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revision 3297 by caltinay, Fri Oct 22 02:53:24 2010 UTC revision 3298 by caltinay, Fri Oct 22 06:49:04 2010 UTC
# Line 117  interpolation is not always possible, se Line 117  interpolation is not always possible, se
117  An alternative approach to change the representation (=\FunctionSpace) is  An alternative approach to change the representation (=\FunctionSpace) is
118  projection\index{projection}, see \Sec{SEC Projection}.  projection\index{projection}, see \Sec{SEC Projection}.
119    
120  \subsection{\Data objects}  \subsection{\Data Objects}
121  In \escript the class that stores these functions is called \Data.  In \escript the class that stores these functions is called \Data.
122  The function is represented through its values on \DataSamplePoints where  The function is represented through its values on \DataSamplePoints where
123  the \DataSamplePoints are chosen according to the function space of the  the \DataSamplePoints are chosen according to the function space of the
# Line 222  The following call is equivalent to the Line 222  The following call is equivalent to the
222    mu=Scalar(2., Function(mydomain))    mu=Scalar(2., Function(mydomain))
223    s=getStress(u, lam, mu)    s=getStress(u, lam, mu)
224  \end{python}  \end{python}
225    %
226  The function \var{lam} belongs to the \ContinuousFunction but with \var{g} the  The function \var{lam} belongs to the \ContinuousFunction but with \var{g} the
227  function \var{trace(g)} is in the \Function.  function \var{trace(g)} is in the \Function.
228  In the evaluation of the product \var{lam*trace(g)} we have different function  In the evaluation of the product \var{lam*trace(g)} we have different function
# Line 274  The \code{getStress} method does not nee Line 274  The \code{getStress} method does not nee
274    
275  This brings us to a very important point about \escript.  This brings us to a very important point about \escript.
276  You can develop a simulation with constant Lame coefficients, and then later  You can develop a simulation with constant Lame coefficients, and then later
277  switch to tagged Lame coefficients without otherwise changing your python script.  switch to tagged Lame coefficients without otherwise changing your \PYTHON script.
278  In short, you can use the same script for models with different domains and  In short, you can use the same script for models with different domains and
279  different types of input data.  different types of input data.
280    
# Line 286  In the expanded case, each sample point Line 286  In the expanded case, each sample point
286  This is where your largest data sets will be created because the values are  This is where your largest data sets will be created because the values are
287  stored as a complete array.  stored as a complete array.
288  The tagged case has already been discussed above.  The tagged case has already been discussed above.
289    Expanded data is created when specifying \code{expanded=True} in the \Data
290  Expanded data is created when you create a \Data object with \code{expanded=True}.  object constructor, while tagged data requires calling the \member{insertTaggedValue}
 Tagged data sets are created when you use the \member{insertTaggedValue}  
291  method as shown above.  method as shown above.
292    
293  Values are accessed through a sample reference number.  Values are accessed through a sample reference number.
# Line 305  read back using the \member{load} method Line 304  read back using the \member{load} method
304  \netCDF\cite{NETCDF} file format.  \netCDF\cite{NETCDF} file format.
305  Use these to save data for checkpoint/restart or simply to save and reuse data  Use these to save data for checkpoint/restart or simply to save and reuse data
306  that was expensive to compute.  that was expensive to compute.
