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1
2 % $Id$
3
4 \chapter{The module \escript}
5
6 \declaremodule{extension}{escript}
7 \modulesynopsis{Data manipulation}
8
9 \begin{figure}
10 \includegraphics[width=\textwidth]{EscriptDiagram1.eps}
11 \caption{\label{ESCRIPT DEP}Dependency of Function Spaces. An arrow indicates that a function in the
12 function space at the starting point can be interpreted as a function in the function space of the arrow target.}
13 \end{figure}
14
15 \escript is an extension of Python to handle functions represented by their values on
16 \DataSamplePoints for the geometrical region on which
17 the function is defined. The region as well as the method which is used
18 to interpolate value on the \DataSamplePoints is defined by
19 \Domain class objects. For instance when using
20 the finite element method (FEM) \index{finite element method}
21 \Domain object holds the information about the FEM mesh, eg.
22 a table of nodes and a table of elements. Although \Domain contains
23 the discretization method to be used \escript does not use this information directly.
24 \Domain objects are created from a module which want to make use
25 \escript, e.g. \finley.
26
27 The solution of a PDE is a function of its location in the domain of interest $\Omega$.
28 When solving a partial differential equation \index{partial differential equation} (PDE) using FEM
29 the solution is (piecewise) differentiable but, in general, its gradient
30 is discontinuous. To reflect these different degrees of smoothness different
31 representations of the functions are used. For instance; in FEM
32 the displacement field is represented by its values at the nodes of the mesh, while the
33 strain, which is the symmetric part of the gradient of the displacement field, is stored on the
34 element centers. To be able to classify functions with respect to their smoothness, \escript has the
35 concept of the "function space". A function space is described by a \FunctionSpace object.
36 The following statement generates the object \var{solution_space} which is
37 a \FunctionSpace object and provides access to the function space of
38 PDE solutions on the \Domain \var{mydomain}:
39 \begin{python}
40 solution_space=Solution(mydomain)
41 \end{python}
42 The following generators for function spaces on a \Domain \var{mydomain} are available:
43 \begin{itemize}
44 \item \var{Solution(mydomain)}: solutions of a PDE.
45 \item \var{ContinuousFunction(mydomain)}: continuous functions, eg. a temperature distribution.
46 \item \var{Function(mydomain)}: general functions which are not necessarily continuous, eg. a stress field.
47 \item \var{FunctionOnBoundary(mydomain)}: functions on the boundary of the domain, eg. a surface pressure.
48 \item \var{FunctionOnContact0(mydomain)}: functions on side $0$ of the discontinuity.
49 \item \var{FunctionOnContact1(mydomain)}: functions on side $1$ of the discontinuity.
50 \end{itemize}
51 A discontinuity \index{discontinuity} is a region within the domain across which functions may be discontinuous.
52 The location of discontinuity is defined in the \Domain object.
53 \fig{ESCRIPT DEP} shows the dependency between the types of function spaces.
54 The solution of a PDE is a continuous function. Any continuous function can be seen as a general function
55 on the domain and can be restricted to the boundary as well as to any side of the
56 discontinuity (the result will be different depending on
57 which side is chosen). Functions on any side of the
58 discontinuity can be seen as a function on the corresponding other side.
59 A function on the boundary or on one side of
60 the discontinuity cannot be seen as a general function on the domain as there are no values
61 defined for the interior. For most PDE solver libraries
62 the space of the solution and continuous functions is identical, however in some cases, eg.
63 when periodic boundary conditions are used in \finley, a solution
64 fulfils periodic boundary conditions while a continuous function does not have to be periodic.
65
66 The concept of function spaces describes the properties of
67 functions and allows abstraction from the actual representation
68 of the function in the context of a particular application. For instance,
69 in the FEM context a
70 function in the \Function function space
71 is typically represented by its values at the element center,
72 but in a finite difference scheme the edge midpoint of cells is preferred.
73 Using the concept of function spaces
74 allows the user to run the same script on different
75 PDE solver libraries by just changing the creator of the \Domain object.
76 Changing the function space of a particular function
77 will typically lead to a change of its representation.
78 So, when seen as a general function,
79 a continuous function which is typically represented by its values
80 on the node of the FEM mesh or finite difference grid
81 must be interpolated to the element centers or the cell edges,
82 respectively.
83
84 \Data class objects store functions of the location in a domain.
85 The function is represented through its values on \DataSamplePoints where
86 the \DataSamplePoints are chosen according to the function space
87 of the function.
88 \Data class objects are used to define the coefficients
89 of the PDEs to be solved by a PDE solver library
90 and to store the returned solutions.
91
92 The values of the function have a rank which gives the
93 number of indices, and a \Shape defining the range of each index.
94 The rank in \escript is limited to the range $0$ through $4$ and
95 it is assumed that the rank and \Shape is the same for all \DataSamplePoints.
96 The \Shape of a \Data object is a tuple \var{s} of integers. The length
97 of \var{s} is the rank of the \Data object and \var{s[i]} is the maximum
98 value for the \var{i}-th index.
99 For instance, a stress field has rank $2$ and
100 \Shape $(d,d)$ where $d$ is the spatial dimension.
101 The following statement creates the \Data object
102 \var{mydat} representing a
103 continuous function with values
104 of \Shape $(2,3)$ and rank $2$:
105 \begin{python}
106 mydat=Data(value=1,what=ContinuousFunction(myDomain),shape=(2,3))
107 \end{python}
108 The initial value is the constant $1$ for all \DataSamplePoints and
109 all components.
110
111 \Data objects can also be created from any \numarray
112 array or any object, such as a list of floating point numbers,
113 that can be converted into a \numarray.NumArray \Ref{NUMARRAY}.
114 The following two statements
115 create objects which are equivalent to \var{mydat}:
116 \begin{python}
117 mydat1=Data(value=numarray.ones((2,3)),what=ContinuousFunction(myDomain))
118 mydat2=Data(value=[[1,1],[1,1],[1,1]],what=ContinuousFunction(myDomain))
119 \end{python}
120 In the first case the initial value is \var{numarray.ones((2,3))}
121 which generates a $2 \times 3$ matrix as a \numarray.NumArray
122 filled with ones. The \Shape of the created \Data object
123 it taken from the \Shape of the array. In the second
124 case, the creator converts the initial value, which is a list of lists,
125 and converts it into a \numarray.NumArray before creating the actual
126 \Data object.
