src/daComposant/daAlgorithms/UnscentedKalmanFilter.py

   1 #-*-coding:iso-8859-1-*-
   2 #
   3 #  Copyright (C) 2008-2014 EDF R&D
   4 #
   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.
   9 #
  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.
  14 #
  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
  18 #
  19 #  See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  20 #
  21 #  Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  22
  23 import logging
  24 from daCore import BasicObjects, PlatformInfo
  25 m = PlatformInfo.SystemUsage()
  26 import numpy, math
  27
  28 # ==============================================================================
  29 class ElementaryAlgorithm(BasicObjects.Algorithm):
  30     def __init__(self):
  31         BasicObjects.Algorithm.__init__(self, "UNSCENTEDKALMANFILTER")
  32         self.defineRequiredParameter(
  33             name     = "ConstrainedBy",
  34             default  = "EstimateProjection",
  35             typecast = str,
  36             message  = "Prise en compte des contraintes",
  37             listval  = ["EstimateProjection"],
  38             )
  39         self.defineRequiredParameter(
  40             name     = "EstimationOf",
  41             default  = "State",
  42             typecast = str,
  43             message  = "Estimation d'etat ou de parametres",
  44             listval  = ["State", "Parameters"],
  45             )
  46         self.defineRequiredParameter(
  47             name     = "Alpha",
  48             default  = 1.,
  49             typecast = float,
  50             message  = "",
  51             minval   = 1.e-4,
  52             maxval   = 1.,
  53             )
  54         self.defineRequiredParameter(
  55             name     = "Beta",
  56             default  = 2,
  57             typecast = float,
  58             message  = "",
  59             )
  60         self.defineRequiredParameter(
  61             name     = "Kappa",
  62             default  = 0,
  63             typecast = int,
  64             message  = "",
  65             maxval   = 2,
  66             )
  67         self.defineRequiredParameter(
  68             name     = "Reconditioner",
  69             default  = 1.,
  70             typecast = float,
  71             message  = "",
  72             minval   = 1.e-3,
  73             maxval   = 1.e+1,
  74             )
  75         self.defineRequiredParameter(
  76             name     = "StoreInternalVariables",
  77             default  = False,
  78             typecast = bool,
  79             message  = "Stockage des variables internes ou intermédiaires du calcul",
  80             )
  81         self.defineRequiredParameter(
  82             name     = "StoreSupplementaryCalculations",
  83             default  = [],
  84             typecast = tuple,
  85             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  86             listval  = ["APosterioriCovariance", "BMA", "Innovation"]
  87             )
  88
  89     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  90         logging.debug("%s Lancement"%self._name)
  91         logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
  92         #
  93         # Paramètres de pilotage
  94         # ----------------------
  95         self.setParameters(Parameters)
  96         #
  97         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):
  98             Bounds = self._parameters["Bounds"]
  99             logging.debug("%s Prise en compte des bornes effectuee"%(self._name,))
 100         else:
 101             Bounds = None
 102         if self._parameters["EstimationOf"] == "Parameters":
 103             self._parameters["StoreInternalVariables"] = True
 104         #
 105         L     = Xb.size
 106         Alpha = self._parameters["Alpha"]
 107         Beta  = self._parameters["Beta"]
 108         if self._parameters["Kappa"] == 0:
 109             if self._parameters["EstimationOf"] == "State":
 110                 Kappa = 0
 111             elif self._parameters["EstimationOf"] == "Parameters":
 112                 Kappa = 3 - L
 113         else:
 114             Kappa = self._parameters["Kappa"]
 115         Lambda = float( Alpha**2 ) * ( L + Kappa ) - L
 116         Gamma  = math.sqrt( L + Lambda )
 117         #
 118         Ww = []
 119         Ww.append( 0. )
 120         for i in range(2*L):
 121             Ww.append( 1. / (2.*(L + Lambda)) )
 122         #
 123         Wm = numpy.array( Ww )
 124         Wm[0] = Lambda / (L + Lambda)
 125         Wc = numpy.array( Ww )
 126         Wc[0] = Lambda / (L + Lambda) + (1. - Alpha**2 + Beta)
 127         #
 128         # Opérateurs
 129         # ----------
 130         if B is None:
 131             raise ValueError("Background error covariance matrix has to be properly defined!")
 132         if R is None:
 133             raise ValueError("Observation error covariance matrix has to be properly defined!")
