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strange problem with import numarray.linear_algebra fixed
| 1 | # $Id$ |
| 2 | |
| 3 | """ |
| 4 | Utility functions for escript |
| 5 | |
| 6 | @remark: This module is under construction and is still tested!!! |
| 7 | |
| 8 | @var __author__: name of author |
| 9 | @var __licence__: licence agreement |
| 10 | @var __url__: url entry point on documentation |
| 11 | @var __version__: version |
| 12 | @var __date__: date of the version |
| 13 | """ |
| 14 | |
| 15 | __author__="Lutz Gross, l.gross@uq.edu.au" |
| 16 | __copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
| 17 | http://www.access.edu.au |
| 18 | Primary Business: Queensland, Australia""" |
| 19 | __licence__="""Licensed under the Open Software License version 3.0 |
| 20 | http://www.opensource.org/licences/osl-3.0.php""" |
| 21 | __url__="http://www.iservo.edu.au/esys/escript" |
| 22 | __version__="$Revision$" |
| 23 | __date__="$Date$" |
| 24 | |
| 25 | |
| 26 | import math |
| 27 | import numarray |
| 28 | import escript |
| 29 | import os |
| 30 | |
| 31 | #========================================================= |
| 32 | # some helpers: |
| 33 | #========================================================= |
| 34 | def saveVTK(filename,domain=None,**data): |
| 35 | """ |
| 36 | writes a L{Data} objects into a files using the the VTK XML file format. |
| 37 | |
| 38 | Example: |
| 39 | |
| 40 | tmp=Scalar(..) |
| 41 | v=Vector(..) |
| 42 | saveVTK("solution.xml",temperature=tmp,velovity=v) |
| 43 | |
| 44 | tmp and v are written into "solution.xml" where tmp is named "temperature" and v is named "velovity" |
| 45 | |
| 46 | @param filename: file name of the output file |
| 47 | @type filename: C{str} |
| 48 | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. |
| 49 | @type domain: L{escript.Domain} |
| 50 | @keyword <name>: writes the assigned value to the VTK file using <name> as identifier. |
| 51 | @type <name>: L{Data} object. |
| 52 | @note: The data objects have to be defined on the same domain. They may not be in the same L{FunctionSpace} but one cannot expect that all L{FunctionSpace} can be mixed. Typically, data on the boundary and data on the interior cannot be mixed. |
| 53 | """ |
| 54 | if domain==None: |
| 55 | for i in data.keys(): |
| 56 | if not data[i].isEmpty(): domain=data[i].getFunctionSpace().getDomain() |
| 57 | if domain==None: |
| 58 | raise ValueError,"no domain detected." |
| 59 | else: |
| 60 | domain.saveVTK(filename,data) |
| 61 | |
| 62 | def saveDX(filename,domain=None,**data): |
| 63 | """ |
| 64 | writes a L{Data} objects into a files using the the DX file format. |
| 65 | |
| 66 | Example: |
| 67 | |
| 68 | tmp=Scalar(..) |
| 69 | v=Vector(..) |
| 70 | saveDX("solution.dx",temperature=tmp,velovity=v) |
| 71 | |
| 72 | tmp and v are written into "solution.dx" where tmp is named "temperature" and v is named "velovity". |
| 73 | |
| 74 | @param filename: file name of the output file |
| 75 | @type filename: C{str} |
| 76 | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. |
| 77 | @type domain: L{escript.Domain} |
| 78 | @keyword <name>: writes the assigned value to the DX file using <name> as identifier. The identifier can be used to select the data set when data are imported into DX. |
| 79 | @type <name>: L{Data} object. |
| 80 | @note: The data objects have to be defined on the same domain. They may not be in the same L{FunctionSpace} but one cannot expect that all L{FunctionSpace} can be mixed. Typically, data on the boundary and data on the interior cannot be mixed. |
| 81 | """ |
| 82 | if domain==None: |
| 83 | for i in data.keys(): |
| 84 | if not data[i].isEmpty(): domain=data[i].getFunctionSpace().getDomain() |
| 85 | if domain==None: |
| 86 | raise ValueError,"no domain detected." |
| 87 | else: |
| 88 | domain.saveDX(filename,data) |
| 89 | |
| 90 | def kronecker(d=3): |
| 91 | """ |
| 92 | return the kronecker S{delta}-symbol |
| 93 | |
| 94 | @param d: dimension or an object that has the C{getDim} method defining the dimension |
| 95 | @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace} |
| 96 | @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise |
| 97 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2. |
| 98 | """ |
| 99 | return identityTensor(d) |
| 100 | |
| 101 | def identity(shape=()): |
| 102 | """ |
| 103 | return the shape x shape identity tensor |
| 104 | |
| 105 | @param shape: input shape for the identity tensor |
| 106 | @type shape: C{tuple} of C{int} |
| 107 | @return: array of shape shape x shape with M{u[i,k]=1} for M{i=k} and M{u[i,k]=0} otherwise for len(shape)=1 and, for len(shape)=2: M{u[i,j,k,l]=1} for M{i=k and j=l} and M{u[i,j,k,l]=0} otherwise. |
| 108 | @rtype: L{numarray.NumArray} of rank 1, rankk 2 or rank 4. |
| 109 | @raise ValueError: if len(shape)>2. |
| 110 | """ |
| 111 | if len(shape)>0: |
| 112 | out=numarray.zeros(shape+shape,numarray.Float64) |
| 113 | if len(shape)==1: |
| 114 | for i0 in range(shape[0]): |
| 115 | out[i0,i0]=1. |
| 116 | elif len(shape)==2: |
| 117 | for i0 in range(shape[0]): |
| 118 | for i1 in range(shape[1]): |
| 119 | out[i0,i1,i0,i1]=1. |
| 120 | else: |
| 121 | raise ValueError,"identity: length of shape is restricted to 2." |
| 122 | else: |
| 123 | out=1. |
| 124 | return out |
| 125 | |
| 126 | def identityTensor(d=3): |
| 127 | """ |
| 128 | return the dxd identity matrix |
| 129 | |
| 130 | @param d: dimension or an object that has the C{getDim} method defining the dimension |
| 131 | @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace} |
| 132 | @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise |
| 133 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2 |
| 134 | """ |
| 135 | if isinstance(d,escript.FunctionSpace): |
| 136 | return escript.Data(identity((d.getDim(),)),d) |
| 137 | elif isinstance(d,escript.Domain): |
| 138 | return identity((d.getDim(),)) |
| 139 | else: |
| 140 | return identity((d,)) |
| 141 | |
| 142 | def identityTensor4(d=3): |
| 143 | """ |
| 144 | return the dxdxdxd identity tensor |
| 145 | |
| 146 | @param d: dimension or an object that has the C{getDim} method defining the dimension |
| 147 | @type d: C{int} or any object with a C{getDim} method |
| 148 | @return: the object u of rank 4 with M{u[i,j,k,l]=1} for M{i=k and j=l} and M{u[i,j,k,l]=0} otherwise |
| 149 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 4. |
| 150 | """ |
| 151 | if isinstance(d,escript.FunctionSpace): |
| 152 | return escript.Data(identity((d.getDim(),d.getDim())),d) |
| 153 | elif isinstance(d,escript.Domain): |
| 154 | return identity((d.getDim(),d.getDim())) |
| 155 | else: |
| 156 | return identity((d,d)) |
| 157 | |
| 158 | def unitVector(i=0,d=3): |
| 159 | """ |
| 160 | return a unit vector u of dimension d with nonzero index i: |
| 161 | |
| 162 | @param i: index |
| 163 | @type i: C{int} |
| 164 | @param d: dimension or an object that has the C{getDim} method defining the dimension |
| 165 | @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace} |
| 166 | @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise |
| 167 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 1 |
| 168 | """ |
| 169 | return kronecker(d)[i] |
| 170 | |
| 171 | #========================================================================= |
| 172 | # global reduction operations (these functions have no symbolic version) |
| 173 | #========================================================================= |
| 174 | def Lsup(arg): |
| 175 | """ |
| 176 | returns the Lsup-norm of argument arg. This is the maximum absolute value over all data points. |
| 177 | This function is equivalent to sup(abs(arg)). |
| 178 | |
| 179 | @param arg: argument |
| 180 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. |
| 181 | @return: maximum value of the absolute value of arg over all components and all data points |
| 182 | @rtype: C{float} |
| 183 | @raise TypeError: if type of arg cannot be processed |
| 184 | """ |
| 185 | if isinstance(arg,numarray.NumArray): |
| 186 | return sup(abs(arg)) |
| 187 | elif isinstance(arg,escript.Data): |
| 188 | return arg._Lsup() |
| 189 | elif isinstance(arg,float): |
| 190 | return abs(arg) |
| 191 | elif isinstance(arg,int): |
| 192 | return abs(float(arg)) |
| 193 | else: |
| 194 | raise TypeError,"Lsup: Unknown argument type." |
| 195 | |
| 196 | def sup(arg): |
| 197 | """ |
| 198 | returns the maximum value over all data points. |
| 199 | |
| 200 | @param arg: argument |
| 201 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. |
| 202 | @return: maximum value of arg over all components and all data points |
| 203 | @rtype: C{float} |
| 204 | @raise TypeError: if type of arg cannot be processed |
| 205 | """ |
| 206 | if isinstance(arg,numarray.NumArray): |
| 207 | return arg.max() |
| 208 | elif isinstance(arg,escript.Data): |
| 209 | return arg._sup() |
| 210 | elif isinstance(arg,float): |
| 211 | return arg |
| 212 | elif isinstance(arg,int): |
| 213 | return float(arg) |
| 214 | else: |
| 215 | raise TypeError,"sup: Unknown argument type." |
| 216 | |
| 217 | def inf(arg): |
| 218 | """ |
| 219 | returns the maximum value over all data points. |
| 220 | |
| 221 | @param arg: argument |
| 222 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. |
| 223 | @return : minimum value of arg over all components and all data points |
| 224 | @rtype: C{float} |
| 225 | @raise TypeError: if type of arg cannot be processed |
| 226 | """ |
| 227 | if isinstance(arg,numarray.NumArray): |
| 228 | return arg.min() |
| 229 | elif isinstance(arg,escript.Data): |
| 230 | return arg._inf() |
| 231 | elif isinstance(arg,float): |
| 232 | return arg |
| 233 | elif isinstance(arg,int): |
| 234 | return float(arg) |
| 235 | else: |
| 236 | raise TypeError,"inf: Unknown argument type." |
| 237 | |
| 238 | |
| 239 | #========================================================================= |
| 240 | # some little helpers |
| 241 | #========================================================================= |
| 242 | def pokeShape(arg): |
| 243 | """ |
| 244 | identifies the shape of its argument |
| 245 | |
| 246 | @param arg: a given object |
| 247 | @type arg: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} |
| 248 | @return: the shape of the argument |
| 249 | @rtype: C{tuple} of C{int} |
| 250 | @raise TypeError: if type of arg cannot be processed |
| 251 | """ |
| 252 | |
| 253 | if isinstance(arg,numarray.NumArray): |
| 254 | return arg.shape |
| 255 | elif isinstance(arg,escript.Data): |
| 256 | return arg.getShape() |
| 257 | elif isinstance(arg,float): |
| 258 | return () |
| 259 | elif isinstance(arg,int): |
| 260 | return () |
| 261 | elif isinstance(arg,Symbol): |
| 262 | return arg.getShape() |
| 263 | else: |
| 264 | raise TypeError,"pokeShape: cannot identify shape" |
| 265 | |
| 266 | def pokeDim(arg): |
| 267 | """ |
| 268 | identifies the spatial dimension of its argument |
| 269 | |
| 270 | @param arg: a given object |
| 271 | @type arg: any |
| 272 | @return: the spatial dimension of the argument, if available, or C{None} |
| 273 | @rtype: C{int} or C{None} |
| 274 | """ |
| 275 | |
| 276 | if isinstance(arg,escript.Data): |
| 277 | return arg.getFunctionSpace().getDim() |
| 278 | elif isinstance(arg,Symbol): |
| 279 | return arg.getDim() |
| 280 | else: |
| 281 | return None |
| 282 | |
| 283 | def commonShape(arg0,arg1): |
| 284 | """ |
| 285 | returns a shape to which arg0 can be extendent from the right and arg1 can be extended from the left. |
| 286 | |
| 287 | @param arg0: an object with a shape (see L{pokeShape}) |
| 288 | @param arg1: an object with a shape (see L{pokeShape}) |
| 289 | @return: the shape of arg0 or arg1 such that the left port equals the shape of arg0 and the right end equals the shape of arg1. |
| 290 | @rtype: C{tuple} of C{int} |
| 291 | @raise ValueError: if no shape can be found. |
| 292 | """ |
| 293 | sh0=pokeShape(arg0) |
| 294 | sh1=pokeShape(arg1) |
| 295 | if len(sh0)<len(sh1): |
| 296 | if not sh0==sh1[:len(sh0)]: |
| 297 | raise ValueError,"argument 0 cannot be extended to the shape of argument 1" |
| 298 | return sh1 |
| 299 | elif len(sh0)>len(sh1): |
| 300 | if not sh1==sh0[:len(sh1)]: |
| 301 | raise ValueError,"argument 1 cannot be extended to the shape of argument 0" |
| 302 | return sh0 |
| 303 | else: |
| 304 | if not sh0==sh1: |
| 305 | raise ValueError,"argument 1 and argument 0 have not the same shape." |
| 306 | return sh0 |
| 307 | |
| 308 | def commonDim(*args): |
| 309 | """ |
| 310 | identifies, if possible, the spatial dimension across a set of objects which may or my not have a spatial dimension. |
| 311 | |
| 312 | @param *args: given objects |
| 313 | @return: the spatial dimension of the objects with identifiable dimension (see L{pokeDim}). If none the objects has |
| 314 | a spatial dimension C{None} is returned. |
| 315 | @rtype: C{int} or C{None} |
| 316 | @raise ValueError: if the objects with identifiable dimension don't have the same spatial dimension. |
| 317 | """ |
| 318 | out=None |
| 319 | for a in args: |
| 320 | d=pokeDim(a) |
| 321 | if not out==None: |
| 322 | if not (d==None or out==d): |
| 323 | raise ValueError,"dimension of arguments don't match" |
| 324 | else: |
| 325 | out=d |
| 326 | return out |
| 327 | |
| 328 | def testForZero(arg): |
| 329 | """ |
| 330 | test the argument for being identical to Zero |
| 331 | |
| 332 | @param arg: a given object |
| 333 | @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int} |
| 334 | @return : True if the argument is identical to zero. |
| 335 | @rtype : C{bool} |
| 336 | """ |
| 337 | if isinstance(arg,numarray.NumArray): |
| 338 | return not Lsup(arg)>0. |
| 339 | elif isinstance(arg,escript.Data): |
| 340 | return False |
| 341 | elif isinstance(arg,float): |
| 342 | return not Lsup(arg)>0. |
| 343 | elif isinstance(arg,int): |
| 344 | return not Lsup(arg)>0. |
| 345 | elif isinstance(arg,Symbol): |
| 346 | return False |
| 347 | else: |
| 348 | return False |
| 349 | |
| 350 | def matchType(arg0=0.,arg1=0.): |
| 351 | """ |
| 352 | converting arg0 and arg1 both to the same type L{numarray.NumArray} or L{escript.Data} or, if one of arg0 or arg1 is of type L{Symbol}, the other one to be of type L{numarray.NumArray} or L{escript.Data}. |
| 353 | |
| 354 | @param arg0: first argument |
| 355 | @type arg0: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} |
| 356 | @param arg1: second argument |
| 357 | @type arg1: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} |
| 358 | @return: a tuple representing arg0 and arg1 with the same type or with one of them being a L{Symbol} |
| 359 | @rtype: C{tuple} of two L{numarray.NumArray}, two L{escript.Data}, a C{Symbol} and one of the types L{numarray.NumArray} or L{escript.Data}. |
| 360 | @raise TypeError: if type of arg0 or arg1 cannot be processed |
| 361 | """ |
| 362 | if isinstance(arg0,numarray.NumArray): |
| 363 | if isinstance(arg1,numarray.NumArray): |
| 364 | pass |
| 365 | elif isinstance(arg1,escript.Data): |
| 366 | arg0=escript.Data(arg0,arg1.getFunctionSpace()) |
| 367 | elif isinstance(arg1,float): |
| 368 | arg1=numarray.array(arg1,type=numarray.Float64) |
| 369 | elif isinstance(arg1,int): |
| 370 | arg1=numarray.array(float(arg1),type=numarray.Float64) |
| 371 | elif isinstance(arg1,Symbol): |
| 372 | pass |
| 373 | else: |
| 374 | raise TypeError,"function: Unknown type of second argument." |
| 375 | elif isinstance(arg0,escript.Data): |
| 376 | if isinstance(arg1,numarray.NumArray): |
| 377 | arg1=escript.Data(arg1,arg0.getFunctionSpace()) |
| 378 | elif isinstance(arg1,escript.Data): |
| 379 | pass |
| 380 | elif isinstance(arg1,float): |
| 381 | arg1=escript.Data(arg1,(),arg0.getFunctionSpace()) |
| 382 | elif isinstance(arg1,int): |
| 383 | arg1=escript.Data(float(arg1),(),arg0.getFunctionSpace()) |
| 384 | elif isinstance(arg1,Symbol): |
| 385 | pass |
| 386 | else: |
| 387 | raise TypeError,"function: Unknown type of second argument." |
| 388 | elif isinstance(arg0,Symbol): |
| 389 | if isinstance(arg1,numarray.NumArray): |
| 390 | pass |
| 391 | elif isinstance(arg1,escript.Data): |
| 392 | pass |
| 393 | elif isinstance(arg1,float): |
| 394 | arg1=numarray.array(arg1,type=numarray.Float64) |
| 395 | elif isinstance(arg1,int): |
| 396 | arg1=numarray.array(float(arg1),type=numarray.Float64) |
| 397 | elif isinstance(arg1,Symbol): |
| 398 | pass |
| 399 | else: |
| 400 | raise TypeError,"function: Unknown type of second argument." |
| 401 | elif isinstance(arg0,float): |
| 402 | if isinstance(arg1,numarray.NumArray): |
| 403 | arg0=numarray.array(arg0,type=numarray.Float64) |
