/[escript]/trunk/escript/py_src/linearPDEs.py
ViewVC logotype

Diff of /trunk/escript/py_src/linearPDEs.py

Parent Directory Parent Directory | Revision Log Revision Log | View Patch Patch

trunk/esys2/escript/py_src/linearPDEs.py revision 148 by jgs, Tue Aug 23 01:24:31 2005 UTC trunk/escript/py_src/linearPDEs.py revision 2548 by jfenwick, Mon Jul 20 06:20:06 2009 UTC
# Line 1  Line 1 
 # $Id$  
1    
2  ## @file linearPDEs.py  ########################################################
3    #
4    # Copyright (c) 2003-2009 by University of Queensland
5    # Earth Systems Science Computational Center (ESSCC)
6    # http://www.uq.edu.au/esscc
7    #
8    # Primary Business: Queensland, Australia
9    # Licensed under the Open Software License version 3.0
10    # http://www.opensource.org/licenses/osl-3.0.php
11    #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15    Earth Systems Science Computational Center (ESSCC)
16    http://www.uq.edu.au/esscc
17    Primary Business: Queensland, Australia"""
18    __license__="""Licensed under the Open Software License version 3.0
19    http://www.opensource.org/licenses/osl-3.0.php"""
20    __url__="https://launchpad.net/escript-finley"
21    
22  """  """
23  Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
24    differential equations (PDEs) and Transport problems within L{escript}.
25    L{linearPDEs} does not provide any solver capabilities in itself but hands the
26    PDE over to the PDE solver library defined through the L{Domain<escript.Domain>}
27    of the PDE. The general interface is provided through the L{LinearPDE} class.
28    L{TransportProblem} provides an interface to initial value problems dominated
29    by its advective terms.
30    
31    @var __author__: name of author
32    @var __copyright__: copyrights
33    @var __license__: licence agreement
34    @var __url__: url entry point on documentation
35    @var __version__: version
36    @var __date__: date of the version
37  """  """
38    
39    import math
40  import escript  import escript
41  import util  import util
42  import numarray  import numpy
43    
44    __author__="Lutz Gross, l.gross@uq.edu.au"
45    
46    
47    class SolverOptions(object):
48        """
49        this class defines the solver options for a linear or non-linear solver.
50        
51        The option also supports the handling of diagnostic informations.
52        
53        Typical usage is
54        
55        opts=SolverOptions()
56        print opts
57        opts.resetDiagnostics()
58        u=solver(opts)
59        print "number of iteration steps: =",opts.getDiagnostics("num_iter")
60        
61    
62        @cvar DEFAULT: The default method used to solve the system of linear equations
63        @cvar DIRECT: The direct solver based on LDU factorization
64        @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
65        @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
66        @cvar CR: The conjugate residual method
67        @cvar CGS: The conjugate gradient square method
68        @cvar BICGSTAB: The stabilized Bi-Conjugate Gradient method
69        @cvar TFQMR: Transport Free Quasi Minimal Residual method
70        @cvar MINRES: Minimum residual method
71        @cvar SSOR: The symmetric over-relaxation method
72        @cvar ILU0: The incomplete LU factorization preconditioner with no fill-in
73        @cvar ILUT: The incomplete LU factorization preconditioner with fill-in
74        @cvar JACOBI: The Jacobi preconditioner
75        @cvar GMRES: The Gram-Schmidt minimum residual method
76        @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
77        @cvar LUMPING: Matrix lumping
78        @cvar NO_REORDERING: No matrix reordering allowed
79        @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
80        @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
81        @cvar PASO: PASO solver package
82        @cvar SCSL: SGI SCSL solver library
83        @cvar MKL: Intel's MKL solver library
84        @cvar UMFPACK: The UMFPACK library
85        @cvar TRILINOS: The TRILINOS parallel solver class library from Sandia National Labs
86        @cvar ITERATIVE: The default iterative solver
87        @cvar AMG: Algebraic Multi Grid
88        @cvar REC_ILU: recursive ILU0
89        @cvar RILU: relaxed ILU0
90        @cvar GAUSS_SEIDEL: Gauss-Seidel solver
91        @cvar DEFAULT_REORDERING: the reordering method recommended by the solver
92        @cvar SUPER_LU: the Super_LU solver package
93        @cvar PASTIX: the Pastix direct solver_package
94        @cvar YAIR_SHAPIRA_COARSENING: AMG coarsening method by Yair-Shapira
95        @cvar RUGE_STUEBEN_COARSENING: AMG coarsening method by Ruge and Stueben
96        @cvar AGGREGATION_COARSENING: AMG coarsening using (symmetric) aggregation
97        @cvar MIN_COARSE_MATRIX_SIZE: minimum size of the coarsest level matrix to use direct solver.
98        @cvar NO_PRECONDITIONER: no preconditioner is applied.
99        """
100        DEFAULT= 0
101        DIRECT= 1
102        CHOLEVSKY= 2
103        PCG= 3
104        CR= 4
105        CGS= 5
106        BICGSTAB= 6
107        SSOR= 7
108        ILU0= 8
109        ILUT= 9
110        JACOBI= 10
111        GMRES= 11
112        PRES20= 12
113        LUMPING= 13
114        NO_REORDERING= 17
115        MINIMUM_FILL_IN= 18
116        NESTED_DISSECTION= 19
117        MKL= 15
118        UMFPACK= 16
119        ITERATIVE= 20
120        PASO= 21
121        AMG= 22
122        REC_ILU = 23
123        TRILINOS = 24
124        NONLINEAR_GMRES = 25
125        TFQMR = 26
126        MINRES = 27
127        GAUSS_SEIDEL=28
128        RILU=29
129        DEFAULT_REORDERING=30
130        SUPER_LU=31
131        PASTIX=32
132        YAIR_SHAPIRA_COARSENING=33
133        RUGE_STUEBEN_COARSENING=34
134        AGGREGATION_COARSENING=35
135        NO_PRECONDITIONER=36
136        MIN_COARSE_MATRIX_SIZE=37
137        
138        def __init__(self):
139            self.setLevelMax()
140            self.setCoarseningThreshold()
141            self.setNumSweeps()
142            self.setNumPreSweeps()
143            self.setNumPostSweeps()
144            self.setTolerance()
145            self.setAbsoluteTolerance()
146            self.setInnerTolerance()
147            self.setDropTolerance()
148            self.setDropStorage()
149            self.setIterMax()
150            self.setInnerIterMax()
151            self.setTruncation()
152            self.setRestart()
153            self.setSymmetry()
154            self.setVerbosity()
155            self.setInnerToleranceAdaption()
156            self.setAcceptanceConvergenceFailure()
157            self.setReordering()
158            self.setPackage()
159            self.setSolverMethod()
160            self.setPreconditioner()
161            self.setCoarsening()
162            self.setMinCoarseMatrixSize()
163            self.setRelaxationFactor()        
164            self.resetDiagnostics(all=True)
165    
166        def __str__(self):
167            return self.getSummary()
168        def getSummary(self):
169            """
170            Returns a string reporting the current settings
171            """
172            out="Solver Package: %s"%(self.getName(self.getPackage()))
173            out+="\nVerbosity = %s"%self.isVerbose()
174            out+="\nAccept failed convergence = %s"%self.acceptConvergenceFailure()
175            out+="\nRelative tolerance = %e"%self.getTolerance()
176            out+="\nAbsolute tolerance = %e"%self.getAbsoluteTolerance()
177            out+="\nSymmetric problem = %s"%self.isSymmetric()
178            out+="\nMaximum number of iteration steps = %s"%self.getIterMax()
179            out+="\nInner tolerance = %e"%self.getInnerTolerance()
180            out+="\nAdapt innner tolerance = %s"%self.adaptInnerTolerance()
181        
182            if self.getPackage() == self.PASO:
183                out+="\nSolver method = %s"%self.getName(self.getSolverMethod())
184                if self.getSolverMethod() == self.GMRES:
185                    out+="\nTruncation  = %s"%self.getTruncation()
186                    out+="\nRestart  = %s"%self.getRestart()
187                if self.getSolverMethod() == self.AMG:
188                    out+="\nNumber of pre / post sweeps = %s / %s, %s"%(self.getNumPreSweeps(), self.getNumPostSweeps(), self.getNumSweeps())
189                    out+="\nMaximum number of levels = %s"%self.LevelMax()
190                    out+="\nCoarsening threshold = %e"%self.getCoarseningThreshold()
191                    out+="\Coarsening method = %s"%self.getName(self.getCoarsening())
192                out+="\nPreconditioner = %s"%self.getName(self.getPreconditioner())
193                if self.getPreconditioner() == self.AMG:
194                    out+="\nMaximum number of levels = %s"%self.LevelMax()
195                    out+="\nCoarsening method = %s"%self.getName(self.getCoarsening())
196                    out+="\nCoarsening threshold = %e"%self.getMinCoarseMatrixSize()
197                    out+="\nMinimum size of the coarsest level matrix = %e"%self.getCoarseningThreshold()
198                    out+="\nNumber of pre / post sweeps = %s / %s, %s"%(self.getNumPreSweeps(), self.getNumPostSweeps(), self.getNumSweeps())
199                if self.getPreconditioner() == self.GAUSS_SEIDEL:
200                    out+="\nNumber of sweeps = %s"%self.getNumSweeps()
201                if self.getPreconditioner() == self.ILUT:
202                    out+="\nDrop tolerance = %e"%self.getDropTolerance()
203                    out+="\nStorage increase = %e"%self.getDropStorage()
204                if self.getPreconditioner() == self.RILU:
205                    out+="\nRelaxation factor = %e"%self.getRelaxationFactor()
206            return out
207            
208        def getName(self,key):
209            """
210            returns the name of a given key
211            
212            @param key: a valid key
213            """
214            if key == self.DEFAULT: return "DEFAULT"
215            if key == self.DIRECT: return "DIRECT"
216            if key == self.CHOLEVSKY: return "CHOLEVSKY"
217            if key == self.PCG: return "PCG"
218            if key == self.CR: return "CR"
219            if key == self.CGS: return "CGS"
220            if key == self.BICGSTAB: return "BICGSTAB"
221            if key == self.SSOR: return "SSOR"
222            if key == self.ILU0: return "ILU0:"
223            if key == self.ILUT: return "ILUT"
224            if key == self.JACOBI: return "JACOBI"
225            if key == self.GMRES: return "GMRES"
226            if key == self.PRES20: return "PRES20"
227            if key == self.LUMPING: return "LUMPING"
228            if key == self.NO_REORDERING: return "NO_REORDERING"
229            if key == self.MINIMUM_FILL_IN: return "MINIMUM_FILL_IN"
230            if key == self.NESTED_DISSECTION: return "NESTED_DISSECTION"
231            if key == self.MKL: return "MKL"
232            if key == self.UMFPACK: return "UMFPACK"
233            if key == self.ITERATIVE: return "ITERATIVE"
234            if key == self.PASO: return "PASO"
235            if key == self.AMG: return "AMG"
236            if key == self.REC_ILU: return "REC_ILU"
237            if key == self.TRILINOS: return "TRILINOS"
238            if key == self.NONLINEAR_GMRES: return "NONLINEAR_GMRES"
239            if key == self.TFQMR: return "TFQMR"
240            if key == self.MINRES: return "MINRES"
241            if key == self.GAUSS_SEIDEL: return "GAUSS_SEIDEL"
242            if key == self.RILU: return "RILU"
243            if key == self.DEFAULT_REORDERING: return "DEFAULT_REORDERING"
244            if key == self.SUPER_LU: return "SUPER_LU"
245            if key == self.PASTIX: return "PASTIX"
246            if key == self.YAIR_SHAPIRA_COARSENING: return "YAIR_SHAPIRA_COARSENING"
247            if key == self.RUGE_STUEBEN_COARSENING: return "RUGE_STUEBEN_COARSENING"
248            if key == self.AGGREGATION_COARSENING: return "AGGREGATION_COARSENING"
249            if key == self.NO_PRECONDITIONER: return "NO_PRECONDITIONER"
250            if key == self.MIN_COARSE_MATRIX_SIZE: return "MIN_COARSE_MATRIX_SIZE"
251            
252        def resetDiagnostics(self,all=False):
253            """
254            resets the diagnostics
255            
256            @param all: if C{all} is C{True} all diagnostics including accumulative counters are reset.
257            @type all: C{bool}
258            """
259            self.__num_iter=None
260            self.__num_level=None
261            self.__num_inner_iter=None
262            self.__time=None
263            self.__set_up_time=None
264            self.__residual_norm=None
265            self.__converged=None
266            if all:
267                self.__cum_num_inner_iter=0
268                self.__cum_num_iter=0
269                self.__cum_time=0
270                self.__cum_set_up_time=0
271    
272        def _updateDiagnostics(self, name, value):
273            """
274            Updates diagnostic information
275            
276            @param name: name of  diagnostic information
277            @type name: C{str} in the list "num_iter", "num_level", "num_inner_iter", "time", "set_up_time", "residual_norm", "converged".
278            @param vale: new value of the diagnostic information
279            @note: this function is used by a solver to report diagnostics informations.
280            """
281            if name == "num_iter":
282                self.__num_iter=int(value)
283                self.__cum_num_iter+=self.__num_iter
284            if name == "num_level":
285                self.__num_iter=int(value)
286            if name == "num_inner_iter":
287                self.__num_inner_iter=int(value)
288                self.__cum_num_inner_iter+=self.__num_inner_iter
289            if name == "time":
290                self.__time=float(value)
291                self.__cum_time+=self.__time
292            if name == "set_up_time":
293                self.__set_up_time=float(value)
294                self.__cum_set_up_time+=self.__set_up_time
295            if name == "residual_norm":
296                self.__residual_norm=float(value)
297            if name == "converged":
298                self.__converged = (value == True)
299        def getDiagnostics(self, name):
300            """
301            Returns the diagnostic information C{name}
302            
303            @param name: name of diagnostic information where
304            - "num_iter": the number of iteration steps
305            - "cum_num_iter": the cumulative number of iteration steps
306            - "num_level": the number of level in multi level solver
307            - "num_inner_iter": the number of inner iteration steps
308            - "cum_num_inner_iter": the cumulative number of inner iteration steps
309            - "time": execution time
310            - "cum_time": cumulative execution time
311            - "set_up_time": time to set up of the solver, typically this includes factorization and reordering
312            - "cum_set_up_time": cumulative time to set up of the solver
313            - "residual_norm": norm of the final residual
314            - "converged": return self.__converged    
315            @type name: C{str} in the list "num_iter", "num_level", "num_inner_iter", "time", "set_up_time", "residual_norm", "converged".
316            @return: requested value. C{None} is returned if the value is undefined.
317            @note: If the solver has thrown an exception diagnostic values have an undefined status.
318            """
319            if name == "num_iter": return self.__num_iter
320            elif name == "cum_num_iter": return self.__cum_num_iter
321            elif name == "num_level": return self.__num_level
322            elif name == "num_inner_iter": return self.__num_inner_iter
323            elif name == "cum_num_inner_iter": return self.__cum_num_inner_iter
324            elif name == "time": return self.__time
325            elif name == "cum_time": return self.__cum_time
326            elif name == "set_up_time": return self.__set_up_time
327            elif name == "cum_set_up_time": return self.__cum_set_up_time
328            elif name == "residual_norm": return self.__residual_norm
329            elif name == "converged": return self.__converged      
330            else:
331                raise ValueError,"unknown diagnostic item %s"%name
332        def hasConverged(self):
333            """
334            Returns C{True} if the last solver call has been finalized successfully.
335            @note: if an exception has been thrown by the solver the status of this flag is undefined.
336            """
337            return self.getDiagnostics("converged")
338        def setCoarsening(self,method=0):
339            """
340            Sets the key of the coarsening method to be applied in AMG.
341    
342            @param method: selects the coarsening method .
343            @type method: in {SolverOptions.DEFAULT}, L{SolverOptions.YAIR_SHAPIRA_COARSENING},
344            L{SolverOptions.RUGE_STUEBEN_COARSENING}, L{SolverOptions.AGGREGATION_COARSENING}
345            """
346        if method==None: method=0
347            if not method in [self.DEFAULT, self.YAIR_SHAPIRA_COARSENING, self.RUGE_STUEBEN_COARSENING, self.AGGREGATION_COARSENING]:
348                 raise ValueError,"unknown coarsening method %s"%method
349            self.__coarsening=method
350        
351        def getCoarsening(self):
352            """
353            Returns the key of the coarsening algorithm to be applied AMG.
354    
355            @rtype: in the list L{SolverOptions.DEFAULT}, L{SolverOptions.YAIR_SHAPIRA_COARSENING},
356            L{SolverOptions.RUGE_STUEBEN_COARSENING}, L{SolverOptions.AGGREGATION_COARSENING}
357            """
358            return self.__coarsening
359          
360        def setMinCoarseMatrixSize(self,size=500):
361            """
362            Sets the minumum size of the coarsest level matrix in AMG.
363    
364            @param size: minumum size of the coarsest level matrix .
365            @type size: positive C{int} or C{None}
366            """
367            size=int(size)
368            if size<0:
369               raise ValueError,"minumum size of the coarsest level matrix must be non-negative."
370        if size==None: size=500
371            self.__MinCoarseMatrixSize=size
372            
373        def getMinCoarseMatrixSize(self):
374            """
375            Returns the minumum size of the coarsest level matrix in AMG.
376    
377            @rtype: C{int}
378            """
379            return self.__MinCoarseMatrixSize
380          
381        def setPreconditioner(self, preconditioner=10):
382            """
383            Sets the preconditioner to be used.
384    
385            @param preconditioner: key of the preconditioner to be used.
386            @type preconditioner: in L{SolverOptions.SSOR}, L{SolverOptions.ILU0}, L{SolverOptions.ILUT}, L{SolverOptions.JACOBI},
387                                        L{SolverOptions.AMG}, L{SolverOptions.REC_ILU}, L{SolverOptions.GAUSS_SEIDEL}, L{SolverOptions.RILU},
388                                        L{SolverOptions.NO_PRECONDITIONER}
389            @note: Not all packages support all preconditioner. It can be assumed that a package makes a reasonable choice if it encounters
390            an unknown preconditioner.
391            """
392        if preconditioner==None: preconditioner=10
393            if not preconditioner in [ SolverOptions.SSOR, SolverOptions.ILU0, SolverOptions.ILUT, SolverOptions.JACOBI,
394                                        SolverOptions.AMG, SolverOptions.REC_ILU, SolverOptions.GAUSS_SEIDEL, SolverOptions.RILU,
395                                        SolverOptions.NO_PRECONDITIONER] :
396                 raise ValueError,"unknown preconditioner %s"%preconditioner
397            self.__preconditioner=preconditioner    
398        def getPreconditioner(self):
399            """
400            Returns key of the preconditioner to be used.
401    
402            @rtype: in the list L{SolverOptions.SSOR}, L{SolverOptions.ILU0}, L{SolverOptions.ILUT}, L{SolverOptions.JACOBI},
403                                        L{SolverOptions.AMG}, L{SolverOptions.REC_ILU}, L{SolverOptions.GAUSS_SEIDEL}, L{SolverOptions.RILU},
404                                        L{SolverOptions.NO_PRECONDITIONER}
405            """
406            return self.__preconditioner
407        def setSolverMethod(self, method=0):
408            """
409            Sets the solver method to be used. Use C{method}=C{SolverOptions.DIRECT} to indicate that a direct rather than an iterative
410            solver should be used and Use C{method}=C{SolverOptions.ITERATIVE} to indicate that an iterative rather than a direct
411            solver should be used.
412    
413            @param method: key of the solver method to be used.
414            @type method: in L{SolverOptions.DEFAULT}, L{SolverOptions.DIRECT}, L{SolverOptions.CHOLEVSKY}, L{SolverOptions.PCG},
415                            L{SolverOptions.CR}, L{SolverOptions.CGS}, L{SolverOptions.BICGSTAB}, L{SolverOptions.SSOR},
416                            L{SolverOptions.GMRES}, L{SolverOptions.PRES20}, L{SolverOptions.LUMPING}, L{SolverOptions.ITERATIVE},
417                            L{SolverOptions.AMG}, L{SolverOptions.NONLINEAR_GMRES}, L{SolverOptions.TFQMR}, L{SolverOptions.MINRES},
418                            L{SolverOptions.GAUSS_SEIDEL}
419            @note: Not all packages support all solvers. It can be assumed that a package makes a reasonable choice if it encounters
420            an unknown solver method.
