1 # -*- coding: utf-8 -*-
3 # Copyright (C) 2008-2024 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, NumericObjects, PlatformInfo
25 mpr = PlatformInfo.PlatformInfo().MachinePrecision()
26 mfp = PlatformInfo.PlatformInfo().MaximumPrecision()
28 # ==============================================================================
29 class ElementaryAlgorithm(BasicObjects.Algorithm):
31 BasicObjects.Algorithm.__init__(self, "LINEARITYTEST")
32 self.defineRequiredParameter(
33 name = "ResiduFormula",
34 default = "CenteredDL",
36 message = "Formule de résidu utilisée",
37 listval = ["CenteredDL", "Taylor", "NominalTaylor", "NominalTaylorRMS"],
39 self.defineRequiredParameter(
40 name = "EpsilonMinimumExponent",
43 message = "Exposant minimal en puissance de 10 pour le multiplicateur d'incrément",
47 self.defineRequiredParameter(
48 name = "InitialDirection",
51 message = "Direction initiale de la dérivée directionnelle autour du point nominal",
53 self.defineRequiredParameter(
54 name = "AmplitudeOfInitialDirection",
57 message = "Amplitude de la direction initiale de la dérivée directionnelle autour du point nominal",
59 self.defineRequiredParameter(
60 name = "AmplitudeOfTangentPerturbation",
63 message = "Amplitude de la perturbation pour le calcul de la forme tangente",
67 self.defineRequiredParameter(
69 typecast = numpy.random.seed,
70 message = "Graine fixée pour le générateur aléatoire",
72 self.defineRequiredParameter(
73 name = "NumberOfPrintedDigits",
76 message = "Nombre de chiffres affichés pour les impressions de réels",
79 self.defineRequiredParameter(
83 message = "Titre du tableau et de la figure",
85 self.defineRequiredParameter(
86 name = "StoreSupplementaryCalculations",
89 message = "Liste de calculs supplémentaires à stocker et/ou effectuer",
93 "SimulatedObservationAtCurrentState",
96 self.requireInputArguments(
97 mandatory= ("Xb", "HO"),
105 "ParallelDerivativesOnly",
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, Xb, Y, U, HO, EM, CM, R, B, Q)
114 return math.sqrt( ((numpy.ravel(V2) - numpy.ravel(V1))**2).sum() / float(numpy.ravel(V1).size) )
116 Hm = HO["Direct"].appliedTo
117 if self._parameters["ResiduFormula"] in ["Taylor", "NominalTaylor", "NominalTaylorRMS"]:
118 Ht = HO["Tangent"].appliedInXTo
120 X0 = numpy.ravel( Xb ).reshape((-1, 1))
123 __p = self._parameters["NumberOfPrintedDigits"]
126 __flech = 3 * "=" + "> "
128 if len(self._parameters["ResultTitle"]) > 0:
129 __rt = str(self._parameters["ResultTitle"])
130 msgs += (__marge + "====" + "=" * len(__rt) + "====\n")
131 msgs += (__marge + " " + __rt + "\n")
132 msgs += (__marge + "====" + "=" * len(__rt) + "====\n")
134 msgs += (__marge + "%s\n"%self._name)
135 msgs += (__marge + "%s\n"%("=" * len(self._name),))
138 msgs += (__marge + "This test allows to analyze the linearity property of some given\n")
139 msgs += (__marge + "simulation operator F, applied to one single vector argument x.\n")
140 msgs += (__marge + "The output shows simple statistics related to its stability for various\n")
141 msgs += (__marge + "increments, around an input checking point X.\n")
143 msgs += (__flech + "Information before launching:\n")
144 msgs += (__marge + "-----------------------------\n")
146 msgs += (__marge + "Characteristics of input vector X, internally converted:\n")
147 msgs += (__marge + " Type...............: %s\n")%type( X0 )
148 msgs += (__marge + " Length of vector...: %i\n")%max(numpy.ravel( X0 ).shape)
