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| revision 289 by jgs, Wed Nov 9 02:02:19 2005 UTC | revision 290 by gross, Fri Dec 2 03:09:32 2005 UTC | |
|---|---|---|
| # | 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 | Utility functions for escript | Utility functions for escript |
| 14 | ||
| 15 | @todo: | @remark: This module is under construction and is still tested!!! |
| 16 | ||
| 17 | - binary operations @ (@=+,-,*,/,**):: | @var __author__: name of author |
| 18 | (a@b)[:,*]=a[:]@b[:,*] if rank(a)<rank(b) | @var __licence__: licence agreement |
| 19 | (a@b)[:]=a[:]@b[:] if rank(a)=rank(b) | @var __url__: url entry point on documentation |
| 20 | (a@b)[*,:]=a[*,:]@b[:] if rank(a)>rank(b) | @var __version__: version |
| 21 | - implementation of outer:: | @var __date__: date of the version |
| outer(a,b)[:,*]=a[:]*b[*] | ||
| - trace:: | ||
| trace(arg,axis0=a0,axis1=a1)(:,&,*)=sum_i trace(:,i,&,i,*) (i are at index a0 and a1) | ||
| 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 escript | import escript |
| import symbols | ||
| 34 | import os | import os |
| 35 | ||
| 36 | #========================================================= | # missing tests: |
| 37 | # some little helpers | |
| 38 | #========================================================= | # def pokeShape(arg): |
| 39 | def _testForZero(arg): | # def pokeDim(arg): |
| 40 | """ | # def commonShape(arg0,arg1): |
| 41 | Returns True is arg is considered to be zero. | # def commonDim(*args): |
| 42 | """ | # def testForZero(arg): |
| 43 | if isinstance(arg,int): | # def matchType(arg0=0.,arg1=0.): |
| 44 | return not arg>0 | # def matchShape(arg0,arg1): |
| 45 | elif isinstance(arg,float): | |
| 46 | return not arg>0. | # def maximum(arg0,arg1): |
| 47 | elif isinstance(arg,numarray.NumArray): | # def minimum(arg0,arg1): |
| 48 | a=abs(arg) | # def minval(arg0): |
| 49 | while isinstance(a,numarray.NumArray): a=numarray.sometrue(a) | # def maxval(arg0): |
| 50 | return not a>0 | # def transpose(arg,axis=None): |
| 51 | else: | # def trace(arg,axis0=0,axis1=1): |
| 52 | return False | # def length(arg): |
| 53 | # def reorderComponents(arg,index): | |
| 54 | ||
| 55 | # def integrate(arg,where=None): | |
| 56 | # def interpolate(arg,where): | |
| 57 | # def div(arg,where=None): | |
| 58 | # def grad(arg,where=None): | |
| 59 | ||
| 60 | # | |
| 61 | # slicing: get | |
| 62 | # set | |
| 63 | # | |
| 64 | # and derivatives | |
| 65 | ||
| 66 | #========================================================= | #========================================================= |
| 67 | # some helpers: | |
| 68 | #========================================================= | |
| 69 | def saveVTK(filename,domain=None,**data): | def saveVTK(filename,domain=None,**data): |
| 70 | """ | """ |
| 71 | writes a L{Data} objects into a files using the the VTK XML file format. | writes a L{Data} objects into a files using the the VTK XML file format. |
| # | Line 51 def saveVTK(filename,domain=None,**data) | Line 76 def saveVTK(filename,domain=None,**data) |
| 76 | v=Vector(..) | v=Vector(..) |
| 77 | saveVTK("solution.xml",temperature=tmp,velovity=v) | saveVTK("solution.xml",temperature=tmp,velovity=v) |
| 78 | ||
| 79 | tmp and v are written into "solution.dx" where tmp is named "temperature" and v is named "velovity" | tmp and v are written into "solution.xml" where tmp is named "temperature" and v is named "velovity" |
| 80 | ||
| 81 | @param filename: file name of the output file | @param filename: file name of the output file |
| 82 | @type filename: C(str} | @type filename: C{str} |
| 83 | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. |
| 84 | @type domain: L{escript.Domain} | @type domain: L{escript.Domain} |
| 85 | @keyword <name>: writes the assigned value to the VTK file using <name> as identifier. | @keyword <name>: writes the assigned value to the VTK file using <name> as identifier. |
| # | Line 69 def saveVTK(filename,domain=None,**data) | Line 94 def saveVTK(filename,domain=None,**data) |
| 94 | else: | else: |
| 95 | domain.saveVTK(filename,data) | domain.saveVTK(filename,data) |
| 96 | ||
| #========================================================= | ||
| 97 | def saveDX(filename,domain=None,**data): | def saveDX(filename,domain=None,**data): |
| 98 | """ | """ |
| 99 | writes a L{Data} objects into a files using the the DX file format. | writes a L{Data} objects into a files using the the DX file format. |
| # | Line 80 def saveDX(filename,domain=None,**data): | Line 104 def saveDX(filename,domain=None,**data): |
| 104 | v=Vector(..) | v=Vector(..) |
| 105 | saveDX("solution.dx",temperature=tmp,velovity=v) | saveDX("solution.dx",temperature=tmp,velovity=v) |
| 106 | ||
| 107 | tmp and v are written into "solution.dx" where tmp is named "temperature" and v is named "velovity". | tmp and v are written into "solution.dx" where tmp is named "temperature" and v is named "velovity". |
| 108 | ||
| 109 | @param filename: file name of the output file | @param filename: file name of the output file |
| 110 | @type filename: C(str} | @type filename: C{str} |
| 111 | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. | @param domain: domain of the L{Data} object. If not specified, the domain of the given L{Data} objects is used. |
| 112 | @type domain: L{escript.Domain} | @type domain: L{escript.Domain} |
| 113 | @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. | @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. |
| # | Line 98 def saveDX(filename,domain=None,**data): | Line 122 def saveDX(filename,domain=None,**data): |
| 122 | else: | else: |
| 123 | domain.saveDX(filename,data) | domain.saveDX(filename,data) |
| 124 | ||
| 125 | #========================================================= | def kronecker(d=3): |
| 126 | """ | |
| 127 | return the kronecker S{delta}-symbol | |
| 128 | ||
| 129 | def exp(arg): | @param d: dimension or an object that has the C{getDim} method defining the dimension |
| 130 | @type d: C{int} or any object with a C{getDim} method | |
| 131 | @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise | |
| 132 | @rtype d: L{numarray.NumArray} of rank 2. | |
| 133 | @remark: the function is identical L{identity} | |
| 134 | """ | |
| 135 | return identityTensor(d) | |
| 136 | ||
| 137 | def identity(shape=()): | |
| 138 | """ | |
| 139 | return the shape x shape identity tensor | |
| 140 | ||
| 141 | @param shape: input shape for the identity tensor | |
| 142 | @type shape: C{tuple} of C{int} | |
| 143 | @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. | |
| 144 | @rtype: L{numarray.NumArray} of rank 1, rankk 2 or rank 4. | |
| 145 | @raise ValueError: if len(shape)>2. | |
| 146 | """ | |
| 147 | if len(shape)>0: | |
| 148 | out=numarray.zeros(shape+shape,numarray.Float) | |
| 149 | if len(shape)==1: | |
| 150 | for i0 in range(shape[0]): | |
| 151 | out[i0,i0]=1. | |
| 152 | ||
| 153 | elif len(shape)==2: | |
| 154 | for i0 in range(shape[0]): | |
| 155 | for i1 in range(shape[1]): | |
| 156 | out[i0,i1,i0,i1]=1. | |
| 157 | else: | |
| 158 | raise ValueError,"identity: length of shape is restricted to 2." | |
| 159 | else: | |
| 160 | out=1. | |
| 161 | return out | |
| 162 | ||
| 163 | def identityTensor(d=3): | |
| 164 | """ | |
| 165 | return the dxd identity matrix | |
| 166 | ||
| 167 | @param d: dimension or an object that has the C{getDim} method defining the dimension | |
| 168 | @type d: C{int} or any object with a C{getDim} method | |
| 169 | @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise | |
| 170 | @rtype: L{numarray.NumArray} of rank 2. | |
| 171 | """ | |
| 172 | if hasattr(d,"getDim"): | |
| 173 | d=d.getDim() | |
| 174 | return identity(shape=(d,)) | |
| 175 | ||
| 176 | def identityTensor4(d=3): | |
| 177 | """ | |
| 178 | return the dxdxdxd identity tensor | |
| 179 | ||
| 180 | @param d: dimension or an object that has the C{getDim} method defining the dimension | |
| 181 | @type d: C{int} or any object with a C{getDim} method | |
| 182 | @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 | |
| 183 | @rtype: L{numarray.NumArray} of rank 4. | |
| 184 | """ | |
| 185 | if hasattr(d,"getDim"): | |
| 186 | d=d.getDim() | |
| 187 | return identity((d,d)) | |
| 188 | ||
| 189 | def unitVector(i=0,d=3): | |
| 190 | """ | |
| 191 | return a unit vector u of dimension d with nonzero index i: | |
| 192 | ||
| 193 | @param i: index | |
| 194 | @type i: C{int} | |
| 195 | @param d: dimension or an object that has the C{getDim} method defining the dimension | |
| 196 | @type d: C{int} or any object with a C{getDim} method | |
| 197 | @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise | |
| 198 | @rtype: L{numarray.NumArray} of rank 1. | |
| 199 | """ | |
| 200 | return kronecker(d)[i] | |
| 201 | ||
| 202 | #========================================================================= | |
| 203 | # global reduction operations (these functions have no symbolic version) | |
| 204 | #========================================================================= | |
| 205 | def Lsup(arg): | |
| 206 | """ | """ |
| 207 | Applies the exponential function to arg. | returns the Lsup-norm of argument arg. This is the maximum absolute value over all data points. |
| 208 | This function is equivalent to sup(abs(arg)). | |
| 209 | ||
| 210 | @param arg: argument | @param arg: argument |
| 211 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 212 | @return: maximum value of the absolute value of arg over all components and all data points | |
| 213 | @rtype: C{float} | |
| 214 | @raise TypeError: if type of arg cannot be processed | |
| 215 | """ | """ |
| 216 | if isinstance(arg,symbols.Symbol): | if isinstance(arg,numarray.NumArray): |
| 217 | return symbols.Exp_Symbol(arg) | return sup(abs(arg)) |
| 218 | elif hasattr(arg,"exp"): | elif isinstance(arg,escript.Data): |
| 219 | return arg.exp() | return arg._Lsup() |
| 220 | elif isinstance(arg,float): | |
| 221 | return abs(arg) | |
| 222 | elif isinstance(arg,int): | |
| 223 | return abs(float(arg)) | |
| 224 | else: | else: |
| 225 | return numarray.exp(arg) | raise TypeError,"Lsup: Unknown argument type." |
| 226 | ||
| 227 | def sqrt(arg): | def sup(arg): |
| 228 | """ | """ |
| 229 | Applies the squre root function to arg. | returns the maximum value over all data points. |
| 230 | ||
| 231 | @param arg: argument | @param arg: argument |
| 232 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 233 | @return: maximum value of arg over all components and all data points | |
| 234 | @rtype: C{float} | |
| 235 | @raise TypeError: if type of arg cannot be processed | |
| 236 | """ | """ |
| 237 | if isinstance(arg,symbols.Symbol): | if isinstance(arg,numarray.NumArray): |
| 238 | return symbols.Sqrt_Symbol(arg) | return arg.max() |
| 239 | elif hasattr(arg,"sqrt"): | elif isinstance(arg,escript.Data): |
| 240 | return arg.sqrt() | return arg._sup() |
| 241 | elif isinstance(arg,float): | |
| 242 | return arg | |
| 243 | elif isinstance(arg,int): | |
| 244 | return float(arg) | |
| 245 | else: | else: |
| 246 | return numarray.sqrt(arg) | raise TypeError,"sup: Unknown argument type." |
| 247 | ||
| 248 | def log(arg): | def inf(arg): |
| 249 | """ | """ |
| 250 | Applies the logarithmic function base 10 to arg. | returns the maximum value over all data points. |
| 251 | ||
| 252 | @param arg: argument | @param arg: argument |
| 253 | @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 254 | @return : minimum value of arg over all components and all data points | |
| 255 | @rtype: C{float} | |
| 256 | @raise TypeError: if type of arg cannot be processed | |
| 257 | """ | """ |
| 258 | if isinstance(arg,symbols.Symbol): | if isinstance(arg,numarray.NumArray): |
| 259 | return symbols.Log_Symbol(arg) | return arg.min() |
| 260 | elif hasattr(arg,"log"): | elif isinstance(arg,escript.Data): |
| 261 | return arg.log() | return arg._inf() |
| 262 | elif isinstance(arg,float): | |
| 263 | return arg | |
| 264 | elif isinstance(arg,int): | |
| 265 | return float(arg) | |
| 266 | else: | else: |
| 267 | return numarray.log10(arg) | raise TypeError,"inf: Unknown argument type." |
| 268 | ||
| 269 | ||
| 270 | def ln(arg): | #========================================================================= |
| 271 | # some little helpers | |
| 272 | #========================================================================= | |
| 273 | def pokeShape(arg): | |
| 274 | """ | """ |
| 275 | Applies the natural logarithmic function to arg. | identifies the shape of its argument |
| 276 | ||
| 277 | @param arg: argument | @param arg: a given object |
| 278 | @type arg: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 279 | @return: the shape of the argument | |
| 280 | @rtype: C{tuple} of C{int} | |
| 281 | @raise TypeError: if type of arg cannot be processed | |
| 282 | """ | """ |
| if isinstance(arg,symbols.Symbol): | ||
| return symbols.Ln_Symbol(arg) | ||
| elif hasattr(arg,"ln"): | ||
| return arg.ln() | ||
| else: | ||
| return numarray.log(arg) | ||
| 283 | ||
| 284 | def sin(arg): | if isinstance(arg,numarray.NumArray): |
| 285 | return arg.shape | |
| 286 | elif isinstance(arg,escript.Data): | |
| 287 | return arg.getShape() | |
| 288 | elif isinstance(arg,float): | |
| 289 | return () | |
| 290 | elif isinstance(arg,int): | |
| 291 | return () | |
| 292 | elif isinstance(arg,Symbol): | |
| 293 | return arg.getShape() | |
| 294 | else: | |
| 295 | raise TypeError,"pokeShape: cannot identify shape" | |
| 296 | ||
| 297 | def pokeDim(arg): | |
| 298 | """ | |
| 299 | identifies the spatial dimension of its argument | |
| 300 | ||
| 301 | @param arg: a given object | |
| 302 | @type arg: any | |
| 303 | @return: the spatial dimension of the argument, if available, or C{None} | |
| 304 | @rtype: C{int} or C{None} | |
| 305 | """ | """ |
| Applies the sin function to arg. | ||
| 306 | ||
| 307 | @param arg: argument | if isinstance(arg,escript.Data): |
| 308 | return arg.getFunctionSpace().getDim() | |
| 309 | elif isinstance(arg,Symbol): | |
| 310 | return arg.getDim() | |
| 311 | else: | |
| 312 | return None | |
| 313 | ||
| 314 | def commonShape(arg0,arg1): | |
| 315 | """ | |
| 316 | returns a shape to which arg0 can be extendent from the right and arg1 can be extended from the left. | |
| 317 | ||
| 318 | @param arg0: an object with a shape (see L{pokeShape}) | |
| 319 | @param arg1: an object with a shape (see L{pokeShape}) | |
| 320 | @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. | |
| 321 | @rtype: C{tuple} of C{int} | |
| 322 | @raise ValueError: if no shape can be found. | |
| 323 | """ | |
| 324 | sh0=pokeShape(arg0) | |
| 325 | sh1=pokeShape(arg1) | |
| 326 | if len(sh0)<len(sh1): | |
| 327 | if not sh0==sh1[:len(sh0)]: | |
| 328 | raise ValueError,"argument 0 cannot be extended to the shape of argument 1" | |
| 329 | return sh1 | |
| 330 | elif len(sh0)>len(sh1): | |
| 331 | if not sh1==sh0[:len(sh1)]: | |
| 332 | raise ValueError,"argument 1 cannot be extended to the shape of argument 0" | |
| 333 | return sh0 | |
| 334 | else: | |
| 335 | if not sh0==sh1: | |
| 336 | raise ValueError,"argument 1 and argument 0 have not the same shape." | |
| 337 | return sh0 | |
| 338 | ||
| 339 | def commonDim(*args): | |
| 340 | """ | |
| 341 | identifies, if possible, the spatial dimension across a set of objects which may or my not have a spatial dimension. | |
| 342 | ||
| 343 | @param *args: given objects | |
| 344 | @return: the spatial dimension of the objects with identifiable dimension (see L{pokeDim}). If none the objects has | |
| 345 | a spatial dimension C{None} is returned. | |
| 346 | @rtype: C{int} or C{None} | |
| 347 | @raise ValueError: if the objects with identifiable dimension don't have the same spatial dimension. | |
| 348 | """ | |
| 349 | out=None | |
| 350 | for a in args: | |
| 351 | d=pokeDim(a) | |
| 352 | if not out==None: | |
| 353 | if not (d==None or out==d): | |
| 354 | raise ValueError,"dimension of arguments don't match" | |
| 355 | else: | |
| 356 | out=d | |
| 357 | return out | |
| 358 | ||
| 359 | def testForZero(arg): | |
| 360 | """ | """ |
| 361 | if isinstance(arg,symbols.Symbol): | test the argument for being identical to Zero |
| 362 | return symbols.Sin_Symbol(arg) | |