421            """
422        if method==None: method=0
423            if not method in [ SolverOptions.DEFAULT, SolverOptions.DIRECT, SolverOptions.CHOLEVSKY, SolverOptions.PCG,
424                               SolverOptions.CR, SolverOptions.CGS, SolverOptions.BICGSTAB, SolverOptions.SSOR,
425                               SolverOptions.GMRES, SolverOptions.PRES20, SolverOptions.LUMPING, SolverOptions.ITERATIVE, SolverOptions.AMG,
426                               SolverOptions.NONLINEAR_GMRES, SolverOptions.TFQMR, SolverOptions.MINRES, SolverOptions.GAUSS_SEIDEL]:
427                 raise ValueError,"unknown solver method %s"%method
428            self.__method=method
429        def getSolverMethod(self):
430            """
431            Returns key of the solver method to be used.
432    
433            @rtype: in the list L{SolverOptions.DEFAULT}, L{SolverOptions.DIRECT}, L{SolverOptions.CHOLEVSKY}, L{SolverOptions.PCG},
434                            L{SolverOptions.CR}, L{SolverOptions.CGS}, L{SolverOptions.BICGSTAB}, L{SolverOptions.SSOR},
435                            L{SolverOptions.GMRES}, L{SolverOptions.PRES20}, L{SolverOptions.LUMPING}, L{SolverOptions.ITERATIVE},
436                            L{SolverOptions.AMG}, L{SolverOptions.NONLINEAR_GMRES}, L{SolverOptions.TFQMR}, L{SolverOptions.MINRES},
437                            L{SolverOptions.GAUSS_SEIDEL}
438            """
439            return self.__method
440            
441        def setPackage(self, package=0):
442            """
443            Sets the solver package to be used as a solver.  
444    
445            @param package: key of the solver package to be used.
446            @type package: in L{SolverOptions.DEFAULT}, L{SolverOptions.PASO}, L{SolverOptions.SUPER_LU}, L{SolverOptions.PASTIX}, L{SolverOptions.MKL}, L{SolverOptions.UMFPACK}, L{SolverOptions.TRILINOS}
447            @note: Not all packages are support on all implementation. An exception may be thrown on some platforms if a particular is requested.
448            """
449        if package==None: package=0
450            if not package in [SolverOptions.DEFAULT, SolverOptions.PASO, SolverOptions.SUPER_LU, SolverOptions.PASTIX, SolverOptions.MKL, SolverOptions.UMFPACK, SolverOptions.TRILINOS]:
451                 raise ValueError,"unknown solver package %s"%package
452            self.__package=package
453        def getPackage(self):
454            """
455            Returns the solver package key
456    
457            @rtype: in the list L{SolverOptions.DEFAULT}, L{SolverOptions.PASO}, L{SolverOptions.SUPER_LU}, L{SolverOptions.PASTIX}, L{SolverOptions.MKL}, L{SolverOptions.UMFPACK}, L{SolverOptions.TRILINOS}
458            """
459            return self.__package
460        def setReordering(self,ordering=30):
461            """
462            Sets the key of the reordering method to be applied if supported by the solver. Some direct solvers support reordering
463            to optimize compute time and storage use during elimination.
464    
465            @param ordering: selects the reordering strategy.
466            @type ordering: in L{SolverOptions.NO_REORDERING}, L{SolverOptions.NO_REORDERING},
467            L{SolverOptions.NO_REORDERING}, L{SolverOptions.DEFAULT_REORDERING}
468            """
469            if not ordering in [self.NO_REORDERING, self.MINIMUM_FILL_IN, self.NESTED_DISSECTION, self.DEFAULT_REORDERING]:
470                 raise ValueError,"unknown reordering strategy %s"%ordering
471            self.__reordering=ordering
472        def getReordering(self):
473            """
474            Returns the key of the reordering method to be applied if supported by the solver.
475    
476            @rtype: in the list L{SolverOptions.NO_REORDERING}, L{SolverOptions.NO_REORDERING},
477            L{SolverOptions.NO_REORDERING}, L{SolverOptions.DEFAULT_REORDERING}
478            """
479            return self.__reordering
480        def setRestart(self,restart=None):
481            """
482            Sets the number of iterations steps after which GMRES is performing a restart.
483    
484            @param restart: number of iteration steps after which to perform a restart. If equal to C{None} no
485                            restart is performed.
486            @type restart: C{int} or C{None}
487            """
488            if restart == None:
489                self.__restart=restart
490            else:
491                restart=int(restart)
492                if restart<1:
493                    raise ValueError,"restart must be positive."
494                self.__restart=restart
495            
496        def getRestart(self):
497            """
498            Returns the number of iterations steps after which GMRES is performing a restart.
499            If C{None} is returned no restart is performed.
500    
501            @rtype: C{int} or C{None}
502            """
503            if self.__restart < 0:
504                return None
505            else:
506                return self.__restart
507        def _getRestartForC(self):
508            r=self.getRestart()
509            if r == None:
510                return -1
511                else:
512                return r
513        def setTruncation(self,truncation=20):
514            """
515            Sets the number of residuals in GMRES to be stored for orthogonalization.  The more residuals are stored
516            the faster GMRES converged but
517    
518            @param truncation: truncation
519            @type truncation: C{int}
520            """
521            truncation=int(truncation)
522            if truncation<1:
523               raise ValueError,"truncation must be positive."
524            self.__truncation=truncation
525        def getTruncation(self):
526            """
527            Returns the number of residuals in GMRES to be stored for orthogonalization
528    
529            @rtype: C{int}
530            """
531            return self.__truncation
532        def setInnerIterMax(self,iter_max=10):
533            """
534            Sets the maximum number of iteration steps for the inner iteration.
535    
536            @param iter_max: maximum number of inner iterations
537            @type iter_max: C{int}
538            """
539            iter_max=int(iter_max)
540            if iter_max<1:
541               raise ValueError,"maximum number of inner iteration must be positive."
542            self.__inner_iter_max=iter_max
543        def getInnerIterMax(self):
544            """
545            Returns maximum number of inner iteration steps
546    
547            @rtype: C{int}
548            """
549            return self.__inner_iter_max
550        def setIterMax(self,iter_max=100000):
551            """
552            Sets the maximum number of iteration steps
553    
554            @param iter_max: maximum number of iteration steps
555            @type iter_max: C{int}
556            """
557            iter_max=int(iter_max)
558            if iter_max<1:
559               raise ValueError,"maximum number of iteration steps must be positive."
560            self.__iter_max=iter_max
561        def getIterMax(self):
562            """
563            Returns maximum number of iteration steps
564    
565            @rtype: C{int}
566            """
567            return self.__iter_max
568        def setLevelMax(self,level_max=10):
569            """
570            Sets the maximum number of coarsening levels to be used in an algebraic multi level solver or preconditioner
571    
572            @param level_max: maximum number of levels
573            @type level_max: C{int}
574            """
575            level_max=int(level_max)
576            if level_max<0:
577               raise ValueError,"maximum number of coarsening levels must be non-negative."
578            self.__level_max=level_max
579        def getLevelMax(self):
580            """
581            Returns the maximum number of coarsening levels to be used in an algebraic multi level solver or preconditioner
582    
583            @rtype: C{int}
584            """
585            return self.__level_max
586        def setCoarseningThreshold(self,theta=0.05):
587            """
588            Sets the threshold for coarsening in the algebraic multi level solver or preconditioner
589    
590            @param theta: threshold for coarsening
591            @type theta: positive C{float}
592            """
593            theta=float(theta)
594            if theta<0 or theta>1:
595               raise ValueError,"threshold must be non-negative and less or equal 1."
596            self.__coarsening_threshold=theta
597        def getCoarseningThreshold(self):
598            """
599            Returns the threshold for coarsening in the algebraic multi level solver or preconditioner
600    
601            @rtype: C{float}
602            """
603            return self.__coarsening_threshold
604        def setNumSweeps(self,sweeps=2):
605            """
606            Sets the number of sweeps in a Jacobi or Gauss-Seidel/SOR preconditioner.
607    
608            @param sweeps: number of sweeps
609            @type theta: positive C{int}
610            """
611            sweeps=int(sweeps)
612            if sweeps<1:
613               raise ValueError,"number of sweeps must be positive."
614            self.__sweeps=sweeps
615        def getNumSweeps(self):
616            """
617            Returns the number of sweeps in a Jacobi or Gauss-Seidel/SOR preconditioner.
618    
619            @rtype: C{int}
620            """
621            return self.__sweeps
622        def setNumPreSweeps(self,sweeps=2):
623            """
624            Sets the number of sweeps in the pre-smoothing step of a multi level solver or preconditioner
625    
626            @param sweeps: number of sweeps
627            @type theta: positive C{int}
628            """
629            sweeps=int(sweeps)
630            if sweeps<1:
631               raise ValueError,"number of sweeps must be positive."
632            self.__pre_sweeps=sweeps
633        def getNumPreSweeps(self):
634            """
635            Returns he number of sweeps in the pre-smoothing step of a multi level solver or preconditioner
636    
637            @rtype: C{int}
638            """
639            return self.__pre_sweeps
640        def setNumPostSweeps(self,sweeps=2):
641            """
642            Sets the number of sweeps in the post-smoothing step of a multi level solver or preconditioner
643    
644            @param sweeps: number of sweeps
645            @type theta: positive C{int}
646            """
647            sweeps=int(sweeps)
648            if sweeps<1:
649               raise ValueError,"number of sweeps must be positive."
650            self.__post_sweeps=sweeps
651        def getNumPostSweeps(self):
652            """
653            Returns he number of sweeps in the post-smoothing step of a multi level solver or preconditioner
654    
655            @rtype: C{int}
656            """
657            return self.__post_sweeps
658    
659        def setTolerance(self,rtol=1.e-8):
660            """
661            Sets the relative tolerance for the solver
662    
663            @param rtol: relative tolerance
664            @type rtol: non-negative C{float}
665            """
666            rtol=float(rtol)
667            if rtol<0 or rtol>1:
668               raise ValueError,"tolerance must be non-negative and less or equal 1."
669            self.__tolerance=rtol
670        def getTolerance(self):
671            """
672            Returns the relative tolerance for the solver
673    
674            @rtype: C{float}
675            """
676            return self.__tolerance
677        def setAbsoluteTolerance(self,atol=0.):
678            """
679            Sets the absolute tolerance for the solver
680    
681            @param atol:  absolute tolerance
682            @type atol: non-negative C{float}
683            """
684            atol=float(atol)
685            if atol<0:
686               raise ValueError,"tolerance must be non-negative."
687            self.__absolute_tolerance=atol
688        def getAbsoluteTolerance(self):
689            """
690            Returns the absolute tolerance for the solver
691    
692            @rtype: C{float}
693            """
694            return self.__absolute_tolerance
695    
696        def setInnerTolerance(self,rtol=0.9):
697            """
698             Sets the relative tolerance for an inner iteration scheme for instance
699            on the coarsest level in a multi-level scheme.
700    
701            @param rtol: inner relative tolerance
702            @type rtol: positive C{float}
703            """
704            rtol=float(rtol)
705            if rtol<=0 or rtol>1:
706                raise ValueError,"tolerance must be positive and less or equal 1."
707            self.__inner_tolerance=rtol
708        def getInnerTolerance(self):
709            """
710            Returns the relative tolerance for an inner iteration scheme
711    
712            @rtype: C{float}
713            """
714            return self.__inner_tolerance
715        def setDropTolerance(self,drop_tol=0.01):
716            """
717            Sets the relative drop tolerance in ILUT
718    
719            @param drop_tol: drop tolerance
720            @type drop_tol: positive C{float}
721            """
722            drop_tol=float(drop_tol)
723            if drop_tol<=0 or drop_tol>1:
724                raise ValueError,"drop tolerance must be positive and less or equal 1."
725            self.__drop_tolerance=drop_tol
726        def getDropTolerance(self):
727            """
728            Returns the relative drop tolerance in ILUT
729    
730            @rtype: C{float}
731            """
732            return self.__drop_tolerance
733        def setDropStorage(self,storage=2.):
734            """
735            Sets the maximum allowed increase in storage for ILUT. C{storage}=2 would mean that
736            a doubling of the storage needed for the coefficient matrix is allowed in the ILUT factorization.
737    
738            @param storage: allowed storage increase
739            @type storage: C{float}
740            """
741            storage=float(storage)
742            if storage<1:
743                raise ValueError,"allowed storage increase must be greater or equal to 1."
744            self.__drop_storage=storage
745        def getDropStorage(self):
746        
747            """
748            Returns the maximum allowed increase in storage for ILUT
749    
750            @rtype: C{float}
751            """
752            return self.__drop_storage
753        def setRelaxationFactor(self,factor=0.3):
754            """
755            Sets the relaxation factor used to add dropped elements in RILU to the main diagonal.
756    
757            @param factor: relaxation factor
758            @type factor: C{float}
759            @note: RILU with a relaxation factor 0 is identical to ILU0
760            """
761            factor=float(factor)
762            if factor<0:
763                raise ValueError,"relaxation factor must be non-negative."
764            self.__relaxation=factor
765        def getRelaxationFactor(self):
766        
767            """
768            Returns the relaxation factor used to add dropped elements in RILU to the main diagonal.
769    
770            @rtype: C{float}
771            """
772            return self.__relaxation
773        def isSymmetric(self):
774            """
775            Checks if symmetry of the  coefficient matrix is indicated.
776    
777            @return: True if a symmetric PDE is indicated, False otherwise
778            @rtype: C{bool}
779            """
780            return self.__symmetric
781        def setSymmetryOn(self):
782            """
783            Sets the symmetry flag to indicate that the coefficient matrix is symmetric.
784            """
785            self.__symmetric=True
786        def setSymmetryOff(self):
787            """
788            Clears the symmetry flag for the coefficient matrix.
789            """
790            self.__symmetric=False
791        def setSymmetry(self,flag=False):
792            """
793            Sets the symmetry flag for the coefficient matrix to C{flag}.
794    
795            @param flag: If True, the symmetry flag is set otherwise reset.
796            @type flag: C{bool}
797            """
798            if flag:
799                self.setSymmetryOn()
800            else:
801                self.setSymmetryOff()
802        def isVerbose(self):
803            """
804            Returns C{True} if the solver is expected to be verbose.
805    
806            @return: True if verbosity of switched on.
807            @rtype: C{bool}
808            """
809            return self.__verbose
810    
811        def setVerbosityOn(self):
812            """
813            Switches the verbosity of the solver on.
814            """
815            self.__verbose=True
816        def setVerbosityOff(self):
817            """
818            Switches the verbosity of the solver off.
819            """
820            self.__verbose=False
821        def setVerbosity(self,verbose=False):
822            """
823            Sets the verbosity flag for the solver to C{flag}.
824    
825            @param flag: If C{True}, the verbosity of the solver is switched on.
826            @type flag: C{bool}
827            """
828            if verbose:
829                self.setVerbosityOn()
830            else:
831                self.setVerbosityOff()
832            
833        def adaptInnerTolerance(self):
834            """
835            Returns C{True} if the tolerance of the inner solver is selected automatically.
836            Otherwise the inner tolerance set by L{setInnerTolerance} is used.
837    
838            @return: C{True} if inner tolerance adaption is chosen.
839            @rtype: C{bool}
840            """
841            return self.__adapt_inner_tolerance
842    
843        def setInnerToleranceAdaptionOn(self):
844            """
845            Switches the automatic selection of inner tolerance on
846            """
847            self.__adapt_inner_tolerance=True
848        def setInnerToleranceAdaptionOff(self):
849            """
850            Switches the automatic selection of inner tolerance off.
851            """
852            self.__adapt_inner_tolerance=False
853        def setInnerToleranceAdaption(self,adapt=True):
854            """
855            Sets a flag to indicate automatic selection of the inner tolerance.
856    
857            @param adapt: If C{True}, the inner tolerance is selected automatically.
858            @type adapt: C{bool}
859            """
860            if adapt:
861                self.setInnerToleranceAdaptionOn()
862            else:
863                self.setInnerToleranceAdaptionOff()
864    
865        def acceptConvergenceFailure(self):
866            """
867            Returns C{True} if a failure to meet the stopping criteria within the
868            given number of iteration steps is not raising in exception. This is useful
869            if a solver is used in a non-linear context where the non-linear solver can
870            continue even if the returned the solution does not necessarily meet the
871            stopping criteria. One can use the L{hasConverged} method to check if the
872            last call to the solver was successful.
873    
874            @return: C{True} if a failure to achieve convergence is accepted.
875            @rtype: C{bool}
876            """
877            return self.__accept_convergence_failure
878    
879        def setAcceptanceConvergenceFailureOn(self):
880            """
881            Switches the acceptance of a failure of convergence on
882            """
883            self.__accept_convergence_failure=True
884        def setAcceptanceConvergenceFailureOff(self):
885            """
886            Switches the acceptance of a failure of convergence off.
887            """
888            self.__accept_convergence_failure=False
889        def setAcceptanceConvergenceFailure(self,accept=False):
890            """
891            Sets a flag to indicate the acceptance of a failure of convergence.
892    
893            @param accept: If C{True}, any failure to achieve convergence is accepted.
894            @type accept: C{bool}
895            """
896            if accept:
897                self.setAcceptanceConvergenceFailureOn()
898            else:
899                self.setAcceptanceConvergenceFailureOff()
900    
901  class IllegalCoefficient(ValueError):  class IllegalCoefficient(ValueError):
902     """     """
903     raised if an illegal coefficient of the general ar particular PDE is requested.     Exception that is raised if an illegal coefficient of the general or
904       particular PDE is requested.
905     """     """
906       pass
907    
908  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
909     """     """
910     raised if an incorrect value for a coefficient is used.     Exception that is raised if an incorrect value for a coefficient is used.
911       """
912       pass
913    
914    class IllegalCoefficientFunctionSpace(ValueError):
915       """
916       Exception that is raised if an incorrect function space for a coefficient
917       is used.
918     """     """
919    
920  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
921     """     """
922     raised if a PDE is not fully defined yet.     Exception that is raised if a PDE is not fully defined yet.
923     """     """
924       pass
925    
926  def _CompTuple2(t1,t2):  class PDECoef(object):
       """  
       Compare two tuples  
     
