/[escript]/trunk/escript/py_src/util.py
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revision 341 by gross, Mon Dec 12 05:26:10 2005 UTC revision 517 by gross, Tue Feb 14 02:25:02 2006 UTC
# Line 24  Utility functions for escript Line 24  Utility functions for escript
24  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
25  __licence__="contact: esys@access.uq.edu.au"  __licence__="contact: esys@access.uq.edu.au"
26  __url__="http://www.iservo.edu.au/esys/escript"  __url__="http://www.iservo.edu.au/esys/escript"
27  __version__="$Revision: 329 $"  __version__="$Revision$"
28  __date__="$Date$"  __date__="$Date$"
29    
30    
31  import math  import math
32  import numarray  import numarray
33    import numarray.linear_algebra
34  import escript  import escript
35  import os  import os
36    
# Line 43  import os Line 44  import os
44  # def matchType(arg0=0.,arg1=0.):  # def matchType(arg0=0.,arg1=0.):
45  # def matchShape(arg0,arg1):  # def matchShape(arg0,arg1):
46    
 # def maximum(arg0,arg1):  
 # def minimum(arg0,arg1):  
   
 # def transpose(arg,axis=None):  
 # def trace(arg,axis0=0,axis1=1):  
47  # def reorderComponents(arg,index):  # def reorderComponents(arg,index):
48    
 # def integrate(arg,where=None):  
 # def interpolate(arg,where):  
 # def div(arg,where=None):  
 # def grad(arg,where=None):  
   
49  #  #
50  # slicing: get  # slicing: get
51  #          set  #          set
# Line 125  def kronecker(d=3): Line 116  def kronecker(d=3):
116     return the kronecker S{delta}-symbol     return the kronecker S{delta}-symbol
117    
118     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
119     @type d: C{int} or any object with a C{getDim} method     @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
120     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
121     @rtype d: L{numarray.NumArray} of rank 2.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2.
    @remark: the function is identical L{identity}  
122     """     """
123     return identityTensor(d)     return identityTensor(d)
124    
# Line 147  def identity(shape=()): Line 137  def identity(shape=()):
137        if len(shape)==1:        if len(shape)==1:
138            for i0 in range(shape[0]):            for i0 in range(shape[0]):
139               out[i0,i0]=1.               out[i0,i0]=1.
   
140        elif len(shape)==2:        elif len(shape)==2:
141            for i0 in range(shape[0]):            for i0 in range(shape[0]):
142               for i1 in range(shape[1]):               for i1 in range(shape[1]):
# Line 163  def identityTensor(d=3): Line 152  def identityTensor(d=3):
152     return the dxd identity matrix     return the dxd identity matrix
153    
154     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
155     @type d: C{int} or any object with a C{getDim} method     @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
156     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise     @return: the object u of rank 2 with M{u[i,j]=1} for M{i=j} and M{u[i,j]=0} otherwise
157     @rtype: L{numarray.NumArray} of rank 2.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 2
158     """     """
159     if hasattr(d,"getDim"):     if isinstance(d,escript.FunctionSpace):
160        d=d.getDim()         return escript.Data(identity((d.getDim(),)),d)
161     return identity(shape=(d,))     elif isinstance(d,escript.Domain):
162           return identity((d.getDim(),))
163       else:
164           return identity((d,))
165    
166  def identityTensor4(d=3):  def identityTensor4(d=3):
167     """     """
# Line 178  def identityTensor4(d=3): Line 170  def identityTensor4(d=3):
170     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
171     @type d: C{int} or any object with a C{getDim} method     @type d: C{int} or any object with a C{getDim} method
172     @return: the object u of rank 4 with M{u[i,j,k,l]=1} for M{i=k and j=l} and M{u[i,j,k,l]=0} otherwise     @return: the object u of rank 4 with M{u[i,j,k,l]=1} for M{i=k and j=l} and M{u[i,j,k,l]=0} otherwise
173     @rtype: L{numarray.NumArray} of rank 4.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 4.
174     """     """
175     if hasattr(d,"getDim"):     if isinstance(d,escript.FunctionSpace):
176        d=d.getDim()         return escript.Data(identity((d.getDim(),d.getDim())),d)
177     return identity((d,d))     elif isinstance(d,escript.Domain):
178           return identity((d.getDim(),d.getDim()))
179       else:
180           return identity((d,d))
181    
182  def unitVector(i=0,d=3):  def unitVector(i=0,d=3):
183     """     """
# Line 191  def unitVector(i=0,d=3): Line 186  def unitVector(i=0,d=3):
186     @param i: index     @param i: index
187     @type i: C{int}     @type i: C{int}
188     @param d: dimension or an object that has the C{getDim} method defining the dimension     @param d: dimension or an object that has the C{getDim} method defining the dimension
189     @type d: C{int} or any object with a C{getDim} method     @type d: C{int}, L{escript.Domain} or L{escript.FunctionSpace}
190     @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise     @return: the object u of rank 1 with M{u[j]=1} for M{j=i} and M{u[i]=0} otherwise
191     @rtype: L{numarray.NumArray} of rank 1.     @rtype d: L{numarray.NumArray} or L{escript.Data} of rank 1
192     """     """
193     return kronecker(d)[i]     return kronecker(d)[i]
194    
# Line 363  def testForZero(arg): Line 358  def testForZero(arg):
358      @return : True if the argument is identical to zero.      @return : True if the argument is identical to zero.
359      @rtype : C{bool}      @rtype : C{bool}
360      """      """
361      try:      if isinstance(arg,numarray.NumArray):
362           return not Lsup(arg)>0.
363        elif isinstance(arg,escript.Data):
364           return False
365        elif isinstance(arg,float):
366           return not Lsup(arg)>0.
367        elif isinstance(arg,int):
368         return not Lsup(arg)>0.         return not Lsup(arg)>0.
369      except TypeError:      elif isinstance(arg,Symbol):
370           return False
371        else:
372         return False         return False
373    
374  def matchType(arg0=0.,arg1=0.):  def matchType(arg0=0.,arg1=0.):
# Line 825  class Symbol(object): Line 828  class Symbol(object):
828         """         """
829         return power(other,self)         return power(other,self)
830    
831       def __getitem__(self,index):
832           """
833           returns the slice defined by index
834    
835           @param index: defines a
836           @type index: C{slice} or C{int} or a C{tuple} of them
837           @return: a S{Symbol} representing the slice defined by index
838           @rtype: L{DependendSymbol}
839           """
840           return GetSlice_Symbol(self,index)
841    
842  class DependendSymbol(Symbol):  class DependendSymbol(Symbol):
843     """     """
844     DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal.     DependendSymbol extents L{Symbol} by modifying the == operator to allow two instances to be equal.
# Line 875  class DependendSymbol(Symbol): Line 889  class DependendSymbol(Symbol):
889  #=========================================================  #=========================================================
890  #  Unary operations prserving the shape  #  Unary operations prserving the shape
891  #========================================================  #========================================================
892    class GetSlice_Symbol(DependendSymbol):
893       """
894       L{Symbol} representing getting a slice for a L{Symbol}
895       """
896       def __init__(self,arg,index):
897          """
898          initialization of wherePositive L{Symbol} with argument arg
899          @param arg: argument
900          @type arg: L{Symbol}.
901          @param index: defines index
902          @type index: C{slice} or C{int} or a C{tuple} of them
903          @raises IndexError: if length of index is larger than rank of arg or a index start or stop is out of range
904          @raises ValueError: if a step is given
905          """
906          if not isinstance(index,tuple): index=(index,)
907          if len(index)>arg.getRank():
908               raise IndexError,"GetSlice_Symbol: index out of range."
909          sh=()
910          index2=()
911          for i in range(len(index)):
912             ix=index[i]
913             if isinstance(ix,int):
914                if ix<0 or ix>=arg.getShape()[i]:
915                   raise ValueError,"GetSlice_Symbol: index out of range."
916                index2=index2+(ix,)
917             else:
918               if not ix.step==None:
919                 raise ValueError,"GetSlice_Symbol: steping is not supported."
