# Diff of /temp/escript/py_src/pdetools.py

revision 637 by gross, Thu Mar 23 10:55:31 2006 UTC revision 1106 by gross, Thu Apr 19 01:54:57 2007 UTC
# Line 7  Currently includes: Line 7  Currently includes:
7      - Projector - to project a discontinuous      - Projector - to project a discontinuous
8      - Locator - to trace values in data objects at a certain location      - Locator - to trace values in data objects at a certain location
9      - TimeIntegrationManager - to handel extraplotion in time      - TimeIntegrationManager - to handel extraplotion in time
10        - SaddlePointProblem - solver for Saddle point problems using the inexact uszawa scheme
11
12  @var __author__: name of author  @var __author__: name of author
13  @var __copyright__: copyrights  @var __copyright__: copyrights
# Line 36  class TimeIntegrationManager: Line 37  class TimeIntegrationManager:
37    """    """
38    a simple mechanism to manage time dependend values.    a simple mechanism to manage time dependend values.
39
40    typical usage is:    typical usage is::
41
42    dt=0.1 # time increment       dt=0.1 # time increment
43    tm=TimeIntegrationManager(inital_value,p=1)       tm=TimeIntegrationManager(inital_value,p=1)
44    while t<1.       while t<1.
45        v_guess=tm.extrapolate(dt) # extrapolate to t+dt           v_guess=tm.extrapolate(dt) # extrapolate to t+dt
46        v=...           v=...
47        tm.checkin(dt,v)           tm.checkin(dt,v)
48        t+=dt           t+=dt
49
50    @remark: currently only p=1 is supported.    @note: currently only p=1 is supported.
51    """    """
52    def __init__(self,*inital_values,**kwargs):    def __init__(self,*inital_values,**kwargs):
53       """       """
# Line 192  class NoPDE: Line 193  class NoPDE:
193
194       The constraint is overwriting any other condition.       The constraint is overwriting any other condition.
195
196       @remark: This class is similar to the L{LinearPDE} class with A=B=C=X=0 but has the intention       @note: This class is similar to the L{linearPDEs.LinearPDE} class with A=B=C=X=0 but has the intention
197                that all input parameter are given in L{Solution} or L{ReducedSolution}. The whole              that all input parameter are given in L{Solution} or L{ReducedSolution}. The whole
198                thing is a bit strange and I blame Robert.Woodcock@csiro.au for this.              thing is a bit strange and I blame Robert.Woodcock@csiro.au for this.
199       """       """
200       def __init__(self,domain,D=None,Y=None,q=None,r=None):       def __init__(self,domain,D=None,Y=None,q=None,r=None):
201           """           """
# Line 203  class NoPDE: Line 204  class NoPDE:
204           @param domain: domain of the PDE.           @param domain: domain of the PDE.
205           @type domain: L{Domain}           @type domain: L{Domain}
206           @param D: coefficient of the solution.           @param D: coefficient of the solution.
207           @type D: C{float}, C{int}, L{NumArray}, L{Data}           @type D: C{float}, C{int}, L{numarray.NumArray}, L{Data}
208           @param Y: right hand side           @param Y: right hand side
209           @type Y: C{float}, C{int}, L{NumArray}, L{Data}           @type Y: C{float}, C{int}, L{numarray.NumArray}, L{Data}
210           @param q: location of constraints           @param q: location of constraints
211           @type q: C{float}, C{int}, L{NumArray}, L{Data}           @type q: C{float}, C{int}, L{numarray.NumArray}, L{Data}
212           @param r: value of solution at locations of constraints           @param r: value of solution at locations of constraints
213           @type r: C{float}, C{int}, L{NumArray}, L{Data}           @type r: C{float}, C{int}, L{numarray.NumArray}, L{Data}
214           """           """
215           self.__domain=domain           self.__domain=domain
216           self.__D=D           self.__D=D
# Line 237  class NoPDE: Line 238  class NoPDE:
238           assigns values to the parameters.           assigns values to the parameters.
239
240           @param D: coefficient of the solution.           @param D: coefficient of the solution.