       @param t1 The first tuple  
       @param t2 The second tuple  
     
       """  
     
       dif=t1[0]+t1[1]-(t2[0]+t2[1])  
       if dif<0: return 1  
       elif dif>0: return -1  
       else: return 0  
     
 class PDECoefficient:  
927      """      """
928      A class for PDE coefficients      A class for describing a PDE coefficient.
929    
930        @cvar INTERIOR: indicator that coefficient is defined on the interior of
931                        the PDE domain
932        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of
933                        the PDE domain
934        @cvar CONTACT: indicator that coefficient is defined on the contact region
935                       within the PDE domain
936        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the
937                                interior of the PDE domain using a reduced
938                                integration order
939        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the
940                                boundary of the PDE domain using a reduced
941                                integration order
942        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact
943                               region within the PDE domain using a reduced
944                               integration order
945        @cvar SOLUTION: indicator that coefficient is defined through a solution of
946                        the PDE
947        @cvar REDUCED: indicator that coefficient is defined through a reduced
948                       solution of the PDE
949        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is
950                           defined by the number of PDE equations
951        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is
952                           defined by the number of PDE solutions
953        @cvar BY_DIM: indicator that the dimension of the coefficient shape is
954                      defined by the spatial dimension
955        @cvar OPERATOR: indicator that the the coefficient alters the operator of
956                        the PDE
957        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right
958                             hand side of the PDE
959        @cvar BOTH: indicator that the the coefficient alters the operator as well
960                    as the right hand side of the PDE
961    
962      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
963      INTERIOR=0      INTERIOR=0
964      BOUNDARY=1      BOUNDARY=1
965      CONTACT=2      CONTACT=2
966      CONTINUOUS=3      SOLUTION=3
967      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
968      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
969      # number of unknowns.      BY_SOLUTION=6
970      EQUATION=3      BY_DIM=7
971      SOLUTION=4      OPERATOR=10
972      DIM=5      RIGHTHANDSIDE=11
973      # indicator for what is altered if the coefficient is altered:      BOTH=12
974      OPERATOR=5      INTERIOR_REDUCED=13
975      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
976      BOTH=7      CONTACT_REDUCED=15
977      def __init__(self,where,pattern,altering):  
978         """      def __init__(self, where, pattern, altering):
979         Initialise a PDE Coefficient type         """
980           Initialises a PDE coefficient type.
981    
982           @param where: describes where the coefficient lives
983           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION},
984                        L{REDUCED}, L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED},
985                        L{CONTACT_REDUCED}
986           @param pattern: describes the shape of the coefficient and how the shape
987                           is built for a given spatial dimension and numbers of
988                           equations and solutions in then PDE. For instance,
989                           (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) describes a
990                           rank 3 coefficient which is instantiated as shape (3,2,2)
991                           in case of three equations and two solution components
992                           on a 2-dimensional domain. In the case of single equation
993                           and a single solution component the shape components
994                           marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped.
995                           In this case the example would be read as (2,).
996           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
997           @param altering: indicates what part of the PDE is altered if the
998                            coefficient is altered
999           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
1000         """         """
1001           super(PDECoef, self).__init__()
1002         self.what=where         self.what=where
1003         self.pattern=pattern         self.pattern=pattern
1004         self.altering=altering         self.altering=altering
# Line 70  class PDECoefficient: Line 1006  class PDECoefficient:
1006    
1007      def resetValue(self):      def resetValue(self):
1008         """         """
1009         resets coefficient value to default         Resets the coefficient value to the default.
1010         """         """
1011         self.value=escript.Data()         self.value=escript.Data()
1012    
1013      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
1014         """         """
1015         defines the FunctionSpace of the coefficient on the domain         Returns the L{FunctionSpace<escript.FunctionSpace>} of the coefficient.
1016    
1017         @param domain:         @param domain: domain on which the PDE uses the coefficient
1018         """         @type domain: L{Domain<escript.Domain>}
1019         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used
1020         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)                                      to represent the equation
1021         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @type reducedEquationOrder: C{bool}
1022         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used
1023                                        to represent the solution
1024           @type reducedSolutionOrder: C{bool}
1025           @return: L{FunctionSpace<escript.FunctionSpace>} of the coefficient
1026           @rtype: L{FunctionSpace<escript.FunctionSpace>}
1027           """
1028           if self.what==self.INTERIOR:
1029                return escript.Function(domain)
1030           elif self.what==self.INTERIOR_REDUCED:
1031                return escript.ReducedFunction(domain)
1032           elif self.what==self.BOUNDARY:
1033                return escript.FunctionOnBoundary(domain)
1034           elif self.what==self.BOUNDARY_REDUCED:
1035                return escript.ReducedFunctionOnBoundary(domain)
1036           elif self.what==self.CONTACT:
1037                return escript.FunctionOnContactZero(domain)
1038           elif self.what==self.CONTACT_REDUCED:
1039                return escript.ReducedFunctionOnContactZero(domain)
1040           elif self.what==self.SOLUTION:
1041                if reducedEquationOrder and reducedSolutionOrder:
1042                    return escript.ReducedSolution(domain)
1043                else:
1044                    return escript.Solution(domain)
1045           elif self.what==self.REDUCED:
1046                return escript.ReducedSolution(domain)
1047    
1048      def getValue(self):      def getValue(self):
1049         """         """
1050         returns the value of the coefficient:         Returns the value of the coefficient.
1051    
1052           @return: value of the coefficient
1053           @rtype: L{Data<escript.Data>}
1054         """         """
1055         return self.value         return self.value
1056    
1057      def setValue(self,domain,numEquations=1,numSolutions=1,newValue=None):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
1058         """         """
1059         set the value of the coefficient to new value         Sets the value of the coefficient to a new value.
1060    
1061           @param domain: domain on which the PDE uses the coefficient
1062           @type domain: L{Domain<escript.Domain>}
1063           @param numEquations: number of equations of the PDE
1064           @type numEquations: C{int}
1065           @param numSolutions: number of components of the PDE solution
1066           @type numSolutions: C{int}
1067           @param reducedEquationOrder: True to indicate that reduced order is used
1068                                        to represent the equation
1069           @type reducedEquationOrder: C{bool}
1070           @param reducedSolutionOrder: True to indicate that reduced order is used
1071                                        to represent the solution
1072           @type reducedSolutionOrder: C{bool}
1073           @param newValue: number of components of the PDE solution
1074           @type newValue: any object that can be converted into a
1075                           L{Data<escript.Data>} object with the appropriate shape
1076                           and L{FunctionSpace<escript.FunctionSpace>}
1077           @raise IllegalCoefficientValue: if the shape of the assigned value does
1078                                           not match the shape of the coefficient
1079           @raise IllegalCoefficientFunctionSpace: if unable to interpolate value
1080                                                   to appropriate function space
1081         """         """
1082         if newValue==None:         if newValue==None:
1083             newValue=escript.Data()             newValue=escript.Data()
1084         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
1085             if not newValue.isEmpty():             if not newValue.isEmpty():
1086                newValue=escript.Data(newValue,self.getFunctionSpace(domain))                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
1087                    try:
1088                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
1089                    except:
1090                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
1091         else:         else:
1092             newValue=escript.Data(newValue,self.getFunctionSpace(domain))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
1093         if not newValue.isEmpty():         if not newValue.isEmpty():
1094             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
1095                 raise IllegalCoefficientValue,"Expected shape for coefficient %s is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())                 raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
1096         self.value=newValue         self.value=newValue
1097    
1098      def isAlteringOperator(self):      def isAlteringOperator(self):
1099          """          """
1100      return true if the operator of the PDE is changed when the coefficient is changed          Checks if the coefficient alters the operator of the PDE.
1101      """  
1102            @return: True if the operator of the PDE is changed when the
1103                     coefficient is changed
1104            @rtype: C{bool}
1105            """
1106          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
1107              return not None              return not None
1108          else:          else:
# Line 118  class PDECoefficient: Line 1110  class PDECoefficient:
1110    
1111      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
1112          """          """
1113      return true if the right hand side of the PDE is changed when the coefficient is changed          Checks if the coefficient alters the right hand side of the PDE.
1114      """  
1115            @rtype: C{bool}
1116            @return: True if the right hand side of the PDE is changed when the
1117                     coefficient is changed, C{None} otherwise.
1118            """
1119          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
1120              return not None              return not None
1121          else:          else:
# Line 127  class PDECoefficient: Line 1123  class PDECoefficient:
1123    
1124      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
1125         """         """
1126         tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim         Tries to estimate the number of equations and number of solutions if
1127           the coefficient has the given shape.
1128    
1129         @param shape:         @param domain: domain on which the PDE uses the coefficient
1130         @param dim:         @type domain: L{Domain<escript.Domain>}
1131           @param shape: suggested shape of the coefficient
1132           @type shape: C{tuple} of C{int} values
1133           @return: the number of equations and number of solutions of the PDE if
1134                    the coefficient has given shape. If no appropriate numbers
1135                    could be identified, C{None} is returned
1136           @rtype: C{tuple} of two C{int} values or C{None}
1137         """         """
1138         dim=domain.getDim()         dim=domain.getDim()
1139         if len(shape)>0:         if len(shape)>0:
# Line 138  class PDECoefficient: Line 1141  class PDECoefficient:
1141         else:         else:
1142             num=1             num=1
1143         search=[]         search=[]
1144         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
1145            for e in range(num):            for u in range(num):
1146               search.append((e,u))               for e in range(num):
1147         search.sort(_CompTuple2)                  search.append((e,u))
1148         for item in search:            search.sort(self.__CompTuple2)
1149              for item in search:
1150               s=self.getShape(domain,item[0],item[1])               s=self.getShape(domain,item[0],item[1])
1151               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
1152                   return (1,1)                   return (1,1)
1153               else:               else:
1154                   if s==shape: return item                   if s==shape: return item
1155           elif self.definesNumEquation():
1156              for e in range(num,0,-1):
1157                 s=self.getShape(domain,e,0)
1158                 if len(s)==0 and len(shape)==0:
1159                     return (1,None)
1160                 else:
1161                     if s==shape: return (e,None)
1162    
1163           elif self.definesNumSolutions():
1164              for u in range(num,0,-1):
1165                 s=self.getShape(domain,0,u)
1166                 if len(s)==0 and len(shape)==0:
1167                     return (None,1)
1168                 else:
1169                     if s==shape: return (None,u)
1170         return None         return None
1171    
1172        def definesNumSolutions(self):
1173           """
1174           Checks if the coefficient allows to estimate the number of solution
1175           components.
1176    
1177           @return: True if the coefficient allows an estimate of the number of
1178                    solution components, False otherwise
1179           @rtype: C{bool}
1180           """
1181           for i in self.pattern:
1182                 if i==self.BY_SOLUTION: return True
1183           return False
1184    
1185        def definesNumEquation(self):
1186           """
1187           Checks if the coefficient allows to estimate the number of equations.
1188    
1189           @return: True if the coefficient allows an estimate of the number of
1190                    equations, False otherwise
1191           @rtype: C{bool}
1192           """
1193           for i in self.pattern:
1194                 if i==self.BY_EQUATION: return True
1195           return False
1196    
1197        def __CompTuple2(self,t1,t2):
1198          """
1199          Compares two tuples of possible number of equations and number of
1200          solutions.
1201    
1202          @param t1: the first tuple
1203          @param t2: the second tuple
1204          @return: 0, 1, or -1
1205          """
1206    
1207          dif=t1[0]+t1[1]-(t2[0]+t2[1])
1208          if dif<0: return 1
1209          elif dif>0: return -1
1210          else: return 0
1211    
1212      def getShape(self,domain,numEquations=1,numSolutions=1):      def getShape(self,domain,numEquations=1,numSolutions=1):
1213          """         """
1214      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         Builds the required shape of the coefficient.
1215    
1216      @param e:         @param domain: domain on which the PDE uses the coefficient
1217      @param u:         @type domain: L{Domain<escript.Domain>}
1218      @param dim:         @param numEquations: number of equations of the PDE
1219      """         @type numEquations: C{int}
1220          dim=domain.getDim()         @param numSolutions: number of components of the PDE solution
1221          s=()         @type numSolutions: C{int}
1222          for i in self.pattern:         @return: shape of the coefficient
1223               if i==self.EQUATION:         @rtype: C{tuple} of C{int} values
1224           """
1225           dim=domain.getDim()
1226           s=()
1227           for i in self.pattern:
1228                 if i==self.BY_EQUATION:
1229                  if numEquations>1: s=s+(numEquations,)                  if numEquations>1: s=s+(numEquations,)
1230               elif i==self.SOLUTION:               elif i==self.BY_SOLUTION:
1231                  if numSolutions>1: s=s+(numSolutions,)                  if numSolutions>1: s=s+(numSolutions,)
1232               else:               else:
1233                  s=s+(dim,)                  s=s+(dim,)
1234          return s         return s
   
 class LinearPDE:  
    """  
    Class to define a linear PDE of the form  
   
    \f[  
      -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
1235    
1236     with boundary conditons:  #====================================================================================================================
1237    
1238     \f[  class LinearProblem(object):
1239     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i     """
1240     \f]     This is the base class to define a general linear PDE-type problem for
1241       for an unknown function M{u} on a given domain defined through a
1242     and contact conditions     L{Domain<escript.Domain>} object. The problem can be given as a single
1243       equation or as a system of equations.
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i  
    \f]  
1244    
1245     and constraints:     The class assumes that some sort of assembling process is required to form
1246       a problem of the form
1247    
1248     \f[     M{L u=f}
    u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
   
