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

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

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-revision 397 by gross,
Wed Dec 21 05:11:31 2005 UTC
+revision 1044 by gross,
Mon Mar 19 07:29:31 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 32 
 import math
+Line 26 
 import math
  import numarray
  import escript
  import os
+ from esys.escript import C_GeneralTensorProduct
- # missing tests:
- # def pokeShape(arg):
- # def pokeDim(arg):
- # def commonShape(arg0,arg1):
- # def commonDim(*args):
- # def testForZero(arg):
- # def matchType(arg0=0.,arg1=0.):
- # def matchShape(arg0,arg1):
- # def transpose(arg,axis=None):
- # def trace(arg,axis0=0,axis1=1):
- # def reorderComponents(arg,index):
- # def integrate(arg,where=None):
- # def interpolate(arg,where):
- # def div(arg,where=None):
- # def grad(arg,where=None):
- #
- # 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: L{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 insertTagNames(domain,**kwargs):
+     """
+     inserts tag names into the domain
+     @param domain: a domain object
+     @type domain: C{escript.Domain}
+     @keyword <tag name>: tag key assigned to <tag name>
+     @type <tag name>: C{int}
+     """
+     for  k in kwargs:
+          domain.setTagMap(k,kwargs[k])
+ def insertTaggedValues(target,**kwargs):
+     """
+     inserts tagged values into the tagged using tag names
+     @param target: data to be filled by tagged values
+     @type target: L{escript.Data}
+     @keyword <tag name>: value to be used for <tag name>
+     @type <tag name>: C{float} or {numarray.NumArray}
+     @return: C{target}
+     @rtype: L{escript.Data}
+     """
+     for k in kwargs:
+         target.setTaggedValue(k,kwargs[k])
+     return target
  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 93 
 def saveDX(filename,domain=None,**data):
+Line 103 
 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 122 
 def kronecker(d=3):
+Line 132 
 def kronecker(d=3):
     return the kronecker S{delta}-symbol
     @param d: dimension or an object that has the C{getDim} method defining the dimension
-    @type d: C{int} or any object with a C{getDim} method
+    @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
-    @rtype d: L{numarray.NumArray} of rank 2.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 2.
-    @remark: the function is identical L{identity}
     """
     return identityTensor(d)
-Line 140 
 def identity(shape=()):
+Line 149 
 def identity(shape=()):
     @raise ValueError: if len(shape)>2.
     """
     if len(shape)>0:
-       out=numarray.zeros(shape+shape,numarray.Float)
+       out=numarray.zeros(shape+shape,numarray.Float64)
        if len(shape)==1:
            for i0 in range(shape[0]):
               out[i0,i0]=1.
        elif len(shape)==2:
            for i0 in range(shape[0]):
               for i1 in range(shape[1]):
-Line 160 
 def identityTensor(d=3):
+Line 168 
 def identityTensor(d=3):
     return the dxd identity matrix
     @param d: dimension or an object that has the C{getDim} method defining the dimension
-    @type d: C{int} or any object with a C{getDim} method
+    @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
-    @rtype: L{numarray.NumArray} of rank 2.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 2
     """
-    if hasattr(d,"getDim"):
+    if isinstance(d,escript.FunctionSpace):
-       d=d.getDim()
+        return escript.Data(identity((d.getDim(),)),d)
-    return identity(shape=(d,))
+    elif isinstance(d,escript.Domain):
+        return identity((d.getDim(),))
+    else:
+        return identity((d,))
  def identityTensor4(d=3):
     """
-Line 175 
 def identityTensor4(d=3):
+Line 186 
 def identityTensor4(d=3):
     @param d: dimension or an object that has the C{getDim} method defining the dimension
     @type d: C{int} or any object with a C{getDim} method
     @return: the object u of rank 4 with M{u[i,j,k,l]=1} for M{i=k and j=l} and M{u[i,j,k,l]=0} otherwise
-    @rtype: L{numarray.NumArray} of rank 4.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 4.
     """
-    if hasattr(d,"getDim"):
+    if isinstance(d,escript.FunctionSpace):
-       d=d.getDim()
+        return escript.Data(identity((d.getDim(),d.getDim())),d)
-    return identity((d,d))
+    elif isinstance(d,escript.Domain):
+        return identity((d.getDim(),d.getDim()))
+    else:
+        return identity((d,d))
  def unitVector(i=0,d=3):
     """
-Line 188 
 def unitVector(i=0,d=3):
+Line 202 
 def unitVector(i=0,d=3):
     @param i: index
     @type i: C{int}
     @param d: dimension or an object that has the C{getDim} method defining the dimension
-    @type d: C{int} or any object with a C{getDim} method
+    @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
     @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise
-    @rtype: L{numarray.NumArray} of rank 1.
+    @rtype: L{numarray.NumArray} or L{escript.Data} of rank 1
     """
     return kronecker(d)[i]
-Line 246 
 def inf(arg):
+Line 260 
 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 265 
 def inf(arg):
+Line 279 
 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 287 
 def pokeShape(arg):
+Line 324 
 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 310 
 def commonShape(arg0,arg1):
+Line 347 
 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 335 
 def commonDim(*args):
+Line 372 
 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 357 
 def testForZero(arg):
+Line 394 
 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 391 
 def matchType(arg0=0.,arg1=0.):
+Line 428 
 def matchType(arg0=0.,arg1=0.):
         elif isinstance(arg1,escript.Data):
            arg0=escript.Data(arg0,arg1.getFunctionSpace())
         elif isinstance(arg1,float):
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
            pass
         else:
-Line 417 
 def matchType(arg0=0.,arg1=0.):
+Line 454 
 def matchType(arg0=0.,arg1=0.):
         elif isinstance(arg1,escript.Data):
            pass
         elif isinstance(arg1,float):
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
            pass
         else:
            raise TypeError,"function: Unknown type of second argument."
      elif isinstance(arg0,float):
         if isinstance(arg1,numarray.NumArray):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
         elif isinstance(arg1,escript.Data):
            arg0=escript.Data(arg0,arg1.getFunctionSpace())
         elif isinstance(arg1,float):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
-           arg0=numarray.array(arg0)
+           arg0=numarray.array(arg0,type=numarray.Float64)
         else:
            raise TypeError,"function: Unknown type of second argument."