149 msgs += (__marge + " Minimum value......: %." + str(__p) + "e\n")%numpy.min( X0 )
150 msgs += (__marge + " Maximum value......: %." + str(__p) + "e\n")%numpy.max( X0 )
151 msgs += (__marge + " Mean of vector.....: %." + str(__p) + "e\n")%numpy.mean( X0, dtype=mfp )
152 msgs += (__marge + " Standard error.....: %." + str(__p) + "e\n")%numpy.std( X0, dtype=mfp )
153 msgs += (__marge + " L2 norm of vector..: %." + str(__p) + "e\n")%numpy.linalg.norm( X0 )
155 msgs += (__marge + "%s\n\n"%("-" * 75,))
156 msgs += (__flech + "Numerical quality indicators:\n")
157 msgs += (__marge + "-----------------------------\n")
159 msgs += (__marge + "Using the \"%s\" formula, one observes the residue R which is the\n"%self._parameters["ResiduFormula"]) # noqa: E501
160 msgs += (__marge + "following ratio or comparison:\n")
163 if self._parameters["ResiduFormula"] == "CenteredDL":
164 msgs += (__marge + " || F(X+Alpha*dX) + F(X-Alpha*dX) - 2*F(X) ||\n")
165 msgs += (__marge + " R(Alpha) = --------------------------------------------\n")
166 msgs += (__marge + " || F(X) ||\n")
168 msgs += (__marge + "If the residue remains always very small compared to 1, the linearity\n")
169 msgs += (__marge + "assumption of F is verified.\n")
171 msgs += (__marge + "If the residue varies a lot, or is of the order of 1 or more, and is\n")
172 msgs += (__marge + "small only under a certain order of Alpha increment, the linearity\n")
173 msgs += (__marge + "assumption of F is not verified.\n")
175 msgs += (__marge + "If the residue decreases and if the decay is in Alpha**2 according to\n")
176 msgs += (__marge + "Alpha, it means that the gradient is well calculated up to the stopping\n")
177 msgs += (__marge + "precision of the quadratic decay.\n")
179 __entete = u" i Alpha ||X|| ||F(X)|| | R(Alpha) log10( R )"
181 if self._parameters["ResiduFormula"] == "Taylor":
182 msgs += (__marge + " || F(X+Alpha*dX) - F(X) - Alpha * GradientF_X(dX) ||\n")
183 msgs += (__marge + " R(Alpha) = ----------------------------------------------------\n")
184 msgs += (__marge + " || F(X) ||\n")
186 msgs += (__marge + "If the residue remains always very small compared to 1, the linearity\n")
187 msgs += (__marge + "assumption of F is verified.\n")
189 msgs += (__marge + "If the residue varies a lot, or is of the order of 1 or more, and is\n")
190 msgs += (__marge + "small only under a certain order of Alpha increment, the linearity\n")
191 msgs += (__marge + "assumption of F is not verified.\n")
193 msgs += (__marge + "If the residue decreases and if the decay is in Alpha**2 according to\n")
194 msgs += (__marge + "Alpha, it means that the gradient is well calculated up to the stopping\n")
195 msgs += (__marge + "precision of the quadratic decay.\n")
197 __entete = u" i Alpha ||X|| ||F(X)|| | R(Alpha) log10( R )"
199 if self._parameters["ResiduFormula"] == "NominalTaylor":
200 msgs += (__marge + " R(Alpha) = max(\n")
201 msgs += (__marge + " || F(X+Alpha*dX) - Alpha * F(dX) || / || F(X) ||,\n")
202 msgs += (__marge + " || F(X-Alpha*dX) + Alpha * F(dX) || / || F(X) ||,\n")
203 msgs += (__marge + " )\n")
205 msgs += (__marge + "If the residue remains always equal to 1 within 2 or 3 percent (i.e.\n")
206 msgs += (__marge + "|R-1| remains equal to 2 or 3 percent), then the linearity assumption of\n")
207 msgs += (__marge + "F is verified.\n")
