/[escript]/trunk/escript/py_src/pdetools.py
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revision 1514 by artak, Wed Apr 16 00:15:44 2008 UTC revision 1878 by gross, Tue Oct 14 03:39:13 2008 UTC
# Line 1  Line 1 
1    
2    ########################################################
3  #  #
4  # $Id$  # Copyright (c) 2003-2008 by University of Queensland
5  #  # Earth Systems Science Computational Center (ESSCC)
6  #######################################################  # http://www.uq.edu.au/esscc
 #  
 #           Copyright 2003-2007 by ACceSS MNRF  
 #       Copyright 2007 by University of Queensland  
 #  
 #                http://esscc.uq.edu.au  
 #        Primary Business: Queensland, Australia  
 #  Licensed under the Open Software License version 3.0  
 #     http://www.opensource.org/licenses/osl-3.0.php  
7  #  #
8  #######################################################  # Primary Business: Queensland, Australia
9    # Licensed under the Open Software License version 3.0
10    # http://www.opensource.org/licenses/osl-3.0.php
11  #  #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15    Earth Systems Science Computational Center (ESSCC)
16    http://www.uq.edu.au/esscc
17    Primary Business: Queensland, Australia"""
18    __license__="""Licensed under the Open Software License version 3.0
19    http://www.opensource.org/licenses/osl-3.0.php"""
20    __url__="http://www.uq.edu.au/esscc/escript-finley"
21    
22  """  """
23  Provides some tools related to PDEs.  Provides some tools related to PDEs.
# Line 32  Currently includes: Line 37  Currently includes:
37  """  """
38    
39  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
 __copyright__="""  Copyright (c) 2006 by ACcESS MNRF  
                     http://www.access.edu.au  
                 Primary Business: Queensland, Australia"""  
 __license__="""Licensed under the Open Software License version 3.0  
              http://www.opensource.org/licenses/osl-3.0.php"""  
 __url__="http://www.iservo.edu.au/esys"  
 __version__="$Revision$"  
 __date__="$Date$"  
40    
41    
42  import escript  import escript
# Line 474  class IterationHistory(object): Line 471  class IterationHistory(object):
471    
472         """         """
473         self.history.append(norm_r)         self.history.append(norm_r)
474         if self.verbose: print "iter: #s:  inner(rhat,r) = #e"#(len(self.history)-1, self.history[-1])         if self.verbose: print "iter: %s:  inner(rhat,r) = %e"#(len(self.history)-1, self.history[-1])
475         return self.history[-1]<=self.tolerance * self.history[0]         return self.history[-1]<=self.tolerance * self.history[0]
476    
477     def stoppingcriterium2(self,norm_r,norm_b):     def stoppingcriterium2(self,norm_r,norm_b,solver="GMRES",TOL=None):
478         """         """
479         returns True if the C{norm_r} is C{tolerance}*C{norm_b}         returns True if the C{norm_r} is C{tolerance}*C{norm_b}
480    
# Line 490  class IterationHistory(object): Line 487  class IterationHistory(object):
487         @rtype: C{bool}         @rtype: C{bool}
488    
489         """         """
490           if TOL==None:
491              TOL=self.tolerance
492         self.history.append(norm_r)         self.history.append(norm_r)
493         if self.verbose: print "iter: #s:  norm(r) = #e"#(len(self.history)-1, self.history[-1])         if self.verbose: print "iter: %s:  norm(r) = %e"#(len(self.history)-1, self.history[-1])
494         return self.history[-1]<=self.tolerance * norm_b         return self.history[-1]<=TOL * norm_b
495    
496  def PCG(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100):  def PCG(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100):
497     """     """
# Line 561  type like argument C{x}. Line 560  type like argument C{x}.
560    
561     return x,r     return x,r
562    
563    class Defect(object):
564        """
565        defines a non-linear defect F(x) of a variable x
566        """
567        def __init__(self):
568            """
569            initialize defect
570            """
571            self.setDerivativeIncrementLength()
572    
573  ############################      def bilinearform(self, x0, x1):
574  # Added by Artak          """
575  #################################3          returns the inner product of x0 and x1
576            @param x0: a value for x
577            @param x1: a value for x
578            @return: the inner product of x0 and x1
579            @rtype: C{float}
580            """
581            return 0
582          
583        def norm(self,x):
584            """
585            the norm of argument C{x}
586    
587            @param x: a value for x
588            @return: norm of argument x
589            @rtype: C{float}
590            @note: by default C{sqrt(self.bilinearform(x,x)} is retrurned.
591            """
592            s=self.bilinearform(x,x)
593            if s<0: raise NegativeNorm,"negative norm."
594            return math.sqrt(s)
595    
596    
597        def eval(self,x):
598            """
599            returns the value F of a given x
600    
601            @param x: value for which the defect C{F} is evalulated.
602            @return: value of the defect at C{x}
603            """
604            return 0
605    
606        def __call__(self,x):
607            return self.eval(x)
608    
609        def setDerivativeIncrementLength(self,inc=math.sqrt(util.EPSILON)):
610            """
611            sets the relative length of the increment used to approximate the derivative of the defect
612            the increment is inc*norm(x)/norm(v)*v in the direction of v with x as a staring point.
613    
614  #Apply a sequence of k Givens rotations, used within gmres codes          @param inc: relative increment length
615  # vrot=givapp(c, s, vin, k)          @type inc: positive C{float}
616  def givapp(c,s,vin):          """
617      vrot=vin # warning: vin is altered!!!!          if inc<=0: raise ValueError,"positive increment required."
618            self.__inc=inc
619    
620        def getDerivativeIncrementLength(self):
621            """
622            returns the relative increment length used to approximate the derivative of the defect
623            @return: value of the defect at C{x}
624            @rtype: positive C{float}
625            """
626            return self.__inc
627    
628        def derivative(self, F0, x0, v, v_is_normalised=True):
629            """
630            returns the directional derivative at x0 in the direction of v
631    
632            @param F0: value of this defect at x0
633            @param x0: value at which derivative is calculated.
