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| trunk/esys2/escript/py_src/util.py revision 100 by jgs, Wed Dec 15 03:48:48 2004 UTC | trunk/escript/py_src/util.py revision 492 by gross, Fri Feb 3 02:07:24 2006 UTC | |
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| # | Line 1 | Line 1 |
| 1 | # $Id$ | # $Id$ |
| 2 | # | |
| 3 | ## @file util.py | # COPYRIGHT ACcESS 2004 - All Rights Reserved |
| 4 | # | |
| 5 | # This software is the property of ACcESS. No part of this code | |
| 6 | # may be copied in any form or by any means without the expressed written | |
| 7 | # consent of ACcESS. Copying, use or modification of this software | |
| 8 | # by any unauthorised person is illegal unless that | |
| 9 | # person has a software license agreement with ACcESS. | |
| 10 | # | |
| 11 | ||
| 12 | """ | """ |
| 13 | @brief Utility functions for escript | Utility functions for escript |
| 14 | ||
| 15 | @remark: This module is under construction and is still tested!!! | |
| 16 | ||
| 17 | @var __author__: name of author | |
| 18 | @var __licence__: licence agreement | |
| 19 | @var __url__: url entry point on documentation | |
| 20 | @var __version__: version | |
| 21 | @var __date__: date of the version | |
| 22 | """ | """ |
| 23 | ||
| 24 | __author__="Lutz Gross, l.gross@uq.edu.au" | |
| 25 | __licence__="contact: esys@access.uq.edu.au" | |
| 26 | __url__="http://www.iservo.edu.au/esys/escript" | |
| 27 | __version__="$Revision$" | |
| 28 | __date__="$Date$" | |
| 29 | ||
| 30 | ||
| 31 | import math | |
| 32 | import numarray | import numarray |
| 33 | import numarray.linear_algebra | |
| 34 | import escript | |
| 35 | import os | |
| 36 | ||
| 37 | # missing tests: | |
| 38 | ||
| 39 | # def pokeShape(arg): | |
| 40 | # def pokeDim(arg): | |
| 41 | # def commonShape(arg0,arg1): | |
| 42 | # def commonDim(*args): | |
| 43 | # def testForZero(arg): | |
| 44 | # def matchType(arg0=0.,arg1=0.): | |
| 45 | # def matchShape(arg0,arg1): | |
| 46 | ||
| 47 | # def reorderComponents(arg,index): | |
| 48 | ||
| 49 | # | # |
| 50 | # escript constants: | # slicing: get |
| 51 | # | # set |
| FALSE=0 | ||
| TRUE=1 | ||
| UNKNOWN=-1 | ||
| EPSILON=1.e-15 | ||
| Pi=3.1415926535897931 | ||
| # matrix types | ||
| CSC=0 | ||
| CSR=1 | ||
| LUMPED=10 | ||
| # some solver options: | ||
| NO_REORDERING=0 | ||
| MINIMUM_FILL_IN=1 | ||
| NESTED_DISSECTION=2 | ||
| DEFAULT_METHOD=0 | ||
| PCG=1 | ||
| CR=2 | ||
| CGS=3 | ||
| BICGSTAB=4 | ||
| SSOR=5 | ||
| ILU0=6 | ||
| ILUT=7 | ||
| JACOBI=8 | ||
| # supported file formats: | ||
| VRML=1 | ||
| PNG=2 | ||
| JPEG=3 | ||
| JPG=3 | ||
| PS=4 | ||
| OOGL=5 | ||
| BMP=6 | ||
| TIFF=7 | ||
| OPENINVENTOR=8 | ||
| RENDERMAN=9 | ||
| PNM=10 | ||
| # | ||
| # wrapper for various functions: if the argument has attribute the function name | ||
| # as an argument it calls the correspong methods. Otherwise the coresponsing numarray | ||
| # function is called. | ||
| 52 | # | # |
| 53 | def L2(arg): | # and derivatives |
| 54 | ||
| 55 | #========================================================= | |
| 56 | # some helpers: | |
| 57 | #========================================================= | |
| 58 | def saveVTK(filename,domain=None,**data): | |
| 59 | """ | """ |
| 60 | @brief | writes a L{Data} objects into a files using the the VTK XML file format. |
| 61 | ||
| 62 | Example: | |
| 63 | ||
| 64 | tmp=Scalar(..) | |
| 65 | v=Vector(..) | |
| 66 | saveVTK("solution.xml",temperature=tmp,velovity=v) | |
| 67 | ||
| 68 | @param arg | tmp and v are written into "solution.xml" where tmp is named "temperature" and v is named "velovity" |
| 69 | ||
| 70 | @param filename: file name of the output file | |
| 71 | @type filename: C{str} | |
| 72 | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. | |
| 73 | @type domain: L{escript.Domain} | |
| 74 | @keyword <name>: writes the assigned value to the VTK file using <name> as identifier. | |
| 75 | @type <name>: L{Data} object. | |
| 76 | @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. | |
| 77 | """ | """ |
| 78 | return arg.L2() | if domain==None: |
| 79 | for i in data.keys(): | |
| 80 | if not data[i].isEmpty(): domain=data[i].getFunctionSpace().getDomain() | |
| 81 | if domain==None: | |
| 82 | raise ValueError,"no domain detected." | |
| 83 | else: | |
| 84 | domain.saveVTK(filename,data) | |
| 85 | ||
| 86 | def grad(arg,where=None): | def saveDX(filename,domain=None,**data): |
| 87 | """ | """ |
| 88 | @brief | writes a L{Data} objects into a files using the the DX file format. |
| 89 | ||
| 90 | Example: | |
| 91 | ||
| 92 | @param arg | tmp=Scalar(..) |
| 93 | @param where | v=Vector(..) |
| 94 | saveDX("solution.dx",temperature=tmp,velovity=v) | |
| 95 | ||
| 96 | tmp and v are written into "solution.dx" where tmp is named "temperature" and v is named "velovity". | |
| 97 | ||
| 98 | @param filename: file name of the output file | |
| 99 | @type filename: C{str} | |
| 100 | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. | |
| 101 | @type domain: L{escript.Domain} | |
| 102 | @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. | |
| 103 | @type <name>: L{Data} object. | |
| 104 | @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. | |
| 105 | """ | """ |
| 106 | if where==None: | if domain==None: |
| 107 | return arg.grad() | for i in data.keys(): |
| 108 | if not data[i].isEmpty(): domain=data[i].getFunctionSpace().getDomain() | |
| 109 | if domain==None: | |
| 110 | raise ValueError,"no domain detected." | |
| 111 | else: | else: |
| 112 | return arg.grad(where) | domain.saveDX(filename,data) |
| 113 | ||
| 114 | def kronecker(d=3): | |
| 115 | """ | |
| 116 | return the kronecker S{delta}-symbol | |
| 117 | ||
| 118 | @param d: dimension or an object that has the C{getDim} method defining the dimension | |
| 119 | @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace} | |
| 120 | @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise | |
| 121 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2. | |
| 122 | """ | |
| 123 | return identityTensor(d) | |
| 124 | ||
| 125 | def identity(shape=()): | |
| 126 | """ | |
| 127 | return the shape x shape identity tensor | |
| 128 | ||
| 129 | @param shape: input shape for the identity tensor | |
| 130 | @type shape: C{tuple} of C{int} | |
| 131 | @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. | |
| 132 | @rtype: L{numarray.NumArray} of rank 1, rankk 2 or rank 4. | |
| 133 | @raise ValueError: if len(shape)>2. | |
| 134 | """ | |
| 135 | if len(shape)>0: | |
| 136 | out=numarray.zeros(shape+shape,numarray.Float) | |
| 137 | if len(shape)==1: | |
| 138 | for i0 in range(shape[0]): | |
| 139 | out[i0,i0]=1. | |
| 140 | elif len(shape)==2: | |
| 141 | for i0 in range(shape[0]): | |
| 142 | for i1 in range(shape[1]): | |
| 143 | out[i0,i1,i0,i1]=1. | |
| 144 | else: | |
| 145 | raise ValueError,"identity: length of shape is restricted to 2." | |
| 146 | else: | |
| 147 | out=1. | |
| 148 | return out | |
| 149 | ||
| 150 | def identityTensor(d=3): | |
| 151 | """ | |
| 152 | return the dxd identity matrix | |
| 153 | ||
| 154 | @param d: dimension or an object that has the C{getDim} method defining the dimension | |
| 155 | @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace} | |
| 156 | @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise | |
| 157 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2 | |
| 158 | """ | |
| 159 | if isinstance(d,escript.FunctionSpace): | |
| 160 | return escript.Data(identity((d.getDim(),)),d) | |
| 161 | elif isinstance(d,escript.Domain): | |
| 162 | return identity((d.getDim(),)) | |
| 163 | else: | |
| 164 | return identity((d,)) | |
| 165 | ||
| 166 | def identityTensor4(d=3): | |
| 167 | """ | |
| 168 | return the dxdxdxd identity tensor | |
| 169 | ||
| 170 | @param d: dimension or an object that has the C{getDim} method defining the dimension | |
| 171 | @type d: C{int} or any object with a C{getDim} method | |
| 172 | @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 | |
| 173 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 4. | |
| 174 | """ | |
| 175 | if isinstance(d,escript.FunctionSpace): | |
| 176 | return escript.Data(identity((d.getDim(),d.getDim())),d) | |
| 177 | elif isinstance(d,escript.Domain): | |
| 178 | return identity((d.getDim(),d.getDim())) | |
| 179 | else: | |
| 180 | return identity((d,d)) | |
| 181 | ||
| 182 | def unitVector(i=0,d=3): | |
| 183 | """ | |
| 184 | return a unit vector u of dimension d with nonzero index i: | |
| 185 | ||
| 186 | @param i: index | |
| 187 | @type i: C{int} | |
| 188 | @param d: dimension or an object that has the C{getDim} method defining the dimension | |
| 189 | @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace} | |
| 190 | @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise | |
| 191 | @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 1 | |
| 192 | """ | |
| 193 | return kronecker(d)[i] | |
| 194 | ||
| 195 | def integrate(arg): | #========================================================================= |
| 196 | # global reduction operations (these functions have no symbolic version) | |
| 197 | #========================================================================= | |
| 198 | def Lsup(arg): | |
| 199 | """ | """ |
| 200 | @brief | returns the Lsup-norm of argument arg. This is the maximum absolute value over all data points. |
| 201 | This function is equivalent to sup(abs(arg)). | |
| 202 | ||
| 203 | @param arg | @param arg: argument |
| 204 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 205 | @return: maximum value of the absolute value of arg over all components and all data points | |
| 206 | @rtype: C{float} | |
| 207 | @raise TypeError: if type of arg cannot be processed | |
| 208 | """ | """ |
| 209 | return arg.integrate() | if isinstance(arg,numarray.NumArray): |
| 210 | return sup(abs(arg)) | |
| 211 | elif isinstance(arg,escript.Data): | |
| 212 | return arg._Lsup() | |
| 213 | elif isinstance(arg,float): | |
| 214 | return abs(arg) | |
| 215 | elif isinstance(arg,int): | |
| 216 | return abs(float(arg)) | |
| 217 | else: | |
| 218 | raise TypeError,"Lsup: Unknown argument type." | |
| 219 | ||
| 220 | def interpolate(arg,where): | def sup(arg): |
| 221 | """ | """ |
| 222 | @brief | returns the maximum value over all data points. |
| 223 | ||
| 224 | @param arg | @param arg: argument |
| 225 | @param where | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. |
| 226 | @return: maximum value of arg over all components and all data points | |
| 227 | @rtype: C{float} | |
| 228 | @raise TypeError: if type of arg cannot be processed | |
| 229 | """ | """ |
| 230 | return arg.interpolate(where) | if isinstance(arg,numarray.NumArray): |
| 231 | return arg.max() | |
| 232 | elif isinstance(arg,escript.Data): | |
| 233 | return arg._sup() | |
| 234 | elif isinstance(arg,float): | |
| 235 | return arg | |
| 236 | elif isinstance(arg,int): | |
| 237 | return float(arg) | |
| 238 | else: | |
| 239 | raise TypeError,"sup: Unknown argument type." | |
| 240 | ||
| 241 | def transpose(arg): | def inf(arg): |
| 242 | """ | """ |
| 243 | @brief | returns the maximum value over all data points. |
| 244 | ||
| 245 | @param arg | @param arg: argument |
| 246 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 247 | @return : minimum value of arg over all components and all data points | |
| 248 | @rtype: C{float} | |
| 249 | @raise TypeError: if type of arg cannot be processed | |
| 250 | """ | """ |
| 251 | if hasattr(arg,"transpose"): | if isinstance(arg,numarray.NumArray): |
| 252 | return arg.transpose() | return arg.min() |
| 253 | elif isinstance(arg,escript.Data): | |
| 254 | return arg._inf() | |
| 255 | elif isinstance(arg,float): | |
| 256 | return arg | |
| 257 | elif isinstance(arg,int): | |
| 258 | return float(arg) | |
| 259 | else: | else: |
| 260 | return numarray.transpose(arg,axis=None) | raise TypeError,"inf: Unknown argument type." |
| 261 | ||
| 262 | def trace(arg): | |
| 263 | #========================================================================= | |
| 264 | # some little helpers | |
| 265 | #========================================================================= | |
| 266 | def pokeShape(arg): | |
| 267 | """ | """ |
| 268 | @brief | identifies the shape of its argument |
| 269 | ||
| 270 | @param arg | @param arg: a given object |
| 271 | @type arg: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 272 | @return: the shape of the argument | |
| 273 | @rtype: C{tuple} of C{int} | |
| 274 | @raise TypeError: if type of arg cannot be processed | |
| 275 | """ | """ |
| 276 | if hasattr(arg,"trace"): | |
| 277 | return arg.trace() | if isinstance(arg,numarray.NumArray): |
| 278 | return arg.shape | |
| 279 | elif isinstance(arg,escript.Data): | |
| 280 | return arg.getShape() | |
| 281 | elif isinstance(arg,float): | |
| 282 | return () | |
| 283 | elif isinstance(arg,int): | |
| 284 | return () | |
| 285 | elif isinstance(arg,Symbol): | |
| 286 | return arg.getShape() | |
| 287 | else: | else: |
| 288 | return numarray.trace(arg,k=0) | raise TypeError,"pokeShape: cannot identify shape" |
| 289 | ||
| 290 | def exp(arg): | def pokeDim(arg): |
| 291 | """ | """ |
| 292 | @brief | identifies the spatial dimension of its argument |
| 293 | ||
| 294 | @param arg | @param arg: a given object |
| 295 | @type arg: any | |
| 296 | @return: the spatial dimension of the argument, if available, or C{None} | |
| 297 | @rtype: C{int} or C{None} | |
| 298 | """ | """ |
| 299 | if hasattr(arg,"exp"): | |
| 300 | return arg.exp() | if isinstance(arg,escript.Data): |
| 301 | return arg.getFunctionSpace().getDim() | |
| 302 | elif isinstance(arg,Symbol): | |
| 303 | return arg.getDim() | |
| 304 | else: | else: |
| 305 | return numarray.exp(arg) | return None |
| 306 | ||
| 307 | def sqrt(arg): | def commonShape(arg0,arg1): |
| 308 | """ | """ |
| 309 | @brief | returns a shape to which arg0 can be extendent from the right and arg1 can be extended from the left. |
| 310 | ||
| 311 | @param arg | @param arg0: an object with a shape (see L{pokeShape}) |
| 312 | @param arg1: an object with a shape (see L{pokeShape}) | |
| 313 | @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. | |
| 314 | @rtype: C{tuple} of C{int} | |
| 315 | @raise ValueError: if no shape can be found. | |
| 316 | """ | """ |
| 317 | if hasattr(arg,"sqrt"): | sh0=pokeShape(arg0) |
| 318 | return arg.sqrt() | sh1=pokeShape(arg1) |
| 319 | if len(sh0)<len(sh1): | |
| 320 | if not sh0==sh1[:len(sh0)]: | |
| 321 | raise ValueError,"argument 0 cannot be extended to the shape of argument 1" | |
| 322 | return sh1 | |
| 323 | elif len(sh0)>len(sh1): | |
| 324 | if not sh1==sh0[:len(sh1)]: | |
| 325 | raise ValueError,"argument 1 cannot be extended to the shape of argument 0" | |
| 326 | return sh0 | |
| 327 | else: | else: |
| 328 | return numarray.sqrt(arg) | if not sh0==sh1: |
| 329 | raise ValueError,"argument 1 and argument 0 have not the same shape." | |
| 330 | return sh0 | |
| 331 | ||
| 332 | def sin(arg): | def commonDim(*args): |
| 333 | """ | |
| 334 | identifies, if possible, the spatial dimension across a set of objects which may or my not have a spatial dimension. | |
| 335 | ||
| 336 | @param *args: given objects | |
| 337 | @return: the spatial dimension of the objects with identifiable dimension (see L{pokeDim}). If none the objects has | |
| 338 | a spatial dimension C{None} is returned. | |
| 339 | @rtype: C{int} or C{None} | |
| 340 | @raise ValueError: if the objects with identifiable dimension don't have the same spatial dimension. | |
| 341 | """ | |
| 342 | out=None | |
| 343 | for a in args: | |
| 344 | d=pokeDim(a) | |
| 345 | if not out==None: | |
| 346 | if not (d==None or out==d): | |
| 347 | raise ValueError,"dimension of arguments don't match" | |
| 348 | else: | |
| 349 | out=d | |
| 350 | return out | |
| 351 | ||
| 352 | def testForZero(arg): | |
| 353 | """ | """ |
| 354 | @brief | test the argument for being identical to Zero |
| 355 | ||
| 356 | @param arg | @param arg: a given object |
| 357 | @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int} | |
| 358 | @return : True if the argument is identical to zero. | |
| 359 | @rtype : C{bool} | |
| 360 | """ | """ |
| 361 | if hasattr(arg,"sin"): | if isinstance(arg,numarray.NumArray): |
| 362 | return arg.sin() | return not Lsup(arg)>0. |
| 363 | elif isinstance(arg,escript.Data): | |
| 364 | return False | |
| 365 | elif isinstance(arg,float): | |
| 366 | return not Lsup(arg)>0. | |
| 367 | elif isinstance(arg,int): | |
| 368 | return not Lsup(arg)>0. | |
| 369 | elif isinstance(arg,Symbol): | |
| 370 | return False | |
| 371 | else: | else: |
| 372 | return numarray.sin(arg) | return False |
| 373 | ||
| 374 | def cos(arg): | def matchType(arg0=0.,arg1=0.): |
| 375 | """ | """ |
| 376 | @brief | 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}. |
| 377 | ||
| 378 | @param arg | @param arg0: first argument |
| 379 | @type arg0: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 380 | @param arg1: second argument | |