 134         #
 135         H = HO["Direct"].appliedControledFormTo
 136         #
 137         if self._parameters["EstimationOf"] == "State":
 138             M = EM["Direct"].appliedControledFormTo
 139         #
 140         if CM is not None and CM.has_key("Tangent") and U is not None:
 141             Cm = CM["Tangent"].asMatrix(Xb)
 142         else:
 143             Cm = None
 144         #
 145         # Nombre de pas du Kalman identique au nombre de pas d'observations
 146         # -----------------------------------------------------------------
 147         if hasattr(Y,"stepnumber"):
 148             duration = Y.stepnumber()
 149         else:
 150             duration = 2
 151         #
 152         # Précalcul des inversions de B et R
 153         # ----------------------------------
 154         if self._parameters["StoreInternalVariables"]:
 155             BI = B.getI()
 156             RI = R.getI()
 157         #
 158         # Initialisation
 159         # --------------
 160         Xn = Xb
 161         if hasattr(B,"asfullmatrix"):
 162             Pn = B.asfullmatrix(Xn.size)
 163         else:
 164             Pn = B
 165         #
 166         self.StoredVariables["Analysis"].store( Xn.A1 )
 167         if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 168             self.StoredVariables["APosterioriCovariance"].store( Pn )
 169             covarianceXa = Pn
 170         Xa               = Xn
 171         previousJMinimum = numpy.finfo(float).max
 172         #
 173         for step in range(duration-1):
 174             if hasattr(Y,"store"):
 175                 Ynpu = numpy.asmatrix(numpy.ravel( Y[step+1] )).T
 176             else:
 177                 Ynpu = numpy.asmatrix(numpy.ravel( Y )).T
 178             #
 179             if U is not None:
 180                 if hasattr(U,"store") and len(U)>1:
 181                     Un = numpy.asmatrix(numpy.ravel( U[step] )).T
 182                 elif hasattr(U,"store") and len(U)==1:
 183                     Un = numpy.asmatrix(numpy.ravel( U[0] )).T
 184                 else:
 185                     Un = numpy.asmatrix(numpy.ravel( U )).T
 186             else:
 187                 Un = None
 188             #
 189             Pndemi = numpy.linalg.cholesky(Pn)
 190             Xnp = numpy.hstack([Xn, Xn+Gamma*Pndemi, Xn-Gamma*Pndemi])
 191             nbSpts = 2*Xn.size+1
 192             #
 193             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 194                 for point in range(nbSpts):
 195                     Xnp[:,point] = numpy.max(numpy.hstack((Xnp[:,point],numpy.asmatrix(Bounds)[:,0])),axis=1)
 196                     Xnp[:,point] = numpy.min(numpy.hstack((Xnp[:,point],numpy.asmatrix(Bounds)[:,1])),axis=1)
 197             #
 198             XEtnnp = []
 199             for point in range(nbSpts):
 200                 if self._parameters["EstimationOf"] == "State":
 201                     XEtnnpi = numpy.asmatrix(numpy.ravel( M( (Xnp[:,point], Un) ) )).T
 202                     if Cm is not None and Un is not None: # Attention : si Cm est aussi dans M, doublon !
 203                         Cm = Cm.reshape(Xn.size,Un.size) # ADAO & check shape
 204                         XEtnnpi = XEtnnpi + Cm * Un
 205                     if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 206                         XEtnnpi = numpy.max(numpy.hstack((XEtnnpi,numpy.asmatrix(Bounds)[:,0])),axis=1)
 207                         XEtnnpi = numpy.min(numpy.hstack((XEtnnpi,numpy.asmatrix(Bounds)[:,1])),axis=1)
 208                 elif self._parameters["EstimationOf"] == "Parameters":
 209                     # --- > Par principe, M = Id, Q = 0
 210                     XEtnnpi = Xnp[:,point]
 211                 XEtnnp.append( XEtnnpi )
 212             XEtnnp = numpy.hstack( XEtnnp )
 213             #
 214             Xncm = numpy.matrix( XEtnnp.getA()*numpy.array(Wm) ).sum(axis=1)
 215             #
 216             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 217                 Xncm = numpy.max(numpy.hstack((Xncm,numpy.asmatrix(Bounds)[:,0])),axis=1)
 218                 Xncm = numpy.min(numpy.hstack((Xncm,numpy.asmatrix(Bounds)[:,1])),axis=1)
 219             #
 220             if self._parameters["EstimationOf"] == "State":        Pnm = Q
 221             elif self._parameters["EstimationOf"] == "Parameters": Pnm = 0.