634            @param v: direction
635            @param v_is_normalised: is true to indicate that C{v} is nomalized (self.norm(v)=0)
636            @return: derivative of this defect at x0 in the direction of C{v}
637            @note: by default numerical evaluation (self.eval(x0+eps*v)-F0)/eps is used but this method
638            maybe oepsnew verwritten to use exact evalution.
639            """
640            normx=self.norm(x0)
641            if normx>0:
642                 epsnew = self.getDerivativeIncrementLength() * normx
643            else:
644                 epsnew = self.getDerivativeIncrementLength()
645            if not v_is_normalised:
646                normv=self.norm(v)
647                if normv<=0:
648                   return F0*0
649                else:
650                   epsnew /= normv
651            F1=self.eval(x0 + epsnew * v)
652            return (F1-F0)/epsnew
653    
654    ######################################    
655    def NewtonGMRES(defect, x, iter_max=100, sub_iter_max=20, atol=0,rtol=1.e-4, sub_tol_max=0.5, gamma=0.9, verbose=False):
656       """
657       solves a non-linear problem M{F(x)=0} for unknown M{x} using the stopping criterion:
658    
659       M{norm(F(x) <= atol + rtol * norm(F(x0)}
660      
661       where M{x0} is the initial guess.
662    
663       @param defect: object defining the the function M{F}, C{defect.norm} defines the M{norm} used in the stopping criterion.
664       @type defect: L{Defect}
665       @param x: initial guess for the solution, C{x} is altered.
666       @type x: any object type allowing basic operations such as  L{numarray.NumArray}, L{Data}
667       @param iter_max: maximum number of iteration steps
668       @type iter_max: positive C{int}
669       @param sub_iter_max:
670       @type sub_iter_max:
671       @param atol: absolute tolerance for the solution
672       @type atol: positive C{float}
673       @param rtol: relative tolerance for the solution
674       @type rtol: positive C{float}
675       @param gamma: tolerance safety factor for inner iteration
676       @type gamma: positive C{float}, less than 1
677       @param sub_tol_max: upper bound for inner tolerance.
678       @type sub_tol_max: positive C{float}, less than 1
679       @return: an approximation of the solution with the desired accuracy
680       @rtype: same type as the initial guess.
681       """
682       lmaxit=iter_max
683       if atol<0: raise ValueError,"atol needs to be non-negative."
684       if rtol<0: raise ValueError,"rtol needs to be non-negative."
685       if rtol+atol<=0: raise ValueError,"rtol or atol needs to be non-negative."
686       if gamma<=0 or gamma>=1: raise ValueError,"tolerance safety factor for inner iteration (gamma =%s) needs to be positive and less than 1."%gamma
687       if sub_tol_max<=0 or sub_tol_max>=1: raise ValueError,"upper bound for inner tolerance for inner iteration (sub_tol_max =%s) needs to be positive and less than 1."%sub_tol_max
688    
689       F=defect(x)
690       fnrm=defect.norm(F)
691       stop_tol=atol + rtol*fnrm
692       sub_tol=sub_tol_max
693       if verbose: print "NewtonGMRES: initial residual = %e."%fnrm
694       if verbose: print "             tolerance = %e."%sub_tol
695       iter=1
696       #
697       # main iteration loop
698       #
699       while not fnrm<=stop_tol:
700                if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max
701                #
702            #   adjust sub_tol_
703            #
704                if iter > 1:
705               rat=fnrm/fnrmo
706                   sub_tol_old=sub_tol
707               sub_tol=gamma*rat**2
708               if gamma*sub_tol_old**2 > .1: sub_tol=max(sub_tol,gamma*sub_tol_old**2)
709               sub_tol=max(min(sub_tol,sub_tol_max), .5*stop_tol/fnrm)
710            #
711            # calculate newton increment xc
712                #     if iter_max in __FDGMRES is reached MaxIterReached is thrown
713                #     if iter_restart -1 is returned as sub_iter
714                #     if  atol is reached sub_iter returns the numer of steps performed to get there
715                #
716                #  
717                if verbose: print "             subiteration (GMRES) is called with relative tolerance %e."%sub_tol
718                try:
719                   xc, sub_iter=__FDGMRES(F, defect, x, sub_tol*fnrm, iter_max=iter_max-iter, iter_restart=sub_iter_max)
720                except MaxIterReached:
721                   raise MaxIterReached,"maximum number of %s steps reached."%iter_max
722                if sub_iter<0:
723                   iter+=sub_iter_max
724                else:
725                   iter+=sub_iter
726                # ====
727            x+=xc
728                F=defect(x)
729            iter+=1
730                fnrmo, fnrm=fnrm, defect.norm(F)
731                if verbose: print "             step %s: residual %e."%(iter,fnrm)
732       if verbose: print "NewtonGMRES: completed after %s steps."%iter
733       return x
734    
735    def __givapp(c,s,vin):
736        """
737        apply a sequence of Givens rotations (c,s) to the recuirsively to the vector vin
738        @warning: C{vin} is altered.
