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

revision 341 by gross, Mon Dec 12 05:26:10 2005 UTC revision 580 by gross, Wed Mar 8 05:45:51 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 143  def identity(shape=()): Line 133  def identity(shape=()):
133     @raise ValueError: if len(shape)>2.     @raise ValueError: if len(shape)>2.
134     """     """
135     if len(shape)>0:     if len(shape)>0:
136        out=numarray.zeros(shape+shape,numarray.Float)        out=numarray.zeros(shape+shape,numarray.Float64)
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.         return not Lsup(arg)>0.
363      except TypeError:      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.
369        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 386  def matchType(arg0=0.,arg1=0.): Line 389  def matchType(arg0=0.,arg1=0.):
389         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
390            arg0=escript.Data(arg0,arg1.getFunctionSpace())            arg0=escript.Data(arg0,arg1.getFunctionSpace())
391         elif isinstance(arg1,float):         elif isinstance(arg1,float):
392            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
393         elif isinstance(arg1,int):         elif isinstance(arg1,int):
394            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
395         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
396            pass            pass
397         else:         else:
# Line 412  def matchType(arg0=0.,arg1=0.): Line 415  def matchType(arg0=0.,arg1=0.):
415         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
416            pass            pass
417         elif isinstance(arg1,float):         elif isinstance(arg1,float):
418            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
419         elif isinstance(arg1,int):         elif isinstance(arg1,int):
420            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
421         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
422            pass            pass
423         else:         else:
424            raise TypeError,"function: Unknown type of second argument."                raise TypeError,"function: Unknown type of second argument."
425      elif isinstance(arg0,float):      elif isinstance(arg0,float):
426         if isinstance(arg1,numarray.NumArray):         if isinstance(arg1,numarray.NumArray):
427            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
428         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
429            arg0=escript.Data(arg0,arg1.getFunctionSpace())            arg0=escript.Data(arg0,arg1.getFunctionSpace())
430         elif isinstance(arg1,float):         elif isinstance(arg1,float):
431            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
432            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
433         elif isinstance(arg1,int):         elif isinstance(arg1,int):
434            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
435            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
436         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
437            arg0=numarray.array(arg0)            arg0=numarray.array(arg0,type=numarray.Float64)
438         else:         else:
439            raise TypeError,"function: Unknown type of second argument."                raise TypeError,"function: Unknown type of second argument."
440      elif isinstance(arg0,int):      elif isinstance(arg0,int):
441         if isinstance(arg1,numarray.NumArray):         if isinstance(arg1,numarray.NumArray):
442            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
443         elif isinstance(arg1,escript.Data):         elif isinstance(arg1,escript.Data):
444            arg0=escript.Data(float(arg0),arg1.getFunctionSpace())            arg0=escript.Data(float(arg0),arg1.getFunctionSpace())
445         elif isinstance(arg1,float):         elif isinstance(arg1,float):
446            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
447            arg1=numarray.array(arg1)            arg1=numarray.array(arg1,type=numarray.Float64)
448         elif isinstance(arg1,int):         elif isinstance(arg1,int):
449            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
450            arg1=numarray.array(float(arg1))            arg1=numarray.array(float(arg1),type=numarray.Float64)
451         elif isinstance(arg1,Symbol):         elif isinstance(arg1,Symbol):
452            arg0=numarray.array(float(arg0))            arg0=numarray.array(float(arg0),type=numarray.Float64)
453         else:         else:
454            raise TypeError,"function: Unknown type of second argument."                raise TypeError,"function: Unknown type of second argument."
455      else:      else:
# Line 469  def matchShape(arg0,arg1): Line 472  def matchShape(arg0,arg1):
472      sh0=pokeShape(arg0)      sh0=pokeShape(arg0)
473      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
474      if len(sh0)<len(sh):      if len(sh0)<len(sh):
475         return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float)),arg1         return outer(arg0,numarray.ones(sh[len(sh0):],numarray.Float64)),arg1
476      elif len(sh1)<len(sh):      elif len(sh1)<len(sh):
477         return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float))         return arg0,outer(arg1,numarray.ones(sh[len(sh1):],numarray.Float64))
478      else:      else:
479         return arg0,arg1         return arg0,arg1
480  #=========================================================  #=========================================================
# Line 597  class Symbol(object): Line 600  class Symbol(object):
600            else:            else:
601                s=pokeShape(s)+arg.getShape()                s=pokeShape(s)+arg.getShape()
602                if len(s)>0:                if len(s)>0:
603                   out.append(numarray.zeros(s),numarray.Float)                   out.append(numarray.zeros(s),numarray.Float64)
604                else:                else:
605                   out.append(a)                   out.append(a)
606         return out         return out
# Line 687  class Symbol(object): Line 690  class Symbol(object):
690         else:         else:
691            s=self.getShape()+arg.getShape()            s=self.getShape()+arg.getShape()
692            if len(s)>0:            if len(s)>0:
693               return numarray.zeros(s,numarray.Float)               return numarray.zeros(s,numarray.Float64)
694            else:            else:
695               return 0.               return 0.
696
# 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.Float64))*1.
1013           if arg>0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
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.Float64))*1.
1095           if arg<0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
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.Float64))*1.
1177           if arg<0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
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.Float64))*1.
1207           if arg>0:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
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.Float64))*1.
1239           if abs(arg)<=tol:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
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.Float64))*1.
1322          if abs(arg)>tol:        if isinstance(out,float): out=numarray.array(out,type=numarray.Float64)
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.Float64)
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    def symmetric(arg):
3281        """
3282        returns the symmetric part of the square matrix arg. This is (arg+transpose(arg))/2
3283
3284        @param arg: square matrix. Must have rank 2 or 4 and be square.
3285        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3286        @return: symmetric part of arg
3287        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3288        """
3289        if isinstance(arg,numarray.NumArray):
3290          if arg.rank==2:
3291            if not (arg.shape[0]==arg.shape[1]):
3292               raise ValueError,"symmetric: argument must be square."
3293          elif arg.rank==4:
3294            if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
3295               raise ValueError,"symmetric: argument must be square."
3296          else:
3297            raise ValueError,"symmetric: rank 2 or 4 is required."