   
307  For instance, to save the coordinates of the data points of a  For instance, to save the coordinates of the data points of a
308  \ContinuousFunction to the file \file{x.nc} use  \ContinuousFunction to the file \file{x.nc} use
309  \begin{python}  \begin{python}
# Line 313  For instance, to save the coordinates of Line 311  For instance, to save the coordinates of
311    x.dump("x.nc")    x.dump("x.nc")
312    mydomain.dump("dom.nc")    mydomain.dump("dom.nc")
313  \end{python}  \end{python}
314  To recover the object \var{x}, and \var{mydomain} was a \finley mesh use  To recover the object \var{x}, and you know that \var{mydomain} was an \finley
315    mesh, use
316  \begin{python}  \begin{python}
317    from esys.finley import LoadMesh    from esys.finley import LoadMesh
318    mydomain=LoadMesh("dom.nc")    mydomain=LoadMesh("dom.nc")
# Line 328  an individual file for each process cont Line 327  an individual file for each process cont
327  In order to avoid conflicts the file names are extended by the \MPI processor  In order to avoid conflicts the file names are extended by the \MPI processor
328  rank, that is instead of one file \file{dom.nc} you would get  rank, that is instead of one file \file{dom.nc} you would get
329  \file{dom.nc.0000}, \file{dom.nc.0001}, etc. You still call  \file{dom.nc.0000}, \file{dom.nc.0001}, etc. You still call
330  \code{LoadMesh('dom.nc')} to load the domain but you have to make sure that  \code{LoadMesh("dom.nc")} to load the domain but you have to make sure that
331  the appropriate file is accessible from the corresponding rank, and loading  the appropriate file is accessible from the corresponding rank, and loading
332  will only succeed if you run with as many processes as were used when calling  will only succeed if you run with as many processes as were used when calling
333  \member{dump}.  \member{dump}.
# Line 347  It has the advantage of allowing to save Line 346  It has the advantage of allowing to save
346  \Data objects but also other values\footnote{The \PYTHON \emph{pickle} module  \Data objects but also other values\footnote{The \PYTHON \emph{pickle} module
347  is used for other types.} you compute in your simulation script.  is used for other types.} you compute in your simulation script.
348  Further, \class{DataManager} objects can simultaneously create files for  Further, \class{DataManager} objects can simultaneously create files for
349  visualization so no extra calls to, e.g. \code{saveVTK} are needed.  visualization so no extra calls to \code{saveVTK} etc. are needed.
350    
351  The following example shows how the \class{DataManager} class can be used.  The following example shows how the \class{DataManager} class can be used.
352  For an explanation of all member functions and options see the relevant  For an explanation of all member functions and options see the relevant
# Line 383  method. If it returns \True we retrieve Line 382  method. If it returns \True we retrieve
382  variables. Otherwise the same variables are initialized with appropriate  variables. Otherwise the same variables are initialized with appropriate
383  values to start a new simulation.  values to start a new simulation.
384  Note, that \var{t} and \var{t_max} are regular floating point values and not  Note, that \var{t} and \var{t_max} are regular floating point values and not
385  \Data objects but are treated the same way by the \class{DataManager}.  \Data objects. Yet they are treated the same way by the \class{DataManager}.
386    
387  After this initialization step the script enters the main simulation loop  After this initialization step the script enters the main simulation loop
388  where calculations are performed.  where calculations are performed.
389  When these are finalized for a time step we call the \member{addData} method  When these are finalized for a time step we call the \member{addData} method
390  to let the manager know which variables to store on disk.  to let the manager know which variables to store on disk.
391  Note, that this does not actually save the data yet and it is allowed to call  This does not actually save the data yet and it is allowed to call
392  \member{addData} more than once to add information incrementally, e.g. from  \member{addData} more than once to add information incrementally, e.g. from
393  separate functions that have access to the \class{DataManager} instance.  separate functions that have access to the \class{DataManager} instance.
394  Once all variables have been added the \member{export} method has to be called  Once all variables have been added the \member{export} method has to be called
# Line 397  to flush all data to disk and clear the Line 396  to flush all data to disk and clear the
396  In this example, this call dumps \var{mydomain} and \var{val} to files  In this example, this call dumps \var{mydomain} and \var{val} to files
397  in a restart directory and also stores \var{t} and \var{t_max} on disk.  in a restart directory and also stores \var{t} and \var{t_max} on disk.
398  Additionally, it generates a \VTK file for visualization of the data.  Additionally, it generates a \VTK file for visualization of the data.
399    If the script would stop running before its completion for some reason (e.g.
400    because its runtime limit was exceeded in a multiuser environment), you could
401    simply run it again and it would resume at the point it stopped before.
402    
403  \section{\escript Classes}  \section{\escript Classes}
404    
# Line 407  a way of representing functions over thi Line 409  a way of representing functions over thi
409  The \Domain class provides an abstract interface to the domain of \FunctionSpace and \Data objects.  The \Domain class provides an abstract interface to the domain of \FunctionSpace and \Data objects.
