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

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

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-revision 429 by gross,
Wed Jan 11 05:53:40 2006 UTC
+revision 1312 by ksteube,
Mon Sep 24 06:18:44 2007 UTC
 Line 1
+ #
  # $Id$
  #
- #      COPYRIGHT ACcESS 2004 -  All Rights Reserved
+ #######################################################
+ #
+ #           Copyright 2003-2007 by ACceSS MNRF
+ #       Copyright 2007 by University of Queensland
+ #
+ #                http://esscc.uq.edu.au
+ #        Primary Business: Queensland, Australia
+ #  Licensed under the Open Software License version 3.0
+ #     http://www.opensource.org/licenses/osl-3.0.php
  #
- #   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
+ @var EPSILON: smallest positive value with 1.<1.+EPSILON
  """
  __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 41 
 import math
  import numarray
  import escript
  import os
+ from esys.escript import C_GeneralTensorProduct
- # missing tests:
+ from esys.escript import getVersion
- # 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 getEpsilon():
+      #     ------------------------------------------------------------------
+      #     Compute EPSILON, the machine precision.  The call to daxpp is
+      #     inTENded to fool compilers that use extra-length registers.
+      #     31 Map 1999: Hardwire EPSILON so the debugger can step thru easily.
+      #     ------------------------------------------------------------------
+      eps    = 2.**(-12)
+      p=2.
+      while p>1.:
+             eps/=2.
+             p=1.+eps
+      return eps*2.
+ EPSILON=getEpsilon()
+ 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(..)
-        saveVTK("solution.xml",temperature=tmp,velovity=v)
+        saveVTK("solution.xml",temperature=tmp,velocity=v)
-     tmp and v are written into "solution.xml" where tmp is named "temperature" and v is named "velovity"
+     tmp and v are written into "solution.xml" where tmp is named "temperature" and v is named "velocity"
      @param filename: file name of the output file
      @type filename: C{str}
-Line 81 
 def saveVTK(filename,domain=None,**data)
+Line 121 
 def saveVTK(filename,domain=None,**data)
      @type <name>: L{Data} object.
      @note: The data objects have to be defined on the same domain. They may not be in the same L{FunctionSpace} but one cannot expect that all L{FunctionSpace} can be mixed. Typically, data on the boundary and data on the interior cannot be mixed.
      """
-     if domain==None:
+     new_data={}
-        for i in data.keys():
+     for n,d in data.items():
-           if not data[i].isEmpty(): domain=data[i].getFunctionSpace().getDomain()
+           if not d.isEmpty():
+             fs=d.getFunctionSpace()
+             domain2=fs.getDomain()
+             if fs == escript.Solution(domain2):
+                new_data[n]=interpolate(d,escript.ContinuousFunction(domain2))
+             elif fs == escript.ReducedSolution(domain2):
+                new_data[n]=interpolate(d,escript.ReducedContinuousFunction(domain2))
+             else:
+                new_data[n]=d
+             if domain==None: domain=domain2
      if domain==None:
          raise ValueError,"no domain detected."
-     else:
+     domain.saveVTK(filename,new_data)
-         domain.saveVTK(filename,data)
  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(..)
-        saveDX("solution.dx",temperature=tmp,velovity=v)
+        saveDX("solution.dx",temperature=tmp,velocity=v)
-     tmp and v are written into "solution.dx" where tmp is named "temperature" and v is named "velovity".
+     tmp and v are written into "solution.dx" where tmp is named "temperature" and v is named "velocity".
      @param filename: file name of the output file
      @type filename: C{str}
-Line 109 
 def saveDX(filename,domain=None,**data):
+Line 157 
 def saveDX(filename,domain=None,**data):
      @type <name>: L{Data} object.
      @note: The data objects have to be defined on the same domain. They may not be in the same L{FunctionSpace} but one cannot expect that all L{FunctionSpace} can be mixed. Typically, data on the boundary and data on the interior cannot be mixed.
      """
-     if domain==None:
+     new_data={}
-        for i in data.keys():
+     for n,d in data.items():
-           if not data[i].isEmpty(): domain=data[i].getFunctionSpace().getDomain()
+           if not d.isEmpty():
+             fs=d.getFunctionSpace()
+             domain2=fs.getDomain()
+             if fs == escript.Solution(domain2):
+                new_data[n]=interpolate(d,escript.ReducedContinuousFunction(domain2))
+             elif fs == escript.ReducedSolution(domain2):
+                new_data[n]=interpolate(d,escript.ReducedContinuousFunction(domain2))
+             elif fs == escript.ContinuousFunction(domain2):
+                new_data[n]=interpolate(d,escript.ReducedContinuousFunction(domain2))
+             else:
+                new_data[n]=d
+             if domain==None: domain=domain2
      if domain==None:
          raise ValueError,"no domain detected."
-     else:
+     domain.saveDX(filename,new_data)
-         domain.saveDX(filename,data)
  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 197 
 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 216 
 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 234 
 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 250 
 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 308 
 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 327 
 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 372 
 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 395 
 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 420 
 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 442 
 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 476 
 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 502 
 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 546 
 def matchType(arg0=0.,arg1=0.):
  def matchShape(arg0,arg1):
      """
+     return representations of arg0 amd arg1 which ahve the same shape
-     If shape is not given the shape "largest" shape of args is used.
+     @param arg0: a given object
+     @type arg0: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, L{Symbol}
-     @param args: a given ob
+     @param arg1: a given object
-     @type arg: typically L{numarray.NumArray},L{escript.Data},C{float}, C{int}
+     @type arg1: L{numarray.NumArray},L{escript.Data},C{float}, C{int}, L{Symbol}
-     @return: True if the argument is identical to zero.
+     @return: C{arg0} and C{arg1} where copies are returned when the shape has to be changed.
-     @rtype: C{list} of C{int}
+     @rtype: C{tuple}
      """
      sh=commonShape(arg0,arg1)
-     sh0=pokeShape(arg0)
+     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 581 
 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 625 
 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 634 
 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 658 
 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 685 
 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 777 
 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 785 
 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 794 
 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 811 
 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 822 
 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 833 
 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 844 
 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 855 
 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 866 
 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 877 
 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 888 
 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 899 
 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 910 
 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 976 
 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 1092 
 def wherePositive(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._wherePositive()
-Line 954 
 class WherePositive_Symbol(DependendSymb
+Line 1138 
 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 1174 
 def whereNegative(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNegative()
-Line 1036 
 class WhereNegative_Symbol(DependendSymb
+Line 1220 
 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 1256 
 def whereNonNegative(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
     @raises TypeError: if the type of the argument is not expected.