| 381 | @type arg1: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 382 | @return: a tuple representing arg0 and arg1 with the same type or with one of them being a L{Symbol} | |
| 383 | @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}. | |
| 384 | @raise TypeError: if type of arg0 or arg1 cannot be processed | |
| 385 | """ | """ |
| 386 | if hasattr(arg,"cos"): | if isinstance(arg0,numarray.NumArray): |
| 387 | return arg.cos() | if isinstance(arg1,numarray.NumArray): |
| 388 | pass | |
| 389 | elif isinstance(arg1,escript.Data): | |
| 390 | arg0=escript.Data(arg0,arg1.getFunctionSpace()) | |
| 391 | elif isinstance(arg1,float): | |
| 392 | arg1=numarray.array(arg1) | |
| 393 | elif isinstance(arg1,int): | |
| 394 | arg1=numarray.array(float(arg1)) | |
| 395 | elif isinstance(arg1,Symbol): | |
| 396 | pass | |
| 397 | else: | |
| 398 | raise TypeError,"function: Unknown type of second argument." | |
| 399 | elif isinstance(arg0,escript.Data): | |
| 400 | if isinstance(arg1,numarray.NumArray): | |
| 401 | arg1=escript.Data(arg1,arg0.getFunctionSpace()) | |
| 402 | elif isinstance(arg1,escript.Data): | |
| 403 | pass | |
| 404 | elif isinstance(arg1,float): | |
| 405 | arg1=escript.Data(arg1,(),arg0.getFunctionSpace()) | |
| 406 | elif isinstance(arg1,int): | |
| 407 | arg1=escript.Data(float(arg1),(),arg0.getFunctionSpace()) | |
| 408 | elif isinstance(arg1,Symbol): | |
| 409 | pass | |
| 410 | else: | |
| 411 | raise TypeError,"function: Unknown type of second argument." | |
| 412 | elif isinstance(arg0,Symbol): | |
| 413 | if isinstance(arg1,numarray.NumArray): | |
| 414 | pass | |
| 415 | elif isinstance(arg1,escript.Data): | |
| 416 | pass | |
| 417 | elif isinstance(arg1,float): | |
| 418 | arg1=numarray.array(arg1) | |
| 419 | elif isinstance(arg1,int): | |
| 420 | arg1=numarray.array(float(arg1)) | |
| 421 | elif isinstance(arg1,Symbol): | |
| 422 | pass | |
| 423 | else: | |
| 424 | raise TypeError,"function: Unknown type of second argument." | |
| 425 | elif isinstance(arg0,float): | |
| 426 | if isinstance(arg1,numarray.NumArray): | |
| 427 | arg0=numarray.array(arg0) | |
| 428 | elif isinstance(arg1,escript.Data): | |
| 429 | arg0=escript.Data(arg0,arg1.getFunctionSpace()) | |
| 430 | elif isinstance(arg1,float): | |
| 431 | arg0=numarray.array(arg0) | |
| 432 | arg1=numarray.array(arg1) | |
| 433 | elif isinstance(arg1,int): | |
| 434 | arg0=numarray.array(arg0) | |
| 435 | arg1=numarray.array(float(arg1)) | |
| 436 | elif isinstance(arg1,Symbol): | |
| 437 | arg0=numarray.array(arg0) | |
| 438 | else: | |
| 439 | raise TypeError,"function: Unknown type of second argument." | |
| 440 | elif isinstance(arg0,int): | |
| 441 | if isinstance(arg1,numarray.NumArray): | |
| 442 | arg0=numarray.array(float(arg0)) | |
| 443 | elif isinstance(arg1,escript.Data): | |
| 444 | arg0=escript.Data(float(arg0),arg1.getFunctionSpace()) | |
| 445 | elif isinstance(arg1,float): | |
| 446 | arg0=numarray.array(float(arg0)) | |
| 447 | arg1=numarray.array(arg1) | |
| 448 | elif isinstance(arg1,int): | |
| 449 | arg0=numarray.array(float(arg0)) | |
| 450 | arg1=numarray.array(float(arg1)) | |
| 451 | elif isinstance(arg1,Symbol): | |
| 452 | arg0=numarray.array(float(arg0)) | |
| 453 | else: | |
| 454 | raise TypeError,"function: Unknown type of second argument." | |
| 455 | else: | else: |
| 456 | return numarray.cos(arg) | raise TypeError,"function: Unknown type of first argument." |
| 457 | ||
| 458 | def maxval(arg): | return arg0,arg1 |
| 459 | ||
| 460 | def matchShape(arg0,arg1): | |
| 461 | """ | """ |
| 462 | @brief | |
| 463 | ||
| 464 | If shape is not given the shape "largest" shape of args is used. | |
| 465 | ||
| 466 | @param arg | @param args: a given ob |
| 467 | @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int} | |
| 468 | @return: True if the argument is identical to zero. | |
| 469 | @rtype: C{list} of C{int} | |
| 470 | """ | """ |
| 471 | return arg.maxval() | sh=commonShape(arg0,arg1) |
| 472 | sh0=pokeShape(arg0) | |
| 473 | sh1=pokeShape(arg1) | |
| 474 | if len(sh0)<len(sh): | |
| 475 | return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float)),arg1 | |
| 476 | elif len(sh1)<len(sh): | |
| 477 | return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float)) | |
| 478 | else: | |
| 479 | return arg0,arg1 | |
| 480 | #========================================================= | |
| 481 | # symbolic tool box starts here: | |
| 482 | #========================================================= | |
| 483 | class Symbol(object): | |
| 484 | """ | |
| 485 | Symbol class. | |
| 486 | ||
| 487 | Symbol class objects provide the same functionality as L{numarray.NumArray} and L{escript.Data} objects | |
| 488 | but they do not have a value and therefore cannot be plotted or visualize. The main purpose is the possibilty | |
| 489 | calculate derivatives with respect to other Symbols used to define a Symbol. | |
| 490 | ||
| 491 | """ | |
| 492 | def __init__(self,shape=(),args=[],dim=None): | |
| 493 | """ | |
| 494 | Creates an instance of a symbol of a given shape. The symbol may depending on a list of arguments args which may be | |
| 495 | symbols or any other object. | |
| 496 | ||
| 497 | @param arg: the arguments of the symbol. | |
| 498 | @type arg: C{list} | |
| 499 | @param shape: the shape | |
| 500 | @type shape: C{tuple} of C{int} | |
| 501 | @param dim: spatial dimension of the symbol. If dim=C{None} the spatial dimension is undefined. | |
| 502 | @type dim: C{None} or C{int} | |
| 503 | ||
| 504 | """ | |
| 505 | if len(shape)>4: | |
| 506 | raise ValueError,"Symbol supports only tensors up to order 4" | |
| 507 | self.__args=args | |
| 508 | self.__shape=shape | |
| 509 | self.__dim=dim | |
| 510 | ||
| 511 | def getArgument(self,i=None): | |
| 512 | """ | |
| 513 | returns the i-th argument of the symbol | |
| 514 | ||
| 515 | @param i: index of the argument requested. | |
| 516 | @type i: C{int} or C{None} | |
| 517 | @raise IndexError: if the requested index does not exist | |
| 518 | @return: the vlaue of the i-th argument or i is not specified the list of all arguments. | |
| 519 | @rtype: a single object or a list of objects | |
| 520 | """ | |
| 521 | if i==None: | |
| 522 | return self.__args | |
| 523 | else: | |
| 524 | if i<0 or i>=len(self.__args): | |
| 525 | raise IndexError,"there are only %s arguments"%len(self.__args) | |
| 526 | return self.__args[i] | |
| 527 | ||
| 528 | def getRank(self): | |
| 529 | """ | |
| 530 | the rank of the symbol | |
| 531 | ||
| 532 | @return: the rank of the symbol. This is length of the shape | |
| 533 | @rtype: C{int} | |
| 534 | """ | |
| 535 | return len(self.getShape()) | |
| 536 | ||
| 537 | def getShape(self): | |
| 538 | """ | |
| 539 | the shape of the symbol. | |
| 540 | ||
| 541 | @return : the shape of the symbol. | |
| 542 | @rtype: C{tuple} of C{int} | |
| 543 | """ | |
| 544 | return self.__shape | |
| 545 | ||
| 546 | def getDim(self): | |
| 547 | """ | |
| 548 | the spatial dimension | |
| 549 | ||
| 550 | @return : the spatial dimension | |
| 551 | @rtype: C{int} if the dimension is defined. Otherwise C{None} is returned. | |
| 552 | """ | |
| 553 | return self.__dim | |
| 554 | ||
| 555 | def __str__(self): | |
| 556 | """ | |
| 557 | a string representation of the symbol. | |
| 558 | @return: a string representation of the object | |
| 559 | @rtype: C{str} | |
| 560 | """ | |
| 561 | args=[] | |
| 562 | for arg in self.getArgument(): | |
| 563 | args.append(str(arg)) | |
| 564 | try: | |
| 565 | out=self.getMyCode(args,format="str") | |
| 566 | except NotImplementedError: | |
| 567 | out="<Symbol %s>"%id(self) | |
| 568 | return out | |
| 569 | ||
| 570 | def getSubstitutedArguments(self,argvals): | |
| 571 | """ | |
| 572 | substitutes symbols in the arguments of this object and returns the result as a list. | |
| 573 | ||
| 574 | @param argvals: L{Symbols} and their substitutes. The L{Symbol} u in the expression defining this object is replaced by argvals[u]. | |
| 575 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 576 | @rtype: C{list} of objects | |
| 577 | @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. | |
| 578 | """ | |
| 579 | out=[] | |
| 580 | for a in self.getArgument(): | |
| 581 | if isinstance(a,Symbol): | |
| 582 | out.append(a.substitute(argvals)) | |
| 583 | else: | |
| 584 | out.append(a) | |
| 585 | return out | |
| 586 | ||
| 587 | def getDifferentiatedArguments(self,arg): | |
| 588 | """ | |
| 589 | applifies differentials to the arguments of this object and returns the result as a list. | |
| 590 | ||
| 591 | @param arg: the derivative is calculated with respect to arg | |
| 592 | @type arg: typically L{escript.Symbol} but can also be C{float}, L{escript.Data}, L{numarray.NumArray} depending the involved functions and data. | |
| 593 | @rtype: C{list} of objects | |
| 594 | @return: list of object obtained by calculating the derivatives of the argumenst with respct to arg | |
| 595 | """ | |
| 596 | out=[] | |
| 597 | for a in self.getArgument(): | |
| 598 | if isinstance(a,Symbol): | |
| 599 | out.append(a.substitute(argvals)) | |
| 600 | else: | |
| 601 | s=pokeShape(s)+arg.getShape() | |
| 602 | if len(s)>0: | |
| 603 | out.append(numarray.zeros(s),numarray.Float) | |
| 604 | else: | |
| 605 | out.append(a) | |
| 606 | return out | |
| 607 | ||
| 608 | def isAppropriateValue(self,arg): | |
| 609 | """ | |
| 610 | checks if the given argument arg can be used as a substitution of this object. The method checks | |
| 611 | the shape of arg and, if the spatial dimension is defined, the spatial dimension of arg. | |
| 612 | ||
| 613 | @param arg: a given object | |
| 614 | @type arg: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 615 | @return: True if arg is a suitbale object to be used for substitution. Otherwise False is returned. | |
| 616 | @rtype: C{bool} | |
| 617 | """ | |
| 618 | if isinstance(arg,numarray.NumArray): | |
| 619 | return arg.shape==self.getShape() | |
| 620 | elif isinstance(arg,escript.Data): | |
| 621 | if self.getDim()==None: | |
| 622 | return arg.getShape()==self.getShape() | |
| 623 | elif self.getDim()==arg.getFunctionSpace().getDim(): | |
| 624 | return arg.getShape()==self.getShape() | |
| 625 | else: | |
| 626 | return False | |
| 627 | elif isinstance(arg,Symbol): | |
| 628 | if self.getDim()==None: | |
| 629 | return arg.getShape()==self.getShape() | |
| 630 | elif self.getDim()==arg.getDim(): | |
| 631 | return arg.getShape()==self.getShape() | |
| 632 | else: | |
| 633 | return False | |
| 634 | elif isinstance(arg,float): | |
| 635 | return ()==self.getShape() | |
| 636 | elif isinstance(arg,int): | |
| 637 | return ()==self.getShape() | |
| 638 | else: | |
| 639 | return False | |
| 640 | ||
| 641 | def getMyCode(self,argstrs,format="escript"): | |
| 642 | """ | |
| 643 | returns a program code that can be used to evaluate the symbol. | |
| 644 | ||
| 645 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 646 | @type argstrs: C{list} of C{str}. | |
| 647 | @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported. | |
| 648 | @type format: C{str} | |
| 649 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 650 | @rtype: C{str} | |
| 651 | @raise NotImplementedError: if no implementation for the given format is available | |
| 652 | @note: This method has to be overwritten by subclasses. | |
| 653 | """ | |
| 654 | raise NotImplementedError,"no code for %s representation available"%format | |
| 655 | ||
| 656 | def substitute(self,argvals): | |
| 657 | """ | |
| 658 | assigns new values to symbols in the definition of the symbol. | |
| 659 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 660 | ||
| 661 | @param argvals: new values assigned to symbols | |
| 662 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 663 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 664 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 665 | @note: this method has to be overwritten by a particular L{Symbol} | |
| 666 | @raise NotImplementedError: if no implementation for the given format is available | |
| 667 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 668 | """ | |
| 669 | if argvals.has_key(self): | |
| 670 | arg=argvals[self] | |
| 671 | if self.isAppropriateValue(arg): | |
| 672 | return arg | |
| 673 | else: | |
| 674 | raise TypeError,"Symbol: new value is not appropriate." | |
| 675 | else: | |
| 676 | raise NotImplementedError,"no substitution in %s avialable"%str(self) | |
| 677 | ||
| 678 | def diff(self,arg): | |
| 679 | """ | |
| 680 | returns the derivative of the symbol with respect to L{Symbol} arg | |
| 681 | ||
| 682 | @param arg: the derivative is calculated with respect to arg | |
| 683 | @type arg: typically L{escript.Symbol} but can also be C{float}, L{escript.Data}, L{numarray.NumArray} depending the involved functions and data. | |
| 684 | @return: derivative with respect to C{arg} | |
| 685 | @rtype: typically L{escript.Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 686 | @note: this method is overwritten by a particular L{Symbol} | |
| 687 | """ | |
| 688 | if arg==self: | |
| 689 | return identity(self.getShape()) | |
| 690 | else: | |
| 691 | s=self.getShape()+arg.getShape() | |
| 692 | if len(s)>0: | |
| 693 | return numarray.zeros(s,numarray.Float) | |
| 694 | else: | |
| 695 | return 0. | |
| 696 | ||
| 697 | def __neg__(self): | |
| 698 | """ | |
| 699 | returns -self. | |
| 700 | ||
| 701 | @return: a S{Symbol} representing the negative of the object | |
| 702 | @rtype: L{DependendSymbol} | |
| 703 | """ | |
| 704 | return self*(-1.) | |
| 705 | ||
| 706 | def __pos__(self): | |
| 707 | """ | |
| 708 | returns +self. | |
| 709 | ||
| 710 | @return: a S{Symbol} representing the positive of the object | |
| 711 | @rtype: L{DependendSymbol} | |
| 712 | """ | |
| 713 | return self*(1.) | |
| 714 | ||
| 715 | def __abs__(self): | |
| 716 | """ | |
| 717 | returns a S{Symbol} representing the absolute value of the object. | |
| 718 | """ | |
| 719 | return Abs_Symbol(self) | |
| 720 | ||
| 721 | def __add__(self,other): | |
| 722 | """ | |
| 723 | add another object to this object | |
| 724 | ||
| 725 | @param other: object to be added to this object | |
| 726 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 727 | @return: a S{Symbol} representing the sum of this object and C{other} | |
| 728 | @rtype: L{DependendSymbol} | |
| 729 | """ | |
| 730 | return add(self,other) | |
| 731 | ||
| 732 | def __radd__(self,other): | |
| 733 | """ | |
| 734 | add this object to another object | |
| 735 | ||
| 736 | @param other: object this object is added to | |
| 737 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 738 | @return: a S{Symbol} representing the sum of C{other} and this object object | |
| 739 | @rtype: L{DependendSymbol} | |
| 740 | """ | |
| 741 | return add(other,self) | |
| 742 | ||
| 743 | def __sub__(self,other): | |
| 744 | """ | |
| 745 | subtracts another object from this object | |
| 746 | ||
| 747 | @param other: object to be subtracted from this object | |
| 748 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 749 | @return: a S{Symbol} representing the difference of C{other} and this object | |
| 750 | @rtype: L{DependendSymbol} | |
| 751 | """ | |
| 752 | return add(self,-other) | |
| 753 | ||
| 754 | def __rsub__(self,other): | |
| 755 | """ | |
| 756 | subtracts this object from another object | |
| 757 | ||
| 758 | @param other: object this object is been subtracted from | |
| 759 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 760 | @return: a S{Symbol} representing the difference of this object and C{other}. | |
| 761 | @rtype: L{DependendSymbol} | |
| 762 | """ | |
| 763 | return add(-self,other) | |
| 764 | ||
| 765 | def __mul__(self,other): | |
| 766 | """ | |
| 767 | multiplies this object with other object | |
| 768 | ||
| 769 | @param other: object to be mutiplied by this object | |
| 770 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 771 | @return: a S{Symbol} representing the product of the object and C{other}. | |
| 772 | @rtype: L{DependendSymbol} or 0 if other is identical to zero. | |
| 773 | """ | |
| 774 | return mult(self,other) | |
| 775 | ||
| 776 | def __rmul__(self,other): | |
| 777 | """ | |
| 778 | multiplies this object with other object | |
| 779 | ||
| 780 | @param other: object this object is multiplied with | |
| 781 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 782 | @return: a S{Symbol} representing the product of C{other} and the object. | |
| 783 | @rtype: L{DependendSymbol} or 0 if other is identical to zero. | |
| 784 | """ | |
| 785 | return mult(other,self) | |
| 786 | ||
| 787 | def __div__(self,other): | |
| 788 | """ | |
| 789 | divides this object by other object | |
| 790 | ||
| 791 | @param other: object dividing this object | |
| 792 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 793 | @return: a S{Symbol} representing the quotient of this object and C{other} | |
| 794 | @rtype: L{DependendSymbol} | |
| 795 | """ | |