127
128 For convenience \escript provides creators for the most common types
129 of \Data objects in the following forms (\var{d} defines the
130 spatial dimension):
131 \begin{itemize}
132 \item \var{Scalar(0,Function(mydomain))} is the same as \var{Data(0,Function(myDomain),(,))},
133 e.g a temperature field.
134 \item \var{Vector(0,Function(mydomain))}is the same as \var{Data(0,Function(myDomain),(d))}, e.g
135 a velocity field.
136 \item \var{Tensor(0,Function(mydomain))} is the same as \var{Data(0,Function(myDomain),(d,d))},
137 eg. a stress field.
138 \item \var{Tensor4(0,Function(mydomain))} is the same as \var{Data(0,Function(myDomain),(d,d,d,d))}
139 eg. a Hook tensor field.
140 \end{itemize}
141 Here the initial value is $0$ but any object that can be converted into a \numarray.NumArray and whose \Shape
142 is consistent with \Shape of the \Data object to be created can be used as the initial value.
143
144 \Data objects can be manipulated by applying unitary operations (eg. cos, sin, log)
145 and can be combined by applying binary operations (eg. +, - ,* , /).
146 It is to be emphasized that \escript itself does not handle any spatial dependencies as
147 it does not know how values are interpreted by the processing PDE solver library.
148 However \escript invokes interpolation if this is needed during data manipulations.
149 Typically, this occurs in binary operation when both arguments belong to different
150 function spaces or when data are handed over to a PDE solver library
151 which requires functions to be represented in a particular way.
152
153 The following example shows the usage of {\tt Data} objects: Assume we have a
154 displacement field $u$ and we want to calculate the corresponding stress field
155 $\sigma$ using the linear--elastic isotropic material model
156 \begin{eqnarray}\label{eq: linear elastic stress}
157 \sigma\hackscore {ij}=\lambda u\hackscore {k,k} \delta\hackscore {ij} + \mu ( u\hackscore {i,j} + u\hackscore {j,i})
158 \end{eqnarray}
159 where $\delta\hackscore {ij}$ is the Kronecker symbol and
160 $\lambda$ and $\mu$ are the Lame coefficients. The following function
161 takes the displacement {\tt u} and the Lame coefficients
162 \var{lam} and \var{mu} as arguments and returns the corresponding stress:
163 \begin{python}
164 import numarray
165 def getStress(u,lam,mu):
166 d=u.getDomain().getDim()
167 g=grad(u)
168 stress=lam*trace(g)*numarray.identity(d)+ \
169 mu*(g+transpose(g))
170 return stress
171 \end{python}
172 The variable
173 \var{d} gives the spatial dimension of the
174 domain on which the displacements are defined.
175 \var{identity} is a \numarray function which returns the Kronecker symbol with indexes
176 $i$ and $j$ running from $0$ to \var{d}-1. The call \var{grad(u)} requires
177 the displacement field \var{u} to be in the \var{Solution} or \ContinuousFunction
178 function space. The result \var{g} as well as the returned stress will be in the \Function function space.
179 If \var{u} is available, eg. by solving a PDE, \var{getStress} might be called
180 in the following way:
181 \begin{python}
182 s=getStress(u,1.,2.)
183 \end{python}
184 However \var{getStress} can also be called with \Data objects as values for
185 \var{lam} and \var{mu} which,
186 for instance in the case of a temperature dependency, are calculated by an expression.
187 The following call is equivalent to the previous example:
188 \begin{python}
189 lam=Scalar(1.,ContinuousFunction(mydomain))
190 mu=Scalar(2.,Function(mydomain))
191 s=getStress(u,lam,mu)
192 \end{python}
193 The function \var{lam} belongs to the \ContinuousFunction function space
194 but with \var{g} the function \var{trace(g)} is in the \Function function space.
195 Therefore the evaluation of the product \var{lam*trace(g)} in the stress calculation
196 produces a problem, as both functions are represented differently, eg. in FEM
197 \var{lam} by its values on the node, and in \var{trace(g)} by its values at the element centers.
198 In the case of inconsistent function spaces of arguments in a binary operation, \escript
199 interprets the arguments in the appropriate function space according to the inclusion
200 defined in Table~\ref{ESCRIPT DEP}. In this example that means
201 \escript sees \var{lam} as a function of the \Function function space.
202 In the context of FEM this means the nodal values of
203 \var{lam} are interpolated to the element centers. Behind the scenes
204 \escript calls the appropriate function from the PDE solver library.
205
206 \begin{figure}
207 \includegraphics[width=\textwidth]{EscriptDiagram2.eps}
208 \caption{\label{Figure: tag}Element Tagging. A rectangular mesh over a region with two rock types {\it white} and {\it gray}.
209 The number in each cell refers to the major rock type present in the cell ($1$ for {\it white} and $2$ for {\it gray}).
210 }
211 \end{figure}
212
213 Material parameters such as the Lame coefficients are typically dependent on rock types present in the
214 area of interest. A common technique to handle these kinds of material parameters is "tagging". \fig{Figure: tag}
215 shows an example. In this case two rock types {\it white} and {\it gray} can be found in the domain. The domain
216 is subdivided into rectangular shaped cells (which is not necessarily the best subdivision for this case). Each
217 cell has a tag indicating the rock type predominately found in this cell. Here $1$ is used to indicate
218 rock type {\it white} and $2$ for rock type {\it gray}. The tags are assigned at the time when the cells are generated
219 (\escript provides tools to manipulate tags at a later stage)
220 and stored in the \Domain class object. The following statements show how for the
221 example of \fig{Figure: tag} and the stress calculation discussed before tagged values are used for
222 \var{lam}:
223 \begin{python}
224 lam=Scalar(value=2.,what=Function(mydomain))
225 lam.setTaggedValue(1,30.)
226 lam.setTaggedValue(2,5000.)
227 s=getStress(u,lam,2.)
228 \end{python}
229 In this example \var{lam} is set to $30$ for those cells with tag $1$ and to $5000.$ for those cells
230 with tag $2$. The initial value $2$ of \var{lam} is used as a default value for the case when a tag
231 is encountered which has not been linked with a value. Note that the \var{getStress} method
232 is called without modification. \escript resolves the tags when \var{lam*trace(g)} is calculated.
233
234 The \Data class provides a transparent interface to various data representations and the
235 translations between them. As shown in the example of stress calculation, this allows the user to
236 develop and test algorithms for a simple case (for instance with the Lame coefficients as constants)
237 and then without further modifications of the program code to apply the algorithm in a
238 more complex application (for instance a definition of the Lame coefficients using tags).