     """
     if isinstance(arg,numarray.NumArray):
-       out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.
+       out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float64))*1.
-       if isinstance(out,float): out=numarray.array(out)
+       if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
        return out
     elif isinstance(arg,escript.Data):
        return arg._whereNonNegative()
-Line 1102 
 def whereNonPositive(arg):
+Line 1286 
 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 1318 
 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 1364 
 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 1398 
 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 1422 
 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 1480 
 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 1532 
 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 1570 
 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 1622 
 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 1660 
 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 1712 
 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 1750 
 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 1802 
 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 1840 
 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 1892 
 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 1930 
 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 1982 
 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 2020 
 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 2072 
 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 2110 
 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 2162 
 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 2200 
 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 2252 
 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 2290 
 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 2342 
 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 2380 
 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 2432 
 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 2470 
 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 2522 
 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 2560 
 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 2612 
 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 2650 
 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 2702 
 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 2740 
 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 2792 
 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 2840 
 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 2892 
 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 2933 
 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 2969 
 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 3010 
 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 3046 
 def length(arg):
     @param arg: argument
     @type arg: C{float}, L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @rtype:C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
+    @rtype: C{float}, L{escript.Data}, L{Symbol} depending on the type of arg.
     """
     return sqrt(inner(arg,arg))
-Line 2864 
 def trace(arg,axis_offset=0):
+Line 3056 
 def trace(arg,axis_offset=0):
     @param arg: argument
     @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
-    @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
+    @param axis_offset: C{axis_offset} to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
-                   axis_offset and axis_offset+1 must be equal.
+                   C{axis_offset} and axis_offset+1 must be equal.
     @type axis_offset: C{int}
     @return: trace of arg. The rank of the returned object is minus 2 of the rank of arg.
     @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
-Line 2873 
 def trace(arg,axis_offset=0):
+Line 3065 
 def trace(arg,axis_offset=0):
     if isinstance(arg,numarray.NumArray):
        sh=arg.shape
        if len(sh)<2:
-         raise ValueError,"trace: rank of argument must be greater than 1"
+         raise ValueError,"rank of argument must be greater than 1"
        if axis_offset<0 or axis_offset>len(sh)-2:
-         raise ValueError,"trace: axis_offset must be between 0 and %s"%len(sh)-2
+         raise ValueError,"axis_offset must be between 0 and %s"%len(sh)-2
        s1=1
        for i in range(axis_offset): s1*=sh[i]
        s2=1
        for i in range(axis_offset+2,len(sh)): s2*=sh[i]
        if not sh[axis_offset] == sh[axis_offset+1]:
-         raise ValueError,"trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
+         raise ValueError,"dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
        arg_reshaped=numarray.reshape(arg,(s1,sh[axis_offset],sh[axis_offset],s2))
-       out=numarray.zeros([s1,s2],numarray.Float)
+       out=numarray.zeros([s1,s2],numarray.Float64)
        for i1 in range(s1):
          for i2 in range(s2):
              for j in range(sh[axis_offset]): out[i1,i2]+=arg_reshaped[i1,j,j,i2]
        out.resize(sh[:axis_offset]+sh[axis_offset+2:])
        return out
     elif isinstance(arg,escript.Data):
-       return escript_trace(arg,axis_offset)
+       if arg.getRank()<2:
+         raise ValueError,"rank of argument must be greater than 1"
+       if axis_offset<0 or axis_offset>arg.getRank()-2:
+         raise ValueError,"axis_offset must be between 0 and %s"%arg.getRank()-2
+       s=list(arg.getShape())
+       if not s[axis_offset] == s[axis_offset+1]:
+         raise ValueError,"dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
+       return arg._trace(axis_offset)
     elif isinstance(arg,float):
-       raise TypeError,"trace: illegal argument type float."
+       raise TypeError,"illegal argument type float."
     elif isinstance(arg,int):
-       raise TypeError,"trace: illegal argument type int."
+       raise TypeError,"illegal argument type int."
     elif isinstance(arg,Symbol):
        return Trace_Symbol(arg,axis_offset)
     else:
-       raise TypeError,"trace: Unknown argument type."
+       raise TypeError,"Unknown argument type."
- def escript_trace(arg,axis_offset): # this should be escript._trace
-       "arg si a Data objects!!!"
-       if arg.getRank()<2:
-         raise ValueError,"escript_trace: rank of argument must be greater than 1"
-       if axis_offset<0 or axis_offset>arg.getRank()-2:
-         raise ValueError,"escript_trace: axis_offset must be between 0 and %s"%arg.getRank()-2
-       s=list(arg.getShape())
-       if not s[axis_offset] == s[axis_offset+1]:
-         raise ValueError,"escript_trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
-       out=escript.Data(0.,tuple(s[0:axis_offset]+s[axis_offset+2:]),arg.getFunctionSpace())
-       if arg.getRank()==2:
-          for i0 in range(s[0]):
-             out+=arg[i0,i0]
-       elif arg.getRank()==3:
-          if axis_offset==0:
-             for i0 in range(s[0]):
-                   for i2 in range(s[2]):
-                          out[i2]+=arg[i0,i0,i2]
-          elif axis_offset==1:
-             for i0 in range(s[0]):
-                for i1 in range(s[1]):
-                          out[i0]+=arg[i0,i1,i1]
-       elif arg.getRank()==4:
-          if axis_offset==0:
-             for i0 in range(s[0]):
-                   for i2 in range(s[2]):
-                      for i3 in range(s[3]):
-                          out[i2,i3]+=arg[i0,i0,i2,i3]
-          elif axis_offset==1:
-             for i0 in range(s[0]):
-                for i1 in range(s[1]):
-                      for i3 in range(s[3]):
-                          out[i0,i3]+=arg[i0,i1,i1,i3]
-          elif axis_offset==2:
-             for i0 in range(s[0]):
-                for i1 in range(s[1]):
-                   for i2 in range(s[2]):
-                          out[i0,i1]+=arg[i0,i1,i2,i2]
-       return out
  class Trace_Symbol(DependendSymbol):
     """
     L{Symbol} representing the result of the trace function
-Line 2948 
 class Trace_Symbol(DependendSymbol):
+Line 3108 
 class Trace_Symbol(DependendSymbol):
        initialization of trace L{Symbol} with argument arg
        @param arg: argument of function
        @type arg: L{Symbol}.
-       @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
+       @param axis_offset: C{axis_offset} to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
-                   axis_offset and axis_offset+1 must be equal.
+                   C{axis_offset} and axis_offset+1 must be equal.
