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

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

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-revision 587 by gross,
Fri Mar 10 02:26:50 2006 UTC
+revision 1042 by gross,
Mon Mar 19 03:50:34 2007 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 reorderComponents(arg,index):
- #
- # slicing: get
- #          set
- #
- # and derivatives
  #=========================================================
  #   some helpers:
  #=========================================================
+ def getTagNames(domain):
+     """
+     returns a list of the tag names used by the domain
+     @param domain: a domain object
+     @type domain: C{escript.Domain}
+     @return: a list of the tag name used by the domain.
+     @rtype: C{list} of C{str}
+     """
+     return [n.strip() for n in domain.showTagNames().split(",") ]
  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 87 
 def saveDX(filename,domain=None,**data):
+Line 75 
 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 118 
 def kronecker(d=3):
+Line 106 
 def kronecker(d=3):
     @param d: dimension or an object that has the C{getDim} method defining the dimension
     @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} or L{escript.Data} of rank 2.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 2.
     """
     return identityTensor(d)
-Line 154 
 def identityTensor(d=3):
+Line 142 
 def identityTensor(d=3):
     @param d: dimension or an object that has the C{getDim} method defining the dimension
     @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} or L{escript.Data} of rank 2
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 2
     """
     if isinstance(d,escript.FunctionSpace):
         return escript.Data(identity((d.getDim(),)),d)
-Line 170 
 def identityTensor4(d=3):
+Line 158 
 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 d: L{numarray.NumArray} or L{escript.Data} of rank 4.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 4.
     """
     if isinstance(d,escript.FunctionSpace):
         return escript.Data(identity((d.getDim(),d.getDim())),d)
-Line 188 
 def unitVector(i=0,d=3):
+Line 176 
 def unitVector(i=0,d=3):
     @param d: dimension or an object that has the C{getDim} method defining the dimension
     @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 d: L{numarray.NumArray} or L{escript.Data} of rank 1
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 1
     """
     return kronecker(d)[i]
-Line 244 
 def inf(arg):
+Line 232 
 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 263 
 def inf(arg):
+Line 251 
 def inf(arg):
  #=========================================================================
  #   some little helpers
  #=========================================================================
- def pokeShape(arg):
+ def getRank(arg):
+     """
+     identifies the rank of its argument
+     @param arg: a given object
+     @type arg: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, C{Symbol}
+     @return: the rank of the argument
+     @rtype: C{int}
+     @raise TypeError: if type of arg cannot be processed
+     """
+     if isinstance(arg,numarray.NumArray):
+         return arg.rank
+     elif isinstance(arg,escript.Data):
+         return arg.getRank()
+     elif isinstance(arg,float):
+         return 0
+     elif isinstance(arg,int):
+         return 0
+     elif isinstance(arg,Symbol):
+         return arg.getRank()
+     else:
+       raise TypeError,"getShape: cannot identify shape"
+ def getShape(arg):
      """
      identifies the shape of its argument
-Line 285 
 def pokeShape(arg):
+Line 296 
 def pokeShape(arg):
      elif isinstance(arg,Symbol):
          return arg.getShape()
      else:
-       raise TypeError,"pokeShape: cannot identify shape"
+       raise TypeError,"getShape: cannot identify shape"
  def pokeDim(arg):
      """
-Line 308 
 def commonShape(arg0,arg1):
+Line 319 
 def commonShape(arg0,arg1):
      """
      returns a shape to which arg0 can be extendent from the right and arg1 can be extended from the left.
-     @param arg0: an object with a shape (see L{pokeShape})
+     @param arg0: an object with a shape (see L{getShape})
-     @param arg1: an object with a shape (see L{pokeShape})
+     @param arg1: an object with a shape (see L{getShape})
      @return: the shape of arg0 or arg1 such that the left port equals the shape of arg0 and the right end equals the shape of arg1.
      @rtype: C{tuple} of C{int}
      @raise ValueError: if no shape can be found.
      """
-     sh0=pokeShape(arg0)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(arg1)
      if len(sh0)<len(sh1):
         if not sh0==sh1[:len(sh0)]:
               raise ValueError,"argument 0 cannot be extended to the shape of argument 1"
-Line 333 
 def commonDim(*args):
+Line 344 
 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 355 
 def testForZero(arg):
+Line 366 
 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 459 
 def matchType(arg0=0.,arg1=0.):
+Line 470 
 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 args: a given ob
+     @param arg0: a given object
-     @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int}
+     @type arg0: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, L{Symbol}
-     @return: True if the argument is identical to zero.
