| 1 |
# $Id$ |
| 2 |
|
| 3 |
## @file util.py |
| 4 |
|
| 5 |
""" |
| 6 |
@brief Utility functions for escript |
| 7 |
|
| 8 |
TODO for Data: |
| 9 |
|
| 10 |
* binary operations @: (a@b)[:,*]=a[:]@b[:,*] if rank(a)<rank(b) |
| 11 |
@=+,-,*,/,** (a@b)[:]=a[:]@b[:] if rank(a)=rank(b) |
| 12 |
(a@b)[*,:]=a[*,:]@b[:] if rank(a)>rank(b) |
| 13 |
|
| 14 |
* implementation of outer outer(a,b)[:,*]=a[:]*b[*] |
| 15 |
* trace: trace(arg,axis0=a0,axis1=a1)(:,&,*)=sum_i trace(:,i,&,i,*) (i are at index a0 and a1) |
| 16 |
""" |
| 17 |
|
| 18 |
import numarray |
| 19 |
import escript |
| 20 |
|
| 21 |
# |
| 22 |
# escript constants (have to be consistent with utilC.h ) |
| 23 |
# |
| 24 |
UNKNOWN=-1 |
| 25 |
EPSILON=1.e-15 |
| 26 |
Pi=numarray.pi |
| 27 |
# some solver options: |
| 28 |
NO_REORDERING=0 |
| 29 |
MINIMUM_FILL_IN=1 |
| 30 |
NESTED_DISSECTION=2 |
| 31 |
# solver methods |
| 32 |
DEFAULT_METHOD=0 |
| 33 |
DIRECT=1 |
| 34 |
CHOLEVSKY=2 |
| 35 |
PCG=3 |
| 36 |
CR=4 |
| 37 |
CGS=5 |
| 38 |
BICGSTAB=6 |
| 39 |
SSOR=7 |
| 40 |
ILU0=8 |
| 41 |
ILUT=9 |
| 42 |
JACOBI=10 |
| 43 |
GMRES=11 |
| 44 |
PRES20=12 |
| 45 |
|
| 46 |
METHOD_KEY="method" |
| 47 |
SYMMETRY_KEY="symmetric" |
| 48 |
TOLERANCE_KEY="tolerance" |
| 49 |
|
| 50 |
# supported file formats: |
| 51 |
VRML=1 |
| 52 |
PNG=2 |
| 53 |
JPEG=3 |
| 54 |
JPG=3 |
| 55 |
PS=4 |
| 56 |
OOGL=5 |
| 57 |
BMP=6 |
| 58 |
TIFF=7 |
| 59 |
OPENINVENTOR=8 |
| 60 |
RENDERMAN=9 |
| 61 |
PNM=10 |
| 62 |
|
| 63 |
#=========================================================== |
| 64 |
# a simple tool box to deal with _differentials of functions |
| 65 |
#=========================================================== |
| 66 |
|
| 67 |
class Symbol: |
| 68 |
"""symbol class""" |
| 69 |
def __init__(self,name="symbol",shape=(),dim=3,args=[]): |
| 70 |
"""creates an instance of a symbol of shape shape and spatial dimension dim |
| 71 |
The symbol may depending on a list of arguments args which |
| 72 |
may be symbols or other objects. name gives the name of the symbol.""" |
| 73 |
self.__args=args |
| 74 |
self.__name=name |
| 75 |
self.__shape=shape |
| 76 |
if hasattr(dim,"getDim"): |
| 77 |
self.__dim=dim.getDim() |
| 78 |
else: |
| 79 |
self.__dim=dim |
| 80 |
# |
| 81 |
self.__cache_val=None |
| 82 |
self.__cache_argval=None |
| 83 |
|
| 84 |
def getArgument(self,i): |
| 85 |
"""returns the i-th argument""" |
| 86 |
return self.__args[i] |
| 87 |
|
| 88 |
def getDim(self): |
| 89 |
"""returns the spatial dimension of the symbol""" |
| 90 |
return self.__dim |
| 91 |
|
| 92 |
def getRank(self): |
| 93 |
"""returns the rank of the symbol""" |
| 94 |
return len(self.getShape()) |
| 95 |
|
| 96 |
def getShape(self): |
| 97 |
"""returns the shape of the symbol""" |
| 98 |
return self.__shape |
| 99 |
|
| 100 |
def getEvaluatedArguments(self,argval): |
| 101 |
"""returns the list of evaluated arguments by subsituting symbol u by argval[u].""" |
| 102 |
if argval==self.__cache_argval: |
| 103 |
print "%s: cached value used"%self |
| 104 |
return self.__cache_val |
| 105 |
else: |
| 106 |
out=[] |
| 107 |
for a in self.__args: |
| 108 |
if isinstance(a,Symbol): |
| 109 |
out.append(a.eval(argval)) |
| 110 |
else: |
| 111 |
out.append(a) |
| 112 |
self.__cache_argval=argval |
| 113 |
self.__cache_val=out |
| 114 |
return out |
| 115 |
|
| 116 |
def getDifferentiatedArguments(self,arg): |
| 117 |
"""returns the list of the arguments _differentiated by arg""" |
| 118 |
out=[] |
| 119 |
for a in self.__args: |
| 120 |
if isinstance(a,Symbol): |
| 121 |
out.append(a.diff(arg)) |
| 122 |
else: |
| 123 |
out.append(0) |
| 124 |
return out |
| 125 |
|
| 126 |
def diff(self,arg): |
| 127 |
"""returns the _differention of self by arg.""" |
| 128 |
if self==arg: |
| 129 |
out=numarray.zeros(tuple(2*list(self.getShape())),numarray.Float) |
| 130 |
if self.getRank()==0: |
| 131 |
out=1. |
| 132 |
elif self.getRank()==1: |
| 133 |
for i0 in range(self.getShape()[0]): |
| 134 |
out[i0,i0]=1. |
| 135 |
elif self.getRank()==2: |
| 136 |
for i0 in range(self.getShape()[0]): |
| 137 |
for i1 in range(self.getShape()[1]): |
| 138 |
out[i0,i1,i0,i1]=1. |
| 139 |
elif self.getRank()==3: |
| 140 |
for i0 in range(self.getShape()[0]): |
| 141 |
for i1 in range(self.getShape()[1]): |
| 142 |
for i2 in range(self.getShape()[2]): |
| 143 |
out[i0,i1,i2,i0,i1,i2]=1. |
| 144 |
elif self.getRank()==4: |
| 145 |
for i0 in range(self.getShape()[0]): |
| 146 |
for i1 in range(self.getShape()[1]): |
| 147 |
for i2 in range(self.getShape()[2]): |
| 148 |
for i3 in range(self.getShape()[3]): |
| 149 |
out[i0,i1,i2,i3,i0,i1,i2,i3]=1. |
| 150 |
else: |
| 151 |
raise ValueError,"differential support rank<5 only." |
| 152 |
return out |
| 153 |
else: |
| 154 |
return self._diff(arg) |
| 155 |
|
| 156 |
def _diff(self,arg): |
| 157 |
"""return derivate of self with respect to arg (!=self). |
| 158 |
This method is overwritten by a particular symbol""" |
| 159 |
return 0 |
| 160 |
|
| 161 |
def eval(self,argval): |
| 162 |
"""subsitutes symbol u in self by argval[u] and returns the result. If |
| 163 |
self is not a key of argval then self is returned.""" |
| 164 |
if argval.has_key(self): |
| 165 |
return argval[self] |
| 166 |
else: |
| 167 |
return self |
| 168 |
|
| 169 |
def __str__(self): |
| 170 |
"""returns a string representation of the symbol""" |
| 171 |
return self.__name |
| 172 |
|
| 173 |
def __add__(self,other): |
| 174 |
"""adds other to symbol self. if _testForZero(other) self is returned.""" |
| 175 |
if _testForZero(other): |
| 176 |
return self |
| 177 |
else: |
| 178 |
a=_matchShape([self,other]) |
| 179 |
return Add_Symbol(a[0],a[1]) |
| 180 |
|
| 181 |
def __radd__(self,other): |
| 182 |
"""adds other to symbol self. if _testForZero(other) self is returned.""" |
| 183 |
return self+other |
| 184 |
|
| 185 |
def __neg__(self): |
| 186 |
"""returns -self.""" |
| 187 |