      elif isinstance(arg0,int):
         if isinstance(arg1,numarray.NumArray):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
         elif isinstance(arg1,escript.Data):
            arg0=escript.Data(float(arg0),arg1.getFunctionSpace())
         elif isinstance(arg1,float):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
-           arg1=numarray.array(arg1)
+           arg1=numarray.array(arg1,type=numarray.Float64)
         elif isinstance(arg1,int):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
-           arg1=numarray.array(float(arg1))
+           arg1=numarray.array(float(arg1),type=numarray.Float64)
         elif isinstance(arg1,Symbol):
-           arg0=numarray.array(float(arg0))
+           arg0=numarray.array(float(arg0),type=numarray.Float64)
         else:
            raise TypeError,"function: Unknown type of second argument."
      else:
-Line 461 
 def matchType(arg0=0.,arg1=0.):
+Line 498 
 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.Float)),arg1
+        return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float64)),arg1
      elif len(sh1)<len(sh):
-        return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float))
+        return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float64))
      else:
         return arg0,arg1
  #=========================================================
-Line 496 
 class Symbol(object):
+Line 533 
 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 540 
 class Symbol(object):
+Line 577 
 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 549 
 class Symbol(object):
+Line 586 
 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 573 
 class Symbol(object):
+Line 610 
 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 600 
 class Symbol(object):
+Line 637 
 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.Float)
+                  out.append(numarray.zeros(s),numarray.Float64)
                else:
                   out.append(a)
         return out
-Line 692 
 class Symbol(object):
+Line 729 
 class Symbol(object):
         else:
            s=self.getShape()+arg.getShape()
            if len(s)>0:
-              return numarray.zeros(s,numarray.Float)
+              return numarray.zeros(s,numarray.Float64)
            else:
               return 0.
-Line 700 
 class Symbol(object):
+Line 737 
 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 709 
 class Symbol(object):
+Line 746 
 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 726 
 class Symbol(object):
+Line 763 
 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 737 
 class Symbol(object):
+Line 774 
 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 748 
 class Symbol(object):
+Line 785 
 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 759 
 class Symbol(object):
+Line 796 
 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 770 
 class Symbol(object):
+Line 807 
 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 781 
 class Symbol(object):
+Line 818 
 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 792 
 class Symbol(object):
+Line 829 
 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 803 
 class Symbol(object):
+Line 840 
 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 814 
 class Symbol(object):
+Line 851 
 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 825 
 class Symbol(object):
+Line 862 
 class Symbol(object):
         @param other: basis
         @type other: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @return: a S{Symbol} representing the power of C{other} to this object
+        @return: a L{Symbol} representing the power of C{other} to this object
         @rtype: L{DependendSymbol} or 0 if C{other} is identical to zero.
         """
         return power(other,self)
+    def __getitem__(self,index):
+        """
+        returns the slice defined by index
+        @param index: defines a
+        @type index: C{slice} or C{int} or a C{tuple} of them
+        @return: a L{Symbol} representing the slice defined by index
+        @rtype: L{DependendSymbol}
+        """
+        return GetSlice_Symbol(self,index)
  class DependendSymbol(Symbol):
     """
     DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal.
     Two DependendSymbol are equal if they have the same shape, the same arguments and one of them has an unspecified spatial dimension or the spatial dimension is identical
-    Example:
+    Example::
-    u1=Symbol(shape=(3,4),dim=2,args=[4.])
+      u1=Symbol(shape=(3,4),dim=2,args=[4.])
-    u2=Symbol(shape=(3,4),dim=2,args=[4.])
+      u2=Symbol(shape=(3,4),dim=2,args=[4.])
-    print u1==u2
+      print u1==u2
-    False
+      False
-       but
+    but::
-    u1=DependendSymbol(shape=(3,4),dim=2,args=[4.])
+      u1=DependendSymbol(shape=(3,4),dim=2,args=[4.])
-    u2=DependendSymbol(shape=(3,4),dim=2,args=[4.])
+      u2=DependendSymbol(shape=(3,4),dim=2,args=[4.])
-    u3=DependendSymbol(shape=(2,),dim=2,args=[4.])
+      u3=DependendSymbol(shape=(2,),dim=2,args=[4.])
-    print u1==u2, u1==u3
+      print u1==u2, u1==u3
-    True False
+      True False
     @note: DependendSymbol should be used as return value of functions with L{Symbol} arguments. This will allow the optimizer to remove redundant function calls.
     """
-Line 880 
 class DependendSymbol(Symbol):
+Line 928 
 class DependendSymbol(Symbol):
  #=========================================================
  #  Unary operations prserving the shape
  #========================================================
+ class GetSlice_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing getting a slice for a L{Symbol}
+    """
+    def __init__(self,arg,index):
+       """
+       initialization of wherePositive L{Symbol} with argument arg
+       @param arg: argument
+       @type arg: L{Symbol}.
+       @param index: defines index
+       @type index: C{slice} or C{int} or a C{tuple} of them
+       @raises IndexError: if length of index is larger than rank of arg or a index start or stop is out of range
+       @raises ValueError: if a step is given
+       """
+       if not isinstance(index,tuple): index=(index,)
+       if len(index)>arg.getRank():
+            raise IndexError,"GetSlice_Symbol: index out of range."
+       sh=()
+       index2=()
+       for i in range(len(index)):
+          ix=index[i]
+          if isinstance(ix,int):
+             if ix<0 or ix>=arg.getShape()[i]:
+                raise ValueError,"GetSlice_Symbol: index out of range."
+             index2=index2+(ix,)
+          else:
+            if not ix.step==None:
+              raise ValueError,"GetSlice_Symbol: steping is not supported."
+            if ix.start==None:
+               s=0
+            else:
+               s=ix.start
+            if ix.stop==None:
+               e=arg.getShape()[i]
+            else:
+               e=ix.stop
+               if e>arg.getShape()[i]:
+                  raise IndexError,"GetSlice_Symbol: index out of range."
