/[escript]/trunk/escript/py_src/util.py

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

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-revision 441 by gross,
Fri Jan 20 03:40:39 2006 UTC
+revision 881 by gross,
Thu Oct 26 02:54:47 2006 UTC
 Line 1
  # $Id$
- #
- #      COPYRIGHT ACcESS 2004 -  All Rights Reserved
- #
- #   This software is the property of ACcESS.  No part of this code
- #   may be copied in any form or by any means without the expressed written
- #   consent of ACcESS.  Copying, use or modification of this software
- #   by any unauthorised person is illegal unless that
- #   person has a software license agreement with ACcESS.
- #
  """
  Utility functions for escript
- @remark:  This module is under construction and is still tested!!!
  @var __author__: name of author
- @var __licence__: licence agreement
+ @var __copyright__: copyrights
+ @var __license__: licence agreement
  @var __url__: url entry point on documentation
  @var __version__: version
  @var __date__: date of the version
  """
  __author__="Lutz Gross, l.gross@uq.edu.au"
- __licence__="contact: esys@access.uq.edu.au"
+ __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
+                     http://www.access.edu.au
+                 Primary Business: Queensland, Australia"""
+ __license__="""Licensed under the Open Software License version 3.0
+              http://www.opensource.org/licenses/osl-3.0.php"""
  __url__="http://www.iservo.edu.au/esys/escript"
  __version__="$Revision$"
  __date__="$Date$"
-Line 30 
 __date__="$Date$"
+Line 24 
 __date__="$Date$"
  import math
  import numarray
- import numarray.linear_algebra
  import escript
  import os
+ from esys.escript import C_GeneralTensorProduct
- # missing tests:
- # def pokeShape(arg):
- # def pokeDim(arg):
- # def commonShape(arg0,arg1):
- # def commonDim(*args):
- # def testForZero(arg):
- # def matchType(arg0=0.,arg1=0.):
- # def matchShape(arg0,arg1):
- # def transpose(arg,axis=None):
- # def reorderComponents(arg,index):
- #
- # slicing: get
- #          set
- #
- # and derivatives
  #=========================================================
  #   some helpers:
-Line 60 
 def saveVTK(filename,domain=None,**data)
+Line 35 
 def saveVTK(filename,domain=None,**data)
      """
      writes a L{Data} objects into a files using the the VTK XML file format.
-     Example:
+     Example::
         tmp=Scalar(..)
         v=Vector(..)
-Line 88 
 def saveDX(filename,domain=None,**data):
+Line 63 
 def saveDX(filename,domain=None,**data):
      """
      writes a L{Data} objects into a files using the the DX file format.
-     Example:
+     Example::
         tmp=Scalar(..)
         v=Vector(..)
-Line 117 
 def kronecker(d=3):
+Line 92 
 def kronecker(d=3):
     return the kronecker S{delta}-symbol
     @param d: dimension or an object that has the C{getDim} method defining the dimension
-    @type d: C{int} or any object with a C{getDim} method
+    @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
-    @rtype d: L{numarray.NumArray} of rank 2.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 2.
-    @remark: the function is identical L{identity}
     """
     return identityTensor(d)
-Line 135 
 def identity(shape=()):
+Line 109 
 def identity(shape=()):
     @raise ValueError: if len(shape)>2.
     """
     if len(shape)>0:
-       out=numarray.zeros(shape+shape,numarray.Float)
+       out=numarray.zeros(shape+shape,numarray.Float64)
        if len(shape)==1:
            for i0 in range(shape[0]):
               out[i0,i0]=1.
        elif len(shape)==2:
            for i0 in range(shape[0]):
               for i1 in range(shape[1]):
-Line 155 
 def identityTensor(d=3):
+Line 128 
 def identityTensor(d=3):
     return the dxd identity matrix
     @param d: dimension or an object that has the C{getDim} method defining the dimension
-    @type d: C{int} or any object with a C{getDim} method
+    @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
-    @rtype: L{numarray.NumArray} of rank 2.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 2
     """
-    if hasattr(d,"getDim"):
+    if isinstance(d,escript.FunctionSpace):
-       d=d.getDim()
+        return escript.Data(identity((d.getDim(),)),d)
-    return identity(shape=(d,))
+    elif isinstance(d,escript.Domain):
+        return identity((d.getDim(),))
+    else:
+        return identity((d,))
  def identityTensor4(d=3):
     """
-Line 170 
 def identityTensor4(d=3):
+Line 146 
 def identityTensor4(d=3):
     @param d: dimension or an object that has the C{getDim} method defining the dimension
     @type d: C{int} or any object with a C{getDim} method
     @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
-    @rtype: L{numarray.NumArray} of rank 4.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 4.
     """
-    if hasattr(d,"getDim"):
+    if isinstance(d,escript.FunctionSpace):
-       d=d.getDim()
+        return escript.Data(identity((d.getDim(),d.getDim())),d)
-    return identity((d,d))
+    elif isinstance(d,escript.Domain):
+        return identity((d.getDim(),d.getDim()))
+    else:
+        return identity((d,d))
  def unitVector(i=0,d=3):
     """
-Line 183 
 def unitVector(i=0,d=3):
+Line 162 
 def unitVector(i=0,d=3):
     @param i: index
     @type i: C{int}
     @param d: dimension or an object that has the C{getDim} method defining the dimension
-    @type d: C{int} or any object with a C{getDim} method
+    @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
     @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise
-    @rtype: L{numarray.NumArray} of rank 1.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 1
     """
     return kronecker(d)[i]
-Line 241 
 def inf(arg):
+Line 220 
 def inf(arg):
      @param arg: argument
      @type arg: C{float}, C{int}, L{escript.Data}, L{numarray.NumArray}.
-     @return : minimum value of arg over all components and all data points
+     @return: minimum value of arg over all components and all data points
      @rtype: C{float}
      @raise TypeError: if type of arg cannot be processed
      """
-Line 330 
 def commonDim(*args):
+Line 309 
 def commonDim(*args):
      """
      identifies, if possible, the spatial dimension across a set of objects which may or my not have a spatial dimension.
-     @param *args: given objects
+     @param args: given objects
      @return: the spatial dimension of the objects with identifiable dimension (see L{pokeDim}). If none the objects has
               a spatial dimension C{None} is returned.
      @rtype: C{int} or C{None}
-Line 352 
 def testForZero(arg):
+Line 331 
 def testForZero(arg):
      @param arg: a given object
      @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int}
-     @return : True if the argument is identical to zero.
+     @return: True if the argument is identical to zero.
-     @rtype : C{bool}
+     @rtype: C{bool}
      """
      if isinstance(arg,numarray.NumArray):
         return not Lsup(arg)>0.
-Line 386 
 def matchType(arg0=0.,arg1=0.):
+Line 365 
 def matchType(arg0=0.,arg1=0.):
         elif isinstance(arg1,escript.Data):
            arg0=escript.Data(arg0,arg1.getFunctionSpace())
         elif isinstance(arg1,float):
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
            pass
         else:
-Line 412 
 def matchType(arg0=0.,arg1=0.):
+Line 391 
 def matchType(arg0=0.,arg1=0.):
         elif isinstance(arg1,escript.Data):
            pass
         elif isinstance(arg1,float):
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
            pass
         else:
            raise TypeError,"function: Unknown type of second argument."
      elif isinstance(arg0,float):
         if isinstance(arg1,numarray.NumArray):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
         elif isinstance(arg1,escript.Data):
            arg0=escript.Data(arg0,arg1.getFunctionSpace())
         elif isinstance(arg1,float):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
         else:
            raise TypeError,"function: Unknown type of second argument."
      elif isinstance(arg0,int):
         if isinstance(arg1,numarray.NumArray):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
         elif isinstance(arg1,escript.Data):
            arg0=escript.Data(float(arg0),arg1.getFunctionSpace())
         elif isinstance(arg1,float):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
         else:
            raise TypeError,"function: Unknown type of second argument."
      else:
-Line 456 
 def matchType(arg0=0.,arg1=0.):
+Line 435 
 def matchType(arg0=0.,arg1=0.):
  def matchShape(arg0,arg1):
      """
+     return representations of arg0 amd arg1 which ahve the same shape
-     If shape is not given the shape "largest" shape of args is used.
+     @param arg0: a given object
+     @type arg0: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, L{Symbol}
-     @param args: a given ob
+     @param arg1: a given object
-     @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int}
+     @type arg1: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, L{Symbol}
-     @return: True if the argument is identical to zero.
+     @return: C{arg0} and C{arg1} where copies are returned when the shape has to be changed.
-     @rtype: C{list} of C{int}
+     @rtype: C{tuple}
      """
      sh=commonShape(arg0,arg1)
      sh0=pokeShape(arg0)
      sh1=pokeShape(arg1)
      if len(sh0)<len(sh):
-        return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float)),arg1
+        return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float64)),arg1
      elif len(sh1)<len(sh):
-        return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float))
+        return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float64))
      else:
         return arg0,arg1
  #=========================================================
-Line 491 
 class Symbol(object):
+Line 470 
 class Symbol(object):
         Creates an instance of a symbol of a given shape. The symbol may depending on a list of arguments args which may be
         symbols or any other object.