| 796 | return quotient(self,other) | |
| 797 | ||
| 798 | def __rdiv__(self,other): | |
| 799 | """ | |
| 800 | divides this object by other object | |
| 801 | ||
| 802 | @param other: object dividing this object | |
| 803 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 804 | @return: a S{Symbol} representing the quotient of C{other} and this object | |
| 805 | @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero. | |
| 806 | """ | |
| 807 | return quotient(other,self) | |
| 808 | ||
| 809 | def __pow__(self,other): | |
| 810 | """ | |
| 811 | raises this object to the power of other | |
| 812 | ||
| 813 | @param other: exponent | |
| 814 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 815 | @return: a S{Symbol} representing the power of this object to C{other} | |
| 816 | @rtype: L{DependendSymbol} or 1 if C{other} is identical to zero. | |
| 817 | """ | |
| 818 | return power(self,other) | |
| 819 | ||
| 820 | def __rpow__(self,other): | |
| 821 | """ | |
| 822 | raises an object to the power of this object | |
| 823 | ||
| 824 | @param other: basis | |
| 825 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 826 | @return: a S{Symbol} representing the power of C{other} to this object | |
| 827 | @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero. | |
| 828 | """ | |
| 829 | return power(other,self) | |
| 830 | ||
| 831 | class DependendSymbol(Symbol): | |
| 832 | """ | |
| 833 | DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal. | |
| 834 | 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 | |
| 835 | ||
| 836 | Example: | |
| 837 | ||
| 838 | u1=Symbol(shape=(3,4),dim=2,args=[4.]) | |
| 839 | u2=Symbol(shape=(3,4),dim=2,args=[4.]) | |
| 840 | print u1==u2 | |
| 841 | False | |
| 842 | ||
| 843 | but | |
| 844 | ||
| 845 | u1=DependendSymbol(shape=(3,4),dim=2,args=[4.]) | |
| 846 | u2=DependendSymbol(shape=(3,4),dim=2,args=[4.]) | |
| 847 | u3=DependendSymbol(shape=(2,),dim=2,args=[4.]) | |
| 848 | print u1==u2, u1==u3 | |
| 849 | True False | |
| 850 | ||
| 851 | @note: DependendSymbol should be used as return value of functions with L{Symbol} arguments. This will allow the optimizer to remove redundant function calls. | |
| 852 | """ | |
| 853 | def __eq__(self,other): | |
| 854 | """ | |
| 855 | checks if other equals self | |
| 856 | ||
| 857 | @param other: any object | |
| 858 | @return: True if other has the same class like self, and the shape, the spatial diemsnion and the arguments are equal. | |
| 859 | @rtype: C{bool} | |
| 860 | """ | |
| 861 | if isinstance(other,DependendSymbol): | |
| 862 | if self.__class__==other.__class__: | |
| 863 | if self.getShape()==other.getShape(): | |
| 864 | if self.getArgument()==other.getArgument(): | |
| 865 | if self.getDim()==None or other.getDim()==None or self.getDim()==other.getDim(): | |
| 866 | return True | |
| 867 | return False | |
| 868 | ||
| 869 | def __ne__(self,other): | |
| 870 | """ | |
| 871 | checks if other equals self | |
| 872 | ||
| 873 | @param other: any object | |
| 874 | @return: Flase if other has the same class like self, and the shape, the spatial diemsnion and the arguments are equal. | |
| 875 | @rtype: C{bool} | |
| 876 | """ | |
| 877 | return not self==other | |
| 878 | #========================================================= | |
| 879 | # Unary operations prserving the shape | |
| 880 | #======================================================== | |
| 881 | def log10(arg): | |
| 882 | """ | |
| 883 | returns base-10 logarithm of argument arg | |
| 884 | ||
| 885 | @param arg: argument | |
| 886 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 887 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 888 | @raises TypeError: if the type of the argument is not expected. | |
| 889 | """ | |
| 890 | if isinstance(arg,numarray.NumArray): | |
| 891 | return numarray.log10(arg) | |
| 892 | elif isinstance(arg,escript.Data): | |
| 893 | return arg._log10() | |
| 894 | elif isinstance(arg,float): | |
| 895 | return math.log10(arg) | |
| 896 | elif isinstance(arg,int): | |
| 897 | return math.log10(float(arg)) | |
| 898 | elif isinstance(arg,Symbol): | |
| 899 | return log(arg)/log(10.) | |
| 900 | else: | |
| 901 | raise TypeError,"log10: Unknown argument type." | |
| 902 | ||
| 903 | def wherePositive(arg): | |
| 904 | """ | |
| 905 | returns mask of positive values of argument arg | |
| 906 | ||
| 907 | @param arg: argument | |
| 908 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 909 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 910 | @raises TypeError: if the type of the argument is not expected. | |
| 911 | """ | |
| 912 | if isinstance(arg,numarray.NumArray): | |
| 913 | out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))*1. | |
| 914 | if isinstance(out,float): out=numarray.array(out) | |
| 915 | return out | |
| 916 | elif isinstance(arg,escript.Data): | |
| 917 | return arg._wherePositive() | |
| 918 | elif isinstance(arg,float): | |
| 919 | if arg>0: | |
| 920 | return 1. | |
| 921 | else: | |
| 922 | return 0. | |
| 923 | elif isinstance(arg,int): | |
| 924 | if arg>0: | |
| 925 | return 1. | |
| 926 | else: | |
| 927 | return 0. | |
| 928 | elif isinstance(arg,Symbol): | |
| 929 | return WherePositive_Symbol(arg) | |
| 930 | else: | |
| 931 | raise TypeError,"wherePositive: Unknown argument type." | |
| 932 | ||
| 933 | class WherePositive_Symbol(DependendSymbol): | |
| 934 | """ | |
| 935 | L{Symbol} representing the result of the mask of positive values function | |
| 936 | """ | |
| 937 | def __init__(self,arg): | |
| 938 | """ | |
| 939 | initialization of wherePositive L{Symbol} with argument arg | |
| 940 | @param arg: argument of function | |
| 941 | @type arg: typically L{Symbol}. | |
| 942 | """ | |
| 943 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 944 | ||
| 945 | def getMyCode(self,argstrs,format="escript"): | |
| 946 | """ | |
| 947 | returns a program code that can be used to evaluate the symbol. | |
| 948 | ||
| 949 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 950 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 951 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 952 | @type format: C{str} | |
| 953 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 954 | @rtype: C{str} | |
| 955 | @raise: NotImplementedError: if the requested format is not available | |
| 956 | """ | |
| 957 | if isinstance(argstrs,list): | |
| 958 | argstrs=argstrs[0] | |
| 959 | if format=="escript" or format=="str" or format=="text": | |
| 960 | return "wherePositive(%s)"%argstrs | |
| 961 | else: | |
| 962 | raise NotImplementedError,"WherePositive_Symbol does not provide program code for format %s."%format | |
| 963 | ||
| 964 | def substitute(self,argvals): | |
| 965 | """ | |
| 966 | assigns new values to symbols in the definition of the symbol. | |
| 967 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 968 | ||
| 969 | @param argvals: new values assigned to symbols | |
| 970 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 971 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 972 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 973 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 974 | """ | |
| 975 | if argvals.has_key(self): | |
| 976 | arg=argvals[self] | |
| 977 | if self.isAppropriateValue(arg): | |
| 978 | return arg | |
| 979 | else: | |
| 980 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 981 | else: | |
| 982 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 983 | return wherePositive(arg) | |
| 984 | ||
| 985 | def whereNegative(arg): | |
| 986 | """ | |
| 987 | returns mask of positive values of argument arg | |
| 988 | ||
| 989 | @param arg: argument | |
| 990 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 991 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 992 | @raises TypeError: if the type of the argument is not expected. | |
| 993 | """ | |
| 994 | if isinstance(arg,numarray.NumArray): | |
| 995 | out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float))*1. | |
| 996 | if isinstance(out,float): out=numarray.array(out) | |
| 997 | return out | |
| 998 | elif isinstance(arg,escript.Data): | |
| 999 | return arg._whereNegative() | |
| 1000 | elif isinstance(arg,float): | |
| 1001 | if arg<0: | |
| 1002 | return 1. | |
| 1003 | else: | |
| 1004 | return 0. | |
| 1005 | elif isinstance(arg,int): | |
| 1006 | if arg<0: | |
| 1007 | return 1. | |
| 1008 | else: | |
| 1009 | return 0. | |
| 1010 | elif isinstance(arg,Symbol): | |
| 1011 | return WhereNegative_Symbol(arg) | |
| 1012 | else: | |
| 1013 | raise TypeError,"whereNegative: Unknown argument type." | |
| 1014 | ||
| 1015 | class WhereNegative_Symbol(DependendSymbol): | |
| 1016 | """ | |
| 1017 | L{Symbol} representing the result of the mask of positive values function | |
| 1018 | """ | |
| 1019 | def __init__(self,arg): | |
| 1020 | """ | |
| 1021 | initialization of whereNegative L{Symbol} with argument arg | |
| 1022 | @param arg: argument of function | |
| 1023 | @type arg: typically L{Symbol}. | |
| 1024 | """ | |
| 1025 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1026 | ||
| 1027 | def getMyCode(self,argstrs,format="escript"): | |
| 1028 | """ | |
| 1029 | returns a program code that can be used to evaluate the symbol. | |
| 1030 | ||
| 1031 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1032 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1033 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1034 | @type format: C{str} | |
| 1035 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1036 | @rtype: C{str} | |
| 1037 | @raise: NotImplementedError: if the requested format is not available | |
| 1038 | """ | |
| 1039 | if isinstance(argstrs,list): | |
| 1040 | argstrs=argstrs[0] | |
| 1041 | if format=="escript" or format=="str" or format=="text": | |
| 1042 | return "whereNegative(%s)"%argstrs | |
| 1043 | else: | |
| 1044 | raise NotImplementedError,"WhereNegative_Symbol does not provide program code for format %s."%format | |
| 1045 | ||
| 1046 | def substitute(self,argvals): | |
| 1047 | """ | |
| 1048 | assigns new values to symbols in the definition of the symbol. | |
| 1049 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1050 | ||
| 1051 | @param argvals: new values assigned to symbols | |
| 1052 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1053 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1054 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1055 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1056 | """ | |
| 1057 | if argvals.has_key(self): | |
| 1058 | arg=argvals[self] | |
| 1059 | if self.isAppropriateValue(arg): | |
| 1060 | return arg | |
| 1061 | else: | |
| 1062 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1063 | else: | |
| 1064 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1065 | return whereNegative(arg) | |
| 1066 | ||
| 1067 | def whereNonNegative(arg): | |
| 1068 | """ | |
| 1069 | returns mask of non-negative values of argument arg | |
| 1070 | ||
| 1071 | @param arg: argument | |
| 1072 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1073 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1074 | @raises TypeError: if the type of the argument is not expected. | |
| 1075 | """ | |
| 1076 | if isinstance(arg,numarray.NumArray): | |
| 1077 | out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1. | |
| 1078 | if isinstance(out,float): out=numarray.array(out) | |
| 1079 | return out | |
| 1080 | elif isinstance(arg,escript.Data): | |
| 1081 | return arg._whereNonNegative() | |
| 1082 | elif isinstance(arg,float): | |
| 1083 | if arg<0: | |
| 1084 | return 0. | |
| 1085 | else: | |
| 1086 | return 1. | |
| 1087 | elif isinstance(arg,int): | |
| 1088 | if arg<0: | |
| 1089 | return 0. | |
| 1090 | else: | |
| 1091 | return 1. | |
| 1092 | elif isinstance(arg,Symbol): | |
| 1093 | return 1.-whereNegative(arg) | |
| 1094 | else: | |
| 1095 | raise TypeError,"whereNonNegative: Unknown argument type." | |
| 1096 | ||
| 1097 | def whereNonPositive(arg): | |
| 1098 | """ | |
| 1099 | returns mask of non-positive values of argument arg | |
| 1100 | ||
| 1101 | @param arg: argument | |
| 1102 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1103 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1104 | @raises TypeError: if the type of the argument is not expected. | |
| 1105 | """ | |
| 1106 | if isinstance(arg,numarray.NumArray): | |
| 1107 | out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1. | |
| 1108 | if isinstance(out,float): out=numarray.array(out) | |
| 1109 | return out | |
| 1110 | elif isinstance(arg,escript.Data): | |
| 1111 | return arg._whereNonPositive() | |
| 1112 | elif isinstance(arg,float): | |
| 1113 | if arg>0: | |
| 1114 | return 0. | |
| 1115 | else: | |
| 1116 | return 1. | |
| 1117 | elif isinstance(arg,int): | |
| 1118 | if arg>0: | |
| 1119 | return 0. | |
| 1120 | else: | |
| 1121 | return 1. | |
| 1122 | elif isinstance(arg,Symbol): | |
| 1123 | return 1.-wherePositive(arg) | |
| 1124 | else: | |
| 1125 | raise TypeError,"whereNonPositive: Unknown argument type." | |
| 1126 | ||
| 1127 | def whereZero(arg,tol=0.): | |
| 1128 | """ | |
| 1129 | returns mask of zero entries of argument arg | |
| 1130 | ||
| 1131 | @param arg: argument | |
| 1132 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1133 | @param tol: tolerance. values with absolute value less then tol are accepted as zero. | |
| 1134 | @type tol: C{float} | |
| 1135 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1136 | @raises TypeError: if the type of the argument is not expected. | |
| 1137 | """ | |
| 1138 | if isinstance(arg,numarray.NumArray): | |
| 1139 | out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1. | |
| 1140 | if isinstance(out,float): out=numarray.array(out) | |
| 1141 | return out | |
| 1142 | elif isinstance(arg,escript.Data): | |
| 1143 | if tol>0.: | |
| 1144 | return whereNegative(abs(arg)-tol) | |
| 1145 | else: | |
| 1146 | return arg._whereZero() | |
| 1147 | elif isinstance(arg,float): | |
| 1148 | if abs(arg)<=tol: | |
| 1149 | return 1. | |
| 1150 | else: | |
| 1151 | return 0. | |
| 1152 | elif isinstance(arg,int): | |
| 1153 | if abs(float(arg))<=tol: | |
| 1154 | return 1. | |
| 1155 | else: | |
| 1156 | return 0. | |
| 1157 | elif isinstance(arg,Symbol): | |
| 1158 | return WhereZero_Symbol(arg,tol) | |
| 1159 | else: | |
| 1160 | raise TypeError,"whereZero: Unknown argument type." | |
| 1161 | ||
| 1162 | class WhereZero_Symbol(DependendSymbol): | |
| 1163 | """ | |
| 1164 | L{Symbol} representing the result of the mask of zero entries function | |
| 1165 | """ | |
| 1166 | def __init__(self,arg,tol=0.): | |
| 1167 | """ | |
| 1168 | initialization of whereZero L{Symbol} with argument arg | |
| 1169 | @param arg: argument of function | |
| 1170 | @type arg: typically L{Symbol}. | |
| 1171 | """ | |
| 1172 | DependendSymbol.__init__(self,args=[arg,tol],shape=arg.getShape(),dim=arg.getDim()) | |
| 1173 | ||
| 1174 | def getMyCode(self,argstrs,format="escript"): | |
| 1175 | """ | |
| 1176 | returns a program code that can be used to evaluate the symbol. | |
| 1177 | ||
| 1178 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1179 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1180 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1181 | @type format: C{str} | |
| 1182 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1183 | @rtype: C{str} | |
| 1184 | @raise: NotImplementedError: if the requested format is not available | |
| 1185 | """ | |
| 1186 | if format=="escript" or format=="str" or format=="text": | |
| 1187 | return "whereZero(%s,tol=%s)"%(argstrs[0],argstrs[1]) | |
| 1188 | else: | |
| 1189 | raise NotImplementedError,"WhereZero_Symbol does not provide program code for format %s."%format | |
| 1190 | ||
| 1191 | def substitute(self,argvals): | |
| 1192 | """ | |
| 1193 | assigns new values to symbols in the definition of the symbol. | |
| 1194 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1195 | ||
| 1196 | @param argvals: new values assigned to symbols | |
| 1197 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1198 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1199 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1200 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1201 | """ | |
| 1202 | if argvals.has_key(self): | |
| 1203 | arg=argvals[self] | |
| 1204 | if self.isAppropriateValue(arg): | |
| 1205 | return arg | |
| 1206 | else: | |
| 1207 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1208 | else: | |
| 1209 | arg=self.getSubstitutedArguments(argvals) | |
| 1210 | return whereZero(arg[0],arg[1]) | |
| 1211 | ||
| 1212 | def whereNonZero(arg,tol=0.): | |
| 1213 | """ | |
| 1214 | returns mask of values different from zero of argument arg | |
| 1215 | ||
| 1216 | @param arg: argument | |
| 1217 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1218 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1219 | @raises TypeError: if the type of the argument is not expected. | |
