271 if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"] or \
272 "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
273 HtM = HO["Tangent"].asMatrix(ValueForMethodForm = Xa)
274 HtM = HtM.reshape(Y.size,Xa.size) # ADAO & check shape
275 HaM = HO["Adjoint"].asMatrix(ValueForMethodForm = Xa)
276 HaM = HaM.reshape(Xa.size,Y.size) # ADAO & check shape
280 _ee = numpy.matrix(numpy.zeros(nb)).T
282 _HtEE = numpy.dot(HtM,_ee)
283 _HtEE = numpy.asmatrix(numpy.ravel( _HtEE )).T
284 HessienneI.append( numpy.ravel( BI*_ee + HaM * (RI * _HtEE) ) )
285 HessienneI = numpy.matrix( HessienneI )
287 if min(A.shape) != max(A.shape):
288 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)))
289 if (numpy.diag(A) < 0).any():
290 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,))
291 if logging.getLogger().level < logging.WARNING: # La verification n'a lieu qu'en debug
293 L = numpy.linalg.cholesky( A )
295 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,))
296 self.StoredVariables["APosterioriCovariance"].store( A )
298 # Calculs et/ou stockages supplémentaires
299 # ---------------------------------------
300 if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
301 self.StoredVariables["Innovation"].store( numpy.ravel(d) )
302 if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
303 self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
304 if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
305 self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
306 if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
307 self.StoredVariables["OMB"].store( numpy.ravel(d) )
308 if "SigmaObs2" in self._parameters["StoreSupplementaryCalculations"]:
309 TraceR = R.trace(Y.size)
310 self.StoredVariables["SigmaObs2"].store( float( (d.T * (numpy.asmatrix(numpy.ravel(Y)).T-numpy.asmatrix(numpy.ravel(HXa)).T)) ) / TraceR )
311 if "MahalanobisConsistency" in self._parameters["StoreSupplementaryCalculations"]:
312 self.StoredVariables["MahalanobisConsistency"].store( float( 2.*MinJ/d.size ) )
313 if "SimulationQuantiles" in self._parameters["StoreSupplementaryCalculations"]:
314 Qtls = self._parameters["Quantiles"]
315 nech = self._parameters["NumberOfSamplesForQuantiles"]
316 HXa = numpy.matrix(numpy.ravel( HXa )).T
318 for i in range(nech):
319 if self._parameters["SimulationForQuantiles"] == "Linear":
320 dXr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A) - Xa.A1).T
321 dYr = numpy.matrix(numpy.ravel( HtM * dXr )).T
323 elif self._parameters["SimulationForQuantiles"] == "NonLinear":
324 Xr = numpy.matrix(numpy.random.multivariate_normal(Xa.A1,A)).T
325 Yr = numpy.matrix(numpy.ravel( Hm( Xr ) )).T
329 YfQ = numpy.hstack((YfQ,Yr))
332 for quantile in Qtls:
333 if not (0. <= quantile <= 1.): continue
334 indice = int(nech * quantile - 1./nech)
335 if YQ is None: YQ = YfQ[:,indice]
336 else: YQ = numpy.hstack((YQ,YfQ[:,indice]))
337 self.StoredVariables["SimulationQuantiles"].store( YQ )
342 # ==============================================================================
343 if __name__ == "__main__":
344 print '\n AUTODIAGNOSTIC \n'