239 As described here, there are three ways in which \Data objects are represented internally, constant, tagged, and expanded (other representions will become available in later versions of \escript):
240 In the constant case, if the same value is used at each sample point a single value is stored to save memory and compute time.
241 Any operation on this constant data will only be performed on the single value.
242 In the expanded case, each sample point has an individual value, eg. the solution of a PDE,
243 and the values are stored as a complete array. The tagged case has already been discussed above.
244
245 Values are accessed through a sample reference number. Operations on expanded \Data
246 objects have to be performed for each sample point individually. If tagged values are used values are
247 held in a dictionary. Operations on tagged data require processing the set of tagged values only, rather than
248 processing the value for each individual sample point.
249 \escript allows use of constant, tagged and expanded data in a single expression.
250
251
252
253 \section{\Domain class}
254 \begin{classdesc}{Domain}{}
255 A \Domain object is used to describe a geometrical region together with
256 a way of representing functions over this region.
257 The \Domain class provides an abstract access to the domain of \FunctionSpace and \Data objects.
258 \Domain itself has no initialization but implementations of \Domain are
259 instantiated by numerical libraries making use of \Data objects.
260 \end{classdesc}
261 The following methds are available:
262 \begin{methoddesc}[Domain]{getDim}{}
263 returns the spatial dimension of the \Domain.
264 \end{methoddesc}
265
266 \begin{methoddesc}[Domain]{getX}{}
267 returns the locations in the \Domain. The \FunctionSpace of the returned
268 \Data object is chosen by the \Domain implementation. Typically it will be
269 in the \Function.
270 \end{methoddesc}
271
272 \begin{methoddesc}[Domain]{setX}{newX}
273 assigns a new location to the \Domain. \var{newX} has to have \Shape $(d,)$
274 where $d$ is the spatial dimension of the domain. Typically \var{newX} must be
275 in the \ContinuousFunction but the space actually to be used depends on the \Domain implementation.
276 \end{methoddesc}
277
278 \begin{methoddesc}[Domain]{getNormal}{}
279 returns the surface normals on the boundary of the \Domain as \Data object.
280 \end{methoddesc}
281
282 \begin{methoddesc}[Domain]{getSize}{}
283 returns the local sample size, e.g. the element diameter, as \Data object.
284 \end{methoddesc}
285
286 \begin{methoddesc}[Domain]{__eq__}{arg}
287 returns \True of the \Domain \var{arg} describes the same domain. Otherwise
288 \False is returned.
289 \end{methoddesc}
290
291 \begin{methoddesc}[Domain]{__ne__}{arg}
292 returns \True of the \Domain \var{arg} does not describe the same domain.
293 Otherwise \False is returned.
294 \end{methoddesc}
295
296 \begin{methoddesc}[Domain]{__str__}{g}
297 returns string represention of the \Domain.
298 \end{methoddesc}
299
300 \section{\Domain class}
301 \begin{classdesc}{FunctionSpace}{}
302 \FunctionSpace objects are used to define properties of \Data objects, such as continuity. \FunctionSpace objects
303 are instantiated by generator functions. \Data objects in particular \FunctionSpace are
304 represented by their values at \DataSamplePoints which are defined by the type and the \Domain of the
305 \FunctionSpace.
306 \end{classdesc}
307 The following methds are available:
308 \begin{methoddesc}[FunctionSpace]{getDim}{}
309 returns the spatial dimension of the \Domain of the \FunctionSpace.
310 \end{methoddesc}
311
312 \begin{methoddesc}[FunctionSpace]{getX}{}
313 returns the location of the \DataSamplePoints.
314 \end{methoddesc}
315
316 \begin{methoddesc}[FunctionSpace]{getNormal}{}
317 If the domain of functions in the \FunctionSpace
318 is a hypermanifold (e.g. the boundary of a domain)
319 the method returns the outer normal at each of the
320 \DataSamplePoints. Otherwise an exception is raised.
321 \end{methoddesc}
322
323 \begin{methoddesc}[FunctionSpace]{getSize}{}
324 returns a \Data objects measuring the spacing of the \DataSamplePoints.
325 The size may be zero.
326 \end{methoddesc}
327
328 \begin{methoddesc}[FunctionSpace]{getDomain}{}
329 returns the \Domain of the \FunctionSpace.
330 \end{methoddesc}
331
332 \begin{methoddesc}[FunctionSpace]{__eq__}{arg}
333 returns \True of the \Domain \var{arg} describes the same domain. Otherwise
334 \False is returned.
335 \end{methoddesc}
336
337 \begin{methoddesc}[FunctionSpace]{__ne__}{arg}
338 returns \True of the \Domain \var{arg} describes the note same domain.
339 Otherwise \False is returned.
340 \end{methoddesc}
341
342 \begin{methoddesc}[Domain]{__str__}{g}
343 returns string represention of the \Domain.
344 \end{methoddesc}
345
346 The following function provide generators for \FunctionSpace objects:
347 \begin{funcdesc}{Function}{domain}
348 returns the \Function on the \Domain \var{domain}. \Data objects in this type of \Function
349 are defined over the whole geometrical region defined by \var{domain}.
350 \end{funcdesc}
351
352 \begin{funcdesc}{ContinuousFunction}{domain}
353 returns the \ContinuousFunction on the \Domain domain. \Data objects in this type of \Function
354 are defined over the whole geometrical region defined by \var{domain} and assumed to represent
355 a continuous function.
356 \end{funcdesc}
357
358 \begin{funcdesc}{FunctionOnBoundary}{domain}
359 returns the \ContinuousFunction on the \Domain domain. \Data objects in this type of \Function
360 are defined on the boundary of the geometrical region defined by \var{domain}.
361 \end{funcdesc}
362
363 \begin{funcdesc}{FunctionOnContactZero}{domain}
364 returns the \FunctionOnContactZero the \Domain domain. \Data objects in this type of \Function
365 are defined on side 0 of a discontinutiy within the geometrical region defined by \var{domain}.
366 The discontinutiy is defined when \var{domain} is instantiated.
367 \end{funcdesc}
368
369 \begin{funcdesc}{FunctionOnContactOne}{domain}
370 returns the \FunctionOnContactOne on the \Domain domain.
371 \Data objects in this type of \Function
372 are defined on side 1 of a discontinutiy within the geometrical region defined by \var{domain}.