+     @param arg1: a given object
-     @rtype: C{list} of C{int}
+     @type arg1: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, L{Symbol}
+     @return: C{arg0} and C{arg1} where copies are returned when the shape has to be changed.
+     @rtype: C{tuple}
      """
      sh=commonShape(arg0,arg1)
-     sh0=pokeShape(arg0)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(arg1)
      if len(sh0)<len(sh):
         return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float64)),arg1
      elif len(sh1)<len(sh):
-Line 494 
 class Symbol(object):
+Line 505 
 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 538 
 class Symbol(object):
+Line 549 
 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 547 
 class Symbol(object):
+Line 558 
 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 571 
 class Symbol(object):
+Line 582 
 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 598 
 class Symbol(object):
+Line 609 
 class Symbol(object):
            if isinstance(a,Symbol):
               out.append(a.substitute(argvals))
            else:
-               s=pokeShape(s)+arg.getShape()
+               s=getShape(s)+arg.getShape()
                if len(s)>0:
                   out.append(numarray.zeros(s),numarray.Float64)
                else:
-Line 698 
 class Symbol(object):
+Line 709 
 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 707 
 class Symbol(object):
+Line 718 
 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 724 
 class Symbol(object):
+Line 735 
 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 735 
 class Symbol(object):
+Line 746 
 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 746 
 class Symbol(object):
+Line 757 
 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 757 
 class Symbol(object):
+Line 768 
 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 768 
 class Symbol(object):
+Line 779 
 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 779 
 class Symbol(object):
+Line 790 
 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 790 
 class Symbol(object):
+Line 801 
 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 801 
 class Symbol(object):
+Line 812 
 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 812 
 class Symbol(object):
+Line 823 
 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 823 
 class Symbol(object):
+Line 834 
 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)
-Line 834 
 class Symbol(object):
+Line 845 
 class Symbol(object):
         @param index: defines a
         @type index: C{slice} or C{int} or a C{tuple} of them
-        @return: a S{Symbol} representing the slice defined by index
+        @return: a L{Symbol} representing the slice defined by index
         @rtype: L{DependendSymbol}
         """
         return GetSlice_Symbol(self,index)
-Line 844 
 class DependendSymbol(Symbol):
+Line 855 
 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 947 
 class GetSlice_Symbol(DependendSymbol):
+Line 958 
 class GetSlice_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.__getitem__(%s)"%(argstrs[0],argstrs[1])
-Line 983 
 def log10(arg):
+Line 994 
 def log10(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 1005 
 def wherePositive(arg):
+Line 1016 
 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):
-Line 1051 
 class WherePositive_Symbol(DependendSymb
+Line 1062 
 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 1087 
 def whereNegative(arg):
+Line 1098 
 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):
-Line 1133 
 class WhereNegative_Symbol(DependendSymb
+Line 1144 
 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 1169 
 def whereNonNegative(arg):
+Line 1180 
 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):
-Line 1199 
 def whereNonPositive(arg):
+Line 1210 
 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):
-Line 1231 
 def whereZero(arg,tol=0.):
+Line 1242 
 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):
-Line 1239 
 def whereZero(arg,tol=0.):
+Line 1250 
 def whereZero(arg,tol=0.):
        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 1280 
 class WhereZero_Symbol(DependendSymbol):
+Line 1288 
 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 1314 
 def whereNonZero(arg,tol=0.):
+Line 1322 
 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):
-Line 1322 
 def whereNonZero(arg,tol=0.):
+Line 1330 
 def whereNonZero(arg,tol=0.):
        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 1341 
 def whereNonZero(arg,tol=0.):
+Line 1346 
 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 1385 
 class Sin_Symbol(DependendSymbol):
+Line 1404 
 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 1437 
 def cos(arg):
+Line 1456 
 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 1475 
 class Cos_Symbol(DependendSymbol):
+Line 1494 
 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 1527 
 def tan(arg):
+Line 1546 
 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 1565 
 class Tan_Symbol(DependendSymbol):
+Line 1584 
 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 1617 
 def asin(arg):
+Line 1636 
 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 1655 
 class Asin_Symbol(DependendSymbol):
+Line 1674 
 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 1707 
 def acos(arg):
+Line 1726 
 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 1745 
 class Acos_Symbol(DependendSymbol):
+Line 1764 
 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 1797 
 def atan(arg):
+Line 1816 
 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 1835 
 class Atan_Symbol(DependendSymbol):
+Line 1854 
 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 1887 
 def sinh(arg):
+Line 1906 
 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 1925 
 class Sinh_Symbol(DependendSymbol):
+Line 1944 
 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 1977 
 def cosh(arg):
+Line 1996 
 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 2015 
 class Cosh_Symbol(DependendSymbol):
+Line 2034 
 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 2067 
 def tanh(arg):
+Line 2086 
 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 2105 