209 msgs += (__marge + "If the residue is equal to 1 over only a part of the range of variation\n")
210 msgs += (__marge + "of the Alpha increment, it is over this part that the linearity assumption\n")
211 msgs += (__marge + "of F is verified.\n")
213 __entete = u" i Alpha ||X|| ||F(X)|| | R(Alpha) |R-1| in %"
215 if self._parameters["ResiduFormula"] == "NominalTaylorRMS":
216 msgs += (__marge + " R(Alpha) = max(\n")
217 msgs += (__marge + " RMS( F(X), F(X+Alpha*dX) - Alpha * F(dX) ) / || F(X) ||,\n")
218 msgs += (__marge + " RMS( F(X), F(X-Alpha*dX) + Alpha * F(dX) ) / || F(X) ||,\n")
219 msgs += (__marge + " )\n")
221 msgs += (__marge + "If the residue remains always equal to 0 within 1 or 2 percent then the\n")
222 msgs += (__marge + "linearity assumption of F is verified.\n")
224 msgs += (__marge + "If the residue is equal to 0 over only a part of the range of variation\n")
225 msgs += (__marge + "of the Alpha increment, it is over this part that the linearity assumption\n")
226 msgs += (__marge + "of F is verified.\n")
228 __entete = u" i Alpha ||X|| ||F(X)|| | R(Alpha) |R| in %"
231 msgs += (__marge + "We take dX0 = Normal(0,X) and dX = Alpha*dX0. F is the calculation code.\n")
232 if (self._parameters["ResiduFormula"] == "Taylor") and ("DifferentialIncrement" in HO and HO["DifferentialIncrement"] is not None): # noqa: E501
234 msgs += (__marge + "Reminder: gradient operator is obtained internally by finite differences,\n")
235 msgs += (__marge + "with a differential increment of value %.2e.\n"%HO["DifferentialIncrement"])
237 msgs += (__marge + "(Remark: numbers that are (about) under %.0e represent 0 to machine precision)\n"%mpr)
240 Perturbations = [ 10**i for i in range(self._parameters["EpsilonMinimumExponent"], 1) ]
241 Perturbations.reverse()
243 FX = numpy.ravel( Hm( X0 ) ).reshape((-1, 1))
244 NormeX = numpy.linalg.norm( X0 )
245 NormeFX = numpy.linalg.norm( FX )
248 if self._toStore("CurrentState"):
249 self.StoredVariables["CurrentState"].store( X0 )
250 if self._toStore("SimulatedObservationAtCurrentState"):
251 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX )
253 dX0 = NumericObjects.SetInitialDirection(
254 self._parameters["InitialDirection"],
255 self._parameters["AmplitudeOfInitialDirection"],
259 if self._parameters["ResiduFormula"] == "Taylor":
260 dX1 = float(self._parameters["AmplitudeOfTangentPerturbation"]) * dX0
261 GradFxdX = Ht( (X0, dX1) )
262 GradFxdX = numpy.ravel( GradFxdX ).reshape((-1, 1))
263 GradFxdX = float(1. / self._parameters["AmplitudeOfTangentPerturbation"]) * GradFxdX
265 # Boucle sur les perturbations
266 # ----------------------------
267 __nbtirets = len(__entete) + 2
269 msgs += "\n" + __marge + "-" * __nbtirets
270 msgs += "\n" + __marge + __entete
271 msgs += "\n" + __marge + "-" * __nbtirets
274 for ip, amplitude in enumerate(Perturbations):
275 dX = amplitude * dX0.reshape((-1, 1))
277 if self._parameters["ResiduFormula"] == "CenteredDL":
278 if self._toStore("CurrentState"):
279 self.StoredVariables["CurrentState"].store( X0 + dX )
280 self.StoredVariables["CurrentState"].store( X0 - dX )
282 FX_plus_dX = numpy.ravel( Hm( X0 + dX ) ).reshape((-1, 1))
283 FX_moins_dX = numpy.ravel( Hm( X0 - dX ) ).reshape((-1, 1))
285 if self._toStore("SimulatedObservationAtCurrentState"):
286 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX_plus_dX )
287 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX_moins_dX )
