 # Contents of /trunk/doc/user/escript.tex

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 1 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3 % 4 % Copyright (c) 2003-2010 by University of Queensland 5 % Earth Systems Science Computational Center (ESSCC) 6 7 % 8 % Primary Business: Queensland, Australia 9 % Licensed under the Open Software License version 3.0 10 11 % 12 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 13 14 \chapter{The \escript Module}\label{ESCRIPT CHAP} 15 16 \section{Concepts} 17 \escript is a \PYTHON module that allows you to represent the values of 18 a function at points in a \Domain in such a way that the function will 19 be useful for the Finite Element Method (FEM) simulation. It also 20 provides what we call a function space that describes how the data is 21 used in the simulation. Stored along with the data is information 22 about the elements and nodes which will be used by \finley. 23 24 \subsection{Function spaces} 25 In order to understand what we mean by the term 'function space', 26 consider that the solution of a partial differential 27 equation\index{partial differential equation} (PDE) is a function on a domain 28 $\Omega$. When solving a PDE using FEM, the solution is 29 piecewise-differentiable but, in general, its gradient is discontinuous. 30 To reflect these different degrees of smoothness, different function spaces 31 are used. 32 For instance, in FEM, the displacement field is represented by its values at 33 the nodes of the mesh, and so is continuous. 34 The strain, which is the symmetric part of the gradient of the displacement 35 field, is stored on the element centers, and so is considered to be 36 discontinuous. 37 38 A function space is described by a \FunctionSpace object. 39 The following statement generates the object \var{solution_space} which is 40 a \FunctionSpace object and provides access to the function space of 41 PDE solutions on the \Domain \var{mydomain}: 42 43 \begin{python} 44 solution_space=Solution(mydomain) 45 \end{python} 46 The following generators for function spaces on a \Domain \var{mydomain} are commonly used: 47 \begin{itemize} 48 \item \var{Solution(mydomain)}: solutions of a PDE 49 \item \var{ReducedSolution(mydomain)}: solutions of a PDE with a reduced 50 smoothness requirement, e.g. using a lower order approximation on the same 51 element or using macro elements\index{macro elements} 52 \item \var{ContinuousFunction(mydomain)}: continuous functions, e.g. a temperature distribution 53 \item \var{Function(mydomain)}: general functions which are not necessarily continuous, e.g. a stress field 54 \item \var{FunctionOnBoundary(mydomain)}: functions on the boundary of the domain, e.g. a surface pressure 55 \item \var{FunctionOnContact0(mydomain)}: functions on side $0$ of the discontinuity 56 \item \var{FunctionOnContact1(mydomain)}: functions on side $1$ of the discontinuity 57 \end{itemize} 58 In some cases under-integration is used. For these cases the user may use a 59 \FunctionSpace from the following list: 60 \begin{itemize} 61 \item \var{ReducedFunction(mydomain)} 62 \item \var{ReducedFunctionOnBoundary(mydomain)} 63 \item \var{ReducedFunctionOnContact0(mydomain)} 64 \item \var{ReducedFunctionOnContact1(mydomain)} 65 \end{itemize} 66 In comparison to the corresponding full version they use a reduced number of 67 integration nodes (typically one only) to represent values. 68 69 \begin{figure} 70 \centering 71 \includegraphics{EscriptDiagram1} 72 \caption{\label{ESCRIPT DEP}Dependency of function spaces in \finley. 73 An arrow indicates that a function in the \FunctionSpace at the starting point 74 can be interpolated to the \FunctionSpace of the arrow target. 75 All function spaces above the dotted line can be interpolated to any of 76 the function spaces below the line. See also \Sec{SEC Projection}.} 77 \end{figure} 78 79 The reduced smoothness for a PDE solution is often used to fulfill the 80 Ladyzhenskaya-Babuska-Brezzi condition\cite{LBB} when solving saddle point 81 problems\index{saddle point problems}, e.g. the Stokes equation. 