/[escript]/trunk/escript/py_src/pdetools.py
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revision 2548 by jfenwick, Mon Jul 20 06:20:06 2009 UTC revision 2850 by gross, Fri Jan 15 07:14:25 2010 UTC
# Line 11  Line 11 
11  #  #
12  ########################################################  ########################################################
13    
14  __copyright__="""Copyright (c) 2003-2008 by University of Queensland  __copyright__="""Copyright (c) 2003-2009 by University of Queensland
15  Earth Systems Science Computational Center (ESSCC)  Earth Systems Science Computational Center (ESSCC)
16  http://www.uq.edu.au/esscc  http://www.uq.edu.au/esscc
17  Primary Business: Queensland, Australia"""  Primary Business: Queensland, Australia"""
# Line 28  Currently includes: Line 28  Currently includes:
28      - TimeIntegrationManager - to handle extrapolation in time      - TimeIntegrationManager - to handle extrapolation in time
29      - SaddlePointProblem - solver for Saddle point problems using the inexact uszawa scheme      - SaddlePointProblem - solver for Saddle point problems using the inexact uszawa scheme
30    
31  @var __author__: name of author  :var __author__: name of author
32  @var __copyright__: copyrights  :var __copyright__: copyrights
33  @var __license__: licence agreement  :var __license__: licence agreement
34  @var __url__: url entry point on documentation  :var __url__: url entry point on documentation
35  @var __version__: version  :var __version__: version
36  @var __date__: date of the version  :var __date__: date of the version
37  """  """
38    
39  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
# Line 45  import numpy Line 45  import numpy
45  import util  import util
46  import math  import math
47    
 ##### Added by Artak  
 # from Numeric import zeros,Int,Float64  
 ###################################  
   
   
48  class TimeIntegrationManager:  class TimeIntegrationManager:
49    """    """
50    A simple mechanism to manage time dependend values.    A simple mechanism to manage time dependend values.
# Line 64  class TimeIntegrationManager: Line 59  class TimeIntegrationManager:
59           tm.checkin(dt,v)           tm.checkin(dt,v)
60           t+=dt           t+=dt
61    
62    @note: currently only p=1 is supported.    :note: currently only p=1 is supported.
63    """    """
64    def __init__(self,*inital_values,**kwargs):    def __init__(self,*inital_values,**kwargs):
65       """       """
66       Sets up the value manager where C{inital_values} are the initial values       Sets up the value manager where ``inital_values`` are the initial values
67       and p is the order used for extrapolation.       and p is the order used for extrapolation.
68       """       """
69       if kwargs.has_key("p"):       if kwargs.has_key("p"):
# Line 113  class TimeIntegrationManager: Line 108  class TimeIntegrationManager:
108    
109    def extrapolate(self,dt):    def extrapolate(self,dt):
110        """        """
111        Extrapolates to C{dt} forward in time.        Extrapolates to ``dt`` forward in time.
112        """        """
113        if self.__order==0:        if self.__order==0:
114           out=self.__v_mem[0]           out=self.__v_mem[0]
# Line 139  class Projector: Line 134  class Projector:
134      """      """
135      Creates a continuous function space projector for a domain.      Creates a continuous function space projector for a domain.
136    
137      @param domain: Domain of the projection.      :param domain: Domain of the projection.
138      @param reduce: Flag to reduce projection order      :param reduce: Flag to reduce projection order
139      @param fast: Flag to use a fast method based on matrix lumping      :param fast: Flag to use a fast method based on matrix lumping
140      """      """
141      self.__pde = linearPDEs.LinearPDE(domain)      self.__pde = linearPDEs.LinearPDE(domain)
142      if fast:      if fast:
# Line 151  class Projector: Line 146  class Projector:
146      self.__pde.setValue(D = 1.)      self.__pde.setValue(D = 1.)
147      return      return
148    def getSolverOptions(self):    def getSolverOptions(self):
149      """      """
150      Returns the solver options of the PDE solver.      Returns the solver options of the PDE solver.
151            
152      @rtype: L{linearPDEs.SolverOptions}      :rtype: `linearPDEs.SolverOptions`
153      """      """
154        return self.__pde.getSolverOptions()
155    
156    def __call__(self, input_data):    def __call__(self, input_data):
157      """      """
158      Projects C{input_data} onto a continuous function.      Projects ``input_data`` onto a continuous function.
159    
160      @param input_data: the data to be projected      :param input_data: the data to be projected
161      """      """
162      out=escript.Data(0.,input_data.getShape(),self.__pde.getFunctionSpaceForSolution())      out=escript.Data(0.,input_data.getShape(),self.__pde.getFunctionSpaceForSolution())
163      self.__pde.setValue(Y = escript.Data(), Y_reduced = escript.Data())      self.__pde.setValue(Y = escript.Data(), Y_reduced = escript.Data())
# Line 196  class NoPDE: Line 192  class NoPDE:
192       """       """
193       Solves the following problem for u:       Solves the following problem for u:
194    
195       M{kronecker[i,j]*D[j]*u[j]=Y[i]}       *kronecker[i,j]*D[j]*u[j]=Y[i]*
196    
197       with constraint       with constraint
198    
199       M{u[j]=r[j]}  where M{q[j]>0}       *u[j]=r[j]*  where *q[j]>0*
200    
201       where M{D}, M{Y}, M{r} and M{q} are given functions of rank 1.       where *D*, *Y*, *r* and *q* are given functions of rank 1.
202    
203       In the case of scalars this takes the form       In the case of scalars this takes the form
204    
205       M{D*u=Y}       *D*u=Y*
206    
207       with constraint       with constraint
208    
209       M{u=r} where M{q>0}       *u=r* where *q>0*
210    
211       where M{D}, M{Y}, M{r} and M{q} are given scalar functions.       where *D*, *Y*, *r* and *q* are given scalar functions.
212    
213       The constraint overwrites any other condition.       The constraint overwrites any other condition.
214    
215       @note: This class is similar to the L{linearPDEs.LinearPDE} class with       :note: This class is similar to the `linearPDEs.LinearPDE` class with
216              A=B=C=X=0 but has the intention that all input parameters are given              A=B=C=X=0 but has the intention that all input parameters are given
217              in L{Solution} or L{ReducedSolution}.              in `Solution` or `ReducedSolution`.
218       """       """
219       # The whole thing is a bit strange and I blame Rob Woodcock (CSIRO) for       # The whole thing is a bit strange and I blame Rob Woodcock (CSIRO) for
220       # this.       # this.
# Line 226  class NoPDE: Line 222  class NoPDE:
222           """           """
223           Initializes the problem.           Initializes the problem.
224    
225           @param domain: domain of the PDE           :param domain: domain of the PDE
226           @type domain: L{Domain}           :type domain: `Domain`
227           @param D: coefficient of the solution           :param D: coefficient of the solution
228           @type D: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type D: ``float``, ``int``, ``numpy.ndarray``, `Data`
229           @param Y: right hand side           :param Y: right hand side
230           @type Y: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type Y: ``float``, ``int``, ``numpy.ndarray``, `Data`
231           @param q: location of constraints           :param q: location of constraints
232           @type q: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type q: ``float``, ``int``, ``numpy.ndarray``, `Data`
233           @param r: value of solution at locations of constraints           :param r: value of solution at locations of constraints
234           @type r: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type r: ``float``, ``int``, ``numpy.ndarray``, `Data`
235           """           """
236           self.__domain=domain           self.__domain=domain
237           self.__D=D           self.__D=D
# Line 247  class NoPDE: Line 243  class NoPDE:
243    
244       def setReducedOn(self):       def setReducedOn(self):
245           """           """
246           Sets the L{FunctionSpace} of the solution to L{ReducedSolution}.           Sets the `FunctionSpace` of the solution to `ReducedSolution`.
247           """           """
248           self.__function_space=escript.ReducedSolution(self.__domain)           self.__function_space=escript.ReducedSolution(self.__domain)
249           self.__u=None           self.__u=None
250    
251       def setReducedOff(self):       def setReducedOff(self):
252           """           """
253           Sets the L{FunctionSpace} of the solution to L{Solution}.           Sets the `FunctionSpace` of the solution to `Solution`.