        @type axis_offset: C{int}
        """
        if arg.getRank()<2:
-         raise ValueError,"Trace_Symbol: rank of argument must be greater than 1"
+         raise ValueError,"rank of argument must be greater than 1"
        if axis_offset<0 or axis_offset>arg.getRank()-2:
-         raise ValueError,"Trace_Symbol: axis_offset must be between 0 and %s"%arg.getRank()-2
+         raise ValueError,"axis_offset must be between 0 and %s"%arg.getRank()-2
        s=list(arg.getShape())
        if not s[axis_offset] == s[axis_offset+1]:
-         raise ValueError,"Trace_Symbol: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
+         raise ValueError,"dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
        super(Trace_Symbol,self).__init__(args=[arg,axis_offset],shape=tuple(s[0:axis_offset]+s[axis_offset+2:]),dim=arg.getDim())
     def getMyCode(self,argstrs,format="escript"):
-Line 2971 
 class Trace_Symbol(DependendSymbol):
+Line 3131 
 class Trace_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "trace(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
-Line 3013 
 class Trace_Symbol(DependendSymbol):
+Line 3173 
 class Trace_Symbol(DependendSymbol):
        else:
           return trace(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
+ def transpose(arg,axis_offset=None):
+    """
+    returns the transpose of arg by swaping the first C{axis_offset} and the last rank-axis_offset components.
+    @param arg: argument
+    @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}, C{float}, C{int}
+    @param axis_offset: the first C{axis_offset} components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+                        if C{axis_offset} is not present C{int(r/2)} where r is the rank of arg is used.
+    @type axis_offset: C{int}
+    @return: transpose of arg
+    @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray},C{float}, C{int} depending on the type of arg.
+    """
+    if isinstance(arg,numarray.NumArray):
+       if axis_offset==None: axis_offset=int(arg.rank/2)
+       return numarray.transpose(arg,axes=range(axis_offset,arg.rank)+range(0,axis_offset))
+    elif isinstance(arg,escript.Data):
+       r=arg.getRank()
+       if axis_offset==None: axis_offset=int(r/2)
+       if axis_offset<0 or axis_offset>r:
+         raise ValueError,"axis_offset must be between 0 and %s"%r
+       return arg._transpose(axis_offset)
+    elif isinstance(arg,float):
+       if not ( axis_offset==0 or axis_offset==None):
+         raise ValueError,"axis_offset must be 0 for float argument"
+       return arg
+    elif isinstance(arg,int):
+       if not ( axis_offset==0 or axis_offset==None):
+         raise ValueError,"axis_offset must be 0 for int argument"
+       return float(arg)
+    elif isinstance(arg,Symbol):
+       if axis_offset==None: axis_offset=int(arg.getRank()/2)
+       return Transpose_Symbol(arg,axis_offset)
+    else:
+       raise TypeError,"Unknown argument type."
+ class Transpose_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the transpose function
+    """
+    def __init__(self,arg,axis_offset=None):
+       """
+       initialization of transpose L{Symbol} with argument arg
+       @param arg: argument of function
+       @type arg: L{Symbol}.
+       @param axis_offset: the first C{axis_offset} components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
+                        if C{axis_offset} is not present C{int(r/2)} where r is the rank of arg is used.
+       @type axis_offset: C{int}
+       """
+       if axis_offset==None: axis_offset=int(arg.getRank()/2)
+       if axis_offset<0 or axis_offset>arg.getRank():
+         raise ValueError,"axis_offset must be between 0 and %s"%arg.getRank()
+       s=arg.getShape()
+       super(Transpose_Symbol,self).__init__(args=[arg,axis_offset],shape=s[axis_offset:]+s[:axis_offset],dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"Transpose_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          arg=self.getSubstitutedArguments(argvals)
+          return transpose(arg[0],axis_offset=arg[1])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return transpose(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
+ def swap_axes(arg,axis0=0,axis1=1):
+    """
+    returns the swap of arg by swaping the components axis0 and axis1
+    @param arg: argument
+    @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
+    @param axis0: axis. C{axis0} must be non-negative and less than the rank of arg.
+    @type axis0: C{int}
+    @param axis1: axis. C{axis1} must be non-negative and less than the rank of arg.
+    @type axis1: C{int}
+    @return: C{arg} with swaped components
+    @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
+    """
+    if axis0 > axis1:
+       axis0,axis1=axis1,axis0
+    if isinstance(arg,numarray.NumArray):
+       return numarray.swapaxes(arg,axis0,axis1)
+    elif isinstance(arg,escript.Data):
+       return arg._swap_axes(axis0,axis1)
+    elif isinstance(arg,float):
+       raise TyepError,"float argument is not supported."
+    elif isinstance(arg,int):
+       raise TyepError,"int argument is not supported."
+    elif isinstance(arg,Symbol):
+       return SwapAxes_Symbol(arg,axis0,axis1)
+    else:
+       raise TypeError,"Unknown argument type."
+ class SwapAxes_Symbol(DependendSymbol):
+    """
+    L{Symbol} representing the result of the swap function
+    """
+    def __init__(self,arg,axis0=0,axis1=1):
+       """
+       initialization of swap L{Symbol} with argument arg
+       @param arg: argument
+       @type arg: L{Symbol}.
+       @param axis0: axis. C{axis0} must be non-negative and less than the rank of arg.
+       @type axis0: C{int}
+       @param axis1: axis. C{axis1} must be non-negative and less than the rank of arg.
+       @type axis1: C{int}
+       """
+       if arg.getRank()<2:
+          raise ValueError,"argument must have at least rank 2."
+       if axis0<0 or axis0>arg.getRank()-1:
+          raise ValueError,"axis0 must be between 0 and %s"%arg.getRank()-1
+       if axis1<0 or axis1>arg.getRank()-1:
+          raise ValueError,"axis1 must be between 0 and %s"%arg.getRank()-1
+       if axis0 == axis1:
+          raise ValueError,"axis indices must be different."