739        """
740        vrot=vin
741      if isinstance(c,float):      if isinstance(c,float):
742          vrot=[c*vrot[0]-s*vrot[1],s*vrot[0]+c*vrot[1]]          vrot=[c*vrot[0]-s*vrot[1],s*vrot[0]+c*vrot[1]]
743      else:      else:
# Line 579  def givapp(c,s,vin): Line 747  def givapp(c,s,vin):
747              vrot[i:i+2]=w1,w2              vrot[i:i+2]=w1,w2
748      return vrot      return vrot
749    
750    def __FDGMRES(F0, defect, x0, atol, iter_max=100, iter_restart=20):
751       h=numarray.zeros((iter_restart,iter_restart),numarray.Float64)
752       c=numarray.zeros(iter_restart,numarray.Float64)
753       s=numarray.zeros(iter_restart,numarray.Float64)
754       g=numarray.zeros(iter_restart,numarray.Float64)
755       v=[]
756    
757       rho=defect.norm(F0)
758       if rho<=0.: return x0*0
759      
760       v.append(-F0/rho)
761       g[0]=rho
762       iter=0
763       while rho > atol and iter<iter_restart-1:
764    
765        if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max
766    
767            p=defect.derivative(F0,x0,v[iter], v_is_normalised=True)
768        v.append(p)
769    
770        v_norm1=defect.norm(v[iter+1])
771    
772            # Modified Gram-Schmidt
773        for j in range(iter+1):
774             h[j][iter]=defect.bilinearform(v[j],v[iter+1])  
775             v[iter+1]-=h[j][iter]*v[j]
776          
777        h[iter+1][iter]=defect.norm(v[iter+1])
778        v_norm2=h[iter+1][iter]
779    
780            # Reorthogonalize if needed
781        if v_norm1 + 0.001*v_norm2 == v_norm1:   #Brown/Hindmarsh condition (default)
782            for j in range(iter+1):  
783               hr=defect.bilinearform(v[j],v[iter+1])
784                   h[j][iter]=h[j][iter]+hr
785                   v[iter+1] -= hr*v[j]
786    
787            v_norm2=defect.norm(v[iter+1])
788            h[iter+1][iter]=v_norm2
789            #   watch out for happy breakdown
790            if not v_norm2 == 0:
791                    v[iter+1]=v[iter+1]/h[iter+1][iter]
792    
793            #   Form and store the information for the new Givens rotation
794        if iter > 0 :
795            hhat=numarray.zeros(iter+1,numarray.Float64)
796            for i in range(iter+1) : hhat[i]=h[i][iter]
797            hhat=__givapp(c[0:iter],s[0:iter],hhat);
798                for i in range(iter+1) : h[i][iter]=hhat[i]
799    
800        mu=math.sqrt(h[iter][iter]*h[iter][iter]+h[iter+1][iter]*h[iter+1][iter])
801    
802        if mu!=0 :
803            c[iter]=h[iter][iter]/mu
804            s[iter]=-h[iter+1][iter]/mu
805            h[iter][iter]=c[iter]*h[iter][iter]-s[iter]*h[iter+1][iter]
806            h[iter+1][iter]=0.0
807            g[iter:iter+2]=__givapp(c[iter],s[iter],g[iter:iter+2])
808    
809            # Update the residual norm
810            rho=abs(g[iter+1])
811        iter+=1
812    
813       # At this point either iter > iter_max or rho < tol.
814       # It's time to compute x and leave.        
815       if iter > 0 :
816         y=numarray.zeros(iter,numarray.Float64)    
817         y[iter-1] = g[iter-1] / h[iter-1][iter-1]
818         if iter > 1 :  
819            i=iter-2  
820            while i>=0 :
821              y[i] = ( g[i] - numarray.dot(h[i][i+1:iter], y[i+1:iter])) / h[i][i]
822              i=i-1
823         xhat=v[iter-1]*y[iter-1]
824         for i in range(iter-1):
825        xhat += v[i]*y[i]
826       else :
827          xhat=v[0] * 0
828    
829       if iter<iter_restart-1:
830          stopped=iter
831       else:
832          stopped=-1
833    
834       return xhat,stopped
835    
836    ##############################################
837  def GMRES(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100, iter_restart=20):  def GMRES(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100, iter_restart=20):
838    ################################################
839     m=iter_restart     m=iter_restart
840     iter=0     iter=0
841       xc=x
842     while True:     while True:
843        if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached"%iter_max        if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached"%iter_max
844        x,stopped=GMRESm(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=x, iter_max=iter_max-iter, iter_restart=m)        xc,stopped=__GMRESm(b*1, Aprod, Msolve, bilinearform, stoppingcriterium, x=xc*1, iter_max=iter_max-iter, iter_restart=m)
       iter+=iter_restart  
845        if stopped: break        if stopped: break
846     return x        iter+=iter_restart    
847       return xc
848    
849  def GMRESm(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100, iter_restart=20):  def __GMRESm(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100, iter_restart=20):
850     iter=0     iter=0
851     r=Msolve(b)     r=Msolve(b)
852     r_dot_r = bilinearform(r, r)     r_dot_r = bilinearform(r, r)
# Line 597  def GMRESm(b, Aprod, Msolve, bilinearfor Line 854  def GMRESm(b, Aprod, Msolve, bilinearfor
854     norm_b=math.sqrt(r_dot_r)     norm_b=math.sqrt(r_dot_r)
855    
856     if x==None:     if x==None:
857        x=0        x=0*b
858     else:     else:
859        r=Msolve(b-Aprod(x))        r=Msolve(b-Aprod(x))
860        r_dot_r = bilinearform(r, r)        r_dot_r = bilinearform(r, r)
# Line 618  def GMRESm(b, Aprod, Msolve, bilinearfor Line 875  def GMRESm(b, Aprod, Msolve, bilinearfor
875    
876      if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max      if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max
877    
       
878      p=Msolve(Aprod(v[iter]))      p=Msolve(Aprod(v[iter]))
879    
880      v.append(p)      v.append(p)
# Line 626  def GMRESm(b, Aprod, Msolve, bilinearfor Line 882  def GMRESm(b, Aprod, Msolve, bilinearfor
882      v_norm1=math.sqrt(bilinearform(v[iter+1], v[iter+1]))        v_norm1=math.sqrt(bilinearform(v[iter+1], v[iter+1]))  
883    
884  # Modified Gram-Schmidt  # Modified Gram-Schmidt
885      for j in range(iter+1):      for j in range(iter+1):
886        h[j][iter]=bilinearform(v[j],v[iter+1])          h[j][iter]=bilinearform(v[j],v[iter+1])  