| 363 | elif hasattr(arg,"sin"): | @param arg: a given object |
| 364 | return arg.sin() | @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int} |
| 365 | @return : True if the argument is identical to zero. | |
| 366 | @rtype : C{bool} | |
| 367 | """ | |
| 368 | try: | |
| 369 | return not Lsup(arg)>0. | |
| 370 | except TypeError: | |
| 371 | return False | |
| 372 | ||
| 373 | def matchType(arg0=0.,arg1=0.): | |
| 374 | """ | |
| 375 | 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}. | |
| 376 | ||
| 377 | @param arg0: first argument | |
| 378 | @type arg0: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 379 | @param arg1: second argument | |
| 380 | @type arg1: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 381 | @return: a tuple representing arg0 and arg1 with the same type or with one of them being a L{Symbol} | |
| 382 | @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}. | |
| 383 | @raise TypeError: if type of arg0 or arg1 cannot be processed | |
| 384 | """ | |
| 385 | if isinstance(arg0,numarray.NumArray): | |
| 386 | if isinstance(arg1,numarray.NumArray): | |
| 387 | pass | |
| 388 | elif isinstance(arg1,escript.Data): | |
| 389 | arg0=escript.Data(arg0,arg1.getFunctionSpace()) | |
| 390 | elif isinstance(arg1,float): | |
| 391 | arg1=numarray.array(arg1) | |
| 392 | elif isinstance(arg1,int): | |
| 393 | arg1=numarray.array(float(arg1)) | |
| 394 | elif isinstance(arg1,Symbol): | |
| 395 | pass | |
| 396 | else: | |
| 397 | raise TypeError,"function: Unknown type of second argument." | |
| 398 | elif isinstance(arg0,escript.Data): | |
| 399 | if isinstance(arg1,numarray.NumArray): | |
| 400 | arg1=escript.Data(arg1,arg0.getFunctionSpace()) | |
| 401 | elif isinstance(arg1,escript.Data): | |
| 402 | pass | |
| 403 | elif isinstance(arg1,float): | |
| 404 | arg1=escript.Data(arg1,(),arg0.getFunctionSpace()) | |
| 405 | elif isinstance(arg1,int): | |
| 406 | arg1=escript.Data(float(arg1),(),arg0.getFunctionSpace()) | |
| 407 | elif isinstance(arg1,Symbol): | |
| 408 | pass | |
| 409 | else: | |
| 410 | raise TypeError,"function: Unknown type of second argument." | |
| 411 | elif isinstance(arg0,Symbol): | |
| 412 | if isinstance(arg1,numarray.NumArray): | |
| 413 | pass | |
| 414 | elif isinstance(arg1,escript.Data): | |
| 415 | pass | |
| 416 | elif isinstance(arg1,float): | |
| 417 | arg1=numarray.array(arg1) | |
| 418 | elif isinstance(arg1,int): | |
| 419 | arg1=numarray.array(float(arg1)) | |
| 420 | elif isinstance(arg1,Symbol): | |
| 421 | pass | |
| 422 | else: | |
| 423 | raise TypeError,"function: Unknown type of second argument." | |
| 424 | elif isinstance(arg0,float): | |
| 425 | if isinstance(arg1,numarray.NumArray): | |
| 426 | arg0=numarray.array(arg0) | |
| 427 | elif isinstance(arg1,escript.Data): | |
| 428 | arg0=escript.Data(arg0,arg1.getFunctionSpace()) | |
| 429 | elif isinstance(arg1,float): | |
| 430 | arg0=numarray.array(arg0) | |
| 431 | arg1=numarray.array(arg1) | |
| 432 | elif isinstance(arg1,int): | |
| 433 | arg0=numarray.array(arg0) | |
| 434 | arg1=numarray.array(float(arg1)) | |
| 435 | elif isinstance(arg1,Symbol): | |
| 436 | arg0=numarray.array(arg0) | |
| 437 | else: | |
| 438 | raise TypeError,"function: Unknown type of second argument." | |
| 439 | elif isinstance(arg0,int): | |
| 440 | if isinstance(arg1,numarray.NumArray): | |
| 441 | arg0=numarray.array(float(arg0)) | |
| 442 | elif isinstance(arg1,escript.Data): | |
| 443 | arg0=escript.Data(float(arg0),arg1.getFunctionSpace()) | |
| 444 | elif isinstance(arg1,float): | |
| 445 | arg0=numarray.array(float(arg0)) | |
| 446 | arg1=numarray.array(arg1) | |
| 447 | elif isinstance(arg1,int): | |
| 448 | arg0=numarray.array(float(arg0)) | |
| 449 | arg1=numarray.array(float(arg1)) | |
| 450 | elif isinstance(arg1,Symbol): | |
| 451 | arg0=numarray.array(float(arg0)) | |
| 452 | else: | |
| 453 | raise TypeError,"function: Unknown type of second argument." | |
| 454 | else: | else: |
| 455 | return numarray.sin(arg) | raise TypeError,"function: Unknown type of first argument." |
| 456 | ||
| 457 | def cos(arg): | return arg0,arg1 |
| 458 | ||
| 459 | def matchShape(arg0,arg1): | |
| 460 | """ | """ |
| 461 | Applies the cos function to arg. | |
| 462 | ||
| 463 | If shape is not given the shape "largest" shape of args is used. | |
| 464 | ||
| 465 | @param arg: argument | @param args: a given ob |
| 466 | @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int} | |
| 467 | @return: True if the argument is identical to zero. | |
| 468 | @rtype: C{list} of C{int} | |
| 469 | """ | """ |
| 470 | if isinstance(arg,symbols.Symbol): | sh=commonShape(arg0,arg1) |
| 471 | return symbols.Cos_Symbol(arg) | sh0=pokeShape(arg0) |
| 472 | elif hasattr(arg,"cos"): | sh1=pokeShape(arg1) |
| 473 | return arg.cos() | if len(sh0)<len(sh): |
| 474 | else: | return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float)),arg1 |
| 475 | return numarray.cos(arg) | elif len(sh1)<len(sh): |
| 476 | return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float)) | |
| 477 | else: | |
| 478 | return arg0,arg1 | |
| 479 | #========================================================= | |
| 480 | # symbolic tool box starts here: | |
| 481 | #========================================================= | |
| 482 | class Symbol(object): | |
| 483 | """ | |
| 484 | Symbol class. | |
| 485 | ||
| 486 | Symbol class objects provide the same functionality as L{numarray.NumArray} and L{escript.Data} objects | |
| 487 | but they do not have a value and therefore cannot be plotted or visualize. The main purpose is the possibilty | |
| 488 | calculate derivatives with respect to other Symbols used to define a Symbol. | |
| 489 | ||
| 490 | """ | |
| 491 | def __init__(self,shape=(),args=[],dim=None): | |
| 492 | """ | |
| 493 | Creates an instance of a symbol of a given shape. The symbol may depending on a list of arguments args which may be | |
| 494 | symbols or any other object. | |
| 495 | ||
| 496 | @param arg: the arguments of the symbol. | |
| 497 | @type arg: C{list} | |
| 498 | @param shape: the shape | |
| 499 | @type shape: C{tuple} of C{int} | |
| 500 | @param dim: spatial dimension of the symbol. If dim=C{None} the spatial dimension is undefined. | |
| 501 | @type dim: C{None} or C{int} | |
| 502 | ||
| 503 | """ | |
| 504 | if len(shape)>4: | |
| 505 | raise ValueError,"Symbol supports only tensors up to order 4" | |
| 506 | self.__args=args | |
| 507 | self.__shape=shape | |
| 508 | self.__dim=dim | |
| 509 | ||
| 510 | def getArgument(self,i=None): | |
| 511 | """ | |
| 512 | returns the i-th argument of the symbol | |
| 513 | ||
| 514 | @param i: index of the argument requested. | |
| 515 | @type i: C{int} or C{None} | |
| 516 | @raise IndexError: if the requested index does not exist | |
| 517 | @return: the vlaue of the i-th argument or i is not specified the list of all arguments. | |
| 518 | @rtype: a single object or a list of objects | |
| 519 | """ | |
| 520 | if i==None: | |
| 521 | return self.__args | |
| 522 | else: | |
| 523 | if i<0 or i>=len(self.__args): | |
| 524 | raise IndexError,"there are only %s arguments"%len(self.__args) | |
| 525 | return self.__args[i] | |
| 526 | ||
| 527 | def getRank(self): | |
| 528 | """ | |
| 529 | the rank of the symbol | |
| 530 | ||
| 531 | @return: the rank of the symbol. This is length of the shape | |
| 532 | @rtype: C{int} | |
| 533 | """ | |
| 534 | return len(self.getShape()) | |
| 535 | ||
| 536 | def getShape(self): | |
| 537 | """ | |
| 538 | the shape of the symbol. | |
| 539 | ||
| 540 | @return : the shape of the symbol. | |
| 541 | @rtype: C{tuple} of C{int} | |
| 542 | """ | |
| 543 | return self.__shape | |
| 544 | ||
| 545 | def getDim(self): | |
| 546 | """ | |
| 547 | the spatial dimension | |
| 548 | ||
| 549 | @return : the spatial dimension | |
| 550 | @rtype: C{int} if the dimension is defined. Otherwise C{None} is returned. | |
| 551 | """ | |
| 552 | return self.__dim | |
| 553 | ||
| 554 | def __str__(self): | |
| 555 | """ | |
| 556 | a string representation of the symbol. | |
| 557 | @return: a string representation of the object | |
| 558 | @rtype: C{str} | |
| 559 | """ | |
| 560 | args=[] | |
| 561 | for arg in self.getArgument(): | |
| 562 | args.append(str(arg)) | |
| 563 | try: | |
| 564 | out=self.getMyCode(args,format="str") | |
| 565 | except NotImplementedError: | |
| 566 | out="<Symbol %s>"%id(self) | |
| 567 | return out | |
| 568 | ||
| 569 | def getSubstitutedArguments(self,argvals): | |
| 570 | """ | |
| 571 | substitutes symbols in the arguments of this object and returns the result as a list. | |
| 572 | ||
| 573 | @param argvals: L{Symbols} and their substitutes. The L{Symbol} u in the expression defining this object is replaced by argvals[u]. | |
| 574 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 575 | @rtype: C{list} of objects | |
| 576 | @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. | |
| 577 | """ | |
| 578 | out=[] | |
| 579 | for a in self.getArgument(): | |
| 580 | if isinstance(a,Symbol): | |
| 581 | out.append(a.substitute(argvals)) | |
| 582 | else: | |
| 583 | out.append(a) | |
| 584 | return out | |
| 585 | ||
| 586 | def getDifferentiatedArguments(self,arg): | |
| 587 | """ | |
| 588 | applifies differentials to the arguments of this object and returns the result as a list. | |
| 589 | ||
| 590 | @param arg: the derivative is calculated with respect to arg | |
| 591 | @type arg: typically L{escript.Symbol} but can also be C{float}, L{escript.Data}, L{numarray.NumArray} depending the involved functions and data. | |
| 592 | @rtype: C{list} of objects | |
| 593 | @return: list of object obtained by calculating the derivatives of the argumenst with respct to arg | |
| 594 | """ | |
| 595 | out=[] | |
| 596 | for a in self.getArgument(): | |
| 597 | if isinstance(a,Symbol): | |
| 598 | out.append(a.substitute(argvals)) | |
| 599 | else: | |
| 600 | s=pokeShape(s)+arg.getShape() | |
| 601 | if len(s)>0: | |
| 602 | out.append(numarray.zeros(s),numarray.Float) | |
| 603 | else: | |
| 604 | out.append(a) | |
| 605 | return out | |
| 606 | ||
| 607 | def isAppropriateValue(self,arg): | |
| 608 | """ | |
| 609 | checks if the given argument arg can be used as a substitution of this object. The method checks | |
| 610 | the shape of arg and, if the spatial dimension is defined, the spatial dimension of arg. | |
| 611 | ||
| 612 | @param arg: a given object | |
| 613 | @type arg: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol} | |
| 614 | @return: True if arg is a suitbale object to be used for substitution. Otherwise False is returned. | |
| 615 | @rtype: C{bool} | |
| 616 | """ | |
| 617 | if isinstance(arg,numarray.NumArray): | |
| 618 | return arg.shape==self.getShape() | |
| 619 | elif isinstance(arg,escript.Data): | |
| 620 | if self.getDim()==None: | |
| 621 | return arg.getShape()==self.getShape() | |
| 622 | elif self.getDim()==arg.getFunctionSpace().getDim(): | |
| 623 | return arg.getShape()==self.getShape() | |
| 624 | else: | |
| 625 | return False | |
| 626 | elif isinstance(arg,Symbol): | |
| 627 | if self.getDim()==None: | |
| 628 | return arg.getShape()==self.getShape() | |
| 629 | elif self.getDim()==arg.getDim(): | |
| 630 | return arg.getShape()==self.getShape() | |
| 631 | else: | |
| 632 | return False | |
| 633 | elif isinstance(arg,float): | |
| 634 | return ()==self.getShape() | |
| 635 | elif isinstance(arg,int): | |
| 636 | return ()==self.getShape() | |
| 637 | else: | |
| 638 | return False | |
| 639 | ||
| 640 | def getMyCode(self,argstrs,format="escript"): | |
| 641 | """ | |
| 642 | returns a program code that can be used to evaluate the symbol. | |
| 643 | ||
| 644 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 645 | @type argstrs: C{list} of C{str}. | |
| 646 | @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported. | |
| 647 | @type format: C{str} | |
| 648 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 649 | @rtype: C{str} | |
| 650 | @raise NotImplementedError: if no implementation for the given format is available | |
| 651 | @note: This method has to be overwritten by subclasses. | |
| 652 | """ | |
| 653 | raise NotImplementedError,"no code for %s representation available"%format | |
| 654 | ||
| 655 | def substitute(self,argvals): | |
| 656 | """ | |
| 657 | assigns new values to symbols in the definition of the symbol. | |
| 658 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 659 | ||
| 660 | @param argvals: new values assigned to symbols | |
| 661 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 662 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 663 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 664 | @note: this method has to be overwritten by a particular L{Symbol} | |
| 665 | @raise NotImplementedError: if no implementation for the given format is available | |
| 666 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 667 | """ | |
| 668 | if argvals.has_key(self): | |
| 669 | arg=argvals[self] | |
| 670 | if self.isAppropriateValue(arg): | |
| 671 | return arg | |
| 672 | else: | |
| 673 | raise TypeError,"Symbol: new value is not appropriate." | |
| 674 | else: | |
| 675 | raise NotImplementedError,"no substitution in %s avialable"%str(self) | |
| 676 | ||
| 677 | def diff(self,arg): | |
| 678 | """ | |
| 679 | returns the derivative of the symbol with respect to L{Symbol} arg | |
| 680 | ||
| 681 | @param arg: the derivative is calculated with respect to arg | |
| 682 | @type arg: typically L{escript.Symbol} but can also be C{float}, L{escript.Data}, L{numarray.NumArray} depending the involved functions and data. | |
| 683 | @return: derivative with respect to C{arg} | |
| 684 | @rtype: typically L{escript.Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 685 | @note: this method is overwritten by a particular L{Symbol} | |
| 686 | """ | |
| 687 | if arg==self: | |
| 688 | return identity(self.getShape()) | |
| 689 | else: | |
| 690 | s=self.getShape()+arg.getShape() | |
| 691 | if len(s)>0: | |
| 692 | return numarray.zeros(s,numarray.Float) | |
| 693 | else: | |
| 694 | return 0. | |
| 695 | ||
| 696 | def __neg__(self): | |
| 697 | """ | |
| 698 | returns -self. | |
| 699 | ||
| 700 | @return: a S{Symbol} representing the negative of the object | |
| 701 | @rtype: L{DependendSymbol} | |
| 702 | """ | |
| 703 | return self*(-1.) | |
| 704 | ||
| 705 | def __pos__(self): | |
| 706 | """ | |
| 707 | returns +self. | |
| 708 | ||
| 709 | @return: a S{Symbol} representing the positive of the object | |
| 710 | @rtype: L{DependendSymbol} | |
| 711 | """ | |
| 712 | return self*(1.) | |
| 713 | ||
| 714 | def __abs__(self): | |
| 715 | """ | |
| 716 | returns a S{Symbol} representing the absolute value of the object. | |
| 717 | """ | |
| 718 | return Abs_Symbol(self) | |
| 719 | ||
| 720 | def __add__(self,other): | |
| 721 | """ | |
| 722 | add another object to this object | |
| 723 | ||
| 724 | @param other: object to be added to this object | |
| 725 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 726 | @return: a S{Symbol} representing the sum of this object and C{other} | |
| 727 | @rtype: L{DependendSymbol} | |
| 728 | """ | |
| 729 | return add(self,other) | |
| 730 | ||
| 731 | def __radd__(self,other): | |
| 732 | """ | |
| 733 | add this object to another object | |
| 734 | ||
| 735 | @param other: object this object is added to | |
| 736 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 737 | @return: a S{Symbol} representing the sum of C{other} and this object object | |
| 738 | @rtype: L{DependendSymbol} | |
| 739 | """ | |
| 740 | return add(other,self) | |
| 741 | ||
| 742 | def __sub__(self,other): | |
| 743 | """ | |
| 744 | subtracts another object from this object | |
| 745 | ||
| 746 | @param other: object to be subtracted from this object | |
| 747 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 748 | @return: a S{Symbol} representing the difference of C{other} and this object | |
| 749 | @rtype: L{DependendSymbol} | |
| 750 | """ | |
| 751 | return add(self,-other) | |
| 752 | ||
| 753 | def __rsub__(self,other): | |
| 754 | """ | |
| 755 | subtracts this object from another object | |
| 756 | ||
| 757 | @param other: object this object is been subtracted from | |