+       if axis0 > axis1:
+          axis0,axis1=axis1,axis0
+       s=arg.getShape()
+       s_out=[]
+       for i in range(len(s)):
+          if i == axis0:
+             s_out.append(s[axis1])
+          elif i == axis1:
+             s_out.append(s[axis0])
+          else:
+             s_out.append(s[i])
+       super(SwapAxes_Symbol,self).__init__(args=[arg,axis0,axis1],shape=tuple(s_out),dim=arg.getDim())
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{str} or a C{list} of length 1 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str"  or format=="text":
+          return "swap(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
+       else:
+          raise NotImplementedError,"SwapAxes_Symbol does not provide program code for format %s."%format
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          arg=self.getSubstitutedArguments(argvals)
+          return swap_axes(arg[0],axis0=arg[1],axis1=arg[2])
+    def diff(self,arg):
+       """
+       differential of this object
+       @param arg: the derivative is calculated with respect to arg
+       @type arg: L{escript.Symbol}
+       @return: derivative with respect to C{arg}
+       @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
+       """
+       if arg==self:
+          return identity(self.getShape())
+       else:
+          return swap_axes(self.getDifferentiatedArguments(arg)[0],axis0=self.getArgument()[1],axis1=self.getArgument()[2])
+ def symmetric(arg):
+     """
+     returns the symmetric part of the square matrix arg. This is (arg+transpose(arg))/2
+     @param arg: square matrix. Must have rank 2 or 4 and be square.
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: symmetric part of arg
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg,numarray.NumArray):
+       if arg.rank==2:
+         if not (arg.shape[0]==arg.shape[1]):
+            raise ValueError,"argument must be square."
+       elif arg.rank==4:
+         if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
+            raise ValueError,"argument must be square."
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+       return (arg+transpose(arg))/2
+     elif isinstance(arg,escript.Data):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+         return arg._symmetric()
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+         return arg._symmetric()
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     elif isinstance(arg,Symbol):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+       return (arg+transpose(arg))/2
+     else:
+       raise TypeError,"symmetric: Unknown argument type."
+ def nonsymmetric(arg):
+     """
+     returns the nonsymmetric part of the square matrix arg. This is (arg-transpose(arg))/2
+     @param arg: square matrix. Must have rank 2 or 4 and be square.
+     @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: nonsymmetric part of arg
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg,numarray.NumArray):
+       if arg.rank==2:
+         if not (arg.shape[0]==arg.shape[1]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       elif arg.rank==4:
+         if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       else:
+         raise ValueError,"nonsymmetric: rank 2 or 4 is required."
+       return (arg-transpose(arg))/2
+     elif isinstance(arg,escript.Data):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"argument must be square."
+         return arg._nonsymmetric()
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"argument must be square."
+         return arg._nonsymmetric()
+       else:
+         raise ValueError,"rank 2 or 4 is required."
+     elif isinstance(arg,float):
+       return arg
+     elif isinstance(arg,int):
+       return float(arg)
+     elif isinstance(arg,Symbol):
+       if arg.getRank()==2:
+         if not (arg.getShape()[0]==arg.getShape()[1]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       elif arg.getRank()==4:
+         if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
+            raise ValueError,"nonsymmetric: argument must be square."
+       else:
+         raise ValueError,"nonsymmetric: rank 2 or 4 is required."
+       return (arg-transpose(arg))/2
+     else:
+       raise TypeError,"nonsymmetric: Unknown argument type."
+ def inverse(arg):
+     """
+     returns the inverse of the square matrix arg.
+     @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
+     @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 3056 
 class Add_Symbol(DependendSymbol):
+Line 3771 
 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 3072 
 class Add_Symbol(DependendSymbol):
+Line 3787 
 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 3131 
 def mult(arg0,arg1):
+Line 3846 
 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 3155 
 class Mult_Symbol(DependendSymbol):
+Line 3870 
 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 3171 
 class Mult_Symbol(DependendSymbol):
+Line 3886 
 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 3231 
 def quotient(arg0,arg1):
+Line 3946 
 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 3260 
 class Quotient_Symbol(DependendSymbol):
+Line 3975 
 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 3276 
 class Quotient_Symbol(DependendSymbol):
+Line 3991 
 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 3337 
 def power(arg0,arg1):
+Line 4052 
 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 3362 
 class Power_Symbol(DependendSymbol):
+Line 4077 
 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 3380 
 class Power_Symbol(DependendSymbol):
+Line 4095 
 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 3462 
 def minimum(*args):
+Line 4177 
 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 3496 
 def inner(arg0,arg1):
+Line 4219 
 def inner(arg0,arg1):
      @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
      @param arg1: second argument
      @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @return : the inner product of arg0 and arg1 at each data point
+     @return: the inner product of arg0 and arg1 at each data point
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float} depending on the input
      @raise ValueError: if the shapes of the arguments are not identical
      """
-     sh0=pokeShape(arg0)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(arg1)
      if not sh0==sh1:
          raise ValueError,"inner: shape of arguments does not match"
      return generalTensorProduct(arg0,arg1,axis_offset=len(sh0))
+ def outer(arg0,arg1):
+     """
+     the outer product of the two argument:
+     out[t,s]=arg0[t]*arg1[s]
+     where
+         - s runs through arg0.Shape
+         - t runs through arg1.Shape
+     @param arg0: first argument
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @param arg1: second argument
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @return: the outer product of arg0 and arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     return generalTensorProduct(arg0,arg1,axis_offset=0)
  def matrixmult(arg0,arg1):
      """
+     see L{matrix_mult}
+     """
+     return matrix_mult(arg0,arg1)
+ def matrix_mult(arg0,arg1):
+     """
      matrix-matrix or matrix-vector product of the two argument:
      out[s0]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0]
-           or
+     or
      out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0,s1]
-     The second dimension of arg0 and the length of arg1 must match.
+     The second dimension of arg0 and the first dimension of arg1 must match.