    """  
    TOL=1.e-13  
    # solver methods  
    UNKNOWN=-1  
    DEFAULT_METHOD=0  
    DIRECT=1  
    CHOLEVSKY=2  
    PCG=3  
    CR=4  
    CGS=5  
    BICGSTAB=6  
    SSOR=7  
    ILU0=8  
    ILUT=9  
    JACOBI=10  
    GMRES=11  
    PRES20=12  
    LUMPING=13  
    # matrix reordering:  
    NO_REORDERING=0  
    MINIMUM_FILL_IN=1  
    NESTED_DISSECTION=2  
    # important keys in the dictonary used to hand over options to the solver library:  
    METHOD_KEY="method"  
    SYMMETRY_KEY="symmetric"  
    TOLERANCE_KEY="tolerance"  
1249    
1250       where M{L} is an operator and M{f} is the right hand side. This operator
1251       problem will be solved to get the unknown M{u}.
1252    
1253       """
1254     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
1255       """       """
1256       initializes a new linear PDE       Initializes a linear problem.
1257    
1258       @param domain: domain of the PDE       @param domain: domain of the PDE
1259       @type domain: L{Domain}       @type domain: L{Domain<escript.Domain>}
1260       @param numEquations: number of equations. If numEquations==None the number of equations       @param numEquations: number of equations. If C{None} the number of
1261                            is exracted from the PDE coefficients.                            equations is extracted from the coefficients.
1262       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components       @param numSolutions: number of solution components. If C{None} the number
1263                            is exracted from the PDE coefficients.                            of solution components is extracted from the
1264       @param debug: if True debug informations are printed.                            coefficients.
1265         @param debug: if True debug information is printed
1266    
1267       """       """
1268       #       super(LinearProblem, self).__init__()
1269       #   the coefficients of the general PDE:  
      #  
      self.__COEFFICIENTS_OF_GENEARL_PDE={  
        "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
        "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
        "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
        "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
        "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
        "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
        "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
        "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
   
      # COEFFICIENTS can be overwritten by subclasses:  
      self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE  
      # initialize attributes  
1270       self.__debug=debug       self.__debug=debug
1271       self.__domain=domain       self.__domain=domain
1272       self.__numEquations=numEquations       self.__numEquations=numEquations
1273       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
1274       self.__resetSystem()       self.__altered_coefficients=False
1275         self.__reduce_equation_order=False
1276       # set some default values:       self.__reduce_solution_order=False
      self.__homogeneous_constraint=True  
      self.__row_function_space=escript.Solution(self.__domain)  
      self.__column_function_space=escript.Solution(self.__domain)  
      self.__tolerance=1.e-8  
      self.__solver_method=self.DEFAULT_METHOD  
      self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT_METHOD,False)  
1277       self.__sym=False       self.__sym=False
1278         self.setSolverOptions()
1279       self.resetCoefficients()       self.__is_RHS_valid=False
1280       self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))       self.__is_operator_valid=False
1281     # =============================================================================       self.__COEFFICIENTS={}
1282         self.__solution_rtol=1.e99
1283         self.__solution_atol=1.e99
1284         self.setSymmetryOff()
1285         # initialize things:
1286         self.resetAllCoefficients()
1287         self.initializeSystem()
1288       # ==========================================================================
1289     #    general stuff:     #    general stuff:
1290     # =============================================================================     # ==========================================================================
1291     def __str__(self):     def __str__(self):
1292         return "<LinearPDE %d>"%id(self)       """
1293     # =============================================================================       Returns a string representation of the PDE.
1294    
1295         @return: a simple representation of the PDE
1296         @rtype: C{str}
1297         """
1298         return "<LinearProblem %d>"%id(self)
1299       # ==========================================================================
1300     #    debug :     #    debug :
1301     # =============================================================================     # ==========================================================================
1302     def setDebugOn(self):     def setDebugOn(self):
1303       """       """
1304       switches on debugging       Switches debug output on.
1305       """       """
1306       self.__debug=not None       self.__debug=not None
1307    
1308     def setDebugOff(self):     def setDebugOff(self):
1309       """       """
1310       switches off debugging       Switches debug output off.
1311       """       """
1312       self.__debug=None       self.__debug=None
1313    
1314       def setDebug(self, flag):
1315         """
1316         Switches debug output on if C{flag} is True otherwise it is switched off.
1317    
1318         @param flag: desired debug status
1319         @type flag: C{bool}
1320         """
1321         if flag:
1322             self.setDebugOn()
1323         else:
1324             self.setDebugOff()
1325    
1326     def trace(self,text):     def trace(self,text):
1327       """       """
1328       print the text message if debugging is swiched on.       Prints the text message if debug mode is switched on.
1329    
1330       @param name: name of the coefficient enquired.       @param text: message to be printed
1331       @type name: C{string}       @type text: C{string}
1332       """       """
1333       if self.__debug: print "%s: %s"%(str(self),text)       if self.__debug: print "%s: %s"%(str(self),text)
1334    
1335     # =============================================================================     # ==========================================================================
1336     # some service functions:     # some service functions:
1337     # =============================================================================     # ==========================================================================
1338       def introduceCoefficients(self,**coeff):
1339           """
1340           Introduces new coefficients into the problem.
1341    
1342           Use::
1343    
1344           p.introduceCoefficients(A=PDECoef(...), B=PDECoef(...))
1345    
1346           to introduce the coefficients M{A} ans M{B}.
1347           """
1348           for name, type in coeff.items():
1349               if not isinstance(type,PDECoef):
1350                  raise ValueError,"coefficient %s has no type."%name
1351               self.__COEFFICIENTS[name]=type
1352               self.__COEFFICIENTS[name].resetValue()
1353               self.trace("coefficient %s has been introduced."%name)
1354    
1355     def getDomain(self):     def getDomain(self):
1356       """       """
1357       returns the domain of the PDE       Returns the domain of the PDE.
       
      @return : the domain of the PDE  
      @rtype : C{Domain}  
1358    
1359         @return: the domain of the PDE
1360         @rtype: L{Domain<escript.Domain>}
1361       """       """
1362       return self.__domain       return self.__domain
1363       def getDomainStatus(self):
1364         """
1365         Return the status indicator of the domain
1366         """
1367         return self.getDomain().getStatus()
1368    
1369       def getSystemStatus(self):
1370         """
1371         Return the domain status used to build the current system
1372         """
1373         return self.__system_status
1374       def setSystemStatus(self,status=None):
1375         """
1376         Sets the system status to C{status} if C{status} is not present the
1377         current status of the domain is used.
1378         """
1379         if status == None:
1380             self.__system_status=self.getDomainStatus()
1381         else:
1382             self.__system_status=status
1383    
1384     def getDim(self):     def getDim(self):
1385       """       """
1386       returns the spatial dimension of the PDE       Returns the spatial dimension of the PDE.
1387    
1388       @return : the spatial dimension of the PDE domain       @return: the spatial dimension of the PDE domain
1389       @rtype : C{int}       @rtype: C{int}
1390       """       """
1391       return self.getDomain().getDim()       return self.getDomain().getDim()
1392    
1393     def getNumEquations(self):     def getNumEquations(self):
1394       """       """
1395       returns the number of equations       Returns the number of equations.
1396    
1397       @return : the number of equations       @return: the number of equations
1398       @rtype : C{int}       @rtype: C{int}
1399       @raise UndefinedPDEError: if the number of equations is not be specified yet.       @raise UndefinedPDEError: if the number of equations is not specified yet
1400       """       """
1401       if self.__numEquations==None:       if self.__numEquations==None:
1402           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."           if self.__numSolutions==None:
1403       else:              raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
1404           return self.__numEquations           else:
1405                self.__numEquations=self.__numSolutions
1406         return self.__numEquations
1407    
1408     def getNumSolutions(self):     def getNumSolutions(self):
1409       """       """
1410       returns the number of unknowns       Returns the number of unknowns.
1411    
1412       @return : the number of unknowns       @return: the number of unknowns
1413       @rtype : C{int}       @rtype: C{int}
1414       @raise UndefinedPDEError: if the number of unknowns is not be specified yet.       @raise UndefinedPDEError: if the number of unknowns is not specified yet
1415       """       """
1416       if self.__numSolutions==None:       if self.__numSolutions==None:
1417          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."          if self.__numEquations==None:
1418       else:              raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
1419          return self.__numSolutions          else:
1420                self.__numSolutions=self.__numEquations
1421     def getFunctionSpaceForEquation(self):       return self.__numSolutions
      """  
      returns the L{escript.FunctionSpace} used to discretize the equation  
       
      @return : representation space of equation  
      @rtype : L{escript.FunctionSpace}  
   
      """  
      return self.__row_function_space  
1422    
1423     def getFunctionSpaceForSolution(self):     def reduceEquationOrder(self):
1424       """       """
1425       returns the L{escript.FunctionSpace} used to represent the solution       Returns the status of order reduction for the equation.
       
      @return : representation space of solution  
      @rtype : L{escript.FunctionSpace}  
1426    
1427         @return: True if reduced interpolation order is used for the
1428                  representation of the equation, False otherwise
1429         @rtype: L{bool}
1430       """       """
1431       return self.__column_function_space       return self.__reduce_equation_order
1432    
1433       def reduceSolutionOrder(self):
    def getOperator(self):  
1434       """       """
1435       provides access to the operator of the PDE       Returns the status of order reduction for the solution.
1436    
1437       @return : the operator of the PDE       @return: True if reduced interpolation order is used for the
1438       @rtype : L{Operator}                representation of the solution, False otherwise
1439         @rtype: L{bool}
1440       """       """
1441       m=self.getSystem()[0]       return self.__reduce_solution_order
      if self.isUsingLumping():  
          return self.copyConstraint(1./m)  
      else:  
          return m  
1442    
1443     def getRightHandSide(self):     def getFunctionSpaceForEquation(self):
1444       """       """
1445       provides access to the right hand side of the PDE       Returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize
1446         the equation.
1447    
1448       @return : the right hand side of the PDE       @return: representation space of equation
1449       @rtype : L{escript.Data}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1450       """       """
1451       r=self.getSystem()[1]       if self.reduceEquationOrder():
1452       if self.isUsingLumping():           return escript.ReducedSolution(self.getDomain())
          return self.copyConstraint(r)  
1453       else:       else:
1454           return r           return escript.Solution(self.getDomain())
1455    
1456     def applyOperator(self,u=None):     def getFunctionSpaceForSolution(self):
1457       """       """
1458       applies the operator of the PDE to a given u or the solution of PDE if u is not present.       Returns the L{FunctionSpace<escript.FunctionSpace>} used to represent
1459         the solution.
1460    
1461       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}       @return: representation space of solution
1462                 the current solution is used.       @rtype: L{FunctionSpace<escript.FunctionSpace>}
      @type u: L{escript.Data} or None  
      @return : image of u  
      @rtype : L{escript.Data}  
1463       """       """
1464       if u==None:       if self.reduceSolutionOrder():
1465            return self.getOperator()*self.getSolution()           return escript.ReducedSolution(self.getDomain())
1466       else:       else:
1467          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())           return escript.Solution(self.getDomain())
   
    def getResidual(self,u=None):  
      """  
      return the residual of u or the current solution if u is not present.  
   
      @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}  
                the current solution is used.  
      @type u: L{escript.Data} or None  
      @return : residual of u  
      @rtype : L{escript.Data}  
      """  
      return self.applyOperator(u)-self.getRightHandSide()  
   
    def checkSymmetry(self,verbose=True):  
       """  
       test the PDE for symmetry.  
   
   
      @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.  
      @type verbose: C{bool}  
      @return:  True if the PDE is symmetric.  
      @rtype : C{escript.Data}  
   
       @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.  
       """  
       verbose=verbose or self.debug()  
       out=True  
       if self.getNumSolutions()!=self.getNumEquations():  
          if verbose: print "non-symmetric PDE because of different number of equations and solutions"  
          out=False  
       else:  
          A=self.getCoefficientOfGeneralPDE("A")  
          if not A.isEmpty():  
             tol=util.Lsup(A)*self.TOL  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                   for j in range(self.getDim()):  
                      for k in range(self.getNumSolutions()):  
                         for l in range(self.getDim()):  
                             if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:  
                                if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)  
                                out=False  
             else:  
                for j in range(self.getDim()):  
                   for l in range(self.getDim()):  
                      if util.Lsup(A[j,l]-A[l,j])>tol:  
                         if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)  
                         out=False  
          B=self.getCoefficientOfGeneralPDE("B")  
          C=self.getCoefficientOfGeneralPDE("C")  
          if B.isEmpty() and not C.isEmpty():  
             if verbose: print "non-symmetric PDE because B is not present but C is"  
             out=False  
          elif not B.isEmpty() and C.isEmpty():  
             if verbose: print "non-symmetric PDE because C is not present but B is"  
             out=False  
          elif not B.isEmpty() and not C.isEmpty():  
             tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          if util.Lsup(B[i,j,k]-C[k,i,j])>tol:  
                               if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)  
                               out=False  
             else:  
                for j in range(self.getDim()):  
                   if util.Lsup(B[j]-C[j])>tol:  
                      if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)  
                      out=False  
          if self.getNumSolutions()>1:  
            D=self.getCoefficientOfGeneralPDE("D")  
            if not D.isEmpty():  
              tol=util.Lsup(D)*self.TOL  
              for i in range(self.getNumEquations()):  
                 for k in range(self.getNumSolutions()):  
                   if util.Lsup(D[i,k]-D[k,i])>tol:  
                       if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)  
                       out=False  
1468    
1469        return out     # ==========================================================================
   
    def getSolution(self,**options):  
        """  
        returns the solution of the PDE. If the solution is not valid the PDE is solved.  
   
        @return: the solution  
        @rtype: L{escript.Data}  
        @param options: solver options  
        @keyword verbose:  
        @keyword reordering: reordering scheme to be used during elimination  
        @keyword preconditioner: preconditioner method to be used  
        @keyword iter_max: maximum number of iteration steps allowed.  
        @keyword drop_tolerance:  
        @keyword drop_storage:  
        @keyword truncation:  
        @keyword restart:  
        """  
        if not self.__solution_isValid:  
           mat,f=self.getSystem()  
           if self.isUsingLumping():  
              self.__solution=self.copyConstraint(f*mat)  
           else:  
              options[self.TOLERANCE_KEY]=self.getTolerance()  
              options[self.METHOD_KEY]=self.getSolverMethod()  
              options[self.SYMMETRY_KEY]=self.isSymmetric()  
              self.trace("PDE is resolved.")  
              self.trace("solver options: %s"%str(options))  
              self.__solution=mat.solve(f,options)  
           self.__solution_isValid=True  
        return self.__solution  
   
    def getFlux(self,u=None):  
      """  
      returns the flux J_ij for a given u  
   
        \f[  
        J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}  
        \f]  
   
      @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.  
      @type u: L{escript.Data} or None  
      @return : flux  
      @rtype : L{escript.Data}  
   
      """  
      if u==None: u=self.getSolution()  
      return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")  
   
    # =============================================================================  
1470     #   solver settings:     #   solver settings:
1471     # =============================================================================     # ==========================================================================
1472     def setSolverMethod(self,solver=None):     def setSolverOptions(self,options=None):
        """  
        sets a new solver  
   
        @param solver: sets a new solver method.  
        @type solver: C{int}  
   
1473         """         """
1474         if solver==None: solve=self.DEFAULT_METHOD         Sets the solver options.
        if not solver==self.getSolverMethod():  
            self.__solver_method=solver  
            self.__checkMatrixType()  
            self.trace("New solver is %s"%self.getSolverMethodName())  
1475    
1476     def getSolverMethodName(self):         @param options: the new solver options. If equal C{None}, the solver options are set to the default.
1477           @type options: L{SolverOptions} or C{None}
1478           @note: The symmetry flag of options is overwritten by the symmetry flag of the L{LinearProblem}.
1479           """
1480           if options==None:
1481              self.__solver_options=SolverOptions()
1482           elif isinstance(options, SolverOptions):
1483              self.__solver_options=options
1484           else:
1485              raise ValueError,"options must be a SolverOptions object."
1486           self.__solver_options.setSymmetry(self.__sym)
1487        
1488       def getSolverOptions(self):
1489         """         """
1490         returns the name of the solver currently used         Returns the solver options
1491      
1492         @return : the name of the solver currently used.         @rtype: L{SolverOptions}
        @rtype: C{string}  
1493         """         """
1494           self.__solver_options.setSymmetry(self.__sym)
1495         m=self.getSolverMethod()         return self.__solver_options
        if m==self.DEFAULT_METHOD: return "DEFAULT_METHOD"  
        elif m==self.DIRECT: return "DIRECT"  
        elif m==self.CHOLEVSKY: return "CHOLEVSKY"  
        elif m==self.PCG: return "PCG"  
        elif m==self.CR: return "CR"  
        elif m==self.CGS: return "CGS"  
        elif m==self.BICGSTAB: return "BICGSTAB"  
        elif m==self.SSOR: return "SSOR"  
        elif m==self.GMRES: return "GMRES"  
        elif m==self.PRES20: return "PRES20"  
        elif m==self.LUMPING: return "LUMPING"  
        return None  
1496                
   
    def getSolverMethod(self):  
        """  
        returns the solver method  
     
        @return : the solver method currently be used.  
        @rtype : C{int}  
        """  
        return self.__solver_method  
   
1497     def isUsingLumping(self):     def isUsingLumping(self):
1498        """        """
1499        checks if matrix lumping is used a solver method        Checks if matrix lumping is the current solver method.
1500    
1501        @return : True is lumping is currently used a solver method.        @return: True if the current solver method is lumping
1502        @rtype: C{bool}        @rtype: C{bool}
1503        """        """
1504        return self.getSolverMethod()==self.LUMPING        return self.getSolverOptions().getSolverMethod()==self.getSolverOptions().LUMPING
1505       # ==========================================================================
    def setTolerance(self,tol=1.e-8):  
        """  
        resets the tolerance for the solver method to tol where for an appropriate norm |.|  
   
                |self.getResidual()|<tol*|self.getRightHandSide()|  
   
        defines the stopping criterion.  
   