| 758 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 759 | @return: a S{Symbol} representing the difference of this object and C{other}. | |
| 760 | @rtype: L{DependendSymbol} | |
| 761 | """ | |
| 762 | return add(-self,other) | |
| 763 | ||
| 764 | def __mul__(self,other): | |
| 765 | """ | |
| 766 | multiplies this object with other object | |
| 767 | ||
| 768 | @param other: object to be mutiplied by this object | |
| 769 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 770 | @return: a S{Symbol} representing the product of the object and C{other}. | |
| 771 | @rtype: L{DependendSymbol} or 0 if other is identical to zero. | |
| 772 | """ | |
| 773 | return mult(self,other) | |
| 774 | ||
| 775 | def __rmul__(self,other): | |
| 776 | """ | |
| 777 | multiplies this object with other object | |
| 778 | ||
| 779 | @param other: object this object is multiplied with | |
| 780 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 781 | @return: a S{Symbol} representing the product of C{other} and the object. | |
| 782 | @rtype: L{DependendSymbol} or 0 if other is identical to zero. | |
| 783 | """ | |
| 784 | return mult(other,self) | |
| 785 | ||
| 786 | def __div__(self,other): | |
| 787 | """ | |
| 788 | divides this object by other object | |
| 789 | ||
| 790 | @param other: object dividing this object | |
| 791 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 792 | @return: a S{Symbol} representing the quotient of this object and C{other} | |
| 793 | @rtype: L{DependendSymbol} | |
| 794 | """ | |
| 795 | return quotient(self,other) | |
| 796 | ||
| 797 | def __rdiv__(self,other): | |
| 798 | """ | |
| 799 | divides this object by other object | |
| 800 | ||
| 801 | @param other: object dividing this object | |
| 802 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 803 | @return: a S{Symbol} representing the quotient of C{other} and this object | |
| 804 | @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero. | |
| 805 | """ | |
| 806 | return quotient(other,self) | |
| 807 | ||
| 808 | def __pow__(self,other): | |
| 809 | """ | |
| 810 | raises this object to the power of other | |
| 811 | ||
| 812 | @param other: exponent | |
| 813 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 814 | @return: a S{Symbol} representing the power of this object to C{other} | |
| 815 | @rtype: L{DependendSymbol} or 1 if C{other} is identical to zero. | |
| 816 | """ | |
| 817 | return power(self,other) | |
| 818 | ||
| 819 | def __rpow__(self,other): | |
| 820 | """ | |
| 821 | raises an object to the power of this object | |
| 822 | ||
| 823 | @param other: basis | |
| 824 | @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 825 | @return: a S{Symbol} representing the power of C{other} to this object | |
| 826 | @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero. | |
| 827 | """ | |
| 828 | return power(other,self) | |
| 829 | ||
| 830 | class DependendSymbol(Symbol): | |
| 831 | """ | |
| 832 | DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal. | |
| 833 | 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 | |
| 834 | ||
| 835 | Example: | |
| 836 | ||
| 837 | u1=Symbol(shape=(3,4),dim=2,args=[4.]) | |
| 838 | u2=Symbol(shape=(3,4),dim=2,args=[4.]) | |
| 839 | print u1==u2 | |
| 840 | False | |
| 841 | ||
| 842 | but | |
| 843 | ||
| 844 | u1=DependendSymbol(shape=(3,4),dim=2,args=[4.]) | |
| 845 | u2=DependendSymbol(shape=(3,4),dim=2,args=[4.]) | |
| 846 | u3=DependendSymbol(shape=(2,),dim=2,args=[4.]) | |
| 847 | print u1==u2, u1==u3 | |
| 848 | True False | |
| 849 | ||
| 850 | @note: DependendSymbol should be used as return value of functions with L{Symbol} arguments. This will allow the optimizer to remove redundant function calls. | |
| 851 | """ | |
| 852 | def __eq__(self,other): | |
| 853 | """ | |
| 854 | checks if other equals self | |
| 855 | ||
| 856 | @param other: any object | |
| 857 | @return: True if other has the same class like self, and the shape, the spatial diemsnion and the arguments are equal. | |
| 858 | @rtype: C{bool} | |
| 859 | """ | |
| 860 | if isinstance(other,DependendSymbol): | |
| 861 | if self.__class__==other.__class__: | |
| 862 | if self.getShape()==other.getShape(): | |
| 863 | if self.getArgument()==other.getArgument(): | |
| 864 | if self.getDim()==None or other.getDim()==None or self.getDim()==other.getDim(): | |
| 865 | return True | |
| 866 | return False | |
| 867 | ||
| 868 | def __ne__(self,other): | |
| 869 | """ | |
| 870 | checks if other equals self | |
| 871 | ||
| 872 | @param other: any object | |
| 873 | @return: Flase if other has the same class like self, and the shape, the spatial diemsnion and the arguments are equal. | |
| 874 | @rtype: C{bool} | |
| 875 | """ | |
| 876 | return not self==other | |
| 877 | #========================================================= | |
| 878 | # Unary operations prserving the shape | |
| 879 | #======================================================== | |
| 880 | def log10(arg): | |
| 881 | """ | |
| 882 | returns base-10 logarithm of argument arg | |
| 883 | ||
| 884 | @param arg: argument | |
| 885 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 886 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 887 | @raises TypeError: if the type of the argument is not expected. | |
| 888 | """ | |
| 889 | if isinstance(arg,numarray.NumArray): | |
| 890 | return numarray.log10(arg) | |
| 891 | elif isinstance(arg,escript.Data): | |
| 892 | return arg._log10() | |
| 893 | elif isinstance(arg,float): | |
| 894 | return math.log10(arg) | |
| 895 | elif isinstance(arg,int): | |
| 896 | return math.log10(float(arg)) | |
| 897 | elif isinstance(arg,Symbol): | |
| 898 | return log(arg)/log(10.) | |
| 899 | else: | |
| 900 | raise TypeError,"log10: Unknown argument type." | |
| 901 | ||
| 902 | def wherePositive(arg): | |
| 903 | """ | |
| 904 | returns mask of positive values of argument arg | |
| 905 | ||
| 906 | @param arg: argument | |
| 907 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 908 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 909 | @raises TypeError: if the type of the argument is not expected. | |
| 910 | """ | |
| 911 | if isinstance(arg,numarray.NumArray): | |
| 912 | return numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float)) | |
| 913 | elif isinstance(arg,escript.Data): | |
| 914 | return arg._wherePositive() | |
| 915 | elif isinstance(arg,float): | |
| 916 | if arg>0: | |
| 917 | return 1. | |
| 918 | else: | |
| 919 | return 0. | |
| 920 | elif isinstance(arg,int): | |
| 921 | if arg>0: | |
| 922 | return 1. | |
| 923 | else: | |
| 924 | return 0. | |
| 925 | elif isinstance(arg,Symbol): | |
| 926 | return WherePositive_Symbol(arg) | |
| 927 | else: | |
| 928 | raise TypeError,"wherePositive: Unknown argument type." | |
| 929 | ||
| 930 | class WherePositive_Symbol(DependendSymbol): | |
| 931 | """ | |
| 932 | L{Symbol} representing the result of the mask of positive values function | |
| 933 | """ | |
| 934 | def __init__(self,arg): | |
| 935 | """ | |
| 936 | initialization of wherePositive L{Symbol} with argument arg | |
| 937 | @param arg: argument of function | |
| 938 | @type arg: typically L{Symbol}. | |
| 939 | """ | |
| 940 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 941 | ||
| 942 | def getMyCode(self,argstrs,format="escript"): | |
| 943 | """ | |
| 944 | returns a program code that can be used to evaluate the symbol. | |
| 945 | ||
| 946 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 947 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 948 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 949 | @type format: C{str} | |
| 950 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 951 | @rtype: C{str} | |
| 952 | @raise: NotImplementedError: if the requested format is not available | |
| 953 | """ | |
| 954 | if isinstance(argstrs,list): | |
| 955 | argstrs=argstrs[0] | |
| 956 | if format=="escript" or format=="str" or format=="text": | |
| 957 | return "wherePositive(%s)"%argstrs | |
| 958 | else: | |
| 959 | raise NotImplementedError,"WherePositive_Symbol does not provide program code for format %s."%format | |
| 960 | ||
| 961 | def substitute(self,argvals): | |
| 962 | """ | |
| 963 | assigns new values to symbols in the definition of the symbol. | |
| 964 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 965 | ||
| 966 | @param argvals: new values assigned to symbols | |
| 967 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 968 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 969 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 970 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 971 | """ | |
| 972 | if argvals.has_key(self): | |
| 973 | arg=argvals[self] | |
| 974 | if self.isAppropriateValue(arg): | |
| 975 | return arg | |
| 976 | else: | |
| 977 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 978 | else: | |
| 979 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 980 | return wherePositive(arg) | |
| 981 | ||
| 982 | def whereNegative(arg): | |
| 983 | """ | |
| 984 | returns mask of positive values of argument arg | |
| 985 | ||
| 986 | @param arg: argument | |
| 987 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 988 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 989 | @raises TypeError: if the type of the argument is not expected. | |
| 990 | """ | |
| 991 | if isinstance(arg,numarray.NumArray): | |
| 992 | return numarray.less(arg,numarray.zeros(arg.shape,numarray.Float)) | |
| 993 | elif isinstance(arg,escript.Data): | |
| 994 | return arg._whereNegative() | |
| 995 | elif isinstance(arg,float): | |
| 996 | if arg<0: | |
| 997 | return 1. | |
| 998 | else: | |
| 999 | return 0. | |
| 1000 | elif isinstance(arg,int): | |
| 1001 | if arg<0: | |
| 1002 | return 1. | |
| 1003 | else: | |
| 1004 | return 0. | |
| 1005 | elif isinstance(arg,Symbol): | |
| 1006 | return WhereNegative_Symbol(arg) | |
| 1007 | else: | |
| 1008 | raise TypeError,"whereNegative: Unknown argument type." | |
| 1009 | ||
| 1010 | class WhereNegative_Symbol(DependendSymbol): | |
| 1011 | """ | |
| 1012 | L{Symbol} representing the result of the mask of positive values function | |
| 1013 | """ | |
| 1014 | def __init__(self,arg): | |
| 1015 | """ | |
| 1016 | initialization of whereNegative L{Symbol} with argument arg | |
| 1017 | @param arg: argument of function | |
| 1018 | @type arg: typically L{Symbol}. | |
| 1019 | """ | |
| 1020 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1021 | ||
| 1022 | def getMyCode(self,argstrs,format="escript"): | |
| 1023 | """ | |
| 1024 | returns a program code that can be used to evaluate the symbol. | |
| 1025 | ||
| 1026 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1027 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1028 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1029 | @type format: C{str} | |
| 1030 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1031 | @rtype: C{str} | |
| 1032 | @raise: NotImplementedError: if the requested format is not available | |
| 1033 | """ | |
| 1034 | if isinstance(argstrs,list): | |
| 1035 | argstrs=argstrs[0] | |
| 1036 | if format=="escript" or format=="str" or format=="text": | |
| 1037 | return "whereNegative(%s)"%argstrs | |
| 1038 | else: | |
| 1039 | raise NotImplementedError,"WhereNegative_Symbol does not provide program code for format %s."%format | |
| 1040 | ||
| 1041 | def substitute(self,argvals): | |
| 1042 | """ | |
| 1043 | assigns new values to symbols in the definition of the symbol. | |
| 1044 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1045 | ||
| 1046 | @param argvals: new values assigned to symbols | |
| 1047 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1048 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1049 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1050 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1051 | """ | |
| 1052 | if argvals.has_key(self): | |
| 1053 | arg=argvals[self] | |
| 1054 | if self.isAppropriateValue(arg): | |
| 1055 | return arg | |
| 1056 | else: | |
| 1057 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1058 | else: | |
| 1059 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1060 | return whereNegative(arg) | |
| 1061 | ||
| 1062 | def whereNonNegative(arg): | |
| 1063 | """ | |
| 1064 | returns mask of non-negative values of argument arg | |
| 1065 | ||
| 1066 | @param arg: argument | |
| 1067 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1068 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1069 | @raises TypeError: if the type of the argument is not expected. | |
| 1070 | """ | |
| 1071 | if isinstance(arg,numarray.NumArray): | |
| 1072 | return numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float)) | |
| 1073 | elif isinstance(arg,escript.Data): | |
| 1074 | return arg._whereNonNegative() | |
| 1075 | elif isinstance(arg,float): | |
| 1076 | if arg<0: | |
| 1077 | return 0. | |
| 1078 | else: | |
| 1079 | return 1. | |
| 1080 | elif isinstance(arg,int): | |
| 1081 | if arg<0: | |
| 1082 | return 0. | |
| 1083 | else: | |
| 1084 | return 1. | |
| 1085 | elif isinstance(arg,Symbol): | |
| 1086 | return 1.-whereNegative(arg) | |
| 1087 | else: | |
| 1088 | raise TypeError,"whereNonNegative: Unknown argument type." | |
| 1089 | ||
| 1090 | def whereNonPositive(arg): | |
| 1091 | """ | |
| 1092 | returns mask of non-positive values of argument arg | |
| 1093 | ||
| 1094 | @param arg: argument | |
| 1095 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1096 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1097 | @raises TypeError: if the type of the argument is not expected. | |
| 1098 | """ | |
| 1099 | if isinstance(arg,numarray.NumArray): | |
| 1100 | return numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float)) | |
| 1101 | elif isinstance(arg,escript.Data): | |
| 1102 | return arg._whereNonPositive() | |
| 1103 | elif isinstance(arg,float): | |
| 1104 | if arg>0: | |
| 1105 | return 0. | |
| 1106 | else: | |
| 1107 | return 1. | |
| 1108 | elif isinstance(arg,int): | |
| 1109 | if arg>0: | |
| 1110 | return 0. | |
| 1111 | else: | |
| 1112 | return 1. | |
| 1113 | elif isinstance(arg,Symbol): | |
| 1114 | return 1.-wherePositive(arg) | |
| 1115 | else: | |
| 1116 | raise TypeError,"whereNonPositive: Unknown argument type." | |
| 1117 | ||
| 1118 | def whereZero(arg,tol=0.): | |
| 1119 | """ | |
| 1120 | returns mask of zero entries of argument arg | |
| 1121 | ||
| 1122 | @param arg: argument | |
| 1123 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1124 | @param tol: tolerance. values with absolute value less then tol are accepted as zero. | |
| 1125 | @type tol: C{float} | |
| 1126 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1127 | @raises TypeError: if the type of the argument is not expected. | |
| 1128 | """ | |
| 1129 | if isinstance(arg,numarray.NumArray): | |
| 1130 | return numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float)) | |
| 1131 | elif isinstance(arg,escript.Data): | |
| 1132 | if tol>0.: | |
| 1133 | return whereNegative(abs(arg)-tol) | |
| 1134 | else: | |
| 1135 | return arg._whereZero() | |
| 1136 | elif isinstance(arg,float): | |
| 1137 | if abs(arg)<=tol: | |
| 1138 | return 1. | |
| 1139 | else: | |
| 1140 | return 0. | |
| 1141 | elif isinstance(arg,int): | |
| 1142 | if abs(float(arg))<=tol: | |
| 1143 | return 1. | |
| 1144 | else: | |
| 1145 | return 0. | |
| 1146 | elif isinstance(arg,Symbol): | |
| 1147 | return WhereZero_Symbol(arg,tol) | |
| 1148 | else: | |
| 1149 | raise TypeError,"whereZero: Unknown argument type." | |
| 1150 | ||
| 1151 | class WhereZero_Symbol(DependendSymbol): | |
| 1152 | """ | |
| 1153 | L{Symbol} representing the result of the mask of zero entries function | |
| 1154 | """ | |
| 1155 | def __init__(self,arg,tol=0.): | |
| 1156 | """ | |
| 1157 | initialization of whereZero L{Symbol} with argument arg | |
| 1158 | @param arg: argument of function | |
| 1159 | @type arg: typically L{Symbol}. | |
| 1160 | """ | |
| 1161 | DependendSymbol.__init__(self,args=[arg,tol],shape=arg.getShape(),dim=arg.getDim()) | |
| 1162 | ||
| 1163 | def getMyCode(self,argstrs,format="escript"): | |
| 1164 | """ | |
| 1165 | returns a program code that can be used to evaluate the symbol. | |
| 1166 | ||