373 The discontinutiy is defined when \var{domain} is instantiated.
374 \end{funcdesc}
375
376 \begin{funcdesc}{Solution}{domain}
377 returns the \SolutionFS on the \Domain domain. \Data objects in this type of \Function
378 are defined on geometrical region defined by \var{domain} and are solutions of
379 partial differential equations \index{partial differential equation}.
380 \end{funcdesc}
381
382 \begin{funcdesc}{ReducedSolution}{domain}
383 returns the \ReducedSolutionFS on the \Domain domain. \Data objects in this type of \Function
384 are defined on geometrical region defined by \var{domain} and are solutions of
385 partial differential equations \index{partial differential equation} with a reduced smoothness
386 for the solution approximation.
387 \end{funcdesc}
388
389 \section{\Data Class}
390 \label{SEC ESCRIPT DATA}
391
392 The following table shows binary and unitary operations that can be applied to
393 \Data objects:
394 \begin{tableii}{l|l}{textrm}{expression}{Description}
395 \lineii{+\var{arg1}} {just \var{arg} \index{+}}
396 \lineii{-\var{arg1}} {swapping the sign\index{-}}
397 \lineii{\var{arg1}+\var{arg2}} {adds \var{arg1} and \var{arg2} \index{+}}
398 \lineii{\var{arg1}*\var{arg2}} {multiplies \var{arg1} and \var{arg2} \index{*}}
399 \lineii{\var{arg1}-\var{arg2}} {difference \var{arg2} from\var{arg2} \index{-}}
400 \lineii{\var{arg1}/\var{arg2}} {ratio \var{arg1} by \var{arg2} \index{/}}
401 \lineii{\var{arg1}**\var{arg2}} {raises \var{arg1} to the power of \var{arg2} \index{**}}
402 \end{tableii}
403 At least one of the arguments \var{arg1} or \var{arg2} must be a
404 \Data object. One of the arguments may be an object that can be
405 converted into a \Data object. If \var{arg1} or \var{arg2} are
406 defined on different \FunctionSpace an attempt is made to embed \var{arg1}
407 into the \FunctionSpace of \var{arg2} or to embed \var{arg2} into
408 the \FunctionSpace of \var{arg1}. Boths arguments must have the same
409 \Shape or one of the arguments my be of rank 0 or \Shape (1,). In the
410 latter case it is assumed that the particular argument is of the same
411 \Shape as the other argument but constant over all components.
412
413 The returned \Data object has the same \Shape and is defined on
414 the \DataSamplePoints as \var{arg1} or \var{arg2}.
415
416 The following table shows the update operations that can be applied to
417 \Data objects:
418 \begin{tableii}{l|l}{textrm}{expression}{Description}
419 \lineii{\var{arg1}+=\var{arg2}} {adds \var{arg1} to \var{arg2} \index{+}}
420 \lineii{\var{arg1}*=\var{arg2}} {multiplies \var{arg1} with \var{arg2} \index{*}}
421 \lineii{\var{arg1}-=\var{arg2}} {subtracts \var{arg2} from\var{arg2} \index{-}}
422 \lineii{\var{arg1}/=\var{arg2}} {divides \var{arg1} by \var{arg2} \index{/}}
423 \end{tableii}
424 \var{arg1} must be a \Data object. \var{arg1} must be a
425 \Data object or an object that can be converted into a
426 \Data object. \var{arg1} must have the same \Shape like
427 \var{arg1} or has rank 0 or \Shape (1,). In the latter case it is
428 assumed that the values of \var{arg1} are constant for all
429 components. \var{arg2} must be defined on the same \DataSamplePoints as
430 \var{arg1} or it must be possible to interpolate \var{arg2} onto the
431 \DataSamplePoints where \var{arg1} is held.
432
433 The \Data class supports getting slices as well as assigning new values to components in an existing
434 \Data object. \index{slicing}
435 The following expression for getting (expression on the right hand side of the
436 equal sign) and setting slices (expression on the left hand side of the
437 equal sign) are valid:
438 \begin{tableiii}{l|ll}{textrm}{rank of \var{arg}}{slicing expression}{\Shape of returned and assigned object}
439 \lineiii{0}{ no slicing } {-}
440 \lineiii{1}{\var{arg[l0:u0]}} {(\var{u0}-\var{l0},)}
441 \lineiii{2}{\var{arg[l0:u0,l1:u1]}} {(\var{u0}-\var{l0},\var{u1}-\var{l1})}
442 \lineiii{3}{\var{arg[l0:u0,l1:u1,l2:u2]} } {(\var{u0}-\var{l0},\var{u1}-\var{l1},\var{u2}-\var{l2})}
443 \lineiii{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})}
444 \end{tableiii}
445 where
446 $0 \le \var{l0} \le \var{u0} \le \var{s[0]}$,
447 $0 \le \var{l1} \le \var{u1} \le \var{s[1]}$,
448 $0 \le \var{l2} \le \var{u2} \le \var{s[2]}$,
449 $0 \le \var{l3} \le \var{u3} \le \var{s[3]}$ and \var{s} the \Shape if \var{arg}.
450 Any of the lower indexes \var{l0}, \var{l1}, \var{l2} and \var{l3} may not be present in which case
451 $0$ is assumed.
452 Any of the upper indexes \var{u0}, \var{u1}, \var{u2} and \var{u3} may not be present in which case
453 \var{s} is assumed. The lower and upper index may be identical, in which case the column and the lower or upper
454 index may be dropped. In the returned or in the object assigned to a slice the corresponding component is dropped,
455 i.e. the rank is reduced by one in comparison to \var{arg}.
456 The following examples show slicing usage:
457 \begin{python}
458 t=Data(1.,(4,4,6,6),Function(mydomain))
459 t[1,1,1,0]=9.
460 s=t[:2,:,2:6,5] # s has rank 3
461 s[:,:,1]=1.
462 t[:2,:2,5,5]=s[2:4,1,:2]
463 \end{python}
464
465 \subsection{Generation of \Data class objects}
466 \begin{classdesc}{Data}{value=0,shape=(,),what=FunctionSpace(),expand=\False}
467 creates a \Data object with \Shape \var{shape} in the \FunctionSpace \var{what}.
468 The values at all \DataSamplePoints are set to the double value \var{value}. If \var{expanded} is \True
469 the \Data object is represented in expanded from.
470 \end{classdesc}
471
472 \begin{classdesc}{Data}{value,what=FunctionSpace(),expand=\False}
473 creates a \Data object in the \FunctionSpace \var{what}.