        @param tol: new tolerance for the solver. If the tol is lower then the current tolerence  
                    the system will be resolved.  
        @type solver: C{float}  
        @raise ValueException: if tolerance is not positive.  
        """  
        if not tol>0:  
            raise ValueException,"Tolerance as to be positive"  
        if tol<self.getTolerance(): self.__invalidateSolution()  
        self.trace("New tolerance %e"%tol)  
        self.__tolerance=tol  
        return  
   
    def getTolerance(self):  
        """  
        returns the tolerance set for the solution  
   
        @return: tolerance currently used.  
        @rtype: C{float}  
        """  
        return self.__tolerance  
   
    # =============================================================================  
1506     #    symmetry  flag:     #    symmetry  flag:
1507     # =============================================================================     # ==========================================================================
1508     def isSymmetric(self):     def isSymmetric(self):
1509        """        """
1510        checks if symmetry is indicated.        Checks if symmetry is indicated.
1511        
1512        @return : True is a symmetric PDE is indicated, otherwise False is returned        @return: True if a symmetric PDE is indicated, False otherwise
1513        @rtype : C{bool}        @rtype: C{bool}
1514          @note: the method is equivalent to use getSolverOptions().isSymmetric()
1515        """        """
1516        return self.__sym        self.getSolverOptions().isSymmetric()
1517    
1518     def setSymmetryOn(self):     def setSymmetryOn(self):
1519        """        """
1520        sets the symmetry flag.        Sets the symmetry flag.
1521          @note: The method overwrites the symmetry flag set by the solver options
1522        """        """
1523        if not self.isSymmetric():        self.__sym=True
1524           self.trace("PDE is set to be symmetric")        self.getSolverOptions().setSymmetryOn()
          self.__sym=True  
          self.__checkMatrixType()  
1525    
1526     def setSymmetryOff(self):     def setSymmetryOff(self):
1527        """        """
1528        removes the symmetry flag.        Clears the symmetry flag.
1529          @note: The method overwrites the symmetry flag set by the solver options
1530        """        """
1531        if self.isSymmetric():        self.__sym=False
1532           self.trace("PDE is set to be unsymmetric")        self.getSolverOptions().setSymmetryOff()
1533           self.__sym=False  
1534           self.__checkMatrixType()     def setSymmetry(self,flag=False):
   
    def setSymmetryTo(self,flag=False):  
       """  
       sets the symmetry flag to flag  
   