return self*(-1.) |
| 188 |
|
| 189 |
def __pos__(self): |
| 190 |
"""returns +self.""" |
| 191 |
return self |
| 192 |
|
| 193 |
def __abs__(self): |
| 194 |
"""returns absolute value""" |
| 195 |
return Abs_Symbol(self) |
| 196 |
|
| 197 |
def __sub__(self,other): |
| 198 |
"""subtracts other from symbol self. if _testForZero(other) self is returned.""" |
| 199 |
if _testForZero(other): |
| 200 |
return self |
| 201 |
else: |
| 202 |
return self+(-other) |
| 203 |
|
| 204 |
def __rsub__(self,other): |
| 205 |
"""subtracts symbol self from other.""" |
| 206 |
return -self+other |
| 207 |
|
| 208 |
def __div__(self,other): |
| 209 |
"""divides symbol self by other.""" |
| 210 |
if isinstance(other,Symbol): |
| 211 |
a=_matchShape([self,other]) |
| 212 |
return Div_Symbol(a[0],a[1]) |
| 213 |
else: |
| 214 |
return self*(1./other) |
| 215 |
|
| 216 |
def __rdiv__(self,other): |
| 217 |
"""dived other by symbol self. if _testForZero(other) 0 is returned.""" |
| 218 |
if _testForZero(other): |
| 219 |
return 0 |
| 220 |
else: |
| 221 |
a=_matchShape([self,other]) |
| 222 |
return Div_Symbol(a[0],a[1]) |
| 223 |
|
| 224 |
def __pow__(self,other): |
| 225 |
"""raises symbol self to the power of other""" |
| 226 |
a=_matchShape([self,other]) |
| 227 |
return Power_Symbol(a[0],a[1]) |
| 228 |
|
| 229 |
def __rpow__(self,other): |
| 230 |
"""raises other to the symbol self""" |
| 231 |
a=_matchShape([self,other]) |
| 232 |
return Power_Symbol(a[1],a[0]) |
| 233 |
|
| 234 |
def __mul__(self,other): |
| 235 |
"""multiplies other by symbol self. if _testForZero(other) 0 is returned.""" |
| 236 |
if _testForZero(other): |
| 237 |
return 0 |
| 238 |
else: |
| 239 |
a=_matchShape([self,other]) |
| 240 |
return Mult_Symbol(a[0],a[1]) |
| 241 |
|
| 242 |
def __rmul__(self,other): |
| 243 |
"""multiplies other by symbol self. if _testSForZero(other) 0 is returned.""" |
| 244 |
return self*other |
| 245 |
|
| 246 |
def __getitem__(self,sl): |
| 247 |
print sl |
| 248 |
|
| 249 |
def Float_Symbol(Symbol): |
| 250 |
def __init__(self,name="symbol",shape=(),args=[]): |
| 251 |
Symbol.__init__(self,dim=0,name="symbol",shape=(),args=[]) |
| 252 |
|
| 253 |
class ScalarSymbol(Symbol): |
| 254 |
"""a scalar symbol""" |
| 255 |
def __init__(self,dim=3,name="scalar"): |
| 256 |
"""creates a scalar symbol of spatial dimension dim""" |
| 257 |
if hasattr(dim,"getDim"): |
| 258 |
d=dim.getDim() |
| 259 |
else: |
| 260 |
d=dim |
| 261 |
Symbol.__init__(self,shape=(),dim=d,name=name) |
| 262 |
|
| 263 |
class VectorSymbol(Symbol): |
| 264 |
"""a vector symbol""" |
| 265 |
def __init__(self,dim=3,name="vector"): |
| 266 |
"""creates a vector symbol of spatial dimension dim""" |
| 267 |
if hasattr(dim,"getDim"): |
| 268 |
d=dim.getDim() |
| 269 |
else: |
| 270 |
d=dim |
| 271 |
Symbol.__init__(self,shape=(d,),dim=d,name=name) |
| 272 |
|
| 273 |
class TensorSymbol(Symbol): |
| 274 |
"""a tensor symbol""" |
| 275 |
def __init__(self,dim=3,name="tensor"): |
| 276 |
"""creates a tensor symbol of spatial dimension dim""" |
| 277 |
if hasattr(dim,"getDim"): |
| 278 |
d=dim.getDim() |
| 279 |
else: |
| 280 |
d=dim |
| 281 |
Symbol.__init__(self,shape=(d,d),dim=d,name=name) |
| 282 |
|
| 283 |
class Tensor3Symbol(Symbol): |
| 284 |
"""a tensor order 3 symbol""" |
| 285 |
def __init__(self,dim=3,name="tensor3"): |
| 286 |
"""creates a tensor order 3 symbol of spatial dimension dim""" |
| 287 |
if hasattr(dim,"getDim"): |
| 288 |
d=dim.getDim() |
| 289 |
else: |
| 290 |
d=dim |
| 291 |
Symbol.__init__(self,shape=(d,d,d),dim=d,name=name) |
| 292 |
|
| 293 |
class Tensor4Symbol(Symbol): |
| 294 |
"""a tensor order 4 symbol""" |
| 295 |
def __init__(self,dim=3,name="tensor4"): |
| 296 |
"""creates a tensor order 4 symbol of spatial dimension dim""" |
| 297 |
if hasattr(dim,"getDim"): |
| 298 |
d=dim.getDim() |
| 299 |
else: |
| 300 |
d=dim |
| 301 |
Symbol.__init__(self,shape=(d,d,d,d),dim=d,name=name) |
| 302 |
|
| 303 |
class Add_Symbol(Symbol): |
| 304 |
"""symbol representing the sum of two arguments""" |
| 305 |
def __init__(self,arg0,arg1): |
| 306 |
a=[arg0,arg1] |
| 307 |
Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
| 308 |
def __str__(self): |
| 309 |
return "(%s+%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 310 |
def eval(self,argval): |
| 311 |
a=self.getEvaluatedArguments(argval) |
| 312 |
return a[0]+a[1] |
| 313 |
def _diff(self,arg): |
| 314 |
a=self.getDifferentiatedArguments(arg) |
| 315 |
return a[0]+a[1] |
| 316 |
|
| 317 |
class Mult_Symbol(Symbol): |
| 318 |
"""symbol representing the product of two arguments""" |
| 319 |
def __init__(self,arg0,arg1): |
| 320 |
a=[arg0,arg1] |
| 321 |
Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
| 322 |
def __str__(self): |
| 323 |
return "(%s*%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 324 |
def eval(self,argval): |
| 325 |
a=self.getEvaluatedArguments(argval) |
| 326 |
return a[0]*a[1] |
| 327 |
def _diff(self,arg): |
| 328 |
a=self.getDifferentiatedArguments(arg) |
| 329 |
return self.getArgument(1)*a[0]+self.getArgument(0)*a[1] |
| 330 |
|
| 331 |
class Div_Symbol(Symbol): |
| 332 |
"""symbol representing the quotient of two arguments""" |
| 333 |
def __init__(self,arg0,arg1): |
| 334 |
a=[arg0,arg1] |
| 335 |
Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
| 336 |
def __str__(self): |
| 337 |
return "(%s/%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 338 |
def eval(self,argval): |
| 339 |
a=self.getEvaluatedArguments(argval) |
| 340 |
return a[0]/a[1] |
| 341 |
def _diff(self,arg): |
| 342 |
a=self.getDifferentiatedArguments(arg) |
| 343 |
return (a[0]*self.getArgument(1)-self.getArgument(0)*a[1])/ \ |
| 344 |
(self.getArgument(1)*self.getArgument(1)) |
| 345 |
|
| 346 |
class Power_Symbol(Symbol): |
| 347 |
"""symbol representing the power of the first argument to the power of the second argument""" |
| 348 |
