# Diff of /trunk/escript/py_src/util.py

revision 341 by gross, Mon Dec 12 05:26:10 2005 UTC revision 588 by gross, Fri Mar 10 04:45:04 2006 UTC
# Line 24  Utility functions for escript Line 24  Utility functions for escript
24  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
25  __licence__="contact: esys@access.uq.edu.au"  __licence__="contact: esys@access.uq.edu.au"
26  __url__="http://www.iservo.edu.au/esys/escript"  __url__="http://www.iservo.edu.au/esys/escript"
27  __version__="\$Revision: 329 \$"  __version__="\$Revision\$"
28  __date__="\$Date\$"  __date__="\$Date\$"
29
30
31  import math  import math
32  import numarray  import numarray
33    import numarray.linear_algebra
34  import escript  import escript
35  import os  import os
36
# Line 43  import os Line 44  import os
44  # def matchType(arg0=0.,arg1=0.):  # def matchType(arg0=0.,arg1=0.):
45  # def matchShape(arg0,arg1):  # def matchShape(arg0,arg1):
46
# def maximum(arg0,arg1):
# def minimum(arg0,arg1):

# def transpose(arg,axis=None):
# def trace(arg,axis0=0,axis1=1):
47  # def reorderComponents(arg,index):  # def reorderComponents(arg,index):
48
# def integrate(arg,where=None):
# def interpolate(arg,where):
# def div(arg,where=None):

49  #  #
50  # slicing: get  # slicing: get
51  #          set  #          set
# Line 125  def kronecker(d=3): Line 116  def kronecker(d=3):
116     return the kronecker S{delta}-symbol     return the kronecker S{delta}-symbol
117
118     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
119     @type d: C{int} or any object with a C{getDim} method     @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
120     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
121     @rtype d: L{numarray.NumArray} of rank 2.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2.
@remark: the function is identical L{identity}
122     """     """
123     return identityTensor(d)     return identityTensor(d)
124
# Line 143  def identity(shape=()): Line 133  def identity(shape=()):
133     @raise ValueError: if len(shape)>2.     @raise ValueError: if len(shape)>2.
134     """     """
135     if len(shape)>0:     if len(shape)>0:
136        out=numarray.zeros(shape+shape,numarray.Float)        out=numarray.zeros(shape+shape,numarray.Float64)
137        if len(shape)==1:        if len(shape)==1:
138            for i0 in range(shape[0]):            for i0 in range(shape[0]):
139               out[i0,i0]=1.               out[i0,i0]=1.

140        elif len(shape)==2:        elif len(shape)==2:
141            for i0 in range(shape[0]):            for i0 in range(shape[0]):
142               for i1 in range(shape[1]):               for i1 in range(shape[1]):
# Line 163  def identityTensor(d=3): Line 152  def identityTensor(d=3):
152     return the dxd identity matrix     return the dxd identity matrix
153
154     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
155     @type d: C{int} or any object with a C{getDim} method     @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
156     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
157     @rtype: L{numarray.NumArray} of rank 2.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2
158     """     """
159     if hasattr(d,"getDim"):     if isinstance(d,escript.FunctionSpace):
160        d=d.getDim()         return escript.Data(identity((d.getDim(),)),d)
161     return identity(shape=(d,))     elif isinstance(d,escript.Domain):
162           return identity((d.getDim(),))
163       else:
164           return identity((d,))
165
166  def identityTensor4(d=3):  def identityTensor4(d=3):
167     """     """
# Line 178  def identityTensor4(d=3): Line 170  def identityTensor4(d=3):
170     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
171     @type d: C{int} or any object with a C{getDim} method     @type d: C{int} or any object with a C{getDim} method
172     @return: the object u of rank 4 with M{u[i,j,k,l]=1} for M{i=k and j=l} and M{u[i,j,k,l]=0} otherwise     @return: the object u of rank 4 with M{u[i,j,k,l]=1} for M{i=k and j=l} and M{u[i,j,k,l]=0} otherwise
173     @rtype: L{numarray.NumArray} of rank 4.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 4.
174     """     """
175     if hasattr(d,"getDim"):     if isinstance(d,escript.FunctionSpace):
176        d=d.getDim()         return escript.Data(identity((d.getDim(),d.getDim())),d)
177     return identity((d,d))     elif isinstance(d,escript.Domain):
178           return identity((d.getDim(),d.getDim()))
179       else:
180           return identity((d,d))
181
182  def unitVector(i=0,d=3):  def unitVector(i=0,d=3):
183     """     """
# Line 191  def unitVector(i=0,d=3): Line 186  def unitVector(i=0,d=3):
186     @param i: index     @param i: index
187     @type i: C{int}     @type i: C{int}
188     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
189     @type d: C{int} or any object with a C{getDim} method     @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
190     @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise     @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise
191     @rtype: L{numarray.NumArray} of rank 1.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 1
192     """     """
193     return kronecker(d)[i]     return kronecker(d)[i]
194
# Line 363  def testForZero(arg): Line 358  def testForZero(arg):
358      @return : True if the argument is identical to zero.      @return : True if the argument is identical to zero.
359      @rtype : C{bool}      @rtype : C{bool}
360      """      """
361      try:      if isinstance(arg,numarray.NumArray):
362         return not Lsup(arg)>0.         return not Lsup(arg)>0.
363      except TypeError:      elif isinstance(arg,escript.Data):
364           return False
365        elif isinstance(arg,float):
366           return not Lsup(arg)>0.
367        elif isinstance(arg,int):
368           return not Lsup(arg)>0.
369        elif isinstance(arg,Symbol):
370           return False
371        else:
372         return False         return False
373
374  def matchType(arg0=0.,arg1=0.):  def matchType(arg0=0.,arg1=0.):
# Line 386  def matchType(arg0=0.,arg1=0.): Line 389  def matchType(arg0=0.,arg1=0.):
389         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
390            arg0=escript.Data(arg0,arg1.getFunctionSpace())            arg0=escript.Data(arg0,arg1.getFunctionSpace())
391         elif isinstance(arg1,float):         elif isinstance(arg1,float):
392            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
393         elif isinstance(arg1,int):         elif isinstance(arg1,int):
394            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
395         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
396            pass            pass
397         else:         else:
# Line 412  def matchType(arg0=0.,arg1=0.): Line 415  def matchType(arg0=0.,arg1=0.):
415         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
416            pass            pass
417         elif isinstance(arg1,float):         elif isinstance(arg1,float):
418            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
419         elif isinstance(arg1,int):         elif isinstance(arg1,int):
420            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
421         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
422            pass            pass
423         else:         else:
424            raise TypeError,"function: Unknown type of second argument."                raise TypeError,"function: Unknown type of second argument."
425      elif isinstance(arg0,float):      elif isinstance(arg0,float):
426         if isinstance(arg1,numarray.NumArray):         if isinstance(arg1,numarray.NumArray):
427            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
428         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
429            arg0=escript.Data(arg0,arg1.getFunctionSpace())            arg0=escript.Data(arg0,arg1.getFunctionSpace())
430         elif isinstance(arg1,float):         elif isinstance(arg1,float):
431            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
432            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
433         elif isinstance(arg1,int):         elif isinstance(arg1,int):
434            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
435            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
436         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
437            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
438         else:         else:
439            raise TypeError,"function: Unknown type of second argument."                raise TypeError,"function: Unknown type of second argument."
440      elif isinstance(arg0,int):      elif isinstance(arg0,int):
441         if isinstance(arg1,numarray.NumArray):         if isinstance(arg1,numarray.NumArray):
442            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
443         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
444            arg0=escript.Data(float(arg0),arg1.getFunctionSpace())            arg0=escript.Data(float(arg0),arg1.getFunctionSpace())
445         elif isinstance(arg1,float):         elif isinstance(arg1,float):
446            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
447            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
448         elif isinstance(arg1,int):         elif isinstance(arg1,int):
449            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
450            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
451         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
452            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
453         else:         else:
454            raise TypeError,"function: Unknown type of second argument."                raise TypeError,"function: Unknown type of second argument."
455      else:      else:
# Line 469  def matchShape(arg0,arg1): Line 472  def matchShape(arg0,arg1):
472      sh0=pokeShape(arg0)      sh0=pokeShape(arg0)
473      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
474      if len(sh0)<len(sh):      if len(sh0)<len(sh):
475         return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float)),arg1         return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float64)),arg1
476      elif len(sh1)<len(sh):      elif len(sh1)<len(sh):
477         return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float))         return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float64))
478      else:      else:
479         return arg0,arg1         return arg0,arg1
480  #=========================================================  #=========================================================
# Line 597  class Symbol(object): Line 600  class Symbol(object):
600            else:            else:
601                s=pokeShape(s)+arg.getShape()                s=pokeShape(s)+arg.getShape()
602                if len(s)>0:                if len(s)>0:
603                   out.append(numarray.zeros(s),numarray.Float)                   out.append(numarray.zeros(s),numarray.Float64)
604                else:                else:
605                   out.append(a)                   out.append(a)
606         return out         return out
# Line 687  class Symbol(object): Line 690  class Symbol(object):
690         else:         else:
691            s=self.getShape()+arg.getShape()            s=self.getShape()+arg.getShape()
692            if len(s)>0:            if len(s)>0:
693               return numarray.zeros(s,numarray.Float)               return numarray.zeros(s,numarray.Float64)
694            else:            else:
695               return 0.               return 0.