82 A discontinuity\index{discontinuity} is a region within the domain across 83 which functions may be discontinuous. 84 The location of a discontinuity is defined in the \Domain object. 85 \fig{ESCRIPT DEP} shows the dependency between the types of function spaces 86 in \finley (other libraries may have different relationships). 87 88 The solution of a PDE is a continuous function. Any continuous function can 89 be seen as a general function on the domain and can be restricted to the 90 boundary as well as to one side of a discontinuity (the result will be 91 different depending on which side is chosen). Functions on any side of the 92 discontinuity can be seen as a function on the corresponding other side. 93 94 A function on the boundary or on one side of the discontinuity cannot be seen 95 as a general function on the domain as there are no values defined for the 96 interior. For most PDE solver libraries the space of the solution and 97 continuous functions is identical, however in some cases, for example when 98 periodic boundary conditions are used in \finley, a solution fulfills periodic 99 boundary conditions while a continuous function does not have to be periodic. 100 101 The concept of function spaces describes the properties of functions and 102 allows abstraction from the actual representation of the function in the 103 context of a particular application. For instance, in the FEM context a 104 function of the \Function type (written as \emph{Function()} in \fig{ESCRIPT DEP}) 105 is usually represented by its values at the element center, 106 but in a finite difference scheme the edge midpoint of cells is preferred. 107 By changing its function space you can use the same function in a Finite 108 Difference scheme instead of Finite Element scheme. 109 Changing the function space of a particular function will typically lead to 110 a change of its representation. 111 So, when seen as a general function, a continuous function which is typically 112 represented by its values on the nodes of the FEM mesh or finite difference 113 grid must be interpolated to the element centers or the cell edges, 114 respectively. Interpolation happens automatically in \escript whenever it is 115 required\index{interpolation}. The user needs to be aware that an 116 interpolation is not always possible, see \fig{ESCRIPT DEP} for \finley. 117 An alternative approach to change the representation (=\FunctionSpace) is 118 projection\index{projection}, see \Sec{SEC Projection}. 119 120 \subsection{\Data Objects} 121 In \escript the class that stores these functions is called \Data. 122 The function is represented through its values on \DataSamplePoints where 123 the \DataSamplePoints are chosen according to the function space of the 124 function. 125 \Data class objects are used to define the coefficients of the PDEs to be 126 solved by a PDE solver library and also to store the solutions of the PDE. 127 128 The values of the function have a rank which gives the number of indices, 129 and a \Shape defining the range of each index. 130 The rank in \escript is limited to the range 0 through 4 and it is assumed 131 that the rank and \Shape is the same for all \DataSamplePoints. 132 The \Shape of a \Data object is a tuple (list) \var{s} of integers. 133 The length of \var{s} is the rank of the \Data object and the \var{i}-th 134 index ranges between 0 and $\var{s[i]}-1$. 135 For instance, a stress field has rank 2 and \Shape $(d,d)$ where $d$ is the 136 spatial dimension. 137 The following statement creates the \Data object \var{mydat} representing a 138 continuous function with values of \Shape $(2,3)$ and rank $2$: 139 \begin{python} 140 mydat=Data(value=1, what=ContinuousFunction(myDomain), shape=(2,3)) 141 \end{python} 142 The initial value is the constant 1 for all \DataSamplePoints and all 143 components. 144 145 \Data objects can also be created from any \numpy array or any object, such 146 as a list of floating point numbers, that can be converted into 147 a \numpyNDA\cite{NUMPY}. 