| 1167 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1168 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1169 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1170 | @type format: C{str} | |
| 1171 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1172 | @rtype: C{str} | |
| 1173 | @raise: NotImplementedError: if the requested format is not available | |
| 1174 | """ | |
| 1175 | if format=="escript" or format=="str" or format=="text": | |
| 1176 | return "whereZero(%s,tol=%s)"%(argstrs[0],argstrs[1]) | |
| 1177 | else: | |
| 1178 | raise NotImplementedError,"WhereZero_Symbol does not provide program code for format %s."%format | |
| 1179 | ||
| 1180 | def substitute(self,argvals): | |
| 1181 | """ | |
| 1182 | assigns new values to symbols in the definition of the symbol. | |
| 1183 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1184 | ||
| 1185 | @param argvals: new values assigned to symbols | |
| 1186 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1187 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1188 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1189 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1190 | """ | |
| 1191 | if argvals.has_key(self): | |
| 1192 | arg=argvals[self] | |
| 1193 | if self.isAppropriateValue(arg): | |
| 1194 | return arg | |
| 1195 | else: | |
| 1196 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1197 | else: | |
| 1198 | arg=self.getSubstitutedArguments(argvals) | |
| 1199 | return whereZero(arg[0],arg[1]) | |
| 1200 | ||
| 1201 | def whereNonZero(arg,tol=0.): | |
| 1202 | """ | |
| 1203 | returns mask of values different from zero of argument arg | |
| 1204 | ||
| 1205 | @param arg: argument | |
| 1206 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1207 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1208 | @raises TypeError: if the type of the argument is not expected. | |
| 1209 | """ | |
| 1210 | if isinstance(arg,numarray.NumArray): | |
| 1211 | return numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float)) | |
| 1212 | elif isinstance(arg,escript.Data): | |
| 1213 | if tol>0.: | |
| 1214 | return 1.-whereZero(arg,tol) | |
| 1215 | else: | |
| 1216 | return arg._whereNonZero() | |
| 1217 | elif isinstance(arg,float): | |
| 1218 | if abs(arg)>tol: | |
| 1219 | return 1. | |
| 1220 | else: | |
| 1221 | return 0. | |
| 1222 | elif isinstance(arg,int): | |
| 1223 | if abs(float(arg))>tol: | |
| 1224 | return 1. | |
| 1225 | else: | |
| 1226 | return 0. | |
| 1227 | elif isinstance(arg,Symbol): | |
| 1228 | return 1.-whereZero(arg,tol) | |
| 1229 | else: | |
| 1230 | raise TypeError,"whereNonZero: Unknown argument type." | |
| 1231 | ||
| 1232 | def sin(arg): | |
| 1233 | """ | |
| 1234 | returns sine of argument arg | |
| 1235 | ||
| 1236 | @param arg: argument | |
| 1237 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1238 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1239 | @raises TypeError: if the type of the argument is not expected. | |
| 1240 | """ | |
| 1241 | if isinstance(arg,numarray.NumArray): | |
| 1242 | return numarray.sin(arg) | |
| 1243 | elif isinstance(arg,escript.Data): | |
| 1244 | return arg._sin() | |
| 1245 | elif isinstance(arg,float): | |
| 1246 | return math.sin(arg) | |
| 1247 | elif isinstance(arg,int): | |
| 1248 | return math.sin(arg) | |
| 1249 | elif isinstance(arg,Symbol): | |
| 1250 | return Sin_Symbol(arg) | |
| 1251 | else: | |
| 1252 | raise TypeError,"sin: Unknown argument type." | |
| 1253 | ||
| 1254 | class Sin_Symbol(DependendSymbol): | |
| 1255 | """ | |
| 1256 | L{Symbol} representing the result of the sine function | |
| 1257 | """ | |
| 1258 | def __init__(self,arg): | |
| 1259 | """ | |
| 1260 | initialization of sin L{Symbol} with argument arg | |
| 1261 | @param arg: argument of function | |
| 1262 | @type arg: typically L{Symbol}. | |
| 1263 | """ | |
| 1264 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1265 | ||
| 1266 | def getMyCode(self,argstrs,format="escript"): | |
| 1267 | """ | |
| 1268 | returns a program code that can be used to evaluate the symbol. | |
| 1269 | ||
| 1270 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1271 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1272 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1273 | @type format: C{str} | |
| 1274 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1275 | @rtype: C{str} | |
| 1276 | @raise: NotImplementedError: if the requested format is not available | |
| 1277 | """ | |
| 1278 | if isinstance(argstrs,list): | |
| 1279 | argstrs=argstrs[0] | |
| 1280 | if format=="escript" or format=="str" or format=="text": | |
| 1281 | return "sin(%s)"%argstrs | |
| 1282 | else: | |
| 1283 | raise NotImplementedError,"Sin_Symbol does not provide program code for format %s."%format | |
| 1284 | ||
| 1285 | def substitute(self,argvals): | |
| 1286 | """ | |
| 1287 | assigns new values to symbols in the definition of the symbol. | |
| 1288 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1289 | ||
| 1290 | @param argvals: new values assigned to symbols | |
| 1291 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1292 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1293 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1294 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1295 | """ | |
| 1296 | if argvals.has_key(self): | |
| 1297 | arg=argvals[self] | |
| 1298 | if self.isAppropriateValue(arg): | |
| 1299 | return arg | |
| 1300 | else: | |
| 1301 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1302 | else: | |
| 1303 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1304 | return sin(arg) | |
| 1305 | ||
| 1306 | def diff(self,arg): | |
| 1307 | """ | |
| 1308 | differential of this object | |
| 1309 | ||
| 1310 | @param arg: the derivative is calculated with respect to arg | |
| 1311 | @type arg: L{escript.Symbol} | |
| 1312 | @return: derivative with respect to C{arg} | |
| 1313 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1314 | """ | |
| 1315 | if arg==self: | |
| 1316 | return identity(self.getShape()) | |
| 1317 | else: | |
| 1318 | myarg=self.getArgument()[0] | |
| 1319 | val=matchShape(cos(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1320 | return val[0]*val[1] | |
| 1321 | ||
| 1322 | def cos(arg): | |
| 1323 | """ | |
| 1324 | returns cosine of argument arg | |
| 1325 | ||
| 1326 | @param arg: argument | |
| 1327 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 1328 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 1329 | @raises TypeError: if the type of the argument is not expected. | |
| 1330 | """ | |
| 1331 | if isinstance(arg,numarray.NumArray): | |
| 1332 | return numarray.cos(arg) | |
| 1333 | elif isinstance(arg,escript.Data): | |
| 1334 | return arg._cos() | |
| 1335 | elif isinstance(arg,float): | |
| 1336 | return math.cos(arg) | |
| 1337 | elif isinstance(arg,int): | |
| 1338 | return math.cos(arg) | |
| 1339 | elif isinstance(arg,Symbol): | |
| 1340 | return Cos_Symbol(arg) | |
| 1341 | else: | |
| 1342 | raise TypeError,"cos: Unknown argument type." | |
| 1343 | ||
| 1344 | class Cos_Symbol(DependendSymbol): | |
| 1345 | """ | |
| 1346 | L{Symbol} representing the result of the cosine function | |
| 1347 | """ | |
| 1348 | def __init__(self,arg): | |
| 1349 | """ | |
| 1350 | initialization of cos L{Symbol} with argument arg | |
| 1351 | @param arg: argument of function | |
| 1352 | @type arg: typically L{Symbol}. | |
| 1353 | """ | |
| 1354 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1355 | ||
| 1356 | def getMyCode(self,argstrs,format="escript"): | |
| 1357 | """ | |
| 1358 | returns a program code that can be used to evaluate the symbol. | |
| 1359 | ||
| 1360 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1361 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1362 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1363 | @type format: C{str} | |
| 1364 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1365 | @rtype: C{str} | |
| 1366 | @raise: NotImplementedError: if the requested format is not available | |
| 1367 | """ | |
| 1368 | if isinstance(argstrs,list): | |
| 1369 | argstrs=argstrs[0] | |
| 1370 | if format=="escript" or format=="str" or format=="text": | |
| 1371 | return "cos(%s)"%argstrs | |
| 1372 | else: | |
| 1373 | raise NotImplementedError,"Cos_Symbol does not provide program code for format %s."%format | |
| 1374 | ||
| 1375 | def substitute(self,argvals): | |
| 1376 | """ | |
| 1377 | assigns new values to symbols in the definition of the symbol. | |
| 1378 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1379 | ||
| 1380 | @param argvals: new values assigned to symbols | |
| 1381 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1382 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1383 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1384 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1385 | """ | |
| 1386 | if argvals.has_key(self): | |
| 1387 | arg=argvals[self] | |
| 1388 | if self.isAppropriateValue(arg): | |
| 1389 | return arg | |
| 1390 | else: | |
| 1391 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1392 | else: | |
| 1393 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1394 | return cos(arg) | |
| 1395 | ||
| 1396 | def diff(self,arg): | |
| 1397 | """ | |
| 1398 | differential of this object | |
| 1399 | ||
| 1400 | @param arg: the derivative is calculated with respect to arg | |
| 1401 | @type arg: L{escript.Symbol} | |
| 1402 | @return: derivative with respect to C{arg} | |
| 1403 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1404 | """ | |
| 1405 | if arg==self: | |
| 1406 | return identity(self.getShape()) | |
| 1407 | else: | |
| 1408 | myarg=self.getArgument()[0] | |
| 1409 | val=matchShape(-sin(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1410 | return val[0]*val[1] | |
| 1411 | ||
| 1412 | def tan(arg): | def tan(arg): |
| 1413 | """ | """ |
| 1414 | Applies the tan function to arg. | returns tangent of argument arg |
| 1415 | ||
| 1416 | @param arg: argument | @param arg: argument |
| 1417 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1418 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1419 | return symbols.Tan_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 1420 | elif hasattr(arg,"tan"): | """ |
| 1421 | return arg.tan() | if isinstance(arg,numarray.NumArray): |
| 1422 | else: | return numarray.tan(arg) |
| 1423 | return numarray.tan(arg) | elif isinstance(arg,escript.Data): |
| 1424 | return arg._tan() | |
| 1425 | elif isinstance(arg,float): | |
| 1426 | return math.tan(arg) | |
| 1427 | elif isinstance(arg,int): | |
| 1428 | return math.tan(arg) | |
| 1429 | elif isinstance(arg,Symbol): | |
| 1430 | return Tan_Symbol(arg) | |
| 1431 | else: | |
| 1432 | raise TypeError,"tan: Unknown argument type." | |
| 1433 | ||
| 1434 | class Tan_Symbol(DependendSymbol): | |
| 1435 | """ | |
| 1436 | L{Symbol} representing the result of the tangent function | |
| 1437 | """ | |
| 1438 | def __init__(self,arg): | |
| 1439 | """ | |
| 1440 | initialization of tan L{Symbol} with argument arg | |
| 1441 | @param arg: argument of function | |
| 1442 | @type arg: typically L{Symbol}. | |
| 1443 | """ | |
| 1444 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1445 | ||
| 1446 | def getMyCode(self,argstrs,format="escript"): | |
| 1447 | """ | |
| 1448 | returns a program code that can be used to evaluate the symbol. | |
| 1449 | ||
| 1450 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1451 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1452 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1453 | @type format: C{str} | |
| 1454 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1455 | @rtype: C{str} | |
| 1456 | @raise: NotImplementedError: if the requested format is not available | |
| 1457 | """ | |
| 1458 | if isinstance(argstrs,list): | |
| 1459 | argstrs=argstrs[0] | |
| 1460 | if format=="escript" or format=="str" or format=="text": | |
| 1461 | return "tan(%s)"%argstrs | |
| 1462 | else: | |
| 1463 | raise NotImplementedError,"Tan_Symbol does not provide program code for format %s."%format | |
| 1464 | ||
| 1465 | def substitute(self,argvals): | |
| 1466 | """ | |
| 1467 | assigns new values to symbols in the definition of the symbol. | |
| 1468 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1469 | ||
| 1470 | @param argvals: new values assigned to symbols | |
| 1471 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1472 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1473 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1474 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1475 | """ | |
| 1476 | if argvals.has_key(self): | |
| 1477 | arg=argvals[self] | |
| 1478 | if self.isAppropriateValue(arg): | |
| 1479 | return arg | |
| 1480 | else: | |
| 1481 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1482 | else: | |
| 1483 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1484 | return tan(arg) | |
| 1485 | ||
| 1486 | def diff(self,arg): | |
| 1487 | """ | |
| 1488 | differential of this object | |
| 1489 | ||
| 1490 | @param arg: the derivative is calculated with respect to arg | |
| 1491 | @type arg: L{escript.Symbol} | |
| 1492 | @return: derivative with respect to C{arg} | |
| 1493 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1494 | """ | |
| 1495 | if arg==self: | |
| 1496 | return identity(self.getShape()) | |
| 1497 | else: | |
| 1498 | myarg=self.getArgument()[0] | |
| 1499 | val=matchShape(1./cos(myarg)**2,self.getDifferentiatedArguments(arg)[0]) | |
| 1500 | return val[0]*val[1] | |
| 1501 | ||
| 1502 | def asin(arg): | def asin(arg): |
| 1503 | """ | """ |
| 1504 | Applies the asin function to arg. | returns inverse sine of argument arg |
| 1505 | ||
| 1506 | @param arg: argument | @param arg: argument |
| 1507 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1508 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1509 | return symbols.Asin_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 1510 | elif hasattr(arg,"asin"): | """ |
| 1511 | return arg.asin() | if isinstance(arg,numarray.NumArray): |
| 1512 | else: | return numarray.arcsin(arg) |
| 1513 | return numarray.asin(arg) | elif isinstance(arg,escript.Data): |
| 1514 | return arg._asin() | |
| 1515 | elif isinstance(arg,float): | |
| 1516 | return math.asin(arg) | |
| 1517 | elif isinstance(arg,int): | |
| 1518 | return math.asin(arg) | |
| 1519 | elif isinstance(arg,Symbol): | |
| 1520 | return Asin_Symbol(arg) | |
| 1521 | else: | |
| 1522 | raise TypeError,"asin: Unknown argument type." | |
| 1523 | ||
| 1524 | class Asin_Symbol(DependendSymbol): | |
| 1525 | """ | |
| 1526 | L{Symbol} representing the result of the inverse sine function | |
| 1527 | """ | |
| 1528 | def __init__(self,arg): | |
| 1529 | """ | |
| 1530 | initialization of asin L{Symbol} with argument arg | |
| 1531 | @param arg: argument of function | |
| 1532 | @type arg: typically L{Symbol}. | |
| 1533 | """ | |
| 1534 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1535 | ||
| 1536 | def getMyCode(self,argstrs,format="escript"): | |
| 1537 | """ | |
| 1538 | returns a program code that can be used to evaluate the symbol. | |
| 1539 | ||
| 1540 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1541 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1542 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1543 | @type format: C{str} | |
| 1544 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1545 | @rtype: C{str} | |
| 1546 | @raise: NotImplementedError: if the requested format is not available | |
| 1547 | """ | |
| 1548 | if isinstance(argstrs,list): | |
| 1549 | argstrs=argstrs[0] | |
| 1550 | if format=="escript" or format=="str" or format=="text": | |
| 1551 | return "asin(%s)"%argstrs | |
| 1552 | else: | |
| 1553 | raise NotImplementedError,"Asin_Symbol does not provide program code for format %s."%format | |
| 1554 | ||
| 1555 | def substitute(self,argvals): | |
| 1556 | """ | |
| 1557 | assigns new values to symbols in the definition of the symbol. | |
| 1558 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1559 | ||
| 1560 | @param argvals: new values assigned to symbols | |