 class Tanh_Symbol(DependendSymbol):
+Line 2124 
 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 2157 
 def asinh(arg):
+Line 2176 
 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 2195 
 class Asinh_Symbol(DependendSymbol):
+Line 2214 
 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 2247 
 def acosh(arg):
+Line 2266 
 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 2285 
 class Acosh_Symbol(DependendSymbol):
+Line 2304 
 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 2337 
 def atanh(arg):
+Line 2356 
 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 2375 
 class Atanh_Symbol(DependendSymbol):
+Line 2394 
 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 2427 
 def exp(arg):
+Line 2446 
 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 2465 
 class Exp_Symbol(DependendSymbol):
+Line 2484 
 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 2517 
 def sqrt(arg):
+Line 2536 
 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 2555 
 class Sqrt_Symbol(DependendSymbol):
+Line 2574 
 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 2607 
 def log(arg):
+Line 2626 
 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 2645 
 class Log_Symbol(DependendSymbol):
+Line 2664 
 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 2697 
 def sign(arg):
+Line 2716 
 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 2745 
 class Abs_Symbol(DependendSymbol):
+Line 2764 
 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 2797 
 def minval(arg):
+Line 2816 
 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 2838 
 class Minval_Symbol(DependendSymbol):
+Line 2857 
 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 2874 
 def maxval(arg):
+Line 2893 
 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 2915 
 class Maxval_Symbol(DependendSymbol):
+Line 2934 
 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 2951 
 def length(arg):
+Line 2970 
 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 2961 
 def trace(arg,axis_offset=0):
+Line 2980 
 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 2970 
 def trace(arg,axis_offset=0):
+Line 2989 
 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.Float64)
        for i1 in range(s1):
-Line 2987 
 def trace(arg,axis_offset=0):
+Line 3006 
 def trace(arg,axis_offset=0):
        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 3045 
 class Trace_Symbol(DependendSymbol):
+Line 3032 
 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 3068 
 class Trace_Symbol(DependendSymbol):
+Line 3055 
 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 3112 
 class Trace_Symbol(DependendSymbol):
+Line 3099 
 class Trace_Symbol(DependendSymbol):
  def transpose(arg,axis_offset=None):
     """
-    returns the transpose of arg by swaping the first axis_offset and the last rank-axis_offset components.
+    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 axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+    @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 axis_offset is not present C{int(r/2)} where r is the rank of arg is used.
+                        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.
-Line 3126 
 def transpose(arg,axis_offset=None):
+Line 3113 
 def transpose(arg,axis_offset=None):
        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):
-       if axis_offset==None: axis_offset=int(arg.getRank()/2)
+       r=arg.getRank()
-       return escript_transpose(arg,axis_offset)
+       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,"transpose: axis_offset must be 0 for float argument"
+         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,"transpose: axis_offset must be 0 for int argument"
+         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,"transpose: Unknown argument type."
+       raise TypeError,"Unknown argument type."
- def escript_transpose(arg,axis_offset): # this should be escript._transpose
-       "arg si a Data objects!!!"
-       r=arg.getRank()
-       if axis_offset<0 or axis_offset>r:
-         raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r
-       s=arg.getShape()
-       s_out=s[axis_offset:]+s[:axis_offset]
-       out=escript.Data(0.,s_out,arg.getFunctionSpace())
-       if r==4:
-          if axis_offset==1:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                   for i2 in range(s_out[2]):
-                      for i3 in range(s_out[3]):
-                          out[i0,i1,i2,i3]=arg[i3,i0,i1,i2]
-          elif axis_offset==2:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                   for i2 in range(s_out[2]):
-                      for i3 in range(s_out[3]):
-                          out[i0,i1,i2,i3]=arg[i2,i3,i0,i1]
-          elif axis_offset==3:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                   for i2 in range(s_out[2]):
-                      for i3 in range(s_out[3]):
-                          out[i0,i1,i2,i3]=arg[i1,i2,i3,i0]
-          else:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                   for i2 in range(s_out[2]):
-                      for i3 in range(s_out[3]):
-                          out[i0,i1,i2,i3]=arg[i0,i1,i2,i3]
-       elif r==3:
-          if axis_offset==1:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                   for i2 in range(s_out[2]):
-                          out[i0,i1,i2]=arg[i2,i0,i1]
-          elif axis_offset==2:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                   for i2 in range(s_out[2]):
-                          out[i0,i1,i2]=arg[i1,i2,i0]
-          else:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                   for i2 in range(s_out[2]):
-                          out[i0,i1,i2]=arg[i0,i1,i2]
-       elif r==2:
-          if axis_offset==1:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                          out[i0,i1]=arg[i1,i0]
-          else:
-             for i0 in range(s_out[0]):
-                for i1 in range(s_out[1]):
-                          out[i0,i1]=arg[i0,i1]
-       elif r==1:
-           for i0 in range(s_out[0]):
-                out[i0]=arg[i0]
-       elif r==0:
-              out=arg+0.