 222             for point in range(nbSpts):
 223                 Pnm += Wc[i] * (XEtnnp[:,point]-Xncm) * (XEtnnp[:,point]-Xncm).T
 224             #
 225             if self._parameters["EstimationOf"] == "Parameters" and Bounds is not None:
 226                 Pnmdemi = self._parameters["Reconditioner"] * numpy.linalg.cholesky(Pnm)
 227             else:
 228                 Pnmdemi = numpy.linalg.cholesky(Pnm)
 229             #
 230             Xnnp = numpy.hstack([Xncm, Xncm+Gamma*Pnmdemi, Xncm-Gamma*Pnmdemi])
 231             #
 232             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 233                 for point in range(nbSpts):
 234                     Xnnp[:,point] = numpy.max(numpy.hstack((Xnnp[:,point],numpy.asmatrix(Bounds)[:,0])),axis=1)
 235                     Xnnp[:,point] = numpy.min(numpy.hstack((Xnnp[:,point],numpy.asmatrix(Bounds)[:,1])),axis=1)
 236             #
 237             Ynnp = []
 238             for point in range(nbSpts):
 239                 if self._parameters["EstimationOf"] == "State":
 240                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], None) ) )).T
 241                 elif self._parameters["EstimationOf"] == "Parameters":
 242                     Ynnpi = numpy.asmatrix(numpy.ravel( H( (Xnnp[:,point], Un) ) )).T
 243                 Ynnp.append( Ynnpi )
 244             Ynnp = numpy.hstack( Ynnp )
 245             #
 246             Yncm = numpy.matrix( Ynnp.getA()*numpy.array(Wm) ).sum(axis=1)
 247             #
 248             Pyyn = R
 249             Pxyn = 0.
 250             for point in range(nbSpts):
 251                 Pyyn += Wc[i] * (Ynnp[:,point]-Yncm) * (Ynnp[:,point]-Yncm).T
 252                 Pxyn += Wc[i] * (Xnnp[:,point]-Xncm) * (Ynnp[:,point]-Yncm).T
 253             #
 254             d  = Ynpu - Yncm
 255             if self._parameters["EstimationOf"] == "Parameters":
 256                 if Cm is not None and Un is not None: # Attention : si Cm est aussi dans H, doublon !
 257                     d = d - Cm * Un
 258             #
 259             Kn = Pxyn * Pyyn.I
 260             Xn = Xncm + Kn * d
 261             Pn = Pnm - Kn * Pyyn * Kn.T
 262             #
 263             if Bounds is not None and self._parameters["ConstrainedBy"] == "EstimateProjection":
 264                 Xn = numpy.max(numpy.hstack((Xn,numpy.asmatrix(Bounds)[:,0])),axis=1)
 265                 Xn = numpy.min(numpy.hstack((Xn,numpy.asmatrix(Bounds)[:,1])),axis=1)
 266             #
 267             self.StoredVariables["Analysis"].store( Xn.A1 )
 268             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 269                 self.StoredVariables["APosterioriCovariance"].store( Pn )
 270             if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 271                 self.StoredVariables["Innovation"].store( numpy.ravel( d.A1 ) )
 272             if self._parameters["StoreInternalVariables"]:
 273                 Jb  = 0.5 * (Xn - Xb).T * BI * (Xn - Xb)
 274                 Jo  = 0.5 * d.T * RI * d
 275                 J   = float( Jb ) + float( Jo )
 276                 self.StoredVariables["CurrentState"].store( Xn )
 277                 self.StoredVariables["CostFunctionJb"].store( Jb )
 278                 self.StoredVariables["CostFunctionJo"].store( Jo )
 279                 self.StoredVariables["CostFunctionJ" ].store( J )
 280                 if J < previousJMinimum:
 281                     previousJMinimum  = J
 282                     Xa                = Xn
 283                     if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 284                         covarianceXa  = Pn
 285             else:
 286                 Xa = Xn
 287             #
 288         #
 289         # Stockage supplementaire de l'optimum en estimation de parametres
 290         # ----------------------------------------------------------------
 291         if self._parameters["EstimationOf"] == "Parameters":
 292             self.StoredVariables["Analysis"].store( Xa.A1 )
 293             if "APosterioriCovariance" in self._parameters["StoreSupplementaryCalculations"]:
 294                 self.StoredVariables["APosterioriCovariance"].store( covarianceXa )
 295         #
 296         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 297             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 298         #
 299         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)))
 300         logging.debug("%s Nombre d'appels au cache d'opérateur d'observation direct/tangent/adjoint..: %i/%i/%i"%(self._name, HO["Direct"].nbcalls(3),HO["Tangent"].nbcalls(3),HO["Adjoint"].nbcalls(3)))
 301         logging.debug("%s Taille mémoire utilisée de %.1f Mo"%(self._name, m.getUsedMemory("M")))
 302         logging.debug("%s Terminé"%self._name)
 303         #
 304         return 0
 305
 306 # ==============================================================================
 307 if __name__ == "__main__":
 308     print '\n AUTODIAGNOSTIC \n'