      @param arg0: first argument of rank 2
      @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-Line 3526 
 def matrixmult(arg0,arg1):
+Line 4275 
 def matrixmult(arg0,arg1):
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
      @raise ValueError: if the shapes of the arguments are not appropriate
      """
-     sh0=pokeShape(arg0)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(arg1)
      if not len(sh0)==2 :
          raise ValueError,"first argument must have rank 2"
      if not len(sh1)==2 and not len(sh1)==1:
          raise ValueError,"second argument must have rank 1 or 2"
      return generalTensorProduct(arg0,arg1,axis_offset=1)
- def outer(arg0,arg1):
+ def tensormult(arg0,arg1):
      """
-     the outer product of the two argument:
+     use L{tensor_mult}
-     out[t,s]=arg0[t]*arg1[s]
-     where s runs through arg0.Shape
-           t runs through arg1.Shape
-     @param arg0: first argument
-     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @param arg1: second argument
-     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @return: the outer product of arg0 and arg1 at each data point
-     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
      """
-     return generalTensorProduct(arg0,arg1,axis_offset=0)
+     return tensor_mult(arg0,arg1)
- def tensormult(arg0,arg1):
+ def tensor_mult(arg0,arg1):
      """
      the tensor product of the two argument:
      for arg0 of rank 2 this is
      out[s0]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0]
-                  or
+     or
      out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[r0,s1]
-Line 3571 
 def tensormult(arg0,arg1):
+Line 4306 
 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 3589 
 def tensormult(arg0,arg1):
+Line 4324 
 def tensormult(arg0,arg1):
      @return: the tensor product of arg0 and arg1 at each data point
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
      """
-     sh0=pokeShape(arg0)
+     sh0=getShape(arg0)
-     sh1=pokeShape(arg1)
+     sh1=getShape(arg1)
      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
         return generalTensorProduct(arg0,arg1,axis_offset=1)
      elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
         return generalTensorProduct(arg0,arg1,axis_offset=2)
      else:
-         raise ValueError,"tensormult: first argument must have rank 2 or 4"
+         raise ValueError,"tensor_mult: first argument must have rank 2 or 4"
  def generalTensorProduct(arg0,arg1,axis_offset=0):
      """
-Line 3604 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4339 
 def generalTensorProduct(arg0,arg1,axis_
      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]
-     where s runs through arg0.Shape[:arg0.Rank-axis_offset]
+     where
-           r runs trough arg0.Shape[:axis_offset]
-           t runs through arg1.Shape[axis_offset:]
-     In the first case the the second dimension of arg0 and the length of arg1 must match and
+         - s runs through arg0.Shape[:arg0.Rank-axis_offset]
-     in the second case the two last dimensions of arg0 must match the shape of arg1.
+         - r runs trough arg0.Shape[:axis_offset]
+         - t runs through arg1.Shape[axis_offset:]
      @param arg0: first argument
      @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
-     @param arg1: second argument of shape greater of 1 or 2 depending on rank of arg0
+     @param arg1: second argument
      @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
      @return: the general tensor product of arg0 and arg1 at each data point.
      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
-Line 3626 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4360 
 def generalTensorProduct(arg0,arg1,axis_
             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
         else:
             if not arg0.shape[arg0.rank-axis_offset:]==arg1.shape[:axis_offset]:
-                raise ValueError,"generalTensorProduct: dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
+                raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
             arg0_c=arg0.copy()
             arg1_c=arg1.copy()
             sh0,sh1=arg0.shape,arg1.shape
-Line 3636 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4370 
 def generalTensorProduct(arg0,arg1,axis_
             for i in sh1[:axis_offset]: d01*=i
             arg0_c.resize((d0,d01))
             arg1_c.resize((d01,d1))
-            out=numarray.zeros((d0,d1),numarray.Float)
+            out=numarray.zeros((d0,d1),numarray.Float64)
             for i0 in range(d0):
                      for i1 in range(d1):
                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])
-Line 3652 
 def generalTensorProduct(arg0,arg1,axis_
+Line 4386 
 def generalTensorProduct(arg0,arg1,axis_
  class GeneralTensorProduct_Symbol(DependendSymbol):
     """
-    Symbol representing the quotient of two arguments.
+    Symbol representing the general tensor product of two arguments
     """
     def __init__(self,arg0,arg1,axis_offset=0):
         """
-        initialization of L{Symbol} representing the quotient of two arguments
+        initialization of L{Symbol} representing the general tensor product of two arguments.
-        @param arg0: numerator
+        @param arg0: first argument
         @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @param arg1: denominator
+        @param arg1: second argument
         @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
-        @raise ValueError: if both arguments do not have the same shape.
+        @raise ValueError: illegal dimension
         @note: if both arguments have a spatial dimension, they must equal.
         """
-        sh_arg0=pokeShape(arg0)
+        sh_arg0=getShape(arg0)
-        sh_arg1=pokeShape(arg1)
+        sh_arg1=getShape(arg1)
         sh0=sh_arg0[:len(sh_arg0)-axis_offset]
         sh01=sh_arg0[len(sh_arg0)-axis_offset:]
         sh10=sh_arg1[:axis_offset]
-Line 3685 
 class GeneralTensorProduct_Symbol(Depend
+Line 4419 
 class GeneralTensorProduct_Symbol(Depend
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str" or format=="text":
           return "generalTensorProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
-Line 3713 
 class GeneralTensorProduct_Symbol(Depend
+Line 4447 
 class GeneralTensorProduct_Symbol(Depend
           args=self.getSubstitutedArguments(argvals)
           return generalTensorProduct(args[0],args[1],args[2])
- def escript_generalTensorProduct(arg0,arg1,axis_offset): # this should be escript._generalTensorProduct
+ def escript_generalTensorProduct(arg0,arg1,axis_offset,transpose=0):
      "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
-     # calculate the return shape:
+     return C_GeneralTensorProduct(arg0, arg1, axis_offset, transpose)
-     shape0=arg0.getShape()[:arg0.getRank()-axis_offset]
-     shape01=arg0.getShape()[arg0.getRank()-axis_offset:]
+ def transposed_matrix_mult(arg0,arg1):
-     shape10=arg1.getShape()[:axis_offset]
+     """
-     shape1=arg1.getShape()[axis_offset:]
+     transposed(matrix)-matrix or transposed(matrix)-vector product of the two argument:
-     if not shape01==shape10:
-         raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
+     out[s0]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0]
-     # whatr function space should be used? (this here is not good!)
+     or
-     fs=(escript.Scalar(0.,arg0.getFunctionSpace())+escript.Scalar(0.,arg1.getFunctionSpace())).getFunctionSpace()
-     # create return value:
+     out[s0,s1]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0,s1]
-     out=escript.Data(0.,tuple(shape0+shape1),fs)
-     #
+     The function call transposed_matrix_mult(arg0,arg1) is equivalent to matrix_mult(transpose(arg0),arg1).
-     s0=[[]]
-     for k in shape0:
+     The first dimension of arg0 and arg1 must match.