-       return out
  class Transpose_Symbol(DependendSymbol):
     """
     L{Symbol} representing the result of the transpose function
-Line 3216 
 class Transpose_Symbol(DependendSymbol):
+Line 3142 
 class Transpose_Symbol(DependendSymbol):
        @param arg: argument of function
        @type arg: L{Symbol}.
-        @param axis_offset: the first axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+       @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 axis_offset is not present C{int(r/2)} where r is the rank of arg is used.
+                        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,"escript_transpose: axis_offset must be between 0 and %s"%r
+         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())
-Line 3236 
 class Transpose_Symbol(DependendSymbol):
+Line 3162 
 class Transpose_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 "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
-Line 3277 
 class Transpose_Symbol(DependendSymbol):
+Line 3203 
 class Transpose_Symbol(DependendSymbol):
           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
-Line 3289 
 def symmetric(arg):
+Line 3332 
 def symmetric(arg):
      if isinstance(arg,numarray.NumArray):
        if arg.rank==2:
          if not (arg.shape[0]==arg.shape[1]):
-            raise ValueError,"symmetric: argument must be square."
+            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,"symmetric: argument must be square."
+            raise ValueError,"argument must be square."
        else:
-         raise ValueError,"symmetric: rank 2 or 4 is required."
+         raise ValueError,"rank 2 or 4 is required."
        return (arg+transpose(arg))/2
      elif isinstance(arg,escript.Data):
-       return escript_symmetric(arg)
+       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):
-Line 3305 
 def symmetric(arg):
+Line 3357 
 def symmetric(arg):
      elif isinstance(arg,Symbol):
        if arg.getRank()==2:
          if not (arg.getShape()[0]==arg.getShape()[1]):
-            raise ValueError,"symmetric: argument must be square."
+            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,"symmetric: argument must be square."
+            raise ValueError,"argument must be square."
        else:
-         raise ValueError,"symmetric: rank 2 or 4 is required."
+         raise ValueError,"rank 2 or 4 is required."
        return (arg+transpose(arg))/2
      else:
        raise TypeError,"symmetric: Unknown argument type."
- def escript_symmetric(arg): # this should be implemented in c++
-       if arg.getRank()==2:
-         if not (arg.getShape()[0]==arg.getShape()[1]):
-            raise ValueError,"escript_symmetric: argument must be square."
-         out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
-         for i0 in range(arg.getShape()[0]):
-            for i1 in range(arg.getShape()[1]):
-               out[i0,i1]=(arg[i0,i1]+arg[i1,i0])/2.
-       elif arg.getRank()==4:
-         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
-            raise ValueError,"escript_symmetric: argument must be square."
-         out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
-         for i0 in range(arg.getShape()[0]):
-            for i1 in range(arg.getShape()[1]):
-               for i2 in range(arg.getShape()[2]):
-                  for i3 in range(arg.getShape()[3]):
-                      out[i0,i1,i2,i3]=(arg[i0,i1,i2,i3]+arg[i2,i3,i0,i1])/2.
-       else:
-         raise ValueError,"escript_symmetric: rank 2 or 4 is required."
-       return out
  def nonsymmetric(arg):
      """
      returns the nonsymmetric part of the square matrix arg. This is (arg-transpose(arg))/2
-Line 3356 
 def nonsymmetric(arg):
+Line 3387 
 def nonsymmetric(arg):
          raise ValueError,"nonsymmetric: rank 2 or 4 is required."
        return (arg-transpose(arg))/2
      elif isinstance(arg,escript.Data):
-       return escript_nonsymmetric(arg)
+       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):
-Line 3374 
 def nonsymmetric(arg):
+Line 3414 
 def nonsymmetric(arg):
      else:
        raise TypeError,"nonsymmetric: Unknown argument type."