474 The value for each \DataSamplePoints is set to \numarray, \Data object \var{value} or a dictionary of
475 \numarray or floating point numbers. In the latter case the keys muts be integers and are used
476 as tags.
477 The \Shape of the returned object is equal to the \Shape of \var{value}. If \var{expanded} is \True
478 the \Data object is represented in expanded from.
479 \end{classdesc}
480
481 \begin{classdesc}{Data}{}
482 creates an \EmptyData object. The \EmptyData object is used to indicate that an argument is not present
483 where a \Data object is required.
484 \end{classdesc}
485
486 \begin{funcdesc}{Scalar}{value=0.,what=escript::FunctionSpace(),expand=\False}
487 returns a \Data object of rank 0 in the \FunctionSpace \var{what}.
488 Values are initialed with the double \var{value}. If \var{expanded} is \True
489 the \Data object is represented in expanded from.
490 \end{funcdesc}
491
492 \begin{funcdesc}{Vector}{value=0.,what=escript::FunctionSpace(),expand=\False}
493 returns a \Data object of \Shape \var{(d,)} in the \FunctionSpace \var{what}
494 where \var{d} is the spatial dimension of the \Domain of \var{what}.
495 Values are initialed with the double \var{value}. If \var{expanded} is \True
496 the \Data object is represented in expanded from.
497 \end{funcdesc}
498
499 \begin{funcdesc}{Tensor}{value=0.,what=escript::FunctionSpace(),expand=\False}
500 returns a \Data object of \Shape \var{(d,d)} in the \FunctionSpace \var{what}
501 where \var{d} is the spatial dimension of the \Domain of \var{what}.
502 Values are initialed with the double \var{value}. If \var{expanded} is \True
503 the \Data object is represented in expanded from.
504 \end{funcdesc}
505
506 \begin{funcdesc}{Tensor3}{value=0.,what=escript::FunctionSpace(),expand=\False}
507 returns a \Data object of \Shape \var{(d,d,d)} in the \FunctionSpace \var{what}
508 where \var{d} is the spatial dimension of the \Domain of \var{what}.
509 Values are initialed with the double \var{value}. If \var{expanded} is \True
510 the \Data object is re\var{arg}presented in expanded from.
511 \end{funcdesc}
512
513 \begin{funcdesc}{Tensor4}{value=0.,what=escript::FunctionSpace(),expand=\False}
514 returns a \Data object of \Shape \var{(d,d,d,d)} in the \FunctionSpace \var{what}
515 where \var{d} is the spatial dimension of the \Domain of \var{what}.
516 Values are initialed with the double \var{value}. If \var{expanded} is \True
517 the \Data object is represented in expanded from.
518 \end{funcdesc}
519
520 \subsection{\Data class methods}
521 This is a list of frequently used methods of the
522 \Data class. A complete list can be fond on \ReferenceGuide.
523 \begin{methoddesc}[Data]{getFunctionSpace}{}
524 returns the \FunctionSpace of the object.
525 \end{methoddesc}
526
527 \begin{methoddesc}[Data]{getDomain}{}
528 returns the \Domain of the object.
529 \end{methoddesc}
530
531 \begin{methoddesc}[Data]{getShape}{}
532 returns the \Shape of the object as a \class{tuple} of
533 integers.
534 \end{methoddesc}
535
536 \begin{methoddesc}[Data]{getRank}{}
537 returns the rank of the data on each data point. \index{rank}
538 \end{methoddesc}
539
540 \begin{methoddesc}[Data]{isEmpty}{}
541 returns \True id the \Data object is the \EmptyData object.
542 Otherwise \False is returned.
543 \end{methoddesc}
544
545 \begin{methoddesc}[Data]{setTaggedValue}{tag,value}
546 assigns the \var{value} to all \DataSamplePoints which have the tag
547 \var{tag}. \var{value} must be an object of class
548 \class{numarray.NumArray} or must be convertible into a
549 \class{numarray.NumArray} object. \var{value} (or the corresponding
550 \class{numarray.NumArray} object) must be of rank $0$ or must have the
551 same rank like the object.
552 If a value has already be defined for tag \var{tag} within the object
553 it is overwritten by the new \var{value}. If the object is expanded,
554 the value assigned to \DataSamplePoints with tag \var{tag} is replaced by
555 \var{value}.
556 \end{methoddesc}
557
558 \begin{methoddesc}[Data]{__str__}{}
559 returns a string representation of the object.
560 \end{methoddesc}
561
562 \section{Functions of \Data class objects}
563 This section lists the most important functions for \Data class objects \var{a}.
564 A complete list and a more detailed description of the functionality can be fond on \ReferenceGuide.
565 \begin{funcdesc}{saveVTK}{filename,\optional{domain},**data}
566 writes a
567 \end{funcdesc}
568 \begin{funcdesc}{saveDX}{filename,domain=None,**data}
569 \end{funcdesc}
570 \begin{funcdesc}{kronecker}{d}
571 returns a \RankTwo \Data object \var{o} in \FunctionSpace \var{d} such that
572 \begin{equation}
573 o\left[ i,j\right] = \left\{
574 \begin{array}{cc}
575 1 & \mbox{ if } i=j \\
576 0 & \mbox{ otherwise }
577 \end{array}
578 \right.
579 \end{equation}
580 \end{funcdesc}
581
582 \begin{funcdesc}{identityTensor}{d}
583 \end{funcdesc}
584 \begin{funcdesc}{identityTensor4}{d}
585 \end{funcdesc}
586 \begin{funcdesc}{unitVector}{i,d}
587 \end{funcdesc}
588
589 \begin{funcdesc}{Lsup}{a}
590 returns the $L^{sup}$ norm of \var{arg}. This is the maximum of the absolute values
591 over all components and all \DataSamplePoints of \var{a}.
592 \end{funcdesc}
593
594 \begin{funcdesc}{sup}{a}
595 returns the maximum value over all components and all \DataSamplePoints of \var{a}.
596 \end{funcdesc}
597
598 \begin{funcdesc}{inf}{a}
599 returns the minimum value over all components and all \DataSamplePoints of \var{a}
600 \end{funcdesc}
601
602 \begin{funcdesc}{sin}{a}
603 applies sine function to \var{a}.
604 \end{funcdesc}
605
606 \begin{funcdesc}{cos}{a}
607 applies cosine function to \var{a}.
608 \end{funcdesc}
609
610 \begin{funcdesc}{tan}{a}
611 applies tangent function to \var{a}.