| 404 | elif isinstance(arg1,escript.Data): |
| 405 | arg0=escript.Data(arg0,arg1.getFunctionSpace()) |
| 406 | elif isinstance(arg1,float): |
| 407 | arg0=numarray.array(arg0,type=numarray.Float64) |
| 408 | arg1=numarray.array(arg1,type=numarray.Float64) |
| 409 | elif isinstance(arg1,int): |
| 410 | arg0=numarray.array(arg0,type=numarray.Float64) |
| 411 | arg1=numarray.array(float(arg1),type=numarray.Float64) |
| 412 | elif isinstance(arg1,Symbol): |
| 413 | arg0=numarray.array(arg0,type=numarray.Float64) |
| 414 | else: |
| 415 | raise TypeError,"function: Unknown type of second argument." |
| 416 | elif isinstance(arg0,int): |
| 417 | if isinstance(arg1,numarray.NumArray): |
| 418 | arg0=numarray.array(float(arg0),type=numarray.Float64) |
| 419 | elif isinstance(arg1,escript.Data): |
| 420 | arg0=escript.Data(float(arg0),arg1.getFunctionSpace()) |
| 421 | elif isinstance(arg1,float): |
| 422 | arg0=numarray.array(float(arg0),type=numarray.Float64) |
| 423 | arg1=numarray.array(arg1,type=numarray.Float64) |
| 424 | elif isinstance(arg1,int): |
| 425 | arg0=numarray.array(float(arg0),type=numarray.Float64) |
| 426 | arg1=numarray.array(float(arg1),type=numarray.Float64) |
| 427 | elif isinstance(arg1,Symbol): |
| 428 | arg0=numarray.array(float(arg0),type=numarray.Float64) |
| 429 | else: |
| 430 | raise TypeError,"function: Unknown type of second argument." |
| 431 | else: |
| 432 | raise TypeError,"function: Unknown type of first argument." |
| 433 | |
| 434 | return arg0,arg1 |
| 435 | |
| 436 | def matchShape(arg0,arg1): |
| 437 | """ |
| 438 | |
| 439 | |
| 440 | If shape is not given the shape "largest" shape of args is used. |
| 441 | |
| 442 | @param args: a given ob |
| 443 | @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int} |
| 444 | @return: True if the argument is identical to zero. |
| 445 | @rtype: C{list} of C{int} |
| 446 | """ |
| 447 | sh=commonShape(arg0,arg1) |
| 448 | sh0=pokeShape(arg0) |
| 449 | sh1=pokeShape(arg1) |
| 450 | if len(sh0)<len(sh): |
| 451 | return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float64)),arg1 |
| 452 | elif len(sh1)<len(sh): |
| 453 | return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float64)) |
| 454 | else: |
| 455 | return arg0,arg1 |
| 456 | #========================================================= |
| 457 | # symbolic tool box starts here: |
| 458 | #========================================================= |
| 459 | class Symbol(object): |
| 460 | """ |
| 461 | Symbol class. |
| 462 | |
| 463 | Symbol class objects provide the same functionality as L{numarray.NumArray} and L{escript.Data} objects |
| 464 | but they do not have a value and therefore cannot be plotted or visualize. The main purpose is the possibilty |
| 465 | calculate derivatives with respect to other Symbols used to define a Symbol. |
| 466 | |
| 467 | """ |
| 468 | def __init__(self,shape=(),args=[],dim=None): |
| 469 | """ |
| 470 | Creates an instance of a symbol of a given shape. The symbol may depending on a list of arguments args which may be |
| 471 | symbols or any other object. |
| 472 | |
| 473 | @param arg: the arguments of the symbol. |
| 474 | @type arg: C{list} |
| 475 | @param shape: the shape |
| 476 | @type shape: C{tuple} of C{int} |
| 477 | @param dim: spatial dimension of the symbol. If dim=C{None} the spatial dimension is undefined. |
| 478 | @type dim: C{None} or C{int} |
| 479 | |
| 480 | """ |
| 481 | if len(shape)>4: |
| 482 | raise ValueError,"Symbol supports only tensors up to order 4" |
| 483 | self.__args=args |
| 484 | self.__shape=shape |
| 485 | self.__dim=dim |
| 486 | |
| 487 | def getArgument(self,i=None): |
| 488 | """ |
| 489 | returns the i-th argument of the symbol |
| 490 | |
| 491 | @param i: index of the argument requested. |
| 492 | @type i: C{int} or C{None} |
| 493 | @raise IndexError: if the requested index does not exist |
| 494 | @return: the vlaue of the i-th argument or i is not specified the list of all arguments. |
| 495 | @rtype: a single object or a list of objects |
| 496 | """ |
| 497 | if i==None: |
| 498 | return self.__args |
| 499 | else: |
| 500 | if i<0 or i>=len(self.__args): |
| 501 | raise IndexError,"there are only %s arguments"%len(self.__args) |
| 502 | return self.__args[i] |
| 503 | |
| 504 | def getRank(self): |
| 505 | """ |
| 506 | the rank of the symbol |
| 507 | |
| 508 | @return: the rank of the symbol. This is length of the shape |
| 509 | @rtype: C{int} |
| 510 | """ |
| 511 | return len(self.getShape()) |
| 512 | |
| 513 | def getShape(self): |
| 514 | """ |
| 515 | the shape of the symbol. |
| 516 | |
| 517 | @return : the shape of the symbol. |
| 518 | @rtype: C{tuple} of C{int} |
| 519 | """ |
| 520 | return self.__shape |
| 521 | |
| 522 | def getDim(self): |
| 523 | """ |
| 524 | the spatial dimension |
| 525 | |
| 526 | @return : the spatial dimension |
| 527 | @rtype: C{int} if the dimension is defined. Otherwise C{None} is returned. |
| 528 | """ |
| 529 | return self.__dim |
| 530 | |
| 531 | def __str__(self): |
| 532 | """ |
| 533 | a string representation of the symbol. |
| 534 | @return: a string representation of the object |
| 535 | @rtype: C{str} |
| 536 | """ |
| 537 | args=[] |
| 538 | for arg in self.getArgument(): |
| 539 | args.append(str(arg)) |
| 540 | try: |
| 541 | out=self.getMyCode(args,format="str") |
| 542 | except NotImplementedError: |
| 543 | out="<Symbol %s>"%id(self) |
| 544 | return out |
| 545 | |
| 546 | def getSubstitutedArguments(self,argvals): |
| 547 | """ |
| 548 | substitutes symbols in the arguments of this object and returns the result as a list. |
| 549 | |
| 550 | @param argvals: L{Symbols} and their substitutes. The L{Symbol} u in the expression defining this object is replaced by argvals[u]. |
| 551 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 552 | @rtype: C{list} of objects |
| 553 | @return: list of the object assigned to the arguments through substitution or for the arguments which are not L{Symbols} the value assigned to the argument at instantiation. |
| 554 | """ |
| 555 | out=[] |
| 556 | for a in self.getArgument(): |
| 557 | if isinstance(a,Symbol): |
| 558 | out.append(a.substitute(argvals)) |
| 559 | else: |
| 560 | out.append(a) |
| 561 | return out |
| 562 | |
| 563 | def getDifferentiatedArguments(self,arg): |
| 564 | """ |
| 565 | applifies differentials to the arguments of this object and returns the result as a list. |
| 566 | |
| 567 | @param arg: the derivative is calculated with respect to arg |
| 568 | @type arg: typically L{escript.Symbol} but can also be C{float}, L{escript.Data}, L{numarray.NumArray} depending the involved functions and data. |
| 569 | @rtype: C{list} of objects |
| 570 | @return: list of object obtained by calculating the derivatives of the argumenst with respct to arg |
| 571 | """ |
| 572 | out=[] |
| 573 | for a in self.getArgument(): |
| 574 | if isinstance(a,Symbol): |
| 575 | out.append(a.substitute(argvals)) |
| 576 | else: |
| 577 | s=pokeShape(s)+arg.getShape() |
| 578 | if len(s)>0: |
| 579 | out.append(numarray.zeros(s),numarray.Float64) |
| 580 | else: |
| 581 | out.append(a) |
| 582 | return out |
| 583 | |
| 584 | def isAppropriateValue(self,arg): |
| 585 | """ |
| 586 | checks if the given argument arg can be used as a substitution of this object. The method checks |
| 587 | the shape of arg and, if the spatial dimension is defined, the spatial dimension of arg. |
| 588 | |
| 589 | @param arg: a given object |
| 590 | @type arg: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} |
| 591 | @return: True if arg is a suitbale object to be used for substitution. Otherwise False is returned. |
| 592 | @rtype: C{bool} |
| 593 | """ |
| 594 | if isinstance(arg,numarray.NumArray): |
| 595 | return arg.shape==self.getShape() |
| 596 | elif isinstance(arg,escript.Data): |
| 597 | if self.getDim()==None: |
| 598 | return arg.getShape()==self.getShape() |
| 599 | elif self.getDim()==arg.getFunctionSpace().getDim(): |
| 600 | return arg.getShape()==self.getShape() |
| 601 | else: |
| 602 | return False |
| 603 | elif isinstance(arg,Symbol): |
| 604 | if self.getDim()==None: |
| 605 | return arg.getShape()==self.getShape() |
| 606 | elif self.getDim()==arg.getDim(): |
| 607 | return arg.getShape()==self.getShape() |
| 608 | else: |
| 609 | return False |
| 610 | elif isinstance(arg,float): |
| 611 | return ()==self.getShape() |
| 612 | elif isinstance(arg,int): |
| 613 | return ()==self.getShape() |
| 614 | else: |
| 615 | return False |
| 616 | |
| 617 | def getMyCode(self,argstrs,format="escript"): |
| 618 | """ |
| 619 | returns a program code that can be used to evaluate the symbol. |
| 620 | |
| 621 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 622 | @type argstrs: C{list} of C{str}. |
| 623 | @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported. |
| 624 | @type format: C{str} |
| 625 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 626 | @rtype: C{str} |
| 627 | @raise NotImplementedError: if no implementation for the given format is available |
| 628 | @note: This method has to be overwritten by subclasses. |
| 629 | """ |
| 630 | raise NotImplementedError,"no code for %s representation available"%format |
| 631 | |
| 632 | def substitute(self,argvals): |
| 633 | """ |
| 634 | assigns new values to symbols in the definition of the symbol. |
| 635 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 636 | |
| 637 | @param argvals: new values assigned to symbols |
| 638 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 639 | @return: result of the substitution process. Operations are executed as much as possible. |
| 640 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 641 | @note: this method has to be overwritten by a particular L{Symbol} |
| 642 | @raise NotImplementedError: if no implementation for the given format is available |
| 643 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 644 | """ |
| 645 | if argvals.has_key(self): |
| 646 | arg=argvals[self] |
| 647 | if self.isAppropriateValue(arg): |
| 648 | return arg |
| 649 | else: |
| 650 | raise TypeError,"Symbol: new value is not appropriate." |
| 651 | else: |
| 652 | raise NotImplementedError,"no substitution in %s avialable"%str(self) |
| 653 | |
| 654 | def diff(self,arg): |
| 655 | """ |
| 656 | returns the derivative of the symbol with respect to L{Symbol} arg |
| 657 | |
| 658 | @param arg: the derivative is calculated with respect to arg |
| 659 | @type arg: typically L{escript.Symbol} but can also be C{float}, L{escript.Data}, L{numarray.NumArray} depending the involved functions and data. |
| 660 | @return: derivative with respect to C{arg} |
| 661 | @rtype: typically L{escript.Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 662 | @note: this method is overwritten by a particular L{Symbol} |
| 663 | """ |
| 664 | if arg==self: |
| 665 | return identity(self.getShape()) |
| 666 | else: |
| 667 | s=self.getShape()+arg.getShape() |
| 668 | if len(s)>0: |
| 669 | return numarray.zeros(s,numarray.Float64) |
| 670 | else: |
| 671 | return 0. |
| 672 | |
| 673 | def __neg__(self): |
| 674 | """ |
| 675 | returns -self. |
| 676 | |
| 677 | @return: a S{Symbol} representing the negative of the object |
| 678 | @rtype: L{DependendSymbol} |
| 679 | """ |
| 680 | return self*(-1.) |
| 681 | |
| 682 | def __pos__(self): |
| 683 | """ |
| 684 | returns +self. |
| 685 | |
| 686 | @return: a S{Symbol} representing the positive of the object |
| 687 | @rtype: L{DependendSymbol} |
| 688 | """ |
| 689 | return self*(1.) |
| 690 | |
| 691 | def __abs__(self): |
| 692 | """ |
| 693 | returns a S{Symbol} representing the absolute value of the object. |
| 694 | """ |
| 695 | return Abs_Symbol(self) |
| 696 | |
| 697 | def __add__(self,other): |
| 698 | """ |
| 699 | add another object to this object |
| 700 | |
| 701 | @param other: object to be added to this object |
| 702 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 703 | @return: a S{Symbol} representing the sum of this object and C{other} |
| 704 | @rtype: L{DependendSymbol} |
| 705 | """ |
| 706 | return add(self,other) |
| 707 | |
| 708 | def __radd__(self,other): |
| 709 | """ |
| 710 | add this object to another object |
| 711 | |
| 712 | @param other: object this object is added to |
| 713 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 714 | @return: a S{Symbol} representing the sum of C{other} and this object object |
| 715 | @rtype: L{DependendSymbol} |
| 716 | """ |
| 717 | return add(other,self) |
| 718 | |
| 719 | def __sub__(self,other): |
| 720 | """ |
| 721 | subtracts another object from this object |
| 722 | |
| 723 | @param other: object to be subtracted from this object |
| 724 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 725 | @return: a S{Symbol} representing the difference of C{other} and this object |
| 726 | @rtype: L{DependendSymbol} |
| 727 | """ |
| 728 | return add(self,-other) |
| 729 | |
| 730 | def __rsub__(self,other): |
| 731 | """ |
| 732 | subtracts this object from another object |
| 733 | |
| 734 | @param other: object this object is been subtracted from |
| 735 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 736 | @return: a S{Symbol} representing the difference of this object and C{other}. |
| 737 | @rtype: L{DependendSymbol} |
| 738 | """ |
| 739 | return add(-self,other) |
| 740 | |
| 741 | def __mul__(self,other): |
| 742 | """ |
| 743 | multiplies this object with other object |
| 744 | |
| 745 | @param other: object to be mutiplied by this object |
| 746 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 747 | @return: a S{Symbol} representing the product of the object and C{other}. |
| 748 | @rtype: L{DependendSymbol} or 0 if other is identical to zero. |
| 749 | """ |
| 750 | return mult(self,other) |
| 751 | |
| 752 | def __rmul__(self,other): |
| 753 | """ |
| 754 | multiplies this object with other object |
| 755 | |
| 756 | @param other: object this object is multiplied with |
| 757 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 758 | @return: a S{Symbol} representing the product of C{other} and the object. |
| 759 | @rtype: L{DependendSymbol} or 0 if other is identical to zero. |
| 760 | """ |
| 761 | return mult(other,self) |
| 762 | |
| 763 | def __div__(self,other): |
| 764 | """ |
| 765 | divides this object by other object |
| 766 | |
| 767 | @param other: object dividing this object |
| 768 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 769 | @return: a S{Symbol} representing the quotient of this object and C{other} |
| 770 | @rtype: L{DependendSymbol} |
| 771 | """ |
| 772 | return quotient(self,other) |
| 773 | |
| 774 | def __rdiv__(self,other): |
| 775 | """ |
| 776 | divides this object by other object |
| 777 | |
| 778 | @param other: object dividing this object |
| 779 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 780 | @return: a S{Symbol} representing the quotient of C{other} and this object |
| 781 | @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero. |
| 782 | """ |
| 783 | return quotient(other,self) |
| 784 | |
| 785 | def __pow__(self,other): |
| 786 | """ |
| 787 | raises this object to the power of other |
| 788 | |
| 789 | @param other: exponent |
| 790 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 791 | @return: a S{Symbol} representing the power of this object to C{other} |
| 792 | @rtype: L{DependendSymbol} or 1 if C{other} is identical to zero. |
| 793 | """ |
| 794 | return power(self,other) |
| 795 | |
| 796 | def __rpow__(self,other): |
| 797 | """ |
| 798 | raises an object to the power of this object |
| 799 | |
| 800 | @param other: basis |
| 801 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 802 | @return: a S{Symbol} representing the power of C{other} to this object |
| 803 | @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero. |
| 804 | """ |
| 805 | return power(other,self) |
| 806 | |
| 807 | def __getitem__(self,index): |
| 808 | """ |
| 809 | returns the slice defined by index |
| 810 | |
| 811 | @param index: defines a |
| 812 | @type index: C{slice} or C{int} or a C{tuple} of them |
| 813 | @return: a S{Symbol} representing the slice defined by index |
| 814 | @rtype: L{DependendSymbol} |
| 815 | """ |
| 816 | return GetSlice_Symbol(self,index) |
| 817 | |
| 818 | class DependendSymbol(Symbol): |
| 819 | """ |
| 820 | DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal. |
| 821 | Two DependendSymbol are equal if they have the same shape, the same arguments and one of them has an unspecified spatial dimension or the spatial dimension is identical |
| 822 | |
| 823 | Example: |
| 824 | |
| 825 | u1=Symbol(shape=(3,4),dim=2,args=[4.]) |
| 826 | u2=Symbol(shape=(3,4),dim=2,args=[4.]) |