920               if ix.start==None:
921                  s=0
922               else:
923                  s=ix.start
924               if ix.stop==None:
925                  e=arg.getShape()[i]
926               else:
927                  e=ix.stop
928                  if e>arg.getShape()[i]:
929                     raise IndexError,"GetSlice_Symbol: index out of range."
930               index2=index2+(slice(s,e),)
931               if e>s:
932                   sh=sh+(e-s,)
933               elif s>e:
934                   raise IndexError,"GetSlice_Symbol: slice start must be less or equal slice end"
935          for i in range(len(index),arg.getRank()):
936              index2=index2+(slice(0,arg.getShape()[i]),)
937              sh=sh+(arg.getShape()[i],)
938          super(GetSlice_Symbol, self).__init__(args=[arg,index2],shape=sh,dim=arg.getDim())
939    
940       def getMyCode(self,argstrs,format="escript"):
941          """
942          returns a program code that can be used to evaluate the symbol.
943    
944          @param argstrs: gives for each argument a string representing the argument for the evaluation.
945          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
946          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
947          @type format: C{str}
948          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
949          @rtype: C{str}
950          @raise: NotImplementedError: if the requested format is not available
951          """
952          if format=="escript" or format=="str"  or format=="text":
953             return "%s.__getitem__(%s)"%(argstrs[0],argstrs[1])
954          else:
955             raise NotImplementedError,"GetItem_Symbol does not provide program code for format %s."%format
956    
957       def substitute(self,argvals):
958          """
959          assigns new values to symbols in the definition of the symbol.
960          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
961    
962          @param argvals: new values assigned to symbols
963          @type argvals: C{dict} with keywords of type L{Symbol}.
964          @return: result of the substitution process. Operations are executed as much as possible.
965          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
966          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
967          """
968          if argvals.has_key(self):
969             arg=argvals[self]
970             if self.isAppropriateValue(arg):
971                return arg
972             else:
973                raise TypeError,"%s: new value is not appropriate."%str(self)
974          else:
975             args=self.getSubstitutedArguments(argvals)
976             arg=args[0]
977             index=args[1]
978             return arg.__getitem__(index)
979    
980  def log10(arg):  def log10(arg):
981     """     """
982     returns base-10 logarithm of argument arg     returns base-10 logarithm of argument arg
# Line 907  def wherePositive(arg): Line 1009  def wherePositive(arg):
1009     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1010     """     """
1011     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1012        if arg.rank==0:        out=numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))*1.
1013           if arg>0:        if isinstance(out,float): out=numarray.array(out)
1014             return numarray.array(1.)        return out
          else:  
            return numarray.array(0.)  
       else:  
          return numarray.greater(arg,numarray.zeros(arg.shape,numarray.Float))  
1015     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1016        return arg._wherePositive()        return arg._wherePositive()
1017     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 993  def whereNegative(arg): Line 1091  def whereNegative(arg):
1091     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1092     """     """
1093     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1094        if arg.rank==0:        out=numarray.less(arg,numarray.zeros(arg.shape,numarray.Float))*1.
1095           if arg<0:        if isinstance(out,float): out=numarray.array(out)
1096             return numarray.array(1.)        return out
          else:  
            return numarray.array(0.)  
       else:  
          return numarray.less(arg,numarray.zeros(arg.shape,numarray.Float))  
1097     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1098        return arg._whereNegative()        return arg._whereNegative()
1099     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 1079  def whereNonNegative(arg): Line 1173  def whereNonNegative(arg):
1173     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1174     """     """
1175     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1176        if arg.rank==0:        out=numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.
1177           if arg<0:        if isinstance(out,float): out=numarray.array(out)
1178             return numarray.array(0.)        return out
          else:  
            return numarray.array(1.)  
       else:  
          return numarray.greater_equal(arg,numarray.zeros(arg.shape,numarray.Float))  
1179     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1180        return arg._whereNonNegative()        return arg._whereNonNegative()
1181     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 1113  def whereNonPositive(arg): Line 1203  def whereNonPositive(arg):
1203     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1204     """     """
1205     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1206        if arg.rank==0:        out=numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.
1207           if arg>0:        if isinstance(out,float): out=numarray.array(out)
1208             return numarray.array(0.)        return out
          else:  
            return numarray.array(1.)  
       else:  
          return numarray.less_equal(arg,numarray.zeros(arg.shape,numarray.Float))*1.  
1209     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1210        return arg._whereNonPositive()        return arg._whereNonPositive()
1211     elif isinstance(arg,float):     elif isinstance(arg,float):
# Line 1149  def whereZero(arg,tol=0.): Line 1235  def whereZero(arg,tol=0.):
1235     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1236     """     """
1237     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1238        if arg.rank==0:        out=numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
1239           if abs(arg)<=tol:        if isinstance(out,float): out=numarray.array(out)
1240             return numarray.array(1.)        return out
          else:  
            return numarray.array(0.)  
       else:  
          return numarray.less_equal(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.  
1241     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1242        if tol>0.:        if tol>0.:
1243           return whereNegative(abs(arg)-tol)           return whereNegative(abs(arg)-tol)
# Line 1236  def whereNonZero(arg,tol=0.): Line 1318  def whereNonZero(arg,tol=0.):
1318     @raises TypeError: if the type of the argument is not expected.     @raises TypeError: if the type of the argument is not expected.
1319     """     """
1320     if isinstance(arg,numarray.NumArray):     if isinstance(arg,numarray.NumArray):
1321        if arg.rank==0:        out=numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.
1322          if abs(arg)>tol:        if isinstance(out,float): out=numarray.array(out)
1323             return numarray.array(1.)        return out
         else:  
            return numarray.array(0.)  
       else:  
          return numarray.greater(abs(arg)-tol,numarray.zeros(arg.shape,numarray.Float))*1.  
1324     elif isinstance(arg,escript.Data):     elif isinstance(arg,escript.Data):
1325        if tol>0.:        if tol>0.:
1326           return 1.-whereZero(arg,tol)           return 1.-whereZero(arg,tol)
# Line 2877  def length(arg): Line 2955  def length(arg):
2955     """     """
2956     return sqrt(inner(arg,arg))     return sqrt(inner(arg,arg))
2957    
2958    def trace(arg,axis_offset=0):
2959       """
2960       returns the trace of arg which the sum of arg[k,k] over k.
2961    
2962       @param arg: argument
2963       @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}.
2964       @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
2965                      axis_offset and axis_offset+1 must be equal.
2966       @type axis_offset: C{int}
2967       @return: trace of arg. The rank of the returned object is minus 2 of the rank of arg.
2968       @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray} depending on the type of arg.
2969       """
2970       if isinstance(arg,numarray.NumArray):
2971          sh=arg.shape
2972          if len(sh)<2:
2973            raise ValueError,"trace: rank of argument must be greater than 1"
2974          if axis_offset<0 or axis_offset>len(sh)-2:
2975            raise ValueError,"trace: axis_offset must be between 0 and %s"%len(sh)-2
2976          s1=1
2977          for i in range(axis_offset): s1*=sh[i]
2978          s2=1
2979          for i in range(axis_offset+2,len(sh)): s2*=sh[i]
2980          if not sh[axis_offset] == sh[axis_offset+1]:
2981            raise ValueError,"trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
2982          arg_reshaped=numarray.reshape(arg,(s1,sh[axis_offset],sh[axis_offset],s2))
2983          out=numarray.zeros([s1,s2],numarray.Float)
2984          for i1 in range(s1):
2985            for i2 in range(s2):
2986                for j in range(sh[axis_offset]): out[i1,i2]+=arg_reshaped[i1,j,j,i2]
2987          out.resize(sh[:axis_offset]+sh[axis_offset+2:])
2988          return out
2989       elif isinstance(arg,escript.Data):
2990          return escript_trace(arg,axis_offset)
2991       elif isinstance(arg,float):
2992          raise TypeError,"trace: illegal argument type float."
2993       elif isinstance(arg,int):
2994          raise TypeError,"trace: illegal argument type int."