887        v[iter+1]+=(-1.)*h[j][iter]*v[j]        v[iter+1]-=h[j][iter]*v[j]
888                
889      h[iter+1][iter]=math.sqrt(bilinearform(v[iter+1],v[iter+1]))      h[iter+1][iter]=math.sqrt(bilinearform(v[iter+1],v[iter+1]))
890      v_norm2=h[iter+1][iter]      v_norm2=h[iter+1][iter]
891    
   
892  # Reorthogonalize if needed  # Reorthogonalize if needed
893      if v_norm1 + 0.001*v_norm2 == v_norm1:   #Brown/Hindmarsh condition (default)      if v_norm1 + 0.001*v_norm2 == v_norm1:   #Brown/Hindmarsh condition (default)
894       for j in range(iter+1):       for j in range(iter+1):  
895          hr=bilinearform(v[j],v[iter+1])          hr=bilinearform(v[j],v[iter+1])
896              h[j][iter]=h[j][iter]+hr #vhat              h[j][iter]=h[j][iter]+hr
897              v[iter+1] +=(-1.)*hr*v[j]              v[iter+1] -= hr*v[j]
898    
899       v_norm2=math.sqrt(bilinearform(v[iter+1], v[iter+1]))         v_norm2=math.sqrt(bilinearform(v[iter+1], v[iter+1]))  
900       h[iter+1][iter]=v_norm2       h[iter+1][iter]=v_norm2
901    
902  #   watch out for happy breakdown  #   watch out for happy breakdown
903          if v_norm2 != 0:          if not v_norm2 == 0:
904           v[iter+1]=v[iter+1]/h[iter+1][iter]           v[iter+1]=v[iter+1]/h[iter+1][iter]
905    
906  #   Form and store the information for the new Givens rotation  #   Form and store the information for the new Givens rotation
907      if iter > 0 :      if iter > 0 :
908          hhat=[]          hhat=numarray.zeros(iter+1,numarray.Float64)
909          for i in range(iter+1) : hhat.append(h[i][iter])          for i in range(iter+1) : hhat[i]=h[i][iter]
910          hhat=givapp(c[0:iter],s[0:iter],hhat);          hhat=__givapp(c[0:iter],s[0:iter],hhat);
911              for i in range(iter+1) : h[i][iter]=hhat[i]              for i in range(iter+1) : h[i][iter]=hhat[i]
912    
913      mu=math.sqrt(h[iter][iter]*h[iter][iter]+h[iter+1][iter]*h[iter+1][iter])      mu=math.sqrt(h[iter][iter]*h[iter][iter]+h[iter+1][iter]*h[iter+1][iter])
914    
915      if mu!=0 :      if mu!=0 :
916          c[iter]=h[iter][iter]/mu          c[iter]=h[iter][iter]/mu
917          s[iter]=-h[iter+1][iter]/mu          s[iter]=-h[iter+1][iter]/mu
918          h[iter][iter]=c[iter]*h[iter][iter]-s[iter]*h[iter+1][iter]          h[iter][iter]=c[iter]*h[iter][iter]-s[iter]*h[iter+1][iter]
919          h[iter+1][iter]=0.0          h[iter+1][iter]=0.0
920          g[iter:iter+2]=givapp(c[iter],s[iter],g[iter:iter+2])          g[iter:iter+2]=__givapp(c[iter],s[iter],g[iter:iter+2])
921    
922  # Update the residual norm  # Update the residual norm
923                  
924          rho=abs(g[iter+1])          rho=abs(g[iter+1])
925      iter+=1      iter+=1
926    
# Line 682  def GMRESm(b, Aprod, Msolve, bilinearfor Line 939  def GMRESm(b, Aprod, Msolve, bilinearfor
939       for i in range(iter-1):       for i in range(iter-1):
940      xhat += v[i]*y[i]      xhat += v[i]*y[i]
941     else : xhat=v[0]     else : xhat=v[0]
942        
943     x += xhat     x += xhat
944     if iter<iter_restart-1:     if iter<iter_restart-1:
945        stopped=True        stopped=True
# Line 691  def GMRESm(b, Aprod, Msolve, bilinearfor Line 948  def GMRESm(b, Aprod, Msolve, bilinearfor
948    
949     return x,stopped     return x,stopped
950    
951    #################################################
952  def MINRES(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100):  def MINRES(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100):
953    #################################################
954      #      #
955      #  minres solves the system of linear equations Ax = b      #  minres solves the system of linear equations Ax = b
956      #  where A is a symmetric matrix (possibly indefinite or singular)      #  where A is a symmetric matrix (possibly indefinite or singular)
# Line 722  def MINRES(b, Aprod, Msolve, bilinearfor Line 980  def MINRES(b, Aprod, Msolve, bilinearfor
980    
981      r1    = b      r1    = b
982      y = Msolve(b)      y = Msolve(b)
983      beta1 = bilinearform(b,y)      beta1 = bilinearform(y,b)
984    
985      if beta1< 0: raise NegativeNorm,"negative norm."      if beta1< 0: raise NegativeNorm,"negative norm."
986    
# Line 758  def MINRES(b, Aprod, Msolve, bilinearfor Line 1016  def MINRES(b, Aprod, Msolve, bilinearfor
1016      #---------------------------------------------------------------------      #---------------------------------------------------------------------
1017      # Main iteration loop.      # Main iteration loop.
1018      # --------------------------------------------------------------------      # --------------------------------------------------------------------
1019      while not stoppingcriterium(rnorm,Anorm*ynorm):    #  checks ||r|| < (||A|| ||x||) * TOL      while not stoppingcriterium(rnorm,Anorm*ynorm,'MINRES'):    #  checks ||r|| < (||A|| ||x||) * TOL
1020    
1021      if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max      if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max
1022          iter    = iter  +  1          iter    = iter  +  1
# Line 784  def MINRES(b, Aprod, Msolve, bilinearfor Line 1042  def MINRES(b, Aprod, Msolve, bilinearfor
1042            y = y - (beta/oldb)*r1            y = y - (beta/oldb)*r1
1043    
1044          alfa   = bilinearform(v,y)              # alphak          alfa   = bilinearform(v,y)              # alphak
1045          y      = (- alfa/beta)*r2 + y          y      += (- alfa/beta)*r2
1046          r1     = r2          r1     = r2
1047          r2     = y          r2     = y
1048          y = Msolve(r2)          y = Msolve(r2)
1049          oldb   = beta                           # oldb = betak          oldb   = beta                           # oldb = betak
1050          beta   = bilinearform(r2,y)             # beta = betak+1^2          beta   = bilinearform(y,r2)             # beta = betak+1^2
1051          if beta < 0: raise NegativeNorm,"negative norm."          if beta < 0: raise NegativeNorm,"negative norm."