| 1561 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1562 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1563 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1564 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1565 | """ | |
| 1566 | if argvals.has_key(self): | |
| 1567 | arg=argvals[self] | |
| 1568 | if self.isAppropriateValue(arg): | |
| 1569 | return arg | |
| 1570 | else: | |
| 1571 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1572 | else: | |
| 1573 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1574 | return asin(arg) | |
| 1575 | ||
| 1576 | def diff(self,arg): | |
| 1577 | """ | |
| 1578 | differential of this object | |
| 1579 | ||
| 1580 | @param arg: the derivative is calculated with respect to arg | |
| 1581 | @type arg: L{escript.Symbol} | |
| 1582 | @return: derivative with respect to C{arg} | |
| 1583 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1584 | """ | |
| 1585 | if arg==self: | |
| 1586 | return identity(self.getShape()) | |
| 1587 | else: | |
| 1588 | myarg=self.getArgument()[0] | |
| 1589 | val=matchShape(1./sqrt(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 1590 | return val[0]*val[1] | |
| 1591 | ||
| 1592 | def acos(arg): | def acos(arg): |
| 1593 | """ | """ |
| 1594 | Applies the acos function to arg. | returns inverse cosine of argument arg |
| 1595 | ||
| 1596 | @param arg: argument | @param arg: argument |
| 1597 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1598 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1599 | return symbols.Acos_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 1600 | elif hasattr(arg,"acos"): | """ |
| 1601 | return arg.acos() | if isinstance(arg,numarray.NumArray): |
| 1602 | else: | return numarray.arccos(arg) |
| 1603 | return numarray.acos(arg) | elif isinstance(arg,escript.Data): |
| 1604 | return arg._acos() | |
| 1605 | elif isinstance(arg,float): | |
| 1606 | return math.acos(arg) | |
| 1607 | elif isinstance(arg,int): | |
| 1608 | return math.acos(arg) | |
| 1609 | elif isinstance(arg,Symbol): | |
| 1610 | return Acos_Symbol(arg) | |
| 1611 | else: | |
| 1612 | raise TypeError,"acos: Unknown argument type." | |
| 1613 | ||
| 1614 | class Acos_Symbol(DependendSymbol): | |
| 1615 | """ | |
| 1616 | L{Symbol} representing the result of the inverse cosine function | |
| 1617 | """ | |
| 1618 | def __init__(self,arg): | |
| 1619 | """ | |
| 1620 | initialization of acos L{Symbol} with argument arg | |
| 1621 | @param arg: argument of function | |
| 1622 | @type arg: typically L{Symbol}. | |
| 1623 | """ | |
| 1624 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1625 | ||
| 1626 | def getMyCode(self,argstrs,format="escript"): | |
| 1627 | """ | |
| 1628 | returns a program code that can be used to evaluate the symbol. | |
| 1629 | ||
| 1630 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1631 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1632 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1633 | @type format: C{str} | |
| 1634 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1635 | @rtype: C{str} | |
| 1636 | @raise: NotImplementedError: if the requested format is not available | |
| 1637 | """ | |
| 1638 | if isinstance(argstrs,list): | |
| 1639 | argstrs=argstrs[0] | |
| 1640 | if format=="escript" or format=="str" or format=="text": | |
| 1641 | return "acos(%s)"%argstrs | |
| 1642 | else: | |
| 1643 | raise NotImplementedError,"Acos_Symbol does not provide program code for format %s."%format | |
| 1644 | ||
| 1645 | def substitute(self,argvals): | |
| 1646 | """ | |
| 1647 | assigns new values to symbols in the definition of the symbol. | |
| 1648 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1649 | ||
| 1650 | @param argvals: new values assigned to symbols | |
| 1651 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1652 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1653 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1654 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1655 | """ | |
| 1656 | if argvals.has_key(self): | |
| 1657 | arg=argvals[self] | |
| 1658 | if self.isAppropriateValue(arg): | |
| 1659 | return arg | |
| 1660 | else: | |
| 1661 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1662 | else: | |
| 1663 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1664 | return acos(arg) | |
| 1665 | ||
| 1666 | def diff(self,arg): | |
| 1667 | """ | |
| 1668 | differential of this object | |
| 1669 | ||
| 1670 | @param arg: the derivative is calculated with respect to arg | |
| 1671 | @type arg: L{escript.Symbol} | |
| 1672 | @return: derivative with respect to C{arg} | |
| 1673 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1674 | """ | |
| 1675 | if arg==self: | |
| 1676 | return identity(self.getShape()) | |
| 1677 | else: | |
| 1678 | myarg=self.getArgument()[0] | |
| 1679 | val=matchShape(-1./sqrt(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 1680 | return val[0]*val[1] | |
| 1681 | ||
| 1682 | def atan(arg): | def atan(arg): |
| 1683 | """ | """ |
| 1684 | Applies the atan function to arg. | returns inverse tangent of argument arg |
| 1685 | ||
| 1686 | @param arg: argument | @param arg: argument |
| 1687 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1688 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1689 | return symbols.Atan_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 1690 | elif hasattr(arg,"atan"): | """ |
| 1691 | return arg.atan() | if isinstance(arg,numarray.NumArray): |
| 1692 | else: | return numarray.arctan(arg) |
| 1693 | return numarray.atan(arg) | elif isinstance(arg,escript.Data): |
| 1694 | return arg._atan() | |
| 1695 | elif isinstance(arg,float): | |
| 1696 | return math.atan(arg) | |
| 1697 | elif isinstance(arg,int): | |
| 1698 | return math.atan(arg) | |
| 1699 | elif isinstance(arg,Symbol): | |
| 1700 | return Atan_Symbol(arg) | |
| 1701 | else: | |
| 1702 | raise TypeError,"atan: Unknown argument type." | |
| 1703 | ||
| 1704 | class Atan_Symbol(DependendSymbol): | |
| 1705 | """ | |
| 1706 | L{Symbol} representing the result of the inverse tangent function | |
| 1707 | """ | |
| 1708 | def __init__(self,arg): | |
| 1709 | """ | |
| 1710 | initialization of atan L{Symbol} with argument arg | |
| 1711 | @param arg: argument of function | |
| 1712 | @type arg: typically L{Symbol}. | |
| 1713 | """ | |
| 1714 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1715 | ||
| 1716 | def getMyCode(self,argstrs,format="escript"): | |
| 1717 | """ | |
| 1718 | returns a program code that can be used to evaluate the symbol. | |
| 1719 | ||
| 1720 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1721 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1722 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1723 | @type format: C{str} | |
| 1724 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1725 | @rtype: C{str} | |
| 1726 | @raise: NotImplementedError: if the requested format is not available | |
| 1727 | """ | |
| 1728 | if isinstance(argstrs,list): | |
| 1729 | argstrs=argstrs[0] | |
| 1730 | if format=="escript" or format=="str" or format=="text": | |
| 1731 | return "atan(%s)"%argstrs | |
| 1732 | else: | |
| 1733 | raise NotImplementedError,"Atan_Symbol does not provide program code for format %s."%format | |
| 1734 | ||
| 1735 | def substitute(self,argvals): | |
| 1736 | """ | |
| 1737 | assigns new values to symbols in the definition of the symbol. | |
| 1738 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1739 | ||
| 1740 | @param argvals: new values assigned to symbols | |
| 1741 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1742 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1743 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1744 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1745 | """ | |
| 1746 | if argvals.has_key(self): | |
| 1747 | arg=argvals[self] | |
| 1748 | if self.isAppropriateValue(arg): | |
| 1749 | return arg | |
| 1750 | else: | |
| 1751 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1752 | else: | |
| 1753 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1754 | return atan(arg) | |
| 1755 | ||
| 1756 | def diff(self,arg): | |
| 1757 | """ | |
| 1758 | differential of this object | |
| 1759 | ||
| 1760 | @param arg: the derivative is calculated with respect to arg | |
| 1761 | @type arg: L{escript.Symbol} | |
| 1762 | @return: derivative with respect to C{arg} | |
| 1763 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1764 | """ | |
| 1765 | if arg==self: | |
| 1766 | return identity(self.getShape()) | |
| 1767 | else: | |
| 1768 | myarg=self.getArgument()[0] | |
| 1769 | val=matchShape(1./(1+myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 1770 | return val[0]*val[1] | |
| 1771 | ||
| 1772 | def sinh(arg): | def sinh(arg): |
| 1773 | """ | """ |
| 1774 | Applies the sinh function to arg. | returns hyperbolic sine of argument arg |
| 1775 | ||
| 1776 | @param arg: argument | @param arg: argument |
| 1777 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1778 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1779 | return symbols.Sinh_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 1780 | elif hasattr(arg,"sinh"): | """ |
| 1781 | return arg.sinh() | if isinstance(arg,numarray.NumArray): |
| 1782 | else: | return numarray.sinh(arg) |
| 1783 | return numarray.sinh(arg) | elif isinstance(arg,escript.Data): |
| 1784 | return arg._sinh() | |
| 1785 | elif isinstance(arg,float): | |
| 1786 | return math.sinh(arg) | |
| 1787 | elif isinstance(arg,int): | |
| 1788 | return math.sinh(arg) | |
| 1789 | elif isinstance(arg,Symbol): | |
| 1790 | return Sinh_Symbol(arg) | |
| 1791 | else: | |
| 1792 | raise TypeError,"sinh: Unknown argument type." | |
| 1793 | ||
| 1794 | class Sinh_Symbol(DependendSymbol): | |
| 1795 | """ | |
| 1796 | L{Symbol} representing the result of the hyperbolic sine function | |
| 1797 | """ | |
| 1798 | def __init__(self,arg): | |
| 1799 | """ | |
| 1800 | initialization of sinh L{Symbol} with argument arg | |
| 1801 | @param arg: argument of function | |
| 1802 | @type arg: typically L{Symbol}. | |
| 1803 | """ | |
| 1804 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1805 | ||
| 1806 | def getMyCode(self,argstrs,format="escript"): | |
| 1807 | """ | |
| 1808 | returns a program code that can be used to evaluate the symbol. | |
| 1809 | ||
| 1810 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1811 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1812 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1813 | @type format: C{str} | |
| 1814 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1815 | @rtype: C{str} | |
| 1816 | @raise: NotImplementedError: if the requested format is not available | |
| 1817 | """ | |
| 1818 | if isinstance(argstrs,list): | |
| 1819 | argstrs=argstrs[0] | |
| 1820 | if format=="escript" or format=="str" or format=="text": | |
| 1821 | return "sinh(%s)"%argstrs | |
| 1822 | else: | |
| 1823 | raise NotImplementedError,"Sinh_Symbol does not provide program code for format %s."%format | |
| 1824 | ||
| 1825 | def substitute(self,argvals): | |
| 1826 | """ | |
| 1827 | assigns new values to symbols in the definition of the symbol. | |
| 1828 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1829 | ||
| 1830 | @param argvals: new values assigned to symbols | |
| 1831 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1832 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1833 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1834 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1835 | """ | |
| 1836 | if argvals.has_key(self): | |
| 1837 | arg=argvals[self] | |
| 1838 | if self.isAppropriateValue(arg): | |
| 1839 | return arg | |
| 1840 | else: | |
| 1841 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1842 | else: | |
| 1843 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1844 | return sinh(arg) | |
| 1845 | ||
| 1846 | def diff(self,arg): | |
| 1847 | """ | |
| 1848 | differential of this object | |
| 1849 | ||
| 1850 | @param arg: the derivative is calculated with respect to arg | |
| 1851 | @type arg: L{escript.Symbol} | |
| 1852 | @return: derivative with respect to C{arg} | |
| 1853 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1854 | """ | |
| 1855 | if arg==self: | |
| 1856 | return identity(self.getShape()) | |
| 1857 | else: | |
| 1858 | myarg=self.getArgument()[0] | |
| 1859 | val=matchShape(cosh(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1860 | return val[0]*val[1] | |
| 1861 | ||
| 1862 | def cosh(arg): | def cosh(arg): |
| 1863 | """ | """ |
| 1864 | Applies the cosh function to arg. | returns hyperbolic cosine of argument arg |
| 1865 | ||
| 1866 | @param arg: argument | @param arg: argument |
| 1867 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1868 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1869 | return symbols.Cosh_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 1870 | elif hasattr(arg,"cosh"): | """ |
| 1871 | return arg.cosh() | if isinstance(arg,numarray.NumArray): |
| 1872 | else: | return numarray.cosh(arg) |
| 1873 | return numarray.cosh(arg) | elif isinstance(arg,escript.Data): |
| 1874 | return arg._cosh() | |
| 1875 | elif isinstance(arg,float): | |
| 1876 | return math.cosh(arg) | |
| 1877 | elif isinstance(arg,int): | |
| 1878 | return math.cosh(arg) | |
| 1879 | elif isinstance(arg,Symbol): | |
| 1880 | return Cosh_Symbol(arg) | |
| 1881 | else: | |
| 1882 | raise TypeError,"cosh: Unknown argument type." | |
| 1883 | ||
| 1884 | class Cosh_Symbol(DependendSymbol): | |
| 1885 | """ | |
| 1886 | L{Symbol} representing the result of the hyperbolic cosine function | |
| 1887 | """ | |
| 1888 | def __init__(self,arg): | |
| 1889 | """ | |
| 1890 | initialization of cosh L{Symbol} with argument arg | |
| 1891 | @param arg: argument of function | |
| 1892 | @type arg: typically L{Symbol}. | |
| 1893 | """ | |
| 1894 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1895 | ||
| 1896 | def getMyCode(self,argstrs,format="escript"): | |
| 1897 | """ | |
| 1898 | returns a program code that can be used to evaluate the symbol. | |
| 1899 | ||
| 1900 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1901 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1902 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1903 | @type format: C{str} | |
| 1904 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1905 | @rtype: C{str} | |
| 1906 | @raise: NotImplementedError: if the requested format is not available | |
| 1907 | """ | |
| 1908 | if isinstance(argstrs,list): | |
| 1909 | argstrs=argstrs[0] | |
| 1910 | if format=="escript" or format=="str" or format=="text": | |
| 1911 | return "cosh(%s)"%argstrs | |
| 1912 | else: | |
| 1913 | raise NotImplementedError,"Cosh_Symbol does not provide program code for format %s."%format | |
| 1914 | ||
| 1915 | def substitute(self,argvals): | |
| 1916 | """ | |
| 1917 | assigns new values to symbols in the definition of the symbol. | |
| 1918 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 1919 | ||
| 1920 | @param argvals: new values assigned to symbols | |
| 1921 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 1922 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 1923 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 1924 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 1925 | """ | |
| 1926 | if argvals.has_key(self): | |
| 1927 | arg=argvals[self] | |
| 1928 | if self.isAppropriateValue(arg): | |
| 1929 | return arg | |
| 1930 | else: | |
| 1931 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 1932 | else: | |
| 1933 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 1934 | return cosh(arg) | |
| 1935 | ||
| 1936 | def diff(self,arg): | |
| 1937 | """ | |
| 1938 | differential of this object | |
| 1939 | ||
| 1940 | @param arg: the derivative is calculated with respect to arg | |
| 1941 | @type arg: L{escript.Symbol} | |
| 1942 | @return: derivative with respect to C{arg} | |
| 1943 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 1944 | """ | |
| 1945 | if arg==self: | |
| 1946 | return identity(self.getShape()) | |
| 1947 | else: | |
| 1948 | myarg=self.getArgument()[0] | |
| 1949 | val=matchShape(sinh(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 1950 | return val[0]*val[1] | |
| 1951 | ||