410  \Domain needs to be subclassed in order to provide a complete implementation.  \Domain needs to be subclassed in order to provide a complete implementation.
411  \end{classdesc}  \end{classdesc}
412    %
413  The following methods are available:  The following methods are available:
414    %
415  \begin{methoddesc}[Domain]{getDim}{}  \begin{methoddesc}[Domain]{getDim}{}
416  returns the spatial dimension of the \Domain.      returns the spatial dimension of the \Domain.
417  \end{methoddesc}  \end{methoddesc}
418    %
419  \begin{methoddesc}[Domain]{dump}{filename}  \begin{methoddesc}[Domain]{dump}{filename}
420  dumps the \Domain into the file \var{filename}.      writes the \Domain to the file \var{filename} using the \netCDF file format.
421  \end{methoddesc}  \end{methoddesc}
422    %
423  \begin{methoddesc}[Domain]{getX}{}  \begin{methoddesc}[Domain]{getX}{}
424  returns the locations in the \Domain. The \FunctionSpace of the returned      returns the locations in the \Domain. The \FunctionSpace of the returned
425  \Data object is chosen by the \Domain implementation. Typically it will be      \Data object is chosen by the \Domain implementation. Typically it will be
426  in the \Function.      in the \Function.
427  \end{methoddesc}  \end{methoddesc}
428    %
429  \begin{methoddesc}[Domain]{setX}{newX}  \begin{methoddesc}[Domain]{setX}{newX}
430  assigns a new location to the \Domain. \var{newX} has to have \Shape $(d,)$      assigns new locations to the \Domain. \var{newX} has to have \Shape $(d,)$
431  where $d$ is the spatial dimension of the domain. Typically \var{newX} must be      where $d$ is the spatial dimension of the domain. Typically \var{newX}
432  in the \ContinuousFunction but the space actually to be used depends on the \Domain implementation.      must be in the \ContinuousFunction but the space actually to be used
433        depends on the \Domain implementation.
434  \end{methoddesc}  \end{methoddesc}
435    %
436  \begin{methoddesc}[Domain]{getNormal}{}  \begin{methoddesc}[Domain]{getNormal}{}
437  returns the surface normals on the boundary of the \Domain as \Data object.      returns the surface normals on the boundary of the \Domain as a \Data object.
438  \end{methoddesc}  \end{methoddesc}
439    %
440  \begin{methoddesc}[Domain]{getSize}{}  \begin{methoddesc}[Domain]{getSize}{}
441  returns the local sample size, e.g. the element diameter, as \Data object.      returns the local sample size, i.e. the element diameter, as a \Data object.
442  \end{methoddesc}  \end{methoddesc}
443    %
444  \begin{methoddesc}[Domain]{setTagMap}{tag_name, tag}  \begin{methoddesc}[Domain]{setTagMap}{tag_name, tag}
445  defines a mapping of the tag name  \var{tag_name} to the \var{tag}.      defines a mapping of the tag name \var{tag_name} to the \var{tag}.
446  \end{methoddesc}  \end{methoddesc}
447    %
448  \begin{methoddesc}[Domain]{getTag}{tag_name}  \begin{methoddesc}[Domain]{getTag}{tag_name}
449  returns the tag associated with the tag name \var{tag_name}.      returns the tag associated with the tag name \var{tag_name}.
450  \end{methoddesc}  \end{methoddesc}
451    %
452  \begin{methoddesc}[Domain]{isValidTagName}{tag_name}  \begin{methoddesc}[Domain]{isValidTagName}{tag_name}
453  return \True if \var{tag_name} is a valid tag name.      returns \True if \var{tag_name} is a valid tag name.
454  \end{methoddesc}  \end{methoddesc}
455    %
456  \begin{methoddesc}[Domain]{__eq__}{arg}  \begin{methoddesc}[Domain]{__eq__}{arg}
457  (python == operator) returns \True if the \Domain \var{arg} describes the same domain. Otherwise      (\PYTHON \var{==} operator) returns \True if the \Domain \var{arg}
458  \False is returned.      describes the same domain, \False otherwise.