254           """           """
255           self.__function_space=escript.Solution(self.__domain)           self.__function_space=escript.Solution(self.__domain)
256           self.__u=None           self.__u=None
# Line 263  class NoPDE: Line 259  class NoPDE:
259           """           """
260           Assigns values to the parameters.           Assigns values to the parameters.
261    
262           @param D: coefficient of the solution           :param D: coefficient of the solution
263           @type D: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type D: ``float``, ``int``, ``numpy.ndarray``, `Data`
264           @param Y: right hand side           :param Y: right hand side
265           @type Y: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type Y: ``float``, ``int``, ``numpy.ndarray``, `Data`
266           @param q: location of constraints           :param q: location of constraints
267           @type q: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type q: ``float``, ``int``, ``numpy.ndarray``, `Data`
268           @param r: value of solution at locations of constraints           :param r: value of solution at locations of constraints
269           @type r: C{float}, C{int}, C{numpy.ndarray}, L{Data}           :type r: ``float``, ``int``, ``numpy.ndarray``, `Data`
270           """           """
271           if not D==None:           if not D==None:
272              self.__D=D              self.__D=D
# Line 289  class NoPDE: Line 285  class NoPDE:
285           """           """
286           Returns the solution.           Returns the solution.
287    
288           @return: the solution of the problem           :return: the solution of the problem
289           @rtype: L{Data} object in the L{FunctionSpace} L{Solution} or           :rtype: `Data` object in the `FunctionSpace` `Solution` or
290                   L{ReducedSolution}                   `ReducedSolution`
291           """           """
292           if self.__u==None:           if self.__u==None:
293              if self.__D==None:              if self.__D==None:
# Line 324  class Locator: Line 320  class Locator:
320         or FunctionSpace for the sample point which is closest to the given         or FunctionSpace for the sample point which is closest to the given
321         point x.         point x.
322    
323         @param where: function space         :param where: function space
324         @type where: L{escript.FunctionSpace}         :type where: `escript.FunctionSpace`
325         @param x: location(s) of the Locator         :param x: location(s) of the Locator
326         @type x: C{numpy.ndarray} or C{list} of C{numpy.ndarray}         :type x: ``numpy.ndarray`` or ``list`` of ``numpy.ndarray``
327         """         """
328         if isinstance(where,escript.FunctionSpace):         if isinstance(where,escript.FunctionSpace):
329            self.__function_space=where            self.__function_space=where
# Line 354  class Locator: Line 350  class Locator:
350         Returns the coordinates of the Locator as a string.         Returns the coordinates of the Locator as a string.
351         """         """
352         x=self.getX()         x=self.getX()
353         if instance(x,list):         if isinstance(x,list):
354            out="["            out="["
355            first=True            first=True
356            for xx in x:            for xx in x:
# Line 401  class Locator: Line 397  class Locator:
397    
398       def getValue(self,data):       def getValue(self,data):
399          """          """
400          Returns the value of C{data} at the Locator if C{data} is a L{Data}          Returns the value of ``data`` at the Locator if ``data`` is a `Data`
401          object otherwise the object is returned.          object otherwise the object is returned.
402          """          """
403          if isinstance(data,escript.Data):          if isinstance(data,escript.Data):
# Line 426  class Locator: Line 422  class Locator:
422          else:          else:
423             return data             return data
424    
425    
426    def getInfLocator(arg):
427        """
428        Return a Locator for a point with the inf value over all arg.
429        """
430        if not isinstance(arg, escript.Data):
431        raise TypeError,"getInfLocator: Unknown argument type."
432        a_inf=util.inf(arg)
433        loc=util.length(arg-a_inf).minGlobalDataPoint() # This gives us the location but not coords
434        x=arg.getFunctionSpace().getX()
435        x_min=x.getTupleForGlobalDataPoint(*loc)
436        return Locator(arg.getFunctionSpace(),x_min)
437    
438    def getSupLocator(arg):
439        """
440        Return a Locator for a point with the sup value over all arg.
441        """
442        if not isinstance(arg, escript.Data):
443        raise TypeError,"getInfLocator: Unknown argument type."
444        a_inf=util.sup(arg)
445        loc=util.length(arg-a_inf).minGlobalDataPoint() # This gives us the location but not coords
446        x=arg.getFunctionSpace().getX()
447        x_min=x.getTupleForGlobalDataPoint(*loc)
448        return Locator(arg.getFunctionSpace(),x_min)
449        
450    
451  class SolverSchemeException(Exception):  class SolverSchemeException(Exception):
452     """     """
453     This is a generic exception thrown by solvers.     This is a generic exception thrown by solvers.
# Line 467  def PCG(r, Aprod, x, Msolve, bilinearfor Line 489  def PCG(r, Aprod, x, Msolve, bilinearfor
489     """     """
490     Solver for     Solver for
491    
492     M{Ax=b}     *Ax=b*
493    
494     with a symmetric and positive definite operator A (more details required!).     with a symmetric and positive definite operator A (more details required!).
495     It uses the conjugate gradient method with preconditioner M providing an     It uses the conjugate gradient method with preconditioner M providing an
# Line 475  def PCG(r, Aprod, x, Msolve, bilinearfor Line 497  def PCG(r, Aprod, x, Msolve, bilinearfor
497    
498     The iteration is terminated if     The iteration is terminated if
499    
500     M{|r| <= atol+rtol*|r0|}     *|r| <= atol+rtol*|r0|*
501    
502     where M{r0} is the initial residual and M{|.|} is the energy norm. In fact     where *r0* is the initial residual and *|.|* is the energy norm. In fact
503    
504     M{|r| = sqrt( bilinearform(Msolve(r),r))}     *|r| = sqrt( bilinearform(Msolve(r),r))*
505    
506     For details on the preconditioned conjugate gradient method see the book:     For details on the preconditioned conjugate gradient method see the book:
507    
# Line 487  def PCG(r, Aprod, x, Msolve, bilinearfor Line 509  def PCG(r, Aprod, x, Msolve, bilinearfor
509     T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo,     T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo,
510     C. Romine, and H. van der Vorst}.     C. Romine, and H. van der Vorst}.
511    
512     @param r: initial residual M{r=b-Ax}. C{r} is altered.     :param r: initial residual *r=b-Ax*. ``r`` is altered.
513     @type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)     :type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)
514     @param x: an initial guess for the solution     :param x: an initial guess for the solution
515     @type x: any object supporting inplace add (x+=y) and scaling (x=scalar*y)     :type x: any object supporting inplace add (x+=y) and scaling (x=scalar*y)
516     @param Aprod: returns the value Ax     :param Aprod: returns the value Ax
517     @type Aprod: function C{Aprod(x)} where C{x} is of the same object like     :type Aprod: function ``Aprod(x)`` where ``x`` is of the same object like
518                  argument C{x}. The returned object needs to be of the same type                  argument ``x``. The returned object needs to be of the same type
519                  like argument C{r}.                  like argument ``r``.
520     @param Msolve: solves Mx=r     :param Msolve: solves Mx=r
521     @type Msolve: function C{Msolve(r)} where C{r} is of the same type like     :type Msolve: function ``Msolve(r)`` where ``r`` is of the same type like
522                   argument C{r}. The returned object needs to be of the same                   argument ``r``. The returned object needs to be of the same
523                   type like argument C{x}.                   type like argument ``x``.
524     @param bilinearform: inner product C{<x,r>}     :param bilinearform: inner product ``<x,r>``
525     @type bilinearform: function C{bilinearform(x,r)} where C{x} is of the same     :type bilinearform: function ``bilinearform(x,r)`` where ``x`` is of the same
526                         type like argument C{x} and C{r} is. The returned value                         type like argument ``x`` and ``r`` is. The returned value
527                         is a C{float}.                         is a ``float``.
528     @param atol: absolute tolerance     :param atol: absolute tolerance
529     @type atol: non-negative C{float}     :type atol: non-negative ``float``
530     @param rtol: relative tolerance     :param rtol: relative tolerance
531     @type rtol: non-negative C{float}     :type rtol: non-negative ``float``
532     @param iter_max: maximum number of iteration steps     :param iter_max: maximum number of iteration steps
533     @type iter_max: C{int}     :type iter_max: ``int``
534     @return: the solution approximation and the corresponding residual     :return: the solution approximation and the corresponding residual
535     @rtype: C{tuple}     :rtype: ``tuple``
536     @warning: C{r} and C{x} are altered.     :warning: ``r`` and ``x`` are altered.
537     """     """
538     iter=0     iter=0
539     rhat=Msolve(r)     rhat=Msolve(r)
# Line 564  class Defect(object): Line 586  class Defect(object):
586          """          """
587          Returns the inner product of x0 and x1          Returns the inner product of x0 and x1
588    
589          @param x0: value for x0          :param x0: value for x0
590          @param x1: value for x1          :param x1: value for x1
591          @return: the inner product of x0 and x1          :return: the inner product of x0 and x1
592          @rtype: C{float}          :rtype: ``float``
593          """          """
594          return 0          return 0
595    
596      def norm(self,x):      def norm(self,x):
597          """          """
598          Returns the norm of argument C{x}.          Returns the norm of argument ``x``.
599    
600          @param x: a value          :param x: a value
601          @return: norm of argument x          :return: norm of argument x
602          @rtype: C{float}          :rtype: ``float``
603          @note: by default C{sqrt(self.bilinearform(x,x)} is returned.          :note: by default ``sqrt(self.bilinearform(x,x)`` is returned.