1052    
1053          beta   = math.sqrt( beta )          beta   = math.sqrt( beta )
# Line 824  def MINRES(b, Aprod, Msolve, bilinearfor Line 1082  def MINRES(b, Aprod, Msolve, bilinearfor
1082          w1    = w2          w1    = w2
1083          w2    = w          w2    = w
1084          w     = (v - oldeps*w1 - delta*w2) * denom          w     = (v - oldeps*w1 - delta*w2) * denom
1085          x     = x  +  phi*w          x     +=  phi*w
1086    
1087          # Go round again.          # Go round again.
1088    
# Line 843  def MINRES(b, Aprod, Msolve, bilinearfor Line 1101  def MINRES(b, Aprod, Msolve, bilinearfor
1101          rnorm  = phibar          rnorm  = phibar
1102    
1103      return x      return x
       
1104    
1105  def TFQMR(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100):  def TFQMR(b, Aprod, Msolve, bilinearform, stoppingcriterium, x=None, iter_max=100):
1106    
# Line 888  def TFQMR(b, Aprod, Msolve, bilinearform Line 1145  def TFQMR(b, Aprod, Msolve, bilinearform
1145  #  #
1146  #  while ( iter < kmax-1 ):  #  while ( iter < kmax-1 ):
1147        
1148    while not stoppingcriterium(tau*math.sqrt ( m + 1 ),norm_b):    while not stoppingcriterium(tau*math.sqrt ( m + 1 ),norm_b,'TFQMR'):
1149      if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max      if iter  >= iter_max: raise MaxIterReached,"maximum number of %s steps reached."%iter_max
1150    
1151      sigma = bilinearform(r,v)      sigma = bilinearform(r,v)
# Line 944  def TFQMR(b, Aprod, Msolve, bilinearform Line 1201  def TFQMR(b, Aprod, Msolve, bilinearform
1201            
1202      iter = iter + 1      iter = iter + 1
1203    
   print iter  
1204    return x    return x
1205    
1206    
# Line 1001  class ArithmeticTuple(object): Line 1257  class ArithmeticTuple(object):
1257         @rtype: L{ArithmeticTuple}         @rtype: L{ArithmeticTuple}
1258         """         """
1259         out=[]         out=[]
1260         for i in range(len(self)):         other=1.*other
1261           if isinstance(other,float):
1262        for i in range(len(self)):
1263             out.append(self[i]*other)             out.append(self[i]*other)
1264           else:
1265            for i in range(len(self)):
1266               out.append(self[i]*other[i])
1267         return ArithmeticTuple(*tuple(out))         return ArithmeticTuple(*tuple(out))
1268    
1269     def __rmul__(self,other):     def __rmul__(self,other):
# Line 1015  class ArithmeticTuple(object): Line 1276  class ArithmeticTuple(object):
1276         @rtype: L{ArithmeticTuple}         @rtype: L{ArithmeticTuple}
1277         """         """
1278         out=[]         out=[]
1279         for i in range(len(self)):         other=1.*other
1280           if isinstance(other,float):
1281        for i in range(len(self)):
1282             out.append(other*self[i])             out.append(other*self[i])
1283           else:
1284            for i in range(len(self)):
1285               out.append(other[i]*self[i])
1286         return ArithmeticTuple(*tuple(out))         return ArithmeticTuple(*tuple(out))
1287    
1288  #########################  #########################
# Line 1032  class ArithmeticTuple(object): Line 1298  class ArithmeticTuple(object):
1298         @rtype: L{ArithmeticTuple}         @rtype: L{ArithmeticTuple}
1299         """         """
1300         out=[]         out=[]
1301         for i in range(len(self)):         other=1.*other
1302             out.append(self[i]/other)         if isinstance(other,float):
1303        for i in range(len(self)):
1304               out.append(self[i]*(1./other))
1305           else:
1306            for i in range(len(self)):
1307               out.append(self[i]*(1./other[i]))
1308         return ArithmeticTuple(*tuple(out))         return ArithmeticTuple(*tuple(out))
1309    
1310     def __rdiv__(self,other):     def __rdiv__(self,other):
# Line 1046  class ArithmeticTuple(object): Line 1317  class ArithmeticTuple(object):
1317         @rtype: L{ArithmeticTuple}         @rtype: L{ArithmeticTuple}
1318         """         """
1319         out=[]         out=[]
1320         for i in range(len(self)):         other=1.*other
1321             out.append(other/self[i])         if isinstance(other,float):
1322            for i in range(len(self)):
1323               out.append(other*(1./self[i]))
1324           else:
1325            for i in range(len(self)):
1326               out.append(other[i]*(1./self[i]))
1327         return ArithmeticTuple(*tuple(out))         return ArithmeticTuple(*tuple(out))
1328        
1329  ##########################################33  ##########################################33
# Line 1065  class ArithmeticTuple(object): Line 1341  class ArithmeticTuple(object):
1341             self.__items[i]+=other[i]             self.__items[i]+=other[i]
1342         return self         return self
1343    
1344       def __add__(self,other):
1345           """
1346           add other to self
1347    
1348           @param other: increment
1349           @type other: C{ArithmeticTuple}
1350           """
1351    #      if not isinstance(other,float):
1352           if len(self) != len(other):
1353              raise ValueError,"tuple length must match."
1354           for i in range(len(self)):
1355              self.__items[i]+=other[i]
1356    #       else:
1357    #        for i in range(len(self)):
1358    #           self.__items[i]+=other
1359    
1360           return self
1361    
1362       def __sub__(self,other):
1363           """
1364           subtract other from self
1365    
1366           @param other: increment
1367           @type other: C{ArithmeticTuple}
1368           """
1369           if len(self) != len(other):
1370               raise ValueError,"tuple length must match."