148 The following two statements create objects which are equivalent 149 to \var{mydat}: 150 \begin{python} 151 mydat1=Data(value=numpy.ones((2,3)), what=ContinuousFunction(myDomain)) 152 mydat2=Data(value=[[1,1], [1,1], [1,1]], what=ContinuousFunction(myDomain)) 153 \end{python} 154 In the first case the initial value is \var{numpy.ones((2,3))} which generates 155 a $2 \times 3$ matrix as a \numpyNDA filled with ones. 156 The \Shape of the created \Data object is taken from the \Shape of the array. 157 In the second case, the creator converts the initial value, which is a list of 158 lists, into a \numpyNDA before creating the actual \Data object. 159 160 For convenience \escript provides creators for the most common types 161 of \Data objects in the following forms (\var{d} defines the spatial dimension): 162 \begin{itemize} 163 \item \code{Scalar(0, Function(mydomain))} is the same as \code{Data(0, Function(myDomain),(,))} 164 (each value is a scalar), e.g. a temperature field 165 \item \code{Vector(0, Function(mydomain))} is the same as \code{Data(0, Function(myDomain),(d))} 166 (each value is a vector), e.g. a velocity field 167 \item \code{Tensor(0, Function(mydomain))} is the same as \code{Data(0, Function(myDomain), (d,d))}, 168 e.g. a stress field 169 \item \code{Tensor4(0,Function(mydomain))} is the same as \code{Data(0,Function(myDomain), (d,d,d,d))} 170 e.g. a Hook tensor field 171 \end{itemize} 172 Here the initial value is 0 but any object that can be converted into 173 a \numpyNDA and whose \Shape is consistent with \Shape of the \Data object to 174 be created can be used as the initial value. 175 176 \Data objects can be manipulated by applying unary operations (e.g. cos, sin, 177 log), and they can be combined point-wise by applying arithmetic operations 178 (e.g. +, - ,* , /). 179 We emphasize that \escript itself does not handle any spatial dependencies as 180 it does not know how values are interpreted by the processing PDE solver library. 181 However \escript invokes interpolation if this is needed during data manipulations. 182 Typically, this occurs in binary operations when both arguments belong to 183 different function spaces or when data are handed over to a PDE solver library 184 which requires functions to be represented in a particular way. 185 186 The following example shows the usage of \Data objects. Assume we have a 187 displacement field $u$ and we want to calculate the corresponding stress field 188 $\sigma$ using the linear-elastic isotropic material model 189 \begin{eqnarray}\label{eq: linear elastic stress} 190 \sigma_{ij}=\lambda u_{k,k} \delta_{ij} + \mu ( u_{i,j} + u_{j,i}) 191 \end{eqnarray} 192 where $\delta_{ij}$ is the Kronecker symbol and 193 $\lambda$ and $\mu$ are the Lame coefficients. The following function 194 takes the displacement \var{u} and the Lame coefficients \var{lam} and \var{mu} 195 as arguments and returns the corresponding stress: 196 \begin{python} 197 from esys.escript import * 198 def getStress(u, lam, mu): 199 d=u.getDomain().getDim() 200 g=grad(u) 201 stress=lam*trace(g)*kronecker(d)+mu*(g+transpose(g)) 202 return stress 203 \end{python} 204 The variable \var{d} gives the spatial dimension of the domain on which the 205 displacements are defined. 206 \var{kronecker} returns the Kronecker symbol with indexes $i$ and $j$ running 207 from 0 to \var{d}-1. 208 The call \var{grad(u)} requires the displacement field \var{u} to be in 209 the \var{Solution} or \ContinuousFunction. 210 The result \var{g} as well as the returned stress will be in the \Function. 211 If, for example, \var{u} is the solution of a PDE then \code{getStress} might 212 be called in the following way: 213 \begin{python} 214 s=getStress(u, 1., 2.) 215 \end{python} 216 However \code{getStress} can also be called with \Data objects as values for 217 \var{lam} and \var{mu} which, for instance in the case of a temperature 218 dependency, are calculated by an expression. 