2995       elif isinstance(arg,Symbol):
2996          return Trace_Symbol(arg,axis_offset)
2997       else:
2998          raise TypeError,"trace: Unknown argument type."
2999    
3000    def escript_trace(arg,axis_offset): # this should be escript._trace
3001          "arg si a Data objects!!!"
3002          if arg.getRank()<2:
3003            raise ValueError,"escript_trace: rank of argument must be greater than 1"
3004          if axis_offset<0 or axis_offset>arg.getRank()-2:
3005            raise ValueError,"escript_trace: axis_offset must be between 0 and %s"%arg.getRank()-2
3006          s=list(arg.getShape())        
3007          if not s[axis_offset] == s[axis_offset+1]:
3008            raise ValueError,"escript_trace: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
3009          out=escript.Data(0.,tuple(s[0:axis_offset]+s[axis_offset+2:]),arg.getFunctionSpace())
3010          if arg.getRank()==2:
3011             for i0 in range(s[0]):
3012                out+=arg[i0,i0]
3013          elif arg.getRank()==3:
3014             if axis_offset==0:
3015                for i0 in range(s[0]):
3016                      for i2 in range(s[2]):
3017                             out[i2]+=arg[i0,i0,i2]
3018             elif axis_offset==1:
3019                for i0 in range(s[0]):
3020                   for i1 in range(s[1]):
3021                             out[i0]+=arg[i0,i1,i1]
3022          elif arg.getRank()==4:
3023             if axis_offset==0:
3024                for i0 in range(s[0]):
3025                      for i2 in range(s[2]):
3026                         for i3 in range(s[3]):
3027                             out[i2,i3]+=arg[i0,i0,i2,i3]
3028             elif axis_offset==1:
3029                for i0 in range(s[0]):
3030                   for i1 in range(s[1]):
3031                         for i3 in range(s[3]):
3032                             out[i0,i3]+=arg[i0,i1,i1,i3]
3033             elif axis_offset==2:
3034                for i0 in range(s[0]):
3035                   for i1 in range(s[1]):
3036                      for i2 in range(s[2]):
3037                             out[i0,i1]+=arg[i0,i1,i2,i2]
3038          return out
3039    class Trace_Symbol(DependendSymbol):
3040       """
3041       L{Symbol} representing the result of the trace function
3042       """
3043       def __init__(self,arg,axis_offset=0):
3044          """
3045          initialization of trace L{Symbol} with argument arg
3046          @param arg: argument of function
3047          @type arg: L{Symbol}.
3048          @param axis_offset: axis_offset to components to sum over. C{axis_offset} must be non-negative and less than the rank of arg +1. The dimensions on component
3049                      axis_offset and axis_offset+1 must be equal.
3050          @type axis_offset: C{int}
3051          """
3052          if arg.getRank()<2:
3053            raise ValueError,"Trace_Symbol: rank of argument must be greater than 1"
3054          if axis_offset<0 or axis_offset>arg.getRank()-2:
3055            raise ValueError,"Trace_Symbol: axis_offset must be between 0 and %s"%arg.getRank()-2
3056          s=list(arg.getShape())        
3057          if not s[axis_offset] == s[axis_offset+1]:
3058            raise ValueError,"Trace_Symbol: dimensions of component %s and %s must match."%(axis_offset.axis_offset+1)
3059          super(Trace_Symbol,self).__init__(args=[arg,axis_offset],shape=tuple(s[0:axis_offset]+s[axis_offset+2:]),dim=arg.getDim())
3060    
3061       def getMyCode(self,argstrs,format="escript"):
3062          """
3063          returns a program code that can be used to evaluate the symbol.
3064    
3065          @param argstrs: gives for each argument a string representing the argument for the evaluation.
3066          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
3067          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
3068          @type format: C{str}
3069          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
3070          @rtype: C{str}
3071          @raise: NotImplementedError: if the requested format is not available
3072          """
3073          if format=="escript" or format=="str"  or format=="text":
3074             return "trace(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
3075          else:
3076             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
3077    
3078       def substitute(self,argvals):
3079          """
3080          assigns new values to symbols in the definition of the symbol.
3081          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
3082    
3083          @param argvals: new values assigned to symbols
3084          @type argvals: C{dict} with keywords of type L{Symbol}.
3085          @return: result of the substitution process. Operations are executed as much as possible.
3086          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
3087          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
3088          """
3089          if argvals.has_key(self):
3090             arg=argvals[self]
3091             if self.isAppropriateValue(arg):
3092                return arg
3093             else:
3094                raise TypeError,"%s: new value is not appropriate."%str(self)
3095          else:
3096             arg=self.getSubstitutedArguments(argvals)
3097             return trace(arg[0],axis_offset=arg[1])
3098    
3099       def diff(self,arg):
3100          """
3101          differential of this object
3102    
3103          @param arg: the derivative is calculated with respect to arg
3104          @type arg: L{escript.Symbol}
3105          @return: derivative with respect to C{arg}
3106          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
3107          """
3108          if arg==self:
3109             return identity(self.getShape())
3110          else:
3111             return trace(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
3112    
3113    def transpose(arg,axis_offset=None):
3114       """
3115       returns the transpose of arg by swaping the first axis_offset and the last rank-axis_offset components.
3116    
3117       @param arg: argument
3118       @type arg: L{escript.Data}, L{Symbol}, L{numarray.NumArray}, C{float}, C{int}
3119       @param axis_offset: the first axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
3120                           if axis_offset is not present C{int(r/2)} where r is the rank of arg is used.
3121       @type axis_offset: C{int}
3122       @return: transpose of arg
3123       @rtype: L{escript.Data}, L{Symbol}, L{numarray.NumArray},C{float}, C{int} depending on the type of arg.
3124       """
3125       if isinstance(arg,numarray.NumArray):
3126          if axis_offset==None: axis_offset=int(arg.rank/2)
3127          return numarray.transpose(arg,axes=range(axis_offset,arg.rank)+range(0,axis_offset))
3128       elif isinstance(arg,escript.Data):
3129          if axis_offset==None: axis_offset=int(arg.getRank()/2)
3130          return escript_transpose(arg,axis_offset)
3131       elif isinstance(arg,float):
3132          if not ( axis_offset==0 or axis_offset==None):
3133            raise ValueError,"transpose: axis_offset must be 0 for float argument"
3134          return arg
3135       elif isinstance(arg,int):
3136          if not ( axis_offset==0 or axis_offset==None):
3137            raise ValueError,"transpose: axis_offset must be 0 for int argument"
3138          return float(arg)
3139       elif isinstance(arg,Symbol):
3140          if axis_offset==None: axis_offset=int(arg.getRank()/2)
3141          return Transpose_Symbol(arg,axis_offset)
3142       else:
3143          raise TypeError,"transpose: Unknown argument type."
3144    
3145    def escript_transpose(arg,axis_offset): # this should be escript._transpose
3146          "arg si a Data objects!!!"