+            index2=index2+(slice(s,e),)
+            if e>s:
+                sh=sh+(e-s,)
+            elif s>e:
+                raise IndexError,"GetSlice_Symbol: slice start must be less or equal slice end"
+       for i in range(len(index),arg.getRank()):
+           index2=index2+(slice(0,arg.getShape()[i]),)
+           sh=sh+(arg.getShape()[i],)
+       super(GetSlice_Symbol, self).__init__(args=[arg,index2],shape=sh,dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "%s.__getitem__(%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"GetItem_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          args=self.getSubstitutedArguments(argvals)
+          arg=args[0]
+          index=args[1]
+          return arg.__getitem__(index)
  def log10(arg):
     """
     returns base-10 logarithm of argument arg
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-Line 908 
 def wherePositive(arg):
+Line 1044 
 def wherePositive(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))
+       out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._wherePositive()
-Line 954 
 class WherePositive_Symbol(DependendSymb
+Line 1090 
 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 990 
 def whereNegative(arg):
+Line 1126 
 def whereNegative(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float))
+       out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNegative()
-Line 1036 
 class WhereNegative_Symbol(DependendSymb
+Line 1172 
 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 1072 
 def whereNonNegative(arg):
+Line 1208 
 def whereNonNegative(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float))
+       out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNonNegative()
-Line 1102 
 def whereNonPositive(arg):
+Line 1238 
 def whereNonPositive(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNonPositive()
-Line 1134 
 def whereZero(arg,tol=0.):
+Line 1270 
 def whereZero(arg,tol=0.):
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
     @param tol: tolerance. values with absolute value less then tol are accepted as zero.
     @type tol: C{float}
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
-       if tol>0.:
+       return arg._whereZero(tol)
-          return whereNegative(abs(arg)-tol)
-       else:
-          return arg._whereZero()
     elif isinstance(arg,float):
        if abs(arg)<=tol:
          return 1.
-Line 1183 
 class WhereZero_Symbol(DependendSymbol):
+Line 1316 
 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 1217 
 def whereNonZero(arg,tol=0.):
+Line 1350 
 def whereNonZero(arg,tol=0.):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
-       if tol>0.:
+       return arg._whereNonZero(tol)
-          return 1.-whereZero(arg,tol)
-       else:
-          return arg._whereNonZero()
     elif isinstance(arg,float):
        if abs(arg)>tol:
          return 1.
-Line 1244 
 def whereNonZero(arg,tol=0.):
+Line 1374 
 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 1288 
 class Sin_Symbol(DependendSymbol):
+Line 1432 
 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 1340 
 def cos(arg):
+Line 1484 
 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 1378 
 class Cos_Symbol(DependendSymbol):
+Line 1522 
 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 1430 
 def tan(arg):
+Line 1574 
 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 1468 
 class Tan_Symbol(DependendSymbol):
+Line 1612 
 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 1520 
 def asin(arg):
+Line 1664 
 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 1558 
 class Asin_Symbol(DependendSymbol):
+Line 1702 
 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 1610 
 def acos(arg):
+Line 1754 
 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 1648 
 class Acos_Symbol(DependendSymbol):
+Line 1792 
 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 1700 
 def atan(arg):
+Line 1844 
 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 1738 
 class Atan_Symbol(DependendSymbol):
+Line 1882 
 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 1790 
 def sinh(arg):
+Line 1934 
 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 1828 
 class Sinh_Symbol(DependendSymbol):
+Line 1972 
 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 1880 
 def cosh(arg):
+Line 2024 
 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 1918 
 class Cosh_Symbol(DependendSymbol):
+Line 2062 
 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 1970 
 def tanh(arg):
+Line 2114 
 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 2008 
 class Tanh_Symbol(DependendSymbol):
+Line 2152 
 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 2060 
 def asinh(arg):
+Line 2204 
 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 2098 
 class Asinh_Symbol(DependendSymbol):
+Line 2242 
 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 2150 
 def acosh(arg):
+Line 2294 
 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 2188 
 class Acosh_Symbol(DependendSymbol):
+Line 2332 
 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 2240 
 def atanh(arg):
+Line 2384 
 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 2278 
 class Atanh_Symbol(DependendSymbol):
+Line 2422 
 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 2330 
 def exp(arg):
+Line 2474 
 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 2368 
 class Exp_Symbol(DependendSymbol):
+Line 2512 
 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 2420 
 def sqrt(arg):
+Line 2564 
 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 2458 
 class Sqrt_Symbol(DependendSymbol):
+Line 2602 
 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 2510 
 def log(arg):
+Line 2654 
 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 2548 
 class Log_Symbol(DependendSymbol):
+Line 2692 
 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 2600 
 def sign(arg):
+Line 2744 
 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 2648 
 class Abs_Symbol(DependendSymbol):
+Line 2792 
 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 2700 
 def minval(arg):
+Line 2844 
 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 2741 
 class Minval_Symbol(DependendSymbol):
+Line 2885 
 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 2777 
 def maxval(arg):
+Line 2921 
 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 2818 
 class Maxval_Symbol(DependendSymbol):
+Line 2962 
 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 2854 
 def length(arg):
+Line 2998 
 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))
+ def trace(arg,axis_offset=0):
+    """
+    returns the trace of arg which the sum of arg[k,k] over k.
+    @param arg: argument
+    @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
+    @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
+                   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.
+    """
+    if isinstance(arg,numarray.NumArray):
+       sh=arg.shape
+       if len(sh)<2:
+         raise ValueError,"rank of argument must be greater than 1"
+       if axis_offset<0 or axis_offset>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,"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):
+         for i2 in range(s2):
+             for j in range(sh[axis_offset]): out[i1,i2]+=arg_reshaped[i1,j,j,i2]
+       out.resize(sh[:axis_offset]+sh[axis_offset+2:])
+       return out
+    elif isinstance(arg,escript.Data):
+       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,"illegal argument type float."
+    elif isinstance(arg,int):
+       raise TypeError,"illegal argument type int."
+    elif isinstance(arg,Symbol):
+       return Trace_Symbol(arg,axis_offset)
+    else:
+       raise TypeError,"Unknown argument type."
+ class Trace_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the trace function
+    """
+    def __init__(self,arg,axis_offset=0):
+       """
+       initialization of trace L{Symbol} with argument arg
+       @param arg: argument of function
+       @type arg: L{Symbol}.
+       @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
+                   C{axis_offset} and axis_offset+1 must be equal.
+       @type axis_offset: C{int}
+       """
+       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)
+       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"):
+       """
+       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 "trace(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"Trace_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 trace(arg[0],axis_offset=arg[1])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return trace(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
+ def transpose(arg,axis_offset=None):
+    """
+    returns the transpose of arg by swaping the first C{axis_offset} and the last rank-axis_offset components.
+    @param arg: argument
+    @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}, C{float}, C{int}
+    @param axis_offset: the first C{axis_offset} components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+                        if C{axis_offset} is not present C{int(r/2)} where r is the rank of arg is used.
+    @type axis_offset: C{int}
+    @return: transpose of arg
+    @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray},C{float}, C{int} depending on the type of arg.