def __init__(self,arg0,arg1): |
| 349 |
a=[arg0,arg1] |
| 350 |
Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
| 351 |
def __str__(self): |
| 352 |
return "(%s**%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 353 |
def eval(self,argval): |
| 354 |
a=self.getEvaluatedArguments(argval) |
| 355 |
return a[0]**a[1] |
| 356 |
def _diff(self,arg): |
| 357 |
a=self.getDifferentiatedArguments(arg) |
| 358 |
return self*(a[1]*log(self.getArgument(0))+self.getArgument(1)/self.getArgument(0)*a[0]) |
| 359 |
|
| 360 |
class Abs_Symbol(Symbol): |
| 361 |
"""symbol representing absolute value of its argument""" |
| 362 |
def __init__(self,arg): |
| 363 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 364 |
def __str__(self): |
| 365 |
return "abs(%s)"%str(self.getArgument(0)) |
| 366 |
def eval(self,argval): |
| 367 |
return abs(self.getEvaluatedArguments(argval)[0]) |
| 368 |
def _diff(self,arg): |
| 369 |
return sign(self.getArgument(0))*self.getDifferentiatedArguments(arg)[0] |
| 370 |
|
| 371 |
#========================================================= |
| 372 |
# some little helpers |
| 373 |
#========================================================= |
| 374 |
def _testForZero(arg): |
| 375 |
"""returns True is arg is considered of being zero""" |
| 376 |
if isinstance(arg,int): |
| 377 |
return not arg>0 |
| 378 |
elif isinstance(arg,float): |
| 379 |
return not arg>0. |
| 380 |
elif isinstance(arg,numarray.NumArray): |
| 381 |
a=abs(arg) |
| 382 |
while isinstance(a,numarray.NumArray): a=numarray.sometrue(a) |
| 383 |
return not a>0 |
| 384 |
else: |
| 385 |
return False |
| 386 |
|
| 387 |
def _extractDim(args): |
| 388 |
dim=None |
| 389 |
for a in args: |
| 390 |
if hasattr(a,"getDim"): |
| 391 |
d=a.getDim() |
| 392 |
if dim==None: |
| 393 |
dim=d |
| 394 |
else: |
| 395 |
if dim!=d: raise ValueError,"inconsistent spatial dimension of arguments" |
| 396 |
if dim==None: |
| 397 |
raise ValueError,"cannot recover spatial dimension" |
| 398 |
return dim |
| 399 |
|
| 400 |
def _identifyShape(arg): |
| 401 |
"""identifies the shape of arg.""" |
| 402 |
if hasattr(arg,"getShape"): |
| 403 |
arg_shape=arg.getShape() |
| 404 |
elif hasattr(arg,"shape"): |
| 405 |
s=arg.shape |
| 406 |
if callable(s): |
| 407 |
arg_shape=s() |
| 408 |
else: |
| 409 |
arg_shape=s |
| 410 |
else: |
| 411 |
arg_shape=() |
| 412 |
return arg_shape |
| 413 |
|
| 414 |
def _extractShape(args): |
| 415 |
"""extracts the common shape of the list of arguments args""" |
| 416 |
shape=None |
| 417 |
for a in args: |
| 418 |
a_shape=_identifyShape(a) |
| 419 |
if shape==None: shape=a_shape |
| 420 |
if shape!=a_shape: raise ValueError,"inconsistent shape" |
| 421 |
if shape==None: |
| 422 |
raise ValueError,"cannot recover shape" |
| 423 |
return shape |
| 424 |
|
| 425 |
def _matchShape(args,shape=None): |
| 426 |
"""returns the list of arguments args as object which have all the specified shape. |
| 427 |
if shape is not given the shape "largest" shape of args is used.""" |
| 428 |
# identify the list of shapes: |
| 429 |
arg_shapes=[] |
| 430 |
for a in args: arg_shapes.append(_identifyShape(a)) |
| 431 |
# get the largest shape (currently the longest shape): |
| 432 |
if shape==None: shape=max(arg_shapes) |
| 433 |
|
| 434 |
out=[] |
| 435 |
for i in range(len(args)): |
| 436 |
if shape==arg_shapes[i]: |
| 437 |
out.append(args[i]) |
| 438 |
else: |
| 439 |
if len(shape)==0: # then len(arg_shapes[i])>0 |
| 440 |
raise ValueError,"cannot adopt shape of %s to %s"%(str(args[i]),str(shape)) |
| 441 |
else: |
| 442 |
if len(arg_shapes[i])==0: |
| 443 |
out.append(outer(args[i],numarray.ones(shape))) |
| 444 |
else: |
| 445 |
raise ValueError,"cannot adopt shape of %s to %s"%(str(args[i]),str(shape)) |
| 446 |
return out |
| 447 |
|
| 448 |
#========================================================= |
| 449 |
# wrappers for various mathematical functions: |
| 450 |
#========================================================= |
| 451 |
def diff(arg,dep): |
| 452 |
"""returns the derivative of arg with respect to dep. If arg is not Symbol object |
| 453 |
0 is returned""" |
| 454 |
if isinstance(arg,Symbol): |
| 455 |
return arg.diff(dep) |
| 456 |
elif hasattr(arg,"shape"): |
| 457 |
if callable(arg.shape): |
| 458 |
return numarray.zeros(arg.shape(),numarray.Float) |
| 459 |
else: |
| 460 |
return numarray.zeros(arg.shape,numarray.Float) |
| 461 |
else: |
| 462 |
return 0 |
| 463 |
|
| 464 |
def exp(arg): |
| 465 |
""" |
| 466 |
@brief applies the exponential function to arg |
| 467 |
@param arg (input): argument |
| 468 |
""" |
| 469 |
if isinstance(arg,Symbol): |
| 470 |
return Exp_Symbol(arg) |
| 471 |
elif hasattr(arg,"exp"): |
| 472 |
return arg.exp() |
| 473 |
else: |
| 474 |
return numarray.exp(arg) |
| 475 |
|
| 476 |
class Exp_Symbol(Symbol): |
| 477 |
"""symbol representing the power of the first argument to the power of the second argument""" |
| 478 |
def __init__(self,arg): |
| 479 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 480 |
def __str__(self): |
| 481 |
return "exp(%s)"%str(self.getArgument(0)) |
| 482 |
def eval(self,argval): |
| 483 |
return exp(self.getEvaluatedArguments(argval)[0]) |
| 484 |
def _diff(self,arg): |
| 485 |
return self*self.getDifferentiatedArguments(arg)[0] |
| 486 |
|
| 487 |
def sqrt(arg): |
| 488 |
""" |
| 489 |
@brief applies the squre root function to arg |
| 490 |
@param arg (input): argument |
| 491 |
""" |
| 492 |
if isinstance(arg,Symbol): |
| 493 |
return Sqrt_Symbol(arg) |
| 494 |
elif hasattr(arg,"sqrt"): |
| 495 |
return arg.sqrt() |
| 496 |
else: |
| 497 |
return numarray.sqrt(arg) |
| 498 |
|
| 499 |
class Sqrt_Symbol(Symbol): |
| 500 |
"""symbol representing square root of argument""" |
| 501 |
def __init__(self,arg): |
| 502 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 503 |
def __str__(self): |
| 504 |
return "sqrt(%s)"%str(self.getArgument(0)) |