- def escript_nonsymmetric(arg): # this should be implemented in c++
-       if arg.getRank()==2:
-         if not (arg.getShape()[0]==arg.getShape()[1]):
-            raise ValueError,"escript_nonsymmetric: argument must be square."
-         out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
-         for i0 in range(arg.getShape()[0]):
-            for i1 in range(arg.getShape()[1]):
-               out[i0,i1]=(arg[i0,i1]-arg[i1,i0])/2.
-       elif arg.getRank()==4:
-         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
-            raise ValueError,"escript_nonsymmetric: argument must be square."
-         out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
-         for i0 in range(arg.getShape()[0]):
-            for i1 in range(arg.getShape()[1]):
-               for i2 in range(arg.getShape()[2]):
-                  for i3 in range(arg.getShape()[3]):
-                      out[i0,i1,i2,i3]=(arg[i0,i1,i2,i3]-arg[i2,i3,i0,i1])/2.
-       else:
-         raise ValueError,"escript_nonsymmetric: rank 2 or 4 is required."
-       return out
  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.
      @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
-     @remark: for L{escript.Data} objects the dimension is restricted to 3.
+     @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 3498 
 class Inverse_Symbol(DependendSymbol):
+Line 3517 
 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 3538 
 class Inverse_Symbol(DependendSymbol):
+Line 3557 
 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):
      """
-Line 3549 
 def eigenvalues(arg):
+Line 3568 
 def eigenvalues(arg):
      @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.
-     @remark: for L{escript.Data} and L{Symbol} objects the dimension is restricted to 3.
+     @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.)
-Line 3610 
 def eigenvalues(arg):
+Line 3629 
 def eigenvalues(arg):
  def eigenvalues_and_eigenvectors(arg):
      """
-     returns the eigenvalues of the square matrix 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{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @type arg: L{escript.Data}
-     @return: the eigenvalues in increasing order.
+     @return: the eigenvalues and eigenvectors. The eigenvalues are ordered by increasing value. The
-     @rtype: L{numarray.NumArray},L{escript.Data}, L{Symbol} depending on the input.
+              eigenvectors are orthogonal and normalized. If V are the eigenvectors than V[:,i] is
-     @remark: for L{escript.Data} and L{Symbol} objects the dimension is restricted to 3.
+              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"
-Line 3674 
 class Add_Symbol(DependendSymbol):
+Line 3695 
 class Add_Symbol(DependendSymbol):
         @raise ValueError: if both arguments do not have the same shape.
         @note: if both arguments have a spatial dimension, they must equal.
         """
-        sh0=pokeShape(arg0)
+        sh0=getShape(arg0)
-        sh1=pokeShape(arg1)
+        sh1=getShape(arg1)
         if not sh0==sh1:
            raise ValueError,"Add_Symbol: shape of arguments must match"
         DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0,args=[arg0,arg1])
-Line 3690 
 class Add_Symbol(DependendSymbol):
+Line 3711 
 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 3749 
 def mult(arg0,arg1):
+Line 3770 
 def mult(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]) or testForZero(args[1]):
-           return numarray.zeros(pokeShape(args[0]),numarray.Float64)
+           return numarray.zeros(getShape(args[0]),numarray.Float64)
         else:
            if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) :
                return Mult_Symbol(args[0],args[1])
-Line 3773 
 class Mult_Symbol(DependendSymbol):
+Line 3794 
 class Mult_Symbol(DependendSymbol):
         @raise ValueError: if both arguments do not have the same shape.
         @note: if both arguments have a spatial dimension, they must equal.
         """
-        sh0=pokeShape(arg0)
+        sh0=getShape(arg0)
-        sh1=pokeShape(arg1)
+        sh1=getShape(arg1)
         if not sh0==sh1:
            raise ValueError,"Mult_Symbol: shape of arguments must match"
         DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0,args=[arg0,arg1])
-Line 3789 
 class Mult_Symbol(DependendSymbol):
+Line 3810 
 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 3849 
 def quotient(arg0,arg1):
+Line 3870 
 def quotient(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]):
-           return numarray.zeros(pokeShape(args[0]),numarray.Float64)
+           return numarray.zeros(getShape(args[0]),numarray.Float64)
         elif isinstance(args[0],Symbol):
            if isinstance(args[1],Symbol):
               return Quotient_Symbol(args[0],args[1])
-Line 3878 
 class Quotient_Symbol(DependendSymbol):
+Line 3899 
 class Quotient_Symbol(DependendSymbol):
         @raise ValueError: if both arguments do not have the same shape.