-        @param arg: the arguments of the symbol.
+        @param args: the arguments of the symbol.
-        @type arg: C{list}
+        @type args: C{list}
         @param shape: the shape
         @type shape: C{tuple} of C{int}
         @param dim: spatial dimension of the symbol. If dim=C{None} the spatial dimension is undefined.
-Line 535 
 class Symbol(object):
+Line 514 
 class Symbol(object):
         """
         the shape of the symbol.
-        @return : the shape of the symbol.
+        @return: the shape of the symbol.
         @rtype: C{tuple} of C{int}
         """
         return self.__shape
-Line 544 
 class Symbol(object):
+Line 523 
 class Symbol(object):
         """
         the spatial dimension
-        @return : the spatial dimension
+        @return: the spatial dimension
         @rtype: C{int} if the dimension is defined. Otherwise C{None} is returned.
         """
         return self.__dim
-Line 568 
 class Symbol(object):
+Line 547 
 class Symbol(object):
         """
         substitutes symbols in the arguments of this object and returns the result as a list.
-        @param argvals: L{Symbols} and their substitutes. The L{Symbol} u in the expression defining this object is replaced by argvals[u].
+        @param argvals: L{Symbol} and their substitutes. The L{Symbol} u in the expression defining this object is replaced by argvals[u].
         @type argvals: C{dict} with keywords of type L{Symbol}.
         @rtype: C{list} of objects
-        @return: list of the object assigned to the arguments through substitution or for the arguments which are not L{Symbols} the value assigned to the argument at instantiation.
+        @return: list of the object assigned to the arguments through substitution or for the arguments which are not L{Symbol} the value assigned to the argument at instantiation.
         """
         out=[]
         for a in self.getArgument():
-Line 597 
 class Symbol(object):
+Line 576 
 class Symbol(object):
            else:
                s=pokeShape(s)+arg.getShape()
                if len(s)>0:
-                  out.append(numarray.zeros(s),numarray.Float)
+                  out.append(numarray.zeros(s),numarray.Float64)
                else:
                   out.append(a)
         return out
-Line 687 
 class Symbol(object):
+Line 666 
 class Symbol(object):
         else:
            s=self.getShape()+arg.getShape()
            if len(s)>0:
-              return numarray.zeros(s,numarray.Float)
+              return numarray.zeros(s,numarray.Float64)
            else:
               return 0.
-Line 695 
 class Symbol(object):
+Line 674 
 class Symbol(object):
         """
         returns -self.
-        @return:  a S{Symbol} representing the negative of the object
+        @return:  a L{Symbol} representing the negative of the object
         @rtype: L{DependendSymbol}
         """
         return self*(-1.)
-Line 704 
 class Symbol(object):
+Line 683 
 class Symbol(object):
         """
         returns +self.
-        @return:  a S{Symbol} representing the positive of the object
+        @return:  a L{Symbol} representing the positive of the object
         @rtype: L{DependendSymbol}
         """
         return self*(1.)
     def __abs__(self):
         """
-        returns a S{Symbol} representing the absolute value of the object.
+        returns a L{Symbol} representing the absolute value of the object.
         """
         return Abs_Symbol(self)
-Line 721 
 class Symbol(object):
+Line 700 
 class Symbol(object):
         @param other: object to be added to this object
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return:  a S{Symbol} representing the sum of this object and C{other}
+        @return:  a L{Symbol} representing the sum of this object and C{other}
         @rtype: L{DependendSymbol}
         """
         return add(self,other)
-Line 732 
 class Symbol(object):
+Line 711 
 class Symbol(object):
         @param other: object this object is added to
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the sum of C{other} and this object object
+        @return: a L{Symbol} representing the sum of C{other} and this object object
         @rtype: L{DependendSymbol}
         """
         return add(other,self)
-Line 743 
 class Symbol(object):
+Line 722 
 class Symbol(object):
         @param other: object to be subtracted from this object
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the difference of C{other} and this object
+        @return: a L{Symbol} representing the difference of C{other} and this object
         @rtype: L{DependendSymbol}
         """
         return add(self,-other)
-Line 754 
 class Symbol(object):
+Line 733 
 class Symbol(object):
         @param other: object this object is been subtracted from
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the difference of this object and C{other}.
+        @return: a L{Symbol} representing the difference of this object and C{other}.
         @rtype: L{DependendSymbol}
         """
         return add(-self,other)
-Line 765 
 class Symbol(object):
+Line 744 
 class Symbol(object):
         @param other: object to be mutiplied by this object
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the product of the object and C{other}.
+        @return: a L{Symbol} representing the product of the object and C{other}.
         @rtype: L{DependendSymbol} or 0 if other is identical to zero.
         """
         return mult(self,other)
-Line 776 
 class Symbol(object):
+Line 755 
 class Symbol(object):
         @param other: object this object is multiplied with
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the product of C{other} and the object.
+        @return: a L{Symbol} representing the product of C{other} and the object.
         @rtype: L{DependendSymbol} or 0 if other is identical to zero.
         """
         return mult(other,self)
-Line 787 
 class Symbol(object):
+Line 766 
 class Symbol(object):
         @param other: object dividing this object
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the quotient of this object and C{other}
+        @return: a L{Symbol} representing the quotient of this object and C{other}
         @rtype: L{DependendSymbol}
         """
         return quotient(self,other)
-Line 798 
 class Symbol(object):
+Line 777 
 class Symbol(object):
         @param other: object dividing this object
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the quotient of C{other} and this object
+        @return: a L{Symbol} representing the quotient of C{other} and this object
         @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero.
         """
         return quotient(other,self)
-Line 809 
 class Symbol(object):
+Line 788 
 class Symbol(object):
         @param other: exponent
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the power of this object to C{other}
+        @return: a L{Symbol} representing the power of this object to C{other}
         @rtype: L{DependendSymbol} or 1 if C{other} is identical to zero.
         """
         return power(self,other)
-Line 820 
 class Symbol(object):
+Line 799 
 class Symbol(object):
         @param other: basis
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the power of C{other} to this object
+        @return: a L{Symbol} representing the power of C{other} to this object
         @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero.
         """
         return power(other,self)
+    def __getitem__(self,index):
+        """
+        returns the slice defined by index
+        @param index: defines a
+        @type index: C{slice} or C{int} or a C{tuple} of them
+        @return: a L{Symbol} representing the slice defined by index
+        @rtype: L{DependendSymbol}
+        """
+        return GetSlice_Symbol(self,index)
  class DependendSymbol(Symbol):
     """
     DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal.
     Two DependendSymbol are equal if they have the same shape, the same arguments and one of them has an unspecified spatial dimension or the spatial dimension is identical
-    Example:
+    Example::
-    u1=Symbol(shape=(3,4),dim=2,args=[4.])
+      u1=Symbol(shape=(3,4),dim=2,args=[4.])
-    u2=Symbol(shape=(3,4),dim=2,args=[4.])
+      u2=Symbol(shape=(3,4),dim=2,args=[4.])
-    print u1==u2
+      print u1==u2
-    False
+      False
-       but
+    but::
-    u1=DependendSymbol(shape=(3,4),dim=2,args=[4.])
+      u1=DependendSymbol(shape=(3,4),dim=2,args=[4.])
-    u2=DependendSymbol(shape=(3,4),dim=2,args=[4.])
+      u2=DependendSymbol(shape=(3,4),dim=2,args=[4.])
-    u3=DependendSymbol(shape=(2,),dim=2,args=[4.])
+      u3=DependendSymbol(shape=(2,),dim=2,args=[4.])
-    print u1==u2, u1==u3
+      print u1==u2, u1==u3
-    True False
+      True False
     @note: DependendSymbol should be used as return value of functions with L{Symbol} arguments. This will allow the optimizer to remove redundant function calls.
     """
-Line 875 
 class DependendSymbol(Symbol):
+Line 865 
 class DependendSymbol(Symbol):
  #=========================================================
  #  Unary operations prserving the shape
  #========================================================
+ class GetSlice_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing getting a slice for a L{Symbol}
+    """
+    def __init__(self,arg,index):
+       """
+       initialization of wherePositive L{Symbol} with argument arg
+       @param arg: argument
+       @type arg: L{Symbol}.
+       @param index: defines index
+       @type index: C{slice} or C{int} or a C{tuple} of them
+       @raises IndexError: if length of index is larger than rank of arg or a index start or stop is out of range
+       @raises ValueError: if a step is given
+       """
+       if not isinstance(index,tuple): index=(index,)
+       if len(index)>arg.getRank():
+            raise IndexError,"GetSlice_Symbol: index out of range."
+       sh=()
+       index2=()
+       for i in range(len(index)):
+          ix=index[i]
+          if isinstance(ix,int):
+             if ix<0 or ix>=arg.getShape()[i]:
+                raise ValueError,"GetSlice_Symbol: index out of range."