219 The following call is equivalent to the previous example: 220 \begin{python} 221 lam=Scalar(1., ContinuousFunction(mydomain)) 222 mu=Scalar(2., Function(mydomain)) 223 s=getStress(u, lam, mu) 224 \end{python} 225 % 226 The function \var{lam} belongs to the \ContinuousFunction but with \var{g} the 227 function \var{trace(g)} is in the \Function. 228 In the evaluation of the product \var{lam*trace(g)} we have different function 229 spaces (on the nodes versus in the centers) and at first glance we have incompatible data. 230 \escript converts the arguments into an appropriate function space according 231 to \fig{ESCRIPT DEP}. 232 In this example that means \escript sees \var{lam} as a function of the \Function. 233 In the context of FEM this means the nodal values of \var{lam} are 234 interpolated to the element centers. 235 The interpolation is automatic and requires no special handling. 236 237 \begin{figure} 238 \centering 239 \includegraphics{EscriptDiagram2} 240 \caption{\label{Figure: tag}Element Tagging. A rectangular mesh over a region 241 with two rock types {\it white} and {\it gray} is shown. 242 The number in each cell refers to the major rock type present in the cell 243 ($1$ for {\it white} and $2$ for {\it gray}).} 244 \end{figure} 245 246 \subsection{Tagged, Expanded and Constant Data} 247 Material parameters such as the Lame coefficients are typically dependent on 248 rock types present in the area of interest. 249 A common technique to handle these kinds of material parameters is 250 \emph{tagging}\index{tagging}, which uses storage efficiently. 251 \fig{Figure: tag} shows an example. In this case two rock types {\it white} 252 and {\it gray} can be found in the domain. 253 The domain is subdivided into triangular shaped cells. 254 Each cell has a tag indicating the rock type predominantly found in this cell. 255 Here $1$ is used to indicate rock type {\it white} and $2$ for rock type {\it gray}. 256 The tags are assigned at the time when the cells are generated and stored in 257 the \Domain class object. To allow easier usage of tags, names can be used 258 instead of numbers. These names are typically defined at the time when the 259 geometry is generated. 260 261 The following statements show how to use tagged values for \var{lam} as shown 262 in \fig{Figure: tag} for the stress calculation discussed above: 263 \begin{python} 264 lam=Scalar(value=2., what=Function(mydomain)) 265 insertTaggedValue(lam, white=30., gray=5000.) 266 s=getStress(u, lam, 2.) 267 \end{python} 268 In this example \var{lam} is set to $30$ for those cells with tag {\it white} 269 (=$1$) and to $5000$ for cells with tag {\it gray} (=$2$). 270 The initial value $2$ of \var{lam} is used as a default value for the case 271 when a tag is encountered which has not been linked with a value. 272 The \code{getStress} method does not need to be changed now that we are using tags. 273 \escript resolves the tags when \var{lam*trace(g)} is calculated. 274 275 This brings us to a very important point about \escript. 276 You can develop a simulation with constant Lame coefficients, and then later 277 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 279 different types of input data. 280 281 There are three main ways in which \Data objects are represented internally -- 282 constant, tagged, and expanded. 283 In the constant case, the same value is used at each sample point while only a 284 single value is stored to save memory. 285 In the expanded case, each sample point has an individual value (such as for the solution of a PDE). 286 This is where your largest data sets will be created because the values are 287 stored as a complete array. 288 The tagged case has already been discussed above. 289 Expanded data is created when specifying \code{expanded=True} in the \Data 290 object constructor, while tagged data requires calling the \member{insertTaggedValue} 291 method as shown above. 292 293 Values are accessed through a sample reference number. 294 Operations on expanded \Data objects have to be performed for each sample 295 point individually. 296 When tagged values are used, the values are held in a dictionary. 