| 1952 | def tanh(arg): | def tanh(arg): |
| 1953 | """ | """ |
| 1954 | Applies the tanh function to arg. | returns hyperbolic tangent of argument arg |
| 1955 | ||
| 1956 | @param arg: argument | @param arg: argument |
| 1957 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 1958 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 1959 | return symbols.Tanh_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 1960 | elif hasattr(arg,"tanh"): | """ |
| 1961 | return arg.tanh() | if isinstance(arg,numarray.NumArray): |
| 1962 | else: | return numarray.tanh(arg) |
| 1963 | return numarray.tanh(arg) | elif isinstance(arg,escript.Data): |
| 1964 | return arg._tanh() | |
| 1965 | elif isinstance(arg,float): | |
| 1966 | return math.tanh(arg) | |
| 1967 | elif isinstance(arg,int): | |
| 1968 | return math.tanh(arg) | |
| 1969 | elif isinstance(arg,Symbol): | |
| 1970 | return Tanh_Symbol(arg) | |
| 1971 | else: | |
| 1972 | raise TypeError,"tanh: Unknown argument type." | |
| 1973 | ||
| 1974 | class Tanh_Symbol(DependendSymbol): | |
| 1975 | """ | |
| 1976 | L{Symbol} representing the result of the hyperbolic tangent function | |
| 1977 | """ | |
| 1978 | def __init__(self,arg): | |
| 1979 | """ | |
| 1980 | initialization of tanh L{Symbol} with argument arg | |
| 1981 | @param arg: argument of function | |
| 1982 | @type arg: typically L{Symbol}. | |
| 1983 | """ | |
| 1984 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 1985 | ||
| 1986 | def getMyCode(self,argstrs,format="escript"): | |
| 1987 | """ | |
| 1988 | returns a program code that can be used to evaluate the symbol. | |
| 1989 | ||
| 1990 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 1991 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 1992 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 1993 | @type format: C{str} | |
| 1994 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 1995 | @rtype: C{str} | |
| 1996 | @raise: NotImplementedError: if the requested format is not available | |
| 1997 | """ | |
| 1998 | if isinstance(argstrs,list): | |
| 1999 | argstrs=argstrs[0] | |
| 2000 | if format=="escript" or format=="str" or format=="text": | |
| 2001 | return "tanh(%s)"%argstrs | |
| 2002 | else: | |
| 2003 | raise NotImplementedError,"Tanh_Symbol does not provide program code for format %s."%format | |
| 2004 | ||
| 2005 | def substitute(self,argvals): | |
| 2006 | """ | |
| 2007 | assigns new values to symbols in the definition of the symbol. | |
| 2008 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2009 | ||
| 2010 | @param argvals: new values assigned to symbols | |
| 2011 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2012 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2013 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2014 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2015 | """ | |
| 2016 | if argvals.has_key(self): | |
| 2017 | arg=argvals[self] | |
| 2018 | if self.isAppropriateValue(arg): | |
| 2019 | return arg | |
| 2020 | else: | |
| 2021 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2022 | else: | |
| 2023 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2024 | return tanh(arg) | |
| 2025 | ||
| 2026 | def diff(self,arg): | |
| 2027 | """ | |
| 2028 | differential of this object | |
| 2029 | ||
| 2030 | @param arg: the derivative is calculated with respect to arg | |
| 2031 | @type arg: L{escript.Symbol} | |
| 2032 | @return: derivative with respect to C{arg} | |
| 2033 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2034 | """ | |
| 2035 | if arg==self: | |
| 2036 | return identity(self.getShape()) | |
| 2037 | else: | |
| 2038 | myarg=self.getArgument()[0] | |
| 2039 | val=matchShape(1./cosh(myarg)**2,self.getDifferentiatedArguments(arg)[0]) | |
| 2040 | return val[0]*val[1] | |
| 2041 | ||
| 2042 | def asinh(arg): | def asinh(arg): |
| 2043 | """ | """ |
| 2044 | Applies the asinh function to arg. | returns inverse hyperbolic sine of argument arg |
| 2045 | ||
| 2046 | @param arg: argument | @param arg: argument |
| 2047 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2048 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2049 | return symbols.Asinh_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 2050 | elif hasattr(arg,"asinh"): | """ |
| 2051 | return arg.asinh() | if isinstance(arg,numarray.NumArray): |
| 2052 | else: | return numarray.arcsinh(arg) |
| 2053 | return numarray.asinh(arg) | elif isinstance(arg,escript.Data): |
| 2054 | return arg._asinh() | |
| 2055 | elif isinstance(arg,float): | |
| 2056 | return numarray.arcsinh(arg) | |
| 2057 | elif isinstance(arg,int): | |
| 2058 | return numarray.arcsinh(float(arg)) | |
| 2059 | elif isinstance(arg,Symbol): | |
| 2060 | return Asinh_Symbol(arg) | |
| 2061 | else: | |
| 2062 | raise TypeError,"asinh: Unknown argument type." | |
| 2063 | ||
| 2064 | class Asinh_Symbol(DependendSymbol): | |
| 2065 | """ | |
| 2066 | L{Symbol} representing the result of the inverse hyperbolic sine function | |
| 2067 | """ | |
| 2068 | def __init__(self,arg): | |
| 2069 | """ | |
| 2070 | initialization of asinh L{Symbol} with argument arg | |
| 2071 | @param arg: argument of function | |
| 2072 | @type arg: typically L{Symbol}. | |
| 2073 | """ | |
| 2074 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2075 | ||
| 2076 | def getMyCode(self,argstrs,format="escript"): | |
| 2077 | """ | |
| 2078 | returns a program code that can be used to evaluate the symbol. | |
| 2079 | ||
| 2080 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2081 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2082 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2083 | @type format: C{str} | |
| 2084 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2085 | @rtype: C{str} | |
| 2086 | @raise: NotImplementedError: if the requested format is not available | |
| 2087 | """ | |
| 2088 | if isinstance(argstrs,list): | |
| 2089 | argstrs=argstrs[0] | |
| 2090 | if format=="escript" or format=="str" or format=="text": | |
| 2091 | return "asinh(%s)"%argstrs | |
| 2092 | else: | |
| 2093 | raise NotImplementedError,"Asinh_Symbol does not provide program code for format %s."%format | |
| 2094 | ||
| 2095 | def substitute(self,argvals): | |
| 2096 | """ | |
| 2097 | assigns new values to symbols in the definition of the symbol. | |
| 2098 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2099 | ||
| 2100 | @param argvals: new values assigned to symbols | |
| 2101 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2102 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2103 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2104 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2105 | """ | |
| 2106 | if argvals.has_key(self): | |
| 2107 | arg=argvals[self] | |
| 2108 | if self.isAppropriateValue(arg): | |
| 2109 | return arg | |
| 2110 | else: | |
| 2111 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2112 | else: | |
| 2113 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2114 | return asinh(arg) | |
| 2115 | ||
| 2116 | def diff(self,arg): | |
| 2117 | """ | |
| 2118 | differential of this object | |
| 2119 | ||
| 2120 | @param arg: the derivative is calculated with respect to arg | |
| 2121 | @type arg: L{escript.Symbol} | |
| 2122 | @return: derivative with respect to C{arg} | |
| 2123 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2124 | """ | |
| 2125 | if arg==self: | |
| 2126 | return identity(self.getShape()) | |
| 2127 | else: | |
| 2128 | myarg=self.getArgument()[0] | |
| 2129 | val=matchShape(1./sqrt(myarg**2+1),self.getDifferentiatedArguments(arg)[0]) | |
| 2130 | return val[0]*val[1] | |
| 2131 | ||
| 2132 | def acosh(arg): | def acosh(arg): |
| 2133 | """ | """ |
| 2134 | Applies the acosh function to arg. | returns inverse hyperolic cosine of argument arg |
| 2135 | ||
| 2136 | @param arg: argument | @param arg: argument |
| 2137 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2138 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2139 | return symbols.Acosh_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 2140 | elif hasattr(arg,"acosh"): | """ |
| 2141 | return arg.acosh() | if isinstance(arg,numarray.NumArray): |
| 2142 | else: | return numarray.arccosh(arg) |
| 2143 | return numarray.acosh(arg) | elif isinstance(arg,escript.Data): |
| 2144 | return arg._acosh() | |
| 2145 | elif isinstance(arg,float): | |
| 2146 | return numarray.arccosh(arg) | |
| 2147 | elif isinstance(arg,int): | |
| 2148 | return numarray.arccosh(float(arg)) | |
| 2149 | elif isinstance(arg,Symbol): | |
| 2150 | return Acosh_Symbol(arg) | |
| 2151 | else: | |
| 2152 | raise TypeError,"acosh: Unknown argument type." | |
| 2153 | ||
| 2154 | class Acosh_Symbol(DependendSymbol): | |
| 2155 | """ | |
| 2156 | L{Symbol} representing the result of the inverse hyperolic cosine function | |
| 2157 | """ | |
| 2158 | def __init__(self,arg): | |
| 2159 | """ | |
| 2160 | initialization of acosh L{Symbol} with argument arg | |
| 2161 | @param arg: argument of function | |
| 2162 | @type arg: typically L{Symbol}. | |
| 2163 | """ | |
| 2164 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2165 | ||
| 2166 | def getMyCode(self,argstrs,format="escript"): | |
| 2167 | """ | |
| 2168 | returns a program code that can be used to evaluate the symbol. | |
| 2169 | ||
| 2170 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2171 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2172 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2173 | @type format: C{str} | |
| 2174 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2175 | @rtype: C{str} | |
| 2176 | @raise: NotImplementedError: if the requested format is not available | |
| 2177 | """ | |
| 2178 | if isinstance(argstrs,list): | |
| 2179 | argstrs=argstrs[0] | |
| 2180 | if format=="escript" or format=="str" or format=="text": | |
| 2181 | return "acosh(%s)"%argstrs | |
| 2182 | else: | |
| 2183 | raise NotImplementedError,"Acosh_Symbol does not provide program code for format %s."%format | |
| 2184 | ||
| 2185 | def substitute(self,argvals): | |
| 2186 | """ | |
| 2187 | assigns new values to symbols in the definition of the symbol. | |
| 2188 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2189 | ||
| 2190 | @param argvals: new values assigned to symbols | |
| 2191 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2192 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2193 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2194 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2195 | """ | |
| 2196 | if argvals.has_key(self): | |
| 2197 | arg=argvals[self] | |
| 2198 | if self.isAppropriateValue(arg): | |
| 2199 | return arg | |
| 2200 | else: | |
| 2201 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2202 | else: | |
| 2203 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2204 | return acosh(arg) | |
| 2205 | ||
| 2206 | def diff(self,arg): | |
| 2207 | """ | |
| 2208 | differential of this object | |
| 2209 | ||
| 2210 | @param arg: the derivative is calculated with respect to arg | |
| 2211 | @type arg: L{escript.Symbol} | |
| 2212 | @return: derivative with respect to C{arg} | |
| 2213 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2214 | """ | |
| 2215 | if arg==self: | |
| 2216 | return identity(self.getShape()) | |
| 2217 | else: | |
| 2218 | myarg=self.getArgument()[0] | |
| 2219 | val=matchShape(1./sqrt(myarg**2-1),self.getDifferentiatedArguments(arg)[0]) | |
| 2220 | return val[0]*val[1] | |
| 2221 | ||
| 2222 | def atanh(arg): | def atanh(arg): |
| 2223 | """ | """ |
| 2224 | Applies the atanh function to arg. | returns inverse hyperbolic tangent of argument arg |
| 2225 | ||
| 2226 | @param arg: argument | @param arg: argument |
| 2227 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2228 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2229 | return symbols.Atanh_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 2230 | elif hasattr(arg,"atanh"): | """ |
| 2231 | return arg.atanh() | if isinstance(arg,numarray.NumArray): |
| 2232 | else: | return numarray.arctanh(arg) |
| 2233 | return numarray.atanh(arg) | elif isinstance(arg,escript.Data): |
| 2234 | return arg._atanh() | |
| 2235 | elif isinstance(arg,float): | |
| 2236 | return numarray.arctanh(arg) | |
| 2237 | elif isinstance(arg,int): | |
| 2238 | return numarray.arctanh(float(arg)) | |
| 2239 | elif isinstance(arg,Symbol): | |
| 2240 | return Atanh_Symbol(arg) | |
| 2241 | else: | |
| 2242 | raise TypeError,"atanh: Unknown argument type." | |
| 2243 | ||
| 2244 | class Atanh_Symbol(DependendSymbol): | |
| 2245 | """ | |
| 2246 | L{Symbol} representing the result of the inverse hyperbolic tangent function | |
| 2247 | """ | |
| 2248 | def __init__(self,arg): | |
| 2249 | """ | |
| 2250 | initialization of atanh L{Symbol} with argument arg | |
| 2251 | @param arg: argument of function | |
| 2252 | @type arg: typically L{Symbol}. | |
| 2253 | """ | |
| 2254 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2255 | ||
| 2256 | def getMyCode(self,argstrs,format="escript"): | |
| 2257 | """ | |
| 2258 | returns a program code that can be used to evaluate the symbol. | |
| 2259 | ||
| 2260 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2261 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2262 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2263 | @type format: C{str} | |
| 2264 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2265 | @rtype: C{str} | |
| 2266 | @raise: NotImplementedError: if the requested format is not available | |
| 2267 | """ | |
| 2268 | if isinstance(argstrs,list): | |
| 2269 | argstrs=argstrs[0] | |
| 2270 | if format=="escript" or format=="str" or format=="text": | |
| 2271 | return "atanh(%s)"%argstrs | |
| 2272 | else: | |
| 2273 | raise NotImplementedError,"Atanh_Symbol does not provide program code for format %s."%format | |
| 2274 | ||
| 2275 | def substitute(self,argvals): | |
| 2276 | """ | |
| 2277 | assigns new values to symbols in the definition of the symbol. | |
| 2278 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2279 | ||
| 2280 | @param argvals: new values assigned to symbols | |
| 2281 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2282 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2283 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2284 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2285 | """ | |
| 2286 | if argvals.has_key(self): | |
| 2287 | arg=argvals[self] | |
| 2288 | if self.isAppropriateValue(arg): | |
| 2289 | return arg | |
| 2290 | else: | |
| 2291 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2292 | else: | |
| 2293 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2294 | return atanh(arg) | |
| 2295 | ||
| 2296 | def diff(self,arg): | |
| 2297 | """ | |
| 2298 | differential of this object | |
| 2299 | ||
| 2300 | @param arg: the derivative is calculated with respect to arg | |
| 2301 | @type arg: L{escript.Symbol} | |
| 2302 | @return: derivative with respect to C{arg} | |
| 2303 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2304 | """ | |
| 2305 | if arg==self: | |
| 2306 | return identity(self.getShape()) | |
| 2307 | else: | |
| 2308 | myarg=self.getArgument()[0] | |
| 2309 | val=matchShape(1./(1.-myarg**2),self.getDifferentiatedArguments(arg)[0]) | |
| 2310 | return val[0]*val[1] | |
| 2311 | ||
| 2312 | def exp(arg): | |
| 2313 | """ | |
| 2314 | returns exponential of argument arg | |
| 2315 | ||
| 2316 | @param arg: argument | |
| 2317 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2318 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2319 | @raises TypeError: if the type of the argument is not expected. | |
| 2320 | """ | |
| 2321 | if isinstance(arg,numarray.NumArray): | |
| 2322 | return numarray.exp(arg) | |
| 2323 | elif isinstance(arg,escript.Data): | |
| 2324 | return arg._exp() | |
| 2325 | elif isinstance(arg,float): | |
| 2326 | return math.exp(arg) | |
| 2327 | elif isinstance(arg,int): | |
| 2328 | return math.exp(arg) | |
| 2329 | elif isinstance(arg,Symbol): | |
| 2330 | return Exp_Symbol(arg) | |
| 2331 | else: | |
| 2332 | raise TypeError,"exp: Unknown argument type." | |
| 2333 | ||
| 2334 | class Exp_Symbol(DependendSymbol): | |
| 2335 | """ | |
| 2336 | L{Symbol} representing the result of the exponential function | |