459  \end{methoddesc}  \end{methoddesc}
460    %
461  \begin{methoddesc}[Domain]{__ne__}{arg}  \begin{methoddesc}[Domain]{__ne__}{arg}
462  (python != operator) returns \True if the \Domain \var{arg} does not describe the same domain.      (\PYTHON \var{!=} operator) returns \True if the \Domain \var{arg} does
463  Otherwise \False is returned.      not describe the same domain, \False otherwise.
464  \end{methoddesc}  \end{methoddesc}
465    %
466  \begin{methoddesc}[Domain]{__str__}{arg}  \begin{methoddesc}[Domain]{__str__}{}
467  (python str() function) returns string representation of the \Domain.      (\PYTHON \var{str()} function) returns a string representation of the
468        \Domain.
469  \end{methoddesc}  \end{methoddesc}
470    %
471  \begin{methoddesc}[Domain]{onMasterProcessor)}{}  \begin{methoddesc}[Domain]{onMasterProcessor)}{}
472  returns \True if the processor is the master processor within      returns \True if the processor is the master processor within the \MPI
473  the \MPI processor group used by the \Domain. This is the processor with rank 0.      processor group used by the \Domain. This is the processor with rank 0.
474  If \MPI support is not enabled the return value is always \True.      If \MPI support is not enabled the return value is always \True.
475  \end{methoddesc}  \end{methoddesc}
476    %
477  \begin{methoddesc}[Domain]{getMPISize}{}  \begin{methoddesc}[Domain]{getMPISize}{}
478   returns the number of \MPI processors used for this \Domain. If \MPI support is not enabled      returns the number of \MPI processors used for this \Domain. If \MPI
479  1 is returned.      support is not enabled 1 is returned.
480  \end{methoddesc}  \end{methoddesc}
481    %
482  \begin{methoddesc}[Domain]{getMPIRank}{}  \begin{methoddesc}[Domain]{getMPIRank}{}
483   returns the rank of the processor executing the statement      returns the rank of the processor executing the statement within the
484  within the  \MPI processor group used by the \Domain.      \MPI processor group used by the \Domain. If \MPI support is not enabled
485  If \MPI support is not enabled 0 is returned.      0 is returned.
486  \end{methoddesc}  \end{methoddesc}
487    %
488  \begin{methoddesc}[Domain]{MPIBarrier}{}  \begin{methoddesc}[Domain]{MPIBarrier}{}
489  executes barrier synchronization within      executes barrier synchronization within the \MPI processor group used by
490  the \MPI processor group used by the \Domain.      the \Domain. If \MPI support is not enabled, this command does nothing.
 If \MPI support is not enabled, this command does nothing.  
491  \end{methoddesc}  \end{methoddesc}
492    
493  \subsection{The \FunctionSpace class}  \subsection{The \FunctionSpace class}
494  \begin{classdesc}{FunctionSpace}{}  \begin{classdesc}{FunctionSpace}{}
495  \FunctionSpace objects are used to define properties of \Data objects, such as continuity. \FunctionSpace objects  \FunctionSpace objects are used to define properties of \Data objects such as continuity.
496  are instantiated by generator functions. A \Data object in a particular \FunctionSpace is  \FunctionSpace objects are instantiated by generator functions.
497  represented by its values at \DataSamplePoints which are defined by the type and the \Domain of the  A \Data object in a particular \FunctionSpace is represented by its values at
498  \FunctionSpace.  \DataSamplePoints which are defined by the type and the \Domain of the \FunctionSpace.
499  \end{classdesc}  \end{classdesc}
500    %
501  The following methods are available:  The following methods are available:
502    %
503  \begin{methoddesc}[FunctionSpace]{getDim}{}  \begin{methoddesc}[FunctionSpace]{getDim}{}
504  returns the spatial dimension of the \Domain of the \FunctionSpace.      returns the spatial dimension of the \Domain of the \FunctionSpace.