696
# Line 825  class Symbol(object): Line 828  class Symbol(object):
828         """         """
829         return power(other,self)         return power(other,self)
830
831       def __getitem__(self,index):
832           """
833           returns the slice defined by index
834
835           @param index: defines a
836           @type index: C{slice} or C{int} or a C{tuple} of them
837           @return: a S{Symbol} representing the slice defined by index
838           @rtype: L{DependendSymbol}
839           """
840           return GetSlice_Symbol(self,index)
841
842  class DependendSymbol(Symbol):  class DependendSymbol(Symbol):
843     """     """
844     DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal.     DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal.
# Line 875  class DependendSymbol(Symbol): Line 889  class DependendSymbol(Symbol):
889  #=========================================================  #=========================================================
890  #  Unary operations prserving the shape  #  Unary operations prserving the shape
891  #========================================================  #========================================================
892    class GetSlice_Symbol(DependendSymbol):
893       """
894       L{Symbol} representing getting a slice for a L{Symbol}
895       """
896       def __init__(self,arg,index):
897          """
898          initialization of wherePositive L{Symbol} with argument arg
899          @param arg: argument
900          @type arg: L{Symbol}.
901          @param index: defines index
902          @type index: C{slice} or C{int} or a C{tuple} of them
903          @raises IndexError: if length of index is larger than rank of arg or a index start or stop is out of range
904          @raises ValueError: if a step is given
905          """
906          if not isinstance(index,tuple): index=(index,)
907          if len(index)>arg.getRank():
908               raise IndexError,"GetSlice_Symbol: index out of range."
909          sh=()
910          index2=()
911          for i in range(len(index)):
912             ix=index[i]
913             if isinstance(ix,int):
914                if ix<0 or ix>=arg.getShape()[i]:
915                   raise ValueError,"GetSlice_Symbol: index out of range."
916                index2=index2+(ix,)
917             else:
918               if not ix.step==None:
919                 raise ValueError,"GetSlice_Symbol: steping is not supported."
920               if ix.start==None:
921                  s=0
922               else:
923                  s=ix.start
924               if ix.stop==None:
925                  e=arg.getShape()[i]
926               else:
927                  e=ix.stop
928                  if e>arg.getShape()[i]:
929                     raise IndexError,"GetSlice_Symbol: index out of range."
930               index2=index2+(slice(s,e),)
931               if e>s:
932                   sh=sh+(e-s,)
933               elif s>e:
934                   raise IndexError,"GetSlice_Symbol: slice start must be less or equal slice end"
935          for i in range(len(index),arg.getRank()):
936              index2=index2+(slice(0,arg.getShape()[i]),)
937              sh=sh+(arg.getShape()[i],)
938          super(GetSlice_Symbol, self).__init__(args=[arg,index2],shape=sh,dim=arg.getDim())
939
940       def getMyCode(self,argstrs,format="escript"):
941          """
942          returns a program code that can be used to evaluate the symbol.
943
944          @param argstrs: gives for each argument a string representing the argument for the evaluation.
945          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
946          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
947          @type format: C{str}
948          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
949          @rtype: C{str}
950          @raise: NotImplementedError: if the requested format is not available
951          """
952          if format=="escript" or format=="str"  or format=="text":
953             return "%s.__getitem__(%s)"%(argstrs[0],argstrs[1])
954          else:
955             raise NotImplementedError,"GetItem_Symbol does not provide program code for format %s."%format
956
957       def substitute(self,argvals):
958          """
959          assigns new values to symbols in the definition of the symbol.
960          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
961
962          @param argvals: new values assigned to symbols
963          @type argvals: C{dict} with keywords of type L{Symbol}.
964          @return: result of the substitution process. Operations are executed as much as possible.
965          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
966          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
967          """
968          if argvals.has_key(self):
969             arg=argvals[self]
970             if self.isAppropriateValue(arg):
971                return arg
972             else:
973                raise TypeError,"%s: new value is not appropriate."%str(self)
974          else:
975             args=self.getSubstitutedArguments(argvals)
976             arg=args[0]
977             index=args[1]
978             return arg.__getitem__(index)
979
980  def log10(arg):  def log10(arg):
981     """     """
982     returns base-10 logarithm of argument arg     returns base-10 logarithm of argument arg
# Line 907  def wherePositive(arg): Line 1009  def wherePositive(arg):
1009     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1010     """     """
1011     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1012        if arg.rank==0:        out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
1013           if arg>0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
1014             return numarray.array(1.)        return out
else:
return numarray.array(0.)
else:
return numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))
1015     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1016        return arg._wherePositive()        return arg._wherePositive()
1017     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 993  def whereNegative(arg): Line 1091  def whereNegative(arg):
1091     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1092     """     """
1093     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1094        if arg.rank==0:        out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
1095           if arg<0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
1096             return numarray.array(1.)        return out
else:
return numarray.array(0.)
else:
return numarray.less(arg,numarray.zeros(arg.shape,numarray.Float))
1097     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1098        return arg._whereNegative()        return arg._whereNegative()
1099     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 1079  def whereNonNegative(arg): Line 1173  def whereNonNegative(arg):
1173     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1174     """     """
1175     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1176        if arg.rank==0:        out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
1177           if arg<0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
1178             return numarray.array(0.)        return out
else:
return numarray.array(1.)
else:
return numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float))
1179     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1180        return arg._whereNonNegative()        return arg._whereNonNegative()
1181     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 1113  def whereNonPositive(arg): Line 1203  def whereNonPositive(arg):
1203     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1204     """     """
1205     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1206        if arg.rank==0:        out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
1207           if arg>0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
1208             return numarray.array(0.)        return out
else:
return numarray.array(1.)
else:
return numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.
1209     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1210        return arg._whereNonPositive()        return arg._whereNonPositive()
1211     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 1149  def whereZero(arg,tol=0.): Line 1235  def whereZero(arg,tol=0.):
1235     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1236     """     """
1237     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1238        if arg.rank==0:        out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1.
1239           if abs(arg)<=tol:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
1240             return numarray.array(1.)        return out
else:
return numarray.array(0.)
else:
return numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
1241     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1242        if tol>0.:        if tol>0.:
1243           return whereNegative(abs(arg)-tol)           return whereNegative(abs(arg)-tol)
# Line 1236  def whereNonZero(arg,tol=0.): Line 1318  def whereNonZero(arg,tol=0.):
1318     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1319     """     """
1320     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1321        if arg.rank==0:        out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1.
1322          if abs(arg)>tol:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
1323             return numarray.array(1.)        return out
else:
return numarray.array(0.)
else:
return numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
1324     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1325        if tol>0.:        if tol>0.:
1326           return 1.-whereZero(arg,tol)           return 1.-whereZero(arg,tol)
# Line 2877  def length(arg): Line 2955  def length(arg):
2955     """     """
2956     return sqrt(inner(arg,arg))     return sqrt(inner(arg,arg))
2957
2958    def trace(arg,axis_offset=0):
2959       """
2960       returns the trace of arg which the sum of arg[k,k] over k.
2961
2962       @param arg: argument
2963       @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
2964       @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
2965                      axis_offset and axis_offset+1 must be equal.
2966       @type axis_offset: C{int}
2967       @return: trace of arg. The rank of the returned object is minus 2 of the rank of arg.
2968       @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
2969       """
2970       if isinstance(arg,numarray.NumArray):
2971          sh=arg.shape
2972          if len(sh)<2:
2973            raise ValueError,"trace: rank of argument must be greater than 1"
2974          if axis_offset<0 or axis_offset>len(sh)-2:
2975            raise ValueError,"trace: axis_offset must be between 0 and %s"%len(sh)-2
2976          s1=1
2977          for i in range(axis_offset): s1*=sh[i]
2978          s2=1
2979          for i in range(axis_offset+2,len(sh)): s2*=sh[i]
2980          if not sh[axis_offset] == sh[axis_offset+1]:
2981            raise ValueError,"trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
2982          arg_reshaped=numarray.reshape(arg,(s1,sh[axis_offset],sh[axis_offset],s2))
2983          out=numarray.zeros([s1,s2],numarray.Float64)
2984          for i1 in range(s1):
2985            for i2 in range(s2):
2986                for j in range(sh[axis_offset]): out[i1,i2]+=arg_reshaped[i1,j,j,i2]
2987          out.resize(sh[:axis_offset]+sh[axis_offset+2:])
2988          return out
2989       elif isinstance(arg,escript.Data):
2990          return escript_trace(arg,axis_offset)
2991       elif isinstance(arg,float):
2992          raise TypeError,"trace: illegal argument type float."
2993       elif isinstance(arg,int):
2994          raise TypeError,"trace: illegal argument type int."
2995       elif isinstance(arg,Symbol):
2996          return Trace_Symbol(arg,axis_offset)
2997       else:
2998          raise TypeError,"trace: Unknown argument type."
2999
3000    def escript_trace(arg,axis_offset): # this should be escript._trace
3001          "arg si a Data objects!!!"