| 1220 | """ | |
| 1221 | if isinstance(arg,numarray.NumArray): | |
| 1222 | out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1. | |
| 1223 | if isinstance(out,float): out=numarray.array(out) | |
| 1224 | return out | |
| 1225 | elif isinstance(arg,escript.Data): | |
| 1226 | if tol>0.: | |
| 1227 | return 1.-whereZero(arg,tol) | |
| 1228 | else: | |
| 1229 | return arg._whereNonZero() | |
| 1230 | elif isinstance(arg,float): | |
| 1231 | if abs(arg)>tol: | |
| 1232 | return 1. | |
| 1233 | else: | |
| 1234 | return 0. | |
| 1235 | elif isinstance(arg,int): | |
| 1236 | if abs(float(arg))>tol: | |
| 1237 | return 1. | |
| 1238 | else: | |
| 1239 | return 0. | |
| 1240 | elif isinstance(arg,Symbol): | |
| 1241 | return 1.-whereZero(arg,tol) | |
| 1242 | else: | |
| 1243 | raise TypeError,"whereNonZero: Unknown argument type." | |
| 1244 | ||
| 1245 | def sin(arg): | |
| 1246 | """ | |
| 1247 | returns sine of argument arg | |
| 1248 | ||
| 1249 | @param arg: argument | |
| 1250 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1251 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1252 | @raises TypeError: if the type of the argument is not expected. | |
| 1253 | """ | |
| 1254 | if isinstance(arg,numarray.NumArray): | |
| 1255 | return numarray.sin(arg) | |
| 1256 | elif isinstance(arg,escript.Data): | |
| 1257 | return arg._sin() | |
| 1258 | elif isinstance(arg,float): | |
| 1259 | return math.sin(arg) | |
| 1260 | elif isinstance(arg,int): | |
| 1261 | return math.sin(arg) | |
| 1262 | elif isinstance(arg,Symbol): | |
| 1263 | return Sin_Symbol(arg) | |
| 1264 | else: | |
| 1265 | raise TypeError,"sin: Unknown argument type." | |
| 1266 | ||
| 1267 | class Sin_Symbol(DependendSymbol): | |
| 1268 | """ | |
| 1269 | L{Symbol} representing the result of the sine function | |
| 1270 | """ | |
| 1271 | def __init__(self,arg): | |
| 1272 | """ | |
| 1273 | initialization of sin L{Symbol} with argument arg | |
| 1274 | @param arg: argument of function | |
| 1275 | @type arg: typically L{Symbol}. | |
| 1276 | """ | |
| 1277 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1278 | ||
| 1279 | def getMyCode(self,argstrs,format="escript"): | |
| 1280 | """ | |
| 1281 | returns a program code that can be used to evaluate the symbol. | |
| 1282 | ||
| 1283 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1284 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1285 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1286 | @type format: C{str} | |
| 1287 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1288 | @rtype: C{str} | |
| 1289 | @raise: NotImplementedError: if the requested format is not available | |
| 1290 | """ | |
| 1291 | if isinstance(argstrs,list): | |
| 1292 | argstrs=argstrs[0] | |
| 1293 | if format=="escript" or format=="str" or format=="text": | |
| 1294 | return "sin(%s)"%argstrs | |
| 1295 | else: | |
| 1296 | raise NotImplementedError,"Sin_Symbol does not provide program code for format %s."%format | |
| 1297 | ||
| 1298 | def substitute(self,argvals): | |
| 1299 | """ | |
| 1300 | assigns new values to symbols in the definition of the symbol. | |
| 1301 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1302 | ||
| 1303 | @param argvals: new values assigned to symbols | |
| 1304 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1305 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1306 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1307 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1308 | """ | |
| 1309 | if argvals.has_key(self): | |
| 1310 | arg=argvals[self] | |
| 1311 | if self.isAppropriateValue(arg): | |
| 1312 | return arg | |
| 1313 | else: | |
| 1314 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1315 | else: | |
| 1316 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1317 | return sin(arg) | |
| 1318 | ||
| 1319 | def diff(self,arg): | |
| 1320 | """ | |
| 1321 | differential of this object | |
| 1322 | ||
| 1323 | @param arg: the derivative is calculated with respect to arg | |
| 1324 | @type arg: L{escript.Symbol} | |
| 1325 | @return: derivative with respect to C{arg} | |
| 1326 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1327 | """ | |
| 1328 | if arg==self: | |
| 1329 | return identity(self.getShape()) | |
| 1330 | else: | |
| 1331 | myarg=self.getArgument()[0] | |
| 1332 | val=matchShape(cos(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1333 | return val[0]*val[1] | |
| 1334 | ||
| 1335 | def cos(arg): | |
| 1336 | """ | |
| 1337 | returns cosine of argument arg | |
| 1338 | ||
| 1339 | @param arg: argument | |
| 1340 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1341 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1342 | @raises TypeError: if the type of the argument is not expected. | |
| 1343 | """ | |
| 1344 | if isinstance(arg,numarray.NumArray): | |
| 1345 | return numarray.cos(arg) | |
| 1346 | elif isinstance(arg,escript.Data): | |
| 1347 | return arg._cos() | |
| 1348 | elif isinstance(arg,float): | |
| 1349 | return math.cos(arg) | |
| 1350 | elif isinstance(arg,int): | |
| 1351 | return math.cos(arg) | |
| 1352 | elif isinstance(arg,Symbol): | |
| 1353 | return Cos_Symbol(arg) | |
| 1354 | else: | |
| 1355 | raise TypeError,"cos: Unknown argument type." | |
| 1356 | ||
| 1357 | class Cos_Symbol(DependendSymbol): | |
| 1358 | """ | |
| 1359 | L{Symbol} representing the result of the cosine function | |
| 1360 | """ | |
| 1361 | def __init__(self,arg): | |
| 1362 | """ | |
| 1363 | initialization of cos L{Symbol} with argument arg | |
| 1364 | @param arg: argument of function | |
| 1365 | @type arg: typically L{Symbol}. | |
| 1366 | """ | |
| 1367 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1368 | ||
| 1369 | def getMyCode(self,argstrs,format="escript"): | |
| 1370 | """ | |
| 1371 | returns a program code that can be used to evaluate the symbol. | |
| 1372 | ||
| 1373 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1374 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1375 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1376 | @type format: C{str} | |
| 1377 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1378 | @rtype: C{str} | |
| 1379 | @raise: NotImplementedError: if the requested format is not available | |
| 1380 | """ | |
| 1381 | if isinstance(argstrs,list): | |
| 1382 | argstrs=argstrs[0] | |
| 1383 | if format=="escript" or format=="str" or format=="text": | |
| 1384 | return "cos(%s)"%argstrs | |
| 1385 | else: | |
| 1386 | raise NotImplementedError,"Cos_Symbol does not provide program code for format %s."%format | |
| 1387 | ||
| 1388 | def substitute(self,argvals): | |
| 1389 | """ | |
| 1390 | assigns new values to symbols in the definition of the symbol. | |
| 1391 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1392 | ||
| 1393 | @param argvals: new values assigned to symbols | |
| 1394 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1395 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1396 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1397 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1398 | """ | |
| 1399 | if argvals.has_key(self): | |
| 1400 | arg=argvals[self] | |
| 1401 | if self.isAppropriateValue(arg): | |
| 1402 | return arg | |
| 1403 | else: | |
| 1404 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1405 | else: | |
| 1406 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1407 | return cos(arg) | |
| 1408 | ||
| 1409 | def diff(self,arg): | |
| 1410 | """ | |
| 1411 | differential of this object | |
| 1412 | ||
| 1413 | @param arg: the derivative is calculated with respect to arg | |
| 1414 | @type arg: L{escript.Symbol} | |
| 1415 | @return: derivative with respect to C{arg} | |
| 1416 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1417 | """ | |
| 1418 | if arg==self: | |
| 1419 | return identity(self.getShape()) | |
| 1420 | else: | |
| 1421 | myarg=self.getArgument()[0] | |
| 1422 | val=matchShape(-sin(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1423 | return val[0]*val[1] | |
| 1424 | ||
| 1425 | def tan(arg): | |
| 1426 | """ | |
| 1427 | returns tangent of argument arg | |
| 1428 | ||
| 1429 | @param arg: argument | |
| 1430 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1431 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1432 | @raises TypeError: if the type of the argument is not expected. | |
| 1433 | """ | |
| 1434 | if isinstance(arg,numarray.NumArray): | |
| 1435 | return numarray.tan(arg) | |
| 1436 | elif isinstance(arg,escript.Data): | |
| 1437 | return arg._tan() | |
| 1438 | elif isinstance(arg,float): | |
| 1439 | return math.tan(arg) | |
| 1440 | elif isinstance(arg,int): | |
| 1441 | return math.tan(arg) | |
| 1442 | elif isinstance(arg,Symbol): | |
| 1443 | return Tan_Symbol(arg) | |
| 1444 | else: | |
| 1445 | raise TypeError,"tan: Unknown argument type." | |
| 1446 | ||
| 1447 | class Tan_Symbol(DependendSymbol): | |
| 1448 | """ | |
| 1449 | L{Symbol} representing the result of the tangent function | |
| 1450 | """ | |
| 1451 | def __init__(self,arg): | |
| 1452 | """ | |
| 1453 | initialization of tan L{Symbol} with argument arg | |
| 1454 | @param arg: argument of function | |
| 1455 | @type arg: typically L{Symbol}. | |
| 1456 | """ | |
| 1457 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1458 | ||
| 1459 | def getMyCode(self,argstrs,format="escript"): | |
| 1460 | """ | |
| 1461 | returns a program code that can be used to evaluate the symbol. | |
| 1462 | ||
| 1463 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1464 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1465 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1466 | @type format: C{str} | |
| 1467 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1468 | @rtype: C{str} | |
| 1469 | @raise: NotImplementedError: if the requested format is not available | |
| 1470 | """ | |
| 1471 | if isinstance(argstrs,list): | |
| 1472 | argstrs=argstrs[0] | |
| 1473 | if format=="escript" or format=="str" or format=="text": | |
| 1474 | return "tan(%s)"%argstrs | |
| 1475 | else: | |
| 1476 | raise NotImplementedError,"Tan_Symbol does not provide program code for format %s."%format | |
| 1477 | ||
| 1478 | def substitute(self,argvals): | |
| 1479 | """ | |
| 1480 | assigns new values to symbols in the definition of the symbol. | |
| 1481 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1482 | ||
| 1483 | @param argvals: new values assigned to symbols | |
| 1484 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1485 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1486 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1487 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1488 | """ | |
| 1489 | if argvals.has_key(self): | |
| 1490 | arg=argvals[self] | |
| 1491 | if self.isAppropriateValue(arg): | |
| 1492 | return arg | |
| 1493 | else: | |
| 1494 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1495 | else: | |
| 1496 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1497 | return tan(arg) | |
| 1498 | ||
| 1499 | def diff(self,arg): | |
| 1500 | """ | |
| 1501 | differential of this object | |
| 1502 | ||
| 1503 | @param arg: the derivative is calculated with respect to arg | |
| 1504 | @type arg: L{escript.Symbol} | |
| 1505 | @return: derivative with respect to C{arg} | |
| 1506 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1507 | """ | |
| 1508 | if arg==self: | |
| 1509 | return identity(self.getShape()) | |
| 1510 | else: | |
| 1511 | myarg=self.getArgument()[0] | |
| 1512 | val=matchShape(1./cos(myarg)**2,self.getDifferentiatedArguments(arg)[0]) | |
| 1513 | return val[0]*val[1] | |
| 1514 | ||
| 1515 | def asin(arg): | |
| 1516 | """ | |
| 1517 | returns inverse sine of argument arg | |
| 1518 | ||
| 1519 | @param arg: argument | |
| 1520 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1521 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1522 | @raises TypeError: if the type of the argument is not expected. | |
| 1523 | """ | |
| 1524 | if isinstance(arg,numarray.NumArray): | |
| 1525 | return numarray.arcsin(arg) | |
| 1526 | elif isinstance(arg,escript.Data): | |
| 1527 | return arg._asin() | |
| 1528 | elif isinstance(arg,float): | |
| 1529 | return math.asin(arg) | |
| 1530 | elif isinstance(arg,int): | |
| 1531 | return math.asin(arg) | |
| 1532 | elif isinstance(arg,Symbol): | |
| 1533 | return Asin_Symbol(arg) | |
| 1534 | else: | |
| 1535 | raise TypeError,"asin: Unknown argument type." | |
| 1536 | ||
| 1537 | class Asin_Symbol(DependendSymbol): | |
| 1538 | """ | |
| 1539 | L{Symbol} representing the result of the inverse sine function | |
| 1540 | """ | |
| 1541 | def __init__(self,arg): | |
| 1542 | """ | |
| 1543 | initialization of asin L{Symbol} with argument arg | |
| 1544 | @param arg: argument of function | |
| 1545 | @type arg: typically L{Symbol}. | |
| 1546 | """ | |
| 1547 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1548 | ||
| 1549 | def getMyCode(self,argstrs,format="escript"): | |
| 1550 | """ | |
| 1551 | returns a program code that can be used to evaluate the symbol. | |
| 1552 | ||
| 1553 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1554 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1555 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1556 | @type format: C{str} | |
| 1557 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1558 | @rtype: C{str} | |
| 1559 | @raise: NotImplementedError: if the requested format is not available | |
| 1560 | """ | |
| 1561 | if isinstance(argstrs,list): | |
| 1562 | argstrs=argstrs[0] | |
| 1563 | if format=="escript" or format=="str" or format=="text": | |
| 1564 | return "asin(%s)"%argstrs | |
| 1565 | else: | |
| 1566 | raise NotImplementedError,"Asin_Symbol does not provide program code for format %s."%format | |
| 1567 | ||
| 1568 | def substitute(self,argvals): | |
| 1569 | """ | |
| 1570 | assigns new values to symbols in the definition of the symbol. | |
| 1571 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1572 | ||
| 1573 | @param argvals: new values assigned to symbols | |
| 1574 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1575 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1576 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1577 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1578 | """ | |
| 1579 | if argvals.has_key(self): | |
| 1580 | arg=argvals[self] | |
| 1581 | if self.isAppropriateValue(arg): | |
| 1582 | return arg | |
| 1583 | else: | |
| 1584 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1585 | else: | |
| 1586 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1587 | return asin(arg) | |
| 1588 | ||
| 1589 | def diff(self,arg): | |
| 1590 | """ | |
| 1591 | differential of this object | |
| 1592 | ||
| 1593 | @param arg: the derivative is calculated with respect to arg | |
| 1594 | @type arg: L{escript.Symbol} | |
| 1595 | @return: derivative with respect to C{arg} | |
| 1596 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1597 | """ | |
| 1598 | if arg==self: | |
| 1599 | return identity(self.getShape()) | |
| 1600 | else: | |
| 1601 | myarg=self.getArgument()[0] | |
| 1602 | val=matchShape(1./sqrt(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 1603 | return val[0]*val[1] | |
| 1604 | ||
| 1605 | def acos(arg): | |
| 1606 | """ | |
| 1607 | returns inverse cosine of argument arg | |
| 1608 | ||
| 1609 | @param arg: argument | |
| 1610 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1611 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1612 | @raises TypeError: if the type of the argument is not expected. | |
| 1613 | """ | |
| 1614 | if isinstance(arg,numarray.NumArray): | |
| 1615 | return numarray.arccos(arg) | |
| 1616 | elif isinstance(arg,escript.Data): | |
| 1617 | return arg._acos() | |
| 1618 | elif isinstance(arg,float): | |
| 1619 | return math.acos(arg) | |
| 1620 | elif isinstance(arg,int): | |
| 1621 | return math.acos(arg) | |
| 1622 | elif isinstance(arg,Symbol): | |
| 1623 | return Acos_Symbol(arg) | |
| 1624 | else: | |
| 1625 | raise TypeError,"acos: Unknown argument type." | |
| 1626 | ||
| 1627 | class Acos_Symbol(DependendSymbol): | |
| 1628 | """ | |
| 1629 | L{Symbol} representing the result of the inverse cosine function | |
| 1630 | """ | |
| 1631 | def __init__(self,arg): | |
| 1632 | """ | |
| 1633 | initialization of acos L{Symbol} with argument arg | |
| 1634 | @param arg: argument of function | |
| 1635 | @type arg: typically L{Symbol}. | |
| 1636 | """ | |
| 1637 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1638 | ||
| 1639 | def getMyCode(self,argstrs,format="escript"): | |
| 1640 | """ | |
| 1641 | returns a program code that can be used to evaluate the symbol. | |
| 1642 | ||
| 1643 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1644 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1645 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1646 | @type format: C{str} | |
| 1647 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1648 | @rtype: C{str} | |