+    """
+    if isinstance(arg,numarray.NumArray):
+       if axis_offset==None: axis_offset=int(arg.rank/2)
+       return numarray.transpose(arg,axes=range(axis_offset,arg.rank)+range(0,axis_offset))
+    elif isinstance(arg,escript.Data):
+       r=arg.getRank()
+       if axis_offset==None: axis_offset=int(r/2)
+       if axis_offset<0 or axis_offset>r:
+         raise ValueError,"axis_offset must be between 0 and %s"%r
+       return arg._transpose(axis_offset)
+    elif isinstance(arg,float):
+       if not ( axis_offset==0 or axis_offset==None):
+         raise ValueError,"axis_offset must be 0 for float argument"
+       return arg
+    elif isinstance(arg,int):
+       if not ( axis_offset==0 or axis_offset==None):
+         raise ValueError,"axis_offset must be 0 for int argument"
+       return float(arg)
+    elif isinstance(arg,Symbol):
+       if axis_offset==None: axis_offset=int(arg.getRank()/2)
+       return Transpose_Symbol(arg,axis_offset)
+    else:
+       raise TypeError,"Unknown argument type."
+ class Transpose_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the transpose function
+    """
+    def __init__(self,arg,axis_offset=None):
+       """
+       initialization of transpose L{Symbol} with argument arg
+       @param arg: argument of function
+       @type arg: L{Symbol}.
+       @param axis_offset: the first C{axis_offset} components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+                        if C{axis_offset} is not present C{int(r/2)} where r is the rank of arg is used.
+       @type axis_offset: C{int}
+       """
+       if axis_offset==None: axis_offset=int(arg.getRank()/2)
+       if axis_offset<0 or axis_offset>arg.getRank():
+         raise ValueError,"axis_offset must be between 0 and %s"%arg.getRank()
+       s=arg.getShape()
+       super(Transpose_Symbol,self).__init__(args=[arg,axis_offset],shape=s[axis_offset:]+s[:axis_offset],dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"Transpose_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          arg=self.getSubstitutedArguments(argvals)
+          return transpose(arg[0],axis_offset=arg[1])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return transpose(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
+ def swap_axes(arg,axis0=0,axis1=1):
+    """
+    returns the swap of arg by swaping the components axis0 and axis1
+    @param arg: argument
+    @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
+    @param axis0: axis. C{axis0} must be non-negative and less than the rank of arg.
+    @type axis0: C{int}
+    @param axis1: axis. C{axis1} must be non-negative and less than the rank of arg.
+    @type axis1: C{int}
+    @return: C{arg} with swaped components
+    @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    """
+    if axis0 > axis1:
+       axis0,axis1=axis1,axis0
+    if isinstance(arg,numarray.NumArray):
+       return numarray.swapaxes(arg,axis0,axis1)
+    elif isinstance(arg,escript.Data):
+       return arg._swap_axes(axis0,axis1)
+    elif isinstance(arg,float):
+       raise TyepError,"float argument is not supported."
+    elif isinstance(arg,int):
+       raise TyepError,"int argument is not supported."
+    elif isinstance(arg,Symbol):
+       return SwapAxes_Symbol(arg,axis0,axis1)
+    else:
+       raise TypeError,"Unknown argument type."
+ class SwapAxes_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the swap function
+    """
+    def __init__(self,arg,axis0=0,axis1=1):
+       """
+       initialization of swap L{Symbol} with argument arg
+       @param arg: argument
+       @type arg: L{Symbol}.
+       @param axis0: axis. C{axis0} must be non-negative and less than the rank of arg.
+       @type axis0: C{int}
+       @param axis1: axis. C{axis1} must be non-negative and less than the rank of arg.
+       @type axis1: C{int}
+       """
+       if arg.getRank()<2:
+          raise ValueError,"argument must have at least rank 2."
+       if axis0<0 or axis0>arg.getRank()-1:
+          raise ValueError,"axis0 must be between 0 and %s"%arg.getRank()-1
+       if axis1<0 or axis1>arg.getRank()-1:
+          raise ValueError,"axis1 must be between 0 and %s"%arg.getRank()-1
+       if axis0 == axis1:
+          raise ValueError,"axis indices must be different."
+       if axis0 > axis1:
+          axis0,axis1=axis1,axis0
+       s=arg.getShape()
+       s_out=[]
+       for i in range(len(s)):
+          if i == axis0:
+             s_out.append(s[axis1])
+          elif i == axis1:
+             s_out.append(s[axis0])
+          else:
+             s_out.append(s[i])
+       super(SwapAxes_Symbol,self).__init__(args=[arg,axis0,axis1],shape=tuple(s_out),dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "swap(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"SwapAxes_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          arg=self.getSubstitutedArguments(argvals)
+          return swap_axes(arg[0],axis0=arg[1],axis1=arg[2])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return swap_axes(self.getDifferentiatedArguments(arg)[0],axis0=self.getArgument()[1],axis1=self.getArgument()[2])
+ def symmetric(arg):
+     """
+     returns the symmetric part of the square matrix arg. This is (arg+transpose(arg))/2
+     @param arg: square matrix. Must have rank 2 or 4 and be square.
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: symmetric part of arg
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg,numarray.NumArray):
+       if arg.rank==2:
+         if not (arg.shape[0]==arg.shape[1]):
+            raise ValueError,"argument must be square."
+       elif arg.rank==4:
+         if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
+            raise ValueError,"argument must be square."
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+       return (arg+transpose(arg))/2
+     elif isinstance(arg,escript.Data):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+         return arg._symmetric()
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+         return arg._symmetric()
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     elif isinstance(arg,Symbol):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+       return (arg+transpose(arg))/2
+     else:
+       raise TypeError,"symmetric: Unknown argument type."
+ def nonsymmetric(arg):
+     """
+     returns the nonsymmetric part of the square matrix arg. This is (arg-transpose(arg))/2
+     @param arg: square matrix. Must have rank 2 or 4 and be square.
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: nonsymmetric part of arg
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg,numarray.NumArray):
+       if arg.rank==2:
+         if not (arg.shape[0]==arg.shape[1]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       elif arg.rank==4:
+         if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       else:
+         raise ValueError,"nonsymmetric: rank 2 or 4 is required."
+       return (arg-transpose(arg))/2
+     elif isinstance(arg,escript.Data):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+         return arg._nonsymmetric()
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+         return arg._nonsymmetric()
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     elif isinstance(arg,Symbol):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       else:
+         raise ValueError,"nonsymmetric: rank 2 or 4 is required."
+       return (arg-transpose(arg))/2
+     else:
+       raise TypeError,"nonsymmetric: Unknown argument type."