| 2337 | """ | |
| 2338 | def __init__(self,arg): | |
| 2339 | """ | |
| 2340 | initialization of exp L{Symbol} with argument arg | |
| 2341 | @param arg: argument of function | |
| 2342 | @type arg: typically L{Symbol}. | |
| 2343 | """ | |
| 2344 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2345 | ||
| 2346 | def getMyCode(self,argstrs,format="escript"): | |
| 2347 | """ | |
| 2348 | returns a program code that can be used to evaluate the symbol. | |
| 2349 | ||
| 2350 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2351 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2352 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2353 | @type format: C{str} | |
| 2354 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2355 | @rtype: C{str} | |
| 2356 | @raise: NotImplementedError: if the requested format is not available | |
| 2357 | """ | |
| 2358 | if isinstance(argstrs,list): | |
| 2359 | argstrs=argstrs[0] | |
| 2360 | if format=="escript" or format=="str" or format=="text": | |
| 2361 | return "exp(%s)"%argstrs | |
| 2362 | else: | |
| 2363 | raise NotImplementedError,"Exp_Symbol does not provide program code for format %s."%format | |
| 2364 | ||
| 2365 | def substitute(self,argvals): | |
| 2366 | """ | |
| 2367 | assigns new values to symbols in the definition of the symbol. | |
| 2368 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2369 | ||
| 2370 | @param argvals: new values assigned to symbols | |
| 2371 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2372 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2373 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2374 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2375 | """ | |
| 2376 | if argvals.has_key(self): | |
| 2377 | arg=argvals[self] | |
| 2378 | if self.isAppropriateValue(arg): | |
| 2379 | return arg | |
| 2380 | else: | |
| 2381 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2382 | else: | |
| 2383 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2384 | return exp(arg) | |
| 2385 | ||
| 2386 | def diff(self,arg): | |
| 2387 | """ | |
| 2388 | differential of this object | |
| 2389 | ||
| 2390 | @param arg: the derivative is calculated with respect to arg | |
| 2391 | @type arg: L{escript.Symbol} | |
| 2392 | @return: derivative with respect to C{arg} | |
| 2393 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2394 | """ | |
| 2395 | if arg==self: | |
| 2396 | return identity(self.getShape()) | |
| 2397 | else: | |
| 2398 | myarg=self.getArgument()[0] | |
| 2399 | val=matchShape(self,self.getDifferentiatedArguments(arg)[0]) | |
| 2400 | return val[0]*val[1] | |
| 2401 | ||
| 2402 | def sqrt(arg): | |
| 2403 | """ | |
| 2404 | returns square root of argument arg | |
| 2405 | ||
| 2406 | @param arg: argument | |
| 2407 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2408 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2409 | @raises TypeError: if the type of the argument is not expected. | |
| 2410 | """ | |
| 2411 | if isinstance(arg,numarray.NumArray): | |
| 2412 | return numarray.sqrt(arg) | |
| 2413 | elif isinstance(arg,escript.Data): | |
| 2414 | return arg._sqrt() | |
| 2415 | elif isinstance(arg,float): | |
| 2416 | return math.sqrt(arg) | |
| 2417 | elif isinstance(arg,int): | |
| 2418 | return math.sqrt(arg) | |
| 2419 | elif isinstance(arg,Symbol): | |
| 2420 | return Sqrt_Symbol(arg) | |
| 2421 | else: | |
| 2422 | raise TypeError,"sqrt: Unknown argument type." | |
| 2423 | ||
| 2424 | class Sqrt_Symbol(DependendSymbol): | |
| 2425 | """ | |
| 2426 | L{Symbol} representing the result of the square root function | |
| 2427 | """ | |
| 2428 | def __init__(self,arg): | |
| 2429 | """ | |
| 2430 | initialization of sqrt L{Symbol} with argument arg | |
| 2431 | @param arg: argument of function | |
| 2432 | @type arg: typically L{Symbol}. | |
| 2433 | """ | |
| 2434 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2435 | ||
| 2436 | def getMyCode(self,argstrs,format="escript"): | |
| 2437 | """ | |
| 2438 | returns a program code that can be used to evaluate the symbol. | |
| 2439 | ||
| 2440 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2441 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2442 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2443 | @type format: C{str} | |
| 2444 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2445 | @rtype: C{str} | |
| 2446 | @raise: NotImplementedError: if the requested format is not available | |
| 2447 | """ | |
| 2448 | if isinstance(argstrs,list): | |
| 2449 | argstrs=argstrs[0] | |
| 2450 | if format=="escript" or format=="str" or format=="text": | |
| 2451 | return "sqrt(%s)"%argstrs | |
| 2452 | else: | |
| 2453 | raise NotImplementedError,"Sqrt_Symbol does not provide program code for format %s."%format | |
| 2454 | ||
| 2455 | def substitute(self,argvals): | |
| 2456 | """ | |
| 2457 | assigns new values to symbols in the definition of the symbol. | |
| 2458 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2459 | ||
| 2460 | @param argvals: new values assigned to symbols | |
| 2461 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2462 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2463 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2464 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2465 | """ | |
| 2466 | if argvals.has_key(self): | |
| 2467 | arg=argvals[self] | |
| 2468 | if self.isAppropriateValue(arg): | |
| 2469 | return arg | |
| 2470 | else: | |
| 2471 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2472 | else: | |
| 2473 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2474 | return sqrt(arg) | |
| 2475 | ||
| 2476 | def diff(self,arg): | |
| 2477 | """ | |
| 2478 | differential of this object | |
| 2479 | ||
| 2480 | @param arg: the derivative is calculated with respect to arg | |
| 2481 | @type arg: L{escript.Symbol} | |
| 2482 | @return: derivative with respect to C{arg} | |
| 2483 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2484 | """ | |
| 2485 | if arg==self: | |
| 2486 | return identity(self.getShape()) | |
| 2487 | else: | |
| 2488 | myarg=self.getArgument()[0] | |
| 2489 | val=matchShape(0.5/self,self.getDifferentiatedArguments(arg)[0]) | |
| 2490 | return val[0]*val[1] | |
| 2491 | ||
| 2492 | def log(arg): | |
| 2493 | """ | |
| 2494 | returns natural logarithm of argument arg | |
| 2495 | ||
| 2496 | @param arg: argument | |
| 2497 | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. | |
| 2498 | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. | |
| 2499 | @raises TypeError: if the type of the argument is not expected. | |
| 2500 | """ | |
| 2501 | if isinstance(arg,numarray.NumArray): | |
| 2502 | return numarray.log(arg) | |
| 2503 | elif isinstance(arg,escript.Data): | |
| 2504 | return arg._log() | |
| 2505 | elif isinstance(arg,float): | |
| 2506 | return math.log(arg) | |
| 2507 | elif isinstance(arg,int): | |
| 2508 | return math.log(arg) | |
| 2509 | elif isinstance(arg,Symbol): | |
| 2510 | return Log_Symbol(arg) | |
| 2511 | else: | |
| 2512 | raise TypeError,"log: Unknown argument type." | |
| 2513 | ||
| 2514 | class Log_Symbol(DependendSymbol): | |
| 2515 | """ | |
| 2516 | L{Symbol} representing the result of the natural logarithm function | |
| 2517 | """ | |
| 2518 | def __init__(self,arg): | |
| 2519 | """ | |
| 2520 | initialization of log L{Symbol} with argument arg | |
| 2521 | @param arg: argument of function | |
| 2522 | @type arg: typically L{Symbol}. | |
| 2523 | """ | |
| 2524 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2525 | ||
| 2526 | def getMyCode(self,argstrs,format="escript"): | |
| 2527 | """ | |
| 2528 | returns a program code that can be used to evaluate the symbol. | |
| 2529 | ||
| 2530 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2531 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2532 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2533 | @type format: C{str} | |
| 2534 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2535 | @rtype: C{str} | |
| 2536 | @raise: NotImplementedError: if the requested format is not available | |
| 2537 | """ | |
| 2538 | if isinstance(argstrs,list): | |
| 2539 | argstrs=argstrs[0] | |
| 2540 | if format=="escript" or format=="str" or format=="text": | |
| 2541 | return "log(%s)"%argstrs | |
| 2542 | else: | |
| 2543 | raise NotImplementedError,"Log_Symbol does not provide program code for format %s."%format | |
| 2544 | ||
| 2545 | def substitute(self,argvals): | |
| 2546 | """ | |
| 2547 | assigns new values to symbols in the definition of the symbol. | |
| 2548 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2549 | ||
| 2550 | @param argvals: new values assigned to symbols | |
| 2551 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2552 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2553 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2554 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2555 | """ | |
| 2556 | if argvals.has_key(self): | |
| 2557 | arg=argvals[self] | |
| 2558 | if self.isAppropriateValue(arg): | |
| 2559 | return arg | |
| 2560 | else: | |
| 2561 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2562 | else: | |
| 2563 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2564 | return log(arg) | |
| 2565 | ||
| 2566 | def diff(self,arg): | |
| 2567 | """ | |
| 2568 | differential of this object | |
| 2569 | ||
| 2570 | @param arg: the derivative is calculated with respect to arg | |
| 2571 | @type arg: L{escript.Symbol} | |
| 2572 | @return: derivative with respect to C{arg} | |
| 2573 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2574 | """ | |
| 2575 | if arg==self: | |
| 2576 | return identity(self.getShape()) | |
| 2577 | else: | |
| 2578 | myarg=self.getArgument()[0] | |
| 2579 | val=matchShape(1./arg,self.getDifferentiatedArguments(arg)[0]) | |
| 2580 | return val[0]*val[1] | |
| 2581 | ||
| 2582 | def sign(arg): | def sign(arg): |
| 2583 | """ | """ |
| 2584 | Applies the sign function to arg. | returns sign of argument arg |
| 2585 | ||
| 2586 | @param arg: argument | @param arg: argument |
| 2587 | """ | @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}. |
| 2588 | if isinstance(arg,symbols.Symbol): | @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg. |
| 2589 | return symbols.Sign_Symbol(arg) | @raises TypeError: if the type of the argument is not expected. |
| 2590 | elif hasattr(arg,"sign"): | """ |
| 2591 | return arg.sign() | if isinstance(arg,numarray.NumArray): |
| 2592 | else: | return numarray.sign(arg) |
| 2593 | return numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))- \ | elif isinstance(arg,escript.Data): |
| 2594 | numarray.less(arg,numarray.zeros(arg.shape,numarray.Float)) | return arg._sign() |
| 2595 | elif isinstance(arg,float): | |
| 2596 | if arg>0: | |
| 2597 | return 1. | |
| 2598 | elif arg<0: | |
| 2599 | return -1. | |
| 2600 | else: | |
| 2601 | return 0. | |
| 2602 | elif isinstance(arg,int): | |
| 2603 | if float(arg)>0: | |
| 2604 | return 1. | |
| 2605 | elif float(arg)<0: | |
| 2606 | return -1. | |
| 2607 | else: | |
| 2608 | return 0. | |
| 2609 | elif isinstance(arg,Symbol): | |
| 2610 | return wherePositive(arg)-whereNegative(arg) | |
| 2611 | else: | |
| 2612 | raise TypeError,"sign: Unknown argument type." | |
| 2613 | ||
| 2614 | def maxval(arg): | class Abs_Symbol(DependendSymbol): |
| 2615 | """ | """ |
| 2616 | Returns the maximum value of argument arg. | L{Symbol} representing the result of the absolute value function |
| 2617 | """ | |
| 2618 | def __init__(self,arg): | |
| 2619 | """ | |
| 2620 | initialization of abs L{Symbol} with argument arg | |
| 2621 | @param arg: argument of function | |
| 2622 | @type arg: typically L{Symbol}. | |
| 2623 | """ | |
| 2624 | DependendSymbol.__init__(self,args=[arg],shape=arg.getShape(),dim=arg.getDim()) | |
| 2625 | ||
| 2626 | def getMyCode(self,argstrs,format="escript"): | |
| 2627 | """ | |
| 2628 | returns a program code that can be used to evaluate the symbol. | |
| 2629 | ||
| 2630 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2631 | @type argstrs: C{str} or a C{list} of length 1 of C{str}. | |
| 2632 | @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported. | |
| 2633 | @type format: C{str} | |
| 2634 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2635 | @rtype: C{str} | |
| 2636 | @raise: NotImplementedError: if the requested format is not available | |
| 2637 | """ | |
| 2638 | if isinstance(argstrs,list): | |
| 2639 | argstrs=argstrs[0] | |
| 2640 | if format=="escript" or format=="str" or format=="text": | |
| 2641 | return "abs(%s)"%argstrs | |
| 2642 | else: | |
| 2643 | raise NotImplementedError,"Abs_Symbol does not provide program code for format %s."%format | |
| 2644 | ||
| 2645 | @param arg: argument | def substitute(self,argvals): |
| 2646 | """ | """ |
| 2647 | if isinstance(arg,symbols.Symbol): | assigns new values to symbols in the definition of the symbol. |
| 2648 | return symbols.Max_Symbol(arg) | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2649 | elif hasattr(arg,"maxval"): | |
| 2650 | return arg.maxval() | @param argvals: new values assigned to symbols |
| 2651 | elif hasattr(arg,"max"): | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2652 | return arg.max() | @return: result of the substitution process. Operations are executed as much as possible. |
| 2653 | else: | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2654 | return arg | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2655 | """ | |
| 2656 | if argvals.has_key(self): | |
| 2657 | arg=argvals[self] | |
| 2658 | if self.isAppropriateValue(arg): | |
| 2659 | return arg | |
| 2660 | else: | |
| 2661 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2662 | else: | |
| 2663 | arg=self.getSubstitutedArguments(argvals)[0] | |
| 2664 | return abs(arg) | |
| 2665 | ||
| 2666 | def minval(arg): | def diff(self,arg): |
| 2667 | """ | """ |
| 2668 | Returns the minimum value of argument arg. | differential of this object |
| 2669 | ||
| 2670 | @param arg: the derivative is calculated with respect to arg | |
| 2671 | @type arg: L{escript.Symbol} | |
| 2672 | @return: derivative with respect to C{arg} | |
| 2673 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2674 | """ | |
| 2675 | if arg==self: | |
| 2676 | return identity(self.getShape()) | |
| 2677 | else: | |
| 2678 | myarg=self.getArgument()[0] | |
| 2679 | val=matchShape(sign(myarg),self.getDifferentiatedArguments(arg)[0]) | |
| 2680 | return val[0]*val[1] | |
| 2681 | ||
| 2682 | ||
| 2683 | #======================================================= | |
| 2684 | # Binary operations: | |
| 2685 | #======================================================= | |
| 2686 | def add(arg0,arg1): | |
| 2687 | """ | |
| 2688 | adds arg0 and arg1 together. | |
| 2689 | ||
| 2690 | @param arg0: first term | |
| 2691 | @type arg0: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2692 | @param arg1: second term | |
| 2693 | @type arg1: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2694 | @return: the some of arg0 and arg1 | |
| 2695 | @rtype: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2696 | @note: The shape of both arguments is matched according to the rules in used in L{matchShape} | |
| 2697 | """ | |
| 2698 | args=matchShape(arg0,arg1) | |
| 2699 | if testForZero(args[0]): | |
| 2700 | return args[1] | |
| 2701 | elif testForZero(args[1]): | |
| 2702 | return args[0] | |
| 2703 | else: | |
| 2704 | if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) : | |
| 2705 | return Add_Symbol(args[0],args[1]) | |
| 2706 | elif isinstance(args[0],numarray.NumArray): | |
| 2707 | return args[1]+args[0] | |
| 2708 | else: | |
| 2709 | return args[0]+args[1] | |
| 2710 | ||
| 2711 | @param arg: argument | class Add_Symbol(DependendSymbol): |
| 2712 | """ | """ |
| 2713 | if isinstance(arg,symbols.Symbol): | Symbol representing the sum of two arguments. |
| 2714 | return symbols.Min_Symbol(arg) | """ |
| 2715 | elif hasattr(arg,"maxval"): | def __init__(self,arg0,arg1): |
| 2716 | return arg.minval() | """ |
| 2717 | elif hasattr(arg,"min"): | initialization of the L{Symbol} representing the sum of two arguments |
| 2718 | return arg.min() | |