+             index2=index2+(ix,)
+          else:
+            if not ix.step==None:
+              raise ValueError,"GetSlice_Symbol: steping is not supported."
+            if ix.start==None:
+               s=0
+            else:
+               s=ix.start
+            if ix.stop==None:
+               e=arg.getShape()[i]
+            else:
+               e=ix.stop
+               if e>arg.getShape()[i]:
+                  raise IndexError,"GetSlice_Symbol: index out of range."
+            index2=index2+(slice(s,e),)
+            if e>s:
+                sh=sh+(e-s,)
+            elif s>e:
+                raise IndexError,"GetSlice_Symbol: slice start must be less or equal slice end"
+       for i in range(len(index),arg.getRank()):
+           index2=index2+(slice(0,arg.getShape()[i]),)
+           sh=sh+(arg.getShape()[i],)
+       super(GetSlice_Symbol, self).__init__(args=[arg,index2],shape=sh,dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "%s.__getitem__(%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"GetItem_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          args=self.getSubstitutedArguments(argvals)
+          arg=args[0]
+          index=args[1]
+          return arg.__getitem__(index)
  def log10(arg):
     """
     returns base-10 logarithm of argument arg
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 903 
 def wherePositive(arg):
+Line 981 
 def wherePositive(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._wherePositive()
-Line 949 
 class WherePositive_Symbol(DependendSymb
+Line 1027 
 class WherePositive_Symbol(DependendSymb
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 985 
 def whereNegative(arg):
+Line 1063 
 def whereNegative(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNegative()
-Line 1031 
 class WhereNegative_Symbol(DependendSymb
+Line 1109 
 class WhereNegative_Symbol(DependendSymb
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1067 
 def whereNonNegative(arg):
+Line 1145 
 def whereNonNegative(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNonNegative()
-Line 1097 
 def whereNonPositive(arg):
+Line 1175 
 def whereNonPositive(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNonPositive()
-Line 1129 
 def whereZero(arg,tol=0.):
+Line 1207 
 def whereZero(arg,tol=0.):
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
     @param tol: tolerance. values with absolute value less then tol are accepted as zero.
     @type tol: C{float}
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
-       if tol>0.:
+       return arg._whereZero(tol)
-          return whereNegative(abs(arg)-tol)
-       else:
-          return arg._whereZero()
     elif isinstance(arg,float):
        if abs(arg)<=tol:
          return 1.
-Line 1178 
 class WhereZero_Symbol(DependendSymbol):
+Line 1253 
 class WhereZero_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "whereZero(%s,tol=%s)"%(argstrs[0],argstrs[1])
-Line 1212 
 def whereNonZero(arg,tol=0.):
+Line 1287 
 def whereNonZero(arg,tol=0.):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
-       if tol>0.:
+       return arg._whereNonZero(tol)
-          return 1.-whereZero(arg,tol)
-       else:
-          return arg._whereNonZero()
     elif isinstance(arg,float):
        if abs(arg)>tol:
          return 1.
-Line 1239 
 def whereNonZero(arg,tol=0.):
+Line 1311 
 def whereNonZero(arg,tol=0.):
     else:
        raise TypeError,"whereNonZero: Unknown argument type."
+ def erf(arg):
+    """
+    returns erf of argument arg
+    @param arg: argument
+    @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @raises TypeError: if the type of the argument is not expected.
+    """
+    if isinstance(arg,escript.Data):
+       return arg._erf()
+    else:
+       raise TypeError,"erf: Unknown argument type."
  def sin(arg):
     """
     returns sine of argument arg
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1283 
 class Sin_Symbol(DependendSymbol):
+Line 1369 
 class Sin_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1335 
 def cos(arg):
+Line 1421 
 def cos(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1373 
 class Cos_Symbol(DependendSymbol):
+Line 1459 
 class Cos_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1425 
 def tan(arg):
+Line 1511 
 def tan(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1463 
 class Tan_Symbol(DependendSymbol):
+Line 1549 
 class Tan_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1515 
 def asin(arg):
+Line 1601 
 def asin(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1553 
 class Asin_Symbol(DependendSymbol):
+Line 1639 
 class Asin_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1605 
 def acos(arg):
+Line 1691 
 def acos(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1643 
 class Acos_Symbol(DependendSymbol):
+Line 1729 
 class Acos_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1695 
 def atan(arg):
+Line 1781 
 def atan(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1733 
 class Atan_Symbol(DependendSymbol):
+Line 1819 
 class Atan_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1785 
 def sinh(arg):
+Line 1871 
 def sinh(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1823 
 class Sinh_Symbol(DependendSymbol):
+Line 1909 
 class Sinh_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1875 
 def cosh(arg):
+Line 1961 
 def cosh(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 1913 
 class Cosh_Symbol(DependendSymbol):
+Line 1999 
 class Cosh_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 1965 
 def tanh(arg):
+Line 2051 
 def tanh(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2003 
 class Tanh_Symbol(DependendSymbol):
+Line 2089 
 class Tanh_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2055 
 def asinh(arg):
+Line 2141 
 def asinh(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2093 
 class Asinh_Symbol(DependendSymbol):
+Line 2179 
 class Asinh_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2145 
 def acosh(arg):
+Line 2231 
 def acosh(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2183 
 class Acosh_Symbol(DependendSymbol):
+Line 2269 
 class Acosh_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2235 
 def atanh(arg):
+Line 2321 
 def atanh(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2273 
 class Atanh_Symbol(DependendSymbol):
+Line 2359 
 class Atanh_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2325 
 def exp(arg):
+Line 2411 
 def exp(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2363 
 class Exp_Symbol(DependendSymbol):
+Line 2449 
 class Exp_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2415 
 def sqrt(arg):
+Line 2501 
 def sqrt(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2453 
 class Sqrt_Symbol(DependendSymbol):
+Line 2539 
 class Sqrt_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2505 
 def log(arg):
+Line 2591 
 def log(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2543 
 class Log_Symbol(DependendSymbol):
+Line 2629 
 class Log_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2595 
 def sign(arg):
+Line 2681 
 def sign(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2643 
 class Abs_Symbol(DependendSymbol):
+Line 2729 
 class Abs_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2695 
 def minval(arg):
+Line 2781 
 def minval(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2736 
 class Minval_Symbol(DependendSymbol):
+Line 2822 
 class Minval_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2772 
 def maxval(arg):
+Line 2858 
 def maxval(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 2813 
 class Maxval_Symbol(DependendSymbol):
+Line 2899 
 class Maxval_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if isinstance(argstrs,list):
            argstrs=argstrs[0]
-Line 2849 
 def length(arg):
+Line 2935 
 def length(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
     """
     return sqrt(inner(arg,arg))
-Line 2859 
 def trace(arg,axis_offset=0):
+Line 2945 
 def trace(arg,axis_offset=0):
     @param arg: argument
     @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @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
+    @param axis_offset: C{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
-                   axis_offset and axis_offset+1 must be equal.
+                   C{axis_offset} and axis_offset+1 must be equal.
     @type axis_offset: C{int}
     @return: trace of arg. The rank of the returned object is minus 2 of the rank of arg.
     @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
-Line 2868 
 def trace(arg,axis_offset=0):
+Line 2954 
 def trace(arg,axis_offset=0):
     if isinstance(arg,numarray.NumArray):
        sh=arg.shape
        if len(sh)<2:
-         raise ValueError,"trace: rank of argument must be greater than 1"
+         raise ValueError,"rank of argument must be greater than 1"
        if axis_offset<0 or axis_offset>len(sh)-2:
-         raise ValueError,"trace: axis_offset must be between 0 and %s"%len(sh)-2
+         raise ValueError,"axis_offset must be between 0 and %s"%len(sh)-2
        s1=1
        for i in range(axis_offset): s1*=sh[i]
        s2=1
        for i in range(axis_offset+2,len(sh)): s2*=sh[i]
        if not sh[axis_offset] == sh[axis_offset+1]:
-         raise ValueError,"trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
+         raise ValueError,"dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
        arg_reshaped=numarray.reshape(arg,(s1,sh[axis_offset],sh[axis_offset],s2))
-       out=numarray.zeros([s1,s2],numarray.Float)
+       out=numarray.zeros([s1,s2],numarray.Float64)
        for i1 in range(s1):
          for i2 in range(s2):
              for j in range(sh[axis_offset]): out[i1,i2]+=arg_reshaped[i1,j,j,i2]
        out.resize(sh[:axis_offset]+sh[axis_offset+2:])
        return out
     elif isinstance(arg,escript.Data):
-       return escript_trace(arg,axis_offset)
+       if arg.getRank()<2:
+         raise ValueError,"rank of argument must be greater than 1"
+       if axis_offset<0 or axis_offset>arg.getRank()-2:
+         raise ValueError,"axis_offset must be between 0 and %s"%arg.getRank()-2
+       s=list(arg.getShape())
+       if not s[axis_offset] == s[axis_offset+1]:
+         raise ValueError,"dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
+       return arg._trace(axis_offset)
     elif isinstance(arg,float):
-       raise TypeError,"trace: illegal argument type float."