3298          return (arg+transpose(arg))/2
3299        elif isinstance(arg,escript.Data):
3300          return escript_symmetric(arg)
3301        elif isinstance(arg,float):
3302          return arg
3303        elif isinstance(arg,int):
3304          return float(arg)
3305        elif isinstance(arg,Symbol):
3306          if arg.getRank()==2:
3307            if not (arg.getShape()[0]==arg.getShape()[1]):
3308               raise ValueError,"symmetric: argument must be square."
3309          elif arg.getRank()==4:
3310            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3311               raise ValueError,"symmetric: argument must be square."
3312          else:
3313            raise ValueError,"symmetric: rank 2 or 4 is required."
3314          return (arg+transpose(arg))/2
3315        else:
3316          raise TypeError,"symmetric: Unknown argument type."
3317
3318    def escript_symmetric(arg): # this should be implemented in c++
3319          if arg.getRank()==2:
3320            if not (arg.getShape()[0]==arg.getShape()[1]):
3321               raise ValueError,"escript_symmetric: argument must be square."
3322            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3323            for i0 in range(arg.getShape()[0]):
3324               for i1 in range(arg.getShape()[1]):
3325                  out[i0,i1]=(arg[i0,i1]+arg[i1,i0])/2.
3326          elif arg.getRank()==4:
3327            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3328               raise ValueError,"escript_symmetric: argument must be square."
3329            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3330            for i0 in range(arg.getShape()[0]):
3331               for i1 in range(arg.getShape()[1]):
3332                  for i2 in range(arg.getShape()[2]):
3333                     for i3 in range(arg.getShape()[3]):
3334                         out[i0,i1,i2,i3]=(arg[i0,i1,i2,i3]+arg[i2,i3,i0,i1])/2.
3335          else:
3336            raise ValueError,"escript_symmetric: rank 2 or 4 is required."
3337          return out
3338
3339    def nonsymmetric(arg):
3340        """
3341        returns the nonsymmetric part of the square matrix arg. This is (arg-transpose(arg))/2
3342
3343        @param arg: square matrix. Must have rank 2 or 4 and be square.
3344        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3345        @return: nonsymmetric part of arg
3346        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3347        """
3348        if isinstance(arg,numarray.NumArray):
3349          if arg.rank==2:
3350            if not (arg.shape[0]==arg.shape[1]):
3351               raise ValueError,"nonsymmetric: argument must be square."
3352          elif arg.rank==4:
3353            if not (arg.shape[0]==arg.shape[2] and arg.shape[1]==arg.shape[3]):
3354               raise ValueError,"nonsymmetric: argument must be square."
3355          else:
3356            raise ValueError,"nonsymmetric: rank 2 or 4 is required."
3357          return (arg-transpose(arg))/2
3358        elif isinstance(arg,escript.Data):
3359          return escript_nonsymmetric(arg)
3360        elif isinstance(arg,float):
3361          return arg
3362        elif isinstance(arg,int):
3363          return float(arg)
3364        elif isinstance(arg,Symbol):
3365          if arg.getRank()==2:
3366            if not (arg.getShape()[0]==arg.getShape()[1]):
3367               raise ValueError,"nonsymmetric: argument must be square."
3368          elif arg.getRank()==4:
3369            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3370               raise ValueError,"nonsymmetric: argument must be square."
3371          else:
3372            raise ValueError,"nonsymmetric: rank 2 or 4 is required."
3373          return (arg-transpose(arg))/2
3374        else:
3375          raise TypeError,"nonsymmetric: Unknown argument type."
3376
3377    def escript_nonsymmetric(arg): # this should be implemented in c++
3378          if arg.getRank()==2:
3379            if not (arg.getShape()[0]==arg.getShape()[1]):
3380               raise ValueError,"escript_nonsymmetric: argument must be square."
3381            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3382            for i0 in range(arg.getShape()[0]):
3383               for i1 in range(arg.getShape()[1]):
3384                  out[i0,i1]=(arg[i0,i1]-arg[i1,i0])/2.
3385          elif arg.getRank()==4:
3386            if not (arg.getShape()[0]==arg.getShape()[2] and arg.getShape()[1]==arg.getShape()[3]):
3387               raise ValueError,"escript_nonsymmetric: argument must be square."
3388            out=escript.Data(0.,arg.getShape(),arg.getFunctionSpace())
3389            for i0 in range(arg.getShape()[0]):
3390               for i1 in range(arg.getShape()[1]):
3391                  for i2 in range(arg.getShape()[2]):
3392                     for i3 in range(arg.getShape()[3]):
3393                         out[i0,i1,i2,i3]=(arg[i0,i1,i2,i3]-arg[i2,i3,i0,i1])/2.
3394          else:
3395            raise ValueError,"escript_nonsymmetric: rank 2 or 4 is required."
3396          return out
3397
3398
3399    def inverse(arg):
3400        """
3401        returns the inverse of the square matrix arg.
3402
3403        @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
3404        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3405        @return: inverse arg_inv of the argument. It will be matrixmul(inverse(arg),arg) almost equal to kronecker(arg.getShape()[0])
3406        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol} depending on the input
3407        @remark: for L{escript.Data} objects the dimension is restricted to 3.
3408        """
3409        if isinstance(arg,numarray.NumArray):
3410          return numarray.linear_algebra.inverse(arg)
3411        elif isinstance(arg,escript.Data):
3412          return escript_inverse(arg)
3413        elif isinstance(arg,float):
3414          return 1./arg
3415        elif isinstance(arg,int):
3416          return 1./float(arg)
3417        elif isinstance(arg,Symbol):
3418          return Inverse_Symbol(arg)
3419        else:
3420          raise TypeError,"inverse: Unknown argument type."
3421
3422    def escript_inverse(arg): # this should be escript._inverse and use LAPACK
3423          "arg is a Data objects!!!"
3424          if not arg.getRank()==2:
3425            raise ValueError,"escript_inverse: argument must have rank 2"
3426          s=arg.getShape()
3427          if not s[0] == s[1]:
3428            raise ValueError,"escript_inverse: argument must be a square matrix."