+ def inverse(arg):
+     """
+     returns the inverse of the square matrix arg.
+     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: inverse arg_inv of the argument. It will be matrix_mult(inverse(arg),arg) almost equal to kronecker(arg.getShape()[0])
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     @note: for L{escript.Data} objects the dimension is restricted to 3.
+     """
+     import numarray.linear_algebra # This statement should be after the next statement but then somehow numarray is gone.
+     if isinstance(arg,numarray.NumArray):
+       return numarray.linear_algebra.inverse(arg)
+     elif isinstance(arg,escript.Data):
+       return escript_inverse(arg)
+     elif isinstance(arg,float):
+       return 1./arg
+     elif isinstance(arg,int):
+       return 1./float(arg)
+     elif isinstance(arg,Symbol):
+       return Inverse_Symbol(arg)
+     else:
+       raise TypeError,"inverse: Unknown argument type."
+ def escript_inverse(arg): # this should be escript._inverse and use LAPACK
+       "arg is a Data objects!!!"
+       if not arg.getRank()==2:
+         raise ValueError,"escript_inverse: argument must have rank 2"
+       s=arg.getShape()
+       if not s[0] == s[1]:
+         raise ValueError,"escript_inverse: argument must be a square matrix."
+       out=escript.Data(0.,s,arg.getFunctionSpace())
+       if s[0]==1:
+           if inf(abs(arg[0,0]))==0: # in c this should be done point wise as abs(arg[0,0](i))<=0.
+               raise ZeroDivisionError,"escript_inverse: argument not invertible"
+           out[0,0]=1./arg[0,0]
+       elif s[0]==2:
+           A11=arg[0,0]
+           A12=arg[0,1]
+           A21=arg[1,0]
+           A22=arg[1,1]
+           D = A11*A22-A12*A21
+           if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
+               raise ZeroDivisionError,"escript_inverse: argument not invertible"
+           D=1./D
+           out[0,0]= A22*D
+           out[1,0]=-A21*D
+           out[0,1]=-A12*D
+           out[1,1]= A11*D
+       elif s[0]==3:
+           A11=arg[0,0]
+           A21=arg[1,0]
+           A31=arg[2,0]
+           A12=arg[0,1]
+           A22=arg[1,1]
+           A32=arg[2,1]
+           A13=arg[0,2]
+           A23=arg[1,2]
+           A33=arg[2,2]
+           D  =  A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22)
+           if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
+               raise ZeroDivisionError,"escript_inverse: argument not invertible"
+           D=1./D
+           out[0,0]=(A22*A33-A23*A32)*D
+           out[1,0]=(A31*A23-A21*A33)*D
+           out[2,0]=(A21*A32-A31*A22)*D
+           out[0,1]=(A13*A32-A12*A33)*D
+           out[1,1]=(A11*A33-A31*A13)*D
+           out[2,1]=(A12*A31-A11*A32)*D
+           out[0,2]=(A12*A23-A13*A22)*D
+           out[1,2]=(A13*A21-A11*A23)*D
+           out[2,2]=(A11*A22-A12*A21)*D
+       else:
+          raise TypeError,"escript_inverse: only matrix dimensions 1,2,3 are supported right now."
+       return out
+ class Inverse_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the inverse function
+    """
+    def __init__(self,arg):
+       """
+       initialization of inverse L{Symbol} with argument arg
+       @param arg: argument of function
+       @type arg: L{Symbol}.
+       """
+       if not arg.getRank()==2:
+         raise ValueError,"Inverse_Symbol:: argument must have rank 2"
+       s=arg.getShape()
+       if not s[0] == s[1]:
+         raise ValueError,"Inverse_Symbol:: argument must be a square matrix."
+       super(Inverse_Symbol,self).__init__(args=[arg],shape=s,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 "inverse(%s)"%argstrs[0]
+       else:
+          raise NotImplementedError,"Inverse_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 inverse(arg[0])
+    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 -matrix_mult(matrix_mult(self,self.getDifferentiatedArguments(arg)[0]),self)
+ def eigenvalues(arg):
+     """
+     returns the eigenvalues of the square matrix arg.
+     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
+                 arg must be symmetric, ie. transpose(arg)==arg (this is not checked).
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the eigenvalues in increasing order.
+     @rtype: L{numarray.NumArray},L{escript.Data}, L{Symbol} depending on the input.
+     @note: for L{escript.Data} and L{Symbol} objects the dimension is restricted to 3.
+     """
+     if isinstance(arg,numarray.NumArray):
+       out=numarray.linear_algebra.eigenvalues((arg+numarray.transpose(arg))/2.)
+       out.sort()
+       return out
+     elif isinstance(arg,escript.Data):
+       return arg._eigenvalues()
+     elif isinstance(arg,Symbol):
+       if not arg.getRank()==2:
+         raise ValueError,"eigenvalues: argument must have rank 2"
+       s=arg.getShape()
+       if not s[0] == s[1]:
+         raise ValueError,"eigenvalues: argument must be a square matrix."
+       if s[0]==1:
+           return arg[0]
+       elif s[0]==2:
+           arg1=symmetric(arg)
+           A11=arg1[0,0]
+           A12=arg1[0,1]
+           A22=arg1[1,1]
+           trA=(A11+A22)/2.
+           A11-=trA
+           A22-=trA
+           s=sqrt(A12**2-A11*A22)
+           return trA+s*numarray.array([-1.,1.],type=numarray.Float64)
+       elif s[0]==3:
+           arg1=symmetric(arg)
+           A11=arg1[0,0]
+           A12=arg1[0,1]
+           A22=arg1[1,1]
+           A13=arg1[0,2]
+           A23=arg1[1,2]
+           A33=arg1[2,2]
+           trA=(A11+A22+A33)/3.
+           A11-=trA
+           A22-=trA
+           A33-=trA
+           A13_2=A13**2
+           A23_2=A23**2
+           A12_2=A12**2
+           p=A13_2+A23_2+A12_2+(A11**2+A22**2+A33**2)/2.
+           q=A13_2*A22+A23_2*A11+A12_2*A33-A11*A22*A33-2*A12*A23*A13
+           sq_p=sqrt(p/3.)
+           alpha_3=acos(clip(-q*(sq_p+whereZero(p,0.)*1.e-15)**(-3.)/2.,-1.,1.))/3.  # whereZero is protection against divison by zero
+           sq_p*=2.