| 505 |
def eval(self,argval): |
| 506 |
return sqrt(self.getEvaluatedArguments(argval)[0]) |
| 507 |
def _diff(self,arg): |
| 508 |
return (-0.5)/self*self.getDifferentiatedArguments(arg)[0] |
| 509 |
|
| 510 |
def log(arg): |
| 511 |
""" |
| 512 |
@brief applies the logarithmic function bases exp(1.) to arg |
| 513 |
@param arg (input): argument |
| 514 |
""" |
| 515 |
if isinstance(arg,Symbol): |
| 516 |
return Log_Symbol(arg) |
| 517 |
elif hasattr(arg,"log"): |
| 518 |
return arg.log() |
| 519 |
else: |
| 520 |
return numarray.log(arg) |
| 521 |
|
| 522 |
class Log_Symbol(Symbol): |
| 523 |
"""symbol representing logarithm of the argument""" |
| 524 |
def __init__(self,arg): |
| 525 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 526 |
def __str__(self): |
| 527 |
return "log(%s)"%str(self.getArgument(0)) |
| 528 |
def eval(self,argval): |
| 529 |
return log(self.getEvaluatedArguments(argval)[0]) |
| 530 |
def _diff(self,arg): |
| 531 |
return self.getDifferentiatedArguments(arg)[0]/self.getArgument(0) |
| 532 |
|
| 533 |
def ln(arg): |
| 534 |
""" |
| 535 |
@brief applies the natural logarithmic function to arg |
| 536 |
@param arg (input): argument |
| 537 |
""" |
| 538 |
if isinstance(arg,Symbol): |
| 539 |
return Ln_Symbol(arg) |
| 540 |
elif hasattr(arg,"ln"): |
| 541 |
return arg.log() |
| 542 |
else: |
| 543 |
return numarray.log(arg) |
| 544 |
|
| 545 |
class Ln_Symbol(Symbol): |
| 546 |
"""symbol representing natural logarithm of the argument""" |
| 547 |
def __init__(self,arg): |
| 548 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 549 |
def __str__(self): |
| 550 |
return "ln(%s)"%str(self.getArgument(0)) |
| 551 |
def eval(self,argval): |
| 552 |
return ln(self.getEvaluatedArguments(argval)[0]) |
| 553 |
def _diff(self,arg): |
| 554 |
return self.getDifferentiatedArguments(arg)[0]/self.getArgument(0) |
| 555 |
|
| 556 |
def sin(arg): |
| 557 |
""" |
| 558 |
@brief applies the sin function to arg |
| 559 |
@param arg (input): argument |
| 560 |
""" |
| 561 |
if isinstance(arg,Symbol): |
| 562 |
return Sin_Symbol(arg) |
| 563 |
elif hasattr(arg,"sin"): |
| 564 |
return arg.sin() |
| 565 |
else: |
| 566 |
return numarray.sin(arg) |
| 567 |
|
| 568 |
class Sin_Symbol(Symbol): |
| 569 |
"""symbol representing sin of the argument""" |
| 570 |
def __init__(self,arg): |
| 571 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 572 |
def __str__(self): |
| 573 |
return "sin(%s)"%str(self.getArgument(0)) |
| 574 |
def eval(self,argval): |
| 575 |
return sin(self.getEvaluatedArguments(argval)[0]) |
| 576 |
def _diff(self,arg): |
| 577 |
return cos(self.getArgument(0))*self.getDifferentiatedArguments(arg)[0] |
| 578 |
|
| 579 |
def cos(arg): |
| 580 |
""" |
| 581 |
@brief applies the cos function to arg |
| 582 |
@param arg (input): argument |
| 583 |
""" |
| 584 |
if isinstance(arg,Symbol): |
| 585 |
return Cos_Symbol(arg) |
| 586 |
elif hasattr(arg,"cos"): |
| 587 |
return arg.cos() |
| 588 |
else: |
| 589 |
return numarray.cos(arg) |
| 590 |
|
| 591 |
class Cos_Symbol(Symbol): |
| 592 |
"""symbol representing cos of the argument""" |
| 593 |
def __init__(self,arg): |
| 594 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 595 |
def __str__(self): |
| 596 |
return "cos(%s)"%str(self.getArgument(0)) |
| 597 |
def eval(self,argval): |
| 598 |
return cos(self.getEvaluatedArguments(argval)[0]) |
| 599 |
def _diff(self,arg): |
| 600 |
return -sin(self.getArgument(0))*self.getDifferentiatedArguments(arg)[0] |
| 601 |
|
| 602 |
def tan(arg): |
| 603 |
""" |
| 604 |
@brief applies the tan function to arg |
| 605 |
@param arg (input): argument |
| 606 |
""" |
| 607 |
if isinstance(arg,Symbol): |
| 608 |
return Tan_Symbol(arg) |
| 609 |
elif hasattr(arg,"tan"): |
| 610 |
return arg.tan() |
| 611 |
else: |
| 612 |
return numarray.tan(arg) |
| 613 |
|
| 614 |
class Tan_Symbol(Symbol): |
| 615 |
"""symbol representing tan of the argument""" |
| 616 |
def __init__(self,arg): |
| 617 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 618 |
def __str__(self): |
| 619 |
return "tan(%s)"%str(self.getArgument(0)) |
| 620 |
def eval(self,argval): |
| 621 |
return tan(self.getEvaluatedArguments(argval)[0]) |
| 622 |
def _diff(self,arg): |
| 623 |
s=cos(self.getArgument(0)) |
| 624 |
return 1./(s*s)*self.getDifferentiatedArguments(arg)[0] |
| 625 |
|
| 626 |
def sign(arg): |
| 627 |
""" |
| 628 |
@brief applies the sign function to arg |
| 629 |
@param arg (input): argument |
| 630 |
""" |
| 631 |
if isinstance(arg,Symbol): |
| 632 |
return Sign_Symbol(arg) |
| 633 |
elif hasattr(arg,"sign"): |
| 634 |
return arg.sign() |
| 635 |
else: |
| 636 |
return numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))- \ |
| 637 |
numarray.less(arg,numarray.zeros(arg.shape,numarray.Float)) |
| 638 |
|
| 639 |
class Sign_Symbol(Symbol): |
| 640 |
"""symbol representing the sign of the argument""" |
| 641 |
def __init__(self,arg): |
| 642 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 643 |
def __str__(self): |
| 644 |
return "sign(%s)"%str(self.getArgument(0)) |
| 645 |
def eval(self,argval): |
| 646 |
return sign(self.getEvaluatedArguments(argval)[0]) |
| 647 |
|
| 648 |
def maxval(arg): |
| 649 |
""" |
| 650 |
@brief returns the maximum value of argument arg"" |
| 651 |
@param arg (input): argument |
| 652 |
""" |
| 653 |
if isinstance(arg,Symbol): |
| 654 |
return Max_Symbol(arg) |
| 655 |
elif hasattr(arg,"maxval"): |
| 656 |
return arg.maxval() |
| 657 |
elif hasattr(arg,"max"): |
| 658 |
return arg.max() |
| 659 |
else: |
| 660 |
return arg |
| 661 |
|
| 662 |
class Max_Symbol(Symbol): |
| 663 |
"""symbol representing the maximum value of the argument""" |
| 664 |
def __init__(self,arg): |
| 665 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 666 |
def __str__(self): |
| 667 |
return "maxval(%s)"%str(self.getArgument(0)) |
| 668 |
def eval(self,argval): |