505  \end{methoddesc}  \end{methoddesc}
506    %
   
   
507  \begin{methoddesc}[FunctionSpace]{getX}{}  \begin{methoddesc}[FunctionSpace]{getX}{}
508  returns the location of the \DataSamplePoints.      returns the location of the \DataSamplePoints.
509  \end{methoddesc}  \end{methoddesc}
510    %
511  \begin{methoddesc}[FunctionSpace]{getNormal}{}  \begin{methoddesc}[FunctionSpace]{getNormal}{}
512  If the domain of functions in the \FunctionSpace      If the domain of functions in the \FunctionSpace is a hyper-manifold (e.g.
513  is a hyper-manifold (e.g. the boundary of a domain)      the boundary of a domain) the method returns the outer normal at each of
514  the method returns the outer normal at each of the      the \DataSamplePoints. Otherwise an exception is raised.
 \DataSamplePoints. Otherwise an exception is raised.  
515  \end{methoddesc}  \end{methoddesc}
516    %
517  \begin{methoddesc}[FunctionSpace]{getSize}{}  \begin{methoddesc}[FunctionSpace]{getSize}{}
518  returns a \Data objects measuring the spacing of the \DataSamplePoints.      returns a \Data object measuring the spacing of the \DataSamplePoints.
519  The size may be zero.      The size may be zero.
520  \end{methoddesc}  \end{methoddesc}
521    %
522  \begin{methoddesc}[FunctionSpace]{getDomain}{}  \begin{methoddesc}[FunctionSpace]{getDomain}{}
523  returns the \Domain of the \FunctionSpace.      returns the \Domain of the \FunctionSpace.
524  \end{methoddesc}  \end{methoddesc}
525    %
526  \begin{methoddesc}[FunctionSpace]{setTags}{new_tag, mask}  \begin{methoddesc}[FunctionSpace]{setTags}{new_tag, mask}
527  assigns a new tag \var{new_tag} to all data sample      assigns a new tag \var{new_tag} to all data samples where \var{mask} is
528  where \var{mask} is positive for a least one data point.      positive for a least one data point.
529  \var{mask} must be defined on the this \FunctionSpace.      \var{mask} must be defined on this \FunctionSpace.
530  Use the \var{setTagMap} to assign a tag name to \var{new_tag}.      Use the \var{setTagMap} to assign a tag name to \var{new_tag}.
531  \end{methoddesc}  \end{methoddesc}
532    %
533  \begin{methoddesc}[FunctionSpace]{__eq__}{arg}  \begin{methoddesc}[FunctionSpace]{__eq__}{arg}
534  (python == operator) returns \True if the \Domain \var{arg} describes the same domain. Otherwise      (\PYTHON \var{==} operator) returns \True if the \FunctionSpace \var{arg}
535  \False is returned.      describes the same function space, \False otherwise.
536  \end{methoddesc}  \end{methoddesc}
537    %
538  \begin{methoddesc}[FunctionSpace]{__ne__}{arg}  \begin{methoddesc}[FunctionSpace]{__ne__}{arg}
539  (python != operator) returns \True if the \Domain \var{arg} do not describe the same domain.      (\PYTHON \var{!=} operator) returns \True if the \FunctionSpace \var{arg}
540  Otherwise \False is returned.      does not describe the same function space, \False otherwise.
541  \end{methoddesc}  \end{methoddesc}
542    
543  \begin{methoddesc}[Domain]{__str__}{g}  \begin{methoddesc}[Domain]{__str__}{}
544  (python str() function) returns string representation of the \Domain.      (\PYTHON \var{str()} function) returns a string representation of the
545        \FunctionSpace.
546  \end{methoddesc}  \end{methoddesc}
547    %
548  The following function provide generators for \FunctionSpace objects:  The following functions provide generators for \FunctionSpace objects:
549    %
550  \begin{funcdesc}{Function}{domain}  \begin{funcdesc}{Function}{domain}
551  returns the \Function on the \Domain \var{domain}. \Data objects in this type of \Function      returns the \Function on the \Domain \var{domain}. \Data objects in this
552  are defined over the whole geometric region defined by \var{domain}.      type of \Function are defined over the whole geometric region defined by
553        \var{domain}.