| 827 | print u1==u2 |
| 828 | False |
| 829 | |
| 830 | but |
| 831 | |
| 832 | u1=DependendSymbol(shape=(3,4),dim=2,args=[4.]) |
| 833 | u2=DependendSymbol(shape=(3,4),dim=2,args=[4.]) |
| 834 | u3=DependendSymbol(shape=(2,),dim=2,args=[4.]) |
| 835 | print u1==u2, u1==u3 |
| 836 | True False |
| 837 | |
| 838 | @note: DependendSymbol should be used as return value of functions with L{Symbol} arguments. This will allow the optimizer to remove redundant function calls. |
| 839 | """ |
| 840 | def __eq__(self,other): |
| 841 | """ |
| 842 | checks if other equals self |
| 843 | |
| 844 | @param other: any object |
| 845 | @return: True if other has the same class like self, and the shape, the spatial diemsnion and the arguments are equal. |
| 846 | @rtype: C{bool} |
| 847 | """ |
| 848 | if isinstance(other,DependendSymbol): |
| 849 | if self.__class__==other.__class__: |
| 850 | if self.getShape()==other.getShape(): |
| 851 | if self.getArgument()==other.getArgument(): |
| 852 | if self.getDim()==None or other.getDim()==None or self.getDim()==other.getDim(): |
| 853 | return True |
| 854 | return False |
| 855 | |
| 856 | def __ne__(self,other): |
| 857 | """ |
| 858 | checks if other equals self |
| 859 | |
| 860 | @param other: any object |
| 861 | @return: Flase if other has the same class like self, and the shape, the spatial diemsnion and the arguments are equal. |
| 862 | @rtype: C{bool} |
| 863 | """ |
| 864 | return not self==other |
| 865 | #========================================================= |
| 866 | # Unary operations prserving the shape |
| 867 | #======================================================== |
| 868 | class GetSlice_Symbol(DependendSymbol): |
| 869 | """ |
| 870 | L{Symbol} representing getting a slice for a L{Symbol} |
| 871 | """ |
| 872 | def __init__(self,arg,index): |
| 873 | """ |
| 874 | initialization of wherePositive L{Symbol} with argument arg |
| 875 | @param arg: argument |
| 876 | @type arg: L{Symbol}. |
| 877 | @param index: defines index |
| 878 | @type index: C{slice} or C{int} or a C{tuple} of them |
| 879 | @raises IndexError: if length of index is larger than rank of arg or a index start or stop is out of range |
| 880 | @raises ValueError: if a step is given |
| 881 | """ |
| 882 | if not isinstance(index,tuple): index=(index,) |
| 883 | if len(index)>arg.getRank(): |
| 884 | raise IndexError,"GetSlice_Symbol: index out of range." |
| 885 | sh=() |
| 886 | index2=() |
| 887 | for i in range(len(index)): |
| 888 | ix=index[i] |
| 889 | if isinstance(ix,int): |
| 890 | if ix<0 or ix>=arg.getShape()[i]: |
| 891 | raise ValueError,"GetSlice_Symbol: index out of range." |
| 892 | index2=index2+(ix,) |
| 893 | else: |
| 894 | if not ix.step==None: |
| 895 | raise ValueError,"GetSlice_Symbol: steping is not supported." |
| 896 | if ix.start==None: |
| 897 | s=0 |
| 898 | else: |
| 899 | s=ix.start |
| 900 | if ix.stop==None: |
| 901 | e=arg.getShape()[i] |
| 902 | else: |
| 903 | e=ix.stop |
| 904 | if e>arg.getShape()[i]: |
| 905 | raise IndexError,"GetSlice_Symbol: index out of range." |
| 906 | index2=index2+(slice(s,e),) |
| 907 | if e>s: |
| 908 | sh=sh+(e-s,) |
| 909 | elif s>e: |
| 910 | raise IndexError,"GetSlice_Symbol: slice start must be less or equal slice end" |
| 911 | for i in range(len(index),arg.getRank()): |
| 912 | index2=index2+(slice(0,arg.getShape()[i]),) |
| 913 | sh=sh+(arg.getShape()[i],) |
| 914 | super(GetSlice_Symbol, self).__init__(args=[arg,index2],shape=sh,dim=arg.getDim()) |
| 915 | |
| 916 | def getMyCode(self,argstrs,format="escript"): |
| 917 | """ |
| 918 | returns a program code that can be used to evaluate the symbol. |
| 919 | |
| 920 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 921 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 922 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 923 | @type format: C{str} |
| 924 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 925 | @rtype: C{str} |
| 926 | @raise: NotImplementedError: if the requested format is not available |
| 927 | """ |
| 928 | if format=="escript" or format=="str" or format=="text": |
| 929 | return "%s.__getitem__(%s)"%(argstrs[0],argstrs[1]) |
| 930 | else: |
| 931 | raise NotImplementedError,"GetItem_Symbol does not provide program code for format %s."%format |
| 932 | |
| 933 | def substitute(self,argvals): |
| 934 | """ |
| 935 | assigns new values to symbols in the definition of the symbol. |
| 936 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 937 | |
| 938 | @param argvals: new values assigned to symbols |
| 939 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 940 | @return: result of the substitution process. Operations are executed as much as possible. |
| 941 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 942 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 943 | """ |
| 944 | if argvals.has_key(self): |
| 945 | arg=argvals[self] |
| 946 | if self.isAppropriateValue(arg): |
| 947 | return arg |
| 948 | else: |
| 949 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 950 | else: |
| 951 | args=self.getSubstitutedArguments(argvals) |
| 952 | arg=args[0] |
| 953 | index=args[1] |
| 954 | return arg.__getitem__(index) |
| 955 | |
| 956 | def log10(arg): |
| 957 | """ |
| 958 | returns base-10 logarithm of argument arg |
| 959 | |
| 960 | @param arg: argument |
| 961 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 962 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 963 | @raises TypeError: if the type of the argument is not expected. |
| 964 | """ |
| 965 | if isinstance(arg,numarray.NumArray): |
| 966 | return numarray.log10(arg) |
| 967 | elif isinstance(arg,escript.Data): |
| 968 | return arg._log10() |
| 969 | elif isinstance(arg,float): |
| 970 | return math.log10(arg) |
| 971 | elif isinstance(arg,int): |
| 972 | return math.log10(float(arg)) |
| 973 | elif isinstance(arg,Symbol): |
| 974 | return log(arg)/log(10.) |
| 975 | else: |
| 976 | raise TypeError,"log10: Unknown argument type." |
| 977 | |
| 978 | def wherePositive(arg): |
| 979 | """ |
| 980 | returns mask of positive values of argument arg |
| 981 | |
| 982 | @param arg: argument |
| 983 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 984 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 985 | @raises TypeError: if the type of the argument is not expected. |
| 986 | """ |
| 987 | if isinstance(arg,numarray.NumArray): |
| 988 | out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float64))*1. |
| 989 | if isinstance(out,float): out=numarray.array(out,type=numarray.Float64) |
| 990 | return out |
| 991 | elif isinstance(arg,escript.Data): |
| 992 | return arg._wherePositive() |
| 993 | elif isinstance(arg,float): |
| 994 | if arg>0: |
| 995 | return 1. |
| 996 | else: |
| 997 | return 0. |
| 998 | elif isinstance(arg,int): |
| 999 | if arg>0: |
| 1000 | return 1. |
| 1001 | else: |
| 1002 | return 0. |
| 1003 | elif isinstance(arg,Symbol): |
| 1004 | return WherePositive_Symbol(arg) |
| 1005 | else: |
| 1006 | raise TypeError,"wherePositive: Unknown argument type." |
| 1007 | |
| 1008 | class WherePositive_Symbol(DependendSymbol): |
| 1009 | """ |
| 1010 | L{Symbol} representing the result of the mask of positive values function |
| 1011 | """ |
| 1012 | def __init__(self,arg): |
| 1013 | """ |
| 1014 | initialization of wherePositive L{Symbol} with argument arg |
| 1015 | @param arg: argument of function |
| 1016 | @type arg: typically L{Symbol}. |
| 1017 | """ |
| 1018 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1019 | |
| 1020 | def getMyCode(self,argstrs,format="escript"): |
| 1021 | """ |
| 1022 | returns a program code that can be used to evaluate the symbol. |
| 1023 | |
| 1024 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1025 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1026 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1027 | @type format: C{str} |
| 1028 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1029 | @rtype: C{str} |
| 1030 | @raise: NotImplementedError: if the requested format is not available |
| 1031 | """ |
| 1032 | if isinstance(argstrs,list): |
| 1033 | argstrs=argstrs[0] |
| 1034 | if format=="escript" or format=="str" or format=="text": |
| 1035 | return "wherePositive(%s)"%argstrs |
| 1036 | else: |
| 1037 | raise NotImplementedError,"WherePositive_Symbol does not provide program code for format %s."%format |
| 1038 | |
| 1039 | def substitute(self,argvals): |
| 1040 | """ |
| 1041 | assigns new values to symbols in the definition of the symbol. |
| 1042 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1043 | |
| 1044 | @param argvals: new values assigned to symbols |
| 1045 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1046 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1047 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1048 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1049 | """ |
| 1050 | if argvals.has_key(self): |
| 1051 | arg=argvals[self] |
| 1052 | if self.isAppropriateValue(arg): |
| 1053 | return arg |
| 1054 | else: |
| 1055 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1056 | else: |
| 1057 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1058 | return wherePositive(arg) |
| 1059 | |
| 1060 | def whereNegative(arg): |
| 1061 | """ |
| 1062 | returns mask of positive values of argument arg |
| 1063 | |
| 1064 | @param arg: argument |
| 1065 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1066 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1067 | @raises TypeError: if the type of the argument is not expected. |
| 1068 | """ |
| 1069 | if isinstance(arg,numarray.NumArray): |
| 1070 | out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float64))*1. |
| 1071 | if isinstance(out,float): out=numarray.array(out,type=numarray.Float64) |
| 1072 | return out |
| 1073 | elif isinstance(arg,escript.Data): |
| 1074 | return arg._whereNegative() |
| 1075 | elif isinstance(arg,float): |
| 1076 | if arg<0: |
| 1077 | return 1. |
| 1078 | else: |
| 1079 | return 0. |
| 1080 | elif isinstance(arg,int): |
| 1081 | if arg<0: |
| 1082 | return 1. |
| 1083 | else: |
| 1084 | return 0. |
| 1085 | elif isinstance(arg,Symbol): |
| 1086 | return WhereNegative_Symbol(arg) |
| 1087 | else: |
| 1088 | raise TypeError,"whereNegative: Unknown argument type." |
| 1089 | |
| 1090 | class WhereNegative_Symbol(DependendSymbol): |
| 1091 | """ |
| 1092 | L{Symbol} representing the result of the mask of positive values function |
| 1093 | """ |
| 1094 | def __init__(self,arg): |
| 1095 | """ |
| 1096 | initialization of whereNegative L{Symbol} with argument arg |
| 1097 | @param arg: argument of function |
| 1098 | @type arg: typically L{Symbol}. |
| 1099 | """ |
| 1100 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1101 | |
| 1102 | def getMyCode(self,argstrs,format="escript"): |
| 1103 | """ |
| 1104 | returns a program code that can be used to evaluate the symbol. |
| 1105 | |
| 1106 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1107 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1108 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1109 | @type format: C{str} |
| 1110 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1111 | @rtype: C{str} |
| 1112 | @raise: NotImplementedError: if the requested format is not available |
| 1113 | """ |
| 1114 | if isinstance(argstrs,list): |
| 1115 | argstrs=argstrs[0] |
| 1116 | if format=="escript" or format=="str" or format=="text": |
| 1117 | return "whereNegative(%s)"%argstrs |
| 1118 | else: |
| 1119 | raise NotImplementedError,"WhereNegative_Symbol does not provide program code for format %s."%format |
| 1120 | |
| 1121 | def substitute(self,argvals): |
| 1122 | """ |
| 1123 | assigns new values to symbols in the definition of the symbol. |
| 1124 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1125 | |
| 1126 | @param argvals: new values assigned to symbols |
| 1127 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1128 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1129 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1130 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1131 | """ |
| 1132 | if argvals.has_key(self): |
| 1133 | arg=argvals[self] |
| 1134 | if self.isAppropriateValue(arg): |
| 1135 | return arg |
| 1136 | else: |
| 1137 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1138 | else: |
| 1139 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1140 | return whereNegative(arg) |
| 1141 | |
| 1142 | def whereNonNegative(arg): |
| 1143 | """ |
| 1144 | returns mask of non-negative values of argument arg |
| 1145 | |
| 1146 | @param arg: argument |
| 1147 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1148 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1149 | @raises TypeError: if the type of the argument is not expected. |
| 1150 | """ |
| 1151 | if isinstance(arg,numarray.NumArray): |
| 1152 | out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1. |
| 1153 | if isinstance(out,float): out=numarray.array(out,type=numarray.Float64) |
| 1154 | return out |
| 1155 | elif isinstance(arg,escript.Data): |
| 1156 | return arg._whereNonNegative() |
| 1157 | elif isinstance(arg,float): |
| 1158 | if arg<0: |
| 1159 | return 0. |
| 1160 | else: |
| 1161 | return 1. |
| 1162 | elif isinstance(arg,int): |
| 1163 | if arg<0: |
| 1164 | return 0. |
| 1165 | else: |
| 1166 | return 1. |
| 1167 | elif isinstance(arg,Symbol): |
| 1168 | return 1.-whereNegative(arg) |
| 1169 | else: |
| 1170 | raise TypeError,"whereNonNegative: Unknown argument type." |
| 1171 | |
| 1172 | def whereNonPositive(arg): |
| 1173 | """ |
| 1174 | returns mask of non-positive values of argument arg |
| 1175 | |
| 1176 | @param arg: argument |
| 1177 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1178 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1179 | @raises TypeError: if the type of the argument is not expected. |
| 1180 | """ |
| 1181 | if isinstance(arg,numarray.NumArray): |
| 1182 | out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1. |
| 1183 | if isinstance(out,float): out=numarray.array(out,type=numarray.Float64) |
| 1184 | return out |
| 1185 | elif isinstance(arg,escript.Data): |
| 1186 | return arg._whereNonPositive() |
| 1187 | elif isinstance(arg,float): |
| 1188 | if arg>0: |
| 1189 | return 0. |
| 1190 | else: |
| 1191 | return 1. |
| 1192 | elif isinstance(arg,int): |
| 1193 | if arg>0: |
| 1194 | return 0. |
| 1195 | else: |
| 1196 | return 1. |
| 1197 | elif isinstance(arg,Symbol): |
| 1198 | return 1.-wherePositive(arg) |
| 1199 | else: |
| 1200 | raise TypeError,"whereNonPositive: Unknown argument type." |
| 1201 | |
| 1202 | def whereZero(arg,tol=0.): |
| 1203 | """ |
| 1204 | returns mask of zero entries of argument arg |
| 1205 | |
| 1206 | @param arg: argument |
| 1207 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1208 | @param tol: tolerance. values with absolute value less then tol are accepted as zero. |
| 1209 | @type tol: C{float} |
| 1210 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1211 | @raises TypeError: if the type of the argument is not expected. |
| 1212 | """ |
| 1213 | if isinstance(arg,numarray.NumArray): |
| 1214 | out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1. |
| 1215 | if isinstance(out,float): out=numarray.array(out,type=numarray.Float64) |
| 1216 | return out |
| 1217 | elif isinstance(arg,escript.Data): |
| 1218 | if tol>0.: |
| 1219 | return whereNegative(abs(arg)-tol) |
| 1220 | else: |
| 1221 | return arg._whereZero() |
| 1222 | elif isinstance(arg,float): |
| 1223 | if abs(arg)<=tol: |
| 1224 | return 1. |
| 1225 | else: |
| 1226 | return 0. |
| 1227 | elif isinstance(arg,int): |
| 1228 | if abs(float(arg))<=tol: |
| 1229 | return 1. |
| 1230 | else: |
| 1231 | return 0. |
| 1232 | elif isinstance(arg,Symbol): |
| 1233 | return WhereZero_Symbol(arg,tol) |
| 1234 | else: |
| 1235 | raise TypeError,"whereZero: Unknown argument type." |
| 1236 | |
| 1237 | class WhereZero_Symbol(DependendSymbol): |
| 1238 | """ |
| 1239 | L{Symbol} representing the result of the mask of zero entries function |
| 1240 | """ |
| 1241 | def __init__(self,arg,tol=0.): |
| 1242 | """ |
| 1243 | initialization of whereZero L{Symbol} with argument arg |
| 1244 | @param arg: argument of function |
| 1245 | @type arg: typically L{Symbol}. |
| 1246 | """ |
| 1247 | DependendSymbol.__init__(self,args=[arg,tol],shape=arg.getShape(),dim=arg.getDim()) |
| 1248 | |
| 1249 | def getMyCode(self,argstrs,format="escript"): |
| 1250 | """ |
| 1251 | returns a program code that can be used to evaluate the symbol. |
| 1252 | |