-           s=[]
-           for j in s0:
+     @param arg0: first argument of rank 2
-                 for i in range(k): s.append(j+[slice(i,i)])
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-           s0=s
+     @param arg1: second argument of at least rank 1
-     s1=[[]]
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
-     for k in shape1:
+     @return: the product of the transposed of arg0 and arg1 at each data point
-           s=[]
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
-           for j in s1:
+     @raise ValueError: if the shapes of the arguments are not appropriate
-                 for i in range(k): s.append(j+[slice(i,i)])
+     """
-           s1=s
+     sh0=getShape(arg0)
-     s01=[[]]
+     sh1=getShape(arg1)
-     for k in shape01:
+     if not len(sh0)==2 :
-           s=[]
+         raise ValueError,"first argument must have rank 2"
-           for j in s01:
+     if not len(sh1)==2 and not len(sh1)==1:
-                 for i in range(k): s.append(j+[slice(i,i)])
+         raise ValueError,"second argument must have rank 1 or 2"
-           s01=s
+     return generalTransposedTensorProduct(arg0,arg1,axis_offset=1)
-     for i0 in s0:
+ def transposed_tensor_mult(arg0,arg1):
-        for i1 in s1:
+     """
-          s=escript.Scalar(0.,fs)
+     the tensor product of the transposed of the first and the second argument
-          for i01 in s01:
-             s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))
+     for arg0 of rank 2 this is
-          out.__setitem__(tuple(i0+i1),s)
-     return out
+     out[s0]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0]
+     or
+     out[s0,s1]=S{Sigma}_{r0} arg0[r0,s0]*arg1[r0,s1]
+     and for arg0 of rank 4 this is
+     out[s0,s1,s2,s3]=S{Sigma}_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2,s3]
+     or
+     out[s0,s1,s2]=S{Sigma}_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1,s2]
+     or
+     out[s0,s1]=S{Sigma}_{r0,r1} arg0[r0,r1,s0,s1]*arg1[r0,r1]
+     In the first case the the first dimension of arg0 and the first dimension of arg1 must match and
+     in the second case the two first dimensions of arg0 must match the two first dimension of arg1.
+     The function call transposed_tensor_mult(arg0,arg1) is equivalent to tensor_mult(transpose(arg0),arg1).
+     @param arg0: first argument of rank 2 or 4
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @param arg1: second argument of shape greater of 1 or 2 depending on rank of arg0
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the tensor product of tarnsposed of arg0 and arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     sh0=getShape(arg0)
+     sh1=getShape(arg1)
+     if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
+        return generalTransposedTensorProduct(arg0,arg1,axis_offset=1)
+     elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
+        return generalTransposedTensorProduct(arg0,arg1,axis_offset=2)
+     else:
+         raise ValueError,"first argument must have rank 2 or 4"
+ def generalTransposedTensorProduct(arg0,arg1,axis_offset=0):
+     """
+     generalized tensor product of transposed of arg0 and arg1:
+     out[s,t]=S{Sigma}_r arg0[r,s]*arg1[r,t]
+     where
+         - s runs through arg0.Shape[axis_offset:]
+         - r runs trough arg0.Shape[:axis_offset]
+         - t runs through arg1.Shape[axis_offset:]
+     The function call generalTransposedTensorProduct(arg0,arg1,axis_offset) is equivalent
+     to generalTensorProduct(transpose(arg0,arg0.rank-axis_offset),arg1,axis_offset).
+     @param arg0: first argument
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @param arg1: second argument
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @return: the general tensor product of transposed(arg0) and arg1 at each data point.
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg0,float) and isinstance(arg1,float): return arg1*arg0
+     arg0,arg1=matchType(arg0,arg1)
+     # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols
+     if isinstance(arg0,numarray.NumArray):
+        if isinstance(arg1,Symbol):
+            return GeneralTransposedTensorProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            if not arg0.shape[:axis_offset]==arg1.shape[:axis_offset]:
+                raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
+            arg0_c=arg0.copy()
+            arg1_c=arg1.copy()
+            sh0,sh1=arg0.shape,arg1.shape
+            d0,d1,d01=1,1,1
+            for i in sh0[axis_offset:]: d0*=i
+            for i in sh1[axis_offset:]: d1*=i
+            for i in sh0[:axis_offset]: d01*=i
+            arg0_c.resize((d01,d0))
+            arg1_c.resize((d01,d1))
+            out=numarray.zeros((d0,d1),numarray.Float64)
+            for i0 in range(d0):
+                     for i1 in range(d1):
+                          out[i0,i1]=numarray.sum(arg0_c[:,i0]*arg1_c[:,i1])
+            out.resize(sh0[axis_offset:]+sh1[axis_offset:])
+            return out
+     elif isinstance(arg0,escript.Data):
+        if isinstance(arg1,Symbol):
+            return GeneralTransposedTensorProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            return escript_generalTransposedTensorProduct(arg0,arg1,axis_offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,axis_offset)
+     else:
+        return GeneralTransposedTensorProduct_Symbol(arg0,arg1,axis_offset)
+ class GeneralTransposedTensorProduct_Symbol(DependendSymbol):
+    """
+    Symbol representing the general tensor product of the transposed of arg0 and arg1
+    """
+    def __init__(self,arg0,arg1,axis_offset=0):
+        """
+        initialization of L{Symbol} representing tensor product of the transposed of arg0 and arg1
+        @param arg0: first argument
+        @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @param arg1: second argument
+        @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @raise ValueError: inconsistent dimensions of arguments.
+        @note: if both arguments have a spatial dimension, they must equal.
+        """
+        sh_arg0=getShape(arg0)
+        sh_arg1=getShape(arg1)
+        sh01=sh_arg0[:axis_offset]
+        sh10=sh_arg1[:axis_offset]
+        sh0=sh_arg0[axis_offset:]
+        sh1=sh_arg1[axis_offset:]
+        if not sh01==sh10:
+            raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
+        DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,axis_offset])
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{list} of length 2 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str" or format=="text":
+          return "generalTransposedTensorProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
+       else:
+          raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          args=self.getSubstitutedArguments(argvals)
+          return generalTransposedTensorProduct(args[0],args[1],args[2])
+ def escript_generalTransposedTensorProduct(arg0,arg1,axis_offset): # this should be escript._generalTransposedTensorProduct
+     "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
+     return C_GeneralTensorProduct(arg0, arg1, axis_offset, 1)
+ def matrix_transposed_mult(arg0,arg1):
+     """
+     matrix-transposed(matrix) product of the two argument:
+     out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[s1,r0]
+     The function call matrix_transposed_mult(arg0,arg1) is equivalent to matrix_mult(arg0,transpose(arg1)).
+     The last dimensions of arg0 and arg1 must match.