+           f=cos(alpha_3)               *numarray.array([0.,0.,1.],type=numarray.Float64) \
+            -cos(alpha_3+numarray.pi/3.)*numarray.array([0.,1.,0.],type=numarray.Float64) \
+            -cos(alpha_3-numarray.pi/3.)*numarray.array([1.,0.,0.],type=numarray.Float64)
+           return trA+sq_p*f
+       else:
+          raise TypeError,"eigenvalues: only matrix dimensions 1,2,3 are supported right now."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     else:
+       raise TypeError,"eigenvalues: Unknown argument type."
+ def eigenvalues_and_eigenvectors(arg):
+     """
+     returns the eigenvalues and eigenvectors of the square matrix arg.
+     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
+                 arg must be symmetric, ie. transpose(arg)==arg (this is not checked).
+     @type arg: L{escript.Data}
+     @return: the eigenvalues and eigenvectors. The eigenvalues are ordered by increasing value. The
+              eigenvectors are orthogonal and normalized. If V are the eigenvectors than V[:,i] is
+              the eigenvector coresponding to the i-th eigenvalue.
+     @rtype: L{tuple} of L{escript.Data}.
+     @note: The dimension is restricted to 3.
+     """
+     if isinstance(arg,numarray.NumArray):
+       raise TypeError,"eigenvalues_and_eigenvectors is not supporting numarray arguments"
+     elif isinstance(arg,escript.Data):
+       return arg._eigenvalues_and_eigenvectors()
+     elif isinstance(arg,Symbol):
+       raise TypeError,"eigenvalues_and_eigenvectors is not supporting Symbol arguments"
+     elif isinstance(arg,float):
+       return (numarray.array([[arg]],numarray.Float),numarray.ones((1,1),numarray.Float))
+     elif isinstance(arg,int):
+       return (numarray.array([[arg]],numarray.Float),numarray.ones((1,1),numarray.Float))
+     else:
+       raise TypeError,"eigenvalues: Unknown argument type."
  #=======================================================
  #  Binary operations:
  #=======================================================
-Line 2901 
 class Add_Symbol(DependendSymbol):
+Line 3723 
 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 2917 
 class Add_Symbol(DependendSymbol):
+Line 3739 
 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 2976 
 def mult(arg0,arg1):
+Line 3798 
 def mult(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]) or testForZero(args[1]):
-           return numarray.zeros(pokeShape(args[0]),numarray.Float)
+           return numarray.zeros(getShape(args[0]),numarray.Float64)
         else:
            if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) :
                return Mult_Symbol(args[0],args[1])
-Line 3000 
 class Mult_Symbol(DependendSymbol):
+Line 3822 
 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 3016 
 class Mult_Symbol(DependendSymbol):
+Line 3838 
 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 3076 
 def quotient(arg0,arg1):
+Line 3898 
 def quotient(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]):
-           return numarray.zeros(pokeShape(args[0]),numarray.Float)
+           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 3105 
 class Quotient_Symbol(DependendSymbol):
+Line 3927 
 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 3121 
 class Quotient_Symbol(DependendSymbol):
+Line 3943 
 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 3182 
 def power(arg0,arg1):
+Line 4004 
 def power(arg0,arg1):
         """
         args=matchShape(arg0,arg1)
         if testForZero(args[0]):
-           return numarray.zeros(args[0],numarray.Float)
+           return numarray.zeros(getShape(args[0]),numarray.Float64)
         elif testForZero(args[1]):
-           return numarray.ones(args[0],numarray.Float)
+           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 3207 
 class Power_Symbol(DependendSymbol):
+Line 4029 
 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 3225 
 class Power_Symbol(DependendSymbol):
+Line 4047 
 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 3307 
 def minimum(*args):
+Line 4129 
 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 3341 
 def inner(arg0,arg1):
+Line 4171 
 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,offset=len(sh0))
+     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 3371 
 def matrixmult(arg0,arg1):
+Line 4227 
 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,offset=1)
+     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,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 3416 
 def tensormult(arg0,arg1):
+Line 4258 
 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 3434 
 def tensormult(arg0,arg1):
+Line 4276 
 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,offset=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,offset=2)
+        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,offset=0):
+ def generalTensorProduct(arg0,arg1,axis_offset=0):
      """
      generalized tensor product
      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]
-     where s runs through arg0.Shape[:arg0.Rank-offset]
+     where
-           r runs trough arg0.Shape[:offset]
-           t runs through arg1.Shape[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 3468 
 def generalTensorProduct(arg0,arg1,offse
+Line 4309 
 def generalTensorProduct(arg0,arg1,offse
      # 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 GeneralTensorProduct_Symbol(arg0,arg1,offset)
+            return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
         else:
-            if not arg0.shape[arg0.rank-offset:]==arg1.shape[:offset]:
+            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."%(offset,offset)
+                raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
             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-offset]: d0*=i
+            for i in sh0[:arg0.rank-axis_offset]: d0*=i
-            for i in sh1[offset:]: d1*=i
+            for i in sh1[axis_offset:]: d1*=i
-            for i in sh1[:offset]: d01*=i
+            for i in sh1[:axis_offset]: d01*=i
             arg0_c.resize((d0,d01))
             arg1_c.resize((d01,d1))
-            out=numarray.zeros((d0,d1),numarray.Float)
+            out=numarray.zeros((d0,d1),numarray.Float64)
             for i0 in range(d0):
                      for i1 in range(d1):
                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])
-            out.resize(sh0[:arg0.rank-offset]+sh1[offset:])
+            out.resize(sh0[:arg0.rank-axis_offset]+sh1[axis_offset:])
             return out
      elif isinstance(arg0,escript.Data):
         if isinstance(arg1,Symbol):
-            return GeneralTensorProduct_Symbol(arg0,arg1,offset)
+            return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
         else:
-            return escript_generalTensorProduct(arg0,arg1,offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,offset)
+            return escript_generalTensorProduct(arg0,arg1,axis_offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,axis_offset)
      else:
-        return GeneralTensorProduct_Symbol(arg0,arg1,offset)
+        return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
  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,offset=0):
+    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)-offset]
+        sh0=sh_arg0[:len(sh_arg0)-axis_offset]
-        sh01=sh_arg0[len(sh_arg0)-offset:]
+        sh01=sh_arg0[len(sh_arg0)-axis_offset:]
-        sh10=sh_arg1[:offset]
+        sh10=sh_arg1[:axis_offset]
-        sh1=sh_arg1[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."%(offset,offset)
+            raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
-        DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,offset])
+        DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,axis_offset])
     def getMyCode(self,argstrs,format="escript"):
        """
-Line 3530 
 class GeneralTensorProduct_Symbol(Depend
+Line 4371 
 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,offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
+          return "generalTensorProduct(%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)
-Line 3558 
 class GeneralTensorProduct_Symbol(Depend
+Line 4399 
 class GeneralTensorProduct_Symbol(Depend
           args=self.getSubstitutedArguments(argvals)
           return generalTensorProduct(args[0],args[1],args[2])
- def escript_generalTensorProduct(arg0,arg1,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()-offset]
-     shape01=arg0.getShape()[arg0.getRank()-offset:]
+ def transposed_matrix_mult(arg0,arg1):
-     shape10=arg1.getShape()[:offset]
+     """
-     shape1=arg1.getShape()[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."%(offset,offset)
+     out[s0]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0]
-     # create return value:
+     or
-     out=escript.Data(0.,tuple(shape0+shape1),arg0.getFunctionSpace())
-     #
+     out[s0,s1]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0,s1]
-     s0=[[]]
-     for k in shape0:
+     The function call transposed_matrix_mult(arg0,arg1) is equivalent to matrix_mult(transpose(arg0),arg1).