289 Residu = numpy.linalg.norm( FX_plus_dX + FX_moins_dX - 2 * FX ) / NormeFX
291 self.StoredVariables["Residu"].store( Residu )
292 ttsep = " %2i %5.0e %9.3e %9.3e | %9.3e %4.0f\n"%(ip, amplitude, NormeX, NormeFX, Residu, math.log10(max(1.e-99, Residu))) # noqa: E501
293 msgs += __marge + ttsep
295 if self._parameters["ResiduFormula"] == "Taylor":
296 if self._toStore("CurrentState"):
297 self.StoredVariables["CurrentState"].store( X0 + dX )
299 FX_plus_dX = numpy.ravel( Hm( X0 + dX ) ).reshape((-1, 1))
301 if self._toStore("SimulatedObservationAtCurrentState"):
302 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX_plus_dX )
304 Residu = numpy.linalg.norm( FX_plus_dX - FX - amplitude * GradFxdX ) / NormeFX
306 self.StoredVariables["Residu"].store( Residu )
307 ttsep = " %2i %5.0e %9.3e %9.3e | %9.3e %4.0f\n"%(ip, amplitude, NormeX, NormeFX, Residu, math.log10(max(1.e-99, Residu))) # noqa: E501
308 msgs += __marge + ttsep
310 if self._parameters["ResiduFormula"] == "NominalTaylor":
311 if self._toStore("CurrentState"):
312 self.StoredVariables["CurrentState"].store( X0 + dX )
313 self.StoredVariables["CurrentState"].store( X0 - dX )
314 self.StoredVariables["CurrentState"].store( dX )
316 FX_plus_dX = numpy.ravel( Hm( X0 + dX ) ).reshape((-1, 1))
317 FX_moins_dX = numpy.ravel( Hm( X0 - dX ) ).reshape((-1, 1))
318 FdX = numpy.ravel( Hm( dX ) ).reshape((-1, 1))
320 if self._toStore("SimulatedObservationAtCurrentState"):
321 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX_plus_dX )
322 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX_moins_dX )
323 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FdX )
326 numpy.linalg.norm( FX_plus_dX - amplitude * FdX ) / NormeFX,
327 numpy.linalg.norm( FX_moins_dX + amplitude * FdX ) / NormeFX,
330 self.StoredVariables["Residu"].store( Residu )
331 ttsep = " %2i %5.0e %9.3e %9.3e | %9.3e %5i %s\n"%(ip, amplitude, NormeX, NormeFX, Residu, 100. * abs(Residu - 1.), "%") # noqa: E501
332 msgs += __marge + ttsep
334 if self._parameters["ResiduFormula"] == "NominalTaylorRMS":
335 if self._toStore("CurrentState"):
336 self.StoredVariables["CurrentState"].store( X0 + dX )
337 self.StoredVariables["CurrentState"].store( X0 - dX )
338 self.StoredVariables["CurrentState"].store( dX )
340 FX_plus_dX = numpy.ravel( Hm( X0 + dX ) ).reshape((-1, 1))
341 FX_moins_dX = numpy.ravel( Hm( X0 - dX ) ).reshape((-1, 1))
342 FdX = numpy.ravel( Hm( dX ) ).reshape((-1, 1))
344 if self._toStore("SimulatedObservationAtCurrentState"):
345 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX_plus_dX )
346 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FX_moins_dX )
347 self.StoredVariables["SimulatedObservationAtCurrentState"].store( FdX )
350 RMS( FX, FX_plus_dX - amplitude * FdX ) / NormeFX,
351 RMS( FX, FX_moins_dX + amplitude * FdX ) / NormeFX,
354 self.StoredVariables["Residu"].store( Residu )
355 ttsep = " %2i %5.0e %9.3e %9.3e | %9.3e %5i %s\n"%(ip, amplitude, NormeX, NormeFX, Residu, 100. * Residu, "%") # noqa: E501
356 msgs += __marge + ttsep
358 msgs += (__marge + "-" * __nbtirets + "\n\n")
359 msgs += (__marge + "End of the \"%s\" verification by the \"%s\" formula.\n\n"%(self._name, self._parameters["ResiduFormula"])) # noqa: E501
360 msgs += (__marge + "%s\n"%("-" * 75,))
363 self._post_run(HO, EM)
366 # ==============================================================================
367 if __name__ == "__main__":
368 print("\n AUTODIAGNOSTIC\n")