612 \end{funcdesc}
613
614 \begin{funcdesc}{asin}{a}
615 applies arc (inverse) sine function to \var{a}.
616 \end{funcdesc}
617
618 \begin{funcdesc}{acos}{a}
619 applies arc (inverse) cosine function to \var{a}.
620 \end{funcdesc}
621
622 \begin{funcdesc}{atan}{a}
623 applies arc (inverse) tangent function to \var{a}.
624 \end{funcdesc}
625
626 \begin{funcdesc}{sinh}{a}
627 applies hyperbolic sine function to \var{a}.
628 \end{funcdesc}
629
630 \begin{funcdesc}{cosh}{a}
631 applies hyperbolic cosine function to \var{a}.
632 \end{funcdesc}
633
634 \begin{funcdesc}{tanh}{a}
635 applies hyperbolic tangent function to \var{a}.
636 \end{funcdesc}
637
638 \begin{funcdesc}{asinh}{a}
639 applies arc (inverse) hyperbolic sine function to \var{a}.
640 \end{funcdesc}
641
642 \begin{funcdesc}{acosh}{a}
643 applies arc (inverse) hyperbolic cosine function to \var{a}.
644 \end{funcdesc}
645
646 \begin{funcdesc}{atanh}{a}
647 applies arc (inverse) hyperbolic tangent function to \var{a}.
648 \end{funcdesc}
649
650 \begin{funcdesc}{exp}{a}
651 applies exponential function to \var{a}.
652 \end{funcdesc}
653
654 \begin{funcdesc}{sqrt}{a}
655 applies square root function to \var{a}.
656 \end{funcdesc}
657
658 \begin{funcdesc}{log}{a}
659 \end{funcdesc}
660
661 \begin{funcdesc}{log10}{a}
662 \end{funcdesc}
663
664 \begin{funcdesc}{sign}{a}
665 \end{funcdesc}
666
667 \begin{funcdesc}{wherePositive}{a}
668 \end{funcdesc}
669 \begin{funcdesc}{whereNegative}{a}
670 \end{funcdesc}
671 \begin{funcdesc}{whereNonNegative}{a}
672 \end{funcdesc}
673 \begin{funcdesc}{whereNonPositive}{a}
674 \end{funcdesc}
675 \begin{funcdesc}{whereZero}{a,tol=0.}
676 \end{funcdesc}
677 \begin{funcdesc}{whereNonZero}{a,tol=0.}
678 \end{funcdesc}
679 \begin{funcdesc}{minval}{a}
680 \end{funcdesc}
681 \begin{funcdesc}{maxval}{a}
682 \end{funcdesc}
683 \begin{funcdesc}{length}{a}
684 \end{funcdesc}
685 \begin{funcdesc}{trace}{a,axis_offset=0}
686 \end{funcdesc}
687 \begin{funcdesc}{transpose}{a,axis_offset=None}
688 \end{funcdesc}
689 \begin{funcdesc}{symmetric}{a}
690 \end{funcdesc}
691 \begin{funcdesc}{nonsymmetric}{a}
692 \end{funcdesc}
693 \begin{funcdesc}{inverse}{a}
694 \end{funcdesc}
695 \begin{funcdesc}{eigenvalues}{a}
696 \end{funcdesc}
697 \begin{funcdesc}{eigenvalues_and_eigenvectors}{a}
698 \end{funcdesc}
699 \begin{funcdesc}{maximum}{a}
700 \end{funcdesc}
701 \begin{funcdesc}{minimum}{a}
702 \end{funcdesc}
703 \begin{funcdesc}{clip}{a,minval=0.,maxval=1.}
704 \end{funcdesc}
705 \begin{funcdesc}{inner}{a0,a1}
706 \end{funcdesc}
707 \begin{funcdesc}{matrixmult}{a0,a1}
708 \end{funcdesc}
709 \begin{funcdesc}{outer}{a0,a1}
710 \end{funcdesc}
711 \begin{funcdesc}{tensormult}{a0,a1}
712 \end{funcdesc}
713 \begin{funcdesc}{grad}{a,where=None}
714 \end{funcdesc}
715 \begin{funcdesc}{integrate}{a,where=None}
716 \end{funcdesc}
717 \begin{funcdesc}{interpolate}{a,where}
718 \end{funcdesc}
719 \begin{funcdesc}{div}{a,where=None}
720 \end{funcdesc}
721 \begin{funcdesc}{jump}{a,domain=None}
722 \end{funcdesc}
723 \begin{funcdesc}{L2}{a}
724 \end{funcdesc}
725
726 ====
727
728
729 \begin{funcdesc}{wherePositive}{a}
730 returns \Data object which has the same \Shape and is defined on
731 the same \FunctionSpace like the object. The returned values are $1$
732 where the object is positive and $0$ elsewhere.
733 \end{funcdesc}
734
735 \begin{funcdesc}{wherePositive}{a}
736 returns \Data object which has the same \Shape and is defined on
737 the same \FunctionSpace like the object. The returned values are $1$
738 where the object is non-positive and $0$ elsewhere.
739 \end{funcdesc}
740
741 \begin{funcdesc}{whereNonnegative}{a}
742 returns \Data object which has the same \Shape and is defined on
743 the same \FunctionSpace like the object. The returned values are $1$
744 where the object is non-negative and $0$ elsewhere.
745 \end{funcdesc}
746
747 \begin{funcdesc}{whereNegative}{a}
748 returns \Data object which has the same \Shape and is defined on
749 the same \FunctionSpace like the object. The returned values are $1$
750 where the object is negative and $0$ elsewhere.
751 \end{funcdesc}
752
753 \begin{funcdesc}{whereZero}{a,tol=1.e-8}
754 returns \Data object which has the same \Shape and is defined on
755 the same \FunctionSpace like the object. The returned values are $1$
756 where the object is nearly zero, i.e. where the absolute value is less
757 than \var{tolerance}, and $0$ elsewhere.
758 \end{funcdesc}
759
760 \begin{funcdesc}{whereNonzero}{tolerance=1.e-8}
761 returns \Data object which has the same \Shape and is defined on
762 the same \FunctionSpace like the object. The returned values are $1$
763 where the object is nearly non-zero, i.e. where the absolute value is
764 greater or equal than \var{tolerance}, and $0$ elsewhere.
765 \end{funcdesc}
766
767 \begin{funcdesc}{sign}{a}
768 returns \Data object which has the same \Shape and is defined on
769 the same \FunctionSpace like the object. The returned values are $1$
770 where the object is positive, $-1$ where the value is negative and $0$ elsewhere.