241           @type D: C{float}, C{int}, L{NumArray}, L{Data}           @type D: C{float}, C{int}, L{numarray.NumArray}, L{Data}
242           @param Y: right hand side           @param Y: right hand side
243           @type Y: C{float}, C{int}, L{NumArray}, L{Data}           @type Y: C{float}, C{int}, L{numarray.NumArray}, L{Data}
244           @param q: location of constraints           @param q: location of constraints
245           @type q: C{float}, C{int}, L{NumArray}, L{Data}           @type q: C{float}, C{int}, L{numarray.NumArray}, L{Data}
246           @param r: value of solution at locations of constraints           @param r: value of solution at locations of constraints
247           @type r: C{float}, C{int}, L{NumArray}, L{Data}           @type r: C{float}, C{int}, L{numarray.NumArray}, L{Data}
248           """           """
249           if not D==None:           if not D==None:
250              self.__D=D              self.__D=D
# Line 296  class Locator: Line 297  class Locator:
297         Initializes a Locator to access values in Data objects on the Doamin         Initializes a Locator to access values in Data objects on the Doamin
298         or FunctionSpace where for the sample point which         or FunctionSpace where for the sample point which
299         closest to the given point x.         closest to the given point x.
300
301           @param where: function space
302           @type where: L{escript.FunctionSpace}
303           @param x: coefficient of the solution.
304           @type x: L{numarray.NumArray} or C{list} of L{numarray.NumArray}
305         """         """
306         if isinstance(where,escript.FunctionSpace):         if isinstance(where,escript.FunctionSpace):
307            self.__function_space=where            self.__function_space=where
308         else:         else:
309            self.__function_space=escript.ContinuousFunction(where)            self.__function_space=escript.ContinuousFunction(where)
310         self.__id=util.length(self.__function_space.getX()-x[:self.__function_space.getDim()]).mindp()         if isinstance(x, list):
311               self.__id=[]
312               for p in x:
313                  self.__id.append(util.length(self.__function_space.getX()-p[:self.__function_space.getDim()]).minGlobalDataPoint())
314           else:
315               self.__id=util.length(self.__function_space.getX()-x[:self.__function_space.getDim()]).minGlobalDataPoint()
316
317       def __str__(self):       def __str__(self):
318         """         """
319         Returns the coordinates of the Locator as a string.         Returns the coordinates of the Locator as a string.
320         """         """
321         return "<Locator %s>"%str(self.getX())         x=self.getX()
322           if instance(x,list):
323              out="["
324              first=True
325              for xx in x:
326                if not first:
327                    out+=","
328                else:
329                    first=False
330                out+=str(xx)
331              out+="]>"
332           else:
333              out=str(x)
334           return out
335
336         def getX(self):
337            """
338        Returns the exact coordinates of the Locator.
339        """
340            return self(self.getFunctionSpace().getX())
341
342       def getFunctionSpace(self):       def getFunctionSpace(self):
343          """          """
# Line 315  class Locator: Line 345  class Locator:
345      """      """
346          return self.__function_space          return self.__function_space
347
348       def getId(self):       def getId(self,item=None):
349          """          """
350      Returns the identifier of the location.      Returns the identifier of the location.
351      """      """
352          return self.__id          if item == None:
353               return self.__id
354            else:
355               if isinstance(self.__id,list):
356                  return self.__id[item]
357               else:
358                  return self.__id
359
def getX(self):
"""
Returns the exact coordinates of the Locator.
"""
return self(self.getFunctionSpace().getX())
360
361       def __call__(self,data):       def __call__(self,data):
362          """          """
# Line 341  class Locator: Line 372  class Locator:
372      """      """
373          if isinstance(data,escript.Data):          if isinstance(data,escript.Data):
374             if data.getFunctionSpace()==self.getFunctionSpace():             if data.getFunctionSpace()==self.getFunctionSpace():
375               out=data.convertToNumArrayFromDPNo(self.getId()[0],self.getId()[1])               dat=data
376             else:             else:
377               out=data.interpolate(self.getFunctionSpace()).convertToNumArrayFromDPNo(self.getId()[0],self.getId()[1])               dat=data.interpolate(self.getFunctionSpace())
378             if data.getRank()==0:             id=self.getId()
379                return out[0]             r=data.getRank()
380               if isinstance(id,list):
381                   out=[]
382                   for i in id:
383                      o=data.getValueOfGlobalDataPoint(*i)
384                      if data.getRank()==0:
385                         out.append(o[0])
386                      else:
387                         out.append(o)
388                   return out
389             else:             else:
390                return out               out=data.getValueOfGlobalDataPoint(*id)
391                 if data.getRank()==0:
392                    return out[0]
393                 else:
394                    return out
395          else:          else:
396             return data             return data
397
398    class SaddlePointProblem(object):
399       """
400       This implements a solver for a saddlepoint problem
401
402       M{f(u,p)=0}
403       M{g(u)=0}
404
405       for u and p. The problem is solved with an inexact Uszawa scheme for p:
406
407       M{Q_f (u^{k+1}-u^{k}) = - f(u^{k},p^{k})}
408       M{Q_g (p^{k+1}-p^{k}) =   g(u^{k+1})}
409
410       where Q_f is an approximation of the Jacobiean A_f of f with respect to u  and Q_f is an approximation of
411       A_g A_f^{-1} A_g with A_g is the jacobiean of g with respect to p. As a the construction of a 'proper'
412       Q_g can be difficult, non-linear conjugate gradient method is applied to solve for p, so Q_g plays
413       in fact the role of a preconditioner.