| 669 |
return maxval(self.getEvaluatedArguments(argval)[0]) |
| 670 |
|
| 671 |
def minval(arg): |
| 672 |
""" |
| 673 |
@brief returns the minimum value of argument arg"" |
| 674 |
@param arg (input): argument |
| 675 |
""" |
| 676 |
if isinstance(arg,Symbol): |
| 677 |
return Min_Symbol(arg) |
| 678 |
elif hasattr(arg,"maxval"): |
| 679 |
return arg.minval() |
| 680 |
elif hasattr(arg,"min"): |
| 681 |
return arg.min() |
| 682 |
else: |
| 683 |
return arg |
| 684 |
|
| 685 |
class Min_Symbol(Symbol): |
| 686 |
"""symbol representing the minimum value of the argument""" |
| 687 |
def __init__(self,arg): |
| 688 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 689 |
def __str__(self): |
| 690 |
return "minval(%s)"%str(self.getArgument(0)) |
| 691 |
def eval(self,argval): |
| 692 |
return minval(self.getEvaluatedArguments(argval)[0]) |
| 693 |
|
| 694 |
def wherePositive(arg): |
| 695 |
""" |
| 696 |
@brief returns the positive values of argument arg"" |
| 697 |
@param arg (input): argument |
| 698 |
""" |
| 699 |
if _testForZero(arg): |
| 700 |
return 0 |
| 701 |
elif isinstance(arg,Symbol): |
| 702 |
return WherePositive_Symbol(arg) |
| 703 |
elif hasattr(arg,"wherePositive"): |
| 704 |
return arg.minval() |
| 705 |
elif hasattr(arg,"wherePositive"): |
| 706 |
numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float)) |
| 707 |
else: |
| 708 |
if arg>0: |
| 709 |
return 1. |
| 710 |
else: |
| 711 |
return 0. |
| 712 |
|
| 713 |
class WherePositive_Symbol(Symbol): |
| 714 |
"""symbol representing the wherePositive function""" |
| 715 |
def __init__(self,arg): |
| 716 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 717 |
def __str__(self): |
| 718 |
return "wherePositive(%s)"%str(self.getArgument(0)) |
| 719 |
def eval(self,argval): |
| 720 |
return wherePositive(self.getEvaluatedArguments(argval)[0]) |
| 721 |
|
| 722 |
def whereNegative(arg): |
| 723 |
""" |
| 724 |
@brief returns the negative values of argument arg"" |
| 725 |
@param arg (input): argument |
| 726 |
""" |
| 727 |
if _testForZero(arg): |
| 728 |
return 0 |
| 729 |
elif isinstance(arg,Symbol): |
| 730 |
return WhereNegative_Symbol(arg) |
| 731 |
elif hasattr(arg,"whereNegative"): |
| 732 |
return arg.whereNegative() |
| 733 |
elif hasattr(arg,"shape"): |
| 734 |
numarray.less(arg,numarray.zeros(arg.shape,numarray.Float)) |
| 735 |
else: |
| 736 |
if arg<0: |
| 737 |
return 1. |
| 738 |
else: |
| 739 |
return 0. |
| 740 |
|
| 741 |
class WhereNegative_Symbol(Symbol): |
| 742 |
"""symbol representing the whereNegative function""" |
| 743 |
def __init__(self,arg): |
| 744 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 745 |
def __str__(self): |
| 746 |
return "whereNegative(%s)"%str(self.getArgument(0)) |
| 747 |
def eval(self,argval): |
| 748 |
return whereNegative(self.getEvaluatedArguments(argval)[0]) |
| 749 |
|
| 750 |
def outer(arg0,arg1): |
| 751 |
if _testForZero(arg0) or _testForZero(arg1): |
| 752 |
return 0 |
| 753 |
else: |
| 754 |
if isinstance(arg0,Symbol) or isinstance(arg1,Symbol): |
| 755 |
return Outer_Symbol(arg0,arg1) |
| 756 |
elif _identifyShape(arg0)==() or _identifyShape(arg1)==(): |
| 757 |
return arg0*arg1 |
| 758 |
elif isinstance(arg0,numarray.NumArray) and isinstance(arg1,numarray.NumArray): |
| 759 |
return numarray.outer(arg0,arg1) |
| 760 |
else: |
| 761 |
if arg0.getRank()==1 and arg1.getRank()==1: |
| 762 |
out=escript.Data(0,(arg0.getShape()[0],arg1.getShape()[0]),arg1.getFunctionSpace()) |
| 763 |
for i in range(arg0.getShape()[0]): |
| 764 |
for j in range(arg1.getShape()[0]): |
| 765 |
out[i,j]=arg0[i]*arg1[j] |
| 766 |
return out |
| 767 |
else: |
| 768 |
raise ValueError,"outer is not fully implemented yet." |
| 769 |
|
| 770 |
class Outer_Symbol(Symbol): |
| 771 |
"""symbol representing the outer product of its two arguments""" |
| 772 |
def __init__(self,arg0,arg1): |
| 773 |
a=[arg0,arg1] |
| 774 |
s=tuple(list(_identifyShape(arg0))+list(_identifyShape(arg1))) |
| 775 |
Symbol.__init__(self,shape=s,dim=_extractDim(a),args=a) |
| 776 |
def __str__(self): |
| 777 |
return "outer(%s,%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 778 |
def eval(self,argval): |
| 779 |
a=self.getEvaluatedArguments(argval) |
| 780 |
return outer(a[0],a[1]) |
| 781 |
def _diff(self,arg): |
| 782 |
a=self.getDifferentiatedArguments(arg) |
| 783 |
return outer(a[0],self.getArgument(1))+outer(self.getArgument(0),a[1]) |
| 784 |
|
| 785 |
def interpolate(arg,where): |
| 786 |
""" |
| 787 |
@brief interpolates the function into the FunctionSpace where. |
| 788 |
|
| 789 |
@param arg interpolant |
| 790 |
@param where FunctionSpace to interpolate to |
| 791 |
""" |
| 792 |
if _testForZero(arg): |
| 793 |
return 0 |
| 794 |
elif isinstance(arg,Symbol): |
| 795 |
return Interpolated_Symbol(arg,where) |
| 796 |
else: |
| 797 |
return escript.Data(arg,where) |
| 798 |
|
| 799 |
def Interpolated_Symbol(Symbol): |
| 800 |
"""symbol representing the integral of the argument""" |
| 801 |
def __init__(self,arg,where): |
| 802 |
Symbol.__init__(self,shape=_extractShape(arg),dim=_extractDim([arg]),args=[arg,where]) |
| 803 |
def __str__(self): |
| 804 |
return "interpolated(%s)"%(str(self.getArgument(0))) |
| 805 |
def eval(self,argval): |
| 806 |
a=self.getEvaluatedArguments(argval) |
| 807 |
return integrate(a[0],where=self.getArgument(1)) |
| 808 |
def _diff(self,arg): |
| 809 |
a=self.getDifferentiatedArguments(arg) |
| 810 |
return integrate(a[0],where=self.getArgument(1)) |
| 811 |
|
| 812 |
def grad(arg,where=None): |
| 813 |
""" |
| 814 |
@brief returns the spatial gradient of arg at where. |
| 815 |
|
| 816 |
@param arg: Data object representing the function which gradient to be calculated. |
| 817 |
@param where: FunctionSpace in which the gradient will be calculated. If not present or |
| 818 |
None an appropriate default is used. |
| 819 |
""" |
| 820 |
if _testForZero(arg): |