3002          if arg.getRank()<2:
3003            raise ValueError,"escript_trace: rank of argument must be greater than 1"
3004          if axis_offset<0 or axis_offset>arg.getRank()-2:
3005            raise ValueError,"escript_trace: axis_offset must be between 0 and %s"%arg.getRank()-2
3006          s=list(arg.getShape())
3007          if not s[axis_offset] == s[axis_offset+1]:
3008            raise ValueError,"escript_trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
3009          out=escript.Data(0.,tuple(s[0:axis_offset]+s[axis_offset+2:]),arg.getFunctionSpace())
3010          if arg.getRank()==2:
3011             for i0 in range(s[0]):
3012                out+=arg[i0,i0]
3013          elif arg.getRank()==3:
3014             if axis_offset==0:
3015                for i0 in range(s[0]):
3016                      for i2 in range(s[2]):
3017                             out[i2]+=arg[i0,i0,i2]
3018             elif axis_offset==1:
3019                for i0 in range(s[0]):
3020                   for i1 in range(s[1]):
3021                             out[i0]+=arg[i0,i1,i1]
3022          elif arg.getRank()==4:
3023             if axis_offset==0:
3024                for i0 in range(s[0]):
3025                      for i2 in range(s[2]):
3026                         for i3 in range(s[3]):
3027                             out[i2,i3]+=arg[i0,i0,i2,i3]
3028             elif axis_offset==1:
3029                for i0 in range(s[0]):
3030                   for i1 in range(s[1]):
3031                         for i3 in range(s[3]):
3032                             out[i0,i3]+=arg[i0,i1,i1,i3]
3033             elif axis_offset==2:
3034                for i0 in range(s[0]):
3035                   for i1 in range(s[1]):
3036                      for i2 in range(s[2]):
3037                             out[i0,i1]+=arg[i0,i1,i2,i2]
3038          return out
3039    class Trace_Symbol(DependendSymbol):
3040       """
3041       L{Symbol} representing the result of the trace function
3042       """
3043       def __init__(self,arg,axis_offset=0):
3044          """
3045          initialization of trace L{Symbol} with argument arg
3046          @param arg: argument of function
3047          @type arg: L{Symbol}.
3048          @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
3049                      axis_offset and axis_offset+1 must be equal.
3050          @type axis_offset: C{int}
3051          """
3052          if arg.getRank()<2:
3053            raise ValueError,"Trace_Symbol: rank of argument must be greater than 1"
3054          if axis_offset<0 or axis_offset>arg.getRank()-2:
3055            raise ValueError,"Trace_Symbol: axis_offset must be between 0 and %s"%arg.getRank()-2
3056          s=list(arg.getShape())
3057          if not s[axis_offset] == s[axis_offset+1]:
3058            raise ValueError,"Trace_Symbol: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
3059          super(Trace_Symbol,self).__init__(args=[arg,axis_offset],shape=tuple(s[0:axis_offset]+s[axis_offset+2:]),dim=arg.getDim())
3060
3061       def getMyCode(self,argstrs,format="escript"):
3062          """
3063          returns a program code that can be used to evaluate the symbol.
3064
3065          @param argstrs: gives for each argument a string representing the argument for the evaluation.
3066          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
3067          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
3068          @type format: C{str}
3069          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
3070          @rtype: C{str}
3071          @raise: NotImplementedError: if the requested format is not available
3072          """
3073          if format=="escript" or format=="str"  or format=="text":
3074             return "trace(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
3075          else:
3076             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
3077
3078       def substitute(self,argvals):
3079          """
3080          assigns new values to symbols in the definition of the symbol.
3081          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
3082
3083          @param argvals: new values assigned to symbols
3084          @type argvals: C{dict} with keywords of type L{Symbol}.
3085          @return: result of the substitution process. Operations are executed as much as possible.
3086          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
3087          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
3088          """
3089          if argvals.has_key(self):
3090             arg=argvals[self]
3091             if self.isAppropriateValue(arg):
3092                return arg
3093             else:
3094                raise TypeError,"%s: new value is not appropriate."%str(self)
3095          else:
3096             arg=self.getSubstitutedArguments(argvals)
3097             return trace(arg[0],axis_offset=arg[1])
3098
3099       def diff(self,arg):
3100          """
3101          differential of this object
3102
3103          @param arg: the derivative is calculated with respect to arg
3104          @type arg: L{escript.Symbol}
3105          @return: derivative with respect to C{arg}
3106          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
3107          """
3108          if arg==self:
3109             return identity(self.getShape())
3110          else:
3111             return trace(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
3112
3113    def transpose(arg,axis_offset=None):
3114       """
3115       returns the transpose of arg by swaping the first axis_offset and the last rank-axis_offset components.
3116
3117       @param arg: argument
3118       @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}, C{float}, C{int}
3119       @param axis_offset: the first axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
3120                           if axis_offset is not present C{int(r/2)} where r is the rank of arg is used.
3121       @type axis_offset: C{int}
3122       @return: transpose of arg
3123       @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray},C{float}, C{int} depending on the type of arg.
3124       """
3125       if isinstance(arg,numarray.NumArray):
3126          if axis_offset==None: axis_offset=int(arg.rank/2)
3127          return numarray.transpose(arg,axes=range(axis_offset,arg.rank)+range(0,axis_offset))
3128       elif isinstance(arg,escript.Data):
3129          if axis_offset==None: axis_offset=int(arg.getRank()/2)
3130          return escript_transpose(arg,axis_offset)
3131       elif isinstance(arg,float):
3132          if not ( axis_offset==0 or axis_offset==None):
3133            raise ValueError,"transpose: axis_offset must be 0 for float argument"
3134          return arg
3135       elif isinstance(arg,int):
3136          if not ( axis_offset==0 or axis_offset==None):
3137            raise ValueError,"transpose: axis_offset must be 0 for int argument"
3138          return float(arg)
3139       elif isinstance(arg,Symbol):
3140          if axis_offset==None: axis_offset=int(arg.getRank()/2)
3141          return Transpose_Symbol(arg,axis_offset)
3142       else:
3143          raise TypeError,"transpose: Unknown argument type."
3144
3145    def escript_transpose(arg,axis_offset): # this should be escript._transpose
3146          "arg si a Data objects!!!"
3147          r=arg.getRank()
3148          if axis_offset<0 or axis_offset>r:
3149            raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r
3150          s=arg.getShape()
3151          s_out=s[axis_offset:]+s[:axis_offset]
3152          out=escript.Data(0.,s_out,arg.getFunctionSpace())
3153          if r==4:
3154             if axis_offset==1:
3155                for i0 in range(s_out[0]):
3156                   for i1 in range(s_out[1]):
3157                      for i2 in range(s_out[2]):
3158                         for i3 in range(s_out[3]):
3159                             out[i0,i1,i2,i3]=arg[i3,i0,i1,i2]
3160             elif axis_offset==2:
3161                for i0 in range(s_out[0]):
3162                   for i1 in range(s_out[1]):
3163                      for i2 in range(s_out[2]):
3164                         for i3 in range(s_out[3]):
3165                             out[i0,i1,i2,i3]=arg[i2,i3,i0,i1]
3166             elif axis_offset==3:
3167                for i0 in range(s_out[0]):
3168                   for i1 in range(s_out[1]):
3169                      for i2 in range(s_out[2]):
3170                         for i3 in range(s_out[3]):
3171                             out[i0,i1,i2,i3]=arg[i1,i2,i3,i0]
3172             else:
3173                for i0 in range(s_out[0]):
3174                   for i1 in range(s_out[1]):
3175                      for i2 in range(s_out[2]):
3176                         for i3 in range(s_out[3]):
3177                             out[i0,i1,i2,i3]=arg[i0,i1,i2,i3]
3178          elif r==3:
3179             if axis_offset==1:
3180                for i0 in range(s_out[0]):
3181                   for i1 in range(s_out[1]):
3182                      for i2 in range(s_out[2]):
3183                             out[i0,i1,i2]=arg[i2,i0,i1]
3184             elif axis_offset==2:
3185                for i0 in range(s_out[0]):
3186                   for i1 in range(s_out[1]):
3187                      for i2 in range(s_out[2]):
3188                             out[i0,i1,i2]=arg[i1,i2,i0]
3189             else:
3190                for i0 in range(s_out[0]):
3191                   for i1 in range(s_out[1]):
3192                      for i2 in range(s_out[2]):
3193                             out[i0,i1,i2]=arg[i0,i1,i2]
3194          elif r==2:
3195             if axis_offset==1:
3196                for i0 in range(s_out[0]):
3197                   for i1 in range(s_out[1]):
3198                             out[i0,i1]=arg[i1,i0]
3199             else:
3200                for i0 in range(s_out[0]):
3201                   for i1 in range(s_out[1]):
3202                             out[i0,i1]=arg[i0,i1]
3203          elif r==1:
3204              for i0 in range(s_out[0]):
3205                   out[i0]=arg[i0]
3206          elif r==0:
3207                 out=arg+0.
3208          return out
3209    class Transpose_Symbol(DependendSymbol):
3210       """
3211       L{Symbol} representing the result of the transpose function
3212       """
3213       def __init__(self,arg,axis_offset=None):
3214          """
3215          initialization of transpose L{Symbol} with argument arg
3216
3217          @param arg: argument of function
3218          @type arg: L{Symbol}.
3219           @param axis_offset: the first axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
3220                           if axis_offset is not present C{int(r/2)} where r is the rank of arg is used.
3221          @type axis_offset: C{int}
3222          """
3223          if axis_offset==None: axis_offset=int(arg.getRank()/2)
3224          if axis_offset<0 or axis_offset>arg.getRank():
3225            raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r
3226          s=arg.getShape()
3227          super(Transpose_Symbol,self).__init__(args=[arg,axis_offset],shape=s[axis_offset:]+s[:axis_offset],dim=arg.getDim())
3228
3229       def getMyCode(self,argstrs,format="escript"):
3230          """
3231          returns a program code that can be used to evaluate the symbol.