604          """          """
605          s=self.bilinearform(x,x)          s=self.bilinearform(x,x)
606          if s<0: raise NegativeNorm,"negative norm."          if s<0: raise NegativeNorm,"negative norm."
# Line 586  class Defect(object): Line 608  class Defect(object):
608    
609      def eval(self,x):      def eval(self,x):
610          """          """
611          Returns the value F of a given C{x}.          Returns the value F of a given ``x``.
612    
613          @param x: value for which the defect C{F} is evaluated          :param x: value for which the defect ``F`` is evaluated
614          @return: value of the defect at C{x}          :return: value of the defect at ``x``
615          """          """
616          return 0          return 0
617    
618      def __call__(self,x):      def __call__(self,x):
619          return self.eval(x)          return self.eval(x)
620    
621      def setDerivativeIncrementLength(self,inc=math.sqrt(util.EPSILON)):      def setDerivativeIncrementLength(self,inc=1000.*math.sqrt(util.EPSILON)):
622          """          """
623          Sets the relative length of the increment used to approximate the          Sets the relative length of the increment used to approximate the
624          derivative of the defect. The increment is inc*norm(x)/norm(v)*v in the          derivative of the defect. The increment is inc*norm(x)/norm(v)*v in the
625          direction of v with x as a starting point.          direction of v with x as a starting point.
626    
627          @param inc: relative increment length          :param inc: relative increment length
628          @type inc: positive C{float}          :type inc: positive ``float``
629          """          """
630          if inc<=0: raise ValueError,"positive increment required."          if inc<=0: raise ValueError,"positive increment required."
631          self.__inc=inc          self.__inc=inc
# Line 612  class Defect(object): Line 634  class Defect(object):
634          """          """
635          Returns the relative increment length used to approximate the          Returns the relative increment length used to approximate the
636          derivative of the defect.          derivative of the defect.
637          @return: value of the defect at C{x}          :return: value of the defect at ``x``
638          @rtype: positive C{float}          :rtype: positive ``float``
639          """          """
640          return self.__inc          return self.__inc
641    
642      def derivative(self, F0, x0, v, v_is_normalised=True):      def derivative(self, F0, x0, v, v_is_normalised=True):
643          """          """
644          Returns the directional derivative at C{x0} in the direction of C{v}.          Returns the directional derivative at ``x0`` in the direction of ``v``.
645    
646          @param F0: value of this defect at x0          :param F0: value of this defect at x0
647          @param x0: value at which derivative is calculated          :param x0: value at which derivative is calculated
648          @param v: direction          :param v: direction
649          @param v_is_normalised: True to indicate that C{v} is nomalized          :param v_is_normalised: True to indicate that ``v`` is nomalized
650                                  (self.norm(v)=0)                                  (self.norm(v)=0)
651          @return: derivative of this defect at x0 in the direction of C{v}          :return: derivative of this defect at x0 in the direction of ``v``
652          @note: by default numerical evaluation (self.eval(x0+eps*v)-F0)/eps is          :note: by default numerical evaluation (self.eval(x0+eps*v)-F0)/eps is
653                 used but this method maybe overwritten to use exact evaluation.                 used but this method maybe overwritten to use exact evaluation.
654          """          """
655          normx=self.norm(x0)          normx=self.norm(x0)
# Line 645  class Defect(object): Line 667  class Defect(object):
667          return (F1-F0)/epsnew          return (F1-F0)/epsnew
668    
669  ######################################  ######################################
670  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):  def NewtonGMRES(defect, x, iter_max=100, sub_iter_max=20, atol=0,rtol=1.e-4, subtol_max=0.5, gamma=0.9, verbose=False):
671     """     """
672     Solves a non-linear problem M{F(x)=0} for unknown M{x} using the stopping     Solves a non-linear problem *F(x)=0* for unknown *x* using the stopping
673     criterion:     criterion:
674    
675     M{norm(F(x) <= atol + rtol * norm(F(x0)}     *norm(F(x) <= atol + rtol * norm(F(x0)*
676    
677     where M{x0} is the initial guess.     where *x0* is the initial guess.
678    
679     @param defect: object defining the function M{F}. C{defect.norm} defines the     :param defect: object defining the function *F*. ``defect.norm`` defines the
680                    M{norm} used in the stopping criterion.                    *norm* used in the stopping criterion.
681     @type defect: L{Defect}     :type defect: `Defect`
682     @param x: initial guess for the solution, C{x} is altered.     :param x: initial guess for the solution, ``x`` is altered.
683     @type x: any object type allowing basic operations such as     :type x: any object type allowing basic operations such as
684              C{numpy.ndarray}, L{Data}              ``numpy.ndarray``, `Data`
685     @param iter_max: maximum number of iteration steps     :param iter_max: maximum number of iteration steps
686     @type iter_max: positive C{int}     :type iter_max: positive ``int``
687     @param sub_iter_max: maximum number of inner iteration steps     :param sub_iter_max: maximum number of inner iteration steps
688     @type sub_iter_max: positive C{int}     :type sub_iter_max: positive ``int``
689     @param atol: absolute tolerance for the solution     :param atol: absolute tolerance for the solution
690     @type atol: positive C{float}     :type atol: positive ``float``
691     @param rtol: relative tolerance for the solution     :param rtol: relative tolerance for the solution
692     @type rtol: positive C{float}     :type rtol: positive ``float``
693     @param gamma: tolerance safety factor for inner iteration     :param gamma: tolerance safety factor for inner iteration
694     @type gamma: positive C{float}, less than 1     :type gamma: positive ``float``, less than 1
695     @param sub_tol_max: upper bound for inner tolerance     :param subtol_max: upper bound for inner tolerance
696     @type sub_tol_max: positive C{float}, less than 1     :type subtol_max: positive ``float``, less than 1
697     @return: an approximation of the solution with the desired accuracy     :return: an approximation of the solution with the desired accuracy
698     @rtype: same type as the initial guess     :rtype: same type as the initial guess
699     """     """
700     lmaxit=iter_max     lmaxit=iter_max
701     if atol<0: raise ValueError,"atol needs to be non-negative."     if atol<0: raise ValueError,"atol needs to be non-negative."
702     if rtol<0: raise ValueError,"rtol needs to be non-negative."     if rtol<0: raise ValueError,"rtol needs to be non-negative."
703     if rtol+atol<=0: raise ValueError,"rtol or atol needs to be non-negative."     if rtol+atol<=0: raise ValueError,"rtol or atol needs to be non-negative."
704     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     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
705     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     if subtol_max<=0 or subtol_max>=1: raise ValueError,"upper bound for inner tolerance for inner iteration (subtol_max =%s) needs to be positive and less than 1."%subtol_max
706    
707     F=defect(x)     F=defect(x)
708     fnrm=defect.norm(F)     fnrm=defect.norm(F)
709     stop_tol=atol + rtol*fnrm     stop_tol=atol + rtol*fnrm
710     sub_tol=sub_tol_max     subtol=subtol_max
711     if verbose: print "NewtonGMRES: initial residual = %e."%fnrm     if verbose: print "NewtonGMRES: initial residual = %e."%fnrm
712     if verbose: print "             tolerance = %e."%sub_tol     if verbose: print "             tolerance = %e."%subtol
713     iter=1     iter=1
714     #     #
715     # main iteration loop     # main iteration loop
# Line 695  def NewtonGMRES(defect, x, iter_max=100, Line 717  def NewtonGMRES(defect, x, iter_max=100,
717     while not fnrm<=stop_tol:     while not fnrm<=stop_tol:
718              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
719              #              #
720          #   adjust sub_tol_          #   adjust subtol_
721          #          #
722              if iter > 1:              if iter > 1:
723             rat=fnrm/fnrmo             rat=fnrm/fnrmo
724                 sub_tol_old=sub_tol                 subtol_old=subtol
725             sub_tol=gamma*rat**2             subtol=gamma*rat**2
726             if gamma*sub_tol_old**2 > .1: sub_tol=max(sub_tol,gamma*sub_tol_old**2)             if gamma*subtol_old**2 > .1: subtol=max(subtol,gamma*subtol_old**2)
727             sub_tol=max(min(sub_tol,sub_tol_max), .5*stop_tol/fnrm)             subtol=max(min(subtol,subtol_max), .5*stop_tol/fnrm)
728          #          #
729          # calculate newton increment xc          # calculate newton increment xc
730              #     if iter_max in __FDGMRES is reached MaxIterReached is thrown              #     if iter_max in __FDGMRES is reached MaxIterReached is thrown
# Line 710  def NewtonGMRES(defect, x, iter_max=100, Line 732  def NewtonGMRES(defect, x, iter_max=100,
732              #     if  atol is reached sub_iter returns the numer of steps performed to get there              #     if  atol is reached sub_iter returns the numer of steps performed to get there
733              #              #
734              #              #
735              if verbose: print "             subiteration (GMRES) is called with relative tolerance %e."%sub_tol              if verbose: print "             subiteration (GMRES) is called with relative tolerance %e."%subtol
736              try:              try:
737                 xc, sub_iter=__FDGMRES(F, defect, x, sub_tol*fnrm, iter_max=iter_max-iter, iter_restart=sub_iter_max)                 xc, sub_iter=__FDGMRES(F, defect, x, subtol*fnrm, iter_max=iter_max-iter, iter_restart=sub_iter_max)
738              except MaxIterReached:              except MaxIterReached:
739                 raise MaxIterReached,"maximum number of %s steps reached."%iter_max                 raise MaxIterReached,"maximum number of %s steps reached."%iter_max
740              if sub_iter<0:              if sub_iter<0:
# Line 731  def NewtonGMRES(defect, x, iter_max=100, Line 753  def NewtonGMRES(defect, x, iter_max=100,
753  def __givapp(c,s,vin):  def __givapp(c,s,vin):
754      """      """
755      Applies a sequence of Givens rotations (c,s) recursively to the vector      Applies a sequence of Givens rotations (c,s) recursively to the vector
756      C{vin}      ``vin``
757    
758      @warning: C{vin} is altered.      :warning: ``vin`` is altered.