297 Operations on tagged data require processing the set of tagged values only, 298 rather than processing the value for each individual sample point. 299 \escript allows any mixture of constant, tagged and expanded data in a single expression. 300 301 \subsection{Saving and Restoring Simulation Data} 302 \Data objects can be written to disk files with the \member{dump} method and 303 read back using the \member{load} method, both of which use the 304 \netCDF\cite{NETCDF} file format. 305 Use these to save data for checkpoint/restart or simply to save and reuse data 306 that was expensive to compute. 307 For instance, to save the coordinates of the data points of a 308 \ContinuousFunction to the file \file{x.nc} use 309 \begin{python} 310 x=ContinuousFunction(mydomain).getX() 311 x.dump("x.nc") 312 mydomain.dump("dom.nc") 313 \end{python} 314 To recover the object \var{x}, and you know that \var{mydomain} was an \finley 315 mesh, use 316 \begin{python} 317 from esys.finley import LoadMesh 318 mydomain=LoadMesh("dom.nc") 319 x=load("x.nc", mydomain) 320 \end{python} 321 Obviously, it is possible to execute the same steps that were originally used 322 to generate \var{mydomain} to recreate it. However, in most cases using 323 \member{dump} and \member{load} is faster, particularly if optimization has 324 been applied. 325 If \escript is running on more than one \MPI process \member{dump} will create 326 an individual file for each process containing the local data. 327 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 329 \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 331 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 333 \member{dump}. 334 335 The function space of the \Data is stored in \file{x.nc}. 336 If the \Data object is expanded, the number of data points in the file and of 337 the \Domain for the particular \FunctionSpace must match. 338 Moreover, the ordering of the values is checked using the reference 339 identifiers provided by \FunctionSpace on the \Domain. 340 In some cases, data points will be reordered so be aware and confirm that you 341 get what you wanted. 342 343 A newer, more flexible way of saving and restoring \escript simulation data 344 is through a \class{DataManager} class object. 345 It has the advantage of allowing to save and load not only a \Domain and 346 \Data objects but also other values\footnote{The \PYTHON \emph{pickle} module 347 is used for other types.} you compute in your simulation script. 348 Further, \class{DataManager} objects can simultaneously create files for 349 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. 352 For an explanation of all member functions and options see the relevant 353 reference section. 354 \begin{python} 355 from esys.escript import DataManager, Scalar, Function 356 from esys.finley import Rectangle 357 358 dm = DataManager(formats=[DataManager.RESTART, DataManager.VTK]) 359 if dm.hasData(): 360 mydomain=dm.getDomain() 361 val=dm.getValue("val") 362 t=dm.getValue("t") 363 t_max=dm.getValue("t_max") 364 else: 365 mydomain=Rectangle() 366 val=Function(mydomain).getX() 367 t=0. 368 t_max=2.5 369 370 while t$maxval the value maxval is used. 1268 1269 Now we produce our new \Data object. 1270 1271 \begin{python} 1272 result=x0.interpolateTable(sine_table, minval, step, toobig) 1273 \end{python} 1274 Any values which interpolate to larger than \var{toobig} will raise an exception. You can 1275 switch on boundary checking by adding ''check_boundaries=True the argument list. 1276 1277 1278 Now for a 2D example. 1279 We will interpolate a surface such that the bottom edge is the sine curve described above. 1280 The amplitude of the curve decreases as we move towards the top edge. 1281 1282 Our interpolation table will have three rows. 1283 \begin{python} 1284 st=numpy.array(sine_table) 1285 1286 table=[st, 0.5*st, 0*st ] 1287 \end{python} 1288 1289 The use of numpy and multiplication here is just to save typing. 