771 \end{funcdesc}
772
773 \begin{funcdesc}{Lsup}{a}
774 returns the $L^{sup}$-norm of the object. This is maximum absolute values over all components and all \DataSamplePoints. \index{$L^{sup}$-norm}.
775 \end{funcdesc}
776 \begin{funcdesc}{Linf}{a}
777 returns the minimum absolute value over all components and all \DataSamplePoints. \index{$L^{inf}$-norm}.
778 \end{funcdesc}
779 \begin{funcdesc}{inf}{a}
780 returns the minimum value (infimum) of the object. The minimum is
781 taken over all components and all \DataSamplePoints . \index{infimum}
782 \end{funcdesc}
783
784 \begin{funcdesc}{sup}{a}
785 returns the maximum value (supremum) of the object. The maximum is
786 taken over all components and all \DataSamplePoints . \index{supremum}
787 \end{funcdesc}
788
789 \begin{funcdesc}{grad}{a,\optional{where}}
790 returns the gradient of the function represented by the object.
791 \Data object is in \FunctionSpace \var{on} and has rank r+1 where r is the rank of the object.
792 If \var{on} is not present, a suitbale \FunctionSpace is used.
793 \index{gradient}
794 \end{funcdesc}
795
796 \begin{funcdesc}{integrate}{a,\optional{where}}
797 returns the integral of the function represented by the object. The method returns
798 a \class{numarray.NumArray} object of the same \Shape like the object. A
799 component of the returned object is the integral of the corresponding
800 component of the object. \index{integral}
801 \end{funcdesc}
802
803 \begin{funcdesc}{interpolate}{a,where}
804 interpolates
805 the function represented by the object
806 into the \FunctionSpace\var{where}.
807 \index{interpolation}
808 \end{funcdesc}
809
810 \begin{funcdesc}{abs}{a}
811 applies the absolute value function to the object. The
812 return \Data object has the same \Shape and is in the same
813 \FunctionSpace like the object. For all \DataSamplePoints and all
814 components the value is calculated by applying the exponential
815 function. \index{function!absolute value}
816 \end{funcdesc}
817
818 \begin{funcdesc}{exp}{a}
819 applies the exponential function to the object. The
820 return \Data object has the same \Shape and is in the same
821 \FunctionSpace like the object. For all \DataSamplePoints and all
822 components the value is calculated by applying the exponential
823 function. \index{function!exponential}
824 \end{funcdesc}
825
826 \begin{funcdesc}{sqrt}{a}
827 applies the square root function to the object. The
828 return \Data object has the same \Shape and is in the same
829 \FunctionSpace like the object. For all \DataSamplePoints and all
830 components the value is calculated by applying the square root function.
831 An exception is
832 raised if the value is negative. \index{function!square root}
833 \end{funcdesc}
834
835 \begin{funcdesc}{sin}{a}
836 applies the sine function to the object. The
837 return \Data object has the same \Shape and is in the same
838 \FunctionSpace like the object. For all \DataSamplePoints and all
839 components the value is calculated by applying the sine function. \index{function!sine}
840 \end{funcdesc}
841
842 \begin{funcdesc}{cos}{a}
843 applies the cosine function to the object. The
844 return \Data object has the same \Shape and is in the same
845 \FunctionSpace like the object. For all \DataSamplePoints and all
846 components the value is calculated by applying the cosine function. \index{function!cosine}
847 \end{funcdesc}
848
849 \begin{funcdesc}{tan}{a}
850 applies the tangent function to the object. The
851 return \Data object has the same \Shape and is in the same
852 \FunctionSpace like the object. For all \DataSamplePoints and all
853 components the value is calculated by applying the tangent function. \index{function!tangent}
854 \end{funcdesc}
855
856 \begin{funcdesc}{log}{a}
857 applies the logarithmic function to the object. The
858 return \Data object has the same \Shape and is in the same
859 \FunctionSpace like the object. For all \DataSamplePoints and all
860 components the value is calculated by applying the logarithmic function. An exception is
861 raised if the value is negative.\index{function!logarithmic}
862 \end{funcdesc}
863
864 \begin{funcdesc}{maxval}{}
865 returns the maximum value over all components. The
866 return value is a \Data object of rank 0
867 and is in the same
868 \FunctionSpace like the object. For all \DataSamplePoints
869 the value is calculated as the maximum value over all components. \index{function!maximum}
870 \end{funcdesc}
871
872 \begin{funcdesc}{minval}{}
873 returns the minimum value over all components. The
874 return value is a \Data object of rank 0
875 and is in the same
876 \FunctionSpace like the object. For all \DataSamplePoints
877 the value is calculated as the minimum value over all components. \index{function!minimum}
878 \end{funcdesc}
879
880 \begin{funcdesc}{length}{}
881 returns the Euclidean length at all \DataSamplePoints. The
882 return value is a \Data object of rank 0
883 and is in the same
884 \FunctionSpace like the object. For all \DataSamplePoints
885 the value is calculated as the square root of the sum of the square over all over all components. \index{function!length}
886 \end{funcdesc}
887 \begin{funcdesc}{transpose}{axis}
888 returns the transpose of the object around \var{axis}. \var{axis} is a non-negative integer
889 which is less the rank $r$ of the object. Transpose swaps the indexes $0$ to \var{axis}
890 with the indexes \var{axis}+1 to $r$. If the \var{d} is \RankFour one has
891 \begin{python}
892 d[i,j,k,l]=d.transpose(0)[i,j,k,l]
893 d[i,j,k,l]=d.transpose(1)[j,k,l,i]
894 d[i,j,k,l]=d.transpose(2)[k,l,i,j]
895 d[i,j,k,l]=d.transpose(3)[l,i,j,k]
896 \end{python}
897 \index{function!transpose}
898 \end{funcdesc}
899
900 \begin{funcdesc}{trace}{}
901 returns sum of the components with identical indexes.
902 The
903 return value is a \Data object of rank 0
904 and is in the same
905 \FunctionSpace like the object.
906 \index{function!trace}
907 \end{funcdesc}
908 \begin{funcdesc}{saveDX}{fileName}
909 saves the object to an openDX format file of name \var{fileName}, see
910 \ulink{www.opendx.org}{\url{www.opendx.org}}. \index{openDX}
911 \end{funcdesc}
912
913
914 \begin{funcdesc}{abs}{arg}
915 returns the absolute value of \var{arg} where \var{arg}
916 can be double, a \Data object or an \numarray object.