| 1649 | @raise: NotImplementedError: if the requested format is not available | |
| 1650 | """ | |
| 1651 | if isinstance(argstrs,list): | |
| 1652 | argstrs=argstrs[0] | |
| 1653 | if format=="escript" or format=="str" or format=="text": | |
| 1654 | return "acos(%s)"%argstrs | |
| 1655 | else: | |
| 1656 | raise NotImplementedError,"Acos_Symbol does not provide program code for format %s."%format | |
| 1657 | ||
| 1658 | def substitute(self,argvals): | |
| 1659 | """ | |
| 1660 | assigns new values to symbols in the definition of the symbol. | |
| 1661 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1662 | ||
| 1663 | @param argvals: new values assigned to symbols | |
| 1664 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1665 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1666 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1667 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1668 | """ | |
| 1669 | if argvals.has_key(self): | |
| 1670 | arg=argvals[self] | |
| 1671 | if self.isAppropriateValue(arg): | |
| 1672 | return arg | |
| 1673 | else: | |
| 1674 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1675 | else: | |
| 1676 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1677 | return acos(arg) | |
| 1678 | ||
| 1679 | def diff(self,arg): | |
| 1680 | """ | |
| 1681 | differential of this object | |
| 1682 | ||
| 1683 | @param arg: the derivative is calculated with respect to arg | |
| 1684 | @type arg: L{escript.Symbol} | |
| 1685 | @return: derivative with respect to C{arg} | |
| 1686 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1687 | """ | |
| 1688 | if arg==self: | |
| 1689 | return identity(self.getShape()) | |
| 1690 | else: | |
| 1691 | myarg=self.getArgument()[0] | |
| 1692 | val=matchShape(-1./sqrt(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 1693 | return val[0]*val[1] | |
| 1694 | ||
| 1695 | def atan(arg): | |
| 1696 | """ | |
| 1697 | returns inverse tangent of argument arg | |
| 1698 | ||
| 1699 | @param arg: argument | |
| 1700 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1701 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1702 | @raises TypeError: if the type of the argument is not expected. | |
| 1703 | """ | |
| 1704 | if isinstance(arg,numarray.NumArray): | |
| 1705 | return numarray.arctan(arg) | |
| 1706 | elif isinstance(arg,escript.Data): | |
| 1707 | return arg._atan() | |
| 1708 | elif isinstance(arg,float): | |
| 1709 | return math.atan(arg) | |
| 1710 | elif isinstance(arg,int): | |
| 1711 | return math.atan(arg) | |
| 1712 | elif isinstance(arg,Symbol): | |
| 1713 | return Atan_Symbol(arg) | |
| 1714 | else: | |
| 1715 | raise TypeError,"atan: Unknown argument type." | |
| 1716 | ||
| 1717 | class Atan_Symbol(DependendSymbol): | |
| 1718 | """ | |
| 1719 | L{Symbol} representing the result of the inverse tangent function | |
| 1720 | """ | |
| 1721 | def __init__(self,arg): | |
| 1722 | """ | |
| 1723 | initialization of atan L{Symbol} with argument arg | |
| 1724 | @param arg: argument of function | |
| 1725 | @type arg: typically L{Symbol}. | |
| 1726 | """ | |
| 1727 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1728 | ||
| 1729 | def getMyCode(self,argstrs,format="escript"): | |
| 1730 | """ | |
| 1731 | returns a program code that can be used to evaluate the symbol. | |
| 1732 | ||
| 1733 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1734 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1735 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1736 | @type format: C{str} | |
| 1737 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1738 | @rtype: C{str} | |
| 1739 | @raise: NotImplementedError: if the requested format is not available | |
| 1740 | """ | |
| 1741 | if isinstance(argstrs,list): | |
| 1742 | argstrs=argstrs[0] | |
| 1743 | if format=="escript" or format=="str" or format=="text": | |
| 1744 | return "atan(%s)"%argstrs | |
| 1745 | else: | |
| 1746 | raise NotImplementedError,"Atan_Symbol does not provide program code for format %s."%format | |
| 1747 | ||
| 1748 | def substitute(self,argvals): | |
| 1749 | """ | |
| 1750 | assigns new values to symbols in the definition of the symbol. | |
| 1751 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1752 | ||
| 1753 | @param argvals: new values assigned to symbols | |
| 1754 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1755 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1756 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1757 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1758 | """ | |
| 1759 | if argvals.has_key(self): | |
| 1760 | arg=argvals[self] | |
| 1761 | if self.isAppropriateValue(arg): | |
| 1762 | return arg | |
| 1763 | else: | |
| 1764 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1765 | else: | |
| 1766 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1767 | return atan(arg) | |
| 1768 | ||
| 1769 | def diff(self,arg): | |
| 1770 | """ | |
| 1771 | differential of this object | |
| 1772 | ||
| 1773 | @param arg: the derivative is calculated with respect to arg | |
| 1774 | @type arg: L{escript.Symbol} | |
| 1775 | @return: derivative with respect to C{arg} | |
| 1776 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1777 | """ | |
| 1778 | if arg==self: | |
| 1779 | return identity(self.getShape()) | |
| 1780 | else: | |
| 1781 | myarg=self.getArgument()[0] | |
| 1782 | val=matchShape(1./(1+myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 1783 | return val[0]*val[1] | |
| 1784 | ||
| 1785 | def sinh(arg): | |
| 1786 | """ | |
| 1787 | returns hyperbolic sine of argument arg | |
| 1788 | ||
| 1789 | @param arg: argument | |
| 1790 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1791 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1792 | @raises TypeError: if the type of the argument is not expected. | |
| 1793 | """ | |
| 1794 | if isinstance(arg,numarray.NumArray): | |
| 1795 | return numarray.sinh(arg) | |
| 1796 | elif isinstance(arg,escript.Data): | |
| 1797 | return arg._sinh() | |
| 1798 | elif isinstance(arg,float): | |
| 1799 | return math.sinh(arg) | |
| 1800 | elif isinstance(arg,int): | |
| 1801 | return math.sinh(arg) | |
| 1802 | elif isinstance(arg,Symbol): | |
| 1803 | return Sinh_Symbol(arg) | |
| 1804 | else: | |
| 1805 | raise TypeError,"sinh: Unknown argument type." | |
| 1806 | ||
| 1807 | class Sinh_Symbol(DependendSymbol): | |
| 1808 | """ | |
| 1809 | L{Symbol} representing the result of the hyperbolic sine function | |
| 1810 | """ | |
| 1811 | def __init__(self,arg): | |
| 1812 | """ | |
| 1813 | initialization of sinh L{Symbol} with argument arg | |
| 1814 | @param arg: argument of function | |
| 1815 | @type arg: typically L{Symbol}. | |
| 1816 | """ | |
| 1817 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1818 | ||
| 1819 | def getMyCode(self,argstrs,format="escript"): | |
| 1820 | """ | |
| 1821 | returns a program code that can be used to evaluate the symbol. | |
| 1822 | ||
| 1823 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1824 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1825 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1826 | @type format: C{str} | |
| 1827 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1828 | @rtype: C{str} | |
| 1829 | @raise: NotImplementedError: if the requested format is not available | |
| 1830 | """ | |
| 1831 | if isinstance(argstrs,list): | |
| 1832 | argstrs=argstrs[0] | |
| 1833 | if format=="escript" or format=="str" or format=="text": | |
| 1834 | return "sinh(%s)"%argstrs | |
| 1835 | else: | |
| 1836 | raise NotImplementedError,"Sinh_Symbol does not provide program code for format %s."%format | |
| 1837 | ||
| 1838 | def substitute(self,argvals): | |
| 1839 | """ | |
| 1840 | assigns new values to symbols in the definition of the symbol. | |
| 1841 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1842 | ||
| 1843 | @param argvals: new values assigned to symbols | |
| 1844 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1845 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1846 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1847 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1848 | """ | |
| 1849 | if argvals.has_key(self): | |
| 1850 | arg=argvals[self] | |
| 1851 | if self.isAppropriateValue(arg): | |
| 1852 | return arg | |
| 1853 | else: | |
| 1854 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1855 | else: | |
| 1856 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1857 | return sinh(arg) | |
| 1858 | ||
| 1859 | def diff(self,arg): | |
| 1860 | """ | |
| 1861 | differential of this object | |
| 1862 | ||
| 1863 | @param arg: the derivative is calculated with respect to arg | |
| 1864 | @type arg: L{escript.Symbol} | |
| 1865 | @return: derivative with respect to C{arg} | |
| 1866 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1867 | """ | |
| 1868 | if arg==self: | |
| 1869 | return identity(self.getShape()) | |
| 1870 | else: | |
| 1871 | myarg=self.getArgument()[0] | |
| 1872 | val=matchShape(cosh(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1873 | return val[0]*val[1] | |
| 1874 | ||
| 1875 | def cosh(arg): | |
| 1876 | """ | |
| 1877 | returns hyperbolic cosine of argument arg | |
| 1878 | ||
| 1879 | @param arg: argument | |
| 1880 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1881 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1882 | @raises TypeError: if the type of the argument is not expected. | |
| 1883 | """ | |
| 1884 | if isinstance(arg,numarray.NumArray): | |
| 1885 | return numarray.cosh(arg) | |
| 1886 | elif isinstance(arg,escript.Data): | |
| 1887 | return arg._cosh() | |
| 1888 | elif isinstance(arg,float): | |
| 1889 | return math.cosh(arg) | |
| 1890 | elif isinstance(arg,int): | |
| 1891 | return math.cosh(arg) | |
| 1892 | elif isinstance(arg,Symbol): | |
| 1893 | return Cosh_Symbol(arg) | |
| 1894 | else: | |
| 1895 | raise TypeError,"cosh: Unknown argument type." | |
| 1896 | ||
| 1897 | class Cosh_Symbol(DependendSymbol): | |
| 1898 | """ | |
| 1899 | L{Symbol} representing the result of the hyperbolic cosine function | |
| 1900 | """ | |
| 1901 | def __init__(self,arg): | |
| 1902 | """ | |
| 1903 | initialization of cosh L{Symbol} with argument arg | |
| 1904 | @param arg: argument of function | |
| 1905 | @type arg: typically L{Symbol}. | |
| 1906 | """ | |
| 1907 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1908 | ||
| 1909 | def getMyCode(self,argstrs,format="escript"): | |
| 1910 | """ | |
| 1911 | returns a program code that can be used to evaluate the symbol. | |
| 1912 | ||
| 1913 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1914 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1915 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1916 | @type format: C{str} | |
| 1917 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1918 | @rtype: C{str} | |
| 1919 | @raise: NotImplementedError: if the requested format is not available | |
| 1920 | """ | |
| 1921 | if isinstance(argstrs,list): | |
| 1922 | argstrs=argstrs[0] | |
| 1923 | if format=="escript" or format=="str" or format=="text": | |
| 1924 | return "cosh(%s)"%argstrs | |
| 1925 | else: | |
| 1926 | raise NotImplementedError,"Cosh_Symbol does not provide program code for format %s."%format | |
| 1927 | ||
| 1928 | def substitute(self,argvals): | |
| 1929 | """ | |
| 1930 | assigns new values to symbols in the definition of the symbol. | |
| 1931 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1932 | ||
| 1933 | @param argvals: new values assigned to symbols | |
| 1934 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1935 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1936 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1937 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1938 | """ | |
| 1939 | if argvals.has_key(self): | |
| 1940 | arg=argvals[self] | |
| 1941 | if self.isAppropriateValue(arg): | |
| 1942 | return arg | |
| 1943 | else: | |
| 1944 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1945 | else: | |
| 1946 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1947 | return cosh(arg) | |
| 1948 | ||
| 1949 | def diff(self,arg): | |
| 1950 | """ | |
| 1951 | differential of this object | |
| 1952 | ||
| 1953 | @param arg: the derivative is calculated with respect to arg | |
| 1954 | @type arg: L{escript.Symbol} | |
| 1955 | @return: derivative with respect to C{arg} | |
| 1956 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1957 | """ | |
| 1958 | if arg==self: | |
| 1959 | return identity(self.getShape()) | |
| 1960 | else: | |
| 1961 | myarg=self.getArgument()[0] | |
| 1962 | val=matchShape(sinh(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1963 | return val[0]*val[1] | |
| 1964 | ||
| 1965 | def tanh(arg): | |
| 1966 | """ | |
| 1967 | returns hyperbolic tangent of argument arg | |
| 1968 | ||
| 1969 | @param arg: argument | |
| 1970 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1971 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1972 | @raises TypeError: if the type of the argument is not expected. | |
| 1973 | """ | |
| 1974 | if isinstance(arg,numarray.NumArray): | |
| 1975 | return numarray.tanh(arg) | |
| 1976 | elif isinstance(arg,escript.Data): | |
| 1977 | return arg._tanh() | |
| 1978 | elif isinstance(arg,float): | |
| 1979 | return math.tanh(arg) | |
| 1980 | elif isinstance(arg,int): | |
| 1981 | return math.tanh(arg) | |
| 1982 | elif isinstance(arg,Symbol): | |
| 1983 | return Tanh_Symbol(arg) | |
| 1984 | else: | |
| 1985 | raise TypeError,"tanh: Unknown argument type." | |
| 1986 | ||
| 1987 | class Tanh_Symbol(DependendSymbol): | |
| 1988 | """ | |
| 1989 | L{Symbol} representing the result of the hyperbolic tangent function | |
| 1990 | """ | |
| 1991 | def __init__(self,arg): | |
| 1992 | """ | |
| 1993 | initialization of tanh L{Symbol} with argument arg | |
| 1994 | @param arg: argument of function | |
| 1995 | @type arg: typically L{Symbol}. | |
| 1996 | """ | |
| 1997 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1998 | ||
| 1999 | def getMyCode(self,argstrs,format="escript"): | |
| 2000 | """ | |
| 2001 | returns a program code that can be used to evaluate the symbol. | |
| 2002 | ||
| 2003 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2004 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2005 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2006 | @type format: C{str} | |
| 2007 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2008 | @rtype: C{str} | |
| 2009 | @raise: NotImplementedError: if the requested format is not available | |
| 2010 | """ | |
| 2011 | if isinstance(argstrs,list): | |
| 2012 | argstrs=argstrs[0] | |
| 2013 | if format=="escript" or format=="str" or format=="text": | |
| 2014 | return "tanh(%s)"%argstrs | |
| 2015 | else: | |
| 2016 | raise NotImplementedError,"Tanh_Symbol does not provide program code for format %s."%format | |
| 2017 | ||
| 2018 | def substitute(self,argvals): | |
| 2019 | """ | |
| 2020 | assigns new values to symbols in the definition of the symbol. | |
| 2021 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2022 | ||
| 2023 | @param argvals: new values assigned to symbols | |
| 2024 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2025 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2026 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2027 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2028 | """ | |
| 2029 | if argvals.has_key(self): | |
| 2030 | arg=argvals[self] | |
| 2031 | if self.isAppropriateValue(arg): | |
| 2032 | return arg | |
| 2033 | else: | |
| 2034 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2035 | else: | |
| 2036 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2037 | return tanh(arg) | |
| 2038 | ||
| 2039 | def diff(self,arg): | |
| 2040 | """ | |
| 2041 | differential of this object | |
| 2042 | ||
| 2043 | @param arg: the derivative is calculated with respect to arg | |
| 2044 | @type arg: L{escript.Symbol} | |
| 2045 | @return: derivative with respect to C{arg} | |
| 2046 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2047 | """ | |
| 2048 | if arg==self: | |
| 2049 | return identity(self.getShape()) | |
| 2050 | else: | |
| 2051 | myarg=self.getArgument()[0] | |
| 2052 | val=matchShape(1./cosh(myarg)**2,self.getDifferentiatedArguments(arg)[0]) | |
| 2053 | return val[0]*val[1] | |
| 2054 | ||
| 2055 | def asinh(arg): | |
| 2056 | """ | |
| 2057 | returns inverse hyperbolic sine of argument arg | |
| 2058 | ||
| 2059 | @param arg: argument | |
| 2060 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2061 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2062 | @raises TypeError: if the type of the argument is not expected. | |
| 2063 | """ | |
| 2064 | if isinstance(arg,numarray.NumArray): | |
| 2065 | return numarray.arcsinh(arg) | |
| 2066 | elif isinstance(arg,escript.Data): | |
| 2067 | return arg._asinh() | |
| 2068 | elif isinstance(arg,float): | |
| 2069 | return numarray.arcsinh(arg) | |
| 2070 | elif isinstance(arg,int): | |