3429          out=escript.Data(0.,s,arg.getFunctionSpace())
3430          if s[0]==1:
3431              if inf(abs(arg[0,0]))==0: # in c this should be done point wise as abs(arg[0,0](i))<=0.
3432                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3433              out[0,0]=1./arg[0,0]
3434          elif s[0]==2:
3435              A11=arg[0,0]
3436              A12=arg[0,1]
3437              A21=arg[1,0]
3438              A22=arg[1,1]
3439              D = A11*A22-A12*A21
3440              if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
3441                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3442              D=1./D
3443              out[0,0]= A22*D
3444              out[1,0]=-A21*D
3445              out[0,1]=-A12*D
3446              out[1,1]= A11*D
3447          elif s[0]==3:
3448              A11=arg[0,0]
3449              A21=arg[1,0]
3450              A31=arg[2,0]
3451              A12=arg[0,1]
3452              A22=arg[1,1]
3453              A32=arg[2,1]
3454              A13=arg[0,2]
3455              A23=arg[1,2]
3456              A33=arg[2,2]
3457              D  =  A11*(A22*A33-A23*A32)+ A12*(A31*A23-A21*A33)+A13*(A21*A32-A31*A22)
3458              if inf(abs(D))==0: # in c this should be done point wise as abs(D(i))<=0.
3459                  raise ZeroDivisionError,"escript_inverse: argument not invertible"
3460              D=1./D
3461              out[0,0]=(A22*A33-A23*A32)*D
3462              out[1,0]=(A31*A23-A21*A33)*D
3463              out[2,0]=(A21*A32-A31*A22)*D
3464              out[0,1]=(A13*A32-A12*A33)*D
3465              out[1,1]=(A11*A33-A31*A13)*D
3466              out[2,1]=(A12*A31-A11*A32)*D
3467              out[0,2]=(A12*A23-A13*A22)*D
3468              out[1,2]=(A13*A21-A11*A23)*D
3469              out[2,2]=(A11*A22-A12*A21)*D
3470          else:
3471             raise TypeError,"escript_inverse: only matrix dimensions 1,2,3 are supported right now."
3472          return out
3473
3474    class Inverse_Symbol(DependendSymbol):
3475       """
3476       L{Symbol} representing the result of the inverse function
3477       """
3478       def __init__(self,arg):
3479          """
3480          initialization of inverse L{Symbol} with argument arg
3481          @param arg: argument of function
3482          @type arg: L{Symbol}.
3483          """
3484          if not arg.getRank()==2:
3485            raise ValueError,"Inverse_Symbol:: argument must have rank 2"
3486          s=arg.getShape()
3487          if not s[0] == s[1]:
3488            raise ValueError,"Inverse_Symbol:: argument must be a square matrix."
3489          super(Inverse_Symbol,self).__init__(args=[arg],shape=s,dim=arg.getDim())
3490
3491       def getMyCode(self,argstrs,format="escript"):
3492          """
3493          returns a program code that can be used to evaluate the symbol.
3494
3495          @param argstrs: gives for each argument a string representing the argument for the evaluation.
3496          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
3497          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
3498          @type format: C{str}
3499          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
3500          @rtype: C{str}
3501          @raise: NotImplementedError: if the requested format is not available
3502          """
3503          if format=="escript" or format=="str"  or format=="text":
3504             return "inverse(%s)"%argstrs[0]
3505          else:
3506             raise NotImplementedError,"Inverse_Symbol does not provide program code for format %s."%format
3507
3508       def substitute(self,argvals):
3509          """
3510          assigns new values to symbols in the definition of the symbol.
3511          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
3512
3513          @param argvals: new values assigned to symbols
3514          @type argvals: C{dict} with keywords of type L{Symbol}.
3515          @return: result of the substitution process. Operations are executed as much as possible.
3516          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
3517          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
3518          """
3519          if argvals.has_key(self):
3520             arg=argvals[self]
3521             if self.isAppropriateValue(arg):
3522                return arg
3523             else:
3524                raise TypeError,"%s: new value is not appropriate."%str(self)
3525          else:
3526             arg=self.getSubstitutedArguments(argvals)
3527             return inverse(arg[0])
3528
3529       def diff(self,arg):
3530          """
3531          differential of this object
3532
3533          @param arg: the derivative is calculated with respect to arg
3534          @type arg: L{escript.Symbol}
3535          @return: derivative with respect to C{arg}
3536          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
3537          """
3538          if arg==self:
3539             return identity(self.getShape())
3540          else:
3541             return -matrixmult(matrixmult(self,self.getDifferentiatedArguments(arg)[0]),self)
3542
3543    def eigenvalues(arg):
3544        """
3545        returns the eigenvalues of the square matrix arg.
3546
3547        @param arg: square matrix. Must have rank 2 and the first and second dimension must be equal.
3548                    arg must be symmetric, ie. transpose(arg)==arg (this is not checked).
3549        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}
3550        @return: the eigenvalues in increasing order.
3551        @rtype: L{numarray.NumArray},L{escript.Data}, L{Symbol} depending on the input.
3552        @remark: for L{escript.Data} and L{Symbol} objects the dimension is restricted to 3.
3553        """
3554        if isinstance(arg,numarray.NumArray):
3555          out=numarray.linear_algebra.eigenvalues((arg+numarray.transpose(arg))/2.)
3556          out.sort()
3557          return out
3558        elif isinstance(arg,escript.Data):
3559          return arg._eigenvalues()
3560        elif isinstance(arg,Symbol):
3561          if not arg.getRank()==2:
3562            raise ValueError,"eigenvalues: argument must have rank 2"
3563          s=arg.getShape()
3564          if not s[0] == s[1]:
3565            raise ValueError,"eigenvalues: argument must be a square matrix."
3566          if s[0]==1:
3567              return arg[0]
3568          elif s[0]==2:
3569              A11=arg[0,0]
3570              A12=arg[0,1]
3571              A22=arg[1,1]
3572              trA=(A11+A22)/2.