759      """      """
760      vrot=vin      vrot=vin
761      if isinstance(c,float):      if isinstance(c,float):
# Line 838  def GMRES(r, Aprod, x, bilinearform, ato Line 860  def GMRES(r, Aprod, x, bilinearform, ato
860     """     """
861     Solver for     Solver for
862    
863     M{Ax=b}     *Ax=b*
864    
865     with a general operator A (more details required!).     with a general operator A (more details required!).
866     It uses the generalized minimum residual method (GMRES).     It uses the generalized minimum residual method (GMRES).
867    
868     The iteration is terminated if     The iteration is terminated if
869    
870     M{|r| <= atol+rtol*|r0|}     *|r| <= atol+rtol*|r0|*
871    
872     where M{r0} is the initial residual and M{|.|} is the energy norm. In fact     where *r0* is the initial residual and *|.|* is the energy norm. In fact
873    
874     M{|r| = sqrt( bilinearform(r,r))}     *|r| = sqrt( bilinearform(r,r))*
875    
876     @param r: initial residual M{r=b-Ax}. C{r} is altered.     :param r: initial residual *r=b-Ax*. ``r`` is altered.
877     @type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)     :type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)
878     @param x: an initial guess for the solution     :param x: an initial guess for the solution
879     @type x: same like C{r}     :type x: same like ``r``
880     @param Aprod: returns the value Ax     :param Aprod: returns the value Ax
881     @type Aprod: function C{Aprod(x)} where C{x} is of the same object like     :type Aprod: function ``Aprod(x)`` where ``x`` is of the same object like
882                  argument C{x}. The returned object needs to be of the same                  argument ``x``. The returned object needs to be of the same
883                  type like argument C{r}.                  type like argument ``r``.
884     @param bilinearform: inner product C{<x,r>}     :param bilinearform: inner product ``<x,r>``
885     @type bilinearform: function C{bilinearform(x,r)} where C{x} is of the same     :type bilinearform: function ``bilinearform(x,r)`` where ``x`` is of the same
886                         type like argument C{x} and C{r}. The returned value is                         type like argument ``x`` and ``r``. The returned value is
887                         a C{float}.                         a ``float``.
888     @param atol: absolute tolerance     :param atol: absolute tolerance
889     @type atol: non-negative C{float}     :type atol: non-negative ``float``
890     @param rtol: relative tolerance     :param rtol: relative tolerance
891     @type rtol: non-negative C{float}     :type rtol: non-negative ``float``
892     @param iter_max: maximum number of iteration steps     :param iter_max: maximum number of iteration steps
893     @type iter_max: C{int}     :type iter_max: ``int``
894     @param iter_restart: in order to save memory the orthogonalization process     :param iter_restart: in order to save memory the orthogonalization process
895                          is terminated after C{iter_restart} steps and the                          is terminated after ``iter_restart`` steps and the
896                          iteration is restarted.                          iteration is restarted.
897     @type iter_restart: C{int}     :type iter_restart: ``int``
898     @return: the solution approximation and the corresponding residual     :return: the solution approximation and the corresponding residual
899     @rtype: C{tuple}     :rtype: ``tuple``
900     @warning: C{r} and C{x} are altered.     :warning: ``r`` and ``x`` are altered.
901     """     """
902     m=iter_restart     m=iter_restart
903     restarted=False     restarted=False
# Line 1007  def MINRES(r, Aprod, x, Msolve, bilinear Line 1029  def MINRES(r, Aprod, x, Msolve, bilinear
1029      """      """
1030      Solver for      Solver for
1031    
1032      M{Ax=b}      *Ax=b*
1033    
1034      with a symmetric and positive definite operator A (more details required!).      with a symmetric and positive definite operator A (more details required!).
1035      It uses the minimum residual method (MINRES) with preconditioner M      It uses the minimum residual method (MINRES) with preconditioner M
# Line 1015  def MINRES(r, Aprod, x, Msolve, bilinear Line 1037  def MINRES(r, Aprod, x, Msolve, bilinear
1037    
1038      The iteration is terminated if      The iteration is terminated if
1039    
1040      M{|r| <= atol+rtol*|r0|}      *|r| <= atol+rtol*|r0|*
1041    
1042      where M{r0} is the initial residual and M{|.|} is the energy norm. In fact      where *r0* is the initial residual and *|.|* is the energy norm. In fact
1043    
1044      M{|r| = sqrt( bilinearform(Msolve(r),r))}      *|r| = sqrt( bilinearform(Msolve(r),r))*
1045    
1046      For details on the preconditioned conjugate gradient method see the book:      For details on the preconditioned conjugate gradient method see the book:
1047    
# Line 1027  def MINRES(r, Aprod, x, Msolve, bilinear Line 1049  def MINRES(r, Aprod, x, Msolve, bilinear
1049      T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo,      T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo,
1050      C. Romine, and H. van der Vorst}.      C. Romine, and H. van der Vorst}.
1051    
1052      @param r: initial residual M{r=b-Ax}. C{r} is altered.      :param r: initial residual *r=b-Ax*. ``r`` is altered.
1053      @type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)      :type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)
1054      @param x: an initial guess for the solution      :param x: an initial guess for the solution
1055      @type x: any object supporting inplace add (x+=y) and scaling (x=scalar*y)      :type x: any object supporting inplace add (x+=y) and scaling (x=scalar*y)
1056      @param Aprod: returns the value Ax      :param Aprod: returns the value Ax
1057      @type Aprod: function C{Aprod(x)} where C{x} is of the same object like      :type Aprod: function ``Aprod(x)`` where ``x`` is of the same object like
1058                   argument C{x}. The returned object needs to be of the same                   argument ``x``. The returned object needs to be of the same
1059                   type like argument C{r}.                   type like argument ``r``.
1060      @param Msolve: solves Mx=r      :param Msolve: solves Mx=r
1061      @type Msolve: function C{Msolve(r)} where C{r} is of the same type like      :type Msolve: function ``Msolve(r)`` where ``r`` is of the same type like
1062                    argument C{r}. The returned object needs to be of the same                    argument ``r``. The returned object needs to be of the same
1063                    type like argument C{x}.                    type like argument ``x``.
1064      @param bilinearform: inner product C{<x,r>}      :param bilinearform: inner product ``<x,r>``
1065      @type bilinearform: function C{bilinearform(x,r)} where C{x} is of the same      :type bilinearform: function ``bilinearform(x,r)`` where ``x`` is of the same
1066                          type like argument C{x} and C{r} is. The returned value                          type like argument ``x`` and ``r`` is. The returned value
1067                          is a C{float}.                          is a ``float``.
1068      @param atol: absolute tolerance      :param atol: absolute tolerance
1069      @type atol: non-negative C{float}      :type atol: non-negative ``float``
1070      @param rtol: relative tolerance      :param rtol: relative tolerance
1071      @type rtol: non-negative C{float}      :type rtol: non-negative ``float``
1072      @param iter_max: maximum number of iteration steps      :param iter_max: maximum number of iteration steps
1073      @type iter_max: C{int}      :type iter_max: ``int``
1074      @return: the solution approximation and the corresponding residual      :return: the solution approximation and the corresponding residual
1075      @rtype: C{tuple}      :rtype: ``tuple``
1076      @warning: C{r} and C{x} are altered.      :warning: ``r`` and ``x`` are altered.
1077      """      """
1078      #------------------------------------------------------------------      #------------------------------------------------------------------
1079      # Set up y and v for the first Lanczos vector v1.      # Set up y and v for the first Lanczos vector v1.