| 1253 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1254 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1255 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1256 | @type format: C{str} |
| 1257 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1258 | @rtype: C{str} |
| 1259 | @raise: NotImplementedError: if the requested format is not available |
| 1260 | """ |
| 1261 | if format=="escript" or format=="str" or format=="text": |
| 1262 | return "whereZero(%s,tol=%s)"%(argstrs[0],argstrs[1]) |
| 1263 | else: |
| 1264 | raise NotImplementedError,"WhereZero_Symbol does not provide program code for format %s."%format |
| 1265 | |
| 1266 | def substitute(self,argvals): |
| 1267 | """ |
| 1268 | assigns new values to symbols in the definition of the symbol. |
| 1269 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1270 | |
| 1271 | @param argvals: new values assigned to symbols |
| 1272 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1273 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1274 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1275 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1276 | """ |
| 1277 | if argvals.has_key(self): |
| 1278 | arg=argvals[self] |
| 1279 | if self.isAppropriateValue(arg): |
| 1280 | return arg |
| 1281 | else: |
| 1282 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1283 | else: |
| 1284 | arg=self.getSubstitutedArguments(argvals) |
| 1285 | return whereZero(arg[0],arg[1]) |
| 1286 | |
| 1287 | def whereNonZero(arg,tol=0.): |
| 1288 | """ |
| 1289 | returns mask of values different from zero of argument arg |
| 1290 | |
| 1291 | @param arg: argument |
| 1292 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1293 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1294 | @raises TypeError: if the type of the argument is not expected. |
| 1295 | """ |
| 1296 | if isinstance(arg,numarray.NumArray): |
| 1297 | out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1. |
| 1298 | if isinstance(out,float): out=numarray.array(out,type=numarray.Float64) |
| 1299 | return out |
| 1300 | elif isinstance(arg,escript.Data): |
| 1301 | if tol>0.: |
| 1302 | return 1.-whereZero(arg,tol) |
| 1303 | else: |
| 1304 | return arg._whereNonZero() |
| 1305 | elif isinstance(arg,float): |
| 1306 | if abs(arg)>tol: |
| 1307 | return 1. |
| 1308 | else: |
| 1309 | return 0. |
| 1310 | elif isinstance(arg,int): |
| 1311 | if abs(float(arg))>tol: |
| 1312 | return 1. |
| 1313 | else: |
| 1314 | return 0. |
| 1315 | elif isinstance(arg,Symbol): |
| 1316 | return 1.-whereZero(arg,tol) |
| 1317 | else: |
| 1318 | raise TypeError,"whereNonZero: Unknown argument type." |
| 1319 | |
| 1320 | def sin(arg): |
| 1321 | """ |
| 1322 | returns sine of argument arg |
| 1323 | |
| 1324 | @param arg: argument |
| 1325 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1326 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1327 | @raises TypeError: if the type of the argument is not expected. |
| 1328 | """ |
| 1329 | if isinstance(arg,numarray.NumArray): |
| 1330 | return numarray.sin(arg) |
| 1331 | elif isinstance(arg,escript.Data): |
| 1332 | return arg._sin() |
| 1333 | elif isinstance(arg,float): |
| 1334 | return math.sin(arg) |
| 1335 | elif isinstance(arg,int): |
| 1336 | return math.sin(arg) |
| 1337 | elif isinstance(arg,Symbol): |
| 1338 | return Sin_Symbol(arg) |
| 1339 | else: |
| 1340 | raise TypeError,"sin: Unknown argument type." |
| 1341 | |
| 1342 | class Sin_Symbol(DependendSymbol): |
| 1343 | """ |
| 1344 | L{Symbol} representing the result of the sine function |
| 1345 | """ |
| 1346 | def __init__(self,arg): |
| 1347 | """ |
| 1348 | initialization of sin L{Symbol} with argument arg |
| 1349 | @param arg: argument of function |
| 1350 | @type arg: typically L{Symbol}. |
| 1351 | """ |
| 1352 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1353 | |
| 1354 | def getMyCode(self,argstrs,format="escript"): |
| 1355 | """ |
| 1356 | returns a program code that can be used to evaluate the symbol. |
| 1357 | |
| 1358 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1359 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1360 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1361 | @type format: C{str} |
| 1362 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1363 | @rtype: C{str} |
| 1364 | @raise: NotImplementedError: if the requested format is not available |
| 1365 | """ |
| 1366 | if isinstance(argstrs,list): |
| 1367 | argstrs=argstrs[0] |
| 1368 | if format=="escript" or format=="str" or format=="text": |
| 1369 | return "sin(%s)"%argstrs |
| 1370 | else: |
| 1371 | raise NotImplementedError,"Sin_Symbol does not provide program code for format %s."%format |
| 1372 | |
| 1373 | def substitute(self,argvals): |
| 1374 | """ |
| 1375 | assigns new values to symbols in the definition of the symbol. |
| 1376 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1377 | |
| 1378 | @param argvals: new values assigned to symbols |
| 1379 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1380 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1381 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1382 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1383 | """ |
| 1384 | if argvals.has_key(self): |
| 1385 | arg=argvals[self] |
| 1386 | if self.isAppropriateValue(arg): |
| 1387 | return arg |
| 1388 | else: |
| 1389 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1390 | else: |
| 1391 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1392 | return sin(arg) |
| 1393 | |
| 1394 | def diff(self,arg): |
| 1395 | """ |
| 1396 | differential of this object |
| 1397 | |
| 1398 | @param arg: the derivative is calculated with respect to arg |
| 1399 | @type arg: L{escript.Symbol} |
| 1400 | @return: derivative with respect to C{arg} |
| 1401 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 1402 | """ |
| 1403 | if arg==self: |
| 1404 | return identity(self.getShape()) |
| 1405 | else: |
| 1406 | myarg=self.getArgument()[0] |
| 1407 | val=matchShape(cos(myarg),self.getDifferentiatedArguments(arg)[0]) |
| 1408 | return val[0]*val[1] |
| 1409 | |
| 1410 | def cos(arg): |
| 1411 | """ |
| 1412 | returns cosine of argument arg |
| 1413 | |
| 1414 | @param arg: argument |
| 1415 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1416 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1417 | @raises TypeError: if the type of the argument is not expected. |
| 1418 | """ |
| 1419 | if isinstance(arg,numarray.NumArray): |
| 1420 | return numarray.cos(arg) |
| 1421 | elif isinstance(arg,escript.Data): |
| 1422 | return arg._cos() |
| 1423 | elif isinstance(arg,float): |
| 1424 | return math.cos(arg) |
| 1425 | elif isinstance(arg,int): |
| 1426 | return math.cos(arg) |
| 1427 | elif isinstance(arg,Symbol): |
| 1428 | return Cos_Symbol(arg) |
| 1429 | else: |
| 1430 | raise TypeError,"cos: Unknown argument type." |
| 1431 | |
| 1432 | class Cos_Symbol(DependendSymbol): |
| 1433 | """ |
| 1434 | L{Symbol} representing the result of the cosine function |
| 1435 | """ |
| 1436 | def __init__(self,arg): |
| 1437 | """ |
| 1438 | initialization of cos L{Symbol} with argument arg |
| 1439 | @param arg: argument of function |
| 1440 | @type arg: typically L{Symbol}. |
| 1441 | """ |
| 1442 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1443 | |
| 1444 | def getMyCode(self,argstrs,format="escript"): |
| 1445 | """ |
| 1446 | returns a program code that can be used to evaluate the symbol. |
| 1447 | |
| 1448 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1449 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1450 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1451 | @type format: C{str} |
| 1452 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1453 | @rtype: C{str} |
| 1454 | @raise: NotImplementedError: if the requested format is not available |
| 1455 | """ |
| 1456 | if isinstance(argstrs,list): |
| 1457 | argstrs=argstrs[0] |
| 1458 | if format=="escript" or format=="str" or format=="text": |
| 1459 | return "cos(%s)"%argstrs |
| 1460 | else: |
| 1461 | raise NotImplementedError,"Cos_Symbol does not provide program code for format %s."%format |
| 1462 | |
| 1463 | def substitute(self,argvals): |
| 1464 | """ |
| 1465 | assigns new values to symbols in the definition of the symbol. |
| 1466 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1467 | |
| 1468 | @param argvals: new values assigned to symbols |
| 1469 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1470 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1471 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1472 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1473 | """ |
| 1474 | if argvals.has_key(self): |
| 1475 | arg=argvals[self] |
| 1476 | if self.isAppropriateValue(arg): |
| 1477 | return arg |
| 1478 | else: |
| 1479 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1480 | else: |
| 1481 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1482 | return cos(arg) |
| 1483 | |
| 1484 | def diff(self,arg): |
| 1485 | """ |
| 1486 | differential of this object |
| 1487 | |
| 1488 | @param arg: the derivative is calculated with respect to arg |
| 1489 | @type arg: L{escript.Symbol} |
| 1490 | @return: derivative with respect to C{arg} |
| 1491 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 1492 | """ |
| 1493 | if arg==self: |
| 1494 | return identity(self.getShape()) |
| 1495 | else: |
| 1496 | myarg=self.getArgument()[0] |
| 1497 | val=matchShape(-sin(myarg),self.getDifferentiatedArguments(arg)[0]) |
| 1498 | return val[0]*val[1] |
| 1499 | |
| 1500 | def tan(arg): |
| 1501 | """ |
| 1502 | returns tangent of argument arg |
| 1503 | |
| 1504 | @param arg: argument |
| 1505 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1506 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1507 | @raises TypeError: if the type of the argument is not expected. |
| 1508 | """ |
| 1509 | if isinstance(arg,numarray.NumArray): |
| 1510 | return numarray.tan(arg) |
| 1511 | elif isinstance(arg,escript.Data): |
| 1512 | return arg._tan() |
| 1513 | elif isinstance(arg,float): |
| 1514 | return math.tan(arg) |
| 1515 | elif isinstance(arg,int): |
| 1516 | return math.tan(arg) |
| 1517 | elif isinstance(arg,Symbol): |
| 1518 | return Tan_Symbol(arg) |
| 1519 | else: |
| 1520 | raise TypeError,"tan: Unknown argument type." |
| 1521 | |
| 1522 | class Tan_Symbol(DependendSymbol): |
| 1523 | """ |
| 1524 | L{Symbol} representing the result of the tangent function |
| 1525 | """ |
| 1526 | def __init__(self,arg): |
| 1527 | """ |
| 1528 | initialization of tan L{Symbol} with argument arg |
| 1529 | @param arg: argument of function |
| 1530 | @type arg: typically L{Symbol}. |
| 1531 | """ |
| 1532 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1533 | |
| 1534 | def getMyCode(self,argstrs,format="escript"): |
| 1535 | """ |
| 1536 | returns a program code that can be used to evaluate the symbol. |
| 1537 | |
| 1538 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1539 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1540 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1541 | @type format: C{str} |
| 1542 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1543 | @rtype: C{str} |
| 1544 | @raise: NotImplementedError: if the requested format is not available |
| 1545 | """ |
| 1546 | if isinstance(argstrs,list): |
| 1547 | argstrs=argstrs[0] |
| 1548 | if format=="escript" or format=="str" or format=="text": |
| 1549 | return "tan(%s)"%argstrs |
| 1550 | else: |
| 1551 | raise NotImplementedError,"Tan_Symbol does not provide program code for format %s."%format |
| 1552 | |
| 1553 | def substitute(self,argvals): |
| 1554 | """ |
| 1555 | assigns new values to symbols in the definition of the symbol. |
| 1556 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1557 | |
| 1558 | @param argvals: new values assigned to symbols |
| 1559 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1560 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1561 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1562 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1563 | """ |
| 1564 | if argvals.has_key(self): |
| 1565 | arg=argvals[self] |
| 1566 | if self.isAppropriateValue(arg): |
| 1567 | return arg |
| 1568 | else: |
| 1569 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1570 | else: |
| 1571 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1572 | return tan(arg) |
| 1573 | |
| 1574 | def diff(self,arg): |
| 1575 | """ |
| 1576 | differential of this object |
| 1577 | |
| 1578 | @param arg: the derivative is calculated with respect to arg |
| 1579 | @type arg: L{escript.Symbol} |
| 1580 | @return: derivative with respect to C{arg} |
| 1581 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 1582 | """ |
| 1583 | if arg==self: |
| 1584 | return identity(self.getShape()) |
| 1585 | else: |
| 1586 | myarg=self.getArgument()[0] |
| 1587 | val=matchShape(1./cos(myarg)**2,self.getDifferentiatedArguments(arg)[0]) |
| 1588 | return val[0]*val[1] |
| 1589 | |
| 1590 | def asin(arg): |
| 1591 | """ |
| 1592 | returns inverse sine of argument arg |
| 1593 | |
| 1594 | @param arg: argument |
| 1595 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1596 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1597 | @raises TypeError: if the type of the argument is not expected. |
| 1598 | """ |
| 1599 | if isinstance(arg,numarray.NumArray): |
| 1600 | return numarray.arcsin(arg) |
| 1601 | elif isinstance(arg,escript.Data): |
| 1602 | return arg._asin() |
| 1603 | elif isinstance(arg,float): |
| 1604 | return math.asin(arg) |
| 1605 | elif isinstance(arg,int): |
| 1606 | return math.asin(arg) |
| 1607 | elif isinstance(arg,Symbol): |
| 1608 | return Asin_Symbol(arg) |
| 1609 | else: |
| 1610 | raise TypeError,"asin: Unknown argument type." |
| 1611 | |
| 1612 | class Asin_Symbol(DependendSymbol): |
| 1613 | """ |
| 1614 | L{Symbol} representing the result of the inverse sine function |
| 1615 | """ |
| 1616 | def __init__(self,arg): |
| 1617 | """ |
| 1618 | initialization of asin L{Symbol} with argument arg |
| 1619 | @param arg: argument of function |
| 1620 | @type arg: typically L{Symbol}. |
| 1621 | """ |
| 1622 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1623 | |
| 1624 | def getMyCode(self,argstrs,format="escript"): |
| 1625 | """ |
| 1626 | returns a program code that can be used to evaluate the symbol. |
| 1627 | |
| 1628 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1629 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1630 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1631 | @type format: C{str} |
| 1632 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1633 | @rtype: C{str} |
| 1634 | @raise: NotImplementedError: if the requested format is not available |
| 1635 | """ |
| 1636 | if isinstance(argstrs,list): |
| 1637 | argstrs=argstrs[0] |
| 1638 | if format=="escript" or format=="str" or format=="text": |
| 1639 | return "asin(%s)"%argstrs |
| 1640 | else: |
| 1641 | raise NotImplementedError,"Asin_Symbol does not provide program code for format %s."%format |
| 1642 | |
| 1643 | def substitute(self,argvals): |
| 1644 | """ |
| 1645 | assigns new values to symbols in the definition of the symbol. |
| 1646 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1647 | |
| 1648 | @param argvals: new values assigned to symbols |
| 1649 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1650 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1651 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1652 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1653 | """ |
| 1654 | if argvals.has_key(self): |
| 1655 | arg=argvals[self] |
| 1656 | if self.isAppropriateValue(arg): |
| 1657 | return arg |
| 1658 | else: |
| 1659 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1660 | else: |
| 1661 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1662 | return asin(arg) |
| 1663 | |
| 1664 | def diff(self,arg): |
| 1665 | """ |
| 1666 | differential of this object |
| 1667 | |
| 1668 | @param arg: the derivative is calculated with respect to arg |
| 1669 | @type arg: L{escript.Symbol} |
| 1670 | @return: derivative with respect to C{arg} |
| 1671 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 1672 | """ |
| 1673 | if arg==self: |
| 1674 | return identity(self.getShape()) |
| 1675 | else: |
| 1676 | myarg=self.getArgument()[0] |
| 1677 | val=matchShape(1./sqrt(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) |
| 1678 | return val[0]*val[1] |
| 1679 | |
| 1680 | def acos(arg): |
| 1681 | """ |
| 1682 | returns inverse cosine of argument arg |
| 1683 | |
| 1684 | @param arg: argument |