| 2071 | return numarray.arcsinh(float(arg)) | |
| 2072 | elif isinstance(arg,Symbol): | |
| 2073 | return Asinh_Symbol(arg) | |
| 2074 | else: | |
| 2075 | raise TypeError,"asinh: Unknown argument type." | |
| 2076 | ||
| 2077 | class Asinh_Symbol(DependendSymbol): | |
| 2078 | """ | |
| 2079 | L{Symbol} representing the result of the inverse hyperbolic sine function | |
| 2080 | """ | |
| 2081 | def __init__(self,arg): | |
| 2082 | """ | |
| 2083 | initialization of asinh L{Symbol} with argument arg | |
| 2084 | @param arg: argument of function | |
| 2085 | @type arg: typically L{Symbol}. | |
| 2086 | """ | |
| 2087 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2088 | ||
| 2089 | def getMyCode(self,argstrs,format="escript"): | |
| 2090 | """ | |
| 2091 | returns a program code that can be used to evaluate the symbol. | |
| 2092 | ||
| 2093 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2094 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2095 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2096 | @type format: C{str} | |
| 2097 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2098 | @rtype: C{str} | |
| 2099 | @raise: NotImplementedError: if the requested format is not available | |
| 2100 | """ | |
| 2101 | if isinstance(argstrs,list): | |
| 2102 | argstrs=argstrs[0] | |
| 2103 | if format=="escript" or format=="str" or format=="text": | |
| 2104 | return "asinh(%s)"%argstrs | |
| 2105 | else: | |
| 2106 | raise NotImplementedError,"Asinh_Symbol does not provide program code for format %s."%format | |
| 2107 | ||
| 2108 | def substitute(self,argvals): | |
| 2109 | """ | |
| 2110 | assigns new values to symbols in the definition of the symbol. | |
| 2111 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2112 | ||
| 2113 | @param argvals: new values assigned to symbols | |
| 2114 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2115 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2116 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2117 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2118 | """ | |
| 2119 | if argvals.has_key(self): | |
| 2120 | arg=argvals[self] | |
| 2121 | if self.isAppropriateValue(arg): | |
| 2122 | return arg | |
| 2123 | else: | |
| 2124 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2125 | else: | |
| 2126 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2127 | return asinh(arg) | |
| 2128 | ||
| 2129 | def diff(self,arg): | |
| 2130 | """ | |
| 2131 | differential of this object | |
| 2132 | ||
| 2133 | @param arg: the derivative is calculated with respect to arg | |
| 2134 | @type arg: L{escript.Symbol} | |
| 2135 | @return: derivative with respect to C{arg} | |
| 2136 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2137 | """ | |
| 2138 | if arg==self: | |
| 2139 | return identity(self.getShape()) | |
| 2140 | else: | |
| 2141 | myarg=self.getArgument()[0] | |
| 2142 | val=matchShape(1./sqrt(myarg**2+1),self.getDifferentiatedArguments(arg)[0]) | |
| 2143 | return val[0]*val[1] | |
| 2144 | ||
| 2145 | def acosh(arg): | |
| 2146 | """ | |
| 2147 | returns inverse hyperolic cosine of argument arg | |
| 2148 | ||
| 2149 | @param arg: argument | |
| 2150 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2151 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2152 | @raises TypeError: if the type of the argument is not expected. | |
| 2153 | """ | |
| 2154 | if isinstance(arg,numarray.NumArray): | |
| 2155 | return numarray.arccosh(arg) | |
| 2156 | elif isinstance(arg,escript.Data): | |
| 2157 | return arg._acosh() | |
| 2158 | elif isinstance(arg,float): | |
| 2159 | return numarray.arccosh(arg) | |
| 2160 | elif isinstance(arg,int): | |
| 2161 | return numarray.arccosh(float(arg)) | |
| 2162 | elif isinstance(arg,Symbol): | |
| 2163 | return Acosh_Symbol(arg) | |
| 2164 | else: | |
| 2165 | raise TypeError,"acosh: Unknown argument type." | |
| 2166 | ||
| 2167 | class Acosh_Symbol(DependendSymbol): | |
| 2168 | """ | |
| 2169 | L{Symbol} representing the result of the inverse hyperolic cosine function | |
| 2170 | """ | |
| 2171 | def __init__(self,arg): | |
| 2172 | """ | |
| 2173 | initialization of acosh L{Symbol} with argument arg | |
| 2174 | @param arg: argument of function | |
| 2175 | @type arg: typically L{Symbol}. | |
| 2176 | """ | |
| 2177 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2178 | ||
| 2179 | def getMyCode(self,argstrs,format="escript"): | |
| 2180 | """ | |
| 2181 | returns a program code that can be used to evaluate the symbol. | |
| 2182 | ||
| 2183 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2184 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2185 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2186 | @type format: C{str} | |
| 2187 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2188 | @rtype: C{str} | |
| 2189 | @raise: NotImplementedError: if the requested format is not available | |
| 2190 | """ | |
| 2191 | if isinstance(argstrs,list): | |
| 2192 | argstrs=argstrs[0] | |
| 2193 | if format=="escript" or format=="str" or format=="text": | |
| 2194 | return "acosh(%s)"%argstrs | |
| 2195 | else: | |
| 2196 | raise NotImplementedError,"Acosh_Symbol does not provide program code for format %s."%format | |
| 2197 | ||
| 2198 | def substitute(self,argvals): | |
| 2199 | """ | |
| 2200 | assigns new values to symbols in the definition of the symbol. | |
| 2201 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2202 | ||
| 2203 | @param argvals: new values assigned to symbols | |
| 2204 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2205 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2206 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2207 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2208 | """ | |
| 2209 | if argvals.has_key(self): | |
| 2210 | arg=argvals[self] | |
| 2211 | if self.isAppropriateValue(arg): | |
| 2212 | return arg | |
| 2213 | else: | |
| 2214 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2215 | else: | |
| 2216 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2217 | return acosh(arg) | |
| 2218 | ||
| 2219 | def diff(self,arg): | |
| 2220 | """ | |
| 2221 | differential of this object | |
| 2222 | ||
| 2223 | @param arg: the derivative is calculated with respect to arg | |
| 2224 | @type arg: L{escript.Symbol} | |
| 2225 | @return: derivative with respect to C{arg} | |
| 2226 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2227 | """ | |
| 2228 | if arg==self: | |
| 2229 | return identity(self.getShape()) | |
| 2230 | else: | |
| 2231 | myarg=self.getArgument()[0] | |
| 2232 | val=matchShape(1./sqrt(myarg**2-1),self.getDifferentiatedArguments(arg)[0]) | |
| 2233 | return val[0]*val[1] | |
| 2234 | ||
| 2235 | def atanh(arg): | |
| 2236 | """ | |
| 2237 | returns inverse hyperbolic tangent of argument arg | |
| 2238 | ||
| 2239 | @param arg: argument | |
| 2240 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2241 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2242 | @raises TypeError: if the type of the argument is not expected. | |
| 2243 | """ | |
| 2244 | if isinstance(arg,numarray.NumArray): | |
| 2245 | return numarray.arctanh(arg) | |
| 2246 | elif isinstance(arg,escript.Data): | |
| 2247 | return arg._atanh() | |
| 2248 | elif isinstance(arg,float): | |
| 2249 | return numarray.arctanh(arg) | |
| 2250 | elif isinstance(arg,int): | |
| 2251 | return numarray.arctanh(float(arg)) | |
| 2252 | elif isinstance(arg,Symbol): | |
| 2253 | return Atanh_Symbol(arg) | |
| 2254 | else: | |
| 2255 | raise TypeError,"atanh: Unknown argument type." | |
| 2256 | ||
| 2257 | class Atanh_Symbol(DependendSymbol): | |
| 2258 | """ | |
| 2259 | L{Symbol} representing the result of the inverse hyperbolic tangent function | |
| 2260 | """ | |
| 2261 | def __init__(self,arg): | |
| 2262 | """ | |
| 2263 | initialization of atanh L{Symbol} with argument arg | |
| 2264 | @param arg: argument of function | |
| 2265 | @type arg: typically L{Symbol}. | |
| 2266 | """ | |
| 2267 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2268 | ||
| 2269 | def getMyCode(self,argstrs,format="escript"): | |
| 2270 | """ | |
| 2271 | returns a program code that can be used to evaluate the symbol. | |
| 2272 | ||
| 2273 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2274 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2275 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2276 | @type format: C{str} | |
| 2277 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2278 | @rtype: C{str} | |
| 2279 | @raise: NotImplementedError: if the requested format is not available | |
| 2280 | """ | |
| 2281 | if isinstance(argstrs,list): | |
| 2282 | argstrs=argstrs[0] | |
| 2283 | if format=="escript" or format=="str" or format=="text": | |
| 2284 | return "atanh(%s)"%argstrs | |
| 2285 | else: | |
| 2286 | raise NotImplementedError,"Atanh_Symbol does not provide program code for format %s."%format | |
| 2287 | ||
| 2288 | def substitute(self,argvals): | |
| 2289 | """ | |
| 2290 | assigns new values to symbols in the definition of the symbol. | |
| 2291 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2292 | ||
| 2293 | @param argvals: new values assigned to symbols | |
| 2294 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2295 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2296 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2297 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2298 | """ | |
| 2299 | if argvals.has_key(self): | |
| 2300 | arg=argvals[self] | |
| 2301 | if self.isAppropriateValue(arg): | |
| 2302 | return arg | |
| 2303 | else: | |
| 2304 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2305 | else: | |
| 2306 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2307 | return atanh(arg) | |
| 2308 | ||
| 2309 | def diff(self,arg): | |
| 2310 | """ | |
| 2311 | differential of this object | |
| 2312 | ||
| 2313 | @param arg: the derivative is calculated with respect to arg | |
| 2314 | @type arg: L{escript.Symbol} | |
| 2315 | @return: derivative with respect to C{arg} | |
| 2316 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2317 | """ | |
| 2318 | if arg==self: | |
| 2319 | return identity(self.getShape()) | |
| 2320 | else: | |
| 2321 | myarg=self.getArgument()[0] | |
| 2322 | val=matchShape(1./(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 2323 | return val[0]*val[1] | |
| 2324 | ||
| 2325 | def exp(arg): | |
| 2326 | """ | |
| 2327 | returns exponential of argument arg | |
| 2328 | ||
| 2329 | @param arg: argument | |
| 2330 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2331 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2332 | @raises TypeError: if the type of the argument is not expected. | |
| 2333 | """ | |
| 2334 | if isinstance(arg,numarray.NumArray): | |
| 2335 | return numarray.exp(arg) | |
| 2336 | elif isinstance(arg,escript.Data): | |
| 2337 | return arg._exp() | |
| 2338 | elif isinstance(arg,float): | |
| 2339 | return math.exp(arg) | |
| 2340 | elif isinstance(arg,int): | |
| 2341 | return math.exp(arg) | |
| 2342 | elif isinstance(arg,Symbol): | |
| 2343 | return Exp_Symbol(arg) | |
| 2344 | else: | |
| 2345 | raise TypeError,"exp: Unknown argument type." | |
| 2346 | ||
| 2347 | class Exp_Symbol(DependendSymbol): | |
| 2348 | """ | |
| 2349 | L{Symbol} representing the result of the exponential function | |
| 2350 | """ | |
| 2351 | def __init__(self,arg): | |
| 2352 | """ | |
| 2353 | initialization of exp L{Symbol} with argument arg | |
| 2354 | @param arg: argument of function | |
| 2355 | @type arg: typically L{Symbol}. | |
| 2356 | """ | |
| 2357 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2358 | ||
| 2359 | def getMyCode(self,argstrs,format="escript"): | |
| 2360 | """ | |
| 2361 | returns a program code that can be used to evaluate the symbol. | |
| 2362 | ||
| 2363 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2364 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2365 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2366 | @type format: C{str} | |
| 2367 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2368 | @rtype: C{str} | |
| 2369 | @raise: NotImplementedError: if the requested format is not available | |
| 2370 | """ | |
| 2371 | if isinstance(argstrs,list): | |
| 2372 | argstrs=argstrs[0] | |
| 2373 | if format=="escript" or format=="str" or format=="text": | |
| 2374 | return "exp(%s)"%argstrs | |
| 2375 | else: | |
| 2376 | raise NotImplementedError,"Exp_Symbol does not provide program code for format %s."%format | |
| 2377 | ||
| 2378 | def substitute(self,argvals): | |
| 2379 | """ | |
| 2380 | assigns new values to symbols in the definition of the symbol. | |
| 2381 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2382 | ||
| 2383 | @param argvals: new values assigned to symbols | |
| 2384 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2385 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2386 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2387 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2388 | """ | |
| 2389 | if argvals.has_key(self): | |
| 2390 | arg=argvals[self] | |
| 2391 | if self.isAppropriateValue(arg): | |
| 2392 | return arg | |
| 2393 | else: | |
| 2394 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2395 | else: | |
| 2396 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2397 | return exp(arg) | |
| 2398 | ||
| 2399 | def diff(self,arg): | |
| 2400 | """ | |
| 2401 | differential of this object | |
| 2402 | ||
| 2403 | @param arg: the derivative is calculated with respect to arg | |
| 2404 | @type arg: L{escript.Symbol} | |
| 2405 | @return: derivative with respect to C{arg} | |
| 2406 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2407 | """ | |
| 2408 | if arg==self: | |
| 2409 | return identity(self.getShape()) | |
| 2410 | else: | |
| 2411 | myarg=self.getArgument()[0] | |
| 2412 | val=matchShape(self,self.getDifferentiatedArguments(arg)[0]) | |
| 2413 | return val[0]*val[1] | |
| 2414 | ||
| 2415 | def sqrt(arg): | |
| 2416 | """ | |
| 2417 | returns square root of argument arg | |
| 2418 | ||
| 2419 | @param arg: argument | |
| 2420 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2421 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2422 | @raises TypeError: if the type of the argument is not expected. | |
| 2423 | """ | |
| 2424 | if isinstance(arg,numarray.NumArray): | |
| 2425 | return numarray.sqrt(arg) | |
| 2426 | elif isinstance(arg,escript.Data): | |
| 2427 | return arg._sqrt() | |
| 2428 | elif isinstance(arg,float): | |
| 2429 | return math.sqrt(arg) | |
| 2430 | elif isinstance(arg,int): | |
| 2431 | return math.sqrt(arg) | |
| 2432 | elif isinstance(arg,Symbol): | |
| 2433 | return Sqrt_Symbol(arg) | |
| 2434 | else: | |
| 2435 | raise TypeError,"sqrt: Unknown argument type." | |
| 2436 | ||
| 2437 | class Sqrt_Symbol(DependendSymbol): | |
| 2438 | """ | |
| 2439 | L{Symbol} representing the result of the square root function | |
| 2440 | """ | |
| 2441 | def __init__(self,arg): | |
| 2442 | """ | |
| 2443 | initialization of sqrt L{Symbol} with argument arg | |
| 2444 | @param arg: argument of function | |
| 2445 | @type arg: typically L{Symbol}. | |
| 2446 | """ | |
| 2447 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2448 | ||
| 2449 | def getMyCode(self,argstrs,format="escript"): | |
| 2450 | """ | |
| 2451 | returns a program code that can be used to evaluate the symbol. | |
| 2452 | ||
| 2453 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2454 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2455 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2456 | @type format: C{str} | |
| 2457 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2458 | @rtype: C{str} | |
| 2459 | @raise: NotImplementedError: if the requested format is not available | |
| 2460 | """ | |
| 2461 | if isinstance(argstrs,list): | |
| 2462 | argstrs=argstrs[0] | |
| 2463 | if format=="escript" or format=="str" or format=="text": | |
| 2464 | return "sqrt(%s)"%argstrs | |
| 2465 | else: | |
| 2466 | raise NotImplementedError,"Sqrt_Symbol does not provide program code for format %s."%format | |
| 2467 | ||
| 2468 | def substitute(self,argvals): | |
| 2469 | """ | |
| 2470 | assigns new values to symbols in the definition of the symbol. | |
| 2471 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2472 | ||
| 2473 | @param argvals: new values assigned to symbols | |
| 2474 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2475 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2476 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2477 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2478 | """ | |
| 2479 | if argvals.has_key(self): | |
| 2480 | arg=argvals[self] | |
| 2481 | if self.isAppropriateValue(arg): | |
| 2482 | return arg | |
| 2483 | else: | |
| 2484 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2485 | else: | |
| 2486 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2487 | return sqrt(arg) | |
| 2488 | ||
| 2489 | def diff(self,arg): | |
| 2490 | """ | |