+       raise TypeError,"illegal argument type float."
     elif isinstance(arg,int):
-       raise TypeError,"trace: illegal argument type int."
+       raise TypeError,"illegal argument type int."
     elif isinstance(arg,Symbol):
        return Trace_Symbol(arg,axis_offset)
     else:
-       raise TypeError,"trace: Unknown argument type."
+       raise TypeError,"Unknown argument type."
- def escript_trace(arg,axis_offset): # this should be escript._trace
-       "arg si a Data objects!!!"
-       if arg.getRank()<2:
-         raise ValueError,"escript_trace: rank of argument must be greater than 1"
-       if axis_offset<0 or axis_offset>arg.getRank()-2:
-         raise ValueError,"escript_trace: axis_offset must be between 0 and %s"%arg.getRank()-2
-       s=list(arg.getShape())
-       if not s[axis_offset] == s[axis_offset+1]:
-         raise ValueError,"escript_trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
-       out=escript.Data(0.,tuple(s[0:axis_offset]+s[axis_offset+2:]),arg.getFunctionSpace())
-       if arg.getRank()==2:
-          for i0 in range(s[0]):
-             out+=arg[i0,i0]
-       elif arg.getRank()==3:
-          if axis_offset==0:
-             for i0 in range(s[0]):
-                   for i2 in range(s[2]):
-                          out[i2]+=arg[i0,i0,i2]
-          elif axis_offset==1:
-             for i0 in range(s[0]):
-                for i1 in range(s[1]):
-                          out[i0]+=arg[i0,i1,i1]
-       elif arg.getRank()==4:
-          if axis_offset==0:
-             for i0 in range(s[0]):
-                   for i2 in range(s[2]):
-                      for i3 in range(s[3]):
-                          out[i2,i3]+=arg[i0,i0,i2,i3]
-          elif axis_offset==1:
-             for i0 in range(s[0]):
-                for i1 in range(s[1]):
-                      for i3 in range(s[3]):
-                          out[i0,i3]+=arg[i0,i1,i1,i3]
-          elif axis_offset==2:
-             for i0 in range(s[0]):
-                for i1 in range(s[1]):
-                   for i2 in range(s[2]):
-                          out[i0,i1]+=arg[i0,i1,i2,i2]
-       return out
  class Trace_Symbol(DependendSymbol):
     """
     L{Symbol} representing the result of the trace function
-Line 2943 
 class Trace_Symbol(DependendSymbol):
+Line 2997 
 class Trace_Symbol(DependendSymbol):
        initialization of trace L{Symbol} with argument arg
        @param arg: argument of function
        @type arg: L{Symbol}.
-       @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
+       @param axis_offset: C{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
-                   axis_offset and axis_offset+1 must be equal.
+                   C{axis_offset} and axis_offset+1 must be equal.
        @type axis_offset: C{int}
        """
        if arg.getRank()<2:
-         raise ValueError,"Trace_Symbol: rank of argument must be greater than 1"
+         raise ValueError,"rank of argument must be greater than 1"
        if axis_offset<0 or axis_offset>arg.getRank()-2:
-         raise ValueError,"Trace_Symbol: axis_offset must be between 0 and %s"%arg.getRank()-2
+         raise ValueError,"axis_offset must be between 0 and %s"%arg.getRank()-2
        s=list(arg.getShape())
        if not s[axis_offset] == s[axis_offset+1]:
-         raise ValueError,"Trace_Symbol: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
+         raise ValueError,"dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
        super(Trace_Symbol,self).__init__(args=[arg,axis_offset],shape=tuple(s[0:axis_offset]+s[axis_offset+2:]),dim=arg.getDim())
     def getMyCode(self,argstrs,format="escript"):
-Line 2966 
 class Trace_Symbol(DependendSymbol):
+Line 3020 
 class Trace_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "trace(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
-Line 3008 
 class Trace_Symbol(DependendSymbol):
+Line 3062 
 class Trace_Symbol(DependendSymbol):
        else:
           return trace(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
+ def transpose(arg,axis_offset=None):
+    """
+    returns the transpose of arg by swaping the first C{axis_offset} and the last rank-axis_offset components.
+    @param arg: argument
+    @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}, C{float}, C{int}
+    @param axis_offset: the first C{axis_offset} components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+                        if C{axis_offset} is not present C{int(r/2)} where r is the rank of arg is used.
+    @type axis_offset: C{int}
+    @return: transpose of arg
+    @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray},C{float}, C{int} depending on the type of arg.
+    """
+    if isinstance(arg,numarray.NumArray):
+       if axis_offset==None: axis_offset=int(arg.rank/2)
+       return numarray.transpose(arg,axes=range(axis_offset,arg.rank)+range(0,axis_offset))
+    elif isinstance(arg,escript.Data):
+       r=arg.getRank()
+       if axis_offset==None: axis_offset=int(r/2)
+       if axis_offset<0 or axis_offset>r:
+         raise ValueError,"axis_offset must be between 0 and %s"%r
+       return arg._transpose(axis_offset)
+    elif isinstance(arg,float):
+       if not ( axis_offset==0 or axis_offset==None):
+         raise ValueError,"axis_offset must be 0 for float argument"
+       return arg
+    elif isinstance(arg,int):
+       if not ( axis_offset==0 or axis_offset==None):
+         raise ValueError,"axis_offset must be 0 for int argument"
+       return float(arg)
+    elif isinstance(arg,Symbol):
+       if axis_offset==None: axis_offset=int(arg.getRank()/2)
+       return Transpose_Symbol(arg,axis_offset)
+    else:
+       raise TypeError,"Unknown argument type."
+ class Transpose_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the transpose function
+    """
+    def __init__(self,arg,axis_offset=None):
+       """
+       initialization of transpose L{Symbol} with argument arg
+       @param arg: argument of function
+       @type arg: L{Symbol}.
+       @param axis_offset: the first C{axis_offset} components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+                        if C{axis_offset} is not present C{int(r/2)} where r is the rank of arg is used.
+       @type axis_offset: C{int}
+       """
+       if axis_offset==None: axis_offset=int(arg.getRank()/2)
+       if axis_offset<0 or axis_offset>arg.getRank():
+         raise ValueError,"axis_offset must be between 0 and %s"%arg.getRank()
+       s=arg.getShape()
+       super(Transpose_Symbol,self).__init__(args=[arg,axis_offset],shape=s[axis_offset:]+s[:axis_offset],dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"Transpose_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          arg=self.getSubstitutedArguments(argvals)
+          return transpose(arg[0],axis_offset=arg[1])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return transpose(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
+ def swap_axes(arg,axis0=0,axis1=1):
+    """
+    returns the swap of arg by swaping the components axis0 and axis1
+    @param arg: argument
+    @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
+    @param axis0: axis. C{axis0} must be non-negative and less than the rank of arg.
+    @type axis0: C{int}
+    @param axis1: axis. C{axis1} must be non-negative and less than the rank of arg.
+    @type axis1: C{int}
+    @return: C{arg} with swaped components
+    @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    """
+    if axis0 > axis1:
+       axis0,axis1=axis1,axis0
+    if isinstance(arg,numarray.NumArray):
+       return numarray.swapaxes(arg,axis0,axis1)
+    elif isinstance(arg,escript.Data):
+       return arg._swap_axes(axis0,axis1)
+    elif isinstance(arg,float):
+       raise TyepError,"float argument is not supported."
+    elif isinstance(arg,int):
+       raise TyepError,"int argument is not supported."
+    elif isinstance(arg,Symbol):
+       return SwapAxes_Symbol(arg,axis0,axis1)
+    else:
+       raise TypeError,"Unknown argument type."
+ class SwapAxes_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the swap function
+    """
+    def __init__(self,arg,axis0=0,axis1=1):
+       """
+       initialization of swap L{Symbol} with argument arg
+       @param arg: argument
+       @type arg: L{Symbol}.
+       @param axis0: axis. C{axis0} must be non-negative and less than the rank of arg.
+       @type axis0: C{int}
+       @param axis1: axis. C{axis1} must be non-negative and less than the rank of arg.
+       @type axis1: C{int}
+       """
+       if arg.getRank()<2:
+          raise ValueError,"argument must have at least rank 2."
+       if axis0<0 or axis0>arg.getRank()-1:
+          raise ValueError,"axis0 must be between 0 and %s"%arg.getRank()-1
+       if axis1<0 or axis1>arg.getRank()-1:
+          raise ValueError,"axis1 must be between 0 and %s"%arg.getRank()-1
+       if axis0 == axis1:
+          raise ValueError,"axis indices must be different."