1371           for i in range(len(self)):
1372               self.__items[i]-=other[i]
1373           return self
1374      
1375       def __isub__(self,other):
1376           """
1377           subtract other from self
1378    
1379           @param other: increment
1380           @type other: C{ArithmeticTuple}
1381           """
1382           if len(self) != len(other):
1383               raise ValueError,"tuple length must match."
1384           for i in range(len(self)):
1385               self.__items[i]-=other[i]
1386           return self
1387    
1388       def __neg__(self):
1389           """
1390           negate
1391    
1392           """
1393           for i in range(len(self)):
1394               self.__items[i]=-self.__items[i]
1395           return self
1396    
1397    
1398  class HomogeneousSaddlePointProblem(object):  class HomogeneousSaddlePointProblem(object):
1399        """        """
1400        This provides a framwork for solving homogeneous saddle point problem of the form        This provides a framwork for solving linear homogeneous saddle point problem of the form
1401    
1402               Av+B^*p=f               Av+B^*p=f
1403               Bv    =0               Bv    =0
# Line 1136  class HomogeneousSaddlePointProblem(obje Line 1466  class HomogeneousSaddlePointProblem(obje
1466    
1467        def __inner_p(self,p1,p2):        def __inner_p(self,p1,p2):
1468           return self.inner(p1,p2)           return self.inner(p1,p2)
1469          
1470          def __inner_a(self,a1,a2):
1471             return self.inner_a(a1,a2)
1472    
1473          def __inner_a1(self,a1,a2):
1474             return self.inner(a1[1],a2[1])
1475    
1476        def __stoppingcriterium(self,norm_r,r,p):        def __stoppingcriterium(self,norm_r,r,p):
1477            return self.stoppingcriterium(r[1],r[0],p)            return self.stoppingcriterium(r[1],r[0],p)
1478    
1479        def __stoppingcriterium_GMRES(self,norm_r,norm_b):        def __stoppingcriterium2(self,norm_r,norm_b,solver='GMRES',TOL=None):
1480            return self.stoppingcriterium_GMRES(norm_r,norm_b)            return self.stoppingcriterium2(norm_r,norm_b,solver,TOL)
   
       def __stoppingcriterium_MINRES(self,norm_r,norm_Ax):  
           return self.stoppingcriterium_MINRES(norm_r,norm_Ax)  
   
1481    
1482        def setTolerance(self,tolerance=1.e-8):        def setTolerance(self,tolerance=1.e-8):
1483                self.__tol=tolerance                self.__tol=tolerance
# Line 1156  class HomogeneousSaddlePointProblem(obje Line 1488  class HomogeneousSaddlePointProblem(obje
1488        def getSubProblemTolerance(self):        def getSubProblemTolerance(self):
1489                return self.__reduction*self.getTolerance()                return self.__reduction*self.getTolerance()
1490    
1491        def solve(self,v,p,max_iter=20, verbose=False, show_details=False, solver='PCG',iter_restart=10):        def solve(self,v,p,max_iter=20, verbose=False, show_details=False, solver='PCG',iter_restart=20):
1492                """                """
1493                solves the saddle point problem using initial guesses v and p.                solves the saddle point problem using initial guesses v and p.
1494    
# Line 1169  class HomogeneousSaddlePointProblem(obje Line 1501  class HomogeneousSaddlePointProblem(obje
1501                # which leads to BA^-1B^*p = BA^-1f                  # which leads to BA^-1B^*p = BA^-1f  
1502    
1503            # Az=f is solved as A(z-v)=f-Av (z-v = 0 on fixed_u_mask)                  # Az=f is solved as A(z-v)=f-Av (z-v = 0 on fixed_u_mask)      
   
             
1504            self.__z=v+self.solve_A(v,p*0)            self.__z=v+self.solve_A(v,p*0)
1505                  Bz=self.B(self.__z)
               Bz=self.B(self.__z)  
1506                #                #
1507            #   solve BA^-1B^*p = Bz            #   solve BA^-1B^*p = Bz
1508                #                #
               #   note that the residual r=Bz-BA^-1B^*p = B(z-A^-1B^*p) = Bv  
1509                #                #
               #   with                    Av=Az-B^*p = f - B^*p (v=z on fixed_u_mask)  
               #                           A(v-z)=Az-B^*p-Az = f -Az - B^*p (v-z=0 on fixed_u_mask)  
1510                #                #
1511                self.iter=0                self.iter=0
1512            if solver=='GMRES':                  if solver=='GMRES':      
1513                  if self.verbose: print "enter GMRES method (iter_max=%s)"%max_iter                  if self.verbose: print "enter GMRES method (iter_max=%s)"%max_iter
1514                  p=GMRES(Bz,self.__Aprod_GMRES,self.__Msolve_GMRES,self.__inner_p,self.__stoppingcriterium_GMRES,iter_max=max_iter, x=p*1.,iter_restart=iter_restart)                  p=GMRES(Bz,self.__Aprod2,self.__Msolve2,self.__inner_p,self.__stoppingcriterium2,iter_max=max_iter, x=p*1.,iter_restart=iter_restart)
1515                  # solve Au=f-B^*p                  # solve Au=f-B^*p
1516                  #       A(u-v)=f-B^*p-Av                  #       A(u-v)=f-B^*p-Av
1517                  #       u=v+(u-v)                  #       u=v+(u-v)
1518          u=v+self.solve_A(v,p)          u=v+self.solve_A(v,p)
1519    
1520            if solver=='TFQMR':                  if solver=='TFQMR':      
1521                  if self.verbose: print "enter GMRES method (iter_max=%s)"%max_iter                  if self.verbose: print "enter TFQMR method (iter_max=%s)"%max_iter
1522                  p=TFQMR(Bz,self.__Aprod_GMRES,self.__Msolve_GMRES,self.__inner_p,self.__stoppingcriterium_GMRES,iter_max=max_iter, x=p*1.)                  p=TFQMR(Bz,self.__Aprod2,self.__Msolve2,self.__inner_p,self.__stoppingcriterium2,iter_max=max_iter, x=p*1.)