3147          r=arg.getRank()
3148          if axis_offset<0 or axis_offset>r:
3149            raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r
3150          s=arg.getShape()
3151          s_out=s[axis_offset:]+s[:axis_offset]
3152          out=escript.Data(0.,s_out,arg.getFunctionSpace())
3153          if r==4:
3154             if axis_offset==1:
3155                for i0 in range(s_out[0]):
3156                   for i1 in range(s_out[1]):
3157                      for i2 in range(s_out[2]):
3158                         for i3 in range(s_out[3]):
3159                             out[i0,i1,i2,i3]=arg[i3,i0,i1,i2]
3160             elif axis_offset==2:
3161                for i0 in range(s_out[0]):
3162                   for i1 in range(s_out[1]):
3163                      for i2 in range(s_out[2]):
3164                         for i3 in range(s_out[3]):
3165                             out[i0,i1,i2,i3]=arg[i2,i3,i0,i1]
3166             elif axis_offset==3:
3167                for i0 in range(s_out[0]):
3168                   for i1 in range(s_out[1]):
3169                      for i2 in range(s_out[2]):
3170                         for i3 in range(s_out[3]):
3171                             out[i0,i1,i2,i3]=arg[i1,i2,i3,i0]
3172             else:
3173                for i0 in range(s_out[0]):
3174                   for i1 in range(s_out[1]):
3175                      for i2 in range(s_out[2]):
3176                         for i3 in range(s_out[3]):
3177                             out[i0,i1,i2,i3]=arg[i0,i1,i2,i3]
3178          elif r==3:
3179             if axis_offset==1:
3180                for i0 in range(s_out[0]):
3181                   for i1 in range(s_out[1]):
3182                      for i2 in range(s_out[2]):
3183                             out[i0,i1,i2]=arg[i2,i0,i1]
3184             elif axis_offset==2:
3185                for i0 in range(s_out[0]):
3186                   for i1 in range(s_out[1]):
3187                      for i2 in range(s_out[2]):
3188                             out[i0,i1,i2]=arg[i1,i2,i0]
3189             else:
3190                for i0 in range(s_out[0]):
3191                   for i1 in range(s_out[1]):
3192                      for i2 in range(s_out[2]):
3193                             out[i0,i1,i2]=arg[i0,i1,i2]
3194          elif r==2:
3195             if axis_offset==1:
3196                for i0 in range(s_out[0]):
3197                   for i1 in range(s_out[1]):
3198                             out[i0,i1]=arg[i1,i0]
3199             else:
3200                for i0 in range(s_out[0]):
3201                   for i1 in range(s_out[1]):
3202                             out[i0,i1]=arg[i0,i1]
3203          elif r==1:
3204              for i0 in range(s_out[0]):
3205                   out[i0]=arg[i0]
3206          elif r==0:
3207                 out=arg+0.
3208          return out
3209    class Transpose_Symbol(DependendSymbol):
3210       """
3211       L{Symbol} representing the result of the transpose function
3212       """
3213       def __init__(self,arg,axis_offset=None):
3214          """
3215          initialization of transpose L{Symbol} with argument arg
3216    
3217          @param arg: argument of function
3218          @type arg: L{Symbol}.
3219           @param axis_offset: the first axis_offset components are swapped with rest. If C{axis_offset} must be non-negative and less or equal the rank of arg.
3220                           if axis_offset is not present C{int(r/2)} where r is the rank of arg is used.
3221          @type axis_offset: C{int}
3222          """
3223          if axis_offset==None: axis_offset=int(arg.getRank()/2)
3224          if axis_offset<0 or axis_offset>arg.getRank():
3225            raise ValueError,"escript_transpose: axis_offset must be between 0 and %s"%r
3226          s=arg.getShape()
3227          super(Transpose_Symbol,self).__init__(args=[arg,axis_offset],shape=s[axis_offset:]+s[:axis_offset],dim=arg.getDim())
3228    
3229       def getMyCode(self,argstrs,format="escript"):
3230          """
3231          returns a program code that can be used to evaluate the symbol.
3232    
3233          @param argstrs: gives for each argument a string representing the argument for the evaluation.
3234          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
3235          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
3236          @type format: C{str}
3237          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
3238          @rtype: C{str}
3239          @raise: NotImplementedError: if the requested format is not available
3240          """
3241          if format=="escript" or format=="str"  or format=="text":
3242             return "transpose(%s,axis_offset=%s)"%(argstrs[0],argstrs[1])
3243          else:
3244             raise NotImplementedError,"Transpose_Symbol does not provide program code for format %s."%format
3245    
3246       def substitute(self,argvals):
3247          """
3248          assigns new values to symbols in the definition of the symbol.
3249          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
3250    
3251          @param argvals: new values assigned to symbols
3252          @type argvals: C{dict} with keywords of type L{Symbol}.
3253          @return: result of the substitution process. Operations are executed as much as possible.
3254          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
3255          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
3256          """
3257          if argvals.has_key(self):
3258             arg=argvals[self]
3259             if self.isAppropriateValue(arg):
3260                return arg
3261             else:
3262                raise TypeError,"%s: new value is not appropriate."%str(self)
3263          else:
3264             arg=self.getSubstitutedArguments(argvals)
3265             return transpose(arg[0],axis_offset=arg[1])
3266    
3267       def diff(self,arg):
3268          """
3269          differential of this object
3270    
3271          @param arg: the derivative is calculated with respect to arg
3272          @type arg: L{escript.Symbol}
3273          @return: derivative with respect to C{arg}
3274          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
3275          """
3276          if arg==self:
3277             return identity(self.getShape())
3278          else:
3279             return transpose(self.getDifferentiatedArguments(arg)[0],axis_offset=self.getArgument()[1])
3280    
3281    def inverse(arg):
3282        """
3283        returns the inverse of the square matrix arg.
3284    
3285        @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal
3286        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3287        @return: inverse arg_inv of the argument. It will be matrixmul(inverse(arg),arg) almost equal to kronecker(arg.getShape()[0])
3288        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3289        """
3290        if isinstance(arg,numarray.NumArray):
3291          return numarray.linear_algebra.inverse(arg)
3292        elif isinstance(arg,escript.Data):
3293          return escript_inverse(arg)
3294        elif isinstance(arg,float):
3295          return 1./arg
3296        elif isinstance(arg,int):
3297          return 1./float(arg)
3298        elif isinstance(arg,Symbol):
3299          return Inverse_Symbol(arg)
3300        else:
3301          raise TypeError,"inverse: Unknown argument type."
3302    
3303    def escript_inverse(arg): # this should be escript._inverse and use LAPACK
3304          "arg is a Data objects!!!"
3305          if not arg.getRank()==2:
3306            raise ValueError,"escript_inverse: argument must have rank 2"
3307          s=arg.getShape()      
3308          if not s[0] == s[1]:
3309            raise ValueError,"escript_inverse: argument must be a square matrix."
3310          out=escript.Data(0.,s,arg.getFunctionSpace())
3311          if s[0]==1:
3312              if inf(abs(arg[0,0]))==0: # in c this should be done point wise as abs(arg[0,0](i))<=0.
3313                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3314              out[0,0]=1./arg[0,0]
3315          elif s[0]==2:
3316              A11=arg[0,0]
3317              A12=arg[0,1]
3318              A21=arg[1,0]
3319              A22=arg[1,1]
3320              D = A11*A22-A12*A21
3321              if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
3322                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3323              D=1./D
3324              out[0,0]= A22*D
3325              out[1,0]=-A21*D
3326              out[0,1]=-A12*D
3327              out[1,1]= A11*D
3328          elif s[0]==3:
3329              A11=arg[0,0]
3330              A21=arg[1,0]
3331              A31=arg[2,0]
3332              A12=arg[0,1]
3333              A22=arg[1,1]
3334              A32=arg[2,1]
3335              A13=arg[0,2]
3336              A23=arg[1,2]
3337              A33=arg[2,2]
3338              D  =  A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22)
3339              if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
3340                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3341              D=1./D
3342              out[0,0]=(A22*A33-A23*A32)*D
3343              out[1,0]=(A31*A23-A21*A33)*D
3344              out[2,0]=(A21*A32-A31*A22)*D
3345              out[0,1]=(A13*A32-A12*A33)*D
3346              out[1,1]=(A11*A33-A31*A13)*D
3347              out[2,1]=(A12*A31-A11*A32)*D
3348              out[0,2]=(A12*A23-A13*A22)*D
3349              out[1,2]=(A13*A21-A11*A23)*D
3350              out[2,2]=(A11*A22-A12*A21)*D
3351          else:
3352             raise TypeError,"escript_inverse: only matrix dimensions 1,2,3 are supported right now."
3353          return out
3354    
3355    class Inverse_Symbol(DependendSymbol):
3356       """
3357       L{Symbol} representing the result of the inverse function
3358       """
3359       def __init__(self,arg):
3360          """
3361          initialization of inverse L{Symbol} with argument arg
3362          @param arg: argument of function
3363          @type arg: L{Symbol}.
3364          """
3365          if not arg.getRank()==2:
3366            raise ValueError,"Inverse_Symbol:: argument must have rank 2"
3367          s=arg.getShape()
3368          if not s[0] == s[1]:
3369            raise ValueError,"Inverse_Symbol:: argument must be a square matrix."