+       if axis0 > axis1:
+          axis0,axis1=axis1,axis0
+       s=arg.getShape()
+       s_out=[]
+       for i in range(len(s)):
+          if i == axis0:
+             s_out.append(s[axis1])
+          elif i == axis1:
+             s_out.append(s[axis0])
+          else:
+             s_out.append(s[i])
+       super(SwapAxes_Symbol,self).__init__(args=[arg,axis0,axis1],shape=tuple(s_out),dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "swap(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"SwapAxes_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          arg=self.getSubstitutedArguments(argvals)
+          return swap_axes(arg[0],axis0=arg[1],axis1=arg[2])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return swap_axes(self.getDifferentiatedArguments(arg)[0],axis0=self.getArgument()[1],axis1=self.getArgument()[2])
+ def symmetric(arg):
+     """
+     returns the symmetric part of the square matrix arg. This is (arg+transpose(arg))/2
+     @param arg: square matrix. Must have rank 2 or 4 and be square.
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: symmetric part of arg
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg,numarray.NumArray):
+       if arg.rank==2:
+         if not (arg.shape[0]==arg.shape[1]):
+            raise ValueError,"argument must be square."
+       elif arg.rank==4:
+         if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
+            raise ValueError,"argument must be square."
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+       return (arg+transpose(arg))/2
+     elif isinstance(arg,escript.Data):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+         return arg._symmetric()
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+         return arg._symmetric()
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     elif isinstance(arg,Symbol):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+       return (arg+transpose(arg))/2
+     else:
+       raise TypeError,"symmetric: Unknown argument type."
+ def nonsymmetric(arg):
+     """
+     returns the nonsymmetric part of the square matrix arg. This is (arg-transpose(arg))/2
+     @param arg: square matrix. Must have rank 2 or 4 and be square.
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: nonsymmetric part of arg
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg,numarray.NumArray):
+       if arg.rank==2:
+         if not (arg.shape[0]==arg.shape[1]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       elif arg.rank==4:
+         if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       else:
+         raise ValueError,"nonsymmetric: rank 2 or 4 is required."
+       return (arg-transpose(arg))/2
+     elif isinstance(arg,escript.Data):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+         return arg._nonsymmetric()
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+         return arg._nonsymmetric()
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     elif isinstance(arg,Symbol):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       else:
+         raise ValueError,"nonsymmetric: rank 2 or 4 is required."
+       return (arg-transpose(arg))/2
+     else:
+       raise TypeError,"nonsymmetric: Unknown argument type."
  def inverse(arg):
      """
      returns the inverse of the square matrix arg.
-     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal
+     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
      @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-     @return: inverse arg_inv of the argument. It will be matrixmul(inverse(arg),arg) almost equal to kronecker(arg.getShape()[0])
+     @return: inverse arg_inv of the argument. It will be matrix_mult(inverse(arg),arg) almost equal to kronecker(arg.getShape()[0])
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     @note: for L{escript.Data} objects the dimension is restricted to 3.
      """
+     import numarray.linear_algebra # This statement should be after the next statement but then somehow numarray is gone.
      if isinstance(arg,numarray.NumArray):
        return numarray.linear_algebra.inverse(arg)
      elif isinstance(arg,escript.Data):
-Line 3109 
 class Inverse_Symbol(DependendSymbol):
+Line 3482 
 class Inverse_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "inverse(%s)"%argstrs[0]
-Line 3149 
 class Inverse_Symbol(DependendSymbol):
+Line 3522 
 class Inverse_Symbol(DependendSymbol):
        if arg==self:
           return identity(self.getShape())
        else:
-          return -matrixmult(matrixmult(self,self.getDifferentiatedArguments(arg)[0]),self)
+          return -matrix_mult(matrix_mult(self,self.getDifferentiatedArguments(arg)[0]),self)
+ def eigenvalues(arg):
+     """
+     returns the eigenvalues of the square matrix arg.
+     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
+                 arg must be symmetric, ie. transpose(arg)==arg (this is not checked).
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the eigenvalues in increasing order.
+     @rtype: L{numarray.NumArray},L{escript.Data}, L{Symbol} depending on the input.
+     @note: for L{escript.Data} and L{Symbol} objects the dimension is restricted to 3.
+     """
+     if isinstance(arg,numarray.NumArray):
+       out=numarray.linear_algebra.eigenvalues((arg+numarray.transpose(arg))/2.)
+       out.sort()
+       return out
+     elif isinstance(arg,escript.Data):
+       return arg._eigenvalues()
+     elif isinstance(arg,Symbol):
+       if not arg.getRank()==2:
+         raise ValueError,"eigenvalues: argument must have rank 2"
+       s=arg.getShape()
+       if not s[0] == s[1]:
+         raise ValueError,"eigenvalues: argument must be a square matrix."
+       if s[0]==1:
+           return arg[0]
+       elif s[0]==2:
+           arg1=symmetric(arg)
+           A11=arg1[0,0]
+           A12=arg1[0,1]
+           A22=arg1[1,1]
+           trA=(A11+A22)/2.
+           A11-=trA
+           A22-=trA
+           s=sqrt(A12**2-A11*A22)
+           return trA+s*numarray.array([-1.,1.],type=numarray.Float64)
+       elif s[0]==3:
+           arg1=symmetric(arg)
+           A11=arg1[0,0]
+           A12=arg1[0,1]
+           A22=arg1[1,1]
+           A13=arg1[0,2]
+           A23=arg1[1,2]
+           A33=arg1[2,2]
+           trA=(A11+A22+A33)/3.
+           A11-=trA
+           A22-=trA
+           A33-=trA
+           A13_2=A13**2
+           A23_2=A23**2
+           A12_2=A12**2
+           p=A13_2+A23_2+A12_2+(A11**2+A22**2+A33**2)/2.
+           q=A13_2*A22+A23_2*A11+A12_2*A33-A11*A22*A33-2*A12*A23*A13
+           sq_p=sqrt(p/3.)
+           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
+           sq_p*=2.
+           f=cos(alpha_3)               *numarray.array([0.,0.,1.],type=numarray.Float64) \
+            -cos(alpha_3+numarray.pi/3.)*numarray.array([0.,1.,0.],type=numarray.Float64) \
+            -cos(alpha_3-numarray.pi/3.)*numarray.array([1.,0.,0.],type=numarray.Float64)
+           return trA+sq_p*f
+       else:
+          raise TypeError,"eigenvalues: only matrix dimensions 1,2,3 are supported right now."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     else:
+       raise TypeError,"eigenvalues: Unknown argument type."
+ def eigenvalues_and_eigenvectors(arg):
+     """
+     returns the eigenvalues and eigenvectors of the square matrix arg.
+     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
+                 arg must be symmetric, ie. transpose(arg)==arg (this is not checked).
+     @type arg: L{escript.Data}
+     @return: the eigenvalues and eigenvectors. The eigenvalues are ordered by increasing value. The
+              eigenvectors are orthogonal and normalized. If V are the eigenvectors than V[:,i] is
+              the eigenvector coresponding to the i-th eigenvalue.
+     @rtype: L{tuple} of L{escript.Data}.
+     @note: The dimension is restricted to 3.
+     """
+     if isinstance(arg,numarray.NumArray):
+       raise TypeError,"eigenvalues_and_eigenvectors is not supporting numarray arguments"
+     elif isinstance(arg,escript.Data):
+       return arg._eigenvalues_and_eigenvectors()
+     elif isinstance(arg,Symbol):
+       raise TypeError,"eigenvalues_and_eigenvectors is not supporting Symbol arguments"
+     elif isinstance(arg,float):
+       return (numarray.array([[arg]],numarray.Float),numarray.ones((1,1),numarray.Float))
+     elif isinstance(arg,int):
+       return (numarray.array([[arg]],numarray.Float),numarray.ones((1,1),numarray.Float))
+     else:
+       raise TypeError,"eigenvalues: Unknown argument type."