# Line 1185  def TFQMR(r, Aprod, x, bilinearform, ato Line 1207  def TFQMR(r, Aprod, x, bilinearform, ato
1207    """    """
1208    Solver for    Solver for
1209    
1210    M{Ax=b}    *Ax=b*
1211    
1212    with a general operator A (more details required!).    with a general operator A (more details required!).
1213    It uses the Transpose-Free Quasi-Minimal Residual method (TFQMR).    It uses the Transpose-Free Quasi-Minimal Residual method (TFQMR).
1214    
1215    The iteration is terminated if    The iteration is terminated if
1216    
1217    M{|r| <= atol+rtol*|r0|}    *|r| <= atol+rtol*|r0|*
1218    
1219    where M{r0} is the initial residual and M{|.|} is the energy norm. In fact    where *r0* is the initial residual and *|.|* is the energy norm. In fact
1220    
1221    M{|r| = sqrt( bilinearform(r,r))}    *|r| = sqrt( bilinearform(r,r))*
1222    
1223    @param r: initial residual M{r=b-Ax}. C{r} is altered.    :param r: initial residual *r=b-Ax*. ``r`` is altered.
1224    @type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)    :type r: any object supporting inplace add (x+=y) and scaling (x=scalar*y)
1225    @param x: an initial guess for the solution    :param x: an initial guess for the solution
1226    @type x: same like C{r}    :type x: same like ``r``
1227    @param Aprod: returns the value Ax    :param Aprod: returns the value Ax
1228    @type Aprod: function C{Aprod(x)} where C{x} is of the same object like    :type Aprod: function ``Aprod(x)`` where ``x`` is of the same object like
1229                 argument C{x}. The returned object needs to be of the same type                 argument ``x``. The returned object needs to be of the same type
1230                 like argument C{r}.                 like argument ``r``.
1231    @param bilinearform: inner product C{<x,r>}    :param bilinearform: inner product ``<x,r>``
1232    @type bilinearform: function C{bilinearform(x,r)} where C{x} is of the same    :type bilinearform: function ``bilinearform(x,r)`` where ``x`` is of the same
1233                        type like argument C{x} and C{r}. The returned value is                        type like argument ``x`` and ``r``. The returned value is
1234                        a C{float}.                        a ``float``.
1235    @param atol: absolute tolerance    :param atol: absolute tolerance
1236    @type atol: non-negative C{float}    :type atol: non-negative ``float``
1237    @param rtol: relative tolerance    :param rtol: relative tolerance
1238    @type rtol: non-negative C{float}    :type rtol: non-negative ``float``
1239    @param iter_max: maximum number of iteration steps    :param iter_max: maximum number of iteration steps
1240    @type iter_max: C{int}    :type iter_max: ``int``
1241    @rtype: C{tuple}    :rtype: ``tuple``
1242    @warning: C{r} and C{x} are altered.    :warning: ``r`` and ``x`` are altered.
1243    """    """
1244    u1=0    u1=0
1245    u2=0    u2=0
# Line 1287  def TFQMR(r, Aprod, x, bilinearform, ato Line 1309  def TFQMR(r, Aprod, x, bilinearform, ato
1309    
1310  class ArithmeticTuple(object):  class ArithmeticTuple(object):
1311     """     """
1312     Tuple supporting inplace update x+=y and scaling x=a*y where C{x,y} is an     Tuple supporting inplace update x+=y and scaling x=a*y where ``x,y`` is an
1313     ArithmeticTuple and C{a} is a float.     ArithmeticTuple and ``a`` is a float.
1314    
1315     Example of usage::     Example of usage::
1316    
# Line 1302  class ArithmeticTuple(object): Line 1324  class ArithmeticTuple(object):
1324     """     """
1325     def __init__(self,*args):     def __init__(self,*args):
1326         """         """
1327         Initializes object with elements C{args}.         Initializes object with elements ``args``.
1328    
1329         @param args: tuple of objects that support inplace add (x+=y) and         :param args: tuple of objects that support inplace add (x+=y) and
1330                      scaling (x=a*y)                      scaling (x=a*y)
1331         """         """
1332         self.__items=list(args)         self.__items=list(args)
# Line 1313  class ArithmeticTuple(object): Line 1335  class ArithmeticTuple(object):
1335         """         """
1336         Returns the number of items.         Returns the number of items.
1337    
1338         @return: number of items         :return: number of items
1339         @rtype: C{int}         :rtype: ``int``
1340         """         """
1341         return len(self.__items)         return len(self.__items)
1342    
# Line 1322  class ArithmeticTuple(object): Line 1344  class ArithmeticTuple(object):
1344         """         """
1345         Returns item at specified position.         Returns item at specified position.
1346    
1347         @param index: index of item to be returned         :param index: index of item to be returned
1348         @type index: C{int}         :type index: ``int``
1349         @return: item with index C{index}         :return: item with index ``index``
1350         """         """
1351         return self.__items.__getitem__(index)         return self.__items.__getitem__(index)
1352    
1353     def __mul__(self,other):     def __mul__(self,other):
1354         """         """
1355         Scales by C{other} from the right.         Scales by ``other`` from the right.
1356    
1357         @param other: scaling factor         :param other: scaling factor
1358         @type other: C{float}         :type other: ``float``
1359         @return: itemwise self*other         :return: itemwise self*other
1360         @rtype: L{ArithmeticTuple}         :rtype: `ArithmeticTuple`
1361         """         """
1362         out=[]         out=[]
1363         try:         try:
# Line 1349  class ArithmeticTuple(object): Line 1371  class ArithmeticTuple(object):
1371    
1372     def __rmul__(self,other):     def __rmul__(self,other):
1373         """         """
1374         Scales by C{other} from the left.         Scales by ``other`` from the left.
1375    
1376         @param other: scaling factor         :param other: scaling factor
1377         @type other: C{float}         :type other: ``float``
1378         @return: itemwise other*self         :return: itemwise other*self
1379         @rtype: L{ArithmeticTuple}         :rtype: `ArithmeticTuple`
1380         """         """
1381         out=[]         out=[]
1382         try:         try:
# Line 1368  class ArithmeticTuple(object): Line 1390  class ArithmeticTuple(object):
1390    
1391     def __div__(self,other):     def __div__(self,other):
1392         """         """
1393         Scales by (1/C{other}) from the right.         Scales by (1/``other``) from the right.
1394    
1395         @param other: scaling factor         :param other: scaling factor
1396         @type other: C{float}         :type other: ``float``
1397         @return: itemwise self/other         :return: itemwise self/other
1398         @rtype: L{ArithmeticTuple}         :rtype: `ArithmeticTuple`
1399         """         """
1400         return self*(1/other)         return self*(1/other)
1401    
1402     def __rdiv__(self,other):     def __rdiv__(self,other):
1403         """         """
1404         Scales by (1/C{other}) from the left.         Scales by (1/``other``) from the left.
1405    
1406         @param other: scaling factor         :param other: scaling factor
1407         @type other: C{float}         :type other: ``float``
1408         @return: itemwise other/self         :return: itemwise other/self
1409         @rtype: L{ArithmeticTuple}         :rtype: `ArithmeticTuple`
1410         """         """
1411         out=[]         out=[]
1412         try:         try:
# Line 1398  class ArithmeticTuple(object): Line 1420  class ArithmeticTuple(object):
1420    
1421     def __iadd__(self,other):     def __iadd__(self,other):
1422         """         """
1423         Inplace addition of C{other} to self.         Inplace addition of ``other`` to self.
1424    
1425         @param other: increment         :param other: increment
1426         @type other: C{ArithmeticTuple}         :type other: ``ArithmeticTuple``
1427         """         """
1428         if len(self) != len(other):         if len(self) != len(other):
1429             raise ValueError,"tuple lengths must match."             raise ValueError,"tuple lengths must match."
# Line 1411  class ArithmeticTuple(object): Line 1433  class ArithmeticTuple(object):
1433    
1434     def __add__(self,other):     def __add__(self,other):
1435         """         """
1436         Adds C{other} to self.         Adds ``other`` to self.
1437    
1438         @param other: increment         :param other: increment
1439         @type other: C{ArithmeticTuple}         :type other: ``ArithmeticTuple``
1440         """         """
1441         out=[]         out=[]
1442         try:         try:
# Line 1428  class ArithmeticTuple(object): Line 1450  class ArithmeticTuple(object):
1450    
1451     def __sub__(self,other):     def __sub__(self,other):
1452         """         """
1453         Subtracts C{other} from self.         Subtracts ``other`` from self.
1454    
1455         @param other: decrement         :param other: decrement
1456         @type other: C{ArithmeticTuple}         :type other: ``ArithmeticTuple``
1457         """         """
1458         out=[]         out=[]
1459         try:         try:
# Line 1445  class ArithmeticTuple(object): Line 1467  class ArithmeticTuple(object):
1467    
1468     def __isub__(self,other):     def __isub__(self,other):
1469         """         """
1470         Inplace subtraction of C{other} from self.         Inplace subtraction of ``other`` from self.
1471    
1472         @param other: decrement         :param other: decrement
1473         @type other: C{ArithmeticTuple}         :type other: ``ArithmeticTuple``
1474         """         """
1475         if len(self) != len(other):         if len(self) != len(other):
1476             raise ValueError,"tuple length must match."             raise ValueError,"tuple length must match."