3370          super(Inverse_Symbol,self).__init__(args=[arg],shape=s,dim=arg.getDim())
3371    
3372       def getMyCode(self,argstrs,format="escript"):
3373          """
3374          returns a program code that can be used to evaluate the symbol.
3375    
3376          @param argstrs: gives for each argument a string representing the argument for the evaluation.
3377          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
3378          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
3379          @type format: C{str}
3380          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
3381          @rtype: C{str}
3382          @raise: NotImplementedError: if the requested format is not available
3383          """
3384          if format=="escript" or format=="str"  or format=="text":
3385             return "inverse(%s)"%argstrs[0]
3386          else:
3387             raise NotImplementedError,"Inverse_Symbol does not provide program code for format %s."%format
3388    
3389       def substitute(self,argvals):
3390          """
3391          assigns new values to symbols in the definition of the symbol.
3392          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
3393    
3394          @param argvals: new values assigned to symbols
3395          @type argvals: C{dict} with keywords of type L{Symbol}.
3396          @return: result of the substitution process. Operations are executed as much as possible.
3397          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
3398          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
3399          """
3400          if argvals.has_key(self):
3401             arg=argvals[self]
3402             if self.isAppropriateValue(arg):
3403                return arg
3404             else:
3405                raise TypeError,"%s: new value is not appropriate."%str(self)
3406          else:
3407             arg=self.getSubstitutedArguments(argvals)
3408             return inverse(arg[0])
3409    
3410       def diff(self,arg):
3411          """
3412          differential of this object
3413    
3414          @param arg: the derivative is calculated with respect to arg
3415          @type arg: L{escript.Symbol}
3416          @return: derivative with respect to C{arg}
3417          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
3418          """
3419          if arg==self:
3420             return identity(self.getShape())
3421          else:
3422             return -matrixmult(matrixmult(self,self.getDifferentiatedArguments(arg)[0]),self)
3423  #=======================================================  #=======================================================
3424  #  Binary operations:  #  Binary operations:
3425  #=======================================================  #=======================================================
# Line 3304  def maximum(*args): Line 3847  def maximum(*args):
3847         if out==None:         if out==None:
3848            out=a            out=a
3849         else:         else:
3850            m=whereNegative(out-a)            diff=add(a,-out)
3851            out=m*a+(1.-m)*out            out=add(out,mult(wherePositive(diff),diff))
3852      return out      return out
3853        
3854  def minimum(*arg):  def minimum(*args):
3855      """      """
3856      the minimum over arguments args      the minimum over arguments args
3857    
# Line 3322  def minimum(*arg): Line 3865  def minimum(*arg):
3865         if out==None:         if out==None:
3866            out=a            out=a
3867         else:         else:
3868            m=whereNegative(out-a)            diff=add(a,-out)
3869            out=m*out+(1.-m)*a            out=add(out,mult(whereNegative(diff),diff))
3870      return out      return out
3871    
3872    def clip(arg,minval=0.,maxval=1.):
3873        """
3874        cuts the values of arg between minval and maxval
3875    
3876        @param arg: argument
3877        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float}
3878        @param minval: lower range
3879        @type arg: C{float}
3880        @param maxval: upper range
3881        @type arg: C{float}
3882        @return: is on object with all its value between minval and maxval. value of the argument that greater then minval and
3883                 less then maxval are unchanged.
3884        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float} depending on the input
3885        @raise ValueError: if minval>maxval
3886        """
3887        if minval>maxval:
3888           raise ValueError,"minval = %s must be less then maxval %s"%(minval,maxval)
3889        return minimum(maximum(minval,arg),maxval)
3890    
3891        
3892  def inner(arg0,arg1):  def inner(arg0,arg1):
3893      """      """
# Line 3348  def inner(arg0,arg1): Line 3911  def inner(arg0,arg1):
3911      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
3912      if not sh0==sh1:      if not sh0==sh1:
3913          raise ValueError,"inner: shape of arguments does not match"          raise ValueError,"inner: shape of arguments does not match"
3914      return generalTensorProduct(arg0,arg1,offset=len(sh0))      return generalTensorProduct(arg0,arg1,axis_offset=len(sh0))
3915    
3916  def matrixmult(arg0,arg1):  def matrixmult(arg0,arg1):
3917      """      """
# Line 3376  def matrixmult(arg0,arg1): Line 3939  def matrixmult(arg0,arg1):
3939          raise ValueError,"first argument must have rank 2"          raise ValueError,"first argument must have rank 2"
3940      if not len(sh1)==2 and not len(sh1)==1:      if not len(sh1)==2 and not len(sh1)==1:
3941          raise ValueError,"second argument must have rank 1 or 2"          raise ValueError,"second argument must have rank 1 or 2"
3942      return generalTensorProduct(arg0,arg1,offset=1)      return generalTensorProduct(arg0,arg1,axis_offset=1)
3943    
3944  def outer(arg0,arg1):  def outer(arg0,arg1):
3945      """      """
# Line 3394  def outer(arg0,arg1): Line 3957  def outer(arg0,arg1):
3957      @return: the outer product of arg0 and arg1 at each data point      @return: the outer product of arg0 and arg1 at each data point
3958      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input      @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3959      """      """
3960      return generalTensorProduct(arg0,arg1,offset=0)      return generalTensorProduct(arg0,arg1,axis_offset=0)
3961    
3962    
3963  def tensormult(arg0,arg1):  def tensormult(arg0,arg1):
# Line 3436  def tensormult(arg0,arg1): Line 3999  def tensormult(arg0,arg1):
3999      sh0=pokeShape(arg0)      sh0=pokeShape(arg0)
4000      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
4001      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
4002         return generalTensorProduct(arg0,arg1,offset=1)         return generalTensorProduct(arg0,arg1,axis_offset=1)
4003      elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):      elif len(sh0)==4 and (len(sh1)==2 or len(sh1)==3 or len(sh1)==4):
4004         return generalTensorProduct(arg0,arg1,offset=2)         return generalTensorProduct(arg0,arg1,axis_offset=2)
4005      else:      else:
4006          raise ValueError,"tensormult: first argument must have rank 2 or 4"          raise ValueError,"tensormult: first argument must have rank 2 or 4"
4007    
4008  def generalTensorProduct(arg0,arg1,offset=0):  def generalTensorProduct(arg0,arg1,axis_offset=0):
4009      """      """
4010      generalized tensor product      generalized tensor product
4011    
4012      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]
4013    
4014      where s runs through arg0.Shape[:arg0.Rank-offset]      where s runs through arg0.Shape[:arg0.Rank-axis_offset]
4015            r runs trough arg0.Shape[:offset]            r runs trough arg0.Shape[:axis_offset]
4016            t runs through arg1.Shape[offset:]            t runs through arg1.Shape[axis_offset:]
4017    
4018      In the first case the the second dimension of arg0 and the length of arg1 must match and        In the first case the the second dimension of arg0 and the length of arg1 must match and  
4019      in the second case the two last dimensions of arg0 must match the shape of arg1.      in the second case the two last dimensions of arg0 must match the shape of arg1.