| 821 |
return 0 |
| 822 |
elif isinstance(arg,Symbol): |
| 823 |
return Grad_Symbol(arg,where) |
| 824 |
elif hasattr(arg,"grad"): |
| 825 |
if where==None: |
| 826 |
return arg.grad() |
| 827 |
else: |
| 828 |
return arg.grad(where) |
| 829 |
else: |
| 830 |
return arg*0. |
| 831 |
|
| 832 |
def Grad_Symbol(Symbol): |
| 833 |
"""symbol representing the gradient of the argument""" |
| 834 |
def __init__(self,arg,where=None): |
| 835 |
d=_extractDim([arg]) |
| 836 |
s=tuple(list(_identifyShape([arg])).append(d)) |
| 837 |
Symbol.__init__(self,shape=s,dim=_extractDim([arg]),args=[arg,where]) |
| 838 |
def __str__(self): |
| 839 |
return "grad(%s)"%(str(self.getArgument(0))) |
| 840 |
def eval(self,argval): |
| 841 |
a=self.getEvaluatedArguments(argval) |
| 842 |
return grad(a[0],where=self.getArgument(1)) |
| 843 |
def _diff(self,arg): |
| 844 |
a=self.getDifferentiatedArguments(arg) |
| 845 |
return grad(a[0],where=self.getArgument(1)) |
| 846 |
|
| 847 |
def integrate(arg,where=None): |
| 848 |
""" |
| 849 |
@brief return the integral if the function represented by Data object arg over its domain. |
| 850 |
|
| 851 |
@param arg: Data object representing the function which is integrated. |
| 852 |
@param where: FunctionSpace in which the integral is calculated. If not present or |
| 853 |
None an appropriate default is used. |
| 854 |
""" |
| 855 |
if _testForZero(arg): |
| 856 |
return 0 |
| 857 |
elif isinstance(arg,Symbol): |
| 858 |
return Integral_Symbol(arg,where) |
| 859 |
else: |
| 860 |
if not where==None: arg=escript.Data(arg,where) |
| 861 |
if arg.getRank()==0: |
| 862 |
return arg.integrate()[0] |
| 863 |
else: |
| 864 |
return arg.integrate() |
| 865 |
|
| 866 |
def Integral_Symbol(Float_Symbol): |
| 867 |
"""symbol representing the integral of the argument""" |
| 868 |
def __init__(self,arg,where=None): |
| 869 |
Float_Symbol.__init__(self,shape=_identifyShape([arg]),args=[arg,where]) |
| 870 |
def __str__(self): |
| 871 |
return "integral(%s)"%(str(self.getArgument(0))) |
| 872 |
def eval(self,argval): |
| 873 |
a=self.getEvaluatedArguments(argval) |
| 874 |
return integrate(a[0],where=self.getArgument(1)) |
| 875 |
def _diff(self,arg): |
| 876 |
a=self.getDifferentiatedArguments(arg) |
| 877 |
return integrate(a[0],where=self.getArgument(1)) |
| 878 |
|
| 879 |
#============================= |
| 880 |
# |
| 881 |
# wrapper for various functions: if the argument has attribute the function name |
| 882 |
# as an argument it calls the corresponding methods. Otherwise the corresponding |
| 883 |
# numarray function is called. |
| 884 |
|
| 885 |
# functions involving the underlying Domain: |
| 886 |
|
| 887 |
|
| 888 |
# functions returning Data objects: |
| 889 |
|
| 890 |
def transpose(arg,axis=None): |
| 891 |
""" |
| 892 |
@brief returns the transpose of the Data object arg. |
| 893 |
|
| 894 |
@param arg |
| 895 |
""" |
| 896 |
if axis==None: |
| 897 |
r=0 |
| 898 |
if hasattr(arg,"getRank"): r=arg.getRank() |
| 899 |
if hasattr(arg,"rank"): r=arg.rank |
| 900 |
axis=r/2 |
| 901 |
if isinstance(arg,Symbol): |
| 902 |
return Transpose_Symbol(arg,axis=r) |
| 903 |
if isinstance(arg,escript.Data): |
| 904 |
# hack for transpose |
| 905 |
r=arg.getRank() |
| 906 |
if r!=2: raise ValueError,"Tranpose only avalaible for rank 2 objects" |
| 907 |
s=arg.getShape() |
| 908 |
out=escript.Data(0.,(s[1],s[0]),arg.getFunctionSpace()) |
| 909 |
for i in range(s[0]): |
| 910 |
for j in range(s[1]): |
| 911 |
out[j,i]=arg[i,j] |
| 912 |
return out |
| 913 |
# end hack for transpose |
| 914 |
return arg.transpose(axis) |
| 915 |
else: |
| 916 |
return numarray.transpose(arg,axis=axis) |
| 917 |
|
| 918 |
def trace(arg,axis0=0,axis1=1): |
| 919 |
""" |
| 920 |
@brief return |
| 921 |
|
| 922 |
@param arg |
| 923 |
""" |
| 924 |
if isinstance(arg,Symbol): |
| 925 |
s=list(arg.getShape()) |
| 926 |
s=tuple(s[0:axis0]+s[axis0+1:axis1]+s[axis1+1:]) |
| 927 |
return Trace_Symbol(arg,axis0=axis0,axis1=axis1) |
| 928 |
elif isinstance(arg,escript.Data): |
| 929 |
# hack for trace |
| 930 |
s=arg.getShape() |
| 931 |
if s[axis0]!=s[axis1]: |
| 932 |
raise ValueError,"illegal axis in trace" |
| 933 |
out=escript.Scalar(0.,arg.getFunctionSpace()) |
| 934 |
for i in range(s[0]): |
| 935 |
for j in range(s[1]): |
| 936 |
out+=arg[i,j] |
| 937 |
return out |
| 938 |
# end hack for trace |
| 939 |
return arg.transpose(axis0=axis0,axis1=axis1) |
| 940 |
else: |
| 941 |
return numarray.trace(arg,axis0=axis0,axis1=axis1) |
| 942 |
|
| 943 |
def Trace_Symbol(Symbol): |
| 944 |
pass |
| 945 |
|
| 946 |
def length(arg): |
| 947 |
""" |
| 948 |
@brief |
| 949 |
|
| 950 |
@param arg |
| 951 |
""" |
| 952 |
if isinstance(arg,escript.Data): |
| 953 |
if arg.isEmpty(): return escript.Data() |
| 954 |
if arg.getRank()==0: |
| 955 |
return abs(arg) |
| 956 |
elif arg.getRank()==1: |
| 957 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 958 |
for i in range(arg.getShape()[0]): |
| 959 |
sum+=arg[i]**2 |
| 960 |
return sqrt(sum) |
| 961 |
elif arg.getRank()==2: |
| 962 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 963 |
for i in range(arg.getShape()[0]): |
| 964 |
for j in range(arg.getShape()[1]): |
| 965 |
sum+=arg[i,j]**2 |
| 966 |
return sqrt(sum) |
| 967 |
elif arg.getRank()==3: |
| 968 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 969 |
for i in range(arg.getShape()[0]): |
| 970 |
for j in range(arg.getShape()[1]): |
| 971 |
for k in range(arg.getShape()[2]): |
| 972 |
sum+=arg[i,j,k]**2 |
| 973 |
return sqrt(sum) |
| 974 |
elif arg.getRank()==4: |
| 975 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 976 |
for i in range(arg.getShape()[0]): |
| 977 |
for j in range(arg.getShape()[1]): |
| 978 |
for k in range(arg.getShape()[2]): |
| 979 |
for l in range(arg.getShape()[3]): |
| 980 |
sum+=arg[i,j,k,l]**2 |
| 981 |
return sqrt(sum) |
| 982 |
else: |
| 983 |