| 1685 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1686 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1687 | @raises TypeError: if the type of the argument is not expected. |
| 1688 | """ |
| 1689 | if isinstance(arg,numarray.NumArray): |
| 1690 | return numarray.arccos(arg) |
| 1691 | elif isinstance(arg,escript.Data): |
| 1692 | return arg._acos() |
| 1693 | elif isinstance(arg,float): |
| 1694 | return math.acos(arg) |
| 1695 | elif isinstance(arg,int): |
| 1696 | return math.acos(arg) |
| 1697 | elif isinstance(arg,Symbol): |
| 1698 | return Acos_Symbol(arg) |
| 1699 | else: |
| 1700 | raise TypeError,"acos: Unknown argument type." |
| 1701 | |
| 1702 | class Acos_Symbol(DependendSymbol): |
| 1703 | """ |
| 1704 | L{Symbol} representing the result of the inverse cosine function |
| 1705 | """ |
| 1706 | def __init__(self,arg): |
| 1707 | """ |
| 1708 | initialization of acos L{Symbol} with argument arg |
| 1709 | @param arg: argument of function |
| 1710 | @type arg: typically L{Symbol}. |
| 1711 | """ |
| 1712 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1713 | |
| 1714 | def getMyCode(self,argstrs,format="escript"): |
| 1715 | """ |
| 1716 | returns a program code that can be used to evaluate the symbol. |
| 1717 | |
| 1718 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1719 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1720 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1721 | @type format: C{str} |
| 1722 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1723 | @rtype: C{str} |
| 1724 | @raise: NotImplementedError: if the requested format is not available |
| 1725 | """ |
| 1726 | if isinstance(argstrs,list): |
| 1727 | argstrs=argstrs[0] |
| 1728 | if format=="escript" or format=="str" or format=="text": |
| 1729 | return "acos(%s)"%argstrs |
| 1730 | else: |
| 1731 | raise NotImplementedError,"Acos_Symbol does not provide program code for format %s."%format |
| 1732 | |
| 1733 | def substitute(self,argvals): |
| 1734 | """ |
| 1735 | assigns new values to symbols in the definition of the symbol. |
| 1736 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1737 | |
| 1738 | @param argvals: new values assigned to symbols |
| 1739 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1740 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1741 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1742 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1743 | """ |
| 1744 | if argvals.has_key(self): |
| 1745 | arg=argvals[self] |
| 1746 | if self.isAppropriateValue(arg): |
| 1747 | return arg |
| 1748 | else: |
| 1749 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1750 | else: |
| 1751 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1752 | return acos(arg) |
| 1753 | |
| 1754 | def diff(self,arg): |
| 1755 | """ |
| 1756 | differential of this object |
| 1757 | |
| 1758 | @param arg: the derivative is calculated with respect to arg |
| 1759 | @type arg: L{escript.Symbol} |
| 1760 | @return: derivative with respect to C{arg} |
| 1761 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 1762 | """ |
| 1763 | if arg==self: |
| 1764 | return identity(self.getShape()) |
| 1765 | else: |
| 1766 | myarg=self.getArgument()[0] |
| 1767 | val=matchShape(-1./sqrt(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) |
| 1768 | return val[0]*val[1] |
| 1769 | |
| 1770 | def atan(arg): |
| 1771 | """ |
| 1772 | returns inverse tangent of argument arg |
| 1773 | |
| 1774 | @param arg: argument |
| 1775 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1776 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1777 | @raises TypeError: if the type of the argument is not expected. |
| 1778 | """ |
| 1779 | if isinstance(arg,numarray.NumArray): |
| 1780 | return numarray.arctan(arg) |
| 1781 | elif isinstance(arg,escript.Data): |
| 1782 | return arg._atan() |
| 1783 | elif isinstance(arg,float): |
| 1784 | return math.atan(arg) |
| 1785 | elif isinstance(arg,int): |
| 1786 | return math.atan(arg) |
| 1787 | elif isinstance(arg,Symbol): |
| 1788 | return Atan_Symbol(arg) |
| 1789 | else: |
| 1790 | raise TypeError,"atan: Unknown argument type." |
| 1791 | |
| 1792 | class Atan_Symbol(DependendSymbol): |
| 1793 | """ |
| 1794 | L{Symbol} representing the result of the inverse tangent function |
| 1795 | """ |
| 1796 | def __init__(self,arg): |
| 1797 | """ |
| 1798 | initialization of atan L{Symbol} with argument arg |
| 1799 | @param arg: argument of function |
| 1800 | @type arg: typically L{Symbol}. |
| 1801 | """ |
| 1802 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1803 | |
| 1804 | def getMyCode(self,argstrs,format="escript"): |
| 1805 | """ |
| 1806 | returns a program code that can be used to evaluate the symbol. |
| 1807 | |
| 1808 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1809 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1810 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1811 | @type format: C{str} |
| 1812 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1813 | @rtype: C{str} |
| 1814 | @raise: NotImplementedError: if the requested format is not available |
| 1815 | """ |
| 1816 | if isinstance(argstrs,list): |
| 1817 | argstrs=argstrs[0] |
| 1818 | if format=="escript" or format=="str" or format=="text": |
| 1819 | return "atan(%s)"%argstrs |
| 1820 | else: |
| 1821 | raise NotImplementedError,"Atan_Symbol does not provide program code for format %s."%format |
| 1822 | |
| 1823 | def substitute(self,argvals): |
| 1824 | """ |
| 1825 | assigns new values to symbols in the definition of the symbol. |
| 1826 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1827 | |
| 1828 | @param argvals: new values assigned to symbols |
| 1829 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1830 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1831 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1832 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1833 | """ |
| 1834 | if argvals.has_key(self): |
| 1835 | arg=argvals[self] |
| 1836 | if self.isAppropriateValue(arg): |
| 1837 | return arg |
| 1838 | else: |
| 1839 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1840 | else: |
| 1841 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1842 | return atan(arg) |
| 1843 | |
| 1844 | def diff(self,arg): |
| 1845 | """ |
| 1846 | differential of this object |
| 1847 | |
| 1848 | @param arg: the derivative is calculated with respect to arg |
| 1849 | @type arg: L{escript.Symbol} |
| 1850 | @return: derivative with respect to C{arg} |
| 1851 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 1852 | """ |
| 1853 | if arg==self: |
| 1854 | return identity(self.getShape()) |
| 1855 | else: |
| 1856 | myarg=self.getArgument()[0] |
| 1857 | val=matchShape(1./(1+myarg**2),self.getDifferentiatedArguments(arg)[0]) |
| 1858 | return val[0]*val[1] |
| 1859 | |
| 1860 | def sinh(arg): |
| 1861 | """ |
| 1862 | returns hyperbolic sine of argument arg |
| 1863 | |
| 1864 | @param arg: argument |
| 1865 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1866 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1867 | @raises TypeError: if the type of the argument is not expected. |
| 1868 | """ |
| 1869 | if isinstance(arg,numarray.NumArray): |
| 1870 | return numarray.sinh(arg) |
| 1871 | elif isinstance(arg,escript.Data): |
| 1872 | return arg._sinh() |
| 1873 | elif isinstance(arg,float): |
| 1874 | return math.sinh(arg) |
| 1875 | elif isinstance(arg,int): |
| 1876 | return math.sinh(arg) |
| 1877 | elif isinstance(arg,Symbol): |
| 1878 | return Sinh_Symbol(arg) |
| 1879 | else: |
| 1880 | raise TypeError,"sinh: Unknown argument type." |
| 1881 | |
| 1882 | class Sinh_Symbol(DependendSymbol): |
| 1883 | """ |
| 1884 | L{Symbol} representing the result of the hyperbolic sine function |
| 1885 | """ |
| 1886 | def __init__(self,arg): |
| 1887 | """ |
| 1888 | initialization of sinh L{Symbol} with argument arg |
| 1889 | @param arg: argument of function |
| 1890 | @type arg: typically L{Symbol}. |
| 1891 | """ |
| 1892 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1893 | |
| 1894 | def getMyCode(self,argstrs,format="escript"): |
| 1895 | """ |
| 1896 | returns a program code that can be used to evaluate the symbol. |
| 1897 | |
| 1898 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1899 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1900 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1901 | @type format: C{str} |
| 1902 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1903 | @rtype: C{str} |
| 1904 | @raise: NotImplementedError: if the requested format is not available |
| 1905 | """ |
| 1906 | if isinstance(argstrs,list): |
| 1907 | argstrs=argstrs[0] |
| 1908 | if format=="escript" or format=="str" or format=="text": |
| 1909 | return "sinh(%s)"%argstrs |
| 1910 | else: |
| 1911 | raise NotImplementedError,"Sinh_Symbol does not provide program code for format %s."%format |
| 1912 | |
| 1913 | def substitute(self,argvals): |
| 1914 | """ |
| 1915 | assigns new values to symbols in the definition of the symbol. |
| 1916 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 1917 | |
| 1918 | @param argvals: new values assigned to symbols |
| 1919 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 1920 | @return: result of the substitution process. Operations are executed as much as possible. |
| 1921 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 1922 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 1923 | """ |
| 1924 | if argvals.has_key(self): |
| 1925 | arg=argvals[self] |
| 1926 | if self.isAppropriateValue(arg): |
| 1927 | return arg |
| 1928 | else: |
| 1929 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 1930 | else: |
| 1931 | arg=self.getSubstitutedArguments(argvals)[0] |
| 1932 | return sinh(arg) |
| 1933 | |
| 1934 | def diff(self,arg): |
| 1935 | """ |
| 1936 | differential of this object |
| 1937 | |
| 1938 | @param arg: the derivative is calculated with respect to arg |
| 1939 | @type arg: L{escript.Symbol} |
| 1940 | @return: derivative with respect to C{arg} |
| 1941 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 1942 | """ |
| 1943 | if arg==self: |
| 1944 | return identity(self.getShape()) |
| 1945 | else: |
| 1946 | myarg=self.getArgument()[0] |
| 1947 | val=matchShape(cosh(myarg),self.getDifferentiatedArguments(arg)[0]) |
| 1948 | return val[0]*val[1] |
| 1949 | |
| 1950 | def cosh(arg): |
| 1951 | """ |
| 1952 | returns hyperbolic cosine of argument arg |
| 1953 | |
| 1954 | @param arg: argument |
| 1955 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1956 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1957 | @raises TypeError: if the type of the argument is not expected. |
| 1958 | """ |
| 1959 | if isinstance(arg,numarray.NumArray): |
| 1960 | return numarray.cosh(arg) |
| 1961 | elif isinstance(arg,escript.Data): |
| 1962 | return arg._cosh() |
| 1963 | elif isinstance(arg,float): |
| 1964 | return math.cosh(arg) |
| 1965 | elif isinstance(arg,int): |
| 1966 | return math.cosh(arg) |
| 1967 | elif isinstance(arg,Symbol): |
| 1968 | return Cosh_Symbol(arg) |
| 1969 | else: |
| 1970 | raise TypeError,"cosh: Unknown argument type." |
| 1971 | |
| 1972 | class Cosh_Symbol(DependendSymbol): |
| 1973 | """ |
| 1974 | L{Symbol} representing the result of the hyperbolic cosine function |
| 1975 | """ |
| 1976 | def __init__(self,arg): |
| 1977 | """ |
| 1978 | initialization of cosh L{Symbol} with argument arg |
| 1979 | @param arg: argument of function |
| 1980 | @type arg: typically L{Symbol}. |
| 1981 | """ |
| 1982 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 1983 | |
| 1984 | def getMyCode(self,argstrs,format="escript"): |
| 1985 | """ |
| 1986 | returns a program code that can be used to evaluate the symbol. |
| 1987 | |
| 1988 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 1989 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 1990 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 1991 | @type format: C{str} |
| 1992 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 1993 | @rtype: C{str} |
| 1994 | @raise: NotImplementedError: if the requested format is not available |
| 1995 | """ |
| 1996 | if isinstance(argstrs,list): |
| 1997 | argstrs=argstrs[0] |
| 1998 | if format=="escript" or format=="str" or format=="text": |
| 1999 | return "cosh(%s)"%argstrs |
| 2000 | else: |
| 2001 | raise NotImplementedError,"Cosh_Symbol does not provide program code for format %s."%format |
| 2002 | |
| 2003 | def substitute(self,argvals): |
| 2004 | """ |
| 2005 | assigns new values to symbols in the definition of the symbol. |
| 2006 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2007 | |
| 2008 | @param argvals: new values assigned to symbols |
| 2009 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2010 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2011 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2012 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2013 | """ |
| 2014 | if argvals.has_key(self): |
| 2015 | arg=argvals[self] |
| 2016 | if self.isAppropriateValue(arg): |
| 2017 | return arg |
| 2018 | else: |
| 2019 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2020 | else: |
| 2021 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2022 | return cosh(arg) |
| 2023 | |
| 2024 | def diff(self,arg): |
| 2025 | """ |
| 2026 | differential of this object |
| 2027 | |
| 2028 | @param arg: the derivative is calculated with respect to arg |
| 2029 | @type arg: L{escript.Symbol} |
| 2030 | @return: derivative with respect to C{arg} |
| 2031 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2032 | """ |
| 2033 | if arg==self: |
| 2034 | return identity(self.getShape()) |
| 2035 | else: |
| 2036 | myarg=self.getArgument()[0] |
| 2037 | val=matchShape(sinh(myarg),self.getDifferentiatedArguments(arg)[0]) |
| 2038 | return val[0]*val[1] |
| 2039 | |
| 2040 | def tanh(arg): |
| 2041 | """ |
| 2042 | returns hyperbolic tangent of argument arg |
| 2043 | |
| 2044 | @param arg: argument |
| 2045 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2046 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2047 | @raises TypeError: if the type of the argument is not expected. |
| 2048 | """ |
| 2049 | if isinstance(arg,numarray.NumArray): |
| 2050 | return numarray.tanh(arg) |
| 2051 | elif isinstance(arg,escript.Data): |
| 2052 | return arg._tanh() |
| 2053 | elif isinstance(arg,float): |
| 2054 | return math.tanh(arg) |
| 2055 | elif isinstance(arg,int): |
| 2056 | return math.tanh(arg) |
| 2057 | elif isinstance(arg,Symbol): |
| 2058 | return Tanh_Symbol(arg) |
| 2059 | else: |
| 2060 | raise TypeError,"tanh: Unknown argument type." |
| 2061 | |
| 2062 | class Tanh_Symbol(DependendSymbol): |
| 2063 | """ |
| 2064 | L{Symbol} representing the result of the hyperbolic tangent function |
| 2065 | """ |
| 2066 | def __init__(self,arg): |
| 2067 | """ |
| 2068 | initialization of tanh L{Symbol} with argument arg |
| 2069 | @param arg: argument of function |
| 2070 | @type arg: typically L{Symbol}. |
| 2071 | """ |
| 2072 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2073 | |
| 2074 | def getMyCode(self,argstrs,format="escript"): |
| 2075 | """ |
| 2076 | returns a program code that can be used to evaluate the symbol. |
| 2077 | |
| 2078 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2079 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2080 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2081 | @type format: C{str} |
| 2082 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2083 | @rtype: C{str} |
| 2084 | @raise: NotImplementedError: if the requested format is not available |
| 2085 | """ |
| 2086 | if isinstance(argstrs,list): |
| 2087 | argstrs=argstrs[0] |
| 2088 | if format=="escript" or format=="str" or format=="text": |
| 2089 | return "tanh(%s)"%argstrs |
| 2090 | else: |
| 2091 | raise NotImplementedError,"Tanh_Symbol does not provide program code for format %s."%format |
| 2092 | |
| 2093 | def substitute(self,argvals): |
| 2094 | """ |
| 2095 | assigns new values to symbols in the definition of the symbol. |
| 2096 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2097 | |
| 2098 | @param argvals: new values assigned to symbols |
| 2099 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2100 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2101 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2102 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2103 | """ |
| 2104 | if argvals.has_key(self): |
| 2105 | arg=argvals[self] |
| 2106 | if self.isAppropriateValue(arg): |
| 2107 | return arg |
| 2108 | else: |
| 2109 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2110 | else: |