# Line 3467  def generalTensorProduct(arg0,arg1,offse Line 4030  def generalTensorProduct(arg0,arg1,offse
4030      # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols      # at this stage arg0 and arg0 are both numarray.NumArray or escript.Data or Symbols
4031      if isinstance(arg0,numarray.NumArray):      if isinstance(arg0,numarray.NumArray):
4032         if isinstance(arg1,Symbol):         if isinstance(arg1,Symbol):
4033             return GeneralTensorProduct_Symbol(arg0,arg1,offset)             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4034         else:         else:
4035             if not arg0.shape[arg0.rank-offset:]==arg1.shape[:offset]:             if not arg0.shape[arg0.rank-axis_offset:]==arg1.shape[:axis_offset]:
4036                 raise ValueError,"generalTensorProduct: dimensions of last %s components in left argument don't match the first %s components in the right argument."%(offset,offset)                 raise ValueError,"generalTensorProduct: dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
4037             arg0_c=arg0.copy()             arg0_c=arg0.copy()
4038             arg1_c=arg1.copy()             arg1_c=arg1.copy()
4039             sh0,sh1=arg0.shape,arg1.shape             sh0,sh1=arg0.shape,arg1.shape
4040             d0,d1,d01=1,1,1             d0,d1,d01=1,1,1
4041             for i in sh0[:arg0.rank-offset]: d0*=i             for i in sh0[:arg0.rank-axis_offset]: d0*=i
4042             for i in sh1[offset:]: d1*=i             for i in sh1[axis_offset:]: d1*=i
4043             for i in sh1[:offset]: d01*=i             for i in sh1[:axis_offset]: d01*=i
4044             arg0_c.resize((d0,d01))             arg0_c.resize((d0,d01))
4045             arg1_c.resize((d01,d1))             arg1_c.resize((d01,d1))
4046             out=numarray.zeros((d0,d1),numarray.Float)             out=numarray.zeros((d0,d1),numarray.Float)
4047             for i0 in range(d0):             for i0 in range(d0):
4048                      for i1 in range(d1):                      for i1 in range(d1):
4049                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])
4050             out.resize(sh0[:arg0.rank-offset]+sh1[offset:])             out.resize(sh0[:arg0.rank-axis_offset]+sh1[axis_offset:])
4051             return out             return out
4052      elif isinstance(arg0,escript.Data):      elif isinstance(arg0,escript.Data):
4053         if isinstance(arg1,Symbol):         if isinstance(arg1,Symbol):
4054             return GeneralTensorProduct_Symbol(arg0,arg1,offset)             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4055         else:         else:
4056             return escript_generalTensorProduct(arg0,arg1,offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,offset)             return escript_generalTensorProduct(arg0,arg1,axis_offset) # this calls has to be replaced by escript._generalTensorProduct(arg0,arg1,axis_offset)
4057      else:            else:      
4058         return GeneralTensorProduct_Symbol(arg0,arg1,offset)         return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4059                                    
4060  class GeneralTensorProduct_Symbol(DependendSymbol):  class GeneralTensorProduct_Symbol(DependendSymbol):
4061     """     """
4062     Symbol representing the quotient of two arguments.     Symbol representing the quotient of two arguments.
4063     """     """
4064     def __init__(self,arg0,arg1,offset=0):     def __init__(self,arg0,arg1,axis_offset=0):
4065         """         """
4066         initialization of L{Symbol} representing the quotient of two arguments         initialization of L{Symbol} representing the quotient of two arguments
4067    
# Line 3511  class GeneralTensorProduct_Symbol(Depend Line 4074  class GeneralTensorProduct_Symbol(Depend
4074         """         """
4075         sh_arg0=pokeShape(arg0)         sh_arg0=pokeShape(arg0)
4076         sh_arg1=pokeShape(arg1)         sh_arg1=pokeShape(arg1)
4077         sh0=sh_arg0[:len(sh_arg0)-offset]         sh0=sh_arg0[:len(sh_arg0)-axis_offset]
4078         sh01=sh_arg0[len(sh_arg0)-offset:]         sh01=sh_arg0[len(sh_arg0)-axis_offset:]
4079         sh10=sh_arg1[:offset]         sh10=sh_arg1[:axis_offset]
4080         sh1=sh_arg1[offset:]         sh1=sh_arg1[axis_offset:]
4081         if not sh01==sh10:         if not sh01==sh10:
4082             raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(offset,offset)             raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
4083         DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,offset])         DependendSymbol.__init__(self,dim=commonDim(arg0,arg1),shape=sh0+sh1,args=[arg0,arg1,axis_offset])
4084    
4085     def getMyCode(self,argstrs,format="escript"):     def getMyCode(self,argstrs,format="escript"):
4086        """        """
# Line 3532  class GeneralTensorProduct_Symbol(Depend Line 4095  class GeneralTensorProduct_Symbol(Depend
4095        @raise: NotImplementedError: if the requested format is not available        @raise: NotImplementedError: if the requested format is not available
4096        """        """
4097        if format=="escript" or format=="str" or format=="text":        if format=="escript" or format=="str" or format=="text":
4098           return "generalTensorProduct(%s,%s,offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])           return "generalTensorProduct(%s,%s,axis_offset=%s)"%(argstrs[0],argstrs[1],argstrs[2])
4099        else:        else:
4100           raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)           raise NotImplementedError,"%s does not provide program code for format %s."%(str(self),format)
4101    
# Line 3557  class GeneralTensorProduct_Symbol(Depend Line 4120  class GeneralTensorProduct_Symbol(Depend
4120           args=self.getSubstitutedArguments(argvals)           args=self.getSubstitutedArguments(argvals)
4121           return generalTensorProduct(args[0],args[1],args[2])           return generalTensorProduct(args[0],args[1],args[2])
4122    
4123  def escript_generalTensorProduct(arg0,arg1,offset): # this should be escript._generalTensorProduct  def escript_generalTensorProduct(arg0,arg1,axis_offset): # this should be escript._generalTensorProduct
4124      "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"      "arg0 and arg1 are both Data objects but not neccesrily on the same function space. they could be identical!!!"
4125      # calculate the return shape:      # calculate the return shape:
4126      shape0=arg0.getShape()[:arg0.getRank()-offset]      shape0=arg0.getShape()[:arg0.getRank()-axis_offset]
4127      shape01=arg0.getShape()[arg0.getRank()-offset:]      shape01=arg0.getShape()[arg0.getRank()-axis_offset:]
4128      shape10=arg1.getShape()[:offset]      shape10=arg1.getShape()[:axis_offset]
4129      shape1=arg1.getShape()[offset:]      shape1=arg1.getShape()[axis_offset:]
4130      if not shape01==shape10:      if not shape01==shape10:
4131          raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(offset,offset)          raise ValueError,"dimensions of last %s components in left argument don't match the first %s components in the right argument."%(axis_offset,axis_offset)
4132    
4133        # whatr function space should be used? (this here is not good!)
4134        fs=(escript.Scalar(0.,arg0.getFunctionSpace())+escript.Scalar(0.,arg1.getFunctionSpace())).getFunctionSpace()
4135      # create return value:      # create return value:
4136      out=escript.Data(0.,tuple(shape0+shape1),arg0.getFunctionSpace())      out=escript.Data(0.,tuple(shape0+shape1),fs)
4137      #      #
4138      s0=[[]]      s0=[[]]
4139      for k in shape0:      for k in shape0:
# Line 3591  def escript_generalTensorProduct(arg0,ar Line 4156  def escript_generalTensorProduct(arg0,ar
4156    
4157      for i0 in s0:      for i0 in s0:
4158         for i1 in s1:         for i1 in s1:
4159           s=escript.Scalar(0.,arg0.getFunctionSpace())           s=escript.Scalar(0.,fs)
4160           for i01 in s01:           for i01 in s01:
4161              s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))              s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))
4162           out.__setitem__(tuple(i0+i1),s)           out.__setitem__(tuple(i0+i1),s)
4163      return out      return out
4164    
4165    
4166  #=========================================================  #=========================================================
4167  #   some little helpers  #  functions dealing with spatial dependency
4168  #=========================================================  #=========================================================
4169  def grad(arg,where=None):  def grad(arg,where=None):
4170      """      """
4171      Returns the spatial gradient of arg at where.      Returns the spatial gradient of arg at where.
4172    
4173        If C{g} is the returned object, then
4174    
4175      @param arg:   Data object representing the function which gradient        - if C{arg} is rank 0 C{g[s]} is the derivative of C{arg} with respect to the C{s}-th spatial dimension.
4176                    to be calculated.        - if C{arg} is rank 1 C{g[i,s]} is the derivative of C{arg[i]} with respect to the C{s}-th spatial dimension.
4177          - if C{arg} is rank 2 C{g[i,j,s]} is the derivative of C{arg[i,j]} with respect to the C{s}-th spatial dimension.