3232
3233          @param argstrs: gives for each argument a string representing the argument for the evaluation.
3234          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
3235          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
3236          @type format: C{str}
3237          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
3238          @rtype: C{str}
3239          @raise: NotImplementedError: if the requested format is not available
3240          """
3241          if format=="escript" or format=="str"  or format=="text":
3242             return "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
3243          else:
3244             raise NotImplementedError,"Transpose_Symbol does not provide program code for format %s."%format
3245
3246       def substitute(self,argvals):
3247          """
3248          assigns new values to symbols in the definition of the symbol.
3249          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
3250
3251          @param argvals: new values assigned to symbols
3252          @type argvals: C{dict} with keywords of type L{Symbol}.
3253          @return: result of the substitution process. Operations are executed as much as possible.
3254          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
3255          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
3256          """
3257          if argvals.has_key(self):
3258             arg=argvals[self]
3259             if self.isAppropriateValue(arg):
3260                return arg
3261             else:
3262                raise TypeError,"%s: new value is not appropriate."%str(self)
3263          else:
3264             arg=self.getSubstitutedArguments(argvals)
3265             return transpose(arg[0],axis_offset=arg[1])
3266
3267       def diff(self,arg):
3268          """
3269          differential of this object
3270
3271          @param arg: the derivative is calculated with respect to arg
3272          @type arg: L{escript.Symbol}
3273          @return: derivative with respect to C{arg}
3274          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
3275          """
3276          if arg==self:
3277             return identity(self.getShape())
3278          else:
3279             return transpose(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
3280    def symmetric(arg):
3281        """
3282        returns the symmetric part of the square matrix arg. This is (arg+transpose(arg))/2
3283
3284        @param arg: square matrix. Must have rank 2 or 4 and be square.
3285        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3286        @return: symmetric part of arg
3287        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3288        """
3289        if isinstance(arg,numarray.NumArray):
3290          if arg.rank==2:
3291            if not (arg.shape[0]==arg.shape[1]):
3292               raise ValueError,"symmetric: argument must be square."
3293          elif arg.rank==4:
3294            if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
3295               raise ValueError,"symmetric: argument must be square."
3296          else:
3297            raise ValueError,"symmetric: rank 2 or 4 is required."
3298          return (arg+transpose(arg))/2
3299        elif isinstance(arg,escript.Data):
3300          return escript_symmetric(arg)
3301        elif isinstance(arg,float):
3302          return arg
3303        elif isinstance(arg,int):
3304          return float(arg)
3305        elif isinstance(arg,Symbol):
3306          if arg.getRank()==2:
3307            if not (arg.getShape()[0]==arg.getShape()[1]):
3308               raise ValueError,"symmetric: argument must be square."
3309          elif arg.getRank()==4:
3310            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3311               raise ValueError,"symmetric: argument must be square."
3312          else:
3313            raise ValueError,"symmetric: rank 2 or 4 is required."
3314          return (arg+transpose(arg))/2
3315        else:
3316          raise TypeError,"symmetric: Unknown argument type."
3317
3318    def escript_symmetric(arg): # this should be implemented in c++
3319          if arg.getRank()==2:
3320            if not (arg.getShape()[0]==arg.getShape()[1]):
3321               raise ValueError,"escript_symmetric: argument must be square."
3322            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3323            for i0 in range(arg.getShape()[0]):
3324               for i1 in range(arg.getShape()[1]):
3325                  out[i0,i1]=(arg[i0,i1]+arg[i1,i0])/2.
3326          elif arg.getRank()==4:
3327            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3328               raise ValueError,"escript_symmetric: argument must be square."
3329            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3330            for i0 in range(arg.getShape()[0]):
3331               for i1 in range(arg.getShape()[1]):
3332                  for i2 in range(arg.getShape()[2]):
3333                     for i3 in range(arg.getShape()[3]):
3334                         out[i0,i1,i2,i3]=(arg[i0,i1,i2,i3]+arg[i2,i3,i0,i1])/2.
3335          else:
3336            raise ValueError,"escript_symmetric: rank 2 or 4 is required."
3337          return out
3338
3339    def nonsymmetric(arg):
3340        """
3341        returns the nonsymmetric part of the square matrix arg. This is (arg-transpose(arg))/2
3342
3343        @param arg: square matrix. Must have rank 2 or 4 and be square.
3344        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3345        @return: nonsymmetric part of arg
3346        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3347        """
3348        if isinstance(arg,numarray.NumArray):
3349          if arg.rank==2:
3350            if not (arg.shape[0]==arg.shape[1]):
3351               raise ValueError,"nonsymmetric: argument must be square."
3352          elif arg.rank==4:
3353            if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
3354               raise ValueError,"nonsymmetric: argument must be square."
3355          else:
3356            raise ValueError,"nonsymmetric: rank 2 or 4 is required."
3357          return (arg-transpose(arg))/2
3358        elif isinstance(arg,escript.Data):
3359          return escript_nonsymmetric(arg)
3360        elif isinstance(arg,float):
3361          return arg
3362        elif isinstance(arg,int):
3363          return float(arg)
3364        elif isinstance(arg,Symbol):
3365          if arg.getRank()==2:
3366            if not (arg.getShape()[0]==arg.getShape()[1]):
3367               raise ValueError,"nonsymmetric: argument must be square."
3368          elif arg.getRank()==4:
3369            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3370               raise ValueError,"nonsymmetric: argument must be square."
3371          else:
3372            raise ValueError,"nonsymmetric: rank 2 or 4 is required."
3373          return (arg-transpose(arg))/2
3374        else:
3375          raise TypeError,"nonsymmetric: Unknown argument type."
3376
3377    def escript_nonsymmetric(arg): # this should be implemented in c++
3378          if arg.getRank()==2:
3379            if not (arg.getShape()[0]==arg.getShape()[1]):
3380               raise ValueError,"escript_nonsymmetric: argument must be square."
3381            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3382            for i0 in range(arg.getShape()[0]):
3383               for i1 in range(arg.getShape()[1]):
3384                  out[i0,i1]=(arg[i0,i1]-arg[i1,i0])/2.
3385          elif arg.getRank()==4:
3386            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3387               raise ValueError,"escript_nonsymmetric: argument must be square."
3388            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3389            for i0 in range(arg.getShape()[0]):
3390               for i1 in range(arg.getShape()[1]):
3391                  for i2 in range(arg.getShape()[2]):
3392                     for i3 in range(arg.getShape()[3]):
3393                         out[i0,i1,i2,i3]=(arg[i0,i1,i2,i3]-arg[i2,i3,i0,i1])/2.
3394          else:
3395            raise ValueError,"escript_nonsymmetric: rank 2 or 4 is required."
3396          return out
3397
3398
3399    def inverse(arg):
3400        """
3401        returns the inverse of the square matrix arg.
3402
3403        @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
3404        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3405        @return: inverse arg_inv of the argument. It will be matrixmul(inverse(arg),arg) almost equal to kronecker(arg.getShape()[0])
3406        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3407        @remark: for L{escript.Data} objects the dimension is restricted to 3.
3408        """
3409        if isinstance(arg,numarray.NumArray):
3410          return numarray.linear_algebra.inverse(arg)
3411        elif isinstance(arg,escript.Data):
3412          return escript_inverse(arg)
3413        elif isinstance(arg,float):
3414          return 1./arg
3415        elif isinstance(arg,int):
3416          return 1./float(arg)
3417        elif isinstance(arg,Symbol):
3418          return Inverse_Symbol(arg)
3419        else:
3420          raise TypeError,"inverse: Unknown argument type."
3421
3422    def escript_inverse(arg): # this should be escript._inverse and use LAPACK
3423          "arg is a Data objects!!!"
3424          if not arg.getRank()==2:
3425            raise ValueError,"escript_inverse: argument must have rank 2"
3426          s=arg.getShape()
3427          if not s[0] == s[1]:
3428            raise ValueError,"escript_inverse: argument must be a square matrix."
3429          out=escript.Data(0.,s,arg.getFunctionSpace())
3430          if s[0]==1:
3431              if inf(abs(arg[0,0]))==0: # in c this should be done point wise as abs(arg[0,0](i))<=0.
3432                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3433              out[0,0]=1./arg[0,0]
3434          elif s[0]==2:
3435              A11=arg[0,0]
3436              A12=arg[0,1]
3437              A21=arg[1,0]
3438              A22=arg[1,1]
3439              D = A11*A22-A12*A21
3440              if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
3441                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3442              D=1./D
3443              out[0,0]= A22*D
3444              out[1,0]=-A21*D
3445              out[0,1]=-A12*D
3446              out[1,1]= A11*D
3447          elif s[0]==3:
3448              A11=arg[0,0]
3449              A21=arg[1,0]
3450              A31=arg[2,0]
3451              A12=arg[0,1]
3452              A22=arg[1,1]
3453              A32=arg[2,1]
3454              A13=arg[0,2]
3455              A23=arg[1,2]
3456              A33=arg[2,2]
3457              D  =  A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22)
3458              if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
3459                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3460              D=1./D
3461              out[0,0]=(A22*A33-A23*A32)*D
3462              out[1,0]=(A31*A23-A21*A33)*D
3463              out[2,0]=(A21*A32-A31*A22)*D
3464              out[0,1]=(A13*A32-A12*A33)*D
3465              out[1,1]=(A11*A33-A31*A13)*D
3466              out[2,1]=(A12*A31-A11*A32)*D
3467              out[0,2]=(A12*A23-A13*A22)*D
3468              out[1,2]=(A13*A21-A11*A23)*D
3469              out[2,2]=(A11*A22-A12*A21)*D
3470          else:
3471             raise TypeError,"escript_inverse: only matrix dimensions 1,2,3 are supported right now."