-           s=[]
-           for j in s0:
+     The first dimension of arg0 and arg1 must match.
-                 for i in range(k): s.append(j+[slice(i,i)])
-           s0=s
+     @param arg0: first argument of rank 2
-     s1=[[]]
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-     for k in shape1:
+     @param arg1: second argument of at least rank 1
-           s=[]
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-           for j in s1:
+     @return: the product of the transposed of arg0 and arg1 at each data point
-                 for i in range(k): s.append(j+[slice(i,i)])
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
-           s1=s
+     @raise ValueError: if the shapes of the arguments are not appropriate
-     s01=[[]]
+     """
-     for k in shape01:
+     sh0=getShape(arg0)
-           s=[]
+     sh1=getShape(arg1)
-           for j in s01:
+     if not len(sh0)==2 :
-                 for i in range(k): s.append(j+[slice(i,i)])
+         raise ValueError,"first argument must have rank 2"
-           s01=s
+     if not len(sh1)==2 and not len(sh1)==1:
+         raise ValueError,"second argument must have rank 1 or 2"
-     for i0 in s0:
+     return generalTransposedTensorProduct(arg0,arg1,axis_offset=1)
-        for i1 in s1:
-          s=escript.Scalar(0.,arg0.getFunctionSpace())
+ def transposed_tensor_mult(arg0,arg1):
-          for i01 in s01:
+     """
-             s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))
+     the tensor product of the transposed of the first and the second argument
-          out.__setitem__(tuple(i0+i1),s)
-     return out
+     for arg0 of rank 2 this is
+     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)
  #=========================================================
- #   some little helpers
+ #  functions dealing with spatial dependency
  #=========================================================
  def grad(arg,where=None):
      """
      Returns the spatial gradient of arg at where.
+     If C{g} is the returned object, then
+       - if C{arg} is rank 0 C{g[s]} is the derivative of C{arg} with respect to the C{s}-th spatial dimension.
+       - if C{arg} is rank 1 C{g[i,s]} is the derivative of C{arg[i]} with respect to the C{s}-th spatial dimension.
+       - if C{arg} is rank 2 C{g[i,j,s]} is the derivative of C{arg[i,j]} with respect to the C{s}-th spatial dimension.
+       - if C{arg} is rank 3 C{g[i,j,k,s]} is the derivative of C{arg[i,j,k]} with respect to the C{s}-th spatial dimension.
-     @param arg:   Data object representing the function which gradient
+     @param arg: function which gradient to be calculated. Its rank has to be less than 3.
-                   to be calculated.
+     @type arg: L{escript.Data} or L{Symbol}
      @param where: FunctionSpace in which the gradient will be calculated.
                    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}
      """
      if isinstance(arg,Symbol):
         return Grad_Symbol(arg,where)
-Line 3618 
 def grad(arg,where=None):
+Line 4814 
 def grad(arg,where=None):
         else:
            return arg._grad(where)
      else:
-       raise TypeError,"grad: Unknown argument type."
+        raise TypeError,"grad: Unknown argument type."
+ class Grad_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the gradient operator
+    """
+    def __init__(self,arg,where=None):
+       """
+       initialization of gradient L{Symbol} with argument arg
+       @param arg: argument of function
+       @type arg: L{Symbol}.
+       @param where: FunctionSpace in which the gradient will be calculated.
+                   If not present or C{None} an appropriate default is used.
+       @type where: C{None} or L{escript.FunctionSpace}
+       """
+       d=arg.getDim()
+       if d==None:
+          raise ValueError,"argument must have a spatial dimension"
+       super(Grad_Symbol,self).__init__(args=[arg,where],shape=arg.getShape()+(d,),dim=d)
+    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 "grad(%s,where=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"Trace_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 grad(arg[0],where=arg[1])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return grad(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
  def integrate(arg,where=None):
      """
-     Return the integral if the function represented by Data object arg over
+     Return the integral of the function C{arg} over its domain. If C{where} is present C{arg} is interpolated to C{where}
-     its domain.
+     before integration.
-     @param arg:   Data object representing the function which is integrated.
+     @param arg:   the function which is integrated.
+     @type arg: L{escript.Data} or L{Symbol}
      @param where: FunctionSpace in which the integral is calculated.
                    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}
      """
-     if isinstance(arg,numarray.NumArray):
+     if isinstance(arg,Symbol):
-         if checkForZero(arg):
-            return arg
-         else:
-            raise TypeError,"integrate: cannot intergrate argument"
-     elif isinstance(arg,float):
-         if checkForZero(arg):
-            return arg
-         else:
-            raise TypeError,"integrate: cannot intergrate argument"
-     elif isinstance(arg,int):
-         if checkForZero(arg):
-            return float(arg)
-         else:
-            raise TypeError,"integrate: cannot intergrate argument"
-     elif isinstance(arg,Symbol):
         return Integrate_Symbol(arg,where)
      elif isinstance(arg,escript.Data):
         if not where==None: arg=escript.Data(arg,where)
-Line 3655 
 def integrate(arg,where=None):
+Line 4910 
 def integrate(arg,where=None):
      else:
        raise TypeError,"integrate: Unknown argument type."
+ class Integrate_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the spatial integration operator
+    """
+    def __init__(self,arg,where=None):
+       """
+       initialization of integration L{Symbol} with argument arg
+       @param arg: argument of the integration
+       @type arg: L{Symbol}.