1290 1291 \begin{python} 1292 result2=x1.interpolateTable(table, 0, 0.55, x0, minval, step, toobig) 1293 \end{python} 1294 1295 In the 2D case, the parameters for the x1 direction (min=0, step=0.55) come first followed by the x0 data object and 1296 its parameters. 1297 By default, if a point is specified which is outside the boundary, then \var{interpolateTable} will operate 1298 as if the point was on the boundary. 1299 Passing \var{check_boundaries}=\var{True} will \var{interpolateTable} to reject any points outside the boundaries. 1300 1301 \subsection{Saving Data as CSV} 1302 \index{saveDataCSV} 1303 \index{CSV} 1304 For simple post-processing, \Data objects can be saved in comma separated value format. 1305 1306 If \var{mydata1} and \var{mydata2} are scalar data, the following command: 1307 \begin{python} 1308 saveDataCSV('output.csv',U=mydata1, V=mydata2) 1309 \end{python} 1310 will record the values of mydata in \texttt{output.csv} in the following format: 1311 \begin{verbatim} 1312 U, V 1313 1.0000000e+0, 2.0000000e-1 1314 5.0000000e-0, 1.0000000e+1 1315 ... 1316 \end{verbatim} 1317 1318 The names of the keyword parameters form the names of columns in the output. 1319 If the data objects are over different function spaces, then saveDataCSV will attempt to 1320 interpolate to a common function space. 1321 If this is not possible, then an exception will be raised. 1322 1323 Output can be restricted using a scalar mask. 1324 \begin{python} 1325 saveDataCSV('outfile.csv', U=mydata1, V=mydata2, mask=myscalar) 1326 \end{python} 1327 Will only output those rows which correspond to to positive values of \var{myscalar}. 1328 Some aspects of the output can be tuned using additional parameters. 1329 \begin{python} 1330 saveDataCSV('data.csv', append=True, sep=' ', csep='/', mask=mymask, e=mat1) 1331 \end{python} 1332 1333 \begin{itemize} 1334 \item \var{append} - specifies that the output should be written to the end of an existing file. 1335 \item \var{sep} - defines the separator between fields. 1336 \item \var{csep} - defines the separator between components in the header line. For example between the components of a matrix. 1337 \end{itemize} 1338 1339 The above command would produce output like this: 1340 \begin{verbatim} 1341 e/0/0 e/1/0 e/0/1 e/1/1 1342 1.0000000000e+00 2.0000000000e+00 3.0000000000e+00 4.0000000000e+00 1343 ... 1344 \end{verbatim} 1345 1346 Note that while the order in which rows are output can vary, all the elements in a given row 1347 always correspond to the same input. 1348 1349 1350 \subsection{The \Operator Class} 1351 The \Operator class provides an abstract access to operators build 1352 within the \LinearPDE class. \Operator objects are created 1353 when a PDE is handed over to a PDE solver library and handled 1354 by the \LinearPDE object defining the PDE. The user can gain access 1355 to the \Operator of a \LinearPDE object through the \var{getOperator} 1356 method. 1357 1358 \begin{classdesc}{Operator}{} 1359 creates an empty \Operator object. 1360 \end{classdesc} 1361 1362 \begin{methoddesc}[Operator]{isEmpty}{fileName} 1363 returns \True is the object is empty. Otherwise \True is returned. 1364 \end{methoddesc} 1365 1366 \begin{methoddesc}[Operator]{setValue}{value} 1367 resets all entries in the object representation to \var{value} 1368 \end{methoddesc} 1369 1370 \begin{methoddesc}[Operator]{solves}{rhs} 1371 solves the operator equation with right hand side \var{rhs} 1372 \end{methoddesc} 1373 1374 \begin{methoddesc}[Operator]{of}{u} 1375 applies the operator to the \Data object \var{u} 1376 \end{methoddesc} 1377 1378 \begin{methoddesc}[Operator]{saveMM}{fileName} 1379 saves the object to a matrix market format file of name 1380 \var{fileName}, see 1381 \url{http://maths.nist.gov/MatrixMarket} 1382 % \ulink{maths.nist.gov/MatrixMarket}{\url{http://maths.nist.gov/MatrixMarket}}. 