414       """
415       def __init__(self,verbose=False,*args):
416           """
417           initializes the problem
418
419           @param verbose: switches on the printing out some information
420           @type verbose: C{bool}
421           @note: this method may be overwritten by a particular saddle point problem
422           """
423           self.__verbose=verbose
424           self.relaxation=1.
425
426       def trace(self,text):
427           """
428           prints text if verbose has been set
429
430           @param text: a text message
431           @type text: C{str}
432           """
433           if self.__verbose: print "%s: %s"%(str(self),text)
434
435       def solve_f(self,u,p,tol=1.e-8):
436           """
437           solves
438
439           A_f du = f(u,p)
440
441           with tolerance C{tol} and return du. A_f is Jacobiean of f with respect to u.
442
443           @param u: current approximation of u
444           @type u: L{escript.Data}
445           @param p: current approximation of p
446           @type p: L{escript.Data}
447           @param tol: tolerance expected for du
448           @type tol: C{float}
449           @return: increment du
450           @rtype: L{escript.Data}
451           @note: this method has to be overwritten by a particular saddle point problem
452           """
453           pass
454
455       def solve_g(self,u,tol=1.e-8):
456           """
457           solves
458
459           Q_g dp = g(u)
460
461           with Q_g is a preconditioner for A_g A_f^{-1} A_g with  A_g is the jacobiean of g with respect to p.
462
463           @param u: current approximation of u
464           @type u: L{escript.Data}
465           @param tol: tolerance expected for dp
466           @type tol: C{float}
467           @return: increment dp
468           @rtype: L{escript.Data}
469           @note: this method has to be overwritten by a particular saddle point problem
470           """
471           pass
472
473       def inner(self,p0,p1):
474           """
475           inner product of p0 and p1 approximating p. Typically this returns integrate(p0*p1)
476           @return: inner product of p0 and p1
477           @rtype: C{float}
478           """
479           pass
480
481       subiter_max=3
482       def solve(self,u0,p0,tolerance=1.e-6,tolerance_u=None,iter_max=100,accepted_reduction=0.995,relaxation=None):
483            """
484            runs the solver
485
486            @param u0: initial guess for C{u}
487            @type u0: L{esys.escript.Data}
488            @param p0: initial guess for C{p}
489            @type p0: L{esys.escript.Data}
490            @param tolerance: tolerance for relative error in C{u} and C{p}
491            @type tolerance: positive C{float}
492            @param tolerance_u: tolerance for relative error in C{u} if different from C{tolerance}
493            @type tolerance_u: positive C{float}
494            @param iter_max: maximum number of iteration steps.
495            @type iter_max: C{int}
496            @param accepted_reduction: if the norm  g cannot be reduced by C{accepted_reduction} backtracking to adapt the
497                                       relaxation factor. If C{accepted_reduction=None} no backtracking is used.
498            @type accepted_reduction: positive C{float} or C{None}
499            @param relaxation: initial relaxation factor. If C{relaxation==None}, the last relaxation factor is used.
500            @type relaxation: C{float} or C{None}
501            """
502            tol=1.e-2
503            if tolerance_u==None: tolerance_u=tolerance
504            if not relaxation==None: self.relaxation=relaxation
505            if accepted_reduction ==None:
506                  angle_limit=0.
507            elif accepted_reduction>=1.:
508                  angle_limit=0.