# Line 1471  class HomogeneousSaddlePointProblem(obje Line 1493  class HomogeneousSaddlePointProblem(obje
1493        This class provides a framework for solving linear homogeneous saddle        This class provides a framework for solving linear homogeneous saddle
1494        point problems of the form::        point problems of the form::
1495    
1496            M{Av+B^*p=f}            *Av+B^*p=f*
1497            M{Bv     =0}            *Bv     =0*
1498    
1499        for the unknowns M{v} and M{p} and given operators M{A} and M{B} and        for the unknowns *v* and *p* and given operators *A* and *B* and
1500        given right hand side M{f}. M{B^*} is the adjoint operator of M{B}.        given right hand side *f*. *B^** is the adjoint operator of *B*.
1501          *A* may depend weakly on *v* and *p*.
1502        """        """
1503        def __init__(self, adaptSubTolerance=True, **kwargs):        def __init__(self, **kwargs):
1504      """      """
1505      initializes the saddle point problem      initializes the saddle point problem
       
     @param adaptSubTolerance: If True the tolerance for subproblem is set automatically.  
     @type adaptSubTolerance: C{bool}  
1506      """      """
1507            self.resetControlParameters()
1508          self.setTolerance()          self.setTolerance()
1509          self.setAbsoluteTolerance()          self.setAbsoluteTolerance()
1510      self.__adaptSubTolerance=adaptSubTolerance        def resetControlParameters(self, K_p=1., K_v=1., rtol_max=0.1, rtol_min = 1.e-7, chi_max=0.5, reduction_factor=0.3, theta = 0.1):
1511        #=============================================================           """
1512        def initialize(self):           sets a control parameter
1513          """  
1514          Initializes the problem (overwrite).           :param K_p: initial value for constant to adjust pressure tolerance
1515          """           :type K_p: ``float``
1516          pass           :param K_v: initial value for constant to adjust velocity tolerance
1517             :type K_v: ``float``
1518             :param rtol_max: maximuim relative tolerance used to calculate presssure and velocity increment.
1519             :type rtol_max: ``float``
1520             :param chi_max: maximum tolerable converegence rate.
1521             :type chi_max: ``float``
1522             :param reduction_factor: reduction factor for adjustment factors.
1523             :type reduction_factor: ``float``
1524             """
1525             self.setControlParameter(K_p, K_v, rtol_max, rtol_min, chi_max, reduction_factor, theta)
1526    
1527          def setControlParameter(self,K_p=None, K_v=None, rtol_max=None, rtol_min=None, chi_max=None, reduction_factor=None, theta=None):
1528             """
1529             sets a control parameter
1530    
1531    
1532             :param K_p: initial value for constant to adjust pressure tolerance
1533             :type K_p: ``float``
1534             :param K_v: initial value for constant to adjust velocity tolerance
1535             :type K_v: ``float``
1536             :param rtol_max: maximuim relative tolerance used to calculate presssure and velocity increment.
1537             :type rtol_max: ``float``
1538             :param chi_max: maximum tolerable converegence rate.
1539             :type chi_max: ``float``
1540             :type reduction_factor: ``float``
1541             """
1542             if not K_p == None:
1543                if K_p<1:
1544                   raise ValueError,"K_p need to be greater or equal to 1."
1545             else:
1546                K_p=self.__K_p
1547    
1548             if not K_v == None:
1549                if K_v<1:
1550                   raise ValueError,"K_v need to be greater or equal to 1."
1551             else:
1552                K_v=self.__K_v
1553    
1554             if not rtol_max == None:
1555                if rtol_max<=0 or rtol_max>=1:
1556                   raise ValueError,"rtol_max needs to be positive and less than 1."
1557             else:
1558                rtol_max=self.__rtol_max
1559    
1560             if not rtol_min == None:
1561                if rtol_min<=0 or rtol_min>=1:
1562                   raise ValueError,"rtol_min needs to be positive and less than 1."
1563             else:
1564                rtol_min=self.__rtol_min
1565    
1566             if not chi_max == None:
1567                if chi_max<=0 or chi_max>=1:
1568                   raise ValueError,"chi_max needs to be positive and less than 1."
1569             else:
1570                chi_max = self.__chi_max
1571    
1572             if not reduction_factor == None:
1573                if reduction_factor<=0 or reduction_factor>1:
1574                   raise ValueError,"reduction_factor need to be between zero and one."
1575             else:
1576                reduction_factor=self.__reduction_factor
1577    
1578             if not theta == None:
1579                if theta<=0 or theta>1:
1580                   raise ValueError,"theta need to be between zero and one."
1581             else:
1582                theta=self.__theta
1583    
1584             if rtol_min>=rtol_max:
1585                 raise ValueError,"rtol_max = %e needs to be greater than rtol_min = %e"%(rtol_max,rtol_min)
1586             self.__chi_max = chi_max
1587             self.__rtol_max = rtol_max
1588             self.__K_p = K_p
1589             self.__K_v = K_v
1590             self.__reduction_factor = reduction_factor
1591             self.__theta = theta
1592             self.__rtol_min=rtol_min
1593    
1594          #=============================================================
1595        def inner_pBv(self,p,Bv):        def inner_pBv(self,p,Bv):
1596           """           """
1597           Returns inner product of element p and Bv (overwrite).           Returns inner product of element p and Bv (overwrite).
1598    
1599           @param p: a pressure increment           :param p: a pressure increment
1600           @param v: a residual           :param Bv: a residual
1601           @return: inner product of element p and Bv           :return: inner product of element p and Bv
1602           @rtype: C{float}           :rtype: ``float``
1603           @note: used if PCG is applied.           :note: used if PCG is applied.
1604           """           """
1605           raise NotImplementedError,"no inner product for p and Bv implemented."           raise NotImplementedError,"no inner product for p and Bv implemented."
1606    
# Line 1510  class HomogeneousSaddlePointProblem(obje Line 1608  class HomogeneousSaddlePointProblem(obje
1608           """           """
1609           Returns inner product of p0 and p1 (overwrite).           Returns inner product of p0 and p1 (overwrite).
1610    
1611           @param p0: a pressure           :param p0: a pressure
1612           @param p1: a pressure           :param p1: a pressure
1613           @return: inner product of p0 and p1           :return: inner product of p0 and p1
1614           @rtype: C{float}           :rtype: ``float``
1615           """           """
1616           raise NotImplementedError,"no inner product for p implemented."           raise NotImplementedError,"no inner product for p implemented."
1617        
# Line 1521  class HomogeneousSaddlePointProblem(obje Line 1619  class HomogeneousSaddlePointProblem(obje
1619           """           """
1620           Returns the norm of v (overwrite).           Returns the norm of v (overwrite).
1621    
1622           @param v: a velovity           :param v: a velovity
1623           @return: norm of v           :return: norm of v
1624           @rtype: non-negative C{float}           :rtype: non-negative ``float``
1625           """           """
1626           raise NotImplementedError,"no norm of v implemented."           raise NotImplementedError,"no norm of v implemented."
1627        def getV(self, p, v0):        def getDV(self, p, v, tol):
1628           """           """
1629           return the value for v for a given p (overwrite)           return a correction to the value for a given v and a given p with accuracy `tol` (overwrite)
1630    
1631           @param p: a pressure           :param p: pressure
1632           @param v0: a initial guess for the value v to return.           :param v: pressure
1633           @return: v given as M{v= A^{-1} (f-B^*p)}           :return: dv given as *dv= A^{-1} (f-A v-B^*p)*
1634             :note: Only *A* may depend on *v* and *p*
1635           """           """
1636           raise NotImplementedError,"no v calculation implemented."           raise NotImplementedError,"no dv calculation implemented."
1637    
1638                    
1639        def Bv(self,v):        def Bv(self,v, tol):
1640          """          """
1641          Returns Bv (overwrite).          Returns Bv with accuracy `tol` (overwrite)
1642    
1643          @rtype: equal to the type of p          :rtype: equal to the type of p
1644          @note: boundary conditions on p should be zero!          :note: boundary conditions on p should be zero!
1645          """          """
1646          raise NotImplementedError, "no operator B implemented."          raise NotImplementedError, "no operator B implemented."
1647    
# Line 1550  class HomogeneousSaddlePointProblem(obje Line 1649  class HomogeneousSaddlePointProblem(obje
1649          """          """
1650          Returns the norm of Bv (overwrite).          Returns the norm of Bv (overwrite).
1651    
1652          @rtype: equal to the type of p          :rtype: equal to the type of p
1653          @note: boundary conditions on p should be zero!          :note: boundary conditions on p should be zero!