1383 \index{Matrix Market} 1384 \end{methoddesc} 1385 1386 \section{Physical Units} 1387 \escript provides support for physical units in the SI system \index{SI units} including unit conversion. So the 1388 user can define variables in the form 1389 \begin{python} 1390 from esys.escript.unitsSI import * 1391 l=20*m 1392 w=30*kg 1393 w2=40*lb 1394 T=100*Celsius 1395 \end{python} 1396 In the two latter cases an conversion from pounds\index{pounds} and degree Celsius\index{Celsius} is performed into the appropriate SI units kg and Kelvin is performed. In addition 1397 composed units can be used, for instance 1398 \begin{python} 1399 from esys.escript.unitsSI import * 1400 rho=40*lb/cm**3 1401 \end{python} 1402 to define the density in the units of pounds per cubic centimeter. The value$40$will be converted 1403 into SI units, in this case kg per cubic meter. 1404 Moreover unit prefixes are supported: 1405 \begin{python} 1406 from esys.escript.unitsSI import * 1407 p=40*Mega*Pa 1408 \end{python} 1409 to the the pressure to 40 Mega Pascal. Units can also be converted back from the SI system into 1410 a desired unit, e.g 1411 \begin{python} 1412 from esys.escript.unitsSI import * 1413 print p/atm 1414 \end{python} 1415 can be used print the pressure in units of atmosphere\index{atmosphere}. 1416 1417 This is an incomplete list of supported physical units: 1418 1419 \begin{datadesc}{km} 1420 unit of kilo meter 1421 \end{datadesc} 1422 1423 \begin{datadesc}{m} 1424 unit of meter 1425 \end{datadesc} 1426 1427 \begin{datadesc}{cm} 1428 unit of centi meter 1429 \end{datadesc} 1430 1431 \begin{datadesc}{mm} 1432 unit of milli meter 1433 \end{datadesc} 1434 1435 \begin{datadesc}{sec} 1436 unit of second 1437 \end{datadesc} 1438 1439 \begin{datadesc}{minute} 1440 unit of minute 1441 \end{datadesc} 1442 1443 \begin{datadesc}{h} 1444 unit of hour 1445 \end{datadesc} 1446 \begin{datadesc}{day} 1447 unit of day 1448 \end{datadesc} 1449 \begin{datadesc}{yr} 1450 unit of year 1451 \end{datadesc} 1452 1453 \begin{datadesc}{gram} 1454 unit of gram 1455 \end{datadesc} 1456 \begin{datadesc}{kg} 1457 unit of kilo gram 1458 \end{datadesc} 1459 \begin{datadesc}{lb} 1460 unit of pound 1461 \end{datadesc} 1462 \begin{datadesc}{ton} 1463 metric ton 1464 \end{datadesc} 1465 1466 \begin{datadesc}{A} 1467 unit of Ampere 1468 \end{datadesc} 1469 1470 \begin{datadesc}{Hz} 1471 unit of Hertz 1472 \end{datadesc} 1473 1474 \begin{datadesc}{N} 1475 unit of Newton 1476 \end{datadesc} 1477 \begin{datadesc}{Pa} 1478 unit of Pascal 1479 \end{datadesc} 1480 \begin{datadesc}{atm} 1481 unit of atmosphere 1482 \end{datadesc} 1483 \begin{datadesc}{J} 1484 unit of Joule 1485 \end{datadesc} 1486 1487 \begin{datadesc}{W} 1488 unit of Watt 1489 \end{datadesc} 1490 1491 \begin{datadesc}{C} 1492 unit of Coulomb 1493 \end{datadesc} 1494 \begin{datadesc}{V} 1495 unit of Volt 1496 \end{datadesc} 1497 \begin{datadesc}{F} 1498 unit of Farad 1499 \end{datadesc} 1500 1501 \begin{datadesc}{Ohm} 1502 unit of Ohm 1503 \end{datadesc} 1504 \begin{datadesc}{K} 1505 unit of Kelvin 1506 \end{datadesc} 1507 \begin{datadesc}{Celsius} 1508 unit of Celsius 1509 \end{datadesc} 1510 1511 \begin{datadesc}{Fahrenheit} 1512 unit of Fahrenheit 1513 \end{datadesc} 1514 1515 Moreover unit prefixes are supported: 1516 1517 \begin{datadesc}{Yotta} 1518 prefix yotta =$10^{24}$. 1519 1520 \end{datadesc} 1521 1522 \begin{datadesc}{Zetta} 1523 prefix zetta=$10^{21}$. 1524 \end{datadesc} 1525 1526 \begin{datadesc}{Exa} 1527 prefix exa=$10^{18}$. 1528 \end{datadesc} 1529 1530 \begin{datadesc}{Peta} 1531 prefix peta=$10^{15}$. 1532 \end{datadesc} 1533 1534 \begin{datadesc}{Tera} 1535 prefix tera=$10^{12}$. 1536 \end{datadesc} 1537 1538 \begin{datadesc}{Giga} 1539 prefix giga=$10^9$. 1540 \end{datadesc} 1541 1542 \begin{datadesc}{Mega} 1543 prefix mega=$10^6$. 1544 \end{datadesc} 1545 1546 \begin{datadesc}{Kilo} 1547 prefix kilo=$10^3$. 1548 \end{datadesc} 1549 1550 \begin{datadesc}{Hecto} 1551 prefix hecto=$10^2$. 1552 \end{datadesc} 1553 1554 \begin{datadesc}{Deca} 1555 prefix deca=$10^1$. 1556 \end{datadesc} 1557 1558 \begin{datadesc}{Deci} 1559 prefix deci=$10^{-1}$. 1560 \end{datadesc} 1561 1562 \begin{datadesc}{Centi} 1563 prefix centi=$10^{-2}$. 1564 \end{datadesc} 1565 1566 \begin{datadesc}{Milli} 1567 prefix milli=$10^{-3}$. 