509            else:
510                  angle_limit=util.sqrt(1-accepted_reduction**2)
511            self.iter=0
512            u=u0
513            p=p0
514            #
515            #   initialize things:
516            #
517            converged=False
518            #
519            #  start loop:
520            #
521            #  initial search direction is g
522            #
523            while not converged :
524                if self.iter>iter_max:
525                    raise ArithmeticError("no convergence after %s steps."%self.iter)
526                f_new=self.solve_f(u,p,tol)
527                norm_f_new = util.Lsup(f_new)
528                u_new=u-f_new
529                g_new=self.solve_g(u_new,tol)
530                self.iter+=1
531                norm_g_new = util.sqrt(self.inner(g_new,g_new))
532                if norm_f_new==0. and norm_g_new==0.: return u, p
533                if self.iter>1 and not accepted_reduction==None:
534                   #
535                   #   did we manage to reduce the norm of G? I
536                   #   if not we start a backtracking procedure
537                   #
538                   # print "new/old norm = ",norm_g_new, norm_g, norm_g_new/norm_g
539                   if norm_g_new > accepted_reduction * norm_g:
540                      sub_iter=0
541                      s=self.relaxation
542                      d=g
543                      g_last=g
544                      self.trace("    start substepping: f = %s, g = %s, relaxation = %s."%(norm_f_new, norm_g_new, s))
545                      while sub_iter < self.subiter_max and  norm_g_new > accepted_reduction * norm_g:
546                         dg= g_new-g_last
547                         norm_dg=abs(util.sqrt(self.inner(dg,dg))/self.relaxation)
548                         rad=self.inner(g_new,dg)/self.relaxation
549                         # print "   ",sub_iter,": rad, norm_dg:",abs(rad), norm_dg*norm_g_new * angle_limit
550                         # print "   ",sub_iter,": rad, norm_dg:",rad, norm_dg, norm_g_new, norm_g
551                         if abs(rad) < norm_dg*norm_g_new * angle_limit:
552                             if sub_iter>0: self.trace("    no further improvements expected from backtracking.")
553                             break
554                         r=self.relaxation
555                         self.relaxation= - rad/norm_dg**2
556                         s+=self.relaxation
557                         #####
558                         # a=g_new+self.relaxation*dg/r
559                         # print "predicted new norm = ",util.sqrt(self.inner(a,a)),util.sqrt(self.inner(g_new,g_new)), self.relaxation
560                         #####
561                         g_last=g_new
562                         p+=self.relaxation*d
563                         f_new=self.solve_f(u,p,tol)
564                         u_new=u-f_new
565                         g_new=self.solve_g(u_new,tol)
566                         self.iter+=1
567                         norm_f_new = util.Lsup(f_new)
568                         norm_g_new = util.sqrt(self.inner(g_new,g_new))
569                         # print "   ",sub_iter," new g norm",norm_g_new
570                         self.trace("    %s th sub-step: f = %s, g = %s, relaxation = %s."%(sub_iter, norm_f_new, norm_g_new, s))
571                         #
572                         #   can we expect reduction of g?
573                         #
574                         # u_last=u_new
575                         sub_iter+=1
576                      self.relaxation=s
577                #
578                #  check for convergence:
579                #
580                norm_u_new = util.Lsup(u_new)
581                p_new=p+self.relaxation*g_new
582                norm_p_new = util.sqrt(self.inner(p_new,p_new))
583                self.trace("%s th step: f/u = %s, g/p = %s, relaxation = %s."%(self.iter,norm_f_new/norm_u_new, norm_g_new/norm_p_new, self.relaxation))
584
585                if self.iter>1:
586                   dg2=g_new-g
587                   df2=f_new-f
588                   norm_dg2=util.sqrt(self.inner(dg2,dg2))
589                   norm_df2=util.Lsup(df2)
590                   # print norm_g_new, norm_g, norm_dg, norm_p, tolerance
591                   tol_eq_g=tolerance*norm_dg2/(norm_g*abs(self.relaxation))*norm_p_new
592                   tol_eq_f=tolerance_u*norm_df2/norm_f*norm_u_new
593                   if norm_g_new <= tol_eq_g and norm_f_new <= tol_eq_f:
594                       converged=True
595                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
596            self.trace("convergence after %s steps."%self.iter)
597            return u,p
598    #   def solve(self,u0,p0,tolerance=1.e-6,iter_max=10,self.relaxation=1.):
599    #      tol=1.e-2
600    #      iter=0
601    #      converged=False
602    #      u=u0*1.
603    #      p=p0*1.
604    #      while not converged and iter<iter_max:
605    #          du=self.solve_f(u,p,tol)
606    #          u-=du
607    #          norm_du=util.Lsup(du)
608    #          norm_u=util.Lsup(u)
609    #
610    #          dp=self.relaxation*self.solve_g(u,tol)
611    #          p+=dp
612    #          norm_dp=util.sqrt(self.inner(dp,dp))
613    #          norm_p=util.sqrt(self.inner(p,p))
614    #          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)
615    #          iter+=1
616    #
617    #          converged = (norm_du <= tolerance*norm_u) and  (norm_dp <= tolerance*norm_p)
618    #      if converged:
619    #          print "convergence after %s steps."%iter
620    #      else:
621    #          raise ArithmeticError("no convergence after %s steps."%iter)
622    #
623    #      return u,p
624
625  # vim: expandtab shiftwidth=4:  # vim: expandtab shiftwidth=4:

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