| 1 |
# $Id$ |
| 2 |
|
| 3 |
""" |
| 4 |
symbolic tool box for escript |
| 5 |
""" |
| 6 |
|
| 7 |
import numarray |
| 8 |
|
| 9 |
#=========================================================== |
| 10 |
# a simple tool box to deal with _differentials of functions |
| 11 |
#=========================================================== |
| 12 |
|
| 13 |
class Symbol: |
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""" |
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Symbol class. |
| 16 |
""" |
| 17 |
def __init__(self,name="symbol",shape=(),dim=3,args=[]): |
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""" |
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Creates an instance of a symbol of shape shape and spatial dimension |
| 20 |
dim. |
| 21 |
|
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The symbol may depending on a list of arguments args which may be |
| 23 |
symbols or other objects. name gives the name of the symbol. |
| 24 |
""" |
| 25 |
|
| 26 |
self.__args=args |
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self.__name=name |
| 28 |
self.__shape=shape |
| 29 |
if hasattr(dim,"getDim"): |
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self.__dim=dim.getDim() |
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else: |
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self.__dim=dim |
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# |
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self.__cache_val=None |
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self.__cache_argval=None |
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|
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def getArgument(self,i): |
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""" |
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Returns the i-th argument. |
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""" |
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return self.__args[i] |
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|
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def getDim(self): |
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""" |
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Returns the spatial dimension of the symbol. |
| 46 |
""" |
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return self.__dim |
| 48 |
|
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def getRank(self): |
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""" |
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Returns the rank of the symbol. |
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""" |
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return len(self.getShape()) |
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|
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def getShape(self): |
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""" |
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Returns the shape of the symbol. |
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""" |
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return self.__shape |
| 60 |
|
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def getEvaluatedArguments(self,argval): |
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""" |
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Returns the list of evaluated arguments by subsituting symbol u by |
| 64 |
argval[u]. |
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""" |
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if argval==self.__cache_argval: |
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print "%s: cached value used"%self |
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return self.__cache_val |
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else: |
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out=[] |
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for a in self.__args: |
| 72 |
if isinstance(a,Symbol): |
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out.append(a.eval(argval)) |
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else: |
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out.append(a) |
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self.__cache_argval=argval |
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self.__cache_val=out |
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return out |
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|
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def getDifferentiatedArguments(self,arg): |
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""" |
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Returns the list of the arguments _differentiated by arg. |
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""" |
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out=[] |
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for a in self.__args: |
| 86 |
if isinstance(a,Symbol): |
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out.append(a.diff(arg)) |
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else: |
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out.append(0) |
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return out |
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|
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def diff(self,arg): |
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""" |
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Returns the _differention of self by arg. |
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""" |
| 96 |
if self==arg: |
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out=numarray.zeros(tuple(2*list(self.getShape())),numarray.Float) |
| 98 |
if self.getRank()==0: |
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out=1. |
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elif self.getRank()==1: |
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for i0 in range(self.getShape()[0]): |
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out[i0,i0]=1. |
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elif self.getRank()==2: |
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for i0 in range(self.getShape()[0]): |
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for i1 in range(self.getShape()[1]): |
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out[i0,i1,i0,i1]=1. |
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elif self.getRank()==3: |
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for i0 in range(self.getShape()[0]): |
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for i1 in range(self.getShape()[1]): |
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for i2 in range(self.getShape()[2]): |
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out[i0,i1,i2,i0,i1,i2]=1. |
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elif self.getRank()==4: |
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for i0 in range(self.getShape()[0]): |
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for i1 in range(self.getShape()[1]): |
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for i2 in range(self.getShape()[2]): |
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for i3 in range(self.getShape()[3]): |
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out[i0,i1,i2,i3,i0,i1,i2,i3]=1. |
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else: |
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raise ValueError,"differential support rank<5 only." |
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return out |
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else: |
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return self._diff(arg) |
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|
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def _diff(self,arg): |
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""" |
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Return derivate of self with respect to arg (!=self). |
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|
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This method is overwritten by a particular symbol. |
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""" |
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return 0 |
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|
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def eval(self,argval): |
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""" |
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Subsitutes symbol u in self by argval[u] and returns the result. If |
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self is not a key of argval then self is returned. |
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""" |
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if argval.has_key(self): |
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return argval[self] |
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else: |
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return self |
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|
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def __str__(self): |
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""" |
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Returns a string representation of the symbol. |
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""" |
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return self.__name |
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|
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def __add__(self,other): |
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""" |
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Adds other to symbol self. if _testForZero(other) self is returned. |
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""" |
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if _testForZero(other): |
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return self |
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else: |
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a=_matchShape([self,other]) |
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return Add_Symbol(a[0],a[1]) |
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|
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def __radd__(self,other): |
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""" |
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Adds other to symbol self. if _testForZero(other) self is returned. |
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""" |
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return self+other |
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|
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def __neg__(self): |
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""" |
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Returns -self. |
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""" |
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return self*(-1.) |
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|
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def __pos__(self): |
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""" |
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Returns +self. |
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""" |
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return self |
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|
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def __abs__(self): |
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""" |
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Returns absolute value. |
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""" |
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return Abs_Symbol(self) |
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|
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def __sub__(self,other): |
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""" |
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Subtracts other from symbol self. |
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|
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If _testForZero(other) self is returned. |
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""" |
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if _testForZero(other): |
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return self |
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else: |
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return self+(-other) |
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|
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def __rsub__(self,other): |
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""" |
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Subtracts symbol self from other. |
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""" |
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return -self+other |
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|
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def __div__(self,other): |
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""" |
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Divides symbol self by other. |
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""" |
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if isinstance(other,Symbol): |
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a=_matchShape([self,other]) |
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return Div_Symbol(a[0],a[1]) |
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else: |
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return self*(1./other) |
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|
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def __rdiv__(self,other): |
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""" |
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Dived other by symbol self. if _testForZero(other) 0 is returned. |
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""" |
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if _testForZero(other): |
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return 0 |
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else: |
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a=_matchShape([self,other]) |
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return Div_Symbol(a[0],a[1]) |
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|