| 2491 | differential of this object | |
| 2492 | ||
| 2493 | @param arg: the derivative is calculated with respect to arg | |
| 2494 | @type arg: L{escript.Symbol} | |
| 2495 | @return: derivative with respect to C{arg} | |
| 2496 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2497 | """ | |
| 2498 | if arg==self: | |
| 2499 | return identity(self.getShape()) | |
| 2500 | else: | |
| 2501 | myarg=self.getArgument()[0] | |
| 2502 | val=matchShape(0.5/self,self.getDifferentiatedArguments(arg)[0]) | |
| 2503 | return val[0]*val[1] | |
| 2504 | ||
| 2505 | def log(arg): | |
| 2506 | """ | |
| 2507 | returns natural logarithm of argument arg | |
| 2508 | ||
| 2509 | @param arg: argument | |
| 2510 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2511 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2512 | @raises TypeError: if the type of the argument is not expected. | |
| 2513 | """ | |
| 2514 | if isinstance(arg,numarray.NumArray): | |
| 2515 | return numarray.log(arg) | |
| 2516 | elif isinstance(arg,escript.Data): | |
| 2517 | return arg._log() | |
| 2518 | elif isinstance(arg,float): | |
| 2519 | return math.log(arg) | |
| 2520 | elif isinstance(arg,int): | |
| 2521 | return math.log(arg) | |
| 2522 | elif isinstance(arg,Symbol): | |
| 2523 | return Log_Symbol(arg) | |
| 2524 | else: | |
| 2525 | raise TypeError,"log: Unknown argument type." | |
| 2526 | ||
| 2527 | class Log_Symbol(DependendSymbol): | |
| 2528 | """ | |
| 2529 | L{Symbol} representing the result of the natural logarithm function | |
| 2530 | """ | |
| 2531 | def __init__(self,arg): | |
| 2532 | """ | |
| 2533 | initialization of log L{Symbol} with argument arg | |
| 2534 | @param arg: argument of function | |
| 2535 | @type arg: typically L{Symbol}. | |
| 2536 | """ | |
| 2537 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2538 | ||
| 2539 | def getMyCode(self,argstrs,format="escript"): | |
| 2540 | """ | |
| 2541 | returns a program code that can be used to evaluate the symbol. | |
| 2542 | ||
| 2543 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2544 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2545 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2546 | @type format: C{str} | |
| 2547 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2548 | @rtype: C{str} | |
| 2549 | @raise: NotImplementedError: if the requested format is not available | |
| 2550 | """ | |
| 2551 | if isinstance(argstrs,list): | |
| 2552 | argstrs=argstrs[0] | |
| 2553 | if format=="escript" or format=="str" or format=="text": | |
| 2554 | return "log(%s)"%argstrs | |
| 2555 | else: | |
| 2556 | raise NotImplementedError,"Log_Symbol does not provide program code for format %s."%format | |
| 2557 | ||
| 2558 | def substitute(self,argvals): | |
| 2559 | """ | |
| 2560 | assigns new values to symbols in the definition of the symbol. | |
| 2561 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2562 | ||
| 2563 | @param argvals: new values assigned to symbols | |
| 2564 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2565 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2566 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2567 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2568 | """ | |
| 2569 | if argvals.has_key(self): | |
| 2570 | arg=argvals[self] | |
| 2571 | if self.isAppropriateValue(arg): | |
| 2572 | return arg | |
| 2573 | else: | |
| 2574 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2575 | else: | |
| 2576 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2577 | return log(arg) | |
| 2578 | ||
| 2579 | def diff(self,arg): | |
| 2580 | """ | |
| 2581 | differential of this object | |
| 2582 | ||
| 2583 | @param arg: the derivative is calculated with respect to arg | |
| 2584 | @type arg: L{escript.Symbol} | |
| 2585 | @return: derivative with respect to C{arg} | |
| 2586 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2587 | """ | |
| 2588 | if arg==self: | |
| 2589 | return identity(self.getShape()) | |
| 2590 | else: | |
| 2591 | myarg=self.getArgument()[0] | |
| 2592 | val=matchShape(1./arg,self.getDifferentiatedArguments(arg)[0]) | |
| 2593 | return val[0]*val[1] | |
| 2594 | ||
| 2595 | def sign(arg): | |
| 2596 | """ | |
| 2597 | returns sign of argument arg | |
| 2598 | ||
| 2599 | @param arg: argument | |
| 2600 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2601 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2602 | @raises TypeError: if the type of the argument is not expected. | |
| 2603 | """ | |
| 2604 | if isinstance(arg,numarray.NumArray): | |
| 2605 | return wherePositive(arg)-whereNegative(arg) | |
| 2606 | elif isinstance(arg,escript.Data): | |
| 2607 | return arg._sign() | |
| 2608 | elif isinstance(arg,float): | |
| 2609 | if arg>0: | |
| 2610 | return 1. | |
| 2611 | elif arg<0: | |
| 2612 | return -1. | |
| 2613 | else: | |
| 2614 | return 0. | |
| 2615 | elif isinstance(arg,int): | |
| 2616 | if float(arg)>0: | |
| 2617 | return 1. | |
| 2618 | elif float(arg)<0: | |
| 2619 | return -1. | |
| 2620 | else: | |
| 2621 | return 0. | |
| 2622 | elif isinstance(arg,Symbol): | |
| 2623 | return wherePositive(arg)-whereNegative(arg) | |
| 2624 | else: | |
| 2625 | raise TypeError,"sign: Unknown argument type." | |
| 2626 | ||
| 2627 | class Abs_Symbol(DependendSymbol): | |
| 2628 | """ | |
| 2629 | L{Symbol} representing the result of the absolute value function | |
| 2630 | """ | |
| 2631 | def __init__(self,arg): | |
| 2632 | """ | |
| 2633 | initialization of abs L{Symbol} with argument arg | |
| 2634 | @param arg: argument of function | |
| 2635 | @type arg: typically L{Symbol}. | |
| 2636 | """ | |
| 2637 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2638 | ||
| 2639 | def getMyCode(self,argstrs,format="escript"): | |
| 2640 | """ | |
| 2641 | returns a program code that can be used to evaluate the symbol. | |
| 2642 | ||
| 2643 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2644 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2645 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2646 | @type format: C{str} | |
| 2647 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2648 | @rtype: C{str} | |
| 2649 | @raise: NotImplementedError: if the requested format is not available | |
| 2650 | """ | |
| 2651 | if isinstance(argstrs,list): | |
| 2652 | argstrs=argstrs[0] | |
| 2653 | if format=="escript" or format=="str" or format=="text": | |
| 2654 | return "abs(%s)"%argstrs | |
| 2655 | else: | |
| 2656 | raise NotImplementedError,"Abs_Symbol does not provide program code for format %s."%format | |
| 2657 | ||
| 2658 | def substitute(self,argvals): | |
| 2659 | """ | |
| 2660 | assigns new values to symbols in the definition of the symbol. | |
| 2661 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2662 | ||
| 2663 | @param argvals: new values assigned to symbols | |
| 2664 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2665 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2666 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2667 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2668 | """ | |
| 2669 | if argvals.has_key(self): | |
| 2670 | arg=argvals[self] | |
| 2671 | if self.isAppropriateValue(arg): | |
| 2672 | return arg | |
| 2673 | else: | |
| 2674 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2675 | else: | |
| 2676 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2677 | return abs(arg) | |
| 2678 | ||
| 2679 | def diff(self,arg): | |
| 2680 | """ | |
| 2681 | differential of this object | |
| 2682 | ||
| 2683 | @param arg: the derivative is calculated with respect to arg | |
| 2684 | @type arg: L{escript.Symbol} | |
| 2685 | @return: derivative with respect to C{arg} | |
| 2686 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2687 | """ | |
| 2688 | if arg==self: | |
| 2689 | return identity(self.getShape()) | |
| 2690 | else: | |
| 2691 | myarg=self.getArgument()[0] | |
| 2692 | val=matchShape(sign(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 2693 | return val[0]*val[1] | |
| 2694 | ||
| 2695 | def minval(arg): | def minval(arg): |
| 2696 | """ | |
| 2697 | returns minimum value over all components of arg at each data point | |
| 2698 | ||
| 2699 | @param arg: argument | |
| 2700 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2701 | @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg. | |
| 2702 | @raises TypeError: if the type of the argument is not expected. | |
| 2703 | """ | |
| 2704 | if isinstance(arg,numarray.NumArray): | |
| 2705 | if arg.rank==0: | |
| 2706 | return float(arg) | |
| 2707 | else: | |
| 2708 | return arg.min() | |
| 2709 | elif isinstance(arg,escript.Data): | |
| 2710 | return arg._minval() | |
| 2711 | elif isinstance(arg,float): | |
| 2712 | return arg | |
| 2713 | elif isinstance(arg,int): | |
| 2714 | return float(arg) | |
| 2715 | elif isinstance(arg,Symbol): | |
| 2716 | return Minval_Symbol(arg) | |
| 2717 | else: | |
| 2718 | raise TypeError,"minval: Unknown argument type." | |
| 2719 | ||
| 2720 | class Minval_Symbol(DependendSymbol): | |
| 2721 | """ | |
| 2722 | L{Symbol} representing the result of the minimum value function | |
| 2723 | """ | |
| 2724 | def __init__(self,arg): | |
| 2725 | """ | |
| 2726 | initialization of minimum value L{Symbol} with argument arg | |
| 2727 | @param arg: argument of function | |
| 2728 | @type arg: typically L{Symbol}. | |
| 2729 | """ | |
| 2730 | DependendSymbol.__init__(self,args=[arg],shape=(),dim=arg.getDim()) | |
| 2731 | ||
| 2732 | def getMyCode(self,argstrs,format="escript"): | |
| 2733 | """ | |
| 2734 | returns a program code that can be used to evaluate the symbol. | |
| 2735 | ||
| 2736 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2737 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2738 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2739 | @type format: C{str} | |
| 2740 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2741 | @rtype: C{str} | |
| 2742 | @raise: NotImplementedError: if the requested format is not available | |
| 2743 | """ | |
| 2744 | if isinstance(argstrs,list): | |
| 2745 | argstrs=argstrs[0] | |
| 2746 | if format=="escript" or format=="str" or format=="text": | |
| 2747 | return "minval(%s)"%argstrs | |
| 2748 | else: | |
| 2749 | raise NotImplementedError,"Minval_Symbol does not provide program code for format %s."%format | |
| 2750 | ||
| 2751 | def substitute(self,argvals): | |
| 2752 | """ | |
| 2753 | assigns new values to symbols in the definition of the symbol. | |
| 2754 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2755 | ||
| 2756 | @param argvals: new values assigned to symbols | |
| 2757 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2758 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2759 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2760 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2761 | """ | |
| 2762 | if argvals.has_key(self): | |
| 2763 | arg=argvals[self] | |
| 2764 | if self.isAppropriateValue(arg): | |
| 2765 | return arg | |
| 2766 | else: | |
| 2767 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2768 | else: | |
| 2769 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2770 | return minval(arg) | |
| 2771 | ||
| 2772 | def maxval(arg): | |
| 2773 | """ | |
| 2774 | returns maximum value over all components of arg at each data point | |
| 2775 | ||
| 2776 | @param arg: argument | |
| 2777 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2778 | @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg. | |
| 2779 | @raises TypeError: if the type of the argument is not expected. | |
| 2780 | """ | |
| 2781 | if isinstance(arg,numarray.NumArray): | |
| 2782 | if arg.rank==0: | |
| 2783 | return float(arg) | |
| 2784 | else: | |
| 2785 | return arg.max() | |
| 2786 | elif isinstance(arg,escript.Data): | |
| 2787 | return arg._maxval() | |
| 2788 | elif isinstance(arg,float): | |
| 2789 | return arg | |
| 2790 | elif isinstance(arg,int): | |
| 2791 | return float(arg) | |
| 2792 | elif isinstance(arg,Symbol): | |
| 2793 | return Maxval_Symbol(arg) | |
| 2794 | else: | |
| 2795 | raise TypeError,"maxval: Unknown argument type." | |
| 2796 | ||
| 2797 | class Maxval_Symbol(DependendSymbol): | |
| 2798 | """ | |
| 2799 | L{Symbol} representing the result of the maximum value function | |
| 2800 | """ | |
| 2801 | def __init__(self,arg): | |
| 2802 | """ | |
| 2803 | initialization of maximum value L{Symbol} with argument arg | |
| 2804 | @param arg: argument of function | |
| 2805 | @type arg: typically L{Symbol}. | |
| 2806 | """ | |
| 2807 | DependendSymbol.__init__(self,args=[arg],shape=(),dim=arg.getDim()) | |
| 2808 | ||
| 2809 | def getMyCode(self,argstrs,format="escript"): | |
| 2810 | """ | |
| 2811 | returns a program code that can be used to evaluate the symbol. | |
| 2812 | ||
| 2813 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2814 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2815 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2816 | @type format: C{str} | |
| 2817 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2818 | @rtype: C{str} | |
| 2819 | @raise: NotImplementedError: if the requested format is not available | |
| 2820 | """ | |
| 2821 | if isinstance(argstrs,list): | |
| 2822 | argstrs=argstrs[0] | |
| 2823 | if format=="escript" or format=="str" or format=="text": | |
| 2824 | return "maxval(%s)"%argstrs | |
| 2825 | else: | |
| 2826 | raise NotImplementedError,"Maxval_Symbol does not provide program code for format %s."%format | |
| 2827 | ||
| 2828 | def substitute(self,argvals): | |
| 2829 | """ | |
| 2830 | assigns new values to symbols in the definition of the symbol. | |
| 2831 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2832 | ||
| 2833 | @param argvals: new values assigned to symbols | |
| 2834 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2835 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2836 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2837 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2838 | """ | |
| 2839 | if argvals.has_key(self): | |
| 2840 | arg=argvals[self] | |
| 2841 | if self.isAppropriateValue(arg): | |
| 2842 | return arg | |
| 2843 | else: | |
| 2844 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2845 | else: | |
| 2846 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2847 | return maxval(arg) | |
| 2848 | ||
| 2849 | def length(arg): | |
| 2850 | """ | |
| 2851 | returns length/Euclidean norm of argument arg at each data point | |
| 2852 | ||
| 2853 | @param arg: argument | |
| 2854 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2855 | @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg. | |
| 2856 | """ | |
| 2857 | return sqrt(inner(arg,arg)) | |
| 2858 | ||
| 2859 | def trace(arg,axis_offset=0): | |
| 2860 | """ | |
| 2861 | returns the trace of arg which the sum of arg[k,k] over k. | |
| 2862 | ||
| 2863 | @param arg: argument | |
| 2864 | @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2865 | @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 | |
| 2866 | axis_offset and axis_offset+1 must be equal. | |
| 2867 | @type axis_offset: C{int} | |
| 2868 | @return: trace of arg. The rank of the returned object is minus 2 of the rank of arg. | |
| 2869 | @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2870 | """ | |
| 2871 | if isinstance(arg,numarray.NumArray): | |
| 2872 | sh=arg.shape | |
| 2873 | if len(sh)<2: | |
| 2874 | raise ValueError,"trace: rank of argument must be greater than 1" | |
| 2875 | if axis_offset<0 or axis_offset>len(sh)-2: | |
| 2876 | raise ValueError,"trace: axis_offset must be between 0 and %s"%len(sh)-2 | |
| 2877 | s1=1 | |
| 2878 | for i in range(axis_offset): s1*=sh[i] | |
| 2879 | s2=1 | |
| 2880 | for i in range(axis_offset+2,len(sh)): s2*=sh[i] | |
| 2881 | if not sh[axis_offset] == sh[axis_offset+1]: | |
| 2882 | raise ValueError,"trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1) | |
| 2883 | arg_reshaped=numarray.reshape(arg,(s1,sh[axis_offset],sh[axis_offset],s2)) | |
| 2884 | out=numarray.zeros([s1,s2],numarray.Float) | |
| 2885 | for i1 in range(s1): | |
| 2886 | for i2 in range(s2): | |
| 2887 | for j in range(sh[axis_offset]): out[i1,i2]+=arg_reshaped[i1,j,j,i2] | |
| 2888 | out.resize(sh[:axis_offset]+sh[axis_offset+2:]) | |
| 2889 | return out | |
| 2890 | elif isinstance(arg,escript.Data): | |
| 2891 | return escript_trace(arg,axis_offset) | |
| 2892 | elif isinstance(arg,float): | |
| 2893 | raise TypeError,"trace: illegal argument type float." | |
| 2894 | elif isinstance(arg,int): | |
| 2895 | raise TypeError,"trace: illegal argument type int." | |
| 2896 | elif isinstance(arg,Symbol): | |
| 2897 | return Trace_Symbol(arg,axis_offset) | |
| 2898 | else: | |
| 2899 | raise TypeError,"trace: Unknown argument type." | |
| 2900 | ||
| 2901 | def escript_trace(arg,axis_offset): # this should be escript._trace | |
| 2902 | "arg si a Data objects!!!" | |
| 2903 | if arg.getRank()<2: | |
| 2904 | raise ValueError,"escript_trace: rank of argument must be greater than 1" | |