       @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.  
       @type flag: C{bool}  
1535        """        """
1536        if flag:        Sets the symmetry flag to C{flag}.
          self.setSymmetryOn()  
       else:  
          self.setSymmetryOff()  
1537    
1538            @param flag: If True, the symmetry flag is set otherwise reset.
1539     # =============================================================================        @type flag: C{bool}
1540          @note: The method overwrites the symmetry flag set by the solver options
1541          """
1542          self.getSolverOptions().setSymmetry(flag)
1543       # ==========================================================================
1544     # function space handling for the equation as well as the solution     # function space handling for the equation as well as the solution
1545     # =============================================================================     # ==========================================================================
1546     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1547       """       """
1548       switches on reduced order for solution and equation representation       Switches reduced order on for solution and equation representation.
1549    
1550         @raise RuntimeError: if order reduction is altered after a coefficient has
1551                              been set
1552       """       """
1553       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1554       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1555    
1556     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1557       """       """
1558       switches off reduced order for solution and equation representation       Switches reduced order off for solution and equation representation
1559    
1560         @raise RuntimeError: if order reduction is altered after a coefficient has
1561                              been set
1562       """       """
1563       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1564       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1565    
1566     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1567       """       """
1568       sets order reduction for both solution and equation representation according to flag.       Sets order reduction state for both solution and equation representation
1569         according to flag.
1570    
1571       @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or       @param flag: if True, the order reduction is switched on for both solution
1572                    if flag is not present order reduction is switched off                    and equation representation, otherwise or if flag is not
1573                      present order reduction is switched off
1574       @type flag: C{bool}       @type flag: C{bool}
1575         @raise RuntimeError: if order reduction is altered after a coefficient has
1576                              been set
1577       """       """
1578       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1579       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
# Line 702  class LinearPDE: Line 1581  class LinearPDE:
1581    
1582     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1583       """       """
1584       switches on reduced order for solution representation       Switches reduced order on for solution representation.
1585    
1586         @raise RuntimeError: if order reduction is altered after a coefficient has
1587                              been set
1588       """       """
1589       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1590       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1591           self.trace("Reduced order is used to solution representation.")                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1592           self.__column_function_space=new_fs           self.trace("Reduced order is used for solution representation.")
1593           self.__resetSystem()           self.__reduce_solution_order=True
1594             self.initializeSystem()
1595    
1596     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1597       """       """
1598       switches off reduced order for solution representation       Switches reduced order off for solution representation
1599    
1600         @raise RuntimeError: if order reduction is altered after a coefficient has
1601                              been set.
1602       """       """
1603       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1604       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1605                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1606           self.trace("Full order is used to interpolate solution.")           self.trace("Full order is used to interpolate solution.")
1607           self.__column_function_space=new_fs           self.__reduce_solution_order=False
1608           self.__resetSystem()           self.initializeSystem()
1609    
1610     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1611       """       """
1612       sets order for test functions according to flag       Sets order reduction state for solution representation according to flag.
1613    
1614       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or       @param flag: if flag is True, the order reduction is switched on for
1615                    if flag is not present order reduction is switched off                    solution representation, otherwise or if flag is not present
1616                      order reduction is switched off
1617       @type flag: C{bool}       @type flag: C{bool}
1618         @raise RuntimeError: if order reduction is altered after a coefficient has
1619                              been set
1620       """       """
1621       if flag:       if flag:
1622          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
# Line 735  class LinearPDE: Line 1625  class LinearPDE:
1625    
1626     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1627       """       """
1628       switches on reduced order for equation representation       Switches reduced order on for equation representation.
1629    
1630         @raise RuntimeError: if order reduction is altered after a coefficient has
1631                              been set
1632       """       """
1633       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1634       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1635                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1636           self.trace("Reduced order is used for test functions.")           self.trace("Reduced order is used for test functions.")
1637           self.__row_function_space=new_fs           self.__reduce_equation_order=True
1638           self.__resetSystem()           self.initializeSystem()
1639    
1640     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1641       """       """
1642       switches off reduced order for equation representation       Switches reduced order off for equation representation.
1643    
1644         @raise RuntimeError: if order reduction is altered after a coefficient has
1645                              been set
1646       """       """
1647       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1648       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1649                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1650           self.trace("Full order is used for test functions.")           self.trace("Full order is used for test functions.")
1651           self.__row_function_space=new_fs           self.__reduce_equation_order=False
1652           self.__resetSystem()           self.initializeSystem()
1653    
1654     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1655       """       """
1656       sets order for test functions according to flag       Sets order reduction state for equation representation according to flag.
1657    
1658       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or       @param flag: if flag is True, the order reduction is switched on for
1659                    if flag is not present order reduction is switched off                    equation representation, otherwise or if flag is not present
1660                      order reduction is switched off
1661       @type flag: C{bool}       @type flag: C{bool}
1662         @raise RuntimeError: if order reduction is altered after a coefficient has
1663                              been set
1664       """       """
1665       if flag:       if flag:
1666          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1667       else:       else:
1668          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1669       def getOperatorType(self):
1670          """
1671          Returns the current system type.
1672          """
1673          return self.__operator_type
1674    
1675     # =============================================================================     def checkSymmetricTensor(self,name,verbose=True):
1676     # private method:        """
1677     # =============================================================================        Tests a coefficient for symmetry.
1678     def __checkMatrixType(self):  
1679          @param name: name of the coefficient
1680          @type name: C{str}
1681          @param verbose: if set to True or not present a report on coefficients
1682                          which break the symmetry is printed.
1683          @type verbose: C{bool}
1684          @return: True if coefficient C{name} is symmetric
1685          @rtype: C{bool}
1686          """
1687          SMALL_TOLERANCE=util.EPSILON*10.
1688          A=self.getCoefficient(name)
1689          verbose=verbose or self.__debug
1690          out=True
1691          if not A.isEmpty():
1692             tol=util.Lsup(A)*SMALL_TOLERANCE
1693             s=A.getShape()
1694             if A.getRank() == 4:
1695                if s[0]==s[2] and s[1] == s[3]:
1696                   for i in range(s[0]):
1697                      for j in range(s[1]):
1698                         for k in range(s[2]):
1699                            for l in range(s[3]):
1700                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
1701                                   if verbose: print "non-symmetric problem as %s[%d,%d,%d,%d]!=%s[%d,%d,%d,%d]"%(name,i,j,k,l,name,k,l,i,j)
1702                                   out=False
1703                else:
1704                     if verbose: print "non-symmetric problem because of inappropriate shape %s of coefficient %s."%(s,name)
1705                     out=False
1706             elif A.getRank() == 2:
1707                if s[0]==s[1]:
1708                   for j in range(s[0]):
1709                      for l in range(s[1]):
1710                         if util.Lsup(A[j,l]-A[l,j])>tol:
1711                            if verbose: print "non-symmetric problem because %s[%d,%d]!=%s[%d,%d]"%(name,j,l,name,l,j)
1712                            out=False
1713                else:
1714                     if verbose: print "non-symmetric problem because of inappropriate shape %s of coefficient %s."%(s,name)
1715                     out=False
1716             elif A.getRank() == 0:
1717                pass
1718             else:
1719                 raise ValueError,"Cannot check rank %s of %s."%(A.getRank(),name)
1720          return out
1721    
1722       def checkReciprocalSymmetry(self,name0,name1,verbose=True):
1723          """
1724          Tests two coefficients for reciprocal symmetry.
1725    
1726          @param name0: name of the first coefficient
1727          @type name0: C{str}
1728          @param name1: name of the second coefficient
1729          @type name1: C{str}
1730          @param verbose: if set to True or not present a report on coefficients
1731                          which break the symmetry is printed
1732          @type verbose: C{bool}
1733          @return: True if coefficients C{name0} and C{name1} are reciprocally
1734                   symmetric.
1735          @rtype: C{bool}
1736          """
1737          SMALL_TOLERANCE=util.EPSILON*10.
1738          B=self.getCoefficient(name0)
1739          C=self.getCoefficient(name1)
1740          verbose=verbose or self.__debug
1741          out=True
1742          if B.isEmpty() and not C.isEmpty():
1743             if verbose: print "non-symmetric problem because %s is not present but %s is"%(name0,name1)
1744             out=False
1745          elif not B.isEmpty() and C.isEmpty():
1746             if verbose: print "non-symmetric problem because %s is not present but %s is"%(name0,name1)
1747             out=False
1748          elif not B.isEmpty() and not C.isEmpty():
1749             sB=B.getShape()
1750             sC=C.getShape()
1751             tol=(util.Lsup(B)+util.Lsup(C))*SMALL_TOLERANCE/2.
1752             if len(sB) != len(sC):
1753                 if verbose: print "non-symmetric problem because ranks of %s (=%s) and %s (=%s) are different."%(name0,len(sB),name1,len(sC))
1754                 out=False
1755             else:
1756                 if len(sB)==0:
1757                   if util.Lsup(B-C)>tol:
1758                      if verbose: print "non-symmetric problem because %s!=%s"%(name0,name1)
1759                      out=False
1760                 elif len(sB)==1:
1761                   if sB[0]==sC[0]:
1762                      for j in range(sB[0]):
1763                         if util.Lsup(B[j]-C[j])>tol:
1764                            if verbose: print "non-symmetric PDE because %s[%d]!=%s[%d]"%(name0,j,name1,j)
1765                            out=False
1766                   else:
1767                     if verbose: print "non-symmetric problem because of inappropriate shapes %s and %s of coefficients %s and %s, respectively."%(sB,sC,name0,name1)
1768                 elif len(sB)==3:
1769                   if sB[0]==sC[1] and sB[1]==sC[2] and sB[2]==sC[0]:
1770                       for i in range(sB[0]):
1771                          for j in range(sB[1]):
1772                             for k in range(sB[2]):
1773                                if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
1774                                     if verbose: print "non-symmetric problem because %s[%d,%d,%d]!=%s[%d,%d,%d]"%(name0,i,j,k,name1,k,i,j)
1775                                     out=False
1776                   else:
1777                     if verbose: print "non-symmetric problem because of inappropriate shapes %s and %s of coefficients %s and %s, respectively."%(sB,sC,name0,name1)
1778                 else:
1779                     raise ValueError,"Cannot check rank %s of %s and %s."%(len(sB),name0,name1)
1780          return out
1781    
1782       def getCoefficient(self,name):
1783       """       """
1784       reassess the matrix type and, if a new matrix is needed, resets the system.       Returns the value of the coefficient C{name}.
1785    
1786         @param name: name of the coefficient requested
1787         @type name: C{string}
1788         @return: the value of the coefficient
1789         @rtype: L{Data<escript.Data>}
1790         @raise IllegalCoefficient: if C{name} is not a coefficient of the PDE
1791       """       """
1792       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       if self.hasCoefficient(name):
1793       if not new_matrix_type==self.__matrix_type:           return self.__COEFFICIENTS[name].getValue()
1794           self.trace("Matrix type is now %d."%new_matrix_type)       else:
1795           self.__matrix_type=new_matrix_type          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1796           self.__resetSystem()  
1797     #     def hasCoefficient(self,name):
1798     #   rebuild switches :       """
1799     #       Returns True if C{name} is the name of a coefficient.
1800     def __invalidateSolution(self):  
1801         @param name: name of the coefficient enquired
1802         @type name: C{string}
1803         @return: True if C{name} is the name of a coefficient of the general PDE,
1804                  False otherwise
1805         @rtype: C{bool}
1806         """
1807         return self.__COEFFICIENTS.has_key(name)
1808    
1809       def createCoefficient(self, name):
1810         """
1811         Creates a L{Data<escript.Data>} object corresponding to coefficient
1812         C{name}.
1813    
1814         @return: the coefficient C{name} initialized to 0
1815         @rtype: L{Data<escript.Data>}
1816         @raise IllegalCoefficient: if C{name} is not a coefficient of the PDE
1817         """
1818         if self.hasCoefficient(name):
1819            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1820         else:
1821            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1822    
1823       def getFunctionSpaceForCoefficient(self,name):
1824         """
1825         Returns the L{FunctionSpace<escript.FunctionSpace>} to be used for
1826         coefficient C{name}.
1827    
1828         @param name: name of the coefficient enquired
1829         @type name: C{string}
1830         @return: the function space to be used for coefficient C{name}
1831         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1832         @raise IllegalCoefficient: if C{name} is not a coefficient of the PDE
1833         """
1834         if self.hasCoefficient(name):
1835            return self.__COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1836         else:
1837            raise ValueError,"unknown coefficient %s requested"%name
1838    
1839       def getShapeOfCoefficient(self,name):
1840         """
1841         Returns the shape of the coefficient C{name}.
1842    
1843         @param name: name of the coefficient enquired
1844         @type name: C{string}
1845         @return: the shape of the coefficient C{name}
1846         @rtype: C{tuple} of C{int}
1847         @raise IllegalCoefficient: if C{name} is not a coefficient of the PDE
1848         """
1849         if self.hasCoefficient(name):
1850            return self.__COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1851         else:
1852            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1853    
1854       def resetAllCoefficients(self):
1855         """
1856         Resets all coefficients to their default values.
1857         """
1858         for i in self.__COEFFICIENTS.iterkeys():
1859             self.__COEFFICIENTS[i].resetValue()
1860    
1861       def alteredCoefficient(self,name):
1862         """
1863         Announces that coefficient C{name} has been changed.
1864    
1865         @param name: name of the coefficient affected
1866         @type name: C{string}
1867         @raise IllegalCoefficient: if C{name} is not a coefficient of the PDE
1868         @note: if C{name} is q or r, the method will not trigger a rebuild of the
1869                system as constraints are applied to the solved system.
1870         """
1871         if self.hasCoefficient(name):
1872            self.trace("Coefficient %s has been altered."%name)
1873            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1874               if self.__COEFFICIENTS[name].isAlteringOperator(): self.invalidateOperator()
1875               if self.__COEFFICIENTS[name].isAlteringRightHandSide(): self.invalidateRightHandSide()
1876         else:
1877            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1878    
1879       def validSolution(self):
1880           """
1881           Marks the solution as valid.
1882           """
1883           self.__is_solution_valid=True
1884    
1885       def invalidateSolution(self):
1886           """
1887           Indicates the PDE has to be resolved if the solution is requested.
1888           """
1889           self.trace("System will be resolved.")
1890           self.__is_solution_valid=False
1891    
1892       def isSolutionValid(self):
1893           """
1894           Returns True if the solution is still valid.
1895           """
1896           if not self.getDomainStatus()==self.getSystemStatus(): self.invalidateSolution()
1897           if self.__solution_rtol>self.getSolverOptions().getTolerance() or \
1898              self.__solution_atol>self.getSolverOptions().getAbsoluteTolerance():
1899             self.invalidateSolution()  
1900           return self.__is_solution_valid
1901    
1902       def validOperator(self):
1903           """
1904           Marks the operator as valid.
1905         """         """
1906         indicates the PDE has to be resolved if the solution is requested         self.__is_operator_valid=True
1907    
1908       def invalidateOperator(self):
1909           """
1910           Indicates the operator has to be rebuilt next time it is used.
1911           """
1912           self.trace("Operator will be rebuilt.")
1913           self.invalidateSolution()
1914           self.__is_operator_valid=False
1915    
1916       def isOperatorValid(self):
1917           """
1918           Returns True if the operator is still valid.
1919           """
1920           if not self.getDomainStatus()==self.getSystemStatus(): self.invalidateOperator()
1921           if not self.getRequiredOperatorType()==self.getOperatorType(): self.invalidateOperator()
1922           return self.__is_operator_valid
1923    
1924       def validRightHandSide(self):
1925           """
1926           Marks the right hand side as valid.
1927         """         """
1928         if self.__solution_isValid: self.trace("PDE has to be resolved.")         self.__is_RHS_valid=True
        self.__solution_isValid=False  
1929    
1930     def __invalidateOperator(self):     def invalidateRightHandSide(self):
1931         """         """
1932         indicates the operator has to be rebuilt next time it is used         Indicates the right hand side has to be rebuilt next time it is used.
1933         """         """
1934         if self.__operator_isValid: self.trace("Operator has to be rebuilt.")         self.trace("Right hand side has to be rebuilt.")
1935         self.__invalidateSolution()         self.invalidateSolution()
1936         self.__operator_isValid=False         self.__is_RHS_valid=False
1937    
1938     def __invalidateRightHandSide(self):     def isRightHandSideValid(self):
1939         """         """
1940         indicates the right hand side has to be rebuild next time it is used         Returns True if the operator is still valid.
1941         """         """
1942         if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")         if not self.getDomainStatus()==self.getSystemStatus(): self.invalidateRightHandSide()
1943         self.__invalidateSolution()         return self.__is_RHS_valid
        self.__righthandside_isValid=False  
1944    
1945     def __invalidateSystem(self):     def invalidateSystem(self):
1946         """         """
1947         annonced that everthing has to be rebuild:         Announces that everything has to be rebuilt.
1948         """         """
1949         if self.__righthandside_isValid: self.trace("System has to be rebuilt.")         self.invalidateSolution()
1950         self.__invalidateSolution()         self.invalidateOperator()
1951         self.__invalidateOperator()         self.invalidateRightHandSide()
        self.__invalidateRightHandSide()  
1952    
1953     def __resetSystem(self):     def isSystemValid(self):
1954         """         """
1955         annonced that everthing has to be rebuild:         Returns True if the system (including solution) is still vaild.
1956         """         """
1957         self.trace("New System is built from scratch.")         return self.isSolutionValid() and self.isOperatorValid() and self.isRightHandSideValid()
1958    
1959       def initializeSystem(self):
1960           """
1961           Resets the system clearing the operator, right hand side and solution.
1962           """
1963           self.trace("New System has been created.")
1964           self.__operator_type=None
1965           self.setSystemStatus()
1966         self.__operator=escript.Operator()         self.__operator=escript.Operator()
        self.__operator_isValid=False  
1967         self.__righthandside=escript.Data()         self.__righthandside=escript.Data()
        self.__righthandside_isValid=False  
1968         self.__solution=escript.Data()         self.__solution=escript.Data()
1969         self.__solution_isValid=False         self.invalidateSystem()
1970     #  
1971     #    system initialization:     def getOperator(self):
1972     #       """
1973     def __getNewOperator(self):       Returns the operator of the linear problem.
1974         """  
1975         returns an instance of a new operator       @return: the operator of the problem
1976         """       """
1977         self.trace("New operator is allocated.")       return self.getSystem()[0]
        return self.getDomain().newOperator( \  
                            self.getNumEquations(), \  
                            self.getFunctionSpaceForEquation(), \  
                            self.getNumSolutions(), \  
                            self.getFunctionSpaceForSolution(), \  
                            self.__matrix_type)  
1978    
1979     def __getNewRightHandSide(self):     def getRightHandSide(self):
1980         """
1981         Returns the right hand side of the linear problem.
1982    
1983         @return: the right hand side of the problem
1984         @rtype: L{Data<escript.Data>}
1985         """
1986         return self.getSystem()[1]
1987    
1988       def createRightHandSide(self):
1989         """         """
1990         returns an instance of a new right hand side         Returns an instance of a new right hand side.
1991         """         """
1992         self.trace("New right hand side is allocated.")         self.trace("New right hand side is allocated.")
1993         if self.getNumEquations()>1:         if self.getNumEquations()>1:
# Line 849  class LinearPDE: Line 1995  class LinearPDE:
1995         else:         else:
1996             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1997    
1998     def __getNewSolution(self):     def createSolution(self):
1999         """         """
2000         returns an instance of a new solution         Returns an instance of a new solution.
2001         """         """
2002         self.trace("New solution is allocated.")         self.trace("New solution is allocated.")
2003         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
# Line 859  class LinearPDE: Line 2005  class LinearPDE:
2005         else:         else:
2006             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
2007    
2008     def __makeFreshSolution(self):     def resetSolution(self):
2009         """         """
2010         makes sure that the solution is instantiated and returns it initialized by zeros         Sets the solution to zero.
2011         """         """
2012         if self.__solution.isEmpty():         if self.__solution.isEmpty():
2013             self.__solution=self.__getNewSolution()             self.__solution=self.createSolution()
2014         else:         else:
2015             self.__solution*=0             self.__solution.setToZero()
2016             self.trace("Solution is reset to zero.")             self.trace("Solution is reset to zero.")
2017    
2018       def setSolution(self,u):
2019           """
2020           Sets the solution assuming that makes the system valid with the tolrance
2021           defined by the solver options
2022           """
2023           self.__solution_rtol=self.getSolverOptions().getTolerance()
2024           self.__solution_atol=self.getSolverOptions().getAbsoluteTolerance()
2025           self.__solution=u
2026           self.validSolution()
2027    
2028       def getCurrentSolution(self):
2029           """
2030           Returns the solution in its current state.
2031           """
2032           if self.__solution.isEmpty(): self.__solution=self.createSolution()
2033         return self.__solution         return self.__solution
2034    
2035     def __makeFreshRightHandSide(self):     def resetRightHandSide(self):
2036         """         """
2037         makes sure that the right hand side is instantiated and returns it initialized by zeros         Sets the right hand side to zero.
2038         """         """
2039         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
2040             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.createRightHandSide()
2041         else:         else:
2042             self.__righthandside*=0             self.__righthandside.setToZero()
2043             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
2044    
2045       def getCurrentRightHandSide(self):
2046           """
2047           Returns the right hand side in its current state.
2048           """
2049           if self.__righthandside.isEmpty(): self.__righthandside=self.createRightHandSide()
2050         return self.__righthandside         return self.__righthandside
2051    
2052     def __makeFreshOperator(self):     def resetOperator(self):
2053         """         """
2054         makes sure that the operator is instantiated and returns it initialized by zeros         Makes sure that the operator is instantiated and returns it initialized
2055           with zeros.
2056         """         """
2057         if self.__operator.isEmpty():         if self.getOperatorType() == None:
2058             self.__operator=self.__getNewOperator()             if self.isUsingLumping():
2059                   self.__operator=self.createSolution()
2060               else:
2061                   self.__operator=self.createOperator()
2062           self.__operator_type=self.getRequiredOperatorType()
2063         else:         else:
2064             self.__operator.setValue(0.)             if self.isUsingLumping():
2065                   self.__operator.setToZero()
2066               else:
2067                   self.__operator.resetValues()
2068             self.trace("Operator reset to zero")             self.trace("Operator reset to zero")
2069    
2070       def getCurrentOperator(self):
2071           """
2072           Returns the operator in its current state.
2073           """
2074         return self.__operator         return self.__operator
2075    
2076     def __applyConstraint(self):     def setValue(self,**coefficients):
2077          """
2078          Sets new values to coefficients.
2079    
2080          @raise IllegalCoefficient: if an unknown coefficient keyword is used
2081          """
2082          # check if the coefficients are  legal:
2083          for i in coefficients.iterkeys():
2084             if not self.hasCoefficient(i):
2085                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
2086          # if the number of unknowns or equations is still unknown we try to estimate them:
2087          if self.__numEquations==None or self.__numSolutions==None:
2088             for i,d in coefficients.iteritems():
2089                if hasattr(d,"shape"):
2090                    s=d.shape
2091                elif hasattr(d,"getShape"):
2092                    s=d.getShape()
2093                else:
2094                    s=numpy.array(d).shape
2095                if s!=None:
2096                    # get number of equations and number of unknowns:
2097                    res=self.__COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
2098                    if res==None:
2099                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
2100                    else:
2101                        if self.__numEquations==None: self.__numEquations=res[0]
2102                        if self.__numSolutions==None: self.__numSolutions=res[1]
2103          if self.__numEquations==None: raise UndefinedPDEError,"unidentified number of equations"
2104          if self.__numSolutions==None: raise UndefinedPDEError,"unidentified number of solutions"
2105          # now we check the shape of the coefficient if numEquations and numSolutions are set:
2106          for i,d in coefficients.iteritems():
2107            try:
2108               self.__COEFFICIENTS[i].setValue(self.getDomain(),
2109                         self.getNumEquations(),self.getNumSolutions(),
2110                         self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
2111               self.alteredCoefficient(i)
2112            except IllegalCoefficientFunctionSpace,m:
2113                # if the function space is wrong then we try the reduced version:
2114                i_red=i+"_reduced"
2115                if (not i_red in coefficients.keys()) and i_red in self.__COEFFICIENTS.keys():
2116                    try:
2117                        self.__COEFFICIENTS[i_red].setValue(self.getDomain(),
2118                                                          self.getNumEquations(),self.getNumSolutions(),
2119                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
2120                        self.alteredCoefficient(i_red)
2121                    except IllegalCoefficientValue,m:
2122                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
2123                    except IllegalCoefficientFunctionSpace,m:
2124                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
2125                else:
2126                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
2127            except IllegalCoefficientValue,m:
2128               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
2129          self.__altered_coefficients=True
2130    
2131       # ==========================================================================
2132       # methods that are typically overwritten when implementing a particular
2133       # linear problem
2134       # ==========================================================================
2135       def getRequiredOperatorType(self):
2136          """
2137          Returns the system type which needs to be used by the current set up.
2138    
2139          @note: Typically this method is overwritten when implementing a
2140                 particular linear problem.
2141          """
2142          return None
2143    
2144       def createOperator(self):
2145         """         """
2146         applies the constraints defined by q and r to the system         Returns an instance of a new operator.
2147    
2148           @note: This method is overwritten when implementing a particular
2149                  linear problem.
2150         """         """
2151         if not self.isUsingLumping():         return escript.Operator()
           q=self.getCoefficientOfGeneralPDE("q")  
           r=self.getCoefficientOfGeneralPDE("r")  
           if not q.isEmpty() and not self.__operator.isEmpty():  
              # q is the row and column mask to indicate where constraints are set:  
              row_q=escript.Data(q,self.getFunctionSpaceForEquation())  
              col_q=escript.Data(q,self.getFunctionSpaceForSolution())  
              u=self.__getNewSolution()  
              if r.isEmpty():  
                 r_s=self.__getNewSolution()  
              else:  
                 r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
              u.copyWithMask(r_s,col_q)  
              if not self.__righthandside.isEmpty():  
                 self.__righthandside-=self.__operator*u  
                 self.__righthandside=self.copyConstraint(self.__righthandside)  
              self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
    # =============================================================================  
    # function giving access to coefficients of the general PDE:  
    # =============================================================================  
    def getCoefficientOfGeneralPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE.  
2152    
2153       @note This method is called by the assembling routine it can be overwritten     def checkSymmetry(self,verbose=True):
2154             to map coefficients of a particular PDE to the general PDE.        """
2155          Tests the PDE for symmetry.
2156    
2157       @param name: name of the coefficient requested.        @param verbose: if set to True or not present a report on coefficients
2158       @type name: C{string}                        which break the symmetry is printed
2159       @return : the value of the coefficient  name        @type verbose: C{bool}
2160       @rtype : L{escript.Data}        @return: True if the problem is symmetric
2161       @raise IllegalCoefficient: if name is not one of coefficients        @rtype: C{bool}
2162                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".        @note: Typically this method is overwritten when implementing a
2163       """               particular linear problem.
2164       if self.hasCoefficientOfGeneralPDE(name):        """
2165          return self.getCoefficient(name)        out=True
2166       else:        return out
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2167    
2168     def hasCoefficientOfGeneralPDE(self,name):     def getSolution(self,**options):
2169       """         """
2170       checks if name is a the name of a coefficient of the general PDE.         Returns the solution of the problem.
       
      @param name: name of the coefficient enquired.  
      @type name: C{string}  
      @return : True if name is the name of a coefficient of the general PDE. Otherwise False.  
      @rtype : C{bool}  
       