3573              A11-=trA
3574              A22-=trA
3575              s=sqrt(A12**2-A11*A22)
3576              return trA+s*numarray.array([-1.,1.],type=numarray.Float64)
3577          elif s[0]==3:
3578              A11=arg[0,0]
3579              A12=arg[0,1]
3580              A22=arg[1,1]
3581              A13=arg[0,2]
3582              A23=arg[1,2]
3583              A33=arg[2,2]
3584              trA=(A11+A22+A33)/3.
3585              A11-=trA
3586              A22-=trA
3587              A33-=trA
3588              A13_2=A13**2
3589              A23_2=A23**2
3590              A12_2=A12**2
3591              p=A13_2+A23_2+A12_2+(A11**2+A22**2+A33**2)/2.
3592              q=A13_2*A22+A23_2*A11+A12_2*A33-A11*A22*A33-2*A12*A23*A13
3593              sq_p=sqrt(p/3.)
3594              alpha_3=acos(clip(-q*sq_p**(-3.)/2.,-1.,1.))/3.
3595              sq_p*=2.
3596              f=cos(alpha_3)               *numarray.array([0.,0.,1.],type=numarray.Float64) \
3597               -cos(alpha_3+numarray.pi/3.)*numarray.array([0.,1.,0.],type=numarray.Float64) \
3598               -cos(alpha_3-numarray.pi/3.)*numarray.array([1.,0.,0.],type=numarray.Float64)
3599              return trA+sq_p*f
3600          else:
3601             raise TypeError,"eigenvalues: only matrix dimensions 1,2,3 are supported right now."
3602        elif isinstance(arg,float):
3603          return arg
3604        elif isinstance(arg,int):
3605          return float(arg)
3606        else:
3607          raise TypeError,"eigenvalues: Unknown argument type."
3608  #=======================================================  #=======================================================
3609  #  Binary operations:  #  Binary operations:
3610  #=======================================================  #=======================================================
# Line 2995  def mult(arg0,arg1): Line 3723  def mult(arg0,arg1):
3723         """         """
3724         args=matchShape(arg0,arg1)         args=matchShape(arg0,arg1)
3725         if testForZero(args[0]) or testForZero(args[1]):         if testForZero(args[0]) or testForZero(args[1]):
3726            return numarray.zeros(pokeShape(args[0]),numarray.Float)            return numarray.zeros(pokeShape(args[0]),numarray.Float64)
3727         else:         else:
3728            if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) :            if isinstance(args[0],Symbol) or isinstance(args[1],Symbol) :
3729                return Mult_Symbol(args[0],args[1])                return Mult_Symbol(args[0],args[1])
# Line 3095  def quotient(arg0,arg1): Line 3823  def quotient(arg0,arg1):
3823         """         """
3824         args=matchShape(arg0,arg1)         args=matchShape(arg0,arg1)
3825         if testForZero(args[0]):         if testForZero(args[0]):
3826            return numarray.zeros(pokeShape(args[0]),numarray.Float)            return numarray.zeros(pokeShape(args[0]),numarray.Float64)
3827         elif isinstance(args[0],Symbol):         elif isinstance(args[0],Symbol):
3828            if isinstance(args[1],Symbol):            if isinstance(args[1],Symbol):
3829               return Quotient_Symbol(args[0],args[1])               return Quotient_Symbol(args[0],args[1])
# Line 3201  def power(arg0,arg1): Line 3929  def power(arg0,arg1):
3929         """         """
3930         args=matchShape(arg0,arg1)         args=matchShape(arg0,arg1)
3931         if testForZero(args[0]):         if testForZero(args[0]):
3932            return numarray.zeros(args[0],numarray.Float)            return numarray.zeros(args[0],numarray.Float64)
3933         elif testForZero(args[1]):         elif testForZero(args[1]):
3934            return numarray.ones(args[0],numarray.Float)            return numarray.ones(args[0],numarray.Float64)
3935         elif isinstance(args[0],Symbol) or isinstance(args[1],Symbol):         elif isinstance(args[0],Symbol) or isinstance(args[1],Symbol):
3936            return Power_Symbol(args[0],args[1])            return Power_Symbol(args[0],args[1])
3937         elif isinstance(args[0],numarray.NumArray) and not isinstance(args[1],numarray.NumArray):         elif isinstance(args[0],numarray.NumArray) and not isinstance(args[1],numarray.NumArray):
# Line 3304  def maximum(*args): Line 4032  def maximum(*args):
4032         if out==None:         if out==None:
4033            out=a            out=a
4034         else:         else:
4035            m=whereNegative(out-a)            diff=add(a,-out)
4036            out=m*a+(1.-m)*out            out=add(out,mult(wherePositive(diff),diff))
4037      return out      return out
4038
4039  def minimum(*arg):  def minimum(*args):
4040      """      """
4041      the minimum over arguments args      the minimum over arguments args
4042
# Line 3322  def minimum(*arg): Line 4050  def minimum(*arg):
4050         if out==None:         if out==None:
4051            out=a            out=a
4052         else:         else:
4053            m=whereNegative(out-a)            diff=add(a,-out)
4054            out=m*out+(1.-m)*a            out=add(out,mult(whereNegative(diff),diff))
4055      return out      return out
4056
4057    def clip(arg,minval=0.,maxval=1.):
4058        """
4059        cuts the values of arg between minval and maxval
4060
4061        @param arg: argument
4062        @type arg: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float}
4063        @param minval: lower range
4064        @type arg: C{float}
4065        @param maxval: upper range
4066        @type arg: C{float}
4067        @return: is on object with all its value between minval and maxval. value of the argument that greater then minval and
4068                 less then maxval are unchanged.