+       @param where: FunctionSpace in which the integration will be calculated.
+                   If not present or C{None} an appropriate default is used.
+       @type where: C{None} or L{escript.FunctionSpace}
+       """
+       super(Integrate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),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 "integrate(%s,where=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"Trace_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 integrate(arg[0],where=arg[1])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return integrate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
  def interpolate(arg,where):
      """
-     Interpolates the function into the FunctionSpace where.
+     interpolates the function into the FunctionSpace where.
-     @param arg:    interpolant
+     @param arg: interpolant
-     @param where:  FunctionSpace to interpolate to
+     @type arg: L{escript.Data} or L{Symbol}
+     @param where: FunctionSpace to be interpolated to
+     @type where: L{escript.FunctionSpace}
+     @return: interpolated argument
+     @rtype: C{escript.Data} or L{Symbol}
      """
      if isinstance(arg,Symbol):
-        return Interpolated_Symbol(arg,where)
+        return Interpolate_Symbol(arg,where)
      else:
         return escript.Data(arg,where)
- def div(arg,where=None):
+ class Interpolate_Symbol(DependendSymbol):
-     """
+    """
-     Returns the divergence of arg at where.
+    L{Symbol} representing the result of the interpolation operator
+    """
+    def __init__(self,arg,where):
+       """
+       initialization of interpolation L{Symbol} with argument arg
+       @param arg: argument of the interpolation
+       @type arg: L{Symbol}.
+       @param where: FunctionSpace into which the argument is interpolated.
+       @type where: L{escript.FunctionSpace}
+       """
+       super(Interpolate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),dim=arg.getDim())
-     @param arg:   Data object representing the function which gradient to
+    def getMyCode(self,argstrs,format="escript"):
-                   be calculated.
+       """
-     @param where: FunctionSpace in which the gradient will be calculated.
+       returns a program code that can be used to evaluate the symbol.
-                   If not present or C{None} an appropriate default is used.
-     """
-     g=grad(arg,where)
-     return trace(g,axis0=g.getRank()-2,axis1=g.getRank()-1)
- def jump(arg):
+       @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}.
-     Returns the jump of arg across a continuity.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @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 "interpolate(%s,where=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
-     @param arg:   Data object representing the function which gradient
+    def substitute(self,argvals):
-                   to be calculated.
+       """
-     """
+       assigns new values to symbols in the definition of the symbol.
-     d=arg.getDomain()
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
-     return arg.interpolate(escript.FunctionOnContactOne(d))-arg.interpolate(escript.FunctionOnContactZero(d))
- #=============================
+       @param argvals: new values assigned to symbols
- #
+       @type argvals: C{dict} with keywords of type L{Symbol}.
- # wrapper for various functions: if the argument has attribute the function name
+       @return: result of the substitution process. Operations are executed as much as possible.
- # as an argument it calls the corresponding methods. Otherwise the corresponding
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
- # numarray function is called.
+       @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 interpolate(arg[0],where=arg[1])
- # functions involving the underlying Domain:
+    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: L{Symbol} but other types such as L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return interpolate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
- def transpose(arg,axis=None):
+ def div(arg,where=None):
      """
-     Returns the transpose of the Data object arg.
+     returns the divergence of arg at where.
-     @param arg:
+     @param arg: function which divergence to be calculated. Its shape has to be (d,) where d is the spatial dimension.
+     @type arg: L{escript.Data} or L{Symbol}
+     @param where: FunctionSpace in which the divergence will be calculated.
+                   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}
      """
-     if axis==None:
-        r=0
-        if hasattr(arg,"getRank"): r=arg.getRank()
-        if hasattr(arg,"rank"): r=arg.rank
-        axis=r/2
      if isinstance(arg,Symbol):
-        return Transpose_Symbol(arg,axis=r)
+         dim=arg.getDim()
-     if isinstance(arg,escript.Data):
+     elif isinstance(arg,escript.Data):
-        # hack for transpose
+         dim=arg.getDomain().getDim()
-        r=arg.getRank()
-        if r!=2: raise ValueError,"Tranpose only avalaible for rank 2 objects"
-        s=arg.getShape()
-        out=escript.Data(0.,(s[1],s[0]),arg.getFunctionSpace())
-        for i in range(s[0]):
-           for j in range(s[1]):
-              out[j,i]=arg[i,j]
-        return out
-        # end hack for transpose
-        return arg.transpose(axis)
      else:
-        return numarray.transpose(arg,axis=axis)
+         raise TypeError,"div: argument type not supported"
+     if not arg.getShape()==(dim,):
+       raise ValueError,"div: expected shape is (%s,)"%dim
+     return trace(grad(arg,where))
- def trace(arg,axis0=0,axis1=1):
+ def jump(arg,domain=None):
      """
-     Return
+     returns the jump of arg across the continuity of the domain
-     @param arg:
+     @param arg: argument
+     @type arg: L{escript.Data} or L{Symbol}
+     @param domain: the domain where the discontinuity is located. If domain is not present or equal to C{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}
      """
-     if isinstance(arg,Symbol):
+     if domain==None: domain=arg.getDomain()
-        s=list(arg.getShape())
+     return interpolate(arg,escript.FunctionOnContactOne(domain))-interpolate(arg,escript.FunctionOnContactZero(domain))
-        s=tuple(s[0:axis0]+s[axis0+1:axis1]+s[axis1+1:])
-        return Trace_Symbol(arg,axis0=axis0,axis1=axis1)
-     elif isinstance(arg,escript.Data):
-        # hack for trace
-        s=arg.getShape()
-        if s[axis0]!=s[axis1]:
-            raise ValueError,"illegal axis in trace"
-        out=escript.Scalar(0.,arg.getFunctionSpace())
-        for i in range(s[axis0]):
-           out+=arg[i,i]
-        return out
-        # end hack for trace
-     else:
-        return numarray.trace(arg,axis0=axis0,axis1=axis1)
+ def L2(arg):
+     """
+     returns the L2 norm of arg at where
+     @param arg: function which L2 to be calculated.
+     @type arg: L{escript.Data} or L{Symbol}
+     @return: L2 norm of arg.
+     @rtype: L{float} or L{Symbol}
+     @note: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
+     """
+     return sqrt(integrate(inner(arg,arg)))
+ #=============================
+ #
  def reorderComponents(arg,index):
      """
      resorts the component of arg according to index
      """
-     pass
+     raise NotImplementedError
  #
  # $Log: util.py,v $
  # Revision 1.14.2.16  2005/10/19 06:09:57  gross

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