1523                  # solve Au=f-B^*p                  # solve Au=f-B^*p
1524                  #       A(u-v)=f-B^*p-Av                  #       A(u-v)=f-B^*p-Av
1525                  #       u=v+(u-v)                  #       u=v+(u-v)
# Line 1201  class HomogeneousSaddlePointProblem(obje Line 1527  class HomogeneousSaddlePointProblem(obje
1527    
1528            if solver=='MINRES':                  if solver=='MINRES':      
1529                  if self.verbose: print "enter MINRES method (iter_max=%s)"%max_iter                  if self.verbose: print "enter MINRES method (iter_max=%s)"%max_iter
1530                  p=MINRES(Bz,self.__Aprod_GMRES,self.__Msolve_GMRES,self.__inner_p,self.__stoppingcriterium_MINRES,iter_max=max_iter, x=p*1.)                  p=MINRES(Bz,self.__Aprod2,self.__Msolve2,self.__inner_p,self.__stoppingcriterium2,iter_max=max_iter, x=p*1.)
1531                  # solve Au=f-B^*p                  # solve Au=f-B^*p
1532                  #       A(u-v)=f-B^*p-Av                  #       A(u-v)=f-B^*p-Av
1533                  #       u=v+(u-v)                  #       u=v+(u-v)
1534          u=v+self.solve_A(v,p)          u=v+self.solve_A(v,p)
1535                                
1536              if solver=='GMRESC':      
1537                    if self.verbose: print "enter GMRES coupled method (iter_max=%s)"%max_iter
1538                    p0=self.solve_prec1(Bz)
1539                #alfa=(1/self.vol)*util.integrate(util.interpolate(p,escript.Function(self.domain)))
1540                    #p-=alfa
1541                    x=GMRES(ArithmeticTuple(self.__z*1.,p0*1),self.__Anext,self.__Mempty,self.__inner_a,self.__stoppingcriterium2,iter_max=max_iter, x=ArithmeticTuple(v*1,p*1),iter_restart=20)
1542                    #x=NewtonGMRES(ArithmeticTuple(self.__z*1.,p0*1),self.__Aprod_Newton2,self.__Mempty,self.__inner_a,self.__stoppingcriterium2,iter_max=max_iter, x=ArithmeticTuple(v*1,p*1),atol=0,rtol=self.getTolerance())
1543    
1544                    # solve Au=f-B^*p
1545                    #       A(u-v)=f-B^*p-Av
1546                    #       u=v+(u-v)
1547                p=x[1]
1548            u=v+self.solve_A(v,p)      
1549            #p=x[1]
1550            #u=x[0]
1551    
1552                if solver=='PCG':                if solver=='PCG':
1553                    #   note that the residual r=Bz-BA^-1B^*p = B(z-A^-1B^*p) = Bv
1554                    #
1555                    #   with                    Av=Az-B^*p = f - B^*p (v=z on fixed_u_mask)
1556                    #                           A(v-z)= f -Az - B^*p (v-z=0 on fixed_u_mask)
1557                  if self.verbose: print "enter PCG method (iter_max=%s)"%max_iter                  if self.verbose: print "enter PCG method (iter_max=%s)"%max_iter
1558                  p,r=PCG(ArithmeticTuple(self.__z*1.,Bz),self.__Aprod,self.__Msolve,self.__inner,self.__stoppingcriterium,iter_max=max_iter, x=p)                  p,r=PCG(ArithmeticTuple(self.__z*1.,Bz),self.__Aprod,self.__Msolve,self.__inner,self.__stoppingcriterium,iter_max=max_iter, x=p)
1559              u=r[0]                u=r[0]  
1560                    # print "DIFF=",util.integrate(p)
1561    
1562                print "RESULT div(u)=",util.Lsup(self.B(u)),util.Lsup(u)                # print "RESULT div(u)=",util.Lsup(self.B(u)),util.Lsup(u)
1563    
1564            return u,p            return u,p
1565    
1566        def __Msolve(self,r):        def __Msolve(self,r):
1567            return self.solve_prec(r[1])            return self.solve_prec(r[1])
1568    
1569        def __Msolve_GMRES(self,r):        def __Msolve2(self,r):
1570            return self.solve_prec(r)            return self.solve_prec(r*1)
1571    
1572          def __Mempty(self,r):
1573              return r
1574    
1575    
1576        def __Aprod(self,p):        def __Aprod(self,p):
1577            # return BA^-1B*p            # return BA^-1B*p
1578            #solve Av =-B^*p as Av =f-Az-B^*p            #solve Av =B^*p as Av =f-Az-B^*(-p)
1579            v=self.solve_A(self.__z,-p)            v=self.solve_A(self.__z,-p)
1580            return ArithmeticTuple(v, self.B(v))            return ArithmeticTuple(v, self.B(v))
1581    
1582        def __Aprod_GMRES(self,p):        def __Anext(self,x):
1583            # return BA^-1B*p            # return next v,p
1584            #solve Av =-B^*p as Av =f-Az-B^*p            #solve Av =-B^*p as Av =f-Az-B^*p
1585    
1586          pc=x[1]
1587              v=self.solve_A(self.__z,-pc)
1588          p=self.solve_prec1(self.B(v))
1589    
1590              return ArithmeticTuple(v,p)
1591    
1592    
1593          def __Aprod2(self,p):
1594              # return BA^-1B*p
1595              #solve Av =B^*p as Av =f-Az-B^*(-p)
1596        v=self.solve_A(self.__z,-p)        v=self.solve_A(self.__z,-p)
1597            return self.B(v)            return self.B(v)
1598    
1599          def __Aprod_Newton(self,p):
1600              # return BA^-1B*p - Bz
1601              #solve Av =-B^*p as Av =f-Az-B^*p
1602          v=self.solve_A(self.__z,-p)
1603              return self.B(v-self.__z)
1604    
1605          def __Aprod_Newton2(self,x):
1606              # return BA^-1B*p - Bz
1607              #solve Av =-B^*p as Av =f-Az-B^*p
1608              pc=x[1]
1609          v=self.solve_A(self.__z,-pc)
1610              p=self.solve_prec1(self.B(v-self.__z))
1611              return ArithmeticTuple(v,p)
1612    
1613    
1614    def MaskFromBoundaryTag(domain,*tags):
1615       """
1616       create a mask on the Solution(domain) function space which one for samples
1617       that touch the boundary tagged by tags.