3472          return out
3473
3474    class Inverse_Symbol(DependendSymbol):
3475       """
3476       L{Symbol} representing the result of the inverse function
3477       """
3478       def __init__(self,arg):
3479          """
3480          initialization of inverse L{Symbol} with argument arg
3481          @param arg: argument of function
3482          @type arg: L{Symbol}.
3483          """
3484          if not arg.getRank()==2:
3485            raise ValueError,"Inverse_Symbol:: argument must have rank 2"
3486          s=arg.getShape()
3487          if not s[0] == s[1]:
3488            raise ValueError,"Inverse_Symbol:: argument must be a square matrix."
3489          super(Inverse_Symbol,self).__init__(args=[arg],shape=s,dim=arg.getDim())
3490
3491       def getMyCode(self,argstrs,format="escript"):
3492          """
3493          returns a program code that can be used to evaluate the symbol.
3494
3495          @param argstrs: gives for each argument a string representing the argument for the evaluation.
3496          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
3497          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
3498          @type format: C{str}
3499          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
3500          @rtype: C{str}
3501          @raise: NotImplementedError: if the requested format is not available
3502          """
3503          if format=="escript" or format=="str"  or format=="text":
3504             return "inverse(%s)"%argstrs[0]
3505          else:
3506             raise NotImplementedError,"Inverse_Symbol does not provide program code for format %s."%format
3507
3508       def substitute(self,argvals):
3509          """
3510          assigns new values to symbols in the definition of the symbol.
3511          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
3512
3513          @param argvals: new values assigned to symbols
3514          @type argvals: C{dict} with keywords of type L{Symbol}.
3515          @return: result of the substitution process. Operations are executed as much as possible.
3516          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
3517          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
3518          """
3519          if argvals.has_key(self):
3520             arg=argvals[self]
3521             if self.isAppropriateValue(arg):
3522                return arg
3523             else:
3524                raise TypeError,"%s: new value is not appropriate."%str(self)
3525          else:
3526             arg=self.getSubstitutedArguments(argvals)
3527             return inverse(arg[0])
3528
3529       def diff(self,arg):
3530          """
3531          differential of this object
3532
3533          @param arg: the derivative is calculated with respect to arg
3534          @type arg: L{escript.Symbol}
3535          @return: derivative with respect to C{arg}
3536          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
3537          """
3538          if arg==self:
3539             return identity(self.getShape())
3540          else:
3541             return -matrixmult(matrixmult(self,self.getDifferentiatedArguments(arg)[0]),self)
3542
3543    def eigenvalues(arg):
3544        """
3545        returns the eigenvalues of the square matrix arg.
3546
3547        @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
3548                    arg must be symmetric, ie. transpose(arg)==arg (this is not checked).
3549        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3550        @return: the eigenvalues in increasing order.
3551        @rtype: L{numarray.NumArray},L{escript.Data}, L{Symbol} depending on the input.
3552        @remark: for L{escript.Data} and L{Symbol} objects the dimension is restricted to 3.
3553        """
3554        if isinstance(arg,numarray.NumArray):
3555          out=numarray.linear_algebra.eigenvalues((arg+numarray.transpose(arg))/2.)
3556          out.sort()
3557          return out
3558        elif isinstance(arg,escript.Data):
3559          return arg._eigenvalues()
3560        elif isinstance(arg,Symbol):
3561          if not arg.getRank()==2:
3562            raise ValueError,"eigenvalues: argument must have rank 2"
3563          s=arg.getShape()
3564          if not s[0] == s[1]:
3565            raise ValueError,"eigenvalues: argument must be a square matrix."
3566          if s[0]==1:
3567              return arg[0]
3568          elif s[0]==2:
3569              arg1=symmetric(arg)
3570              A11=arg1[0,0]
3571              A12=arg1[0,1]
3572              A22=arg1[1,1]
3573              trA=(A11+A22)/2.
3574              A11-=trA
3575              A22-=trA
3576              s=sqrt(A12**2-A11*A22)
3577              return trA+s*numarray.array([-1.,1.],type=numarray.Float64)
3578          elif s[0]==3:
3579              arg1=symmetric(arg)
3580              A11=arg1[0,0]
3581              A12=arg1[0,1]
3582              A22=arg1[1,1]
3583              A13=arg1[0,2]
3584              A23=arg1[1,2]
3585              A33=arg1[2,2]
3586              trA=(A11+A22+A33)/3.
3587              A11-=trA
3588              A22-=trA
3589              A33-=trA
3590              A13_2=A13**2
3591              A23_2=A23**2
3592              A12_2=A12**2
3593              p=A13_2+A23_2+A12_2+(A11**2+A22**2+A33**2)/2.
3594              q=A13_2*A22+A23_2*A11+A12_2*A33-A11*A22*A33-2*A12*A23*A13
3595              sq_p=sqrt(p/3.)
3596              alpha_3=acos(clip(-q*(sq_p+whereZero(p,0.)*1.e-15)**(-3.)/2.,-1.,1.))/3.  # whereZero is protection against divison by zero
3597              sq_p*=2.
3598              f=cos(alpha_3)               *numarray.array([0.,0.,1.],type=numarray.Float64) \
3599               -cos(alpha_3+numarray.pi/3.)*numarray.array([0.,1.,0.],type=numarray.Float64) \
3600               -cos(alpha_3-numarray.pi/3.)*numarray.array([1.,0.,0.],type=numarray.Float64)
3601              return trA+sq_p*f
3602          else:
3603             raise TypeError,"eigenvalues: only matrix dimensions 1,2,3 are supported right now."
3604        elif isinstance(arg,float):
3605          return arg
3606        elif isinstance(arg,int):
3607          return float(arg)
3608        else:
3609          raise TypeError,"eigenvalues: Unknown argument type."
3610
3611    def eigenvalues_and_eigenvectors(arg):
3612        """
3613        returns the eigenvalues and eigenvectors of the square matrix arg.
3614
3615        @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
3616                    arg must be symmetric, ie. transpose(arg)==arg (this is not checked).
3617        @type arg: L{escript.Data}
3618        @return: the eigenvalues and eigenvectors. The eigenvalues are ordered by increasing value. The
3619                 eigenvectors are orthogonal and normalized. If V are the eigenvectors than V[:,i] is
3620                 the eigenvector coresponding to the i-th eigenvalue.
3621        @rtype: L{tuple} of L{escript.Data}.
3622        @remark: The dimension is restricted to 3.
3623        """
3624        if isinstance(arg,numarray.NumArray):
3625          raise TypeError,"eigenvalues_and_eigenvectors is not supporting numarray arguments"
3626        elif isinstance(arg,escript.Data):
3627          return arg._eigenvalues_and_eigenvectors()
3628        elif isinstance(arg,Symbol):
3629          raise TypeError,"eigenvalues_and_eigenvectors is not supporting Symbol arguments"
3630        elif isinstance(arg,float):
3631          return (numarray.array([[arg]],numarray.Float),numarray.ones((1,1),numarray.Float))
3632        elif isinstance(arg,int):
3633          return (numarray.array([[arg]],numarray.Float),numarray.ones((1,1),numarray.Float))
3634        else:
3635          raise TypeError,"eigenvalues: Unknown argument type."
3636  #=======================================================  #=======================================================
3637  #  Binary operations:  #  Binary operations:
3638  #=======================================================  #=======================================================
# Line 2995  def mult(arg0,arg1): Line 3751  def mult(arg0,arg1):
3751         """         """
3752         args=matchShape(arg0,arg1)         args=matchShape(arg0,arg1)
3753         if testForZero(args[0]) or testForZero(args[1]):         if testForZero(args[0]) or testForZero(args[1]):
3754            return numarray.zeros(pokeShape(args[0]),numarray.Float)            return numarray.zeros(pokeShape(args[0]),numarray.Float64)
3755         else:         else:
3756            if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) :            if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) :
3757                return Mult_Symbol(args[0],args[1])                return Mult_Symbol(args[0],args[1])
# Line 3095  def quotient(arg0,arg1): Line 3851  def quotient(arg0,arg1):
3851         """         """
3852         args=matchShape(arg0,arg1)         args=matchShape(arg0,arg1)
3853         if testForZero(args[0]):         if testForZero(args[0]):
3854            return numarray.zeros(pokeShape(args[0]),numarray.Float)            return numarray.zeros(pokeShape(args[0]),numarray.Float64)
3855         elif isinstance(args[0],Symbol):         elif isinstance(args[0],Symbol):
3856            if isinstance(args[1],Symbol):            if isinstance(args[1],Symbol):
3857               return Quotient_Symbol(args[0],args[1])               return Quotient_Symbol(args[0],args[1])
# Line 3201  def power(arg0,arg1): Line 3957  def power(arg0,arg1):
3957         """         """
3958         args=matchShape(arg0,arg1)         args=matchShape(arg0,arg1)
3959         if testForZero(args[0]):         if testForZero(args[0]):
3960            return numarray.zeros(args[0],numarray.Float)            return numarray.zeros(pokeShape(args[0]),numarray.Float64)
3961         elif testForZero(args[1]):         elif testForZero(args[1]):
3962            return numarray.ones(args[0],numarray.Float)            return numarray.ones(pokeShape(args[1]),numarray.Float64)
3963         elif isinstance(args[0],Symbol) or isinstance(args[1],Symbol):         elif isinstance(args[0],Symbol) or isinstance(args[1],Symbol):
3964            return Power_Symbol(args[0],args[1])            return Power_Symbol(args[0],args[1])
3965         elif isinstance(args[0],numarray.NumArray) and not isinstance(args[1],numarray.NumArray):         elif isinstance(args[0],numarray.NumArray) and not isinstance(args[1],numarray.NumArray):
# Line 3304  def maximum(*args): Line 4060  def maximum(*args):
4060         if out==None:         if out==None:
4061            out=a            out=a
4062         else:         else:
4065      return out      return out
4066
4067  def minimum(*arg):  def minimum(*args):
4068      """      """
4069      the minimum over arguments args      the minimum over arguments args
4070
# Line 3322  def minimum(*arg): Line 4078  def minimum(*arg):
4078         if out==None:         if out==None:
4079            out=a            out=a
4080         else:         else:
4083      return out      return out
4084
4085    def clip(arg,minval=0.,maxval=1.):
4086        """
4087        cuts the values of arg between minval and maxval
4088
4089        @param arg: argument
4090        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float}
4091        @param minval: lower range
4092        @type arg: C{float}
4093        @param maxval: upper range
4094        @type arg: C{float}
4095        @return: is on object with all its value between minval and maxval. value of the argument that greater then minval and
4096                 less then maxval are unchanged.