1568 \end{datadesc} 1569 1570 \begin{datadesc}{Micro} 1571 prefix micro=$10^{-6}$. 1572 \end{datadesc} 1573 1574 \begin{datadesc}{Nano} 1575 prefix nano=$10^{-9}$. 1576 \end{datadesc} 1577 1578 \begin{datadesc}{Pico} 1579 prefix pico=$10^{-12}$. 1580 \end{datadesc} 1581 1582 \begin{datadesc}{Femto} 1583 prefix femto=$10^{-15}$. 1584 \end{datadesc} 1585 1586 \begin{datadesc}{Atto} 1587 prefix atto=$10^{-18}$. 1588 \end{datadesc} 1589 1590 \begin{datadesc}{Zepto} 1591 prefix zepto=$10^{-21}$. 1592 \end{datadesc} 1593 1594 \begin{datadesc}{Yocto} 1595 prefix yocto=$10^{-24}\$. 1596 \end{datadesc} 1597 1598 1599 \section{Utilities} 1600 1601 The \class{FileWriter} provides a mechanism to write data to a file. 1602 In essence, this class wraps the standard \class{file} class to write data 1603 that are global in MPI to a file. In fact, data are written on the processor 1604 with \MPI rank 0 only. It is recommended to use \class{FileWriter} 1605 rather than \class{open} in order to write code that is running 1606 with and without \MPI. It is save to use \class{open} under MPI to read data which are global under \MPI. 1607 1608 \begin{classdesc}{FileWriter}{fn\optional{,append=\False, \optional{createLocalFiles=\False}})} 1609 Opens a file of name \var{fn} for writing. If \var{append} is set to \True 1610 written data are append at the end of the file. 1611 If running under \MPI only the first processor with rank==0 1612 will open the file and write to it. 1613 If \var{createLocalFiles} is set each individual processor will create a file 1614 where for any processor with rank>0 the file name is extended by its rank. This option is normally used for debug purposes only. 1615 \end{classdesc} 1616 1617 The following methods are available: 1618 \begin{methoddesc}[FileWriter]{close}{} 1619 closes the file. 1620 \end{methoddesc} 1621 \begin{methoddesc}[FileWriter]{flush}{} 1622 flushes the internal buffer to disk. 1623 \end{methoddesc} 1624 \begin{methoddesc}[FileWriter]{write}{txt} 1625 Write string \var{txt} to file. 1626 Note that newline is not added. 1627 \end{methoddesc} 1628 \begin{methoddesc}[FileWriter]{writelines}{txts} 1629 Write the list \var{txts} of strings to the file.. 1630 Note that newlines are not added. 1631 This method is equivalent to call write() for each string. 1632 \end{methoddesc} 1633 \begin{memberdesc}[FileWriter]{closed} 1634 \True if file is closed. 1635 \end{memberdesc} 1636 \begin{memberdesc}[FileWriter]{mode} 1637 access mode. 1638 \end{memberdesc} 1639 \begin{memberdesc}[FileWriter]{name} 1640 file name. 1641 \end{memberdesc} 1642 \begin{memberdesc}[FileWriter]{newlines} 1643 line separator 1644 \end{memberdesc} 1645 1646 1647 \begin{funcdesc}{setEscriptParamInt}{name,value} 1648 assigns the integer value \var{value} to the parameter \var{name}. 1649 If \var{name}="TOO_MANY_LINES" conversion of any \Data object to a string switches to a 1650 condensed format if more than \var{value} lines would be created. 1651 \end{funcdesc} 1652 1653 \begin{funcdesc}{getEscriptParamInt}{name} 1654 returns the current value of integer parameter \var{name}. 1655 \end{funcdesc} 1656 1657 \begin{funcdesc}{listEscriptParams}{a} 1658 returns a list of valid parameters and their description. 1659 \end{funcdesc} 1660 1661 \begin{funcdesc}{getMPISizeWorld}{} 1662 returns the number of \MPI processors in use in the \env{MPI_COMM_WORLD} processor group. 1663 If \MPI is not used 1 is returned. 1664 \end{funcdesc} 1665 \begin{funcdesc}{getMPIRankWorld}{} 1666 returns the rank of the process within the \env{MPI_COMM_WORLD} processor group. 1667 If \MPI is not used 0 is returned. 1668 \end{funcdesc} 1669 \begin{funcdesc}{MPIBarrierWorld}{} 1670 performs a barrier synchronization across all processors within \env{MPI_COMM_WORLD} 1671 processor group. 1672 \end{funcdesc} 1673 \begin{funcdesc}{getMPIWorldMax}{a} 1674 returns the maximum value of the integer \var{a} across all 1675 processors within \env{MPI_COMM_WORLD}. 1676 \end{funcdesc} 1677

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