917 \end{funcdesc}
918
919 \begin{funcdesc}{sin}{arg}
920 returns the sine of \var{arg} where \var{arg}
921 can be double, a \Data object or an \numarray object.
922 \end{funcdesc}
923
924 \begin{funcdesc}{cos}{arg}
925 returns the cosine of \var{arg} where \var{arg}
926 can be double, a \Data object or an \numarray object.
927 \end{funcdesc}
928
929 \begin{funcdesc}{exp}{arg}
930 returns the value of the exponential function for \var{arg} where \var{arg}
931 can be double, a \Data object or an \numarray object.
932 \end{funcdesc}
933
934 \begin{funcdesc}{sqrt}{arg}
935 returns the square root of \var{arg} where \var{arg}
936 can be double, a \Data object or an \numarray object.
937 \end{funcdesc}
938
939 \begin{funcdesc}{maxval}{arg}
940 returns the maximum value over all component of \var{arg} where \var{arg}
941 can be double, a \Data object or an \numarray object.
942 \end{funcdesc}
943
944 \begin{funcdesc}{minval}{arg}
945 returns the minumum value over all component of \var{arg} where \var{arg}
946 can be double, a \Data object or an \numarray object.
947 \end{funcdesc}
948
949 \begin{funcdesc}{length}{arg}
950 returns the length of \var{arg} which is the
951 square root of the sum of the squares of all component of \var{arg}. \var{arg}
952 can be double, a \Data object or an \numarray object.
953 \end{funcdesc}
954
955 \begin{funcdesc}{sign}{arg}
956 return the sign of \var{arg} where \var{arg}
957 can be double, a \Data object or an \numarray object.
958 \end{funcdesc}
959
960 \begin{funcdesc}{transpose}{arg,\optional{axis}}
961 returns the transpose of \var{arg} around \var{axis}. \var{axis} is a non-negative integer
962 which is less the rank $r$ of the object. Transpose swaps the indexes $0$ to \var{axis}
963 with the indexes \var{axis}+1 to $r$. If \var{axis} is not present, \var{axis}=$r/2$ is assumed.
964 \var{arg}
965 may be a \Data object or an \numarray object.
966 \end{funcdesc}
967
968 \begin{funcdesc}{transpose}{arg,\optional{axis}}
969 returns the trace the object of \var{arg}. The trace is the sum over those components
970 with identical indexed.
971 \var{arg}
972 may be a \Data object or a \numarray object.
973 \end{funcdesc}
974
975 \begin{funcdesc}{sum}{arg}
976 returns the sum over all components and all
977 \DataSamplePoints of \var{arg}, where \var{arg}
978 is a \Data object.
979 \end{funcdesc}
980
981 \begin{funcdesc}{sup}{arg}
982 returns the maximum over all components and all
983 \DataSamplePoints of \var{arg}, where \var{arg}
984 is a \Data object.
985 \end{funcdesc}
986
987 \begin{funcdesc}{inf}{arg}
988 returns the mimumum over all components and all
989 \DataSamplePoints of \var{arg}, where \var{arg}
990 is a \Data object.
991 \end{funcdesc}
992
993 \begin{funcdesc}{L2}{arg}
994 returns the $L^2$ norm of \var{arg}. This is the square root
995 of the sum of the squared value over all components and all
996 \DataSamplePoints of \var{arg}, where \var{arg}
997 is a \Data object.
998 \end{funcdesc}
999
1000 \begin{funcdesc}{Lsup}{arg}
1001 returns the $L^{sup}$ norm of \var{arg}. This is the maximum of the absolute values
1002 over all components and all
1003 \DataSamplePoints of \var{arg}, where \var{arg}
1004 is a \Data object.
1005 \end{funcdesc}
1006
1007 \begin{funcdesc}{dot}{arg1,arg2}
1008 returns the dot product of of \var{arg1} and \var{arg2}. This is sum
1009 of the product of corresponding entries in \var{arg1} and \var{arg2} over all
1010 components and and all
1011 \DataSamplePoints. \var{arg1} and \var{arg2} are \Data objects of the
1012 same \Shape and in the same \FunctionSpace.
1013 \end{funcdesc}
1014
1015 \begin{funcdesc}{grad}{arg,\optional{where}}
1016 returns the gradient of \var{arg} as a function in the \FunctionSpace \var{where}.
1017 If \var{where} is not present a reasonable \FunctionSpace is chosen.
1018 \var{arg}
1019 is a \Data object.
1020 \end{funcdesc}
1021
1022 \begin{funcdesc}{integrate}{arg}
1023 returns the integral of \var{arg} as a \numarray object.
1024 If \var{where} is not present a reasonable \FunctionSpace is chosen.
1025 \var{arg}
1026 is a \Data object.
1027 \end{funcdesc}
1028
1029 \begin{funcdesc}{interpolate}{arg,where}
1030 interpolate \Data object \var{arg} into the \FunctionSpace \var{where}
1031 \end{funcdesc}
1032
1033
1034 \section{\Operator Class}
1035
1036 The \Operator class provides an abstract access to operators build
1037 within the \LinearPDE class. \Operator objects are created
1038 when a PDE is handed over to a PDE solver library and handled
1039 by the \LinearPDE class defining the PDE. The user can gain access
1040 to the \Operator of a \LinearPDE object through the \var{getOperator}
1041 method.
1042
1043 \begin{classdesc}{Operator}{}
1044 creates an empty \Operator object.
1045 \end{classdesc}
1046
1047 \begin{methoddesc}[Operator]{isEmpty}{fileName}
1048 returns \True is the object is empty. Otherwise \True is returned.
1049 \end{methoddesc}
1050
1051 \begin{methoddesc}[Operator]{setValue}{value}
1052 resets all entires in the obeject representation to \var{value}
1053 \end{methoddesc}
1054
1055 \begin{methoddesc}[Operator]{solves}{rhs}
1056 solves the operator equation with right hand side \var{rhs}
1057 \end{methoddesc}
1058
1059 \begin{methoddesc}[Operator]{of}{u}
1060 applies the operator to the \Data object \var{u}
1061 \end{methoddesc}
1062
1063 \begin{methoddesc}[Operator]{saveMM}{fileName}
1064 saves the object to a matrix market format file of name
1065 \var{fileName}, see
1066 \ulink{maths.nist.gov/MatrixMarket}{\url{http://maths.nist.gov/MatrixMarket}}.
1067 \index{Matrix Market}
1068 \end{methoddesc}
1069

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