554  \end{funcdesc}  \end{funcdesc}
555    %
556  \begin{funcdesc}{ContinuousFunction}{domain}  \begin{funcdesc}{ContinuousFunction}{domain}
557  returns the \ContinuousFunction on the \Domain domain. \Data objects in this type of \Function      returns the \ContinuousFunction on the \Domain domain. \Data objects in
558  are defined over the whole geometric region defined by \var{domain} and assumed to represent      this type of \Function are defined over the whole geometric region defined
559  a continuous function.      by \var{domain} and assumed to represent a continuous function.
560  \end{funcdesc}  \end{funcdesc}
561    %
562  \begin{funcdesc}{FunctionOnBoundary}{domain}  \begin{funcdesc}{FunctionOnBoundary}{domain}
563  returns the \ContinuousFunction on the \Domain domain. \Data objects in this type of \Function      returns the \FunctionOnBoundary on the \Domain domain. \Data objects in
564  are defined on the boundary of the geometric region defined by \var{domain}.      this type of \Function are defined on the boundary of the geometric region
565        defined by \var{domain}.
566  \end{funcdesc}  \end{funcdesc}
567    %
568  \begin{funcdesc}{FunctionOnContactZero}{domain}  \begin{funcdesc}{FunctionOnContactZero}{domain}
569  returns the \FunctionOnContactZero the \Domain domain. \Data objects in this type of \Function      returns the \FunctionOnContactZero the \Domain domain. \Data objects in
570  are defined on side 0 of a discontinuity  within the geometric region defined by \var{domain}.      this type of \Function are defined on side 0 of a discontinuity  within
571  The discontinuity is defined when \var{domain} is instantiated.      the geometric region defined by \var{domain}.
572        The discontinuity is defined when \var{domain} is instantiated.
573  \end{funcdesc}  \end{funcdesc}
574    %
575  \begin{funcdesc}{FunctionOnContactOne}{domain}  \begin{funcdesc}{FunctionOnContactOne}{domain}
576  returns the \FunctionOnContactOne on the \Domain domain.      returns the \FunctionOnContactOne on the \Domain domain. \Data objects in
577  \Data objects in this type of \Function      this type of \Function are defined on side 1 of a discontinuity within
578  are defined on side 1 of a discontinuity  within the geometric region defined by \var{domain}.      the geometric region defined by \var{domain}.
579  The discontinuity is defined when \var{domain} is instantiated.      The discontinuity is defined when \var{domain} is instantiated.
580  \end{funcdesc}  \end{funcdesc}
581    %
582  \begin{funcdesc}{Solution}{domain}  \begin{funcdesc}{Solution}{domain}
583  returns the \SolutionFS on the \Domain domain. \Data objects in this type of \Function      returns the \SolutionFS on the \Domain domain. \Data objects in this type
584  are defined on geometric region defined by \var{domain} and are solutions of      of \Function are defined on the geometric region defined by \var{domain}
585  partial differential equations \index{partial differential equation}.      and are solutions of partial differential equations\index{partial differential equation}.
586  \end{funcdesc}  \end{funcdesc}
587    %
588  \begin{funcdesc}{ReducedSolution}{domain}  \begin{funcdesc}{ReducedSolution}{domain}
589  returns the \ReducedSolutionFS on the \Domain domain. \Data objects in this type of \Function      returns the \ReducedSolutionFS on the \Domain domain. \Data objects in
590  are defined on geometric region defined by \var{domain} and are solutions of      this type of \Function are defined on the geometric region defined by
591  partial differential equations \index{partial differential equation} with a reduced smoothness      \var{domain} and are solutions of partial differential
592  for the solution approximation.      equations\index{partial differential equation} with a reduced smoothness
593        for the solution approximation.