         @note: if both arguments have a spatial dimension, they must equal.
         """
-        sh0=pokeShape(arg0)
+        sh0=getShape(arg0)
-        sh1=pokeShape(arg1)
+        sh1=getShape(arg1)
         if not sh0==sh1:
            raise ValueError,"Quotient_Symbol: shape of arguments must match"
         DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0,args=[arg0,arg1])
-Line 3894 
 class Quotient_Symbol(DependendSymbol):
+Line 3915 
 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 3955 
 def power(arg0,arg1):
+Line 3976 
 def power(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]):
-           return numarray.zeros(pokeShape(args[0]),numarray.Float64)
+           return numarray.zeros(getShape(args[0]),numarray.Float64)
         elif testForZero(args[1]):
-           return numarray.ones(pokeShape(args[1]),numarray.Float64)
+           return numarray.ones(getShape(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 3980 
 class Power_Symbol(DependendSymbol):
+Line 4001 
 class Power_Symbol(DependendSymbol):
         @raise ValueError: if both arguments do not have the same shape.
         @note: if both arguments have a spatial dimension, they must equal.
         """
-        sh0=pokeShape(arg0)
+        sh0=getShape(arg0)
-        sh1=pokeShape(arg1)
+        sh1=getShape(arg1)
         if not sh0==sh1:
            raise ValueError,"Power_Symbol: shape of arguments must match"
         d0=pokeDim(arg0)
-Line 3998 
 class Power_Symbol(DependendSymbol):
+Line 4019 
 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 4080 
 def minimum(*args):
+Line 4101 
 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 4114 
 def inner(arg0,arg1):
+Line 4143 
 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
      """
-     sh0=pokeShape(arg0)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(arg1)
      if not sh0==sh1:
          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 4144 
 def matrixmult(arg0,arg1):
+Line 4199 
 def matrixmult(arg0,arg1):
      @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)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(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 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 tensormult(arg0,arg1):
+ def tensor_mult(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 4189 
 def tensormult(arg0,arg1):
+Line 4230 
 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 4207 
 def tensormult(arg0,arg1):
+Line 4248 
 def tensormult(arg0,arg1):
      @return: the tensor product of arg0 and arg1 at each data point
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
      """
-     sh0=pokeShape(arg0)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(arg1)
      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
         return generalTensorProduct(arg0,arg1,axis_offset=1)
      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 4222 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4263 
 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 4244 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4284 
 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 4270 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4310 
 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)
+        sh_arg0=getShape(arg0)
-        sh_arg1=pokeShape(arg1)
+        sh_arg1=getShape(arg1)
         sh0=sh_arg0[:len(sh_arg0)-axis_offset]
         sh01=sh_arg0[len(sh_arg0)-axis_offset:]
         sh10=sh_arg1[:axis_offset]
-Line 4303 
 class GeneralTensorProduct_Symbol(Depend
+Line 4343 
 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 4331 
 class GeneralTensorProduct_Symbol(Depend
+Line 4371 
 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=getShape(arg0)
-     s01=[[]]
+     sh1=getShape(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=getShape(arg0)
+     sh1=getShape(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=getShape(arg0)
+        sh_arg1=getShape(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=getShape(arg0)
+     sh1=getShape(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=getShape(arg0)
+     sh1=getShape(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=getShape(arg0)
+        sh_arg1=getShape(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 4394 
 def grad(arg,where=None):
+Line 4776 
 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 4434 
 class Grad_Symbol(DependendSymbol):
+Line 4816 
 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 4487 
 def integrate(arg,where=None):
+Line 4869 
 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 4525 
 class Integrate_Symbol(DependendSymbol):
+Line 4907 
 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 4577 
 def interpolate(arg,where):
+Line 4959 
 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 4608 
 class Interpolate_Symbol(DependendSymbol
+Line 4990 
 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 4661 
 def div(arg,where=None):
+Line 5043 
 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 4683 
 def jump(arg,domain=None):
+Line 5065 
 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))
-Line 4695 
 def L2(arg):
+Line 5077 
 def L2(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}
+     @rtype: L{float} or L{Symbol}
      @note: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
      """
      return sqrt(integrate(inner(arg,arg)))

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