| 2111 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2112 | return tanh(arg) |
| 2113 | |
| 2114 | def diff(self,arg): |
| 2115 | """ |
| 2116 | differential of this object |
| 2117 | |
| 2118 | @param arg: the derivative is calculated with respect to arg |
| 2119 | @type arg: L{escript.Symbol} |
| 2120 | @return: derivative with respect to C{arg} |
| 2121 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2122 | """ |
| 2123 | if arg==self: |
| 2124 | return identity(self.getShape()) |
| 2125 | else: |
| 2126 | myarg=self.getArgument()[0] |
| 2127 | val=matchShape(1./cosh(myarg)**2,self.getDifferentiatedArguments(arg)[0]) |
| 2128 | return val[0]*val[1] |
| 2129 | |
| 2130 | def asinh(arg): |
| 2131 | """ |
| 2132 | returns inverse hyperbolic sine of argument arg |
| 2133 | |
| 2134 | @param arg: argument |
| 2135 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2136 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2137 | @raises TypeError: if the type of the argument is not expected. |
| 2138 | """ |
| 2139 | if isinstance(arg,numarray.NumArray): |
| 2140 | return numarray.arcsinh(arg) |
| 2141 | elif isinstance(arg,escript.Data): |
| 2142 | return arg._asinh() |
| 2143 | elif isinstance(arg,float): |
| 2144 | return numarray.arcsinh(arg) |
| 2145 | elif isinstance(arg,int): |
| 2146 | return numarray.arcsinh(float(arg)) |
| 2147 | elif isinstance(arg,Symbol): |
| 2148 | return Asinh_Symbol(arg) |
| 2149 | else: |
| 2150 | raise TypeError,"asinh: Unknown argument type." |
| 2151 | |
| 2152 | class Asinh_Symbol(DependendSymbol): |
| 2153 | """ |
| 2154 | L{Symbol} representing the result of the inverse hyperbolic sine function |
| 2155 | """ |
| 2156 | def __init__(self,arg): |
| 2157 | """ |
| 2158 | initialization of asinh L{Symbol} with argument arg |
| 2159 | @param arg: argument of function |
| 2160 | @type arg: typically L{Symbol}. |
| 2161 | """ |
| 2162 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2163 | |
| 2164 | def getMyCode(self,argstrs,format="escript"): |
| 2165 | """ |
| 2166 | returns a program code that can be used to evaluate the symbol. |
| 2167 | |
| 2168 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2169 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2170 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2171 | @type format: C{str} |
| 2172 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2173 | @rtype: C{str} |
| 2174 | @raise: NotImplementedError: if the requested format is not available |
| 2175 | """ |
| 2176 | if isinstance(argstrs,list): |
| 2177 | argstrs=argstrs[0] |
| 2178 | if format=="escript" or format=="str" or format=="text": |
| 2179 | return "asinh(%s)"%argstrs |
| 2180 | else: |
| 2181 | raise NotImplementedError,"Asinh_Symbol does not provide program code for format %s."%format |
| 2182 | |
| 2183 | def substitute(self,argvals): |
| 2184 | """ |
| 2185 | assigns new values to symbols in the definition of the symbol. |
| 2186 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2187 | |
| 2188 | @param argvals: new values assigned to symbols |
| 2189 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2190 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2191 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2192 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2193 | """ |
| 2194 | if argvals.has_key(self): |
| 2195 | arg=argvals[self] |
| 2196 | if self.isAppropriateValue(arg): |
| 2197 | return arg |
| 2198 | else: |
| 2199 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2200 | else: |
| 2201 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2202 | return asinh(arg) |
| 2203 | |
| 2204 | def diff(self,arg): |
| 2205 | """ |
| 2206 | differential of this object |
| 2207 | |
| 2208 | @param arg: the derivative is calculated with respect to arg |
| 2209 | @type arg: L{escript.Symbol} |
| 2210 | @return: derivative with respect to C{arg} |
| 2211 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2212 | """ |
| 2213 | if arg==self: |
| 2214 | return identity(self.getShape()) |
| 2215 | else: |
| 2216 | myarg=self.getArgument()[0] |
| 2217 | val=matchShape(1./sqrt(myarg**2+1),self.getDifferentiatedArguments(arg)[0]) |
| 2218 | return val[0]*val[1] |
| 2219 | |
| 2220 | def acosh(arg): |
| 2221 | """ |
| 2222 | returns inverse hyperolic cosine of argument arg |
| 2223 | |
| 2224 | @param arg: argument |
| 2225 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2226 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2227 | @raises TypeError: if the type of the argument is not expected. |
| 2228 | """ |
| 2229 | if isinstance(arg,numarray.NumArray): |
| 2230 | return numarray.arccosh(arg) |
| 2231 | elif isinstance(arg,escript.Data): |
| 2232 | return arg._acosh() |
| 2233 | elif isinstance(arg,float): |
| 2234 | return numarray.arccosh(arg) |
| 2235 | elif isinstance(arg,int): |
| 2236 | return numarray.arccosh(float(arg)) |
| 2237 | elif isinstance(arg,Symbol): |
| 2238 | return Acosh_Symbol(arg) |
| 2239 | else: |
| 2240 | raise TypeError,"acosh: Unknown argument type." |
| 2241 | |
| 2242 | class Acosh_Symbol(DependendSymbol): |
| 2243 | """ |
| 2244 | L{Symbol} representing the result of the inverse hyperolic cosine function |
| 2245 | """ |
| 2246 | def __init__(self,arg): |
| 2247 | """ |
| 2248 | initialization of acosh L{Symbol} with argument arg |
| 2249 | @param arg: argument of function |
| 2250 | @type arg: typically L{Symbol}. |
| 2251 | """ |
| 2252 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2253 | |
| 2254 | def getMyCode(self,argstrs,format="escript"): |
| 2255 | """ |
| 2256 | returns a program code that can be used to evaluate the symbol. |
| 2257 | |
| 2258 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2259 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2260 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2261 | @type format: C{str} |
| 2262 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2263 | @rtype: C{str} |
| 2264 | @raise: NotImplementedError: if the requested format is not available |
| 2265 | """ |
| 2266 | if isinstance(argstrs,list): |
| 2267 | argstrs=argstrs[0] |
| 2268 | if format=="escript" or format=="str" or format=="text": |
| 2269 | return "acosh(%s)"%argstrs |
| 2270 | else: |
| 2271 | raise NotImplementedError,"Acosh_Symbol does not provide program code for format %s."%format |
| 2272 | |
| 2273 | def substitute(self,argvals): |
| 2274 | """ |
| 2275 | assigns new values to symbols in the definition of the symbol. |
| 2276 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2277 | |
| 2278 | @param argvals: new values assigned to symbols |
| 2279 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2280 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2281 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2282 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2283 | """ |
| 2284 | if argvals.has_key(self): |
| 2285 | arg=argvals[self] |
| 2286 | if self.isAppropriateValue(arg): |
| 2287 | return arg |
| 2288 | else: |
| 2289 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2290 | else: |
| 2291 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2292 | return acosh(arg) |
| 2293 | |
| 2294 | def diff(self,arg): |
| 2295 | """ |
| 2296 | differential of this object |
| 2297 | |
| 2298 | @param arg: the derivative is calculated with respect to arg |
| 2299 | @type arg: L{escript.Symbol} |
| 2300 | @return: derivative with respect to C{arg} |
| 2301 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2302 | """ |
| 2303 | if arg==self: |
| 2304 | return identity(self.getShape()) |
| 2305 | else: |
| 2306 | myarg=self.getArgument()[0] |
| 2307 | val=matchShape(1./sqrt(myarg**2-1),self.getDifferentiatedArguments(arg)[0]) |
| 2308 | return val[0]*val[1] |
| 2309 | |
| 2310 | def atanh(arg): |
| 2311 | """ |
| 2312 | returns inverse hyperbolic tangent of argument arg |
| 2313 | |
| 2314 | @param arg: argument |
| 2315 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2316 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2317 | @raises TypeError: if the type of the argument is not expected. |
| 2318 | """ |
| 2319 | if isinstance(arg,numarray.NumArray): |
| 2320 | return numarray.arctanh(arg) |
| 2321 | elif isinstance(arg,escript.Data): |
| 2322 | return arg._atanh() |
| 2323 | elif isinstance(arg,float): |
| 2324 | return numarray.arctanh(arg) |
| 2325 | elif isinstance(arg,int): |
| 2326 | return numarray.arctanh(float(arg)) |
| 2327 | elif isinstance(arg,Symbol): |
| 2328 | return Atanh_Symbol(arg) |
| 2329 | else: |
| 2330 | raise TypeError,"atanh: Unknown argument type." |
| 2331 | |
| 2332 | class Atanh_Symbol(DependendSymbol): |
| 2333 | """ |
| 2334 | L{Symbol} representing the result of the inverse hyperbolic tangent function |
| 2335 | """ |
| 2336 | def __init__(self,arg): |
| 2337 | """ |
| 2338 | initialization of atanh L{Symbol} with argument arg |
| 2339 | @param arg: argument of function |
| 2340 | @type arg: typically L{Symbol}. |
| 2341 | """ |
| 2342 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2343 | |
| 2344 | def getMyCode(self,argstrs,format="escript"): |
| 2345 | """ |
| 2346 | returns a program code that can be used to evaluate the symbol. |
| 2347 | |
| 2348 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2349 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2350 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2351 | @type format: C{str} |
| 2352 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2353 | @rtype: C{str} |
| 2354 | @raise: NotImplementedError: if the requested format is not available |
| 2355 | """ |
| 2356 | if isinstance(argstrs,list): |
| 2357 | argstrs=argstrs[0] |
| 2358 | if format=="escript" or format=="str" or format=="text": |
| 2359 | return "atanh(%s)"%argstrs |
| 2360 | else: |
| 2361 | raise NotImplementedError,"Atanh_Symbol does not provide program code for format %s."%format |
| 2362 | |
| 2363 | def substitute(self,argvals): |
| 2364 | """ |
| 2365 | assigns new values to symbols in the definition of the symbol. |
| 2366 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2367 | |
| 2368 | @param argvals: new values assigned to symbols |
| 2369 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2370 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2371 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2372 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2373 | """ |
| 2374 | if argvals.has_key(self): |
| 2375 | arg=argvals[self] |
| 2376 | if self.isAppropriateValue(arg): |
| 2377 | return arg |
| 2378 | else: |
| 2379 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2380 | else: |
| 2381 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2382 | return atanh(arg) |
| 2383 | |
| 2384 | def diff(self,arg): |
| 2385 | """ |
| 2386 | differential of this object |
| 2387 | |
| 2388 | @param arg: the derivative is calculated with respect to arg |
| 2389 | @type arg: L{escript.Symbol} |
| 2390 | @return: derivative with respect to C{arg} |
| 2391 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2392 | """ |
| 2393 | if arg==self: |
| 2394 | return identity(self.getShape()) |
| 2395 | else: |
| 2396 | myarg=self.getArgument()[0] |
| 2397 | val=matchShape(1./(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) |
| 2398 | return val[0]*val[1] |
| 2399 | |
| 2400 | def exp(arg): |
| 2401 | """ |
| 2402 | returns exponential of argument arg |
| 2403 | |
| 2404 | @param arg: argument |
| 2405 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2406 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2407 | @raises TypeError: if the type of the argument is not expected. |
| 2408 | """ |
| 2409 | if isinstance(arg,numarray.NumArray): |
| 2410 | return numarray.exp(arg) |
| 2411 | elif isinstance(arg,escript.Data): |
| 2412 | return arg._exp() |
| 2413 | elif isinstance(arg,float): |
| 2414 | return math.exp(arg) |
| 2415 | elif isinstance(arg,int): |
| 2416 | return math.exp(arg) |
| 2417 | elif isinstance(arg,Symbol): |
| 2418 | return Exp_Symbol(arg) |
| 2419 | else: |
| 2420 | raise TypeError,"exp: Unknown argument type." |
| 2421 | |
| 2422 | class Exp_Symbol(DependendSymbol): |
| 2423 | """ |
| 2424 | L{Symbol} representing the result of the exponential function |
| 2425 | """ |
| 2426 | def __init__(self,arg): |
| 2427 | """ |
| 2428 | initialization of exp L{Symbol} with argument arg |
| 2429 | @param arg: argument of function |
| 2430 | @type arg: typically L{Symbol}. |
| 2431 | """ |
| 2432 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2433 | |
| 2434 | def getMyCode(self,argstrs,format="escript"): |
| 2435 | """ |
| 2436 | returns a program code that can be used to evaluate the symbol. |
| 2437 | |
| 2438 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2439 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2440 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2441 | @type format: C{str} |
| 2442 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2443 | @rtype: C{str} |
| 2444 | @raise: NotImplementedError: if the requested format is not available |
| 2445 | """ |
| 2446 | if isinstance(argstrs,list): |
| 2447 | argstrs=argstrs[0] |
| 2448 | if format=="escript" or format=="str" or format=="text": |
| 2449 | return "exp(%s)"%argstrs |
| 2450 | else: |
| 2451 | raise NotImplementedError,"Exp_Symbol does not provide program code for format %s."%format |
| 2452 | |
| 2453 | def substitute(self,argvals): |
| 2454 | """ |
| 2455 | assigns new values to symbols in the definition of the symbol. |
| 2456 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2457 | |
| 2458 | @param argvals: new values assigned to symbols |
| 2459 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2460 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2461 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2462 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2463 | """ |
| 2464 | if argvals.has_key(self): |
| 2465 | arg=argvals[self] |
| 2466 | if self.isAppropriateValue(arg): |
| 2467 | return arg |
| 2468 | else: |
| 2469 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2470 | else: |
| 2471 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2472 | return exp(arg) |
| 2473 | |
| 2474 | def diff(self,arg): |
| 2475 | """ |
| 2476 | differential of this object |
| 2477 | |
| 2478 | @param arg: the derivative is calculated with respect to arg |
| 2479 | @type arg: L{escript.Symbol} |
| 2480 | @return: derivative with respect to C{arg} |
| 2481 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2482 | """ |
| 2483 | if arg==self: |
| 2484 | return identity(self.getShape()) |
| 2485 | else: |
| 2486 | myarg=self.getArgument()[0] |
| 2487 | val=matchShape(self,self.getDifferentiatedArguments(arg)[0]) |
| 2488 | return val[0]*val[1] |
| 2489 | |
| 2490 | def sqrt(arg): |
| 2491 | """ |
| 2492 | returns square root of argument arg |
| 2493 | |
| 2494 | @param arg: argument |
| 2495 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2496 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2497 | @raises TypeError: if the type of the argument is not expected. |
| 2498 | """ |
| 2499 | if isinstance(arg,numarray.NumArray): |
| 2500 | return numarray.sqrt(arg) |
| 2501 | elif isinstance(arg,escript.Data): |
| 2502 | return arg._sqrt() |
| 2503 | elif isinstance(arg,float): |
| 2504 | return math.sqrt(arg) |
| 2505 | elif isinstance(arg,int): |
| 2506 | return math.sqrt(arg) |
| 2507 | elif isinstance(arg,Symbol): |
| 2508 | return Sqrt_Symbol(arg) |
| 2509 | else: |
| 2510 | raise TypeError,"sqrt: Unknown argument type." |
| 2511 | |
| 2512 | class Sqrt_Symbol(DependendSymbol): |
| 2513 | """ |
| 2514 | L{Symbol} representing the result of the square root function |
| 2515 | """ |
| 2516 | def __init__(self,arg): |
| 2517 | """ |
| 2518 | initialization of sqrt L{Symbol} with argument arg |
| 2519 | @param arg: argument of function |
| 2520 | @type arg: typically L{Symbol}. |
| 2521 | """ |
| 2522 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2523 | |
| 2524 | def getMyCode(self,argstrs,format="escript"): |
| 2525 | """ |
| 2526 | returns a program code that can be used to evaluate the symbol. |
| 2527 | |
| 2528 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2529 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2530 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2531 | @type format: C{str} |
| 2532 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2533 | @rtype: C{str} |
| 2534 | @raise: NotImplementedError: if the requested format is not available |
| 2535 | """ |
| 2536 | if isinstance(argstrs,list): |
| 2537 | argstrs=argstrs[0] |
| 2538 | if format=="escript" or format=="str" or format=="text": |