594  \end{funcdesc}  \end{funcdesc}
595    
596  \subsection{The \Data Class}  \subsection{The \Data Class}
597  \label{SEC ESCRIPT DATA}  \label{SEC ESCRIPT DATA}
598    
599  The following table shows arithmetic operations that can be performed point-wise on  The following table shows arithmetic operations that can be performed
600  \Data objects.  point-wise on \Data objects:
601  \begin{table}  \begin{center}
     \centering  
602      \begin{tabular}{l|l}      \begin{tabular}{l|l}
603          \bfseries expression & Description\\          \textbf{Expression} & \textbf{Description}\\
604          \hline          \hline
605          +\var{arg0} & identical to \var{arg} \index{+}\\          \code{+arg} & identical to \var{arg}\index{+}\\
606          -\var{arg0} & negation\index{-}\\          \code{-arg} & negation of \var{arg}\index{-}\\
607          \var{arg0}+\var{arg1} & adds \var{arg0} and \var{arg1} \index{+}\\          \code{arg0+arg1} & adds \var{arg0} and \var{arg1}\index{+}\\
608          \var{arg0}*\var{arg1} & multiplies \var{arg0} and \var{arg1} \index{*}\\          \code{arg0*arg1} & multiplies \var{arg0} and \var{arg1}\index{*}\\
609          \var{arg0}-\var{arg1} & difference \var{arg1} from\var{arg1} \index{-}\\          \code{arg0-arg1} & subtracts \var{arg1} from \var{arg0}\index{-}\\
610          \var{arg0}/\var{arg1} & divide \var{arg0} by \var{arg1} \index{/}\\          \code{arg0/arg1} & divides \var{arg0} by \var{arg1}\index{/}\\
611          \var{arg0}**\var{arg1} & raises \var{arg0} to the power of \var{arg1} \index{**}\\          \code{arg0**arg1} & raises \var{arg0} to the power of \var{arg1}\index{**}\\
612      \end{tabular}      \end{tabular}
613  \end{table}  \end{center}
614  At least one of the arguments \var{arg0} or \var{arg1} must be a  At least one of the arguments \var{arg0} or \var{arg1} must be a \Data object.
615  \Data object.  Either of the arguments may be a \Data object, a \PYTHON number or a \numpy
616  Either of the arguments may be a \Data object, a python number or a \numpy object.  object.
617    If \var{arg0} or \var{arg1} are not defined on the same \FunctionSpace, then
618  If \var{arg0} or \var{arg1} are  an attempt is made to convert \var{arg0} to the \FunctionSpace of \var{arg1}
619  not defined on the same \FunctionSpace, then an attempt is made to convert \var{arg0}  or to convert \var{arg1} to the \FunctionSpace of \var{arg0}.
620  to the \FunctionSpace of \var{arg1} or to convert \var{arg1} to  Both arguments must have the same \Shape or one of the arguments may be of
621  the \FunctionSpace of \var{arg0}. Both arguments must have the same  rank 0 (a constant).
 \Shape or one of the arguments may be of rank 0 (a constant).  
   
622  The returned \Data object has the same \Shape and is defined on  The returned \Data object has the same \Shape and is defined on
623  the \DataSamplePoints as \var{arg0} or \var{arg1}.  the \DataSamplePoints as \var{arg0} or \var{arg1}.
624    
625  The following table shows the update operations that can be applied to  The following table shows the update operations that can be applied to
626  \Data objects:  \Data objects:
627  \begin{table}  \begin{center}
     \centering  
628      \begin{tabular}{l|l}      \begin{tabular}{l|l}
629          \bfseries Expression & Description\\          \textbf{Expression} & \textbf{Description}\\
630          \hline          \hline
631          \var{arg0}+=\var{arg2} & adds \var{arg0} to \var{arg2}\index{+}\\          \code{arg0+=arg1} & adds \var{arg1} to \var{arg0}\index{+}\\
632          \var{arg0}*=\var{arg2} & multiplies \var{arg0} with \var{arg2}\index{*}\\          \code{arg0*=arg1} & multiplies \var{arg0} by \var{arg1}\index{*}\\
633          \var{arg0}-=\var{arg2} & subtracts \var{arg2} from\var{arg2}\index{-}\\          \code{arg0-=arg1} & subtracts \var{arg1} from\var{arg0}\index{-}\\
634          \var{arg0}/=\var{arg2} & divides \var{arg0} by \var{arg2}\index{/}\\          \code{arg0/=arg1} & divides \var{arg0} by \var{arg1}\index{/}\\
635          \var{arg0}**=\var{arg2} & raises \var{arg0} by \var{arg2}\index{**}\\          \code{arg0**=arg1} & raises \var{arg0} to the power of \var{arg1}\index{**}\\
636      \end{tabular}      \end{tabular}
637  \end{table}  \end{center}
638  \var{arg0} must be a \Data object. \var{arg1} must be a  \var{arg0} must be a \Data object. \var{arg1} must be a \Data object or an
639  \Data object or an object that can be converted into a  object that can be converted into a \Data object.