1654          """          """
1655          raise NotImplementedError, "no norm of Bv implemented."          raise NotImplementedError, "no norm of Bv implemented."
1656    
1657        def solve_AinvBt(self,p):        def solve_AinvBt(self,dp, tol):
1658           """           """
1659           Solves M{Av=B^*p} with accuracy L{self.getSubProblemTolerance()}           Solves *A dv=B^*dp* with accuracy `tol`
          (overwrite).  
1660    
1661           @param p: a pressure increment           :param dp: a pressure increment
1662           @return: the solution of M{Av=B^*p}           :return: the solution of *A dv=B^*dp*
1663           @note: boundary conditions on v should be zero!           :note: boundary conditions on dv should be zero! *A* is the operator used in ``getDV`` and must not be altered.
1664           """           """
1665           raise NotImplementedError,"no operator A implemented."           raise NotImplementedError,"no operator A implemented."
1666    
1667        def solve_prec(self,Bv):        def solve_prec(self,Bv, tol):
1668           """           """
1669           Provides a preconditioner for M{BA^{-1}B^*} applied to Bv with accuracy           Provides a preconditioner for *(BA^{-1}B^ * )* applied to Bv with accuracy `tol`
          L{self.getSubProblemTolerance()} (overwrite).  
1670    
1671           @rtype: equal to the type of p           :rtype: equal to the type of p
1672           @note: boundary conditions on p should be zero!           :note: boundary conditions on p should be zero!
1673           """           """
1674           raise NotImplementedError,"no preconditioner for Schur complement implemented."           raise NotImplementedError,"no preconditioner for Schur complement implemented."
       def setSubProblemTolerance(self):  
          """  
      Updates the tolerance for subproblems  
      @note: method is typically the method is overwritten.  
          """  
          pass  
1675        #=============================================================        #=============================================================
1676        def __Aprod_PCG(self,p):        def __Aprod_PCG(self,dp):
1677            dv=self.solve_AinvBt(p)            dv=self.solve_AinvBt(dp, self.__subtol)
1678            return ArithmeticTuple(dv,self.Bv(dv))            return ArithmeticTuple(dv,self.Bv(dv, self.__subtol))
1679    
1680        def __inner_PCG(self,p,r):        def __inner_PCG(self,p,r):
1681           return self.inner_pBv(p,r[1])           return self.inner_pBv(p,r[1])
1682    
1683        def __Msolve_PCG(self,r):        def __Msolve_PCG(self,r):
1684            return self.solve_prec(r[1])            return self.solve_prec(r[1], self.__subtol)
1685        #=============================================================        #=============================================================
1686        def __Aprod_GMRES(self,p):        def __Aprod_GMRES(self,p):
1687            return self.solve_prec(self.Bv(self.solve_AinvBt(p)))            return self.solve_prec(self.Bv(self.solve_AinvBt(p, self.__subtol), self.__subtol), self.__subtol)
1688        def __inner_GMRES(self,p0,p1):        def __inner_GMRES(self,p0,p1):
1689           return self.inner_p(p0,p1)           return self.inner_p(p0,p1)
1690    
1691        #=============================================================        #=============================================================
1692        def norm_p(self,p):        def norm_p(self,p):
1693            """            """
1694            calculates the norm of C{p}            calculates the norm of ``p``
1695                        
1696            @param p: a pressure            :param p: a pressure
1697            @return: the norm of C{p} using the inner product for pressure            :return: the norm of ``p`` using the inner product for pressure
1698            @rtype: C{float}            :rtype: ``float``
1699            """            """
1700            f=self.inner_p(p,p)            f=self.inner_p(p,p)
1701            if f<0: raise ValueError,"negative pressure norm."            if f<0: raise ValueError,"negative pressure norm."
1702            return math.sqrt(f)            return math.sqrt(f)
       def adaptSubTolerance(self):  
       """  
       Returns True if tolerance adaption for subproblem is choosen.  
       """  
           self.__adaptSubTolerance  
1703                
1704        def solve(self,v,p,max_iter=20, verbose=False, usePCG=True, iter_restart=20, max_correction_steps=10):        def solve(self,v,p,max_iter=20, verbose=False, usePCG=True, iter_restart=20, max_correction_steps=10):
1705           """           """
1706           Solves the saddle point problem using initial guesses v and p.           Solves the saddle point problem using initial guesses v and p.
1707    
1708           @param v: initial guess for velocity           :param v: initial guess for velocity
1709           @param p: initial guess for pressure           :param p: initial guess for pressure
1710           @type v: L{Data}           :type v: `Data`
1711           @type p: L{Data}           :type p: `Data`
1712           @param usePCG: indicates the usage of the PCG rather than GMRES scheme.           :param usePCG: indicates the usage of the PCG rather than GMRES scheme.
1713           @param max_iter: maximum number of iteration steps per correction           :param max_iter: maximum number of iteration steps per correction
1714                            attempt                            attempt
1715           @param verbose: if True, shows information on the progress of the           :param verbose: if True, shows information on the progress of the
1716                           saddlepoint problem solver.                           saddlepoint problem solver.
1717           @param iter_restart: restart the iteration after C{iter_restart} steps           :param iter_restart: restart the iteration after ``iter_restart`` steps
1718                                (only used if useUzaw=False)                                (only used if useUzaw=False)
1719           @type usePCG: C{bool}           :type usePCG: ``bool``
1720           @type max_iter: C{int}           :type max_iter: ``int``
1721           @type verbose: C{bool}           :type verbose: ``bool``
1722           @type iter_restart: C{int}           :type iter_restart: ``int``
1723           @rtype: C{tuple} of L{Data} objects           :rtype: ``tuple`` of `Data` objects
1724             :note: typically this method is overwritten by a subclass. It provides a wrapper for the ``_solve`` method.
1725             """
1726             return self._solve(v=v,p=p,max_iter=max_iter,verbose=verbose, usePCG=usePCG, iter_restart=iter_restart, max_correction_steps=max_correction_steps)
1727    
1728          def _solve(self,v,p,max_iter=20, verbose=False, usePCG=True, iter_restart=20, max_correction_steps=10):
1729             """
1730             see `_solve` method.
1731           """           """
1732           self.verbose=verbose           self.verbose=verbose
1733           rtol=self.getTolerance()           rtol=self.getTolerance()
1734           atol=self.getAbsoluteTolerance()           atol=self.getAbsoluteTolerance()
1735       if self.adaptSubTolerance(): self.setSubProblemTolerance()  
1736             K_p=self.__K_p
1737             K_v=self.__K_v
1738           correction_step=0           correction_step=0
1739           converged=False           converged=False
1740             chi=None
1741             eps=None
1742    
1743             if self.verbose: print "HomogeneousSaddlePointProblem: start iteration: rtol= %e, atol=%e"%(rtol, atol)
1744           while not converged:           while not converged:
1745                # calculate velocity for current pressure:  
1746                v=self.getV(p,v)               # get tolerance for velecity increment:
1747                Bv=self.Bv(v)               if chi == None:
1748                norm_v=self.norm_v(v)                  rtol_v=self.__rtol_max
1749                norm_Bv=self.norm_Bv(Bv)               else:
1750                ATOL=norm_v*rtol+atol                  rtol_v=min(chi/K_v,self.__rtol_max)
1751                if self.verbose: print "HomogeneousSaddlePointProblem: norm v= %e, norm_Bv= %e, tolerance = %e."%(norm_v, norm_Bv,ATOL)               rtol_v=max(rtol_v, self.__rtol_min)
1752                if not ATOL>0: raise ValueError,"overall absolute tolerance needs to be positive."               if self.verbose: print "HomogeneousSaddlePointProblem: step %s: rtol_v= %e"%(correction_step,rtol_v)
1753                if norm_Bv <= ATOL:               # get velocity increment:
1754                   converged=True               dv1=self.getDV(p,v,rtol_v)
1755                else:               v1=v+dv1
1756                   correction_step+=1               Bv1=self.Bv(v1, rtol_v)
1757                   if correction_step>max_correction_steps:               norm_Bv1=self.norm_Bv(Bv1)
1758                        raise CorrectionFailed,"Given up after %d correction steps."%correction_step               norm_dv1=self.norm_v(dv1)
1759                   dp=self.solve_prec(Bv)               if self.verbose: print "HomogeneousSaddlePointProblem: step %s: norm_Bv1 = %e, norm_dv1 = %e"%(correction_step, norm_Bv1, norm_dv1)
1760                   if usePCG:               if norm_dv1*self.__theta < norm_Bv1:
1761                     norm2=self.inner_pBv(dp,Bv)                  # get tolerance for pressure increment:
1762                     if norm2<0: raise ValueError,"negative PCG norm."                  large_Bv1=True
1763                     norm2=math.sqrt(norm2)                  if chi == None or eps == None:
1764                   else:                     rtol_p=self.__rtol_max
1765                     norm2=self.norm_p(dp)                  else:
1766                   ATOL_ITER=ATOL/norm_Bv*norm2*0.5                     rtol_p=min(chi**2*eps/K_p/norm_Bv1, self.__rtol_max)
1767                   if self.verbose: print "HomogeneousSaddlePointProblem: tolerance for solver: %e"%ATOL_ITER                  self.__subtol=max(rtol_p**2, self.__rtol_min)
1768                   if usePCG:                  if self.verbose: print "HomogeneousSaddlePointProblem: step %s: rtol_p= %e"%(correction_step,rtol_p)
1769                         p,v0,a_norm=PCG(ArithmeticTuple(v,Bv),self.__Aprod_PCG,p,self.__Msolve_PCG,self.__inner_PCG,atol=ATOL_ITER, rtol=0.,iter_max=max_iter, verbose=self.verbose)                  # now we solve for the pressure increment dp from B*A^{-1}B^* dp = Bv1
1770                    if usePCG:
1771                        dp,r,a_norm=PCG(ArithmeticTuple(v1,Bv1),self.__Aprod_PCG,0*p,self.__Msolve_PCG,self.__inner_PCG,atol=0, rtol=rtol_p,iter_max=max_iter, verbose=self.verbose)
1772                        v2=r[0]
1773                        Bv2=r[1]
1774                    else:
1775                        # don't use!!!!