| 2905 | if axis_offset<0 or axis_offset>arg.getRank()-2: | |
| 2906 | raise ValueError,"escript_trace: axis_offset must be between 0 and %s"%arg.getRank()-2 | |
| 2907 | s=list(arg.getShape()) | |
| 2908 | if not s[axis_offset] == s[axis_offset+1]: | |
| 2909 | raise ValueError,"escript_trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1) | |
| 2910 | out=escript.Data(0.,tuple(s[0:axis_offset]+s[axis_offset+2:]),arg.getFunctionSpace()) | |
| 2911 | if arg.getRank()==2: | |
| 2912 | for i0 in range(s[0]): | |
| 2913 | out+=arg[i0,i0] | |
| 2914 | elif arg.getRank()==3: | |
| 2915 | if axis_offset==0: | |
| 2916 | for i0 in range(s[0]): | |
| 2917 | for i2 in range(s[2]): | |
| 2918 | out[i2]+=arg[i0,i0,i2] | |
| 2919 | elif axis_offset==1: | |
| 2920 | for i0 in range(s[0]): | |
| 2921 | for i1 in range(s[1]): | |
| 2922 | out[i0]+=arg[i0,i1,i1] | |
| 2923 | elif arg.getRank()==4: | |
| 2924 | if axis_offset==0: | |
| 2925 | for i0 in range(s[0]): | |
| 2926 | for i2 in range(s[2]): | |
| 2927 | for i3 in range(s[3]): | |
| 2928 | out[i2,i3]+=arg[i0,i0,i2,i3] | |
| 2929 | elif axis_offset==1: | |
| 2930 | for i0 in range(s[0]): | |
| 2931 | for i1 in range(s[1]): | |
| 2932 | for i3 in range(s[3]): | |
| 2933 | out[i0,i3]+=arg[i0,i1,i1,i3] | |
| 2934 | elif axis_offset==2: | |
| 2935 | for i0 in range(s[0]): | |
| 2936 | for i1 in range(s[1]): | |
| 2937 | for i2 in range(s[2]): | |
| 2938 | out[i0,i1]+=arg[i0,i1,i2,i2] | |
| 2939 | return out | |
| 2940 | class Trace_Symbol(DependendSymbol): | |
| 2941 | """ | |
| 2942 | L{Symbol} representing the result of the trace function | |
| 2943 | """ | |
| 2944 | def __init__(self,arg,axis_offset=0): | |
| 2945 | """ | |
| 2946 | initialization of trace L{Symbol} with argument arg | |
| 2947 | @param arg: argument of function | |
| 2948 | @type arg: L{Symbol}. | |
| 2949 | @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 | |
| 2950 | axis_offset and axis_offset+1 must be equal. | |
| 2951 | @type axis_offset: C{int} | |
| 2952 | """ | |
| 2953 | if arg.getRank()<2: | |
| 2954 | raise ValueError,"Trace_Symbol: rank of argument must be greater than 1" | |
| 2955 | if axis_offset<0 or axis_offset>arg.getRank()-2: | |
| 2956 | raise ValueError,"Trace_Symbol: axis_offset must be between 0 and %s"%arg.getRank()-2 | |
| 2957 | s=list(arg.getShape()) | |
| 2958 | if not s[axis_offset] == s[axis_offset+1]: | |
| 2959 | raise ValueError,"Trace_Symbol: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1) | |
| 2960 | super(Trace_Symbol,self).__init__(args=[arg,axis_offset],shape=tuple(s[0:axis_offset]+s[axis_offset+2:]),dim=arg.getDim()) | |
| 2961 | ||
| 2962 | def getMyCode(self,argstrs,format="escript"): | |
| 2963 | """ | |
| 2964 | returns a program code that can be used to evaluate the symbol. | |
| 2965 | ||
| 2966 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2967 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2968 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2969 | @type format: C{str} | |
| 2970 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2971 | @rtype: C{str} | |
| 2972 | @raise: NotImplementedError: if the requested format is not available | |
| 2973 | """ | |
| 2974 | if format=="escript" or format=="str" or format=="text": | |
| 2975 | return "trace(%s,axis_offset=%s)"%(argstrs[0],argstrs[1]) | |
| 2976 | else: | |
| 2977 | raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format | |
| 2978 | ||
| 2979 | def substitute(self,argvals): | |
| 2980 | """ | |
| 2981 | assigns new values to symbols in the definition of the symbol. | |
| 2982 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2983 | ||
| 2984 | @param argvals: new values assigned to symbols | |
| 2985 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2986 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2987 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2988 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2989 | """ | |
| 2990 | if argvals.has_key(self): | |
| 2991 | arg=argvals[self] | |
| 2992 | if self.isAppropriateValue(arg): | |
| 2993 | return arg | |
| 2994 | else: | |
| 2995 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2996 | else: | |
| 2997 | arg=self.getSubstitutedArguments(argvals) | |
| 2998 | return trace(arg[0],axis_offset=arg[1]) | |
| 2999 | ||
| 3000 | def diff(self,arg): | |
| 3001 | """ | |
| 3002 | differential of this object | |
| 3003 | ||
| 3004 | @param arg: the derivative is calculated with respect to arg | |
| 3005 | @type arg: L{escript.Symbol} | |
| 3006 | @return: derivative with respect to C{arg} | |
| 3007 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 3008 | """ | |
| 3009 | if arg==self: | |
| 3010 | return identity(self.getShape()) | |
| 3011 | else: | |
| 3012 | return trace(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1]) | |
| 3013 | ||
| 3014 | def transpose(arg,axis_offset=None): | |
| 3015 | """ | |
| 3016 | returns the transpose of arg by swaping the first axis_offset and the last rank-axis_offset components. | |
| 3017 | ||
| 3018 | @param arg: argument | |
| 3019 | @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}, C{float}, C{int} | |
| 3020 | @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. | |
| 3021 | if axis_offset is not present C{int(r/2)} where r is the rank of arg is used. | |
| 3022 | @type axis_offset: C{int} | |
| 3023 | @return: transpose of arg | |
| 3024 | @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray},C{float}, C{int} depending on the type of arg. | |
| 3025 | """ | |
| 3026 | if isinstance(arg,numarray.NumArray): | |
| 3027 | if axis_offset==None: axis_offset=int(arg.rank/2) | |
| 3028 | return numarray.transpose(arg,axes=range(axis_offset,arg.rank)+range(0,axis_offset)) | |
| 3029 | elif isinstance(arg,escript.Data): | |
| 3030 | if axis_offset==None: axis_offset=int(arg.getRank()/2) | |
| 3031 | return escript_transpose(arg,axis_offset) | |
| 3032 | elif isinstance(arg,float): | |
| 3033 | if not ( axis_offset==0 or axis_offset==None): | |
| 3034 | raise ValueError,"transpose: axis_offset must be 0 for float argument" | |
| 3035 | return arg | |
| 3036 | elif isinstance(arg,int): | |
| 3037 | if not ( axis_offset==0 or axis_offset==None): | |
| 3038 | raise ValueError,"transpose: axis_offset must be 0 for int argument" | |
| 3039 | return float(arg) | |
| 3040 | elif isinstance(arg,Symbol): | |
| 3041 | if axis_offset==None: axis_offset=int(arg.getRank()/2) | |
| 3042 | return Transpose_Symbol(arg,axis_offset) | |
| 3043 | else: | |
| 3044 | raise TypeError,"transpose: Unknown argument type." | |
| 3045 | ||
| 3046 | def escript_transpose(arg,axis_offset): # this should be escript._transpose | |
| 3047 | "arg si a Data objects!!!" | |
| 3048 | r=arg.getRank() | |
| 3049 | if axis_offset<0 or axis_offset>r: | |
| 3050 | raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r | |
| 3051 | s=arg.getShape() | |
| 3052 | s_out=s[axis_offset:]+s[:axis_offset] | |
| 3053 | out=escript.Data(0.,s_out,arg.getFunctionSpace()) | |
| 3054 | if r==4: | |
| 3055 | if axis_offset==1: | |
| 3056 | for i0 in range(s_out[0]): | |
| 3057 | for i1 in range(s_out[1]): | |
| 3058 | for i2 in range(s_out[2]): | |
| 3059 | for i3 in range(s_out[3]): | |
| 3060 | out[i0,i1,i2,i3]=arg[i3,i0,i1,i2] | |
| 3061 | elif axis_offset==2: | |
| 3062 | for i0 in range(s_out[0]): | |
| 3063 | for i1 in range(s_out[1]): | |
| 3064 | for i2 in range(s_out[2]): | |
| 3065 | for i3 in range(s_out[3]): | |
| 3066 | out[i0,i1,i2,i3]=arg[i2,i3,i0,i1] | |
| 3067 | elif axis_offset==3: | |
| 3068 | for i0 in range(s_out[0]): | |
| 3069 | for i1 in range(s_out[1]): | |
| 3070 | for i2 in range(s_out[2]): | |
| 3071 | for i3 in range(s_out[3]): | |
| 3072 | out[i0,i1,i2,i3]=arg[i1,i2,i3,i0] | |
| 3073 | else: | |
| 3074 | for i0 in range(s_out[0]): | |
| 3075 | for i1 in range(s_out[1]): | |
| 3076 | for i2 in range(s_out[2]): | |
| 3077 | for i3 in range(s_out[3]): | |
| 3078 | out[i0,i1,i2,i3]=arg[i0,i1,i2,i3] | |
| 3079 | elif r==3: | |
| 3080 | if axis_offset==1: | |
| 3081 | for i0 in range(s_out[0]): | |
| 3082 | for i1 in range(s_out[1]): | |
| 3083 | for i2 in range(s_out[2]): | |
| 3084 | out[i0,i1,i2]=arg[i2,i0,i1] | |
| 3085 | elif axis_offset==2: | |
| 3086 | for i0 in range(s_out[0]): | |
| 3087 | for i1 in range(s_out[1]): | |
| 3088 | for i2 in range(s_out[2]): | |
| 3089 | out[i0,i1,i2]=arg[i1,i2,i0] | |
| 3090 | else: | |
| 3091 | for i0 in range(s_out[0]): | |
| 3092 | for i1 in range(s_out[1]): | |
| 3093 | for i2 in range(s_out[2]): | |
| 3094 | out[i0,i1,i2]=arg[i0,i1,i2] | |
| 3095 | elif r==2: | |
| 3096 | if axis_offset==1: | |
| 3097 | for i0 in range(s_out[0]): | |
| 3098 | for i1 in range(s_out[1]): | |
| 3099 | out[i0,i1]=arg[i1,i0] | |
| 3100 | else: | |
| 3101 | for i0 in range(s_out[0]): | |
| 3102 | for i1 in range(s_out[1]): | |
| 3103 | out[i0,i1]=arg[i0,i1] | |
| 3104 | elif r==1: | |
| 3105 | for i0 in range(s_out[0]): | |
| 3106 | out[i0]=arg[i0] | |
| 3107 | elif r==0: | |
| 3108 | out=arg+0. | |
| 3109 | return out | |
| 3110 | class Transpose_Symbol(DependendSymbol): | |
| 3111 | """ | |
| 3112 | L{Symbol} representing the result of the transpose function | |
| 3113 | """ | |
| 3114 | def __init__(self,arg,axis_offset=None): | |
| 3115 | """ | |
| 3116 | initialization of transpose L{Symbol} with argument arg | |
| 3117 | ||
| 3118 | @param arg: argument of function | |
| 3119 | @type arg: L{Symbol}. | |
| 3120 | @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. | |
| 3121 | if axis_offset is not present C{int(r/2)} where r is the rank of arg is used. | |
| 3122 | @type axis_offset: C{int} | |
| 3123 | """ | |
| 3124 | if axis_offset==None: axis_offset=int(arg.getRank()/2) | |
| 3125 | if axis_offset<0 or axis_offset>arg.getRank(): | |
| 3126 | raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r | |
| 3127 | s=arg.getShape() | |
| 3128 | super(Transpose_Symbol,self).__init__(args=[arg,axis_offset],shape=s[axis_offset:]+s[:axis_offset],dim=arg.getDim()) | |
| 3129 | ||
| 3130 | def getMyCode(self,argstrs,format="escript"): | |
| 3131 | """ | |
| 3132 | returns a program code that can be used to evaluate the symbol. | |
| 3133 | ||
| 3134 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 3135 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 3136 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 3137 | @type format: C{str} | |
| 3138 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 3139 | @rtype: C{str} | |
| 3140 | @raise: NotImplementedError: if the requested format is not available | |
| 3141 | """ | |
| 3142 | if format=="escript" or format=="str" or format=="text": | |
| 3143 | return "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1]) | |
| 3144 | else: | |
| 3145 | raise NotImplementedError,"Transpose_Symbol does not provide program code for format %s."%format | |
| 3146 | ||
| 3147 | def substitute(self,argvals): | |
| 3148 | """ | |
| 3149 | assigns new values to symbols in the definition of the symbol. | |
| 3150 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 3151 | ||
| 3152 | @param argvals: new values assigned to symbols | |
| 3153 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 3154 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 3155 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 3156 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 3157 | """ | |
| 3158 | if argvals.has_key(self): | |
| 3159 | arg=argvals[self] | |
| 3160 | if self.isAppropriateValue(arg): | |
| 3161 | return arg | |
| 3162 | else: | |
| 3163 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 3164 | else: | |
| 3165 | arg=self.getSubstitutedArguments(argvals) | |
| 3166 | return transpose(arg[0],axis_offset=arg[1]) | |
| 3167 | ||
| 3168 | def diff(self,arg): | |
| 3169 | """ | |
| 3170 | differential of this object | |
| 3171 | ||
| 3172 | @param arg: the derivative is calculated with respect to arg | |
| 3173 | @type arg: L{escript.Symbol} | |
| 3174 | @return: derivative with respect to C{arg} | |
| 3175 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 3176 | """ | |
| 3177 | if arg==self: | |
| 3178 | return identity(self.getShape()) | |
| 3179 | else: | |
| 3180 | return transpose(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1]) | |
| 3181 | ||
| 3182 | def inverse(arg): | |
| 3183 | """ | """ |
| 3184 | @brief | returns the inverse of the square matrix arg. |
| 3185 | ||
| 3186 | @param arg | @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal |
| 3187 | @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol} | |
| 3188 | @return: inverse arg_inv of the argument. It will be matrixmul(inverse(arg),arg) almost equal to kronecker(arg.getShape()[0]) | |
| 3189 | @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input | |
| 3190 | """ | """ |
| 3191 | return arg.minval() | if isinstance(arg,numarray.NumArray): |
| 3192 | return numarray.linear_algebra.inverse(arg) | |
| 3193 | elif isinstance(arg,escript.Data): | |
| 3194 | return escript_inverse(arg) | |
| 3195 | elif isinstance(arg,float): | |
| 3196 | return 1./arg | |
| 3197 | elif isinstance(arg,int): | |
| 3198 | return 1./float(arg) | |
| 3199 | elif isinstance(arg,Symbol): | |
| 3200 | return Inverse_Symbol(arg) | |
| 3201 | else: | |
| 3202 | raise TypeError,"inverse: Unknown argument type." | |
| 3203 | ||
| 3204 | def sup(arg): | def escript_inverse(arg): # this should be escript._inverse and use LAPACK |
| 3205 | "arg is a Data objects!!!" | |
| 3206 | if not arg.getRank()==2: | |
| 3207 | raise ValueError,"escript_inverse: argument must have rank 2" | |
| 3208 | s=arg.getShape() | |
| 3209 | if not s[0] == s[1]: | |
| 3210 | raise ValueError,"escript_inverse: argument must be a square matrix." | |
| 3211 | out=escript.Data(0.,s,arg.getFunctionSpace()) | |
| 3212 | if s[0]==1: | |
| 3213 | if inf(abs(arg[0,0]))==0: # in c this should be done point wise as abs(arg[0,0](i))<=0. | |
| 3214 | raise ZeroDivisionError,"escript_inverse: argument not invertible" | |
| 3215 | out[0,0]=1./arg[0,0] | |
| 3216 | elif s[0]==2: | |
| 3217 | A11=arg[0,0] | |
| 3218 | A12=arg[0,1] | |
| 3219 | A21=arg[1,0] | |
| 3220 | A22=arg[1,1] | |
| 3221 | D = A11*A22-A12*A21 | |
| 3222 | if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0. | |
| 3223 | raise ZeroDivisionError,"escript_inverse: argument not invertible" | |
| 3224 | D=1./D | |
| 3225 | out[0,0]= A22*D | |
| 3226 | out[1,0]=-A21*D | |
| 3227 | out[0,1]=-A12*D | |
| 3228 | out[1,1]= A11*D | |
| 3229 | elif s[0]==3: | |
| 3230 | A11=arg[0,0] | |
| 3231 | A21=arg[1,0] | |
| 3232 | A31=arg[2,0] | |
| 3233 | A12=arg[0,1] | |
| 3234 | A22=arg[1,1] | |
| 3235 | A32=arg[2,1] | |
| 3236 | A13=arg[0,2] | |
| 3237 | A23=arg[1,2] | |
| 3238 | A33=arg[2,2] | |
| 3239 | D = A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22) | |
| 3240 | if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0. | |
| 3241 | raise ZeroDivisionError,"escript_inverse: argument not invertible" | |
| 3242 | D=1./D | |
| 3243 | out[0,0]=(A22*A33-A23*A32)*D | |
| 3244 | out[1,0]=(A31*A23-A21*A33)*D | |
| 3245 | out[2,0]=(A21*A32-A31*A22)*D | |
| 3246 | out[0,1]=(A13*A32-A12*A33)*D | |
| 3247 | out[1,1]=(A11*A33-A31*A13)*D | |
| 3248 | out[2,1]=(A12*A31-A11*A32)*D | |
| 3249 | out[0,2]=(A12*A23-A13*A22)*D | |
| 3250 | out[1,2]=(A13*A21-A11*A23)*D | |
| 3251 | out[2,2]=(A11*A22-A12*A21)*D | |
| 3252 | else: | |
| 3253 | raise TypeError,"escript_inverse: only matrix dimensions 1,2,3 are supported right now." | |
| 3254 | return out | |
| 3255 | ||
| 3256 | class Inverse_Symbol(DependendSymbol): | |
| 3257 | """ | |
| 3258 | L{Symbol} representing the result of the inverse function | |
| 3259 | """ | |
| 3260 | def __init__(self,arg): | |
| 3261 | """ | |
| 3262 | initialization of inverse L{Symbol} with argument arg | |
| 3263 | @param arg: argument of function | |
| 3264 | @type arg: L{Symbol}. | |
| 3265 | """ | |
| 3266 | if not arg.getRank()==2: | |
| 3267 | raise ValueError,"Inverse_Symbol:: argument must have rank 2" | |
| 3268 | s=arg.getShape() | |
| 3269 | if not s[0] == s[1]: | |
| 3270 | raise ValueError,"Inverse_Symbol:: argument must be a square matrix." | |
| 3271 | super(Inverse_Symbol,self).__init__(args=[arg],shape=s,dim=arg.getDim()) | |
| 3272 | ||
| 3273 | def getMyCode(self,argstrs,format="escript"): | |
| 3274 | """ | |
| 3275 | returns a program code that can be used to evaluate the symbol. | |
| 3276 | ||
| 3277 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 3278 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 3279 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 3280 | @type format: C{str} | |
| 3281 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 3282 | @rtype: C{str} | |
| 3283 | @raise: NotImplementedError: if the requested format is not available | |
| 3284 | """ | |
| 3285 | if format=="escript" or format=="str" or format=="text": | |
| 3286 | return "inverse(%s)"%argstrs[0] | |
| 3287 | else: | |
| 3288 | raise NotImplementedError,"Inverse_Symbol does not provide program code for format %s."%format | |
| 3289 |