4069        @rtype: L{numarray.NumArray}, L{escript.Data}, L{Symbol}, C{int} or C{float} depending on the input
4070        @raise ValueError: if minval>maxval
4071        """
4072        if minval>maxval:
4073           raise ValueError,"minval = %s must be less then maxval %s"%(minval,maxval)
4074        return minimum(maximum(minval,arg),maxval)
4075
4076
4077  def inner(arg0,arg1):  def inner(arg0,arg1):
4078      """      """
# Line 3348  def inner(arg0,arg1): Line 4096  def inner(arg0,arg1):
4096      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
4097      if not sh0==sh1:      if not sh0==sh1:
4098          raise ValueError,"inner: shape of arguments does not match"          raise ValueError,"inner: shape of arguments does not match"
4099      return generalTensorProduct(arg0,arg1,offset=len(sh0))      return generalTensorProduct(arg0,arg1,axis_offset=len(sh0))
4100
4101  def matrixmult(arg0,arg1):  def matrixmult(arg0,arg1):
4102      """      """
# Line 3376  def matrixmult(arg0,arg1): Line 4124  def matrixmult(arg0,arg1):
4124          raise ValueError,"first argument must have rank 2"          raise ValueError,"first argument must have rank 2"
4125      if not len(sh1)==2 and not len(sh1)==1:      if not len(sh1)==2 and not len(sh1)==1:
4126          raise ValueError,"second argument must have rank 1 or 2"          raise ValueError,"second argument must have rank 1 or 2"
4127      return generalTensorProduct(arg0,arg1,offset=1)      return generalTensorProduct(arg0,arg1,axis_offset=1)
4128
4129  def outer(arg0,arg1):  def outer(arg0,arg1):
4130      """      """
# Line 3394  def outer(arg0,arg1): Line 4142  def outer(arg0,arg1):
4142      @return: the outer product of arg0 and arg1 at each data point      @return: the outer product of arg0 and arg1 at each data point
4143      @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
4144      """      """
4145      return generalTensorProduct(arg0,arg1,offset=0)      return generalTensorProduct(arg0,arg1,axis_offset=0)
4146
4147
4148  def tensormult(arg0,arg1):  def tensormult(arg0,arg1):
# Line 3436  def tensormult(arg0,arg1): Line 4184  def tensormult(arg0,arg1):
4184      sh0=pokeShape(arg0)      sh0=pokeShape(arg0)
4185      sh1=pokeShape(arg1)      sh1=pokeShape(arg1)
4186      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):      if len(sh0)==2 and ( len(sh1)==2 or len(sh1)==1 ):
4187         return generalTensorProduct(arg0,arg1,offset=1)         return generalTensorProduct(arg0,arg1,axis_offset=1)
4188      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):
4189         return generalTensorProduct(arg0,arg1,offset=2)         return generalTensorProduct(arg0,arg1,axis_offset=2)
4190      else:      else:
4191          raise ValueError,"tensormult: first argument must have rank 2 or 4"          raise ValueError,"tensormult: first argument must have rank 2 or 4"
4192
4193  def generalTensorProduct(arg0,arg1,offset=0):  def generalTensorProduct(arg0,arg1,axis_offset=0):
4194      """      """
4195      generalized tensor product      generalized tensor product
4196
4197      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]      out[s,t]=S{Sigma}_r arg0[s,r]*arg1[r,t]
4198
4199      where s runs through arg0.Shape[:arg0.Rank-offset]      where s runs through arg0.Shape[:arg0.Rank-axis_offset]
4200            r runs trough arg0.Shape[:offset]            r runs trough arg0.Shape[:axis_offset]
4201            t runs through arg1.Shape[offset:]            t runs through arg1.Shape[axis_offset:]
4202
4203      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
4204      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 4215  def generalTensorProduct(arg0,arg1,offse
4215      # 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
4216      if isinstance(arg0,numarray.NumArray):      if isinstance(arg0,numarray.NumArray):
4217         if isinstance(arg1,Symbol):         if isinstance(arg1,Symbol):
4218             return GeneralTensorProduct_Symbol(arg0,arg1,offset)             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4219         else:         else:
4220             if not arg0.shape[arg0.rank-offset:]==arg1.shape[:offset]:             if not arg0.shape[arg0.rank-axis_offset:]==arg1.shape[:axis_offset]:
4221                 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)
4222             arg0_c=arg0.copy()             arg0_c=arg0.copy()
4223             arg1_c=arg1.copy()             arg1_c=arg1.copy()
4224             sh0,sh1=arg0.shape,arg1.shape             sh0,sh1=arg0.shape,arg1.shape
4225             d0,d1,d01=1,1,1             d0,d1,d01=1,1,1
4226             for i in sh0[:arg0.rank-offset]: d0*=i             for i in sh0[:arg0.rank-axis_offset]: d0*=i
4227             for i in sh1[offset:]: d1*=i             for i in sh1[axis_offset:]: d1*=i
4228             for i in sh1[:offset]: d01*=i             for i in sh1[:axis_offset]: d01*=i
4229             arg0_c.resize((d0,d01))             arg0_c.resize((d0,d01))
4230             arg1_c.resize((d01,d1))             arg1_c.resize((d01,d1))
4231             out=numarray.zeros((d0,d1),numarray.Float)             out=numarray.zeros((d0,d1),numarray.Float64)
4232             for i0 in range(d0):             for i0 in range(d0):
4233                      for i1 in range(d1):                      for i1 in range(d1):
4234                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])                           out[i0,i1]=numarray.sum(arg0_c[i0,:]*arg1_c[:,i1])
4235             out.resize(sh0[:arg0.rank-offset]+sh1[offset:])             out.resize(sh0[:arg0.rank-axis_offset]+sh1[axis_offset:])
4236             return out             return out
4237      elif isinstance(arg0,escript.Data):      elif isinstance(arg0,escript.Data):
4238         if isinstance(arg1,Symbol):         if isinstance(arg1,Symbol):
4239             return GeneralTensorProduct_Symbol(arg0,arg1,offset)             return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4240         else:         else:
4241             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)
4242      else:            else:
4243         return GeneralTensorProduct_Symbol(arg0,arg1,offset)         return GeneralTensorProduct_Symbol(arg0,arg1,axis_offset)
4244
4245  class GeneralTensorProduct_Symbol(DependendSymbol):  class GeneralTensorProduct_Symbol(DependendSymbol):
4246     """     """