1776                        dp=GMRES(self.solve_prec(Bv1,self.__subtol),self.__Aprod_GMRES, 0*p, self.__inner_GMRES,atol=0, rtol=rtol_p,iter_max=max_iter, iter_restart=iter_restart, verbose=self.verbose)
1777                        dv2=self.solve_AinvBt(dp, self.__subtol)
1778                        v2=v1-dv2
1779                        Bv2=self.Bv(v2, self.__subtol)
1780                    p2=p+dp
1781                 else:
1782                    large_Bv1=False
1783                    v2=v1
1784                    p2=p
1785                 # update business:
1786                 norm_dv2=self.norm_v(v2-v)
1787                 norm_v2=self.norm_v(v2)
1788                 if self.verbose: print "HomogeneousSaddlePointProblem: step %s: v2 = %e, norm_dv2 = %e"%(correction_step, norm_v2, self.norm_v(v2-v))
1789                 eps, eps_old = max(norm_Bv1, norm_dv2), eps
1790                 if eps_old == None:
1791                      chi, chi_old = None, chi
1792                 else:
1793                      chi, chi_old = min(eps/ eps_old, self.__chi_max), chi
1794                 if eps != None:
1795                     if chi !=None:
1796                        if self.verbose: print "HomogeneousSaddlePointProblem: step %s: convergence rate = %e, correction = %e"%(correction_step,chi, eps)
1797                   else:                   else:
1798                         p=GMRES(dp,self.__Aprod_GMRES, p, self.__inner_GMRES,atol=ATOL_ITER, rtol=0.,iter_max=max_iter, iter_restart=iter_restart, verbose=self.verbose)                      if self.verbose: print "HomogeneousSaddlePointProblem: step %s: correction = %e"%(correction_step, eps)
1799           if self.verbose: print "HomogeneousSaddlePointProblem: tolerance reached."               if eps <= rtol*norm_v2+atol :
1800                     converged = True
1801                 else:
1802                     if correction_step>=max_correction_steps:
1803                          raise CorrectionFailed,"Given up after %d correction steps."%correction_step
1804                     if chi_old!=None:
1805                        K_p=max(1,self.__reduction_factor*K_p,(chi-chi_old)/chi_old**2*K_p)
1806                        K_v=max(1,self.__reduction_factor*K_v,(chi-chi_old)/chi_old**2*K_p)
1807                        if self.verbose: print "HomogeneousSaddlePointProblem: step %s: new adjustment factor K = %e"%(correction_step,K_p)
1808                 correction_step+=1
1809                 v,p =v2, p2
1810             if self.verbose: print "HomogeneousSaddlePointProblem: tolerance reached after %s steps."%correction_step
1811       return v,p       return v,p
   
1812        #========================================================================        #========================================================================
1813        def setTolerance(self,tolerance=1.e-4):        def setTolerance(self,tolerance=1.e-4):
1814           """           """
1815           Sets the relative tolerance for (v,p).           Sets the relative tolerance for (v,p).
1816    
1817           @param tolerance: tolerance to be used           :param tolerance: tolerance to be used
1818           @type tolerance: non-negative C{float}           :type tolerance: non-negative ``float``
1819           """           """
1820           if tolerance<0:           if tolerance<0:
1821               raise ValueError,"tolerance must be positive."               raise ValueError,"tolerance must be positive."
# Line 1689  class HomogeneousSaddlePointProblem(obje Line 1825  class HomogeneousSaddlePointProblem(obje
1825           """           """
1826           Returns the relative tolerance.           Returns the relative tolerance.
1827    
1828           @return: relative tolerance           :return: relative tolerance
1829           @rtype: C{float}           :rtype: ``float``
1830           """           """
1831           return self.__rtol           return self.__rtol
1832    
# Line 1698  class HomogeneousSaddlePointProblem(obje Line 1834  class HomogeneousSaddlePointProblem(obje
1834           """           """
1835           Sets the absolute tolerance.           Sets the absolute tolerance.
1836    
1837           @param tolerance: tolerance to be used           :param tolerance: tolerance to be used
1838           @type tolerance: non-negative C{float}           :type tolerance: non-negative ``float``
1839           """           """
1840           if tolerance<0:           if tolerance<0:
1841               raise ValueError,"tolerance must be non-negative."               raise ValueError,"tolerance must be non-negative."
# Line 1709  class HomogeneousSaddlePointProblem(obje Line 1845  class HomogeneousSaddlePointProblem(obje
1845           """           """
1846           Returns the absolute tolerance.           Returns the absolute tolerance.
1847    
1848           @return: absolute tolerance           :return: absolute tolerance
1849           @rtype: C{float}           :rtype: ``float``
1850           """           """
1851           return self.__atol           return self.__atol
1852    
       def getSubProblemTolerance(self):  
          """  
          Sets the relative tolerance to solve the subproblem(s).  
   
          @param rtol: relative tolerence  
          @type rtol: positive C{float}  
          """  
          return max(200.*util.EPSILON,self.getTolerance()**2)  
1853    
1854  def MaskFromBoundaryTag(domain,*tags):  def MaskFromBoundaryTag(domain,*tags):
1855     """     """
# Line 1730  def MaskFromBoundaryTag(domain,*tags): Line 1858  def MaskFromBoundaryTag(domain,*tags):
1858    
1859     Usage: m=MaskFromBoundaryTag(domain, "left", "right")     Usage: m=MaskFromBoundaryTag(domain, "left", "right")
1860    
1861     @param domain: domain to be used     :param domain: domain to be used
1862     @type domain: L{escript.Domain}     :type domain: `escript.Domain`
1863     @param tags: boundary tags     :param tags: boundary tags
1864     @type tags: C{str}     :type tags: ``str``
1865     @return: a mask which marks samples that are touching the boundary tagged     :return: a mask which marks samples that are touching the boundary tagged
1866              by any of the given tags              by any of the given tags
1867     @rtype: L{escript.Data} of rank 0     :rtype: `escript.Data` of rank 0
1868     """     """
1869     pde=linearPDEs.LinearPDE(domain,numEquations=1, numSolutions=1)     pde=linearPDEs.LinearPDE(domain,numEquations=1, numSolutions=1)
1870     d=escript.Scalar(0.,escript.FunctionOnBoundary(domain))     d=escript.Scalar(0.,escript.FunctionOnBoundary(domain))
# Line 1751  def MaskFromTag(domain,*tags): Line 1879  def MaskFromTag(domain,*tags):
1879    
1880     Usage: m=MaskFromTag(domain, "ham")     Usage: m=MaskFromTag(domain, "ham")
1881    
1882     @param domain: domain to be used     :param domain: domain to be used
1883     @type domain: L{escript.Domain}     :type domain: `escript.Domain`
1884     @param tags: boundary tags     :param tags: boundary tags
1885     @type tags: C{str}     :type tags: ``str``
1886     @return: a mask which marks samples that are touching the boundary tagged     :return: a mask which marks samples that are touching the boundary tagged
1887              by any of the given tags              by any of the given tags
1888     @rtype: L{escript.Data} of rank 0     :rtype: `escript.Data` of rank 0
1889     """     """
1890     pde=linearPDEs.LinearPDE(domain,numEquations=1, numSolutions=1)     pde=linearPDEs.LinearPDE(domain,numEquations=1, numSolutions=1)
1891     d=escript.Scalar(0.,escript.Function(domain))     d=escript.Scalar(0.,escript.Function(domain))

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