  #=======================================================
  #  Binary operations:
  #=======================================================
-Line 3209 
 class Add_Symbol(DependendSymbol):
+Line 3676 
 class Add_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="str" or format=="text":
           return "(%s)+(%s)"%(argstrs[0],argstrs[1])
-Line 3268 
 def mult(arg0,arg1):
+Line 3735 
 def mult(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]) or testForZero(args[1]):
-           return numarray.zeros(pokeShape(args[0]),numarray.Float)
+           return numarray.zeros(pokeShape(args[0]),numarray.Float64)
         else:
            if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) :
                return Mult_Symbol(args[0],args[1])
-Line 3308 
 class Mult_Symbol(DependendSymbol):
+Line 3775 
 class Mult_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="str" or format=="text":
           return "(%s)*(%s)"%(argstrs[0],argstrs[1])
-Line 3368 
 def quotient(arg0,arg1):
+Line 3835 
 def quotient(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]):
-           return numarray.zeros(pokeShape(args[0]),numarray.Float)
+           return numarray.zeros(pokeShape(args[0]),numarray.Float64)
         elif isinstance(args[0],Symbol):
            if isinstance(args[1],Symbol):
               return Quotient_Symbol(args[0],args[1])
-Line 3413 
 class Quotient_Symbol(DependendSymbol):
+Line 3880 
 class Quotient_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="str" or format=="text":
           return "(%s)/(%s)"%(argstrs[0],argstrs[1])
-Line 3474 
 def power(arg0,arg1):
+Line 3941 
 def power(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]):
-           return numarray.zeros(args[0],numarray.Float)
+           return numarray.zeros(pokeShape(args[0]),numarray.Float64)
         elif testForZero(args[1]):
-           return numarray.ones(args[0],numarray.Float)
+           return numarray.ones(pokeShape(args[1]),numarray.Float64)
         elif isinstance(args[0],Symbol) or isinstance(args[1],Symbol):
            return Power_Symbol(args[0],args[1])
         elif isinstance(args[0],numarray.NumArray) and not isinstance(args[1],numarray.NumArray):
-Line 3517 
 class Power_Symbol(DependendSymbol):
+Line 3984 
 class Power_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str" or format=="text":
           return "(%s)**(%s)"%(argstrs[0],argstrs[1])
-Line 3599 
 def minimum(*args):
+Line 4066 
 def minimum(*args):
            out=add(out,mult(whereNegative(diff),diff))
      return out
- def clip(arg,minval=0.,maxval=1.):
+ def clip(arg,minval=None,maxval=None):
      """
      cuts the values of arg between minval and maxval
      @param arg: argument
      @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float}
-     @param minval: lower range
+     @param minval: lower range. If None no lower range is applied
-     @type arg: C{float}
+     @type minval: C{float} or C{None}
-     @param maxval: upper range
+     @param maxval: upper range. If None no upper range is applied
-     @type arg: C{float}
+     @type maxval: C{float} or C{None}
      @return: is on object with all its value between minval and maxval. value of the argument that greater then minval and
               less then maxval are unchanged.
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float} depending on the input
      @raise ValueError: if minval>maxval
      """
-     if minval>maxval:
+     if not minval==None and not maxval==None:
-        raise ValueError,"minval = %s must be less then maxval %s"%(minval,maxval)
+        if minval>maxval:
-     return minimum(maximum(minval,arg),maxval)
+           raise ValueError,"minval = %s must be less then maxval %s"%(minval,maxval)
+     if minval == None:
+         tmp=arg
+     else:
+         tmp=maximum(minval,arg)
+     if maxval == None:
+         return tmp
+     else:
+         return minimum(tmp,maxval)
  def inner(arg0,arg1):
-Line 3633 
 def inner(arg0,arg1):
+Line 4108 
 def inner(arg0,arg1):
      @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
      @param arg1: second argument
      @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @return : the inner product of arg0 and arg1 at each data point
+     @return: the inner product of arg0 and arg1 at each data point
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float} depending on the input
      @raise ValueError: if the shapes of the arguments are not identical
      """
-Line 3643 
 def inner(arg0,arg1):
+Line 4118 
 def inner(arg0,arg1):
          raise ValueError,"inner: shape of arguments does not match"
      return generalTensorProduct(arg0,arg1,axis_offset=len(sh0))
+ def outer(arg0,arg1):
+     """
+     the outer product of the two argument:
+     out[t,s]=arg0[t]*arg1[s]
+     where
+         - s runs through arg0.Shape
+         - t runs through arg1.Shape
+     @param arg0: first argument
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @param arg1: second argument
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @return: the outer product of arg0 and arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     return generalTensorProduct(arg0,arg1,axis_offset=0)
  def matrixmult(arg0,arg1):
      """
+     see L{matrix_mult}
+     """
+     return matrix_mult(arg0,arg1)
+ def matrix_mult(arg0,arg1):
+     """
      matrix-matrix or matrix-vector product of the two argument:
      out[s0]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0]
-           or
+     or
      out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0,s1]
-     The second dimension of arg0 and the length of arg1 must match.
+     The second dimension of arg0 and the first dimension of arg1 must match.
      @param arg0: first argument of rank 2
      @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-Line 3671 
 def matrixmult(arg0,arg1):
+Line 4172 
 def matrixmult(arg0,arg1):
          raise ValueError,"second argument must have rank 1 or 2"
      return generalTensorProduct(arg0,arg1,axis_offset=1)
- def outer(arg0,arg1):
+ def tensormult(arg0,arg1):
      """
-     the outer product of the two argument:
+     use L{tensor_mult}
-     out[t,s]=arg0[t]*arg1[s]
-     where s runs through arg0.Shape
-           t runs through arg1.Shape
-     @param arg0: first argument
-     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @param arg1: second argument
-     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @return: the outer product of arg0 and arg1 at each data point
-     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
      """
-     return generalTensorProduct(arg0,arg1,axis_offset=0)
+     return tensor_mult(arg0,arg1)
+ def tensor_mult(arg0,arg1):
- def tensormult(arg0,arg1):
      """
      the tensor product of the two argument:
      for arg0 of rank 2 this is
      out[s0]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0]
-                  or
+     or
      out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0,s1]
-Line 3708 
 def tensormult(arg0,arg1):
+Line 4195 
 def tensormult(arg0,arg1):
      out[s0,s1,s2,s3]=S{Sigma}_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1,s2,s3]
-                  or
+     or
      out[s0,s1,s2]=S{Sigma}_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1,s2]
-                  or
+     or
      out[s0,s1]=S{Sigma}_{r0,r1} arg0[s0,s1,r0,r1]*arg1[r0,r1]
-     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 last dimension of arg1 must match and
-     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 two first dimensions of arg1.
      @param arg0: first argument of rank 2 or 4
      @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-Line 3733 
 def tensormult(arg0,arg1):
+Line 4220 
 def tensormult(arg0,arg1):
      elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
         return generalTensorProduct(arg0,arg1,axis_offset=2)
      else:
-         raise ValueError,"tensormult: first argument must have rank 2 or 4"
+         raise ValueError,"tensor_mult: first argument must have rank 2 or 4"
  def generalTensorProduct(arg0,arg1,axis_offset=0):
      """
-Line 3741 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4228 
 def generalTensorProduct(arg0,arg1,axis_
      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]
-     where s runs through arg0.Shape[:arg0.Rank-axis_offset]
+     where
-           r runs trough arg0.Shape[:axis_offset]
-           t runs through arg1.Shape[axis_offset:]
-     In the first case the the second dimension of arg0 and the length of arg1 must match and
+         - s runs through arg0.Shape[:arg0.Rank-axis_offset]
-     in the second case the two last dimensions of arg0 must match the shape of arg1.
+         - r runs trough arg0.Shape[:axis_offset]
+         - t runs through arg1.Shape[axis_offset:]
      @param arg0: first argument
      @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @param arg1: second argument of shape greater of 1 or 2 depending on rank of arg0
+     @param arg1: second argument
      @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
      @return: the general tensor product of arg0 and arg1 at each data point.
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
-Line 3763 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4249 
 def generalTensorProduct(arg0,arg1,axis_
             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
         else:
             if not arg0.shape[arg0.rank-axis_offset:]==arg1.shape[:axis_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)
+                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)
             arg0_c=arg0.copy()
             arg1_c=arg1.copy()
             sh0,sh1=arg0.shape,arg1.shape
-Line 3773 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4259 
 def generalTensorProduct(arg0,arg1,axis_
             for i in sh1[:axis_offset]: d01*=i
             arg0_c.resize((d0,d01))
             arg1_c.resize((d01,d1))
-            out=numarray.zeros((d0,d1),numarray.Float)
+            out=numarray.zeros((d0,d1),numarray.Float64)
             for i0 in range(d0):
                      for i1 in range(d1):
                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])
-Line 3789 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4275 
 def generalTensorProduct(arg0,arg1,axis_
  class GeneralTensorProduct_Symbol(DependendSymbol):
     """
-    Symbol representing the quotient of two arguments.
+    Symbol representing the general tensor product of two arguments
     """
     def __init__(self,arg0,arg1,axis_offset=0):
         """
-        initialization of L{Symbol} representing the quotient of two arguments
+        initialization of L{Symbol} representing the general tensor product of two arguments.
-        @param arg0: numerator
+        @param arg0: first argument
         @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @param arg1: denominator
+        @param arg1: second argument
         @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @raise ValueError: if both arguments do not have the same shape.
+        @raise ValueError: illegal dimension
         @note: if both arguments have a spatial dimension, they must equal.
         """
         sh_arg0=pokeShape(arg0)
-Line 3822 
 class GeneralTensorProduct_Symbol(Depend
+Line 4308 
 class GeneralTensorProduct_Symbol(Depend
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str" or format=="text":
           return "generalTensorProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
-Line 3850 
 class GeneralTensorProduct_Symbol(Depend
+Line 4336 
 class GeneralTensorProduct_Symbol(Depend
           args=self.getSubstitutedArguments(argvals)
           return generalTensorProduct(args[0],args[1],args[2])
- def escript_generalTensorProduct(arg0,arg1,axis_offset): # this should be escript._generalTensorProduct
+ def escript_generalTensorProduct(arg0,arg1,axis_offset,transpose=0):
      "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
-     # calculate the return shape:
+     return C_GeneralTensorProduct(arg0, arg1, axis_offset, transpose)
-     shape0=arg0.getShape()[:arg0.getRank()-axis_offset]
-     shape01=arg0.getShape()[arg0.getRank()-axis_offset:]
+ def transposed_matrix_mult(arg0,arg1):
-     shape10=arg1.getShape()[:axis_offset]
+     """
-     shape1=arg1.getShape()[axis_offset:]
+     transposed(matrix)-matrix or transposed(matrix)-vector product of the two argument:
-     if not shape01==shape10:
-         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)
+     out[s0]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0]
-     # whatr function space should be used? (this here is not good!)