4247     Symbol representing the quotient of two arguments.     Symbol representing the quotient of two arguments.
4248     """     """
4249     def __init__(self,arg0,arg1,offset=0):     def __init__(self,arg0,arg1,axis_offset=0):
4250         """         """
4251         initialization of L{Symbol} representing the quotient of two arguments         initialization of L{Symbol} representing the quotient of two arguments
4252
# Line 3511  class GeneralTensorProduct_Symbol(Depend Line 4259  class GeneralTensorProduct_Symbol(Depend
4259         """         """
4260         sh_arg0=pokeShape(arg0)         sh_arg0=pokeShape(arg0)
4261         sh_arg1=pokeShape(arg1)         sh_arg1=pokeShape(arg1)
4262         sh0=sh_arg0[:len(sh_arg0)-offset]         sh0=sh_arg0[:len(sh_arg0)-axis_offset]
4263         sh01=sh_arg0[len(sh_arg0)-offset:]         sh01=sh_arg0[len(sh_arg0)-axis_offset:]
4264         sh10=sh_arg1[:offset]         sh10=sh_arg1[:axis_offset]
4265         sh1=sh_arg1[offset:]         sh1=sh_arg1[axis_offset:]
4266         if not sh01==sh10:         if not sh01==sh10:
4267             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)
4268         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])
4269
4270     def getMyCode(self,argstrs,format="escript"):     def getMyCode(self,argstrs,format="escript"):
4271        """        """
# Line 3532  class GeneralTensorProduct_Symbol(Depend Line 4280  class GeneralTensorProduct_Symbol(Depend
4280        @raise: NotImplementedError: if the requested format is not available        @raise: NotImplementedError: if the requested format is not available
4281        """        """
4282        if format=="escript" or format=="str" or format=="text":        if format=="escript" or format=="str" or format=="text":
4283           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])
4284        else:        else:
4285           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)
4286
# Line 3557  class GeneralTensorProduct_Symbol(Depend Line 4305  class GeneralTensorProduct_Symbol(Depend
4305           args=self.getSubstitutedArguments(argvals)           args=self.getSubstitutedArguments(argvals)
4306           return generalTensorProduct(args[0],args[1],args[2])           return generalTensorProduct(args[0],args[1],args[2])
4307
4308  def escript_generalTensorProduct(arg0,arg1,offset): # this should be escript._generalTensorProduct  def escript_generalTensorProduct(arg0,arg1,axis_offset): # this should be escript._generalTensorProduct
4309      "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!!!"
4310      # calculate the return shape:      # calculate the return shape:
4311      shape0=arg0.getShape()[:arg0.getRank()-offset]      shape0=arg0.getShape()[:arg0.getRank()-axis_offset]
4312      shape01=arg0.getShape()[arg0.getRank()-offset:]      shape01=arg0.getShape()[arg0.getRank()-axis_offset:]
4313      shape10=arg1.getShape()[:offset]      shape10=arg1.getShape()[:axis_offset]
4314      shape1=arg1.getShape()[offset:]      shape1=arg1.getShape()[axis_offset:]
4315      if not shape01==shape10:      if not shape01==shape10:
4316          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)
4317
4318        # whatr function space should be used? (this here is not good!)
4319        fs=(escript.Scalar(0.,arg0.getFunctionSpace())+escript.Scalar(0.,arg1.getFunctionSpace())).getFunctionSpace()
4320      # create return value:      # create return value:
4321      out=escript.Data(0.,tuple(shape0+shape1),arg0.getFunctionSpace())      out=escript.Data(0.,tuple(shape0+shape1),fs)
4322      #      #
4323      s0=[[]]      s0=[[]]
4324      for k in shape0:      for k in shape0:
# Line 3591  def escript_generalTensorProduct(arg0,ar Line 4341  def escript_generalTensorProduct(arg0,ar
4341
4342      for i0 in s0:      for i0 in s0:
4343         for i1 in s1:         for i1 in s1:
4344           s=escript.Scalar(0.,arg0.getFunctionSpace())           s=escript.Scalar(0.,fs)
4345           for i01 in s01:           for i01 in s01:
4346              s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))              s+=arg0.__getitem__(tuple(i0+i01))*arg1.__getitem__(tuple(i01+i1))
4347           out.__setitem__(tuple(i0+i1),s)           out.__setitem__(tuple(i0+i1),s)
4348      return out      return out
4349
4350
4351  #=========================================================  #=========================================================
4352  #   some little helpers  #  functions dealing with spatial dependency
4353  #=========================================================  #=========================================================
4354  def grad(arg,where=None):  def grad(arg,where=None):
4355      """      """
4356      Returns the spatial gradient of arg at where.      Returns the spatial gradient of arg at where.
4357
4358        If C{g} is the returned object, then
4359
4360      @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.
4361                    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.
4362          - 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.
4363          - 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.
4364
4365        @param arg: function which gradient to be calculated. Its rank has to be less than 3.
4366        @type arg: L{escript.Data} or L{Symbol}
4367      @param where: FunctionSpace in which the gradient will be calculated.      @param where: FunctionSpace in which the gradient will be calculated.
4368                    If not present or C{None} an appropriate default is used.                    If not present or C{None} an appropriate default is used.
4369        @type where: C{None} or L{escript.FunctionSpace}
4370        @return: gradient of arg.
4371        @rtype:  L{escript.Data} or L{Symbol}
4372      """      """
4373      if isinstance(arg,Symbol):      if isinstance(arg,Symbol):
4374         return Grad_Symbol(arg,where)         return Grad_Symbol(arg,where)
# Line 3617  def grad(arg,where=None): Line 4378  def grad(arg,where=None):
4378         else:         else:
4379            return arg._grad(where)            return arg._grad(where)
4380      else:      else:
4381        raise TypeError,"grad: Unknown argument type."         raise TypeError,"grad: Unknown argument type."
4382
4383    class Grad_Symbol(DependendSymbol):
4384       """
4385       L{Symbol} representing the result of the gradient operator
4386       """
4387       def __init__(self,arg,where=None):
4388          """
4389          initialization of gradient L{Symbol} with argument arg
4390          @param arg: argument of function
4391          @type arg: L{Symbol}.
4392          @param where: FunctionSpace in which the gradient will be calculated.
4393                      If not present or C{None} an appropriate default is used.
4394          @type where: C{None} or L{escript.FunctionSpace}
4395          """
4396          d=arg.getDim()
4397          if d==None:
4398             raise ValueError,"argument must have a spatial dimension"
4399          super(Grad_Symbol,self).__init__(args=[arg,where],shape=arg.getShape()+(d,),dim=d)
4400
4401       def getMyCode(self,argstrs,format="escript"):
4402          """
4403          returns a program code that can be used to evaluate the symbol.