raise SystemError,"length is not been fully implemented yet" |
| 984 |
# return arg.length() |
| 985 |
else: |
| 986 |
return sqrt((arg**2).sum()) |
| 987 |
|
| 988 |
def deviator(arg): |
| 989 |
""" |
| 990 |
@brief |
| 991 |
|
| 992 |
@param arg0 |
| 993 |
""" |
| 994 |
if isinstance(arg,escript.Data): |
| 995 |
shape=arg.getShape() |
| 996 |
else: |
| 997 |
shape=arg.shape |
| 998 |
if len(shape)!=2: |
| 999 |
raise ValueError,"Deviator requires rank 2 object" |
| 1000 |
if shape[0]!=shape[1]: |
| 1001 |
raise ValueError,"Deviator requires a square matrix" |
| 1002 |
return arg-1./(shape[0]*1.)*trace(arg)*kronecker(shape[0]) |
| 1003 |
|
| 1004 |
def inner(arg0,arg1): |
| 1005 |
""" |
| 1006 |
@brief |
| 1007 |
|
| 1008 |
@param arg0, arg1 |
| 1009 |
""" |
| 1010 |
sum=escript.Scalar(0,arg0.getFunctionSpace()) |
| 1011 |
if arg.getRank()==0: |
| 1012 |
return arg0*arg1 |
| 1013 |
elif arg.getRank()==1: |
| 1014 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 1015 |
for i in range(arg.getShape()[0]): |
| 1016 |
sum+=arg0[i]*arg1[i] |
| 1017 |
elif arg.getRank()==2: |
| 1018 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 1019 |
for i in range(arg.getShape()[0]): |
| 1020 |
for j in range(arg.getShape()[1]): |
| 1021 |
sum+=arg0[i,j]*arg1[i,j] |
| 1022 |
elif arg.getRank()==3: |
| 1023 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 1024 |
for i in range(arg.getShape()[0]): |
| 1025 |
for j in range(arg.getShape()[1]): |
| 1026 |
for k in range(arg.getShape()[2]): |
| 1027 |
sum+=arg0[i,j,k]*arg1[i,j,k] |
| 1028 |
elif arg.getRank()==4: |
| 1029 |
sum=escript.Scalar(0,arg.getFunctionSpace()) |
| 1030 |
for i in range(arg.getShape()[0]): |
| 1031 |
for j in range(arg.getShape()[1]): |
| 1032 |
for k in range(arg.getShape()[2]): |
| 1033 |
for l in range(arg.getShape()[3]): |
| 1034 |
sum+=arg0[i,j,k,l]*arg1[i,j,k,l] |
| 1035 |
else: |
| 1036 |
raise SystemError,"inner is not been implemented yet" |
| 1037 |
return sum |
| 1038 |
|
| 1039 |
def matrixmult(arg0,arg1): |
| 1040 |
|
| 1041 |
if isinstance(arg1,numarray.NumArray) and isinstance(arg0,numarray.NumArray): |
| 1042 |
numarray.matrixmult(arg0,arg1) |
| 1043 |
else: |
| 1044 |
# escript.matmult(arg0,arg1) |
| 1045 |
if isinstance(arg1,escript.Data) and not isinstance(arg0,escript.Data): |
| 1046 |
arg0=escript.Data(arg0,arg1.getFunctionSpace()) |
| 1047 |
elif isinstance(arg0,escript.Data) and not isinstance(arg1,escript.Data): |
| 1048 |
arg1=escript.Data(arg1,arg0.getFunctionSpace()) |
| 1049 |
if arg0.getRank()==2 and arg1.getRank()==1: |
| 1050 |
out=escript.Data(0,(arg0.getShape()[0],),arg0.getFunctionSpace()) |
| 1051 |
for i in range(arg0.getShape()[0]): |
| 1052 |
for j in range(arg0.getShape()[1]): |
| 1053 |
# uses Data object slicing, plus Data * and += operators |
| 1054 |
out[i]+=arg0[i,j]*arg1[j] |
| 1055 |
return out |
| 1056 |
else: |
| 1057 |
raise SystemError,"matrixmult is not fully implemented yet!" |
| 1058 |
|
| 1059 |
#========================================================= |
| 1060 |
# reduction operations: |
| 1061 |
#========================================================= |
| 1062 |
def sum(arg): |
| 1063 |
""" |
| 1064 |
@brief |
| 1065 |
|
| 1066 |
@param arg |
| 1067 |
""" |
| 1068 |
return arg.sum() |
| 1069 |
|
| 1070 |
def sup(arg): |
| 1071 |
""" |
| 1072 |
@brief |
| 1073 |
|
| 1074 |
@param arg |
| 1075 |
""" |
| 1076 |
if isinstance(arg,escript.Data): |
| 1077 |
return arg.sup() |
| 1078 |
elif isinstance(arg,float) or isinstance(arg,int): |
| 1079 |
return arg |
| 1080 |
else: |
| 1081 |
return arg.max() |
| 1082 |
|
| 1083 |
def inf(arg): |
| 1084 |
""" |
| 1085 |
@brief |
| 1086 |
|
| 1087 |
@param arg |
| 1088 |
""" |
| 1089 |
if isinstance(arg,escript.Data): |
| 1090 |
return arg.inf() |
| 1091 |
elif isinstance(arg,float) or isinstance(arg,int): |
| 1092 |
return arg |
| 1093 |
else: |
| 1094 |
return arg.min() |
| 1095 |
|
| 1096 |
def L2(arg): |
| 1097 |
""" |
| 1098 |
@brief returns the L2-norm of the |
| 1099 |
|
| 1100 |
@param arg |
| 1101 |
""" |
| 1102 |
if isinstance(arg,escript.Data): |
| 1103 |
return arg.L2() |
| 1104 |
elif isinstance(arg,float) or isinstance(arg,int): |
| 1105 |
return abs(arg) |
| 1106 |
else: |
| 1107 |
return numarry.sqrt(dot(arg,arg)) |
| 1108 |
|
| 1109 |
def Lsup(arg): |
| 1110 |
""" |
| 1111 |
@brief |
| 1112 |
|
| 1113 |
@param arg |
| 1114 |
""" |
| 1115 |
if isinstance(arg,escript.Data): |
| 1116 |
return arg.Lsup() |
| 1117 |
elif isinstance(arg,float) or isinstance(arg,int): |
| 1118 |
return abs(arg) |
| 1119 |
else: |
| 1120 |
return max(numarray.abs(arg)) |
| 1121 |
|
| 1122 |
def dot(arg0,arg1): |
| 1123 |
""" |
| 1124 |
@brief |
| 1125 |
|
| 1126 |
@param arg |
| 1127 |
""" |
| 1128 |
if isinstance(arg0,escript.Data): |
| 1129 |
return arg0.dot(arg1) |
| 1130 |
elif isinstance(arg1,escript.Data): |
| 1131 |
return arg1.dot(arg0) |
| 1132 |
else: |
| 1133 |
return numarray.dot(arg0,arg1) |
| 1134 |
|
| 1135 |
def kronecker(d): |
| 1136 |
if hasattr(d,"getDim"): |
| 1137 |
return numarray.identity(d.getDim()) |
| 1138 |
else: |
| 1139 |
return numarray.identity(d) |
| 1140 |
|
| 1141 |
def unit(i,d): |
| 1142 |
""" |
| 1143 |
@brief return a unit vector of dimension d with nonzero index i |
| 1144 |
@param d dimension |
| 1145 |
@param i index |
| 1146 |
""" |
| 1147 |
e = numarray.zeros((d,),numarray.Float) |
| 1148 |
e[i] = 1.0 |
| 1149 |
return e |
| 1150 |
|
| 1151 |
# ============================================ |
| 1152 |
# testing |
| 1153 |
# ============================================ |
| 1154 |
|
| 1155 |
if __name__=="__main__": |
| 1156 |
u=ScalarSymbol(dim=2,name="u") |
| 1157 |
v=ScalarSymbol(dim=2,name="v") |
| 1158 |
v=VectorSymbol(2,"v") |
| 1159 |
u=VectorSymbol(2,"u") |
| 1160 |
|
| 1161 |
print u+5,(u+5).diff(u) |
| 1162 |
print 5+u,(5+u).diff(u) |
| 1163 |
print u+v,(u+v).diff(u) |
| 1164 |
print v+u,(v+u).diff(u) |