4097        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float} depending on the input
4098        @raise ValueError: if minval>maxval
4099        """
4100        if minval>maxval:
4101           raise ValueError,"minval = %s must be less then maxval %s"%(minval,maxval)
4102        return minimum(maximum(minval,arg),maxval)
4103
4104
4105  def inner(arg0,arg1):  def inner(arg0,arg1):
4106      """      """
# Line 3348  def inner(arg0,arg1): Line 4124  def inner(arg0,arg1):
4124      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
4125      if not sh0==sh1:      if not sh0==sh1:
4126          raise ValueError,"inner: shape of arguments does not match"          raise ValueError,"inner: shape of arguments does not match"
4127      return generalTensorProduct(arg0,arg1,offset=len(sh0))      return generalTensorProduct(arg0,arg1,axis_offset=len(sh0))
4128
4129  def matrixmult(arg0,arg1):  def matrixmult(arg0,arg1):
4130      """      """
# Line 3376  def matrixmult(arg0,arg1): Line 4152  def matrixmult(arg0,arg1):
4152          raise ValueError,"first argument must have rank 2"          raise ValueError,"first argument must have rank 2"
4153      if not len(sh1)==2 and not len(sh1)==1:      if not len(sh1)==2 and not len(sh1)==1:
4154          raise ValueError,"second argument must have rank 1 or 2"          raise ValueError,"second argument must have rank 1 or 2"
4155      return generalTensorProduct(arg0,arg1,offset=1)      return generalTensorProduct(arg0,arg1,axis_offset=1)
4156
4157  def outer(arg0,arg1):  def outer(arg0,arg1):
4158      """      """
# Line 3394  def outer(arg0,arg1): Line 4170  def outer(arg0,arg1):
4170      @return: the outer product of arg0 and arg1 at each data point      @return: the outer product of arg0 and arg1 at each data point
4171      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
4172      """      """
4173      return generalTensorProduct(arg0,arg1,offset=0)      return generalTensorProduct(arg0,arg1,axis_offset=0)
4174
4175
4176  def tensormult(arg0,arg1):  def tensormult(arg0,arg1):
# Line 3436  def tensormult(arg0,arg1): Line 4212  def tensormult(arg0,arg1):
4212      sh0=pokeShape(arg0)      sh0=pokeShape(arg0)
4213      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
4214      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
4215         return generalTensorProduct(arg0,arg1,offset=1)         return generalTensorProduct(arg0,arg1,axis_offset=1)
4216      elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):      elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
4217         return generalTensorProduct(arg0,arg1,offset=2)         return generalTensorProduct(arg0,arg1,axis_offset=2)
4218      else:      else:
4219          raise ValueError,"tensormult: first argument must have rank 2 or 4"          raise ValueError,"tensormult: first argument must have rank 2 or 4"
4220
4221  def generalTensorProduct(arg0,arg1,offset=0):  def generalTensorProduct(arg0,arg1,axis_offset=0):
4222      """      """
4223      generalized tensor product      generalized tensor product
4224
4225      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]
4226
4227      where s runs through arg0.Shape[:arg0.Rank-offset]      where s runs through arg0.Shape[:arg0.Rank-axis_offset]
4228            r runs trough arg0.Shape[:offset]            r runs trough arg0.Shape[:axis_offset]
4229            t runs through arg1.Shape[offset:]            t runs through arg1.Shape[axis_offset:]
4230
4231      In the first case the the second dimension of arg0 and the length of arg1 must match and        In the first case the the second dimension of arg0 and the length of arg1 must match and
4232      in the second case the two last dimensions of arg0 must match the shape of arg1.      in the second case the two last dimensions of arg0 must match the shape of arg1.
# Line 3467  def generalTensorProduct(arg0,arg1,offse Line 4243  def generalTensorProduct(arg0,arg1,offse
4243      # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols      # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols
4244      if isinstance(arg0,numarray.NumArray):      if isinstance(arg0,numarray.NumArray):
4245         if isinstance(arg1,Symbol):         if isinstance(arg1,Symbol):
4246             return GeneralTensorProduct_Symbol(arg0,arg1,offset)             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4247         else:         else:
4248             if not arg0.shape[arg0.rank-offset:]==arg1.shape[:offset]:             if not arg0.shape[arg0.rank-axis_offset:]==arg1.shape[:axis_offset]:
4249                 raise ValueError,"generalTensorProduct: dimensions of last %s components in left argument don't match the first %s components in the right argument."%(offset,offset)                 raise ValueError,"generalTensorProduct: dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
4250             arg0_c=arg0.copy()             arg0_c=arg0.copy()
4251             arg1_c=arg1.copy()             arg1_c=arg1.copy()
4252             sh0,sh1=arg0.shape,arg1.shape             sh0,sh1=arg0.shape,arg1.shape
4253             d0,d1,d01=1,1,1             d0,d1,d01=1,1,1
4254             for i in sh0[:arg0.rank-offset]: d0*=i             for i in sh0[:arg0.rank-axis_offset]: d0*=i
4255             for i in sh1[offset:]: d1*=i             for i in sh1[axis_offset:]: d1*=i
4256             for i in sh1[:offset]: d01*=i             for i in sh1[:axis_offset]: d01*=i
4257             arg0_c.resize((d0,d01))             arg0_c.resize((d0,d01))
4258             arg1_c.resize((d01,d1))             arg1_c.resize((d01,d1))
4259             out=numarray.zeros((d0,d1),numarray.Float)             out=numarray.zeros((d0,d1),numarray.Float64)
4260             for i0 in range(d0):             for i0 in range(d0):
4261                      for i1 in range(d1):                      for i1 in range(d1):
4262                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])
4263             out.resize(sh0[:arg0.rank-offset]+sh1[offset:])             out.resize(sh0[:arg0.rank-axis_offset]+sh1[axis_offset:])
4264             return out             return out
4265      elif isinstance(arg0,escript.Data):      elif isinstance(arg0,escript.Data):
4266         if isinstance(arg1,Symbol):         if isinstance(arg1,Symbol):
4267             return GeneralTensorProduct_Symbol(arg0,arg1,offset)             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4268         else:         else:
4269             return escript_generalTensorProduct(arg0,arg1,offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,offset)             return escript_generalTensorProduct(arg0,arg1,axis_offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,axis_offset)
4270      else:            else:
4271         return GeneralTensorProduct_Symbol(arg0,arg1,offset)         return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4272
4273  class GeneralTensorProduct_Symbol(DependendSymbol):  class GeneralTensorProduct_Symbol(DependendSymbol):
4274     """     """