4404
4405          @param argstrs: gives for each argument a string representing the argument for the evaluation.
4406          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4407          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4408          @type format: C{str}
4409          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4410          @rtype: C{str}
4411          @raise: NotImplementedError: if the requested format is not available
4412          """
4413          if format=="escript" or format=="str"  or format=="text":
4414             return "grad(%s,where=%s)"%(argstrs[0],argstrs[1])
4415          else:
4416             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4417
4418       def substitute(self,argvals):
4419          """
4420          assigns new values to symbols in the definition of the symbol.
4421          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
4422
4423          @param argvals: new values assigned to symbols
4424          @type argvals: C{dict} with keywords of type L{Symbol}.
4425          @return: result of the substitution process. Operations are executed as much as possible.
4426          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4427          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4428          """
4429          if argvals.has_key(self):
4430             arg=argvals[self]
4431             if self.isAppropriateValue(arg):
4432                return arg
4433             else:
4434                raise TypeError,"%s: new value is not appropriate."%str(self)
4435          else:
4436             arg=self.getSubstitutedArguments(argvals)
4437             return grad(arg[0],where=arg[1])
4438
4439       def diff(self,arg):
4440          """
4441          differential of this object
4442
4443          @param arg: the derivative is calculated with respect to arg
4444          @type arg: L{escript.Symbol}
4445          @return: derivative with respect to C{arg}
4446          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
4447          """
4448          if arg==self:
4449             return identity(self.getShape())
4450          else:
4451             return grad(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4452
4453  def integrate(arg,where=None):  def integrate(arg,where=None):
4454      """      """
4455      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}
4456      its domain.      before integration.
4457
4458      @param arg:   Data object representing the function which is integrated.      @param arg:   the function which is integrated.
4459        @type arg: L{escript.Data} or L{Symbol}
4460      @param where: FunctionSpace in which the integral is calculated.      @param where: FunctionSpace in which the integral is calculated.
4461                    If not present or C{None} an appropriate default is used.                    If not present or C{None} an appropriate default is used.
4462        @type where: C{None} or L{escript.FunctionSpace}
4463        @return: integral of arg.
4464        @rtype:  C{float}, C{numarray.NumArray} or L{Symbol}
4465      """      """
4466      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):
4467         return Integrate_Symbol(arg,where)         return Integrate_Symbol(arg,where)
4468      elif isinstance(arg,escript.Data):      elif isinstance(arg,escript.Data):
4469         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 4474  def integrate(arg,where=None):
4474      else:      else:
4475        raise TypeError,"integrate: Unknown argument type."        raise TypeError,"integrate: Unknown argument type."
4476
4477    class Integrate_Symbol(DependendSymbol):
4478       """
4479       L{Symbol} representing the result of the spatial integration operator
4480       """
4481       def __init__(self,arg,where=None):
4482          """
4483          initialization of integration L{Symbol} with argument arg
4484          @param arg: argument of the integration
4485          @type arg: L{Symbol}.
4486          @param where: FunctionSpace in which the integration will be calculated.
4487                      If not present or C{None} an appropriate default is used.
4488          @type where: C{None} or L{escript.FunctionSpace}
4489          """
4490          super(Integrate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),dim=arg.getDim())
4491
4492       def getMyCode(self,argstrs,format="escript"):
4493          """
4494          returns a program code that can be used to evaluate the symbol.
4495
4496          @param argstrs: gives for each argument a string representing the argument for the evaluation.
4497          @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4498          @param format: specifies the format to be used. At the moment only "escript" ,"text" and "str" are supported.
4499          @type format: C{str}
4500          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4501          @rtype: C{str}
4502          @raise: NotImplementedError: if the requested format is not available
4503          """
4504          if format=="escript" or format=="str"  or format=="text":
4505             return "integrate(%s,where=%s)"%(argstrs[0],argstrs[1])
4506          else:
4507             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4508
4509       def substitute(self,argvals):
4510          """
4511          assigns new values to symbols in the definition of the symbol.
4512          The method replaces the L{Symbol} u by argvals[u] in the expression defining this object.
4513
4514          @param argvals: new values assigned to symbols
4515          @type argvals: C{dict} with keywords of type L{Symbol}.
4516          @return: result of the substitution process. Operations are executed as much as possible.
4517          @rtype: L{escript.Symbol}, C{float}, L{escript.Data}, L{numarray.NumArray} depending on the degree of substitution
4518          @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4519          """
4520          if argvals.has_key(self):
4521             arg=argvals[self]
4522             if self.isAppropriateValue(arg):
4523                return arg
4524             else:
4525                raise TypeError,"%s: new value is not appropriate."%str(self)
4526          else:
4527             arg=self.getSubstitutedArguments(argvals)
4528             return integrate(arg[0],where=arg[1])
4529
4530       def diff(self,arg):
4531          """
4532          differential of this object
4533
4534          @param arg: the derivative is calculated with respect to arg
4535          @type arg: L{escript.Symbol}
4536          @return: derivative with respect to C{arg}
4537          @rtype: typically L{Symbol} but other types such as C{float}, L{escript.Data}, L{numarray.NumArray}  are possible.
4538          """
4539          if arg==self:
4540             return identity(self.getShape())
4541          else:
4542             return integrate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4543
4544
4545  def interpolate(arg,where):  def interpolate(arg,where):
4546      """      """
4547      Interpolates the function into the FunctionSpace where.      interpolates the function into the FunctionSpace where.