+     @param arg0: first argument of rank 2
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @param arg1: second argument of rank 2
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the product of arg0 and the transposed of arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     @raise ValueError: if the shapes of the arguments are not appropriate
+     """
+     sh0=getShape(arg0)
+     sh1=getShape(arg1)
+     if not len(sh0)==2 :
+         raise ValueError,"first argument must have rank 2"
+     if not len(sh1)==2 and not len(sh1)==1:
+         raise ValueError,"second argument must have rank 1 or 2"
+     return generalTensorTransposedProduct(arg0,arg1,axis_offset=1)
+ def tensor_transposed_mult(arg0,arg1):
+     """
+     the tensor product of the first and the transpose of the second argument
+     for arg0 of rank 2 this is
+     out[s0,s1]=S{Sigma}_{r0} arg0[s0,r0]*arg1[s1,r0]
+     and for arg0 of rank 4 this is
+     out[s0,s1,s2,s3]=S{Sigma}_{r0,r1} arg0[s0,s1,r0,r1]*arg1[s2,s3,r0,r1]
+     or
+     out[s0,s1,s2]=S{Sigma}_{r0,r1} arg0[s0,s1,r0,r1]*arg1[s2,r0,r1]
+     In the first case the the second dimension of arg0 and arg1 must match and
+     in the second case the two last dimensions of arg0 must match the two last dimension of arg1.
+     The function call tensor_transpose_mult(arg0,arg1) is equivalent to tensor_mult(arg0,transpose(arg1)).
+     @param arg0: first argument of rank 2 or 4
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @param arg1: second argument of shape greater of 1 or 2 depending on rank of arg0
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
+     @return: the tensor product of tarnsposed of arg0 and arg1 at each data point
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     sh0=getShape(arg0)
+     sh1=getShape(arg1)
+     if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
+        return generalTensorTransposedProduct(arg0,arg1,axis_offset=1)
+     elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
+        return generalTensorTransposedProduct(arg0,arg1,axis_offset=2)
+     else:
+         raise ValueError,"first argument must have rank 2 or 4"
+ def generalTensorTransposedProduct(arg0,arg1,axis_offset=0):
+     """
+     generalized tensor product of transposed of arg0 and arg1:
+     out[s,t]=S{Sigma}_r arg0[s,r]*arg1[t,r]
+     where
+         - s runs through arg0.Shape[:arg0.Rank-axis_offset]
+         - r runs trough arg0.Shape[arg1.Rank-axis_offset:]
+         - t runs through arg1.Shape[arg1.Rank-axis_offset:]
+     The function call generalTensorTransposedProduct(arg0,arg1,axis_offset) is equivalent
+     to generalTensorProduct(arg0,transpose(arg1,arg1.Rank-axis_offset),axis_offset).
+     @param arg0: first argument
+     @type arg0: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @param arg1: second argument
+     @type arg1: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{float}, C{int}
+     @return: the general tensor product of transposed(arg0) and arg1 at each data point.
+     @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
+     """
+     if isinstance(arg0,float) and isinstance(arg1,float): return arg1*arg0
+     arg0,arg1=matchType(arg0,arg1)
+     # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols
+     if isinstance(arg0,numarray.NumArray):
+        if isinstance(arg1,Symbol):
+            return GeneralTensorTransposedProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            if not arg0.shape[arg0.rank-axis_offset:]==arg1.shape[arg1.rank-axis_offset:]:
+                raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
+            arg0_c=arg0.copy()
+            arg1_c=arg1.copy()
+            sh0,sh1=arg0.shape,arg1.shape
+            d0,d1,d01=1,1,1
+            for i in sh0[:arg0.rank-axis_offset]: d0*=i
+            for i in sh1[:arg1.rank-axis_offset]: d1*=i
+            for i in sh1[arg1.rank-axis_offset:]: d01*=i
+            arg0_c.resize((d0,d01))
+            arg1_c.resize((d1,d01))
+            out=numarray.zeros((d0,d1),numarray.Float64)
+            for i0 in range(d0):
+                     for i1 in range(d1):
+                          out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[i1,:])
+            out.resize(sh0[:arg0.rank-axis_offset]+sh1[:arg1.rank-axis_offset])
+            return out
+     elif isinstance(arg0,escript.Data):
+        if isinstance(arg1,Symbol):
+            return GeneralTensorTransposedProduct_Symbol(arg0,arg1,axis_offset)
+        else:
+            return escript_generalTensorTransposedProduct(arg0,arg1,axis_offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,axis_offset)
+     else:
+        return GeneralTensorTransposedProduct_Symbol(arg0,arg1,axis_offset)
+ class GeneralTensorTransposedProduct_Symbol(DependendSymbol):
+    """
+    Symbol representing the general tensor product of arg0 and the transpose of arg1
+    """
+    def __init__(self,arg0,arg1,axis_offset=0):
+        """
+        initialization of L{Symbol} representing the general tensor product of arg0 and the transpose of arg1
+        @param arg0: first argument
+        @type arg0: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @param arg1: second argument
+        @type arg1: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray}.
+        @raise ValueError: inconsistent dimensions of arguments.
+        @note: if both arguments have a spatial dimension, they must equal.
+        """
+        sh_arg0=getShape(arg0)
+        sh_arg1=getShape(arg1)
+        sh0=sh_arg0[:len(sh_arg0)-axis_offset]
+        sh01=sh_arg0[len(sh_arg0)-axis_offset:]
+        sh10=sh_arg1[len(sh_arg1)-axis_offset:]
+        sh1=sh_arg1[:len(sh_arg1)-axis_offset]
+        if not sh01==sh10:
+            raise ValueError,"dimensions of last %s components in left argument don't match the last %s components in the right argument."%(axis_offset,axis_offset)
+        DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,axis_offset])
+    def getMyCode(self,argstrs,format="escript"):
+       """
+       returns a program code that can be used to evaluate the symbol.
+       @param argstrs: gives for each argument a string representing the argument for the evaluation.
+       @type argstrs: C{list} of length 2 of C{str}.
+       @param format: specifies the format to be used. At the moment only "escript", "str" and "text" are supported.
+       @type format: C{str}
+       @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
+       @rtype: C{str}
+       @raise NotImplementedError: if the requested format is not available
+       """
+       if format=="escript" or format=="str" or format=="text":
+          return "generalTensorTransposedProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
+       else:
+          raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)
+    def substitute(self,argvals):
+       """
+       assigns new values to symbols in the definition of the symbol.
+       The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
+       @param argvals: new values assigned to symbols
+       @type argvals: C{dict} with keywords of type L{Symbol}.
+       @return: result of the substitution process. Operations are executed as much as possible.
+       @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
+       @raise TypeError: if a value for a L{Symbol} cannot be substituted.
+       """
+       if argvals.has_key(self):
+          arg=argvals[self]
+          if self.isAppropriateValue(arg):
+             return arg
+          else:
+             raise TypeError,"%s: new value is not appropriate."%str(self)
+       else:
+          args=self.getSubstitutedArguments(argvals)
+          return generalTensorTransposedProduct(args[0],args[1],args[2])
+ def escript_generalTensorTransposedProduct(arg0,arg1,axis_offset): # this should be escript._generalTensorTransposedProduct
+     "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
+     return C_GeneralTensorProduct(arg0, arg1, axis_offset, 2)
  #=========================================================
  #  functions dealing with spatial dependency
-Line 3776 
 def grad(arg,where=None):
+Line 4852 
 def grad(arg,where=None):
                    If not present or C{None} an appropriate default is used.