      """  
      return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)  
2171    
2172     def createCoefficientOfGeneralPDE(self,name):         @return: the solution
2173       """         @rtype: L{Data<escript.Data>}
      returns a new instance of a coefficient for coefficient name of the general PDE  
2174    
2175       @param name: name of the coefficient requested.         @note: This method is overwritten when implementing a particular
2176       @type name: C{string}                linear problem.
2177       @return : a coefficient name initialized to 0.         """
2178       @rtype : L{escript.Data}         return self.getCurrentSolution()
      @raise IllegalCoefficient: if name is not one of coefficients  
                   "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".  
      """  
      if self.hasCoefficientOfGeneralPDE(name):  
         return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2179    
2180     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):     def getSystem(self):
2181       """         """
2182       return the L{escript.FunctionSpace} to be used for coefficient name of the general PDE         Returns the operator and right hand side of the PDE.
2183    
2184       @param name: name of the coefficient enquired.         @return: the discrete version of the PDE
2185       @type name: C{string}         @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
      @return : the function space to be used for coefficient name  
      @rtype : L{escript.FunctionSpace}  
      @raise IllegalCoefficient: if name is not one of coefficients  
                   "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".  
      """  
      if self.hasCoefficientOfGeneralPDE(name):  
         return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2186    
2187     def getShapeOfCoefficientOfGeneralPDE(self,name):         @note: This method is overwritten when implementing a particular
2188       """                linear problem.
2189       return the shape of the coefficient name of the general PDE         """
2190           return (self.getCurrentOperator(), self.getCurrentRightHandSide())
2191    
2192       @param name: name of the coefficient enquired.  class LinearPDE(LinearProblem):
2193       @type name: C{string}     """
2194       @return : the shape of the coefficient name     This class is used to define a general linear, steady, second order PDE
2195       @rtype : C{tuple} of C{int}     for an unknown function M{u} on a given domain defined through a
2196       @raise IllegalCoefficient: if name is not one of coefficients     L{Domain<escript.Domain>} object.
                   "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".  
2197    
2198       """     For a single PDE having a solution with a single component the linear PDE
2199       if self.hasCoefficientOfGeneralPDE(name):     is defined in the following form:
         return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2200    
2201     # =============================================================================     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
    # functions giving access to coefficients of a particular PDE implementation:  
    # =============================================================================  
    def getCoefficient(self,name):  
      """  
      returns the value of the coefficient name  
2202    
2203       @param name: name of the coefficient requested.     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's
2204       @type name: C{string}     summation convention, ie. summation over indexes appearing twice in a term
2205       @return : the value of the coefficient name     of a sum performed, is used.
2206       @rtype : L{escript.Data}     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified
2207       @raise IllegalCoefficient: if name is not a coefficient of the PDE.     through L{Data<escript.Data>} objects in L{Function<escript.Function>} and
2208       """     the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced},
2209       if self.hasCoefficient(name):     M{X_reduced} and M{Y_reduced} have to be specified through
2210           return self.COEFFICIENTS[name].getValue()     L{Data<escript.Data>} objects in L{ReducedFunction<escript.ReducedFunction>}.
2211       else:     It is also allowed to use objects that can be converted into such
2212          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name     L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B},
2213       M{C}, M{X}, M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and
2214       M{D}, M{D_reduced}, M{Y} and M{Y_reduced} are scalar.
2215    
2216     def hasCoefficient(self,name):     The following natural boundary conditions are considered:
      """  
      return True if name is the name of a coefficient  
2217    
2218       @param name: name of the coefficient enquired.     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
      @type name: C{string}  
      @return : True if name is the name of a coefficient of the general PDE. Otherwise False.  
      @rtype : C{bool}  
      """  
      return self.COEFFICIENTS.has_key(name)  
2219    
2220     def createCoefficient(self, name):     where M{n} is the outer normal field. Notice that the coefficients M{A},
2221       """     M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the
2222       create a L{escript.Data} object corresponding to coefficient name     PDE. The coefficients M{d} and M{y} are each a scalar in
2223       L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients
2224       M{d_reduced} and M{y_reduced} are each a scalar in
2225       L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
2226    
2227       @return : a coefficient name initialized to 0.     Constraints for the solution prescribe the value of the solution at certain
2228       @rtype : L{escript.Data}     locations in the domain. They have the form
      @raise IllegalCoefficient: if name is not a coefficient of the PDE.  
      """  
      if self.hasCoefficient(name):  
         return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2229    
2230     def getFunctionSpaceForCoefficient(self,name):     M{u=r} where M{q>0}
      """  
      return the L{escript.FunctionSpace} to be used for coefficient name  
2231    
2232       @param name: name of the coefficient enquired.     M{r} and M{q} are each scalar where M{q} is the characteristic function
2233       @type name: C{string}     defining where the constraint is applied. The constraints override any
2234       @return : the function space to be used for coefficient name     other condition set by the PDE or the boundary condition.
      @rtype : L{escript.FunctionSpace}  
      @raise IllegalCoefficient: if name is not a coefficient of the PDE.  
      """  
      if self.hasCoefficient(name):  
         return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())  
      else:  
         raise ValueError,"unknown coefficient %s requested"%name  
2235    
2236     def getShapeOfCoefficient(self,name):     The PDE is symmetrical if
      """  
      return the shape of the coefficient name  
2237    
2238       @param name: name of the coefficient enquired.     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}
2239       @type name: C{string}     and M{B_reduced[j]=C_reduced[j]}
2240       @return : the shape of the coefficient name  
2241       @rtype : C{tuple} of C{int}     For a system of PDEs and a solution with several components the PDE has the
2242       @raise IllegalCoefficient: if name is not a coefficient of the PDE.     form
2243       """  
2244       if self.hasCoefficient(name):     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
2245          return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())  
2246       else:     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and
2247          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name     M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and
2248       M{X} are each of rank two and M{Y} and M{Y_reduced} are of rank one.
2249       The natural boundary conditions take the form:
2250    
2251       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
2252    
2253       The coefficient M{d} is of rank two and M{y} is of rank one both in
2254       L{FunctionOnBoundary<escript.FunctionOnBoundary>}. The coefficients
2255       M{d_reduced} is of rank two and M{y_reduced} is of rank one both in
2256       L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
2257    
2258       Constraints take the form
2259    
2260     def resetCoefficients(self):     M{u[i]=r[i]}  where  M{q[i]>0}
2261    
2262       M{r} and M{q} are each rank one. Notice that at some locations not
2263       necessarily all components must have a constraint.
2264    
2265       The system of PDEs is symmetrical if
2266    
2267          - M{A[i,j,k,l]=A[k,l,i,j]}
2268          - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
2269          - M{B[i,j,k]=C[k,i,j]}
2270          - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
2271          - M{D[i,k]=D[i,k]}
2272          - M{D_reduced[i,k]=D_reduced[i,k]}
2273          - M{d[i,k]=d[k,i]}
2274          - M{d_reduced[i,k]=d_reduced[k,i]}
2275    
2276       L{LinearPDE} also supports solution discontinuities over a contact region
2277       in the domain. To specify the conditions across the discontinuity we are
2278       using the generalised flux M{J} which, in the case of a system of PDEs
2279       and several components of the solution, is defined as
2280    
2281       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
2282    
2283       For the case of single solution component and single PDE M{J} is defined as
2284    
2285       M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
2286    
2287       In the context of discontinuities M{n} denotes the normal on the
2288       discontinuity pointing from side 0 towards side 1 calculated from
2289       L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
2290       For a system of PDEs the contact condition takes the form
2291    
2292       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
2293    
2294       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the
2295       discontinuity, respectively. M{jump(u)}, which is the difference of the
2296       solution at side 1 and at side 0, denotes the jump of M{u} across
2297       discontinuity along the normal calculated by L{jump<util.jump>}.
2298       The coefficient M{d_contact} is of rank two and M{y_contact} is of rank one
2299       both in L{FunctionOnContactZero<escript.FunctionOnContactZero>} or
2300       L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
2301       The coefficient M{d_contact_reduced} is of rank two and M{y_contact_reduced}
2302       is of rank one both in L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}
2303       or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
2304       In case of a single PDE and a single component solution the contact
2305       condition takes the form
2306    
2307       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
2308    
2309       In this case the coefficient M{d_contact} and M{y_contact} are each scalar
2310       both in L{FunctionOnContactZero<escript.FunctionOnContactZero>} or
2311       L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient
2312       M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in
2313       L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or
2314       L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
2315    
2316       Typical usage::
2317    
2318           p = LinearPDE(dom)
2319           p.setValue(A=kronecker(dom), D=1, Y=0.5)
2320           u = p.getSolution()
2321    
2322       """
2323    
2324       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
2325       """       """
2326       resets all coefficients to there default values.       Initializes a new linear PDE.
2327    
2328         @param domain: domain of the PDE
2329         @type domain: L{Domain<escript.Domain>}
2330         @param numEquations: number of equations. If C{None} the number of
2331                              equations is extracted from the PDE coefficients.
2332         @param numSolutions: number of solution components. If C{None} the number
2333                              of solution components is extracted from the PDE
2334                              coefficients.
2335         @param debug: if True debug information is printed
2336    
2337       """       """
2338       for i in self.COEFFICIENTS.iterkeys():       super(LinearPDE, self).__init__(domain,numEquations,numSolutions,debug)
2339           self.COEFFICIENTS[i].resetValue()       #
2340         #   the coefficients of the PDE:
2341         #
2342         self.introduceCoefficients(
2343           A=PDECoef(PDECoef.INTERIOR,(PDECoef.BY_EQUATION,PDECoef.BY_DIM,PDECoef.BY_SOLUTION,PDECoef.BY_DIM),PDECoef.OPERATOR),
2344           B=PDECoef(PDECoef.INTERIOR,(PDECoef.BY_EQUATION,PDECoef.BY_DIM,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2345           C=PDECoef(PDECoef.INTERIOR,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION,PDECoef.BY_DIM),PDECoef.OPERATOR),
2346           D=PDECoef(PDECoef.INTERIOR,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2347           X=PDECoef(PDECoef.INTERIOR,(PDECoef.BY_EQUATION,PDECoef.BY_DIM),PDECoef.RIGHTHANDSIDE),
2348           Y=PDECoef(PDECoef.INTERIOR,(PDECoef.BY_EQUATION,),PDECoef.RIGHTHANDSIDE),
2349           d=PDECoef(PDECoef.BOUNDARY,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2350           y=PDECoef(PDECoef.BOUNDARY,(PDECoef.BY_EQUATION,),PDECoef.RIGHTHANDSIDE),
2351           d_contact=PDECoef(PDECoef.CONTACT,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2352           y_contact=PDECoef(PDECoef.CONTACT,(PDECoef.BY_EQUATION,),PDECoef.RIGHTHANDSIDE),
2353           A_reduced=PDECoef(PDECoef.INTERIOR_REDUCED,(PDECoef.BY_EQUATION,PDECoef.BY_DIM,PDECoef.BY_SOLUTION,PDECoef.BY_DIM),PDECoef.OPERATOR),
2354           B_reduced=PDECoef(PDECoef.INTERIOR_REDUCED,(PDECoef.BY_EQUATION,PDECoef.BY_DIM,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2355           C_reduced=PDECoef(PDECoef.INTERIOR_REDUCED,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION,PDECoef.BY_DIM),PDECoef.OPERATOR),
2356           D_reduced=PDECoef(PDECoef.INTERIOR_REDUCED,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2357           X_reduced=PDECoef(PDECoef.INTERIOR_REDUCED,(PDECoef.BY_EQUATION,PDECoef.BY_DIM),PDECoef.RIGHTHANDSIDE),
2358           Y_reduced=PDECoef(PDECoef.INTERIOR_REDUCED,(PDECoef.BY_EQUATION,),PDECoef.RIGHTHANDSIDE),
2359           d_reduced=PDECoef(PDECoef.BOUNDARY_REDUCED,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2360           y_reduced=PDECoef(PDECoef.BOUNDARY_REDUCED,(PDECoef.BY_EQUATION,),PDECoef.RIGHTHANDSIDE),
2361           d_contact_reduced=PDECoef(PDECoef.CONTACT_REDUCED,(PDECoef.BY_EQUATION,PDECoef.BY_SOLUTION),PDECoef.OPERATOR),
2362           y_contact_reduced=PDECoef(PDECoef.CONTACT_REDUCED,(PDECoef.BY_EQUATION,),PDECoef.RIGHTHANDSIDE),
2363           r=PDECoef(PDECoef.SOLUTION,(PDECoef.BY_SOLUTION,),PDECoef.RIGHTHANDSIDE),
2364           q=PDECoef(PDECoef.SOLUTION,(PDECoef.BY_SOLUTION,),PDECoef.BOTH) )
2365    
2366     def alteredCoefficient(self,name):     def __str__(self):
2367       """       """
2368       announce that coefficient name has been changed       Returns the string representation of the PDE.
2369    
2370       @param name: name of the coefficient enquired.       @return: a simple representation of the PDE
2371       @type name: C{string}       @rtype: C{str}
      @raise IllegalCoefficient: if name is not a coefficient of the PDE.  
2372       """       """
2373       if self.hasCoefficient(name):       return "<LinearPDE %d>"%id(self)
         self.trace("Coefficient %s has been altered."%name)  
         if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()  
         if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2374    
2375     def copyConstraint(self,u):     def getRequiredOperatorType(self):
2376        """        """
2377        copies the constraint into u and returns u.        Returns the system type which needs to be used by the current set up.
   
       @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs  
       @type u: L{escript.Data}  
       @return : the input u modified by the constraints.  
       @rtype : L{escript.Data}  
       @warning: u is altered if it has the appropriate L{escript.FunctionSpace}  
   
2378        """        """
2379        q=self.getCoefficientOfGeneralPDE("q")        solver_options=self.getSolverOptions()
2380        r=self.getCoefficientOfGeneralPDE("r")        return self.getDomain().getSystemMatrixTypeId(solver_options.getSolverMethod(), solver_options.getPreconditioner(),solver_options.getPackage(), solver_options.isSymmetric())
       if not q.isEmpty():  
          if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())  
          if r.isEmpty():  
              r=escript.Data(0,u.getShape(),u.getFunctionSpace())  
          else:  
              r=escript.Data(r,u.getFunctionSpace())  
          u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))  
       return u  
2381    
2382     def setValue(self,**coefficients):     def checkSymmetry(self,verbose=True):
2383        """        """
2384        sets new values to coefficients        Tests the PDE for symmetry.
   
       @note This method is called by the assembling routine it can be overwritten  
            to map coefficients of a particular PDE to the general PDE.  
   