| 1165 |
|
| 1166 |
print u*5,(u*5).diff(u) |
| 1167 |
print 5*u,(5*u).diff(u) |
| 1168 |
print u*v,(u*v).diff(u) |
| 1169 |
print v*u,(v*u).diff(u) |
| 1170 |
|
| 1171 |
print u-5,(u-5).diff(u) |
| 1172 |
print 5-u,(5-u).diff(u) |
| 1173 |
print u-v,(u-v).diff(u) |
| 1174 |
print v-u,(v-u).diff(u) |
| 1175 |
|
| 1176 |
print u/5,(u/5).diff(u) |
| 1177 |
print 5/u,(5/u).diff(u) |
| 1178 |
print u/v,(u/v).diff(u) |
| 1179 |
print v/u,(v/u).diff(u) |
| 1180 |
|
| 1181 |
print u**5,(u**5).diff(u) |
| 1182 |
print 5**u,(5**u).diff(u) |
| 1183 |
print u**v,(u**v).diff(u) |
| 1184 |
print v**u,(v**u).diff(u) |
| 1185 |
|
| 1186 |
print exp(u),exp(u).diff(u) |
| 1187 |
print sqrt(u),sqrt(u).diff(u) |
| 1188 |
print log(u),log(u).diff(u) |
| 1189 |
print sin(u),sin(u).diff(u) |
| 1190 |
print cos(u),cos(u).diff(u) |
| 1191 |
print tan(u),tan(u).diff(u) |
| 1192 |
print sign(u),sign(u).diff(u) |
| 1193 |
print abs(u),abs(u).diff(u) |
| 1194 |
print wherePositive(u),wherePositive(u).diff(u) |
| 1195 |
print whereNegative(u),whereNegative(u).diff(u) |
| 1196 |
print maxval(u),maxval(u).diff(u) |
| 1197 |
print minval(u),minval(u).diff(u) |
| 1198 |
|
| 1199 |
g=grad(u) |
| 1200 |
print diff(5*g,g) |
| 1201 |
4*(g+transpose(g))/2+6*trace(g)*kronecker(3) |
| 1202 |
|
| 1203 |
# |
| 1204 |
# $Log$ |
| 1205 |
# Revision 1.13 2005/07/22 03:53:01 jgs |
| 1206 |
# Merge of development branch back to main trunk on 2005-07-22 |
| 1207 |
# |
| 1208 |
# Revision 1.12 2005/07/20 06:14:58 jgs |
| 1209 |
# added ln(data) style wrapper for data.ln() - also added corresponding |
| 1210 |
# implementation of Ln_Symbol class (not sure if this is right though) |
| 1211 |
# |
| 1212 |
# Revision 1.11 2005/07/08 04:07:35 jgs |
| 1213 |
# Merge of development branch back to main trunk on 2005-07-08 |
| 1214 |
# |
| 1215 |
# Revision 1.10 2005/06/09 05:37:59 jgs |
| 1216 |
# Merge of development branch back to main trunk on 2005-06-09 |
| 1217 |
# |
| 1218 |
# Revision 1.2.2.19 2005/07/21 04:01:28 jgs |
| 1219 |
# minor comment fixes |
| 1220 |
# |
| 1221 |
# Revision 1.2.2.18 2005/07/21 01:02:43 jgs |
| 1222 |
# commit ln() updates to development branch version |
| 1223 |
# |
| 1224 |
# Revision 1.12 2005/07/20 06:14:58 jgs |
| 1225 |
# added ln(data) style wrapper for data.ln() - also added corresponding |
| 1226 |
# implementation of Ln_Symbol class (not sure if this is right though) |
| 1227 |
# |
| 1228 |
# Revision 1.11 2005/07/08 04:07:35 jgs |
| 1229 |
# Merge of development branch back to main trunk on 2005-07-08 |
| 1230 |
# |
| 1231 |
# Revision 1.10 2005/06/09 05:37:59 jgs |
| 1232 |
# Merge of development branch back to main trunk on 2005-06-09 |
| 1233 |
# |
| 1234 |
# Revision 1.2.2.17 2005/07/07 07:28:58 gross |
| 1235 |
# some stuff added to util.py to improve functionality |
| 1236 |
# |
| 1237 |
# Revision 1.2.2.16 2005/06/30 01:53:55 gross |
| 1238 |
# a bug in coloring fixed |
| 1239 |
# |
| 1240 |
# Revision 1.2.2.15 2005/06/29 02:36:43 gross |
| 1241 |
# Symbols have been introduced and some function clarified. needs much more work |
| 1242 |
# |
| 1243 |
# Revision 1.2.2.14 2005/05/20 04:05:23 gross |
| 1244 |
# some work on a darcy flow started |
| 1245 |
# |
| 1246 |
# Revision 1.2.2.13 2005/03/16 05:17:58 matt |
| 1247 |
# Implemented unit(idx, dim) to create cartesian unit basis vectors to |
| 1248 |
# complement kronecker(dim) function. |
| 1249 |
# |
| 1250 |
# Revision 1.2.2.12 2005/03/10 08:14:37 matt |
| 1251 |
# Added non-member Linf utility function to complement Data::Linf(). |
| 1252 |
# |
| 1253 |
# Revision 1.2.2.11 2005/02/17 05:53:25 gross |
| 1254 |
# some bug in saveDX fixed: in fact the bug was in |
| 1255 |
# DataC/getDataPointShape |
| 1256 |
# |
| 1257 |
# Revision 1.2.2.10 2005/01/11 04:59:36 gross |
| 1258 |
# automatic interpolation in integrate switched off |
| 1259 |
# |
| 1260 |
# Revision 1.2.2.9 2005/01/11 03:38:13 gross |
| 1261 |
# Bug in Data.integrate() fixed for the case of rank 0. The problem is not totallly resolved as the method should return a scalar rather than a numarray object in the case of rank 0. This problem is fixed by the util.integrate wrapper. |
| 1262 |
# |
| 1263 |
# Revision 1.2.2.8 2005/01/05 04:21:41 gross |
| 1264 |
# FunctionSpace checking/matchig in slicing added |
| 1265 |
# |
| 1266 |
# Revision 1.2.2.7 2004/12/29 05:29:59 gross |
| 1267 |
# AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data() |
| 1268 |
# |
| 1269 |
# Revision 1.2.2.6 2004/12/24 06:05:41 gross |
| 1270 |
# some changes in linearPDEs to add AdevectivePDE |
| 1271 |
# |
| 1272 |
# Revision 1.2.2.5 2004/12/17 00:06:53 gross |
| 1273 |
# mk sets ESYS_ROOT is undefined |
| 1274 |
# |
| 1275 |
# Revision 1.2.2.4 2004/12/07 03:19:51 gross |
| 1276 |
# options for GMRES and PRES20 added |
| 1277 |
# |
| 1278 |
# Revision 1.2.2.3 2004/12/06 04:55:18 gross |
| 1279 |
# function wraper extended |
| 1280 |
# |
| 1281 |
# Revision 1.2.2.2 2004/11/22 05:44:07 gross |
| 1282 |
# a few more unitary functions have been added but not implemented in Data yet |
| 1283 |
# |
| 1284 |
# Revision 1.2.2.1 2004/11/12 06:58:15 gross |
| 1285 |
# a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry |
| 1286 |
# |
| 1287 |
# Revision 1.2 2004/10/27 00:23:36 jgs |
| 1288 |
# fixed minor syntax error |
| 1289 |
# |
| 1290 |
# Revision 1.1.1.1 2004/10/26 06:53:56 jgs |
| 1291 |
# initial import of project esys2 |
| 1292 |
# |
| 1293 |
# Revision 1.1.2.3 2004/10/26 06:43:48 jgs |
| 1294 |
# committing Lutz's and Paul's changes to brach jgs |
| 1295 |
# |
| 1296 |
# Revision 1.1.4.1 2004/10/20 05:32:51 cochrane |
| 1297 |
# Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form. |
| 1298 |
# |
| 1299 |
# Revision 1.1 2004/08/05 03:58:27 gross |
| 1300 |
# Bug in Assemble_NodeCoordinates fixed |
| 1301 |
# |
| 1302 |
# |
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