+     or
-     fs=(escript.Scalar(0.,arg0.getFunctionSpace())+escript.Scalar(0.,arg1.getFunctionSpace())).getFunctionSpace()
-     # create return value:
+     out[s0,s1]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0,s1]
-     out=escript.Data(0.,tuple(shape0+shape1),fs)
-     #
+     The function call transposed_matrix_mult(arg0,arg1) is equivalent to matrix_mult(transpose(arg0),arg1).
-     s0=[[]]
-     for k in shape0:
+     The first dimension of arg0 and arg1 must match.
-           s=[]
-           for j in s0:
+     @param arg0: first argument of rank 2
-                 for i in range(k): s.append(j+[slice(i,i)])
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-           s0=s
+     @param arg1: second argument of at least rank 1
-     s1=[[]]
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-     for k in shape1:
+     @return: the product of the transposed of arg0 and arg1 at each data point
-           s=[]
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
-           for j in s1:
+     @raise ValueError: if the shapes of the arguments are not appropriate
-                 for i in range(k): s.append(j+[slice(i,i)])
+     """
-           s1=s
+     sh0=pokeShape(arg0)
-     s01=[[]]
+     sh1=pokeShape(arg1)
-     for k in shape01:
+     if not len(sh0)==2 :
-           s=[]
+         raise ValueError,"first argument must have rank 2"
-           for j in s01:
+     if not len(sh1)==2 and not len(sh1)==1:
-                 for i in range(k): s.append(j+[slice(i,i)])
+         raise ValueError,"second argument must have rank 1 or 2"
-           s01=s
+     return generalTransposedTensorProduct(arg0,arg1,axis_offset=1)
-     for i0 in s0:
+ def transposed_tensor_mult(arg0,arg1):
-        for i1 in s1:
+     """
-          s=escript.Scalar(0.,fs)
+     the tensor product of the transposed of the first and the second argument
-          for i01 in s01:
-             s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))
+     for arg0 of rank 2 this is
-          out.__setitem__(tuple(i0+i1),s)
-     return out
+     out[s0]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0]
+     or
+     out[s0,s1]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0,s1]
+     and for arg0 of rank 4 this is
+     out[s0,s1,s2,s3]=S{Sigma}_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2,s3]
+     or
+     out[s0,s1,s2]=S{Sigma}_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2]
+     or
+     out[s0,s1]=S{Sigma}_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1]
+     In the first case the the first dimension of arg0 and the first dimension of arg1 must match and
+     in the second case the two first dimensions of arg0 must match the two first dimension of arg1.
+     The function call transposed_tensor_mult(arg0,arg1) is equivalent to tensor_mult(transpose(arg0),arg1).
+     @param arg0: first argument of rank 2 or 4
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @param arg1: second argument of shape greater of 1 or 2 depending on rank of arg0
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the tensor product of tarnsposed of arg0 and arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     sh0=pokeShape(arg0)
+     sh1=pokeShape(arg1)
+     if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
+        return generalTransposedTensorProduct(arg0,arg1,axis_offset=1)
+     elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
+        return generalTransposedTensorProduct(arg0,arg1,axis_offset=2)
+     else:
+         raise ValueError,"first argument must have rank 2 or 4"
+ def generalTransposedTensorProduct(arg0,arg1,axis_offset=0):
+     """
+     generalized tensor product of transposed of arg0 and arg1:
+     out[s,t]=S{Sigma}_r arg0[r,s]*arg1[r,t]
+     where
+         - s runs through arg0.Shape[axis_offset:]
+         - r runs trough arg0.Shape[:axis_offset]
+         - t runs through arg1.Shape[axis_offset:]
+     The function call generalTransposedTensorProduct(arg0,arg1,axis_offset) is equivalent
+     to generalTensorProduct(transpose(arg0,arg0.rank-axis_offset),arg1,axis_offset).
+     @param arg0: first argument
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @param arg1: second argument
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @return: the general tensor product of transposed(arg0) and arg1 at each data point.
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg0,float) and isinstance(arg1,float): return arg1*arg0
+     arg0,arg1=matchType(arg0,arg1)
+     # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols
+     if isinstance(arg0,numarray.NumArray):
+        if isinstance(arg1,Symbol):
+            return GeneralTransposedTensorProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            if not arg0.shape[:axis_offset]==arg1.shape[:axis_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)
+            arg0_c=arg0.copy()
+            arg1_c=arg1.copy()
+            sh0,sh1=arg0.shape,arg1.shape
+            d0,d1,d01=1,1,1
+            for i in sh0[axis_offset:]: d0*=i
+            for i in sh1[axis_offset:]: d1*=i
+            for i in sh0[:axis_offset]: d01*=i
+            arg0_c.resize((d01,d0))
+            arg1_c.resize((d01,d1))
+            out=numarray.zeros((d0,d1),numarray.Float64)
+            for i0 in range(d0):
+                     for i1 in range(d1):
+                          out[i0,i1]=numarray.sum(arg0_c[:,i0]*arg1_c[:,i1])
+            out.resize(sh0[axis_offset:]+sh1[axis_offset:])
+            return out
+     elif isinstance(arg0,escript.Data):
+        if isinstance(arg1,Symbol):
+            return GeneralTransposedTensorProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            return escript_generalTransposedTensorProduct(arg0,arg1,axis_offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,axis_offset)
+     else:
+        return GeneralTransposedTensorProduct_Symbol(arg0,arg1,axis_offset)
+ class GeneralTransposedTensorProduct_Symbol(DependendSymbol):
+    """
+    Symbol representing the general tensor product of the transposed of arg0 and arg1
+    """
+    def __init__(self,arg0,arg1,axis_offset=0):
+        """
+        initialization of L{Symbol} representing tensor product of the transposed of arg0 and arg1
+        @param arg0: first argument
+        @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @param arg1: second argument
+        @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @raise ValueError: inconsistent dimensions of arguments.
+        @note: if both arguments have a spatial dimension, they must equal.
+        """
+        sh_arg0=pokeShape(arg0)
+        sh_arg1=pokeShape(arg1)
+        sh01=sh_arg0[:axis_offset]
+        sh10=sh_arg1[:axis_offset]
+        sh0=sh_arg0[axis_offset:]
+        sh1=sh_arg1[axis_offset:]
+        if not sh01==sh10:
+            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)
+        DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,axis_offset])
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{list} of length 2 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str" or format=="text":
+          return "generalTransposedTensorProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
+       else:
+          raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          args=self.getSubstitutedArguments(argvals)
+          return generalTransposedTensorProduct(args[0],args[1],args[2])
+ def escript_generalTransposedTensorProduct(arg0,arg1,axis_offset): # this should be escript._generalTransposedTensorProduct
+     "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
+     return C_GeneralTensorProduct(arg0, arg1, axis_offset, 1)
+ def matrix_transposed_mult(arg0,arg1):
+     """
+     matrix-transposed(matrix) product of the two argument:
+     out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[s1,r0]
+     The function call matrix_transposed_mult(arg0,arg1) is equivalent to matrix_mult(arg0,transpose(arg1)).
+     The last dimensions of arg0 and arg1 must match.
+     @param arg0: first argument of rank 2
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @param arg1: second argument of rank 2
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the product of arg0 and the transposed of arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     @raise ValueError: if the shapes of the arguments are not appropriate
+     """
+     sh0=pokeShape(arg0)
+     sh1=pokeShape(arg1)
+     if not len(sh0)==2 :
+         raise ValueError,"first argument must have rank 2"
+     if not len(sh1)==2 and not len(sh1)==1:
+         raise ValueError,"second argument must have rank 1 or 2"
+     return generalTensorTransposedProduct(arg0,arg1,axis_offset=1)
+ def tensor_transposed_mult(arg0,arg1):
+     """
+     the tensor product of the first and the transpose of the second argument
+     for arg0 of rank 2 this is
+     out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[s1,r0]
+     and for arg0 of rank 4 this is
+     out[s0,s1,s2,s3]=S{Sigma}_{r0,r1} arg0[s0,s1,r0,r1]*arg1[s2,s3,r0,r1]
+     or
+     out[s0,s1,s2]=S{Sigma}_{r0,r1} arg0[s0,s1,r0,r1]*arg1[s2,r0,r1]
+     In the first case the the second dimension of arg0 and arg1 must match and
+     in the second case the two last dimensions of arg0 must match the two last dimension of arg1.