       @param name: name of the coefficient requested.  
       @type name: C{string}  
       @keyword A: value for coefficient A.  
       @type A: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
       @keyword B: value for coefficient B  
       @type B: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
       @keyword C: value for coefficient C  
       @type C: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
       @keyword D: value for coefficient D  
       @type D: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
       @keyword X: value for coefficient X  
       @type X: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
       @keyword Y: value for coefficient Y  
       @type Y: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
       @keyword d: value for coefficient d  
       @type d: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnBoundary}.  
       @keyword y: value for coefficient y  
       @type y: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnBoundary}.  
       @keyword d_contact: value for coefficient d_contact  
       @type d_contact: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnContactOne}.  
                        or  L{escript.FunctionOnContactZero}.  
       @keyword y_contact: value for coefficient y_contact  
       @type y_contact: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnContactOne}.  
                        or  L{escript.FunctionOnContactZero}.  
       @keyword r: values prescribed to the solution at the locations of constraints  
       @type r: any type that can be interpreted as L{escript.Data} object on L{escript.Solution} or L{escript.ReducedSolution}  
                depending of reduced order is used for the solution.  
       @keyword q: mask for location of constraints  
       @type q: any type that can be interpreted as L{escript.Data} object on L{escript.Solution} or L{escript.ReducedSolution}  
                depending of reduced order is used for the representation of the equation.  
       @raise IllegalCoefficient: if an unknown coefficient keyword is used.  
2385    
2386          @param verbose: if set to True or not present a report on coefficients
2387                          which break the symmetry is printed.
2388          @type verbose: C{bool}
2389          @return: True if the PDE is symmetric
2390          @rtype: L{bool}
2391          @note: This is a very expensive operation. It should be used for
2392                 degugging only! The symmetry flag is not altered.
2393        """        """
2394        # check if the coefficients are  legal:        out=True
2395        for i in coefficients.iterkeys():        out=out and self.checkSymmetricTensor("A", verbose)
2396           if not self.hasCoefficient(i):        out=out and self.checkSymmetricTensor("A_reduced", verbose)
2397              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i        out=out and self.checkReciprocalSymmetry("B","C", verbose)
2398        # if the number of unknowns or equations is still unknown we try to estimate them:        out=out and self.checkReciprocalSymmetry("B_reduced","C_reduced", verbose)
2399        if self.__numEquations==None or self.__numSolutions==None:        out=out and self.checkSymmetricTensor("D", verbose)
2400           for i,d in coefficients.iteritems():        out=out and self.checkSymmetricTensor("D_reduced", verbose)
2401              if hasattr(d,"shape"):        out=out and self.checkSymmetricTensor("d", verbose)
2402                  s=d.shape        out=out and self.checkSymmetricTensor("d_reduced", verbose)
2403              elif hasattr(d,"getShape"):        out=out and self.checkSymmetricTensor("d_contact", verbose)
2404                  s=d.getShape()        out=out and self.checkSymmetricTensor("d_contact_reduced", verbose)
2405              else:        return out
                 s=numarray.array(d).shape  
             if s!=None:  
                 # get number of equations and number of unknowns:  
                 res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)  
                 if res==None:  
                     raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)  
                 else:  
                     if self.__numEquations==None: self.__numEquations=res[0]  
                     if self.__numSolutions==None: self.__numSolutions=res[1]  
       if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"  
       if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"  
       # now we check the shape of the coefficient if numEquations and numSolutions are set:  
       for i,d in coefficients.iteritems():  
         try:  
            self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),d)  
         except IllegalCoefficientValue,m:  
            raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))  
         self.alteredCoefficient(i)  
2406    
2407        # check if the systrem is inhomogeneous:     def createOperator(self):
2408        if len(coefficients)>0 and not self.isUsingLumping():         """
2409           q=self.getCoefficientOfGeneralPDE("q")         Returns an instance of a new operator.
2410           r=self.getCoefficientOfGeneralPDE("r")         """
2411           homogeneous_constraint=True         optype=self.getRequiredOperatorType()
2412           if not q.isEmpty() and not r.isEmpty():         self.trace("New operator of type %s is allocated."%optype)
2413               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):         return self.getDomain().newOperator( \
2414                 self.trace("Inhomogeneous constraint detected.")                             self.getNumEquations(), \
2415                 self.__invalidateSystem()                             self.getFunctionSpaceForEquation(), \
2416                               self.getNumSolutions(), \
2417                               self.getFunctionSpaceForSolution(), \
2418                               optype)
2419    
2420       def getSolution(self):
2421           """
2422           Returns the solution of the PDE.
2423    
2424           @return: the solution
2425           @rtype: L{Data<escript.Data>}
2426           """
2427           option_class=self.getSolverOptions()
2428           if not self.isSolutionValid():
2429              mat,f=self.getSystem()
2430              if self.isUsingLumping():
2431                 self.setSolution(f*1/mat)
2432              else:
2433                 self.trace("PDE is resolved.")
2434                 self.trace("solver options: %s"%str(option_class))
2435                 self.setSolution(mat.solve(f,option_class))
2436           return self.getCurrentSolution()
2437    
2438     def getSystem(self):     def getSystem(self):
2439         """         """
2440         return the operator and right hand side of the PDE         Returns the operator and right hand side of the PDE.
2441    
2442           @return: the discrete version of the PDE
2443           @rtype: C{tuple} of L{Operator,<escript.Operator>} and
2444                   L{Data<escript.Data>}
2445         """         """
2446         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.isOperatorValid() or not self.isRightHandSideValid():
2447            if self.isUsingLumping():            if self.isUsingLumping():
2448                if not self.__operator_isValid:                if not self.isOperatorValid():
2449                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
2450                   if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient A"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
2451                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient B"                   if not self.getCoefficient("A").isEmpty():
2452                   if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient A in lumped matrix may not be present."
2453                   mat=self.__getNewOperator()                   if not self.getCoefficient("B").isEmpty():
2454                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient B in lumped matrix may not be present."
2455                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficient("C").isEmpty():
2456                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient C in lumped matrix may not be present."
2457                             self.getCoefficientOfGeneralPDE("C"), \                   if not self.getCoefficient("d_contact").isEmpty():
2458                             self.getCoefficientOfGeneralPDE("D"), \                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
2459                             escript.Data(), \                   if not self.getCoefficient("A_reduced").isEmpty():
2460                             escript.Data(), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
2461                             self.getCoefficientOfGeneralPDE("d"), \                   if not self.getCoefficient("B_reduced").isEmpty():
2462                             escript.Data(),\                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
2463                             self.getCoefficientOfGeneralPDE("d_contact"), \                   if not self.getCoefficient("C_reduced").isEmpty():
2464                             escript.Data())                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
2465                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   if not self.getCoefficient("d_contact_reduced").isEmpty():
2466                   del mat                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
2467                     D=self.getCoefficient("D")
2468                     d=self.getCoefficient("d")
2469                     D_reduced=self.getCoefficient("D_reduced")
2470                     d_reduced=self.getCoefficient("d_reduced")
2471                     if not D.isEmpty():
2472                         if self.getNumSolutions()>1:
2473                            D_times_e=util.matrix_mult(D,numpy.ones((self.getNumSolutions(),)))
2474                         else:
2475                            D_times_e=D
2476                     else:
2477                        D_times_e=escript.Data()
2478                     if not d.isEmpty():
2479                         if self.getNumSolutions()>1:
2480                            d_times_e=util.matrix_mult(d,numpy.ones((self.getNumSolutions(),)))
2481                         else:
2482                            d_times_e=d
2483                     else:
2484                        d_times_e=escript.Data()
2485    
2486                     if not D_reduced.isEmpty():
2487                         if self.getNumSolutions()>1:
2488                            D_reduced_times_e=util.matrix_mult(D_reduced,numpy.ones((self.getNumSolutions(),)))
2489                         else:
2490                            D_reduced_times_e=D_reduced
2491                     else:
2492                        D_reduced_times_e=escript.Data()
2493                     if not d_reduced.isEmpty():
2494                         if self.getNumSolutions()>1:
2495                            d_reduced_times_e=util.matrix_mult(d_reduced,numpy.ones((self.getNumSolutions(),)))
2496                         else:
2497                            d_reduced_times_e=d_reduced
2498                     else:
2499                        d_reduced_times_e=escript.Data()
2500    
2501                     self.resetOperator()
2502                     operator=self.getCurrentOperator()
2503                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
2504                        self.getDomain().addPDEToLumpedSystem(operator, D_times_e, d_times_e)
2505                        self.getDomain().addPDEToLumpedSystem(operator, D_reduced_times_e, d_reduced_times_e)
2506                     else:
2507                        self.getDomain().addPDEToRHS(operator, \
2508                                                     escript.Data(), \
2509                                                     D_times_e, \
2510                                                     d_times_e,\
2511                                                     escript.Data())
2512                        self.getDomain().addPDEToRHS(operator, \
2513                                                     escript.Data(), \
2514                                                     D_reduced_times_e, \
2515                                                     d_reduced_times_e,\
2516                                                     escript.Data())
2517                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
2518                   self.__operator_isValid=True                if not self.isRightHandSideValid():
2519                if not self.__righthandside_isValid:                   self.resetRightHandSide()
2520                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   righthandside=self.getCurrentRightHandSide()
2521                                 self.getCoefficientOfGeneralPDE("X"), \                   self.getDomain().addPDEToRHS(righthandside, \
2522                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficient("X"), \
2523                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficient("Y"),\
2524                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficient("y"),\
2525                   self.trace("New right hand side as been built.")                                 self.getCoefficient("y_contact"))
2526                   self.__righthandside_isValid=True                   self.getDomain().addPDEToRHS(righthandside, \
2527                                   self.getCoefficient("X_reduced"), \
2528                                   self.getCoefficient("Y_reduced"),\
2529                                   self.getCoefficient("y_reduced"),\
2530                                   self.getCoefficient("y_contact_reduced"))
2531                     self.trace("New right hand side has been built.")
2532                     self.validRightHandSide()
2533                  self.insertConstraint(rhs_only=False)
2534                  self.validOperator()
2535            else:            else:
2536               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.isOperatorValid() and not self.isRightHandSideValid():
2537                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.resetRightHandSide()
2538                                 self.getCoefficientOfGeneralPDE("A"), \                   righthandside=self.getCurrentRightHandSide()
2539                                 self.getCoefficientOfGeneralPDE("B"), \                   self.resetOperator()
2540                                 self.getCoefficientOfGeneralPDE("C"), \                   operator=self.getCurrentOperator()
2541                                 self.getCoefficientOfGeneralPDE("D"), \                   self.getDomain().addPDEToSystem(operator,righthandside, \
2542                                 self.getCoefficientOfGeneralPDE("X"), \                                 self.getCoefficient("A"), \
2543                                 self.getCoefficientOfGeneralPDE("Y"), \                                 self.getCoefficient("B"), \
2544                                 self.getCoefficientOfGeneralPDE("d"), \                                 self.getCoefficient("C"), \
2545                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficient("D"), \
2546                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficient("X"), \
2547                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficient("Y"), \
2548                   self.__applyConstraint()                                 self.getCoefficient("d"), \
2549                   self.__righthandside=self.copyConstraint(self.__righthandside)                                 self.getCoefficient("y"), \
2550                                   self.getCoefficient("d_contact"), \
2551                                   self.getCoefficient("y_contact"))
2552                     self.getDomain().addPDEToSystem(operator,righthandside, \
2553                                   self.getCoefficient("A_reduced"), \
2554                                   self.getCoefficient("B_reduced"), \
2555                                   self.getCoefficient("C_reduced"), \
2556                                   self.getCoefficient("D_reduced"), \
2557                                   self.getCoefficient("X_reduced"), \
2558                                   self.getCoefficient("Y_reduced"), \
2559                                   self.getCoefficient("d_reduced"), \
2560                                   self.getCoefficient("y_reduced"), \
2561                                   self.getCoefficient("d_contact_reduced"), \
2562                                   self.getCoefficient("y_contact_reduced"))
2563                     self.insertConstraint(rhs_only=False)
2564                   self.trace("New system has been built.")                   self.trace("New system has been built.")
2565                   self.__operator_isValid=True                   self.validOperator()
2566                   self.__righthandside_isValid=True                   self.validRightHandSide()
2567               elif not self.__righthandside_isValid:               elif not self.isRightHandSideValid():
2568                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.resetRightHandSide()
2569                                 self.getCoefficientOfGeneralPDE("X"), \                   righthandside=self.getCurrentRightHandSide()
2570                                 self.getCoefficientOfGeneralPDE("Y"),\                   self.getDomain().addPDEToRHS(righthandside,
2571                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficient("X"), \
2572                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficient("Y"),\
2573                   self.__righthandside=self.copyConstraint(self.__righthandside)                                 self.getCoefficient("y"),\
2574                                   self.getCoefficient("y_contact"))
2575                     self.getDomain().addPDEToRHS(righthandside,
2576                                   self.getCoefficient("X_reduced"), \
2577                                   self.getCoefficient("Y_reduced"),\
2578                                   self.getCoefficient("y_reduced"),\
2579                                   self.getCoefficient("y_contact_reduced"))
2580                     self.insertConstraint(rhs_only=True)
2581                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
2582                   self.__righthandside_isValid=True                   self.validRightHandSide()
2583               elif not self.__operator_isValid:               elif not self.isOperatorValid():
2584                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.resetOperator()
2585                              self.getCoefficientOfGeneralPDE("A"), \                   operator=self.getCurrentOperator()
2586                              self.getCoefficientOfGeneralPDE("B"), \                   self.getDomain().addPDEToSystem(operator,escript.Data(), \
2587                              self.getCoefficientOfGeneralPDE("C"), \                              self.getCoefficient("A"), \
2588                              self.getCoefficientOfGeneralPDE("D"), \                              self.getCoefficient("B"), \
2589                                self.getCoefficient("C"), \
2590                                self.getCoefficient("D"), \
2591                                escript.Data(), \
2592                                escript.Data(), \
2593                                self.getCoefficient("d"), \
2594                                escript.Data(),\
2595                                self.getCoefficient("d_contact"), \
2596                                escript.Data())
2597                     self.getDomain().addPDEToSystem(operator,escript.Data(), \
2598                                self.getCoefficient("A_reduced"), \
2599                                self.getCoefficient("B_reduced"), \
2600                                self.getCoefficient("C_reduced"), \
2601                                self.getCoefficient("D_reduced"), \
2602                              escript.Data(), \                              escript.Data(), \
2603                              escript.Data(), \                              escript.Data(), \
2604                              self.getCoefficientOfGeneralPDE("d"), \                              self.getCoefficient("d_reduced"), \
2605                              escript.Data(),\                              escript.Data(),\
2606                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficient("d_contact_reduced"), \
2607                              escript.Data())                              escript.Data())
2608                   self.__applyConstraint()                   self.insertConstraint(rhs_only=False)
2609                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
2610                   self.__operator_isValid=True                   self.validOperator()
2611         return (self.__operator,self.__righthandside)         self.setSystemStatus()
2612           self.trace("System status is %s."%self.getSystemStatus())
2613           return (self.getCurrentOperator(), self.getCurrentRightHandSide())
2614    
2615       def insertConstraint(self, rhs_only=False):
2616          """
2617          Applies the constraints defined by q and r to the PDE.
2618    
2619          @param rhs_only: if True only the right hand side is altered by the
2620                           constraint
2621          @type rhs_only: C{bool}
2622          """
2623          q=self.getCoefficient("q")
2624          r=self.getCoefficient("r")
2625          righthandside=self.getCurrentRightHandSide()
2626          operator=self.getCurrentOperator()
2627    
2628          if not q.isEmpty():
2629             if r.isEmpty():
2630                r_s=self.createSolution()
2631             else:
2632                r_s=r
2633             if not rhs_only and not operator.isEmpty():
2634                 if self.isUsingLumping():
2635                     operator.copyWithMask(escript.Data(1.,q.getShape(),q.getFunctionSpace()),q)
2636                 else:
2637                     row_q=escript.Data(q,self.getFunctionSpaceForEquation())
2638                     col_q=escript.Data(q,self.getFunctionSpaceForSolution())
2639                     u=self.createSolution()
2640                     u.copyWithMask(r_s,col_q)
2641                     righthandside-=operator*u
2642                     operator.nullifyRowsAndCols(row_q,col_q,1.)
2643             righthandside.copyWithMask(r_s,q)
2644    
2645  class AdvectivePDE(LinearPDE):     def setValue(self,**coefficients):
2646     """        """
2647     Class to handle a linear PDE dominated by advective terms:        Sets new values to coefficients.
2648    
2649     class to define a linear PDE of the form        @param coefficients: new values assigned to coefficients
2650          @keyword A: value for coefficient C{A}
2651          @type A: any type that can be cast to a L{Data<escript.Data>} object on
2652                   L{Function<escript.Function>}
2653          @keyword A_reduced: value for coefficient C{A_reduced}
2654          @type A_reduced: any type that can be cast to a L{Data<escript.Data>}
2655                           object on L{ReducedFunction<escript.ReducedFunction>}
2656          @keyword B: value for coefficient C{B}
2657          @type B: any type that can be cast to a L{Data<escript.Data>} object on
2658                   L{Function<escript.Function>}
2659          @keyword B_reduced: value for coefficient C{B_reduced}
2660          @type B_reduced: any type that can be cast to a L{Data<escript.Data>}
2661                           object on L{ReducedFunction<escript.ReducedFunction>}
2662          @keyword C: value for coefficient C{C}
2663          @type C: any type that can be cast to a L{Data<escript.Data>} object on
2664                   L{Function<escript.Function>}
2665          @keyword C_reduced: value for coefficient C{C_reduced}
2666          @type C_reduced: any type that can be cast to a L{Data<escript.Data>}
2667                           object on L{ReducedFunction<escript.ReducedFunction>}
2668          @keyword D: value for coefficient C{D}
2669          @type D: any type that can be cast to a L{Data<escript.Data>} object on
2670                   L{Function<escript.Function>}
2671          @keyword D_reduced: value for coefficient C{D_reduced}
2672          @type D_reduced: any type that can be cast to a L{Data<escript.Data>}
2673                           object on L{ReducedFunction<escript.ReducedFunction>}
2674          @keyword X: value for coefficient C{X}
2675          @type X: any type that can be cast to a L{Data<escript.Data>} object on
2676                   L{Function<escript.Function>}
2677          @keyword X_reduced: value for coefficient C{X_reduced}
2678          @type X_reduced: any type that can be cast to a L{Data<escript.Data>}
2679                           object on L{ReducedFunction<escript.ReducedFunction>}
2680          @keyword Y: value for coefficient C{Y}
2681          @type Y: any type that can be cast to a L{Data<escript.Data>} object on
2682                   L{Function<escript.Function>}
2683          @keyword Y_reduced: value for coefficient C{Y_reduced}
2684          @type Y_reduced: any type that can be cast to a L{Data<escript.Data>}
2685                           object on L{ReducedFunction<escript.Function>}
2686          @keyword d: value for coefficient C{d}
2687          @type d: any type that can be cast to a L{Data<escript.Data>} object on
2688                   L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2689          @keyword d_reduced: value for coefficient C{d_reduced}
2690          @type d_reduced: any type that can be cast to a L{Data<escript.Data>}
2691                           object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}
2692          @keyword y: value for coefficient C{y}
2693          @type y: any type that can be cast to a L{Data<escript.Data>} object on
2694                   L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2695          @keyword d_contact: value for coefficient C{d_contact}
2696          @type d_contact: any type that can be cast to a L{Data<escript.Data>}
2697                           object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}
2698                           or L{FunctionOnContactZero<escript.FunctionOnContactZero>}
2699          @keyword d_contact_reduced: value for coefficient C{d_contact_reduced}
2700          @type d_contact_reduced: any type that can be cast to a L{Data<escript.Data>}
2701                                   object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
2702                                   or L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}
2703          @keyword y_contact: value for coefficient C{y_contact}
2704          @type y_contact: any type that can be cast to a L{Data<escript.Data>}
2705                           object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}
2706                           or L{FunctionOnContactZero<escript.FunctionOnContactZero>}
2707          @keyword y_contact_reduced: value for coefficient C{y_contact_reduced}
2708          @type y_contact_reduced: any type that can be cast to a L{Data<escript.Data>}
2709                                   object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>}
2710                                   or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}
2711          @keyword r: values prescribed to the solution at the locations of
2712                      constraints
2713          @type r: any type that can be cast to a L{Data<escript.Data>} object on
2714                   L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2715                   depending on whether reduced order is used for the solution
2716          @keyword q: mask for location of constraints
2717          @type q: any type that can be cast to a L{Data<escript.Data>} object on
2718                   L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2719                   depending on whether reduced order is used for the
2720                   representation of the equation
2721          @raise IllegalCoefficient: if an unknown coefficient keyword is used
2722          """
2723          super(LinearPDE,self).setValue(**coefficients)
2724          # check if the systrem is inhomogeneous:
2725          if len(coefficients)>0 and not self.isUsingLumping():
2726             q=self.getCoefficient("q")
2727             r=self.getCoefficient("r")
2728             if not q.isEmpty() and not r.isEmpty():
2729                 if util.Lsup(q*r)>0.:
2730                   self.trace("Inhomogeneous constraint detected.")
2731                   self.invalidateSystem()
2732    
    \f[  
    -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
2733    
2734     with boundary conditons:     def getResidual(self,u=None):
2735         """
2736         Returns the residual of u or the current solution if u is not present.
2737    
2738         @param u: argument in the residual calculation. It must be representable
2739                   in L{self.getFunctionSpaceForSolution()}. If u is not present
2740                   or equals C{None} the current solution is used.
2741         @type u: L{Data<escript.Data>} or None
2742         @return: residual of u
2743         @rtype: L{Data<escript.Data>}
2744         """
2745         if u==None:
2746            return self.getOperator()*self.getSolution()-self.getRightHandSide()
2747         else:
2748            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())-self.getRightHandSide()
2749    
2750       def getFlux(self,u=None):
2751         """
2752         Returns the flux M{J} for a given M{u}.
2753    
2754     \f[       M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
2755    
2756     and contact conditions       or
2757    
2758     \f[       M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
2759     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}  
2760     \f]       @param u: argument in the flux. If u is not present or equals L{None} the
2761                   current solution is used.
2762         @type u: L{Data<escript.Data>} or None
2763         @return: flux
2764         @rtype: L{Data<escript.Data>}
2765         """
2766         if u==None: u=self.getSolution()
2767         return util.tensormult(self.getCoefficient("A"),util.grad(u,Funtion(self.getDomain))) \
2768               +util.matrixmult(self.getCoefficient("B"),u) \
2769               -util.self.getCoefficient("X") \
2770               +util.tensormult(self.getCoefficient("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
2771               +util.matrixmult(self.getCoefficient("B_reduced"),u) \
2772               -util.self.getCoefficient("X_reduced")
2773    
2774    
2775    class Poisson(LinearPDE):
2776       """
2777       Class to define a Poisson equation problem. This is generally a
2778       L{LinearPDE} of the form
2779