4178          - if C{arg} is rank 3 C{g[i,j,k,s]} is the derivative of C{arg[i,j,k]} with respect to the C{s}-th spatial dimension.
4179    
4180        @param arg: function which gradient to be calculated. Its rank has to be less than 3.
4181        @type arg: L{escript.Data} or L{Symbol}
4182      @param where: FunctionSpace in which the gradient will be calculated.      @param where: FunctionSpace in which the gradient will be calculated.
4183                    If not present or C{None} an appropriate default is used.                    If not present or C{None} an appropriate default is used.
4184        @type where: C{None} or L{escript.FunctionSpace}
4185        @return: gradient of arg.
4186        @rtype:  L{escript.Data} or L{Symbol}
4187      """      """
4188      if isinstance(arg,Symbol):      if isinstance(arg,Symbol):
4189         return Grad_Symbol(arg,where)         return Grad_Symbol(arg,where)
# Line 3617  def grad(arg,where=None): Line 4193  def grad(arg,where=None):
4193         else:         else:
4194            return arg._grad(where)            return arg._grad(where)
4195      else:      else:
4196        raise TypeError,"grad: Unknown argument type."         raise TypeError,"grad: Unknown argument type."
4197    
4198    class Grad_Symbol(DependendSymbol):
4199       """
4200       L{Symbol} representing the result of the gradient operator
4201       """
4202       def __init__(self,arg,where=None):
4203          """
4204          initialization of gradient L{Symbol} with argument arg
4205          @param arg: argument of function
4206          @type arg: L{Symbol}.
4207          @param where: FunctionSpace in which the gradient will be calculated.
4208                      If not present or C{None} an appropriate default is used.
4209          @type where: C{None} or L{escript.FunctionSpace}
4210          """
4211          d=arg.getDim()
4212          if d==None:
4213             raise ValueError,"argument must have a spatial dimension"
4214          super(Grad_Symbol,self).__init__(args=[arg,where],shape=arg.getShape()+(d,),dim=d)
4215    
4216       def getMyCode(self,argstrs,format="escript"):
4217          """
4218          returns a program code that can be used to evaluate the symbol.
4219    
4220          @param argstrs: gives for each argument a string representing the argument for the evaluation.
4221          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4222          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4223          @type format: C{str}
4224          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4225          @rtype: C{str}
4226          @raise: NotImplementedError: if the requested format is not available
4227          """
4228          if format=="escript" or format=="str"  or format=="text":
4229             return "grad(%s,where=%s)"%(argstrs[0],argstrs[1])
4230          else:
4231             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4232    
4233       def substitute(self,argvals):
4234          """
4235          assigns new values to symbols in the definition of the symbol.
4236          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
4237    
4238          @param argvals: new values assigned to symbols
4239          @type argvals: C{dict} with keywords of type L{Symbol}.
4240          @return: result of the substitution process. Operations are executed as much as possible.
4241          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4242          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4243          """
4244          if argvals.has_key(self):
4245             arg=argvals[self]
4246             if self.isAppropriateValue(arg):
4247                return arg
4248             else:
4249                raise TypeError,"%s: new value is not appropriate."%str(self)
4250          else:
4251             arg=self.getSubstitutedArguments(argvals)
4252             return grad(arg[0],where=arg[1])
4253    
4254       def diff(self,arg):
4255          """
4256          differential of this object
4257    
4258          @param arg: the derivative is calculated with respect to arg
4259          @type arg: L{escript.Symbol}
4260          @return: derivative with respect to C{arg}
4261          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
4262          """
4263          if arg==self:
4264             return identity(self.getShape())
4265          else:
4266             return grad(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4267    
4268  def integrate(arg,where=None):  def integrate(arg,where=None):
4269      """      """
4270      Return the integral if the function represented by Data object arg over      Return the integral of the function C{arg} over its domain. If C{where} is present C{arg} is interpolated to C{where}
4271      its domain.      before integration.
4272    
4273      @param arg:   Data object representing the function which is integrated.      @param arg:   the function which is integrated.
4274        @type arg: L{escript.Data} or L{Symbol}
4275      @param where: FunctionSpace in which the integral is calculated.      @param where: FunctionSpace in which the integral is calculated.
4276                    If not present or C{None} an appropriate default is used.                    If not present or C{None} an appropriate default is used.
4277        @type where: C{None} or L{escript.FunctionSpace}
4278        @return: integral of arg.
4279        @rtype:  C{float}, C{numarray.NumArray} or L{Symbol}
4280      """      """
4281      if isinstance(arg,numarray.NumArray):      if isinstance(arg,Symbol):
         if checkForZero(arg):  
            return arg  
         else:  
            raise TypeError,"integrate: cannot intergrate argument"  
     elif isinstance(arg,float):  
         if checkForZero(arg):  
            return arg  
         else:  
            raise TypeError,"integrate: cannot intergrate argument"  
     elif isinstance(arg,int):  
         if checkForZero(arg):  
            return float(arg)  
         else:  
            raise TypeError,"integrate: cannot intergrate argument"  
     elif isinstance(arg,Symbol):  
4282         return Integrate_Symbol(arg,where)         return Integrate_Symbol(arg,where)
4283      elif isinstance(arg,escript.Data):      elif isinstance(arg,escript.Data):
4284         if not where==None: arg=escript.Data(arg,where)         if not where==None: arg=escript.Data(arg,where)
# Line 3654  def integrate(arg,where=None): Line 4289  def integrate(arg,where=None):
4289      else:      else:
4290        raise TypeError,"integrate: Unknown argument type."        raise TypeError,"integrate: Unknown argument type."
4291    
4292    class Integrate_Symbol(DependendSymbol):
4293       """
4294       L{Symbol} representing the result of the spatial integration operator
4295       """
4296       def __init__(self,arg,where=None):
4297          """
4298          initialization of integration L{Symbol} with argument arg
4299          @param arg: argument of the integration
4300          @type arg: L{Symbol}.
4301          @param where: FunctionSpace in which the integration will be calculated.
4302                      If not present or C{None} an appropriate default is used.
4303          @type where: C{None} or L{escript.FunctionSpace}
4304          """
4305          super(Integrate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),dim=arg.getDim())
4306    
4307       def getMyCode(self,argstrs,format="escript"):
4308          """
4309          returns a program code that can be used to evaluate the symbol.
4310    
4311          @param argstrs: gives for each argument a string representing the argument for the evaluation.
4312          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4313          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4314          @type format: C{str}
4315          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4316          @rtype: C{str}
4317          @raise: NotImplementedError: if the requested format is not available
4318          """
4319          if format=="escript" or format=="str"  or format=="text":
4320             return "integrate(%s,where=%s)"%(argstrs[0],argstrs[1])
4321          else:
4322             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4323    
4324       def substitute(self,argvals):
4325          """
4326          assigns new values to symbols in the definition of the symbol.
4327          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
4328    
4329          @param argvals: new values assigned to symbols
4330          @type argvals: C{dict} with keywords of type L{Symbol}.
4331          @return: result of the substitution process. Operations are executed as much as possible.
4332          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4333          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4334          """
4335          if argvals.has_key(self):
4336             arg=argvals[self]
4337             if self.isAppropriateValue(arg):
4338                return arg
4339             else:
4340                raise TypeError,"%s: new value is not appropriate."%str(self)
4341          else:
4342             arg=self.getSubstitutedArguments(argvals)
4343             return integrate(arg[0],where=arg[1])
4344    
4345       def diff(self,arg):
4346          """
4347          differential of this object
4348    
4349          @param arg: the derivative is calculated with respect to arg
4350          @type arg: L{escript.Symbol}
4351          @return: derivative with respect to C{arg}
4352          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
4353          """
4354          if arg==self:
4355             return identity(self.getShape())
4356          else:
4357             return integrate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4358    
4359    
4360  def interpolate(arg,where):  def interpolate(arg,where):
4361      """      """
4362      Interpolates the function into the FunctionSpace where.      interpolates the function into the FunctionSpace where.