4275     Symbol representing the quotient of two arguments.     Symbol representing the quotient of two arguments.
4276     """     """
4277     def __init__(self,arg0,arg1,offset=0):     def __init__(self,arg0,arg1,axis_offset=0):
4278         """         """
4279         initialization of L{Symbol} representing the quotient of two arguments         initialization of L{Symbol} representing the quotient of two arguments
4280
# Line 3511  class GeneralTensorProduct_Symbol(Depend Line 4287  class GeneralTensorProduct_Symbol(Depend
4287         """         """
4288         sh_arg0=pokeShape(arg0)         sh_arg0=pokeShape(arg0)
4289         sh_arg1=pokeShape(arg1)         sh_arg1=pokeShape(arg1)
4290         sh0=sh_arg0[:len(sh_arg0)-offset]         sh0=sh_arg0[:len(sh_arg0)-axis_offset]
4291         sh01=sh_arg0[len(sh_arg0)-offset:]         sh01=sh_arg0[len(sh_arg0)-axis_offset:]
4292         sh10=sh_arg1[:offset]         sh10=sh_arg1[:axis_offset]
4293         sh1=sh_arg1[offset:]         sh1=sh_arg1[axis_offset:]
4294         if not sh01==sh10:         if not sh01==sh10:
4295             raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(offset,offset)             raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
4296         DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,offset])         DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,axis_offset])
4297
4298     def getMyCode(self,argstrs,format="escript"):     def getMyCode(self,argstrs,format="escript"):
4299        """        """
# Line 3532  class GeneralTensorProduct_Symbol(Depend Line 4308  class GeneralTensorProduct_Symbol(Depend
4308        @raise: NotImplementedError: if the requested format is not available        @raise: NotImplementedError: if the requested format is not available
4309        """        """
4310        if format=="escript" or format=="str" or format=="text":        if format=="escript" or format=="str" or format=="text":
4311           return "generalTensorProduct(%s,%s,offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])           return "generalTensorProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
4312        else:        else:
4313           raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)           raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)
4314
# Line 3557  class GeneralTensorProduct_Symbol(Depend Line 4333  class GeneralTensorProduct_Symbol(Depend
4333           args=self.getSubstitutedArguments(argvals)           args=self.getSubstitutedArguments(argvals)
4334           return generalTensorProduct(args[0],args[1],args[2])           return generalTensorProduct(args[0],args[1],args[2])
4335
4336  def escript_generalTensorProduct(arg0,arg1,offset): # this should be escript._generalTensorProduct  def escript_generalTensorProduct(arg0,arg1,axis_offset): # this should be escript._generalTensorProduct
4337      "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"      "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
4338      # calculate the return shape:      # calculate the return shape:
4339      shape0=arg0.getShape()[:arg0.getRank()-offset]      shape0=arg0.getShape()[:arg0.getRank()-axis_offset]
4340      shape01=arg0.getShape()[arg0.getRank()-offset:]      shape01=arg0.getShape()[arg0.getRank()-axis_offset:]
4341      shape10=arg1.getShape()[:offset]      shape10=arg1.getShape()[:axis_offset]
4342      shape1=arg1.getShape()[offset:]      shape1=arg1.getShape()[axis_offset:]
4343      if not shape01==shape10:      if not shape01==shape10:
4344          raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(offset,offset)          raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
4345
4346        # whatr function space should be used? (this here is not good!)
4347        fs=(escript.Scalar(0.,arg0.getFunctionSpace())+escript.Scalar(0.,arg1.getFunctionSpace())).getFunctionSpace()
4348      # create return value:      # create return value:
4349      out=escript.Data(0.,tuple(shape0+shape1),arg0.getFunctionSpace())      out=escript.Data(0.,tuple(shape0+shape1),fs)
4350      #      #
4351      s0=[[]]      s0=[[]]
4352      for k in shape0:      for k in shape0:
# Line 3591  def escript_generalTensorProduct(arg0,ar Line 4369  def escript_generalTensorProduct(arg0,ar
4369
4370      for i0 in s0:      for i0 in s0:
4371         for i1 in s1:         for i1 in s1:
4372           s=escript.Scalar(0.,arg0.getFunctionSpace())           s=escript.Scalar(0.,fs)
4373           for i01 in s01:           for i01 in s01:
4374              s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))              s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))
4375           out.__setitem__(tuple(i0+i1),s)           out.__setitem__(tuple(i0+i1),s)
4376      return out      return out
4377
4378
4379  #=========================================================  #=========================================================
4380  #   some little helpers  #  functions dealing with spatial dependency
4381  #=========================================================  #=========================================================
4383      """      """
4384      Returns the spatial gradient of arg at where.      Returns the spatial gradient of arg at where.
4385
4386        If C{g} is the returned object, then
4387
4388      @param arg:   Data object representing the function which gradient        - if C{arg} is rank 0 C{g[s]} is the derivative of C{arg} with respect to the C{s}-th spatial dimension.
4389                    to be calculated.        - if C{arg} is rank 1 C{g[i,s]} is the derivative of C{arg[i]} with respect to the C{s}-th spatial dimension.
4390          - if C{arg} is rank 2 C{g[i,j,s]} is the derivative of C{arg[i,j]} with respect to the C{s}-th spatial dimension.
4391          - if C{arg} is rank 3 C{g[i,j,k,s]} is the derivative of C{arg[i,j,k]} with respect to the C{s}-th spatial dimension.
4392
4393        @param arg: function which gradient to be calculated. Its rank has to be less than 3.
4394        @type arg: L{escript.Data} or L{Symbol}
4395      @param where: FunctionSpace in which the gradient will be calculated.      @param where: FunctionSpace in which the gradient will be calculated.
4396                    If not present or C{None} an appropriate default is used.                    If not present or C{None} an appropriate default is used.
4397        @type where: C{None} or L{escript.FunctionSpace}
4399        @rtype:  L{escript.Data} or L{Symbol}
4400      """      """
4401      if isinstance(arg,Symbol):      if isinstance(arg,Symbol):
4406         else:         else:
4408      else:      else:
4410
4412       """
4413       L{Symbol} representing the result of the gradient operator
4414       """
4415       def __init__(self,arg,where=None):
4416          """
4417          initialization of gradient L{Symbol} with argument arg
4418          @param arg: argument of function
4419          @type arg: L{Symbol}.
4420          @param where: FunctionSpace in which the gradient will be calculated.
4421                      If not present or C{None} an appropriate default is used.
4422          @type where: C{None} or L{escript.FunctionSpace}
4423          """
4424          d=arg.getDim()
4425          if d==None:
4426             raise ValueError,"argument must have a spatial dimension"
4428
4429       def getMyCode(self,argstrs,format="escript"):
4430          """
4431          returns a program code that can be used to evaluate the symbol.
4432
4433          @param argstrs: gives for each argument a string representing the argument for the evaluation.
4434          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4435          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4436          @type format: C{str}
4437          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4438          @rtype: C{str}
4439          @raise: NotImplementedError: if the requested format is not available
4440          """
4441          if format=="escript" or format=="str"  or format=="text":
4443          else:
4444             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4445
4446       def substitute(self,argvals):
4447          """
4448          assigns new values to symbols in the definition of the symbol.
4449          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
4450
4451          @param argvals: new values assigned to symbols
4452          @type argvals: C{dict} with keywords of type L{Symbol}.
4453          @return: result of the substitution process. Operations are executed as much as possible.
4454          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4455          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4456          """
4457          if argvals.has_key(self):
4458             arg=argvals[self]
4459             if self.isAppropriateValue(arg):
4460                return arg
4461             else:
4462                raise TypeError,"%s: new value is not appropriate."%str(self)
4463          else:
4464             arg=self.getSubstitutedArguments(argvals)
4466
4467       def diff(self,arg):
4468          """
4469          differential of this object
4470
4471          @param arg: the derivative is calculated with respect to arg
4472          @type arg: L{escript.Symbol}
4473          @return: derivative with respect to C{arg}
4474          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
4475          """
4476          if arg==self:
4477             return identity(self.getShape())
4478          else:
4480
4481  def integrate(arg,where=None):  def integrate(arg,where=None):
4482      """      """
4483      Return the integral if the function represented by Data object arg over      Return the integral of the function C{arg} over its domain. If C{where} is present C{arg} is interpolated to C{where}
4484      its domain.      before integration.
4485
4486      @param arg:   Data object representing the function which is integrated.      @param arg:   the function which is integrated.
4487        @type arg: L{escript.Data} or L{Symbol}
4488      @param where: FunctionSpace in which the integral is calculated.      @param where: FunctionSpace in which the integral is calculated.
4489                    If not present or C{None} an appropriate default is used.                    If not present or C{None} an appropriate default is used.
4490        @type where: C{None} or L{escript.FunctionSpace}
4491        @return: integral of arg.
4492        @rtype:  C{float}, C{numarray.NumArray} or L{Symbol}
4493      """      """
4494      if isinstance(arg,numarray.NumArray):      if isinstance(arg,Symbol):
if checkForZero(arg):
return arg
else:
raise TypeError,"integrate: cannot intergrate argument"
elif isinstance(arg,float):
if checkForZero(arg):
return arg
else:
raise TypeError,"integrate: cannot intergrate argument"
elif isinstance(arg,int):
if checkForZero(arg):
return float(arg)
else:
raise TypeError,"integrate: cannot intergrate argument"
elif isinstance(arg,Symbol):
4495         return Integrate_Symbol(arg,where)         return Integrate_Symbol(arg,where)
4496      elif isinstance(arg,escript.Data):      elif isinstance(arg,escript.Data):
4497         if not where==None: arg=escript.Data(arg,where)         if not where==None: arg=escript.Data(arg,where)
# Line 3654  def integrate(arg,where=None): Line 4502  def integrate(arg,where=None):
4502      else:      else:
4503        raise TypeError,"integrate: Unknown argument type."        raise TypeError,"integrate: Unknown argument type."
4504
4505    class Integrate_Symbol(DependendSymbol):
4506       """
4507       L{Symbol} representing the result of the spatial integration operator
4508       """
4509       def __init__(self,arg,where=None):
4510          """
4511          initialization of integration L{Symbol} with argument arg
4512          @param arg: argument of the integration
4513          @type arg: L{Symbol}.
4514          @param where: FunctionSpace in which the integration will be calculated.
4515                      If not present or C{None} an appropriate default is used.
4516          @type where: C{None} or L{escript.FunctionSpace}
4517          """
4518          super(Integrate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),dim=arg.getDim())
4519
4520       def getMyCode(self,argstrs,format="escript"):
4521          """
4522          returns a program code that can be used to evaluate the symbol.
4523
4524          @param argstrs: gives for each argument a string representing the argument for the evaluation.