640  \Data object. \var{arg1} must have the same \Shape as  \var{arg1} must have the same \Shape as \var{arg0} or have rank 0.
641  \var{arg0} or have rank 0.  In the latter case it is  In the latter case it is assumed that the values of \var{arg1} are constant
642  assumed that the values of \var{arg1} are constant for all  for all components. \var{arg1} must be defined in the same \FunctionSpace as
 components. \var{arg1} must be defined in the same \FunctionSpace as  
643  \var{arg0} or it must be possible to interpolate \var{arg1} onto the  \var{arg0} or it must be possible to interpolate \var{arg1} onto the
644  \FunctionSpace of \var{arg0}.  \FunctionSpace of \var{arg0}.
645    
646  The \Data class supports taking slices from a \Data object as well as assigning new values to a slice of an existing  The \Data class supports taking slices as well as assigning new values to a
647  \Data object. \index{slicing}  slice of an existing \Data object\index{slicing}.
648  The following expressions for taking and setting slices are valid:  The following expressions for taking and setting slices are valid:
649  \begin{table}  \begin{center}
     \centering  
650      \begin{tabular}{l|ll}      \begin{tabular}{l|ll}
651          \bfseries rank of \var{arg} & slicing expression & \Shape of returned and assigned object\\          \textbf{Rank of \var{arg}} & \textbf{Slicing expression} & \textbf{\Shape of returned and assigned object}\\
652          \hline          \hline
653          0 & no slicing & -\\          0 & no slicing & N/A\\
654          1 & \var{arg[l0:u0]} & (\var{u0}-\var{l0},)\\          1 & \var{arg[l0:u0]} & (\var{u0}-\var{l0},)\\
655          2 & \var{arg[l0:u0,l1:u1]} & (\var{u0}-\var{l0},\var{u1}-\var{l1})\\          2 & \var{arg[l0:u0,l1:u1]} & (\var{u0}-\var{l0},\var{u1}-\var{l1})\\
656          3 & \var{arg[l0:u0,l1:u1,l2:u2]} & (\var{u0}-\var{l0},\var{u1}-\var{l1},\var{u2}-\var{l2})\\          3 & \var{arg[l0:u0,l1:u1,l2:u2]} & (\var{u0}-\var{l0},\var{u1}-\var{l1},\var{u2}-\var{l2})\\
657          4 & \var{arg[l0:u0,l1:u1,l2:u2,l3:u3]} & (\var{u0}-\var{l0},\var{u1}-\var{l1},\var{u2}-\var{l2},\var{u3}-\var{l3})\\          4 & \var{arg[l0:u0,l1:u1,l2:u2,l3:u3]} & (\var{u0}-\var{l0},\var{u1}-\var{l1},\var{u2}-\var{l2},\var{u3}-\var{l3})\\
658      \end{tabular}      \end{tabular}
659  \end{table}  \end{center}
660  where \var{s} is the \Shape of \var{arg} and  where \var{s} is the \Shape of \var{arg} and
661  \[0 \le \var{l0} \le \var{u0} \le \var{s[0]},\]  \[0 \le \var{l0} \le \var{u0} \le \var{s[0]},\]
662  \[0 \le \var{l1} \le \var{u1} \le \var{s[1]},\]  \[0 \le \var{l1} \le \var{u1} \le \var{s[1]},\]
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