+     The function call tensor_transpose_mult(arg0,arg1) is equivalent to tensor_mult(arg0,transpose(arg1)).
+     @param arg0: first argument of rank 2 or 4
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @param arg1: second argument of shape greater of 1 or 2 depending on rank of arg0
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the tensor product of tarnsposed of arg0 and arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     sh0=pokeShape(arg0)
+     sh1=pokeShape(arg1)
+     if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
+        return generalTensorTransposedProduct(arg0,arg1,axis_offset=1)
+     elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
+        return generalTensorTransposedProduct(arg0,arg1,axis_offset=2)
+     else:
+         raise ValueError,"first argument must have rank 2 or 4"
+ def generalTensorTransposedProduct(arg0,arg1,axis_offset=0):
+     """
+     generalized tensor product of transposed of arg0 and arg1:
+     out[s,t]=S{Sigma}_r arg0[s,r]*arg1[t,r]
+     where
+         - s runs through arg0.Shape[:arg0.Rank-axis_offset]
+         - r runs trough arg0.Shape[arg1.Rank-axis_offset:]
+         - t runs through arg1.Shape[arg1.Rank-axis_offset:]
+     The function call generalTensorTransposedProduct(arg0,arg1,axis_offset) is equivalent
+     to generalTensorProduct(arg0,transpose(arg1,arg1.Rank-axis_offset),axis_offset).
+     @param arg0: first argument
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @param arg1: second argument
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @return: the general tensor product of transposed(arg0) and arg1 at each data point.
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg0,float) and isinstance(arg1,float): return arg1*arg0
+     arg0,arg1=matchType(arg0,arg1)
+     # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols
+     if isinstance(arg0,numarray.NumArray):
+        if isinstance(arg1,Symbol):
+            return GeneralTensorTransposedProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            if not arg0.shape[arg0.rank-axis_offset:]==arg1.shape[arg1.rank-axis_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)
+            arg0_c=arg0.copy()
+            arg1_c=arg1.copy()
+            sh0,sh1=arg0.shape,arg1.shape
+            d0,d1,d01=1,1,1
+            for i in sh0[:arg0.rank-axis_offset]: d0*=i
+            for i in sh1[:arg1.rank-axis_offset]: d1*=i
+            for i in sh1[arg1.rank-axis_offset:]: d01*=i
+            arg0_c.resize((d0,d01))
+            arg1_c.resize((d1,d01))
+            out=numarray.zeros((d0,d1),numarray.Float64)
+            for i0 in range(d0):
+                     for i1 in range(d1):
+                          out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[i1,:])
+            out.resize(sh0[:arg0.rank-axis_offset]+sh1[:arg1.rank-axis_offset])
+            return out
+     elif isinstance(arg0,escript.Data):
+        if isinstance(arg1,Symbol):
+            return GeneralTensorTransposedProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            return escript_generalTensorTransposedProduct(arg0,arg1,axis_offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,axis_offset)
+     else:
+        return GeneralTensorTransposedProduct_Symbol(arg0,arg1,axis_offset)
+ class GeneralTensorTransposedProduct_Symbol(DependendSymbol):
+    """
+    Symbol representing the general tensor product of arg0 and the transpose of arg1
+    """
+    def __init__(self,arg0,arg1,axis_offset=0):
+        """
+        initialization of L{Symbol} representing the general tensor product of arg0 and the transpose of arg1
+        @param arg0: first argument
+        @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @param arg1: second argument
+        @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @raise ValueError: inconsistent dimensions of arguments.
+        @note: if both arguments have a spatial dimension, they must equal.
+        """
+        sh_arg0=pokeShape(arg0)
+        sh_arg1=pokeShape(arg1)
+        sh0=sh_arg0[:len(sh_arg0)-axis_offset]
+        sh01=sh_arg0[len(sh_arg0)-axis_offset:]
+        sh10=sh_arg1[len(sh_arg1)-axis_offset:]
+        sh1=sh_arg1[:len(sh_arg1)-axis_offset]
+        if not sh01==sh10:
+            raise ValueError,"dimensions of last %s components in left argument don't match the last %s components in the right argument."%(axis_offset,axis_offset)
+        DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,axis_offset])
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{list} of length 2 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str" or format=="text":
+          return "generalTensorTransposedProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
+       else:
+          raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          args=self.getSubstitutedArguments(argvals)
+          return generalTensorTransposedProduct(args[0],args[1],args[2])
+ def escript_generalTensorTransposedProduct(arg0,arg1,axis_offset): # this should be escript._generalTensorTransposedProduct
+     "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
+     return C_GeneralTensorProduct(arg0, arg1, axis_offset, 2)
  #=========================================================
  #  functions dealing with spatial dependency
-Line 3913 
 def grad(arg,where=None):
+Line 4741 
 def grad(arg,where=None):
                    If not present or C{None} an appropriate default is used.
      @type where: C{None} or L{escript.FunctionSpace}
      @return: gradient of arg.
-     @rtype:  L{escript.Data} or L{Symbol}
+     @rtype: L{escript.Data} or L{Symbol}
      """
      if isinstance(arg,Symbol):
         return Grad_Symbol(arg,where)
-Line 3953 
 class Grad_Symbol(DependendSymbol):
+Line 4781 
 class Grad_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "grad(%s,where=%s)"%(argstrs[0],argstrs[1])
-Line 4006 
 def integrate(arg,where=None):
+Line 4834 
 def integrate(arg,where=None):
                    If not present or C{None} an appropriate default is used.
      @type where: C{None} or L{escript.FunctionSpace}
      @return: integral of arg.
-     @rtype:  C{float}, C{numarray.NumArray} or L{Symbol}
+     @rtype: C{float}, C{numarray.NumArray} or L{Symbol}
      """
      if isinstance(arg,Symbol):
         return Integrate_Symbol(arg,where)
-Line 4044 
 class Integrate_Symbol(DependendSymbol):
+Line 4872 
 class Integrate_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "integrate(%s,where=%s)"%(argstrs[0],argstrs[1])
-Line 4096 
 def interpolate(arg,where):
+Line 4924 
 def interpolate(arg,where):
      @param where: FunctionSpace to be interpolated to
      @type where: L{escript.FunctionSpace}
      @return: interpolated argument
-     @rtype:  C{escript.Data} or L{Symbol}
+     @rtype: C{escript.Data} or L{Symbol}
      """
      if isinstance(arg,Symbol):
         return Interpolate_Symbol(arg,where)
-Line 4127 
 class Interpolate_Symbol(DependendSymbol
+Line 4955 
 class Interpolate_Symbol(DependendSymbol
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "interpolate(%s,where=%s)"%(argstrs[0],argstrs[1])
-Line 4180 
 def div(arg,where=None):
+Line 5008 
 def div(arg,where=None):
                    If not present or C{None} an appropriate default is used.
      @type where: C{None} or L{escript.FunctionSpace}
      @return: divergence of arg.
-     @rtype:  L{escript.Data} or L{Symbol}
+     @rtype: L{escript.Data} or L{Symbol}
      """
      if isinstance(arg,Symbol):
          dim=arg.getDim()
-Line 4202 
 def jump(arg,domain=None):
+Line 5030 
 def jump(arg,domain=None):
                     the domain of arg is used. If arg is a L{Symbol} the domain must be present.
      @type domain: C{None} or L{escript.Domain}
      @return: jump of arg
-     @rtype:  L{escript.Data} or L{Symbol}
+     @rtype: L{escript.Data} or L{Symbol}
      """
      if domain==None: domain=arg.getDomain()
      return interpolate(arg,escript.FunctionOnContactOne(domain))-interpolate(arg,escript.FunctionOnContactZero(domain))
- #=============================
- #
- # wrapper for various functions: if the argument has attribute the function name
- # as an argument it calls the corresponding methods. Otherwise the corresponding
- # numarray function is called.
- # functions involving the underlying Domain:
- def transpose(arg,axis=None):
+ def L2(arg):
      """
-     Returns the transpose of the Data object arg.
+     returns the L2 norm of arg at where
-     @param arg:
+     @param arg: function which L2 to be calculated.
+     @type arg: L{escript.Data} or L{Symbol}
+     @return: L2 norm of arg.
+     @rtype: L{float} or L{Symbol}
+     @note: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
      """
-     if axis==None:
+     return sqrt(integrate(inner(arg,arg)))
-        r=0
+ #=============================
-        if hasattr(arg,"getRank"): r=arg.getRank()
+ #
-        if hasattr(arg,"rank"): r=arg.rank
-        axis=r/2
-     if isinstance(arg,Symbol):
-        return Transpose_Symbol(arg,axis=r)
-     if isinstance(arg,escript.Data):
-        # hack for transpose
-        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)
-     else:
-        return numarray.transpose(arg,axis=axis)
  def reorderComponents(arg,index):
      """
      resorts the component of arg according to index
      """
-     pass
+     raise NotImplementedError
  #
  # $Log: util.py,v $
  # Revision 1.14.2.16  2005/10/19 06:09:57  gross

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