4548
4549      @param arg:    interpolant      @param arg: interpolant
4550      @param where:  FunctionSpace to interpolate to      @type arg: L{escript.Data} or L{Symbol}
4551        @param where: FunctionSpace to be interpolated to
4552        @type where: L{escript.FunctionSpace}
4553        @return: interpolated argument
4554        @rtype:  C{escript.Data} or L{Symbol}
4555      """      """
4556      if testForZero(arg):      if isinstance(arg,Symbol):
4557        return 0         return Interpolate_Symbol(arg,where)
elif isinstance(arg,Symbol):
return Interpolated_Symbol(arg,where)
4558      else:      else:
4559         return escript.Data(arg,where)         return escript.Data(arg,where)
4560
4561  def div(arg,where=None):  class Interpolate_Symbol(DependendSymbol):
4562      """     """
4563      Returns the divergence of arg at where.     L{Symbol} representing the result of the interpolation operator
4564       """
4565       def __init__(self,arg,where):
4566          """
4567          initialization of interpolation L{Symbol} with argument arg
4568          @param arg: argument of the interpolation
4569          @type arg: L{Symbol}.
4570          @param where: FunctionSpace into which the argument is interpolated.
4571          @type where: L{escript.FunctionSpace}
4572          """
4573          super(Interpolate_Symbol,self).__init__(args=[arg,where],shape=arg.getShape(),dim=arg.getDim())
4574
4575      @param arg:   Data object representing the function which gradient to     def getMyCode(self,argstrs,format="escript"):
4576                    be calculated.        """
4577      @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)
4578
4579  def jump(arg):        @param argstrs: gives for each argument a string representing the argument for the evaluation.
4580      """        @type argstrs: C{str} or a C{list} of length 1 of C{str}.
4581      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.
4582          @type format: C{str}
4583          @return: a piece of program code which can be used to evaluate the expression assuming the values for the arguments are available.
4584          @rtype: C{str}
4585          @raise: NotImplementedError: if the requested format is not available
4586          """
4587          if format=="escript" or format=="str"  or format=="text":
4588             return "interpolate(%s,where=%s)"%(argstrs[0],argstrs[1])
4589          else:
4590             raise NotImplementedError,"Trace_Symbol does not provide program code for format %s."%format
4591
4592      @param arg:   Data object representing the function which gradient     def substitute(self,argvals):
4593                    to be calculated.        """
4594      """        assigns new values to symbols in the definition of the symbol.
4595      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())
4596
4597  #=============================        @param argvals: new values assigned to symbols
4598  #        @type argvals: C{dict} with keywords of type L{Symbol}.
4599  # 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.
4600  # 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
4601  # numarray function is called.        @raise TypeError: if a value for a L{Symbol} cannot be substituted.
4602          """
4603          if argvals.has_key(self):
4604             arg=argvals[self]
4605             if self.isAppropriateValue(arg):
4606                return arg
4607             else:
4608                raise TypeError,"%s: new value is not appropriate."%str(self)
4609          else:
4610             arg=self.getSubstitutedArguments(argvals)
4611             return interpolate(arg[0],where=arg[1])
4612
4613       def diff(self,arg):
4614          """
4615          differential of this object
4616
4617          @param arg: the derivative is calculated with respect to arg
4618          @type arg: L{escript.Symbol}
4619          @return: derivative with respect to C{arg}
4620          @rtype: L{Symbol} but other types such as L{escript.Data}, L{numarray.NumArray}  are possible.
4621          """
4622          if arg==self:
4623             return identity(self.getShape())
4624          else:
4625             return interpolate(self.getDifferentiatedArguments(arg)[0],where=self.getArgument()[1])
4626
# functions involving the underlying Domain:
4627
4628  def transpose(arg,axis=None):  def div(arg,where=None):
4629      """      """
4630      Returns the transpose of the Data object arg.      returns the divergence of arg at where.
4631
4632      @param arg:      @param arg: function which divergence to be calculated. Its shape has to be (d,) where d is the spatial dimension.
4633        @type arg: L{escript.Data} or L{Symbol}
4634        @param where: FunctionSpace in which the divergence will be calculated.
4635                      If not present or C{None} an appropriate default is used.
4636        @type where: C{None} or L{escript.FunctionSpace}
4637        @return: divergence of arg.
4638        @rtype:  L{escript.Data} or L{Symbol}
4639      """      """
if axis==None:
r=0
if hasattr(arg,"getRank"): r=arg.getRank()
if hasattr(arg,"rank"): r=arg.rank
axis=r/2
4640      if isinstance(arg,Symbol):      if isinstance(arg,Symbol):
4641         return Transpose_Symbol(arg,axis=r)          dim=arg.getDim()
4642      if isinstance(arg,escript.Data):      elif isinstance(arg,escript.Data):
4643         # 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)
4644      else:      else:
4645         return numarray.transpose(arg,axis=axis)          raise TypeError,"div: argument type not supported"
4646        if not arg.getShape()==(dim,):
4647          raise ValueError,"div: expected shape is (%s,)"%dim
4648        return trace(grad(arg,where))
4649
4650  def trace(arg,axis0=0,axis1=1):  def jump(arg,domain=None):
4651      """      """
4652      Return      returns the jump of arg across the continuity of the domain
4653
4654      @param arg:      @param arg: argument
4655        @type arg: L{escript.Data} or L{Symbol}
4656        @param domain: the domain where the discontinuity is located. If domain is not present or equal to C{None}
4657                       the domain of arg is used. If arg is a L{Symbol} the domain must be present.
4658        @type domain: C{None} or L{escript.Domain}
4659        @return: jump of arg
4660        @rtype:  L{escript.Data} or L{Symbol}
4661      """      """
4662      if isinstance(arg,Symbol):      if domain==None: domain=arg.getDomain()
4663         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)
4664
4665    def L2(arg):
4666        """
4667        returns the L2 norm of arg at where
4668
4669        @param arg: function which L2 to be calculated.
4670        @type arg: L{escript.Data} or L{Symbol}
4671        @return: L2 norm of arg.
4672        @rtype:  L{float} or L{Symbol}
4673        @note: L2(arg) is equivalent to sqrt(integrate(inner(arg,arg)))
4674        """
4675        return sqrt(integrate(inner(arg,arg)))
4676    #=============================
4677    #
4678
4679  def reorderComponents(arg,index):  def reorderComponents(arg,index):
4680      """      """
4681      resorts the component of arg according to index      resorts the component of arg according to index
4682
4683      """      """
4684      pass      raise NotImplementedError
4685  #  #
4686  # \$Log: util.py,v \$  # \$Log: util.py,v \$
4687  # 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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