4525          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4526          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4527          @type format: C{str}
4528          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4529          @rtype: C{str}
4530          @raise: NotImplementedError: if the requested format is not available
4531          """
4532          if format=="escript" or format=="str"  or format=="text":
4533             return "integrate(%s,where=%s)"%(argstrs[0],argstrs[1])
4534          else:
4535             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4536
4537       def substitute(self,argvals):
4538          """
4539          assigns new values to symbols in the definition of the symbol.
4540          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
4541
4542          @param argvals: new values assigned to symbols
4543          @type argvals: C{dict} with keywords of type L{Symbol}.
4544          @return: result of the substitution process. Operations are executed as much as possible.
4545          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4546          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4547          """
4548          if argvals.has_key(self):
4549             arg=argvals[self]
4550             if self.isAppropriateValue(arg):
4551                return arg
4552             else:
4553                raise TypeError,"%s: new value is not appropriate."%str(self)
4554          else:
4555             arg=self.getSubstitutedArguments(argvals)
4556             return integrate(arg[0],where=arg[1])
4557
4558       def diff(self,arg):
4559          """
4560          differential of this object
4561
4562          @param arg: the derivative is calculated with respect to arg
4563          @type arg: L{escript.Symbol}
4564          @return: derivative with respect to C{arg}
4565          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
4566          """
4567          if arg==self:
4568             return identity(self.getShape())
4569          else:
4570             return integrate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4571
4572
4573  def interpolate(arg,where):  def interpolate(arg,where):
4574      """      """
4575      Interpolates the function into the FunctionSpace where.      interpolates the function into the FunctionSpace where.
4576
4577      @param arg:    interpolant      @param arg: interpolant
4578      @param where:  FunctionSpace to interpolate to      @type arg: L{escript.Data} or L{Symbol}
4579        @param where: FunctionSpace to be interpolated to
4580        @type where: L{escript.FunctionSpace}
4581        @return: interpolated argument
4582        @rtype:  C{escript.Data} or L{Symbol}
4583      """      """
4584      if testForZero(arg):      if isinstance(arg,Symbol):
4585        return 0         return Interpolate_Symbol(arg,where)
elif isinstance(arg,Symbol):
return Interpolated_Symbol(arg,where)
4586      else:      else:
4587         return escript.Data(arg,where)         return escript.Data(arg,where)
4588
4589  def div(arg,where=None):  class Interpolate_Symbol(DependendSymbol):
4590      """     """
4591      Returns the divergence of arg at where.     L{Symbol} representing the result of the interpolation operator
4592       """
4593       def __init__(self,arg,where):
4594          """
4595          initialization of interpolation L{Symbol} with argument arg
4596          @param arg: argument of the interpolation
4597          @type arg: L{Symbol}.
4598          @param where: FunctionSpace into which the argument is interpolated.
4599          @type where: L{escript.FunctionSpace}
4600          """
4601          super(Interpolate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),dim=arg.getDim())
4602
4603      @param arg:   Data object representing the function which gradient to     def getMyCode(self,argstrs,format="escript"):
4604                    be calculated.        """
4605      @param where: FunctionSpace in which the gradient will be calculated.        returns a program code that can be used to evaluate the symbol.
If not present or C{None} an appropriate default is used.
"""
return trace(g,axis0=g.getRank()-2,axis1=g.getRank()-1)
4606
4607  def jump(arg):        @param argstrs: gives for each argument a string representing the argument for the evaluation.
4608      """        @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4609      Returns the jump of arg across a continuity.        @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4610          @type format: C{str}
4611          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4612          @rtype: C{str}
4613          @raise: NotImplementedError: if the requested format is not available
4614          """
4615          if format=="escript" or format=="str"  or format=="text":
4616             return "interpolate(%s,where=%s)"%(argstrs[0],argstrs[1])
4617          else:
4618             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4619
4620      @param arg:   Data object representing the function which gradient     def substitute(self,argvals):
4621                    to be calculated.        """
4622      """        assigns new values to symbols in the definition of the symbol.
4623      d=arg.getDomain()        The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
return arg.interpolate(escript.FunctionOnContactOne())-arg.interpolate(escript.FunctionOnContactZero())
4624
4625  #=============================        @param argvals: new values assigned to symbols
4626  #        @type argvals: C{dict} with keywords of type L{Symbol}.
4627  # wrapper for various functions: if the argument has attribute the function name        @return: result of the substitution process. Operations are executed as much as possible.
4628  # as an argument it calls the corresponding methods. Otherwise the corresponding        @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4629  # numarray function is called.        @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4630          """
4631          if argvals.has_key(self):
4632             arg=argvals[self]
4633             if self.isAppropriateValue(arg):
4634                return arg
4635             else:
4636                raise TypeError,"%s: new value is not appropriate."%str(self)
4637          else:
4638             arg=self.getSubstitutedArguments(argvals)
4639             return interpolate(arg[0],where=arg[1])
4640
4641  # functions involving the underlying Domain:     def diff(self,arg):
4642          """
4643          differential of this object
4644
4645          @param arg: the derivative is calculated with respect to arg
4646          @type arg: L{escript.Symbol}
4647          @return: derivative with respect to C{arg}
4648          @rtype: L{Symbol} but other types such as L{escript.Data}, L{numarray.NumArray}  are possible.
4649          """
4650          if arg==self:
4651             return identity(self.getShape())
4652          else:
4653             return interpolate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4654
4655  def transpose(arg,axis=None):
4656    def div(arg,where=None):
4657      """      """
4658      Returns the transpose of the Data object arg.      returns the divergence of arg at where.
4659
4660      @param arg:      @param arg: function which divergence to be calculated. Its shape has to be (d,) where d is the spatial dimension.
4661        @type arg: L{escript.Data} or L{Symbol}
4662        @param where: FunctionSpace in which the divergence will be calculated.
4663                      If not present or C{None} an appropriate default is used.
4664        @type where: C{None} or L{escript.FunctionSpace}
4665        @return: divergence of arg.
4666        @rtype:  L{escript.Data} or L{Symbol}
4667      """      """
if axis==None:
r=0
if hasattr(arg,"getRank"): r=arg.getRank()
if hasattr(arg,"rank"): r=arg.rank
axis=r/2
4668      if isinstance(arg,Symbol):      if isinstance(arg,Symbol):
4669         return Transpose_Symbol(arg,axis=r)          dim=arg.getDim()
4670      if isinstance(arg,escript.Data):      elif isinstance(arg,escript.Data):
4671         # hack for transpose          dim=arg.getDomain().getDim()
r=arg.getRank()
if r!=2: raise ValueError,"Tranpose only avalaible for rank 2 objects"
s=arg.getShape()
out=escript.Data(0.,(s[1],s[0]),arg.getFunctionSpace())
for i in range(s[0]):
for j in range(s[1]):
out[j,i]=arg[i,j]
return out
# end hack for transpose
return arg.transpose(axis)
4672      else:      else:
4673         return numarray.transpose(arg,axis=axis)          raise TypeError,"div: argument type not supported"
4674        if not arg.getShape()==(dim,):
4675          raise ValueError,"div: expected shape is (%s,)"%dim
4677
4678  def trace(arg,axis0=0,axis1=1):  def jump(arg,domain=None):
4679      """      """
4680      Return      returns the jump of arg across the continuity of the domain
4681
4682      @param arg:      @param arg: argument
4683        @type arg: L{escript.Data} or L{Symbol}
4684        @param domain: the domain where the discontinuity is located. If domain is not present or equal to C{None}
4685                       the domain of arg is used. If arg is a L{Symbol} the domain must be present.
4686        @type domain: C{None} or L{escript.Domain}
4687        @return: jump of arg
4688        @rtype:  L{escript.Data} or L{Symbol}
4689      """      """
4690      if isinstance(arg,Symbol):      if domain==None: domain=arg.getDomain()
4691         s=list(arg.getShape())              return interpolate(arg,escript.FunctionOnContactOne(domain))-interpolate(arg,escript.FunctionOnContactZero(domain))
s=tuple(s[0:axis0]+s[axis0+1:axis1]+s[axis1+1:])
return Trace_Symbol(arg,axis0=axis0,axis1=axis1)
elif isinstance(arg,escript.Data):
# hack for trace
s=arg.getShape()
if s[axis0]!=s[axis1]:
raise ValueError,"illegal axis in trace"
out=escript.Scalar(0.,arg.getFunctionSpace())
for i in range(s[axis0]):
out+=arg[i,i]
return out
# end hack for trace
else:
return numarray.trace(arg,axis0=axis0,axis1=axis1)
4692
4693    def L2(arg):
4694        """
4695        returns the L2 norm of arg at where
4696
4697        @param arg: function which L2 to be calculated.
4698        @type arg: L{escript.Data} or L{Symbol}
4699        @return: L2 norm of arg.
4700        @rtype:  L{float} or L{Symbol}
4701        @note: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
4702        """
4703        return sqrt(integrate(inner(arg,arg)))
4704    #=============================
4705    #
4706
4707  def reorderComponents(arg,index):  def reorderComponents(arg,index):
4708      """      """
4709      resorts the component of arg according to index      resorts the component of arg according to index
4710
4711      """      """
4712      pass      raise NotImplementedError
4713  #  #
4714  # \$Log: util.py,v \$  # \$Log: util.py,v \$
4715  # Revision 1.14.2.16  2005/10/19 06:09:57  gross  # Revision 1.14.2.16  2005/10/19 06:09:57  gross

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