| 2539 | return "sqrt(%s)"%argstrs |
| 2540 | else: |
| 2541 | raise NotImplementedError,"Sqrt_Symbol does not provide program code for format %s."%format |
| 2542 | |
| 2543 | def substitute(self,argvals): |
| 2544 | """ |
| 2545 | assigns new values to symbols in the definition of the symbol. |
| 2546 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2547 | |
| 2548 | @param argvals: new values assigned to symbols |
| 2549 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2550 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2551 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2552 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2553 | """ |
| 2554 | if argvals.has_key(self): |
| 2555 | arg=argvals[self] |
| 2556 | if self.isAppropriateValue(arg): |
| 2557 | return arg |
| 2558 | else: |
| 2559 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2560 | else: |
| 2561 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2562 | return sqrt(arg) |
| 2563 | |
| 2564 | def diff(self,arg): |
| 2565 | """ |
| 2566 | differential of this object |
| 2567 | |
| 2568 | @param arg: the derivative is calculated with respect to arg |
| 2569 | @type arg: L{escript.Symbol} |
| 2570 | @return: derivative with respect to C{arg} |
| 2571 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2572 | """ |
| 2573 | if arg==self: |
| 2574 | return identity(self.getShape()) |
| 2575 | else: |
| 2576 | myarg=self.getArgument()[0] |
| 2577 | val=matchShape(0.5/self,self.getDifferentiatedArguments(arg)[0]) |
| 2578 | return val[0]*val[1] |
| 2579 | |
| 2580 | def log(arg): |
| 2581 | """ |
| 2582 | returns natural logarithm of argument arg |
| 2583 | |
| 2584 | @param arg: argument |
| 2585 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2586 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2587 | @raises TypeError: if the type of the argument is not expected. |
| 2588 | """ |
| 2589 | if isinstance(arg,numarray.NumArray): |
| 2590 | return numarray.log(arg) |
| 2591 | elif isinstance(arg,escript.Data): |
| 2592 | return arg._log() |
| 2593 | elif isinstance(arg,float): |
| 2594 | return math.log(arg) |
| 2595 | elif isinstance(arg,int): |
| 2596 | return math.log(arg) |
| 2597 | elif isinstance(arg,Symbol): |
| 2598 | return Log_Symbol(arg) |
| 2599 | else: |
| 2600 | raise TypeError,"log: Unknown argument type." |
| 2601 | |
| 2602 | class Log_Symbol(DependendSymbol): |
| 2603 | """ |
| 2604 | L{Symbol} representing the result of the natural logarithm function |
| 2605 | """ |
| 2606 | def __init__(self,arg): |
| 2607 | """ |
| 2608 | initialization of log L{Symbol} with argument arg |
| 2609 | @param arg: argument of function |
| 2610 | @type arg: typically L{Symbol}. |
| 2611 | """ |
| 2612 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2613 | |
| 2614 | def getMyCode(self,argstrs,format="escript"): |
| 2615 | """ |
| 2616 | returns a program code that can be used to evaluate the symbol. |
| 2617 | |
| 2618 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2619 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2620 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2621 | @type format: C{str} |
| 2622 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2623 | @rtype: C{str} |
| 2624 | @raise: NotImplementedError: if the requested format is not available |
| 2625 | """ |
| 2626 | if isinstance(argstrs,list): |
| 2627 | argstrs=argstrs[0] |
| 2628 | if format=="escript" or format=="str" or format=="text": |
| 2629 | return "log(%s)"%argstrs |
| 2630 | else: |
| 2631 | raise NotImplementedError,"Log_Symbol does not provide program code for format %s."%format |
| 2632 | |
| 2633 | def substitute(self,argvals): |
| 2634 | """ |
| 2635 | assigns new values to symbols in the definition of the symbol. |
| 2636 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2637 | |
| 2638 | @param argvals: new values assigned to symbols |
| 2639 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2640 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2641 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2642 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2643 | """ |
| 2644 | if argvals.has_key(self): |
| 2645 | arg=argvals[self] |
| 2646 | if self.isAppropriateValue(arg): |
| 2647 | return arg |
| 2648 | else: |
| 2649 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2650 | else: |
| 2651 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2652 | return log(arg) |
| 2653 | |
| 2654 | def diff(self,arg): |
| 2655 | """ |
| 2656 | differential of this object |
| 2657 | |
| 2658 | @param arg: the derivative is calculated with respect to arg |
| 2659 | @type arg: L{escript.Symbol} |
| 2660 | @return: derivative with respect to C{arg} |
| 2661 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2662 | """ |
| 2663 | if arg==self: |
| 2664 | return identity(self.getShape()) |
| 2665 | else: |
| 2666 | myarg=self.getArgument()[0] |
| 2667 | val=matchShape(1./arg,self.getDifferentiatedArguments(arg)[0]) |
| 2668 | return val[0]*val[1] |
| 2669 | |
| 2670 | def sign(arg): |
| 2671 | """ |
| 2672 | returns sign of argument arg |
| 2673 | |
| 2674 | @param arg: argument |
| 2675 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2676 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2677 | @raises TypeError: if the type of the argument is not expected. |
| 2678 | """ |
| 2679 | if isinstance(arg,numarray.NumArray): |
| 2680 | return wherePositive(arg)-whereNegative(arg) |
| 2681 | elif isinstance(arg,escript.Data): |
| 2682 | return arg._sign() |
| 2683 | elif isinstance(arg,float): |
| 2684 | if arg>0: |
| 2685 | return 1. |
| 2686 | elif arg<0: |
| 2687 | return -1. |
| 2688 | else: |
| 2689 | return 0. |
| 2690 | elif isinstance(arg,int): |
| 2691 | if float(arg)>0: |
| 2692 | return 1. |
| 2693 | elif float(arg)<0: |
| 2694 | return -1. |
| 2695 | else: |
| 2696 | return 0. |
| 2697 | elif isinstance(arg,Symbol): |
| 2698 | return wherePositive(arg)-whereNegative(arg) |
| 2699 | else: |
| 2700 | raise TypeError,"sign: Unknown argument type." |
| 2701 | |
| 2702 | class Abs_Symbol(DependendSymbol): |
| 2703 | """ |
| 2704 | L{Symbol} representing the result of the absolute value function |
| 2705 | """ |
| 2706 | def __init__(self,arg): |
| 2707 | """ |
| 2708 | initialization of abs L{Symbol} with argument arg |
| 2709 | @param arg: argument of function |
| 2710 | @type arg: typically L{Symbol}. |
| 2711 | """ |
| 2712 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) |
| 2713 | |
| 2714 | def getMyCode(self,argstrs,format="escript"): |
| 2715 | """ |
| 2716 | returns a program code that can be used to evaluate the symbol. |
| 2717 | |
| 2718 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2719 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2720 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2721 | @type format: C{str} |
| 2722 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2723 | @rtype: C{str} |
| 2724 | @raise: NotImplementedError: if the requested format is not available |
| 2725 | """ |
| 2726 | if isinstance(argstrs,list): |
| 2727 | argstrs=argstrs[0] |
| 2728 | if format=="escript" or format=="str" or format=="text": |
| 2729 | return "abs(%s)"%argstrs |
| 2730 | else: |
| 2731 | raise NotImplementedError,"Abs_Symbol does not provide program code for format %s."%format |
| 2732 | |
| 2733 | def substitute(self,argvals): |
| 2734 | """ |
| 2735 | assigns new values to symbols in the definition of the symbol. |
| 2736 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2737 | |
| 2738 | @param argvals: new values assigned to symbols |
| 2739 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2740 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2741 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2742 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2743 | """ |
| 2744 | if argvals.has_key(self): |
| 2745 | arg=argvals[self] |
| 2746 | if self.isAppropriateValue(arg): |
| 2747 | return arg |
| 2748 | else: |
| 2749 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2750 | else: |
| 2751 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2752 | return abs(arg) |
| 2753 | |
| 2754 | def diff(self,arg): |
| 2755 | """ |
| 2756 | differential of this object |
| 2757 | |
| 2758 | @param arg: the derivative is calculated with respect to arg |
| 2759 | @type arg: L{escript.Symbol} |
| 2760 | @return: derivative with respect to C{arg} |
| 2761 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2762 | """ |
| 2763 | if arg==self: |
| 2764 | return identity(self.getShape()) |
| 2765 | else: |
| 2766 | myarg=self.getArgument()[0] |
| 2767 | val=matchShape(sign(myarg),self.getDifferentiatedArguments(arg)[0]) |
| 2768 | return val[0]*val[1] |
| 2769 | |
| 2770 | def minval(arg): |
| 2771 | """ |
| 2772 | returns minimum value over all components of arg at each data point |
| 2773 | |
| 2774 | @param arg: argument |
| 2775 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2776 | @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg. |
| 2777 | @raises TypeError: if the type of the argument is not expected. |
| 2778 | """ |
| 2779 | if isinstance(arg,numarray.NumArray): |
| 2780 | if arg.rank==0: |
| 2781 | return float(arg) |
| 2782 | else: |
| 2783 | return arg.min() |
| 2784 | elif isinstance(arg,escript.Data): |
| 2785 | return arg._minval() |
| 2786 | elif isinstance(arg,float): |
| 2787 | return arg |
| 2788 | elif isinstance(arg,int): |
| 2789 | return float(arg) |
| 2790 | elif isinstance(arg,Symbol): |
| 2791 | return Minval_Symbol(arg) |
| 2792 | else: |
| 2793 | raise TypeError,"minval: Unknown argument type." |
| 2794 | |
| 2795 | class Minval_Symbol(DependendSymbol): |
| 2796 | """ |
| 2797 | L{Symbol} representing the result of the minimum value function |
| 2798 | """ |
| 2799 | def __init__(self,arg): |
| 2800 | """ |
| 2801 | initialization of minimum value L{Symbol} with argument arg |
| 2802 | @param arg: argument of function |
| 2803 | @type arg: typically L{Symbol}. |
| 2804 | """ |
| 2805 | DependendSymbol.__init__(self,args=[arg],shape=(),dim=arg.getDim()) |
| 2806 | |
| 2807 | def getMyCode(self,argstrs,format="escript"): |
| 2808 | """ |
| 2809 | returns a program code that can be used to evaluate the symbol. |
| 2810 | |
| 2811 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2812 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2813 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2814 | @type format: C{str} |
| 2815 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2816 | @rtype: C{str} |
| 2817 | @raise: NotImplementedError: if the requested format is not available |
| 2818 | """ |
| 2819 | if isinstance(argstrs,list): |
| 2820 | argstrs=argstrs[0] |
| 2821 | if format=="escript" or format=="str" or format=="text": |
| 2822 | return "minval(%s)"%argstrs |
| 2823 | else: |
| 2824 | raise NotImplementedError,"Minval_Symbol does not provide program code for format %s."%format |
| 2825 | |
| 2826 | def substitute(self,argvals): |
| 2827 | """ |
| 2828 | assigns new values to symbols in the definition of the symbol. |
| 2829 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2830 | |
| 2831 | @param argvals: new values assigned to symbols |
| 2832 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2833 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2834 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2835 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2836 | """ |
| 2837 | if argvals.has_key(self): |
| 2838 | arg=argvals[self] |
| 2839 | if self.isAppropriateValue(arg): |
| 2840 | return arg |
| 2841 | else: |
| 2842 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2843 | else: |
| 2844 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2845 | return minval(arg) |
| 2846 | |
| 2847 | def maxval(arg): |
| 2848 | """ |
| 2849 | returns maximum value over all components of arg at each data point |
| 2850 | |
| 2851 | @param arg: argument |
| 2852 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2853 | @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg. |
| 2854 | @raises TypeError: if the type of the argument is not expected. |
| 2855 | """ |
| 2856 | if isinstance(arg,numarray.NumArray): |
| 2857 | if arg.rank==0: |
| 2858 | return float(arg) |
| 2859 | else: |
| 2860 | return arg.max() |
| 2861 | elif isinstance(arg,escript.Data): |
| 2862 | return arg._maxval() |
| 2863 | elif isinstance(arg,float): |
| 2864 | return arg |
| 2865 | elif isinstance(arg,int): |
| 2866 | return float(arg) |
| 2867 | elif isinstance(arg,Symbol): |
| 2868 | return Maxval_Symbol(arg) |
| 2869 | else: |
| 2870 | raise TypeError,"maxval: Unknown argument type." |
| 2871 | |
| 2872 | class Maxval_Symbol(DependendSymbol): |
| 2873 | """ |
| 2874 | L{Symbol} representing the result of the maximum value function |
| 2875 | """ |
| 2876 | def __init__(self,arg): |
| 2877 | """ |
| 2878 | initialization of maximum value L{Symbol} with argument arg |
| 2879 | @param arg: argument of function |
| 2880 | @type arg: typically L{Symbol}. |
| 2881 | """ |
| 2882 | DependendSymbol.__init__(self,args=[arg],shape=(),dim=arg.getDim()) |
| 2883 | |
| 2884 | def getMyCode(self,argstrs,format="escript"): |
| 2885 | """ |
| 2886 | returns a program code that can be used to evaluate the symbol. |
| 2887 | |
| 2888 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 2889 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 2890 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 2891 | @type format: C{str} |
| 2892 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 2893 | @rtype: C{str} |
| 2894 | @raise: NotImplementedError: if the requested format is not available |
| 2895 | """ |
| 2896 | if isinstance(argstrs,list): |
| 2897 | argstrs=argstrs[0] |
| 2898 | if format=="escript" or format=="str" or format=="text": |
| 2899 | return "maxval(%s)"%argstrs |
| 2900 | else: |
| 2901 | raise NotImplementedError,"Maxval_Symbol does not provide program code for format %s."%format |
| 2902 | |
| 2903 | def substitute(self,argvals): |
| 2904 | """ |
| 2905 | assigns new values to symbols in the definition of the symbol. |
| 2906 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2907 | |
| 2908 | @param argvals: new values assigned to symbols |
| 2909 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2910 | @return: result of the substitution process. Operations are executed as much as possible. |
| 2911 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2912 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2913 | """ |
| 2914 | if argvals.has_key(self): |
| 2915 | arg=argvals[self] |
| 2916 | if self.isAppropriateValue(arg): |
| 2917 | return arg |
| 2918 | else: |
| 2919 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 2920 | else: |
| 2921 | arg=self.getSubstitutedArguments(argvals)[0] |
| 2922 | return maxval(arg) |
| 2923 | |
| 2924 | def length(arg): |
| 2925 | """ |
| 2926 | returns length/Euclidean norm of argument arg at each data point |
| 2927 | |
| 2928 | @param arg: argument |
| 2929 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2930 | @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg. |
| 2931 | """ |
| 2932 | return sqrt(inner(arg,arg)) |
| 2933 | |
| 2934 | def trace(arg,axis_offset=0): |
| 2935 | """ |
| 2936 | returns the trace of arg which the sum of arg[k,k] over k. |
| 2937 | |
| 2938 | @param arg: argument |
| 2939 | @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2940 | @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component |
| 2941 | axis_offset and axis_offset+1 must be equal. |
| 2942 | @type axis_offset: C{int} |
| 2943 | @return: trace of arg. The rank of the returned object is minus 2 of the rank of arg. |
| 2944 | @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2945 | """ |
| 2946 | if isinstance(arg,numarray.NumArray): |
| 2947 | sh=arg.shape |
| 2948 | if len(sh)<2: |
| 2949 | raise ValueError,"trace: rank of argument must be greater than 1" |
| 2950 | if axis_offset<0 or axis_offset>len(sh)-2: |
| 2951 | raise ValueError,"trace: axis_offset must be between 0 and %s"%len(sh)-2 |
| 2952 | s1=1 |
| 2953 | for i in range(axis_offset): s1*=sh[i] |
| 2954 | s2=1 |
| 2955 | for i in range(axis_offset+2,len(sh)): s2*=sh[i] |
| 2956 | if not sh[axis_offset] == sh[axis_offset+1]: |
| 2957 | raise ValueError,"trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1) |
| 2958 | arg_reshaped=numarray.reshape(arg,(s1,sh[axis_offset],sh[axis_offset],s2)) |
| 2959 | out=numarray.zeros([s1,s2],numarray.Float64) |
| 2960 | for i1 in range(s1): |
| 2961 | for i2 in range(s2): |
| 2962 | for j in range(sh[axis_offset]): out[i1,i2]+=arg_reshaped[i1,j,j,i2] |