1618    
1619       usage: m=MaskFromBoundaryTag(domain,"left", "right")
1620    
1621       @param domain: a given domain
1622       @type domain: L{escript.Domain}
1623       @param tags: boundray tags
1624       @type tags: C{str}
1625       @return: a mask which marks samples that are touching the boundary tagged by any of the given tags.
1626       @rtype: L{escript.Data} of rank 0
1627       """
1628       pde=linearPDEs.LinearPDE(domain,numEquations=1, numSolutions=1)
1629       d=escript.Scalar(0.,escript.FunctionOnBoundary(function_space.getDomain()))
1630       for t in tags: d.setTaggedValue(t,1.)
1631       pde.setValue(y=d)
1632       return util.whereNonZero(pde.getRightHandSide())
1633    #============================================================================================================================================
1634  class SaddlePointProblem(object):  class SaddlePointProblem(object):
1635     """     """
1636     This implements a solver for a saddlepoint problem     This implements a solver for a saddlepoint problem
# Line 1260  class SaddlePointProblem(object): Line 1656  class SaddlePointProblem(object):
1656         @type verbose: C{bool}         @type verbose: C{bool}
1657         @note: this method may be overwritten by a particular saddle point problem         @note: this method may be overwritten by a particular saddle point problem
1658         """         """
1659           print "SaddlePointProblem should not be used anymore!"
1660         if not isinstance(verbose,bool):         if not isinstance(verbose,bool):
1661              raise TypeError("verbose needs to be of type bool.")              raise TypeError("verbose needs to be of type bool.")
1662         self.__verbose=verbose         self.__verbose=verbose
1663         self.relaxation=1.         self.relaxation=1.
1664           DeprecationWarning("SaddlePointProblem should not be used anymore.")
1665    
1666     def trace(self,text):     def trace(self,text):
1667         """         """
# Line 1272  class SaddlePointProblem(object): Line 1670  class SaddlePointProblem(object):
1670         @param text: a text message         @param text: a text message
1671         @type text: C{str}         @type text: C{str}
1672         """         """
1673         if self.__verbose: print "#s: #s"%(str(self),text)         if self.__verbose: print "%s: %s"%(str(self),text)
1674    
1675     def solve_f(self,u,p,tol=1.e-8):     def solve_f(self,u,p,tol=1.e-8):
1676         """         """
# Line 1437  class SaddlePointProblem(object): Line 1835  class SaddlePointProblem(object):
1835              f, norm_f, u, norm_u, g, norm_g, p, norm_p = f_new, norm_f_new, u_new, norm_u_new, g_new, norm_g_new, p_new, norm_p_new              f, norm_f, u, norm_u, g, norm_g, p, norm_p = f_new, norm_f_new, u_new, norm_u_new, g_new, norm_g_new, p_new, norm_p_new
1836          self.trace("convergence after %s steps."%self.iter)          self.trace("convergence after %s steps."%self.iter)
1837          return u,p          return u,p
 #   def solve(self,u0,p0,tolerance=1.e-6,iter_max=10,self.relaxation=1.):  
 #      tol=1.e-2  
 #      iter=0  
 #      converged=False  
 #      u=u0*1.  
 #      p=p0*1.  
 #      while not converged and iter<iter_max:  
 #          du=self.solve_f(u,p,tol)  
 #          u-=du  
 #          norm_du=util.Lsup(du)  
 #          norm_u=util.Lsup(u)  
 #          
 #          dp=self.relaxation*self.solve_g(u,tol)  
 #          p+=dp  
 #          norm_dp=util.sqrt(self.inner(dp,dp))  
 #          norm_p=util.sqrt(self.inner(p,p))  
 #          print iter,"-th step rel. errror u,p= (%s,%s) (%s,%s)(%s,%s)"%(norm_du,norm_dp,norm_du/norm_u,norm_dp/norm_p,norm_u,norm_p)  
 #          iter+=1  
 #  
 #          converged = (norm_du <= tolerance*norm_u) and  (norm_dp <= tolerance*norm_p)  
 #      if converged:  
 #          print "convergence after %s steps."%iter  
 #      else:  
 #          raise ArithmeticError("no convergence after %s steps."%iter)  
 #  
 #      return u,p  
             
 def MaskFromBoundaryTag(function_space,*tags):  
    """  
    create a mask on the given function space which one for samples  
    that touch the boundary tagged by tags.  
   
    usage: m=MaskFromBoundaryTag(Solution(domain),"left", "right")  
   
    @param function_space: a given function space  
    @type function_space: L{escript.FunctionSpace}  
    @param tags: boundray tags  
    @type tags: C{str}  
    @return: a mask which marks samples used by C{function_space} that are touching the  
             boundary tagged by any of the given tags.  
    @rtype: L{escript.Data} of rank 0  
    """  
    pde=linearPDEs.LinearPDE(function_space.getDomain(),numEquations=1, numSolutions=1)  
    d=escript.Scalar(0.,escript.FunctionOnBoundary(function_space.getDomain()))  
    for t in tags: d.setTaggedValue(t,1.)  
    pde.setValue(y=d)  
    out=util.whereNonZero(pde.getRightHandSide())  
    if out.getFunctionSpace() == function_space:  
       return out  
    else:  
       return util.whereNonZero(util.interpolate(out,function_space))  
   
   
   

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