4363    
4364      @param arg:    interpolant      @param arg: interpolant
4365      @param where:  FunctionSpace to interpolate to      @type arg: L{escript.Data} or L{Symbol}
4366        @param where: FunctionSpace to be interpolated to
4367        @type where: L{escript.FunctionSpace}
4368        @return: interpolated argument
4369        @rtype:  C{escript.Data} or L{Symbol}
4370      """      """
4371      if testForZero(arg):      if isinstance(arg,Symbol):
4372        return 0         return Interpolate_Symbol(arg,where)
     elif isinstance(arg,Symbol):  
        return Interpolated_Symbol(arg,where)  
4373      else:      else:
4374         return escript.Data(arg,where)         return escript.Data(arg,where)
4375    
4376  def div(arg,where=None):  class Interpolate_Symbol(DependendSymbol):
4377      """     """
4378      Returns the divergence of arg at where.     L{Symbol} representing the result of the interpolation operator
4379       """
4380       def __init__(self,arg,where):
4381          """
4382          initialization of interpolation L{Symbol} with argument arg
4383          @param arg: argument of the interpolation
4384          @type arg: L{Symbol}.
4385          @param where: FunctionSpace into which the argument is interpolated.
4386          @type where: L{escript.FunctionSpace}
4387          """
4388          super(Interpolate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),dim=arg.getDim())
4389    
4390      @param arg:   Data object representing the function which gradient to     def getMyCode(self,argstrs,format="escript"):
4391                    be calculated.        """
4392      @param where: FunctionSpace in which the gradient will be calculated.        returns a program code that can be used to evaluate the symbol.
                   If not present or C{None} an appropriate default is used.  
     """  
     g=grad(arg,where)  
     return trace(g,axis0=g.getRank()-2,axis1=g.getRank()-1)  
4393    
4394  def jump(arg):        @param argstrs: gives for each argument a string representing the argument for the evaluation.
4395      """        @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4396      Returns the jump of arg across a continuity.        @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4397          @type format: C{str}
4398          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4399          @rtype: C{str}
4400          @raise: NotImplementedError: if the requested format is not available
4401          """
4402          if format=="escript" or format=="str"  or format=="text":
4403             return "interpolate(%s,where=%s)"%(argstrs[0],argstrs[1])
4404          else:
4405             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4406    
4407      @param arg:   Data object representing the function which gradient     def substitute(self,argvals):
4408                    to be calculated.        """
4409      """        assigns new values to symbols in the definition of the symbol.
4410      d=arg.getDomain()        The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
     return arg.interpolate(escript.FunctionOnContactOne())-arg.interpolate(escript.FunctionOnContactZero())  
4411    
4412  #=============================        @param argvals: new values assigned to symbols
4413  #        @type argvals: C{dict} with keywords of type L{Symbol}.
4414  # wrapper for various functions: if the argument has attribute the function name        @return: result of the substitution process. Operations are executed as much as possible.
4415  # as an argument it calls the corresponding methods. Otherwise the corresponding        @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4416  # numarray function is called.        @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4417          """
4418          if argvals.has_key(self):
4419             arg=argvals[self]
4420             if self.isAppropriateValue(arg):
4421                return arg
4422             else:
4423                raise TypeError,"%s: new value is not appropriate."%str(self)
4424          else:
4425             arg=self.getSubstitutedArguments(argvals)
4426             return interpolate(arg[0],where=arg[1])
4427    
4428       def diff(self,arg):
4429          """
4430          differential of this object
4431    
4432          @param arg: the derivative is calculated with respect to arg
4433          @type arg: L{escript.Symbol}
4434          @return: derivative with respect to C{arg}
4435          @rtype: L{Symbol} but other types such as L{escript.Data}, L{numarray.NumArray}  are possible.
4436          """
4437          if arg==self:
4438             return identity(self.getShape())
4439          else:
4440             return interpolate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4441    
 # functions involving the underlying Domain:  
4442    
4443  def transpose(arg,axis=None):  def div(arg,where=None):
4444      """      """
4445      Returns the transpose of the Data object arg.      returns the divergence of arg at where.
4446    
4447      @param arg:      @param arg: function which divergence to be calculated. Its shape has to be (d,) where d is the spatial dimension.
4448        @type arg: L{escript.Data} or L{Symbol}
4449        @param where: FunctionSpace in which the divergence will be calculated.
4450                      If not present or C{None} an appropriate default is used.
4451        @type where: C{None} or L{escript.FunctionSpace}
4452        @return: divergence of arg.
4453        @rtype:  L{escript.Data} or L{Symbol}
4454      """      """
     if axis==None:  
        r=0  
        if hasattr(arg,"getRank"): r=arg.getRank()  
        if hasattr(arg,"rank"): r=arg.rank  
        axis=r/2  
4455      if isinstance(arg,Symbol):      if isinstance(arg,Symbol):
4456         return Transpose_Symbol(arg,axis=r)          dim=arg.getDim()
4457      if isinstance(arg,escript.Data):      elif isinstance(arg,escript.Data):
4458         # hack for transpose          dim=arg.getDomain().getDim()
        r=arg.getRank()  
        if r!=2: raise ValueError,"Tranpose only avalaible for rank 2 objects"  
        s=arg.getShape()  
        out=escript.Data(0.,(s[1],s[0]),arg.getFunctionSpace())  
        for i in range(s[0]):  
           for j in range(s[1]):  
              out[j,i]=arg[i,j]  
        return out  
        # end hack for transpose  
        return arg.transpose(axis)  
4459      else:      else:
4460         return numarray.transpose(arg,axis=axis)          raise TypeError,"div: argument type not supported"
4461        if not arg.getShape()==(dim,):
4462          raise ValueError,"div: expected shape is (%s,)"%dim
4463        return trace(grad(arg,where))
4464    
4465  def trace(arg,axis0=0,axis1=1):  def jump(arg,domain=None):
4466      """      """
4467      Return      returns the jump of arg across the continuity of the domain
4468    
4469      @param arg:      @param arg: argument
4470        @type arg: L{escript.Data} or L{Symbol}
4471        @param domain: the domain where the discontinuity is located. If domain is not present or equal to C{None}
4472                       the domain of arg is used. If arg is a L{Symbol} the domain must be present.
4473        @type domain: C{None} or L{escript.Domain}
4474        @return: jump of arg
4475        @rtype:  L{escript.Data} or L{Symbol}
4476      """      """
4477      if isinstance(arg,Symbol):      if domain==None: domain=arg.getDomain()
4478         s=list(arg.getShape())              return interpolate(arg,escript.FunctionOnContactOne(domain))-interpolate(arg,escript.FunctionOnContactZero(domain))
        s=tuple(s[0:axis0]+s[axis0+1:axis1]+s[axis1+1:])  
        return Trace_Symbol(arg,axis0=axis0,axis1=axis1)  
     elif isinstance(arg,escript.Data):  
        # hack for trace  
        s=arg.getShape()  
        if s[axis0]!=s[axis1]:  
            raise ValueError,"illegal axis in trace"  
        out=escript.Scalar(0.,arg.getFunctionSpace())  
        for i in range(s[axis0]):  
           out+=arg[i,i]  
        return out  
        # end hack for trace  
     else:  
        return numarray.trace(arg,axis0=axis0,axis1=axis1)  
4479    
4480    def L2(arg):
4481        """
4482        returns the L2 norm of arg at where
4483        
4484        @param arg: function which L2 to be calculated.
4485        @type arg: L{escript.Data} or L{Symbol}
4486        @return: L2 norm of arg.
4487        @rtype:  L{float} or L{Symbol}
4488        @note: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
4489        """
4490        return sqrt(integrate(inner(arg,arg)))
4491    #=============================
4492    #
4493    
4494  def reorderComponents(arg,index):  def reorderComponents(arg,index):
4495      """      """
4496      resorts the component of arg according to index      resorts the component of arg according to index
4497    
4498      """      """
4499      pass      raise NotImplementedError
4500  #  #
4501  # $Log: util.py,v $  # $Log: util.py,v $
4502  # Revision 1.14.2.16  2005/10/19 06:09:57  gross  # Revision 1.14.2.16  2005/10/19 06:09:57  gross

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