| 2963 | out.resize(sh[:axis_offset]+sh[axis_offset+2:]) |
| 2964 | return out |
| 2965 | elif isinstance(arg,escript.Data): |
| 2966 | return escript_trace(arg,axis_offset) |
| 2967 | elif isinstance(arg,float): |
| 2968 | raise TypeError,"trace: illegal argument type float." |
| 2969 | elif isinstance(arg,int): |
| 2970 | raise TypeError,"trace: illegal argument type int." |
| 2971 | elif isinstance(arg,Symbol): |
| 2972 | return Trace_Symbol(arg,axis_offset) |
| 2973 | else: |
| 2974 | raise TypeError,"trace: Unknown argument type." |
| 2975 | |
| 2976 | def escript_trace(arg,axis_offset): # this should be escript._trace |
| 2977 | "arg si a Data objects!!!" |
| 2978 | if arg.getRank()<2: |
| 2979 | raise ValueError,"escript_trace: rank of argument must be greater than 1" |
| 2980 | if axis_offset<0 or axis_offset>arg.getRank()-2: |
| 2981 | raise ValueError,"escript_trace: axis_offset must be between 0 and %s"%arg.getRank()-2 |
| 2982 | s=list(arg.getShape()) |
| 2983 | if not s[axis_offset] == s[axis_offset+1]: |
| 2984 | raise ValueError,"escript_trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1) |
| 2985 | out=escript.Data(0.,tuple(s[0:axis_offset]+s[axis_offset+2:]),arg.getFunctionSpace()) |
| 2986 | if arg.getRank()==2: |
| 2987 | for i0 in range(s[0]): |
| 2988 | out+=arg[i0,i0] |
| 2989 | elif arg.getRank()==3: |
| 2990 | if axis_offset==0: |
| 2991 | for i0 in range(s[0]): |
| 2992 | for i2 in range(s[2]): |
| 2993 | out[i2]+=arg[i0,i0,i2] |
| 2994 | elif axis_offset==1: |
| 2995 | for i0 in range(s[0]): |
| 2996 | for i1 in range(s[1]): |
| 2997 | out[i0]+=arg[i0,i1,i1] |
| 2998 | elif arg.getRank()==4: |
| 2999 | if axis_offset==0: |
| 3000 | for i0 in range(s[0]): |
| 3001 | for i2 in range(s[2]): |
| 3002 | for i3 in range(s[3]): |
| 3003 | out[i2,i3]+=arg[i0,i0,i2,i3] |
| 3004 | elif axis_offset==1: |
| 3005 | for i0 in range(s[0]): |
| 3006 | for i1 in range(s[1]): |
| 3007 | for i3 in range(s[3]): |
| 3008 | out[i0,i3]+=arg[i0,i1,i1,i3] |
| 3009 | elif axis_offset==2: |
| 3010 | for i0 in range(s[0]): |
| 3011 | for i1 in range(s[1]): |
| 3012 | for i2 in range(s[2]): |
| 3013 | out[i0,i1]+=arg[i0,i1,i2,i2] |
| 3014 | return out |
| 3015 | class Trace_Symbol(DependendSymbol): |
| 3016 | """ |
| 3017 | L{Symbol} representing the result of the trace function |
| 3018 | """ |
| 3019 | def __init__(self,arg,axis_offset=0): |
| 3020 | """ |
| 3021 | initialization of trace L{Symbol} with argument arg |
| 3022 | @param arg: argument of function |
| 3023 | @type arg: L{Symbol}. |
| 3024 | @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component |
| 3025 | axis_offset and axis_offset+1 must be equal. |
| 3026 | @type axis_offset: C{int} |
| 3027 | """ |
| 3028 | if arg.getRank()<2: |
| 3029 | raise ValueError,"Trace_Symbol: rank of argument must be greater than 1" |
| 3030 | if axis_offset<0 or axis_offset>arg.getRank()-2: |
| 3031 | raise ValueError,"Trace_Symbol: axis_offset must be between 0 and %s"%arg.getRank()-2 |
| 3032 | s=list(arg.getShape()) |
| 3033 | if not s[axis_offset] == s[axis_offset+1]: |
| 3034 | raise ValueError,"Trace_Symbol: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1) |
| 3035 | super(Trace_Symbol,self).__init__(args=[arg,axis_offset],shape=tuple(s[0:axis_offset]+s[axis_offset+2:]),dim=arg.getDim()) |
| 3036 | |
| 3037 | def getMyCode(self,argstrs,format="escript"): |
| 3038 | """ |
| 3039 | returns a program code that can be used to evaluate the symbol. |
| 3040 | |
| 3041 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 3042 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 3043 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 3044 | @type format: C{str} |
| 3045 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 3046 | @rtype: C{str} |
| 3047 | @raise: NotImplementedError: if the requested format is not available |
| 3048 | """ |
| 3049 | if format=="escript" or format=="str" or format=="text": |
| 3050 | return "trace(%s,axis_offset=%s)"%(argstrs[0],argstrs[1]) |
| 3051 | else: |
| 3052 | raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format |
| 3053 | |
| 3054 | def substitute(self,argvals): |
| 3055 | """ |
| 3056 | assigns new values to symbols in the definition of the symbol. |
| 3057 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 3058 | |
| 3059 | @param argvals: new values assigned to symbols |
| 3060 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 3061 | @return: result of the substitution process. Operations are executed as much as possible. |
| 3062 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 3063 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 3064 | """ |
| 3065 | if argvals.has_key(self): |
| 3066 | arg=argvals[self] |
| 3067 | if self.isAppropriateValue(arg): |
| 3068 | return arg |
| 3069 | else: |
| 3070 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 3071 | else: |
| 3072 | arg=self.getSubstitutedArguments(argvals) |
| 3073 | return trace(arg[0],axis_offset=arg[1]) |
| 3074 | |
| 3075 | def diff(self,arg): |
| 3076 | """ |
| 3077 | differential of this object |
| 3078 | |
| 3079 | @param arg: the derivative is calculated with respect to arg |
| 3080 | @type arg: L{escript.Symbol} |
| 3081 | @return: derivative with respect to C{arg} |
| 3082 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 3083 | """ |
| 3084 | if arg==self: |
| 3085 | return identity(self.getShape()) |
| 3086 | else: |
| 3087 | return trace(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1]) |
| 3088 | |
| 3089 | def transpose(arg,axis_offset=None): |
| 3090 | """ |
| 3091 | returns the transpose of arg by swaping the first axis_offset and the last rank-axis_offset components. |
| 3092 | |
| 3093 | @param arg: argument |
| 3094 | @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}, C{float}, C{int} |
| 3095 | @param axis_offset: the first axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg. |
| 3096 | if axis_offset is not present C{int(r/2)} where r is the rank of arg is used. |
| 3097 | @type axis_offset: C{int} |
| 3098 | @return: transpose of arg |
| 3099 | @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray},C{float}, C{int} depending on the type of arg. |
| 3100 | """ |
| 3101 | if isinstance(arg,numarray.NumArray): |
| 3102 | if axis_offset==None: axis_offset=int(arg.rank/2) |
| 3103 | return numarray.transpose(arg,axes=range(axis_offset,arg.rank)+range(0,axis_offset)) |
| 3104 | elif isinstance(arg,escript.Data): |
| 3105 | if axis_offset==None: axis_offset=int(arg.getRank()/2) |
| 3106 | return escript_transpose(arg,axis_offset) |
| 3107 | elif isinstance(arg,float): |
| 3108 | if not ( axis_offset==0 or axis_offset==None): |
| 3109 | raise ValueError,"transpose: axis_offset must be 0 for float argument" |
| 3110 | return arg |
| 3111 | elif isinstance(arg,int): |
| 3112 | if not ( axis_offset==0 or axis_offset==None): |
| 3113 | raise ValueError,"transpose: axis_offset must be 0 for int argument" |
| 3114 | return float(arg) |
| 3115 | elif isinstance(arg,Symbol): |
| 3116 | if axis_offset==None: axis_offset=int(arg.getRank()/2) |
| 3117 | return Transpose_Symbol(arg,axis_offset) |
| 3118 | else: |
| 3119 | raise TypeError,"transpose: Unknown argument type." |
| 3120 | |
| 3121 | def escript_transpose(arg,axis_offset): # this should be escript._transpose |
| 3122 | "arg si a Data objects!!!" |
| 3123 | r=arg.getRank() |
| 3124 | if axis_offset<0 or axis_offset>r: |
| 3125 | raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r |
| 3126 | s=arg.getShape() |
| 3127 | s_out=s[axis_offset:]+s[:axis_offset] |
| 3128 | out=escript.Data(0.,s_out,arg.getFunctionSpace()) |
| 3129 | if r==4: |
| 3130 | if axis_offset==1: |
| 3131 | for i0 in range(s_out[0]): |
| 3132 | for i1 in range(s_out[1]): |
| 3133 | for i2 in range(s_out[2]): |
| 3134 | for i3 in range(s_out[3]): |
| 3135 | out[i0,i1,i2,i3]=arg[i3,i0,i1,i2] |
| 3136 | elif axis_offset==2: |
| 3137 | for i0 in range(s_out[0]): |
| 3138 | for i1 in range(s_out[1]): |
| 3139 | for i2 in range(s_out[2]): |
| 3140 | for i3 in range(s_out[3]): |
| 3141 | out[i0,i1,i2,i3]=arg[i2,i3,i0,i1] |
| 3142 | elif axis_offset==3: |
| 3143 | for i0 in range(s_out[0]): |
| 3144 | for i1 in range(s_out[1]): |
| 3145 | for i2 in range(s_out[2]): |
| 3146 | for i3 in range(s_out[3]): |
| 3147 | out[i0,i1,i2,i3]=arg[i1,i2,i3,i0] |
| 3148 | else: |
| 3149 | for i0 in range(s_out[0]): |
| 3150 | for i1 in range(s_out[1]): |
| 3151 | for i2 in range(s_out[2]): |
| 3152 | for i3 in range(s_out[3]): |
| 3153 | out[i0,i1,i2,i3]=arg[i0,i1,i2,i3] |
| 3154 | elif r==3: |
| 3155 | if axis_offset==1: |
| 3156 | for i0 in range(s_out[0]): |
| 3157 | for i1 in range(s_out[1]): |
| 3158 | for i2 in range(s_out[2]): |
| 3159 | out[i0,i1,i2]=arg[i2,i0,i1] |
| 3160 | elif axis_offset==2: |
| 3161 | for i0 in range(s_out[0]): |
| 3162 | for i1 in range(s_out[1]): |
| 3163 | for i2 in range(s_out[2]): |
| 3164 | out[i0,i1,i2]=arg[i1,i2,i0] |
| 3165 | else: |
| 3166 | for i0 in range(s_out[0]): |
| 3167 | for i1 in range(s_out[1]): |
| 3168 | for i2 in range(s_out[2]): |
| 3169 | out[i0,i1,i2]=arg[i0,i1,i2] |
| 3170 | elif r==2: |
| 3171 | if axis_offset==1: |
| 3172 | for i0 in range(s_out[0]): |
| 3173 | for i1 in range(s_out[1]): |
| 3174 | out[i0,i1]=arg[i1,i0] |
| 3175 | else: |
| 3176 | for i0 in range(s_out[0]): |
| 3177 | for i1 in range(s_out[1]): |
| 3178 | out[i0,i1]=arg[i0,i1] |
| 3179 | elif r==1: |
| 3180 | for i0 in range(s_out[0]): |
| 3181 | out[i0]=arg[i0] |
| 3182 | elif r==0: |
| 3183 | out=arg+0. |
| 3184 | return out |
| 3185 | class Transpose_Symbol(DependendSymbol): |
| 3186 | """ |
| 3187 | L{Symbol} representing the result of the transpose function |
| 3188 | """ |
| 3189 | def __init__(self,arg,axis_offset=None): |
| 3190 | """ |
| 3191 | initialization of transpose L{Symbol} with argument arg |
| 3192 | |
| 3193 | @param arg: argument of function |
| 3194 | @type arg: L{Symbol}. |
| 3195 | @param axis_offset: the first axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg. |
| 3196 | if axis_offset is not present C{int(r/2)} where r is the rank of arg is used. |
| 3197 | @type axis_offset: C{int} |
| 3198 | """ |
| 3199 | if axis_offset==None: axis_offset=int(arg.getRank()/2) |
| 3200 | if axis_offset<0 or axis_offset>arg.getRank(): |
| 3201 | raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r |
| 3202 | s=arg.getShape() |
| 3203 | super(Transpose_Symbol,self).__init__(args=[arg,axis_offset],shape=s[axis_offset:]+s[:axis_offset],dim=arg.getDim()) |
| 3204 | |
| 3205 | def getMyCode(self,argstrs,format="escript"): |
| 3206 | """ |
| 3207 | returns a program code that can be used to evaluate the symbol. |
| 3208 | |
| 3209 | @param argstrs: gives for each argument a string representing the argument for the evaluation. |
| 3210 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. |
| 3211 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. |
| 3212 | @type format: C{str} |
| 3213 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. |
| 3214 | @rtype: C{str} |
| 3215 | @raise: NotImplementedError: if the requested format is not available |
| 3216 | """ |
| 3217 | if format=="escript" or format=="str" or format=="text": |
| 3218 | return "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1]) |
| 3219 | else: |
| 3220 | raise NotImplementedError,"Transpose_Symbol does not provide program code for format %s."%format |
| 3221 | |
| 3222 | def substitute(self,argvals): |
| 3223 | """ |
| 3224 | assigns new values to symbols in the definition of the symbol. |
| 3225 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 3226 | |
| 3227 | @param argvals: new values assigned to symbols |
| 3228 | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 3229 | @return: result of the substitution process. Operations are executed as much as possible. |
| 3230 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 3231 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 3232 | """ |
| 3233 | if argvals.has_key(self): |
| 3234 | arg=argvals[self] |
| 3235 | if self.isAppropriateValue(arg): |
| 3236 | return arg |
| 3237 | else: |
| 3238 | raise TypeError,"%s: new value is not appropriate."%str(self) |
| 3239 | else: |
| 3240 | arg=self.getSubstitutedArguments(argvals) |
| 3241 | return transpose(arg[0],axis_offset=arg[1]) |
| 3242 | |
| 3243 | def diff(self,arg): |
| 3244 | """ |
| 3245 | differential of this object |
| 3246 | |
| 3247 | @param arg: the derivative is calculated with respect to arg |
| 3248 | @type arg: L{escript.Symbol} |
| 3249 | @return: derivative with respect to C{arg} |
| 3250 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 3251 | """ |
| 3252 | if arg==self: |
| 3253 | return identity(self.getShape()) |
| 3254 | else: |
| 3255 | return transpose(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1]) |
| 3256 | def symmetric(arg): |
| 3257 | """ |
| 3258 | returns the symmetric part of the square matrix arg. This is (arg+transpose(arg))/2 |
| 3259 | |
| 3260 | @param arg: square matrix. Must have rank 2 or 4 and be square. |
| 3261 | @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol} |
| 3262 | @return: symmetric part of arg |
| 3263 | @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input |
| 3264 | """ |
| 3265 | if isinstance(arg,numarray.NumArray): |
| 3266 | if arg.rank==2: |
| 3267 | if not (arg.shape[0]==arg.shape[1]): |
| 3268 | raise ValueError,"symmetric: argument must be square." |
| 3269 | elif arg.rank==4: |
| 3270 | if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]): |
| 3271 | raise ValueError,"symmetric: argument must be square." |
| 3272 | else: |
| 3273 | raise ValueError,"symmetric: rank 2 or 4 is required." |
| 3274 | return (arg+transpose(arg))/2 |
| 3275 | elif isinstance(arg,escript.Data): |
| 3276 | return escript_symmetric(arg) |
| 3277 | elif isinstance(arg,float): |
| 3278 | return arg |
| 3279 | elif isinstance(arg,int): |
| 3280 | return float(arg) |
| 3281 | elif isinstance(arg,Symbol): |
| 3282 | if arg.getRank()==2: |
| 3283 | if not (arg.getShape()[0]==arg.getShape()[1]): |
| 3284 | raise ValueError,"symmetric: argument must be square." |
| 3285 | elif arg.getRank()==4: |
| 3286 | if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]): |
| 3287 | raise ValueError,"symmetric: argument must be square." |
| 3288 | else: |
| 3289 | raise ValueError,"symmetric: rank 2 or 4 is required." |
| 3290 | return (arg+transpose(arg))/2 |
| 3291 | else: |
| 3292 | raise TypeError,"symmetric: Unknown argument type." |
| 3293 | |
| 3294 | def escript_symmetric(arg): # this should be implemented in c++ |
| 3295 | if arg.getRank()==2: |
| 3296 | if not (arg.getShape()[0]==arg.getShape()[1]): |
| 3297 | raise ValueError,"escript_symmetric: argument must be square." |
| 3298 | out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace()) |
| 3299 | for i0 in range(arg.getShape()[0]): |
| 3300 | for i1 in range(arg.getShape()[1]): |
| 3301 | out[i0,i1]=(arg[i0,i1]+arg[i1,i0])/2. |
| 3302 | elif arg.getRank()==4: |
| 3303 | if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]): |
| 3304 | raise ValueError,"escript_symmetric: argument must be square." |
| 3305 | out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace()) |
| 3306 | for i0 in range(arg.getShape()[0]): |
| 3307 | for i1 in range(arg.getShape()[1]): |
| 3308 | for i2 in range(arg.getShape()[2]): |
| 3309 | for i3 in range(arg.getShape()[3]): |
| 3310 | out[i0,i1,i2,i3]=(arg[i0,i1,i2,i3]+arg[i2,i3,i0,i1])/2. |
| 3311 | else: |
| 3312 | raise ValueError,"escript_symmetric: rank 2 or 4 is required." |
| 3313 | return out |
| 3314 | |
| 3315 | def nonsymmetric(arg): |
| 3316 | """ |
| 3317 | returns the nonsymmetric part of the square matrix arg. This is (arg-transpose(arg))/2 |
| 3318 | |
| 3319 | @param arg: square matrix. Must have rank 2 or 4 and be square. |
| 3320 | @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol} |
| 3321 | @return: nonsymmetric part of arg |
| 3322 | @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input |
| 3323 | """ |
| 3324 | if isinstance(arg,numarray.NumArray): |
| 3325 | if arg.rank==2: |
| 3326 | if not (arg.shape[0]==arg.shape[1]): |
| 3327 | raise ValueError,"nonsymmetric: argument must be square." |
| 3328 | elif arg.rank==4: |
| 3329 | if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]): |
| 3330 | raise ValueError,"nonsymmetric: argument must be square." |
| 3331 | else: |
| 3332 | raise ValueError,"nonsymmetric: rank 2 or 4 is required." |
| 3333 | return (arg-transpose(arg))/2 |
| 3334 | elif isinstance(arg,escript.Data): |
| 3335 | return escript_nonsymmetric(arg) |
| 3336 | elif isinstance(arg,float): |
| 3337 | return arg |
| 3338 |