      @type where: C{None} or L{escript.FunctionSpace}
      @return: gradient of arg.
-     @rtype:  L{escript.Data} or L{Symbol}
+     @rtype: L{escript.Data} or L{Symbol}
      """
      if isinstance(arg,Symbol):
         return Grad_Symbol(arg,where)
-Line 3804 
 class Grad_Symbol(DependendSymbol):
+Line 4880 
 class Grad_Symbol(DependendSymbol):
        d=arg.getDim()
        if d==None:
           raise ValueError,"argument must have a spatial dimension"
-       super(Grad_Symbol,self).__init__(args=[arg,where],shape=tuple(list(arg.getShape()).extend(d)),dim=d)
+       super(Grad_Symbol,self).__init__(args=[arg,where],shape=arg.getShape()+(d,),dim=d)
     def getMyCode(self,argstrs,format="escript"):
        """
-Line 3816 
 class Grad_Symbol(DependendSymbol):
+Line 4892 
 class Grad_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "grad(%s,where=%s)"%(argstrs[0],argstrs[1])
-Line 3869 
 def integrate(arg,where=None):
+Line 4945 
 def integrate(arg,where=None):
                    If not present or C{None} an appropriate default is used.
      @type where: C{None} or L{escript.FunctionSpace}
      @return: integral of arg.
-     @rtype:  C{float}, C{numarray.NumArray} or L{Symbol}
+     @rtype: C{float}, C{numarray.NumArray} or L{Symbol}
      """
      if isinstance(arg,Symbol):
         return Integrate_Symbol(arg,where)
-Line 3880 
 def integrate(arg,where=None):
+Line 4956 
 def integrate(arg,where=None):
         else:
            return arg._integrate()
      else:
-       raise TypeError,"integrate: Unknown argument type."
+        arg2=escript.Data(arg,where)
+        if arg2.getRank()==0:
+           return arg2._integrate()[0]
+        else:
+           return arg2._integrate()
  class Integrate_Symbol(DependendSymbol):
     """
-Line 3907 
 class Integrate_Symbol(DependendSymbol):
+Line 4987 
 class Integrate_Symbol(DependendSymbol):
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "integrate(%s,where=%s)"%(argstrs[0],argstrs[1])
-Line 3959 
 def interpolate(arg,where):
+Line 5039 
 def interpolate(arg,where):
      @param where: FunctionSpace to be interpolated to
      @type where: L{escript.FunctionSpace}
      @return: interpolated argument
-     @rtype:  C{escript.Data} or L{Symbol}
+     @rtype: C{escript.Data} or L{Symbol}
      """
      if isinstance(arg,Symbol):
         return Interpolate_Symbol(arg,where)
-Line 3990 
 class Interpolate_Symbol(DependendSymbol
+Line 5070 
 class Interpolate_Symbol(DependendSymbol
        @type format: C{str}
        @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
        @rtype: C{str}
-       @raise: NotImplementedError: if the requested format is not available
+       @raise NotImplementedError: if the requested format is not available
        """
        if format=="escript" or format=="str"  or format=="text":
           return "interpolate(%s,where=%s)"%(argstrs[0],argstrs[1])
-Line 4043 
 def div(arg,where=None):
+Line 5123 
 def div(arg,where=None):
                    If not present or C{None} an appropriate default is used.
      @type where: C{None} or L{escript.FunctionSpace}
      @return: divergence of arg.
-     @rtype:  L{escript.Data} or L{Symbol}
+     @rtype: L{escript.Data} or L{Symbol}
      """
-     if not arg.getShape()==(arg.getDim(),):
+     if isinstance(arg,Symbol):
-       raise ValueError,"div: expected shape is (%s,)"%arg.getDim()
+         dim=arg.getDim()
+     elif isinstance(arg,escript.Data):
+         dim=arg.getDomain().getDim()
+     else:
+         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 jump(arg,domain=None):
-Line 4059 
 def jump(arg,domain=None):
+Line 5145 
 def jump(arg,domain=None):
                     the domain of arg is used. If arg is a L{Symbol} the domain must be present.
      @type domain: C{None} or L{escript.Domain}
      @return: jump of arg
-     @rtype:  L{escript.Data} or L{Symbol}
+     @rtype: L{escript.Data} or L{Symbol}
      """
      if domain==None: domain=arg.getDomain()
      return interpolate(arg,escript.FunctionOnContactOne(domain))-interpolate(arg,escript.FunctionOnContactZero(domain))
- #=============================
- #
- # wrapper for various functions: if the argument has attribute the function name
- # as an argument it calls the corresponding methods. Otherwise the corresponding
- # numarray function is called.
- # functions involving the underlying Domain:
+ def L2(arg):
- def transpose(arg,axis=None):
      """
-     Returns the transpose of the Data object arg.
+     returns the L2 norm of arg at where
-     @param arg:
+     @param arg: function which L2 to be calculated.
+     @type arg: L{escript.Data} or L{Symbol}
+     @return: L2 norm of arg.
+     @rtype: L{float} or L{Symbol}
+     @note: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
      """
-     if axis==None:
+     return sqrt(integrate(inner(arg,arg)))
-        r=0
+ #=============================
-        if hasattr(arg,"getRank"): r=arg.getRank()
+ #
-        if hasattr(arg,"rank"): r=arg.rank
-        axis=r/2
-     if isinstance(arg,Symbol):
-        return Transpose_Symbol(arg,axis=r)
-     if isinstance(arg,escript.Data):
-        # hack for transpose
-        r=arg.getRank()
-        if r!=2: raise ValueError,"Tranpose only avalaible for rank 2 objects"
-        s=arg.getShape()
-        out=escript.Data(0.,(s[1],s[0]),arg.getFunctionSpace())
-        for i in range(s[0]):
-           for j in range(s[1]):
-              out[j,i]=arg[i,j]
-        return out
-        # end hack for transpose
-        return arg.transpose(axis)
-     else:
-        return numarray.transpose(arg,axis=axis)
  def reorderComponents(arg,index):
      """
      resorts the component of arg according to index
      """
-     pass
+     raise NotImplementedError
  #
  # $Log: util.py,v $
  # Revision 1.14.2.16  2005/10/19 06:09:57  gross

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