| 2719 | else: | @param arg0: first term in the sum |
| 2720 | return arg | @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. |
| 2721 | @param arg1: second term in the sum | |
| 2722 | @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 2723 | @raise ValueError: if both arguments do not have the same shape. | |
| 2724 | @note: if both arguments have a spatial dimension, they must equal. | |
| 2725 | """ | |
| 2726 | sh0=pokeShape(arg0) | |
| 2727 | sh1=pokeShape(arg1) | |
| 2728 | if not sh0==sh1: | |
| 2729 | raise ValueError,"Add_Symbol: shape of arguments must match" | |
| 2730 | DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0,args=[arg0,arg1]) | |
| 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{list} of length 2 of C{str}. | |
| 2738 | @param format: specifies the format to be used. At the moment only "escript", "str" and "text" 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 format=="str" or format=="text": | |
| 2745 | return "(%s)+(%s)"%(argstrs[0],argstrs[1]) | |
| 2746 | elif format=="escript": | |
| 2747 | return "add(%s,%s)"%(argstrs[0],argstrs[1]) | |
| 2748 | else: | |
| 2749 | raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format) | |
| 2750 | ||
| 2751 | def wherePositive(arg): | def substitute(self,argvals): |
| 2752 | """ | """ |
| 2753 | Returns the positive values of argument arg. | 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 | args=self.getSubstitutedArguments(argvals) | |
| 2770 | return add(args[0],args[1]) | |
| 2771 | ||
| 2772 | @param arg: argument | def diff(self,arg): |
| 2773 | """ | """ |
| 2774 | if _testForZero(arg): | differential of this object |
| 2775 | return 0 | |
| 2776 | elif isinstance(arg,symbols.Symbol): | @param arg: the derivative is calculated with respect to arg |
| 2777 | return symbols.WherePositive_Symbol(arg) | @type arg: L{escript.Symbol} |
| 2778 | elif hasattr(arg,"wherePositive"): | @return: derivative with respect to C{arg} |
| 2779 | return arg.minval() | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. |
| 2780 | elif hasattr(arg,"wherePositive"): | """ |
| 2781 | numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float)) | if arg==self: |
| 2782 | else: | return identity(self.getShape()) |
| 2783 | if arg>0: | else: |
| 2784 | return 1. | dargs=self.getDifferentiatedArguments(arg) |
| 2785 | return add(dargs[0],dargs[1]) | |
| 2786 | ||
| 2787 | def mult(arg0,arg1): | |
| 2788 | """ | |
| 2789 | product of arg0 and arg1 | |
| 2790 | ||
| 2791 | @param arg0: first term | |
| 2792 | @type arg0: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2793 | @param arg1: second term | |
| 2794 | @type arg1: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2795 | @return: the some of arg0 and arg1 | |
| 2796 | @rtype: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2797 | @note: The shape of both arguments is matched according to the rules in used in L{matchShape} | |
| 2798 | """ | |
| 2799 | args=matchShape(arg0,arg1) | |
| 2800 | if testForZero(args[0]) or testForZero(args[1]): | |
| 2801 | return numarray.zeros(pokeShape(args[0]),numarray.Float) | |
| 2802 | else: | else: |
| 2803 | return 0. | if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) : |
| 2804 | return Mult_Symbol(args[0],args[1]) | |
| 2805 | elif isinstance(args[0],numarray.NumArray): | |
| 2806 | return args[1]*args[0] | |
| 2807 | else: | |
| 2808 | return args[0]*args[1] | |
| 2809 | ||
| 2810 | def whereNegative(arg): | class Mult_Symbol(DependendSymbol): |
| 2811 | """ | """ |
| 2812 | Returns the negative values of argument arg. | Symbol representing the product of two arguments. |
| 2813 | """ | |
| 2814 | def __init__(self,arg0,arg1): | |
| 2815 | """ | |
| 2816 | initialization of the L{Symbol} representing the product of two arguments | |
| 2817 | ||
| 2818 | @param arg0: first factor | |
| 2819 | @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 2820 | @param arg1: second factor | |
| 2821 | @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 2822 | @raise ValueError: if both arguments do not have the same shape. | |
| 2823 | @note: if both arguments have a spatial dimension, they must equal. | |
| 2824 | """ | |
| 2825 | sh0=pokeShape(arg0) | |
| 2826 | sh1=pokeShape(arg1) | |
| 2827 | if not sh0==sh1: | |
| 2828 | raise ValueError,"Mult_Symbol: shape of arguments must match" | |
| 2829 | DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0,args=[arg0,arg1]) | |
| 2830 | ||
| 2831 | def getMyCode(self,argstrs,format="escript"): | |
| 2832 | """ | |
| 2833 | returns a program code that can be used to evaluate the symbol. | |
| 2834 | ||
| 2835 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2836 | @type argstrs: C{list} of length 2 of C{str}. | |
| 2837 | @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported. | |
| 2838 | @type format: C{str} | |
| 2839 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2840 | @rtype: C{str} | |
| 2841 | @raise: NotImplementedError: if the requested format is not available | |
| 2842 | """ | |
| 2843 | if format=="str" or format=="text": | |
| 2844 | return "(%s)*(%s)"%(argstrs[0],argstrs[1]) | |
| 2845 | elif format=="escript": | |
| 2846 | return "mult(%s,%s)"%(argstrs[0],argstrs[1]) | |
| 2847 | else: | |
| 2848 | raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format) | |
| 2849 | ||
| 2850 | @param arg: argument | def substitute(self,argvals): |
| 2851 | """ | """ |
| 2852 | if _testForZero(arg): | assigns new values to symbols in the definition of the symbol. |
| 2853 | return 0 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. |
| 2854 | elif isinstance(arg,symbols.Symbol): | |
| 2855 | return symbols.WhereNegative_Symbol(arg) | @param argvals: new values assigned to symbols |
| 2856 | elif hasattr(arg,"whereNegative"): | @type argvals: C{dict} with keywords of type L{Symbol}. |
| 2857 | return arg.whereNegative() | @return: result of the substitution process. Operations are executed as much as possible. |
| 2858 | elif hasattr(arg,"shape"): | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution |
| 2859 | numarray.less(arg,numarray.zeros(arg.shape,numarray.Float)) | @raise TypeError: if a value for a L{Symbol} cannot be substituted. |
| 2860 | else: | """ |
| 2861 | if arg<0: | if argvals.has_key(self): |
| 2862 | return 1. | arg=argvals[self] |
| 2863 | if self.isAppropriateValue(arg): | |
| 2864 | return arg | |
| 2865 | else: | |
| 2866 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2867 | else: | |
| 2868 | args=self.getSubstitutedArguments(argvals) | |
| 2869 | return mult(args[0],args[1]) | |
| 2870 | ||
| 2871 | def diff(self,arg): | |
| 2872 | """ | |
| 2873 | differential of this object | |
| 2874 | ||
| 2875 | @param arg: the derivative is calculated with respect to arg | |
| 2876 | @type arg: L{escript.Symbol} | |
| 2877 | @return: derivative with respect to C{arg} | |
| 2878 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2879 | """ | |
| 2880 | if arg==self: | |
| 2881 | return identity(self.getShape()) | |
| 2882 | else: | |
| 2883 | myargs=self.getArgument() | |
| 2884 | dargs=self.getDifferentiatedArguments(arg) | |
| 2885 | return add(mult(myargs[0],dargs[1]),mult(myargs[1],dargs[0])) | |
| 2886 | ||
| 2887 | def quotient(arg0,arg1): | |
| 2888 | """ | |
| 2889 | quotient of arg0 and arg1 | |
| 2890 | ||
| 2891 | @param arg0: numerator | |
| 2892 | @type arg0: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2893 | @param arg1: denominator | |
| 2894 | @type arg1: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2895 | @return: the some of arg0 and arg1 | |
| 2896 | @rtype: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2897 | @note: The shape of both arguments is matched according to the rules in used in L{matchShape} | |
| 2898 | """ | |
| 2899 | args=matchShape(arg0,arg1) | |
| 2900 | if testForZero(args[0]): | |
| 2901 | return numarray.zeros(pokeShape(args[0]),numarray.Float) | |
| 2902 | elif isinstance(args[0],Symbol): | |
| 2903 | if isinstance(args[1],Symbol): | |
| 2904 | return Quotient_Symbol(args[0],args[1]) | |
| 2905 | else: | |
| 2906 | return mult(args[0],1./args[1]) | |
| 2907 | else: | else: |
| 2908 | return 0. | if isinstance(args[1],Symbol): |
| 2909 | return Quotient_Symbol(args[0],args[1]) | |
| 2910 | elif isinstance(args[0],numarray.NumArray) and not isinstance(args[1],numarray.NumArray): | |
| 2911 | return 1./args[1]*args[0] | |
| 2912 | else: | |
| 2913 | return args[0]/args[1] | |
| 2914 | ||
| 2915 | class Quotient_Symbol(DependendSymbol): | |
| 2916 | """ | |
| 2917 | Symbol representing the quotient of two arguments. | |
| 2918 | """ | |
| 2919 | def __init__(self,arg0,arg1): | |
| 2920 | """ | |
| 2921 | initialization of L{Symbol} representing the quotient of two arguments | |
| 2922 | ||
| 2923 | @param arg0: numerator | |
| 2924 | @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 2925 | @param arg1: denominator | |
| 2926 | @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 2927 | @raise ValueError: if both arguments do not have the same shape. | |
| 2928 | @note: if both arguments have a spatial dimension, they must equal. | |
| 2929 | """ | |
| 2930 | sh0=pokeShape(arg0) | |
| 2931 | sh1=pokeShape(arg1) | |
| 2932 | if not sh0==sh1: | |
| 2933 | raise ValueError,"Quotient_Symbol: shape of arguments must match" | |
| 2934 | DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0,args=[arg0,arg1]) | |
| 2935 | ||
| 2936 | def getMyCode(self,argstrs,format="escript"): | |
| 2937 | """ | |
| 2938 | returns a program code that can be used to evaluate the symbol. | |
| 2939 | ||
| 2940 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 2941 | @type argstrs: C{list} of length 2 of C{str}. | |
| 2942 | @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported. | |
| 2943 | @type format: C{str} | |
| 2944 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 2945 | @rtype: C{str} | |
| 2946 | @raise: NotImplementedError: if the requested format is not available | |
| 2947 | """ | |
| 2948 | if format=="str" or format=="text": | |
| 2949 | return "(%s)/(%s)"%(argstrs[0],argstrs[1]) | |
| 2950 | if format=="escript": | |
| 2951 | return "quotient(%s,%s)"%(argstrs[0],argstrs[1]) | |
| 2952 | else: | |
| 2953 | raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format) | |
| 2954 | ||
| 2955 | def substitute(self,argvals): | |
| 2956 | """ | |
| 2957 | assigns new values to symbols in the definition of the symbol. | |
| 2958 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 2959 | ||
| 2960 | @param argvals: new values assigned to symbols | |
| 2961 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 2962 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 2963 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 2964 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 2965 | """ | |
| 2966 | if argvals.has_key(self): | |
| 2967 | arg=argvals[self] | |
| 2968 | if self.isAppropriateValue(arg): | |
| 2969 | return arg | |
| 2970 | else: | |
| 2971 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 2972 | else: | |
| 2973 | args=self.getSubstitutedArguments(argvals) | |
| 2974 | return quotient(args[0],args[1]) | |
| 2975 | ||
| 2976 | def diff(self,arg): | |
| 2977 | """ | |
| 2978 | differential of this object | |
| 2979 | ||
| 2980 | @param arg: the derivative is calculated with respect to arg | |
| 2981 | @type arg: L{escript.Symbol} | |
| 2982 | @return: derivative with respect to C{arg} | |
| 2983 | @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray} are possible. | |
| 2984 | """ | |
| 2985 | if arg==self: | |
| 2986 | return identity(self.getShape()) | |
| 2987 | else: | |
| 2988 | myargs=self.getArgument() | |
| 2989 | dargs=self.getDifferentiatedArguments(arg) | |
| 2990 | return quotient(add(mult(myargs[1],dargs[0]),mult(-myargs[0],dargs[1])),myargs[1]*myargs[1]) | |
| 2991 | ||
| 2992 | ||
| 2993 | def power(arg0,arg1): | |
| 2994 | """ | |
| 2995 | raises arg0 to the power of arg1 | |
| 2996 | ||
| 2997 | @param arg0: basis | |
| 2998 | @type arg0: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 2999 | @param arg1: exponent | |
| 3000 | @type arg1: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 3001 | @return: of arg0 and arg1 | |
| 3002 | @rtype: L{escript.Symbol}, C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}. | |
| 3003 | @note: The shape of both arguments is matched according to the rules in used in L{matchShape} | |
| 3004 | """ | |
| 3005 | args=matchShape(arg0,arg1) | |
| 3006 | if testForZero(args[0]): | |
| 3007 | return numarray.zeros(args[0],numarray.Float) | |
| 3008 | elif testForZero(args[1]): | |
| 3009 | return numarray.ones(args[0],numarray.Float) | |
| 3010 | elif isinstance(args[0],Symbol) or isinstance(args[1],Symbol): | |
| 3011 | return Power_Symbol(args[0],args[1]) | |
| 3012 | elif isinstance(args[0],numarray.NumArray) and not isinstance(args[1],numarray.NumArray): | |
| 3013 | return exp(args[1]*log(args[0])) | |
| 3014 | else: | |
| 3015 | return args[0]**args[1] | |
| 3016 | ||
| 3017 | class Power_Symbol(DependendSymbol): | |
| 3018 | """ | |
| 3019 | Symbol representing the first argument to the power of the second argument. | |
| 3020 | """ | |
| 3021 | def __init__(self,arg0,arg1): | |
| 3022 | """ | |
| 3023 | initialization of the L{Symbol} representing rasing the first argument to the power of the second. | |
| 3024 | ||
| 3025 | @param arg0: basis | |
| 3026 | @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 3027 | @param arg1: exponent | |
| 3028 | @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}. | |
| 3029 | @raise ValueError: if both arguments do not have the same shape. | |
| 3030 | @note: if both arguments have a spatial dimension, they must equal. | |
| 3031 | """ | |
| 3032 | sh0=pokeShape(arg0) | |
| 3033 | sh1=pokeShape(arg1) | |
| 3034 | if not sh0==sh1: | |
| 3035 | raise ValueError,"Power_Symbol: shape of arguments must match" | |
| 3036 | d0=pokeDim(arg0) | |
| 3037 | d1=pokeDim(arg1) | |
| 3038 | DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0,args=[arg0,arg1]) | |
| 3039 | ||
| 3040 | def getMyCode(self,argstrs,format="escript"): | |
| 3041 | """ | |
| 3042 | returns a program code that can be used to evaluate the symbol. | |
| 3043 | ||
| 3044 | @param argstrs: gives for each argument a string representing the argument for the evaluation. | |
| 3045 | @type argstrs: C{list} of length 2 of C{str}. | |
| 3046 | @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported. | |
| 3047 | @type format: C{str} | |
| 3048 | @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available. | |
| 3049 | @rtype: C{str} | |
| 3050 | @raise: NotImplementedError: if the requested format is not available | |
| 3051 | """ | |
| 3052 | if format=="escript" or format=="str" or format=="text": | |
| 3053 | return "(%s)**(%s)"%(argstrs[0],argstrs[1]) | |
| 3054 | elif format=="escript": | |
| 3055 | return "power(%s,%s)"%(argstrs[0],argstrs[1]) | |
| 3056 | else: | |
| 3057 | raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format) | |
| 3058 | ||
| 3059 | def substitute(self,argvals): | |
| 3060 | """ | |
| 3061 | assigns new values to symbols in the definition of the symbol. | |
| 3062 | The method replaces the L{Symbol} u by argvals[u] in the expression defining this object. | |
| 3063 | ||
| 3064 | @param argvals: new values assigned to symbols | |
| 3065 | @type argvals: C{dict} with keywords of type L{Symbol}. | |
| 3066 | @return: result of the substitution process. Operations are executed as much as possible. | |
| 3067 | @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution | |
| 3068 | @raise TypeError: if a value for a L{Symbol} cannot be substituted. | |
| 3069 | """ | |
| 3070 | if argvals.has_key(self): | |
| 3071 | arg=argvals[self] | |
| 3072 | if self.isAppropriateValue(arg): | |
| 3073 | return arg | |
| 3074 | else: | |
| 3075 | raise TypeError,"%s: new value is not appropriate."%str(self) | |
| 3076 | else: | |
| 3077 | args=self.getSubstitutedArguments(argvals) | |
| 3078 | return power(args[0],args[1]) | |
| 3079 | ||
| 3080 | def diff(self,arg): | |
| 3081 | """ | |
| 3082 | differential of this object | |
| 3083 | ||
| 3084 | @param arg: the derivative is calculated with respect to arg | |
| 3085 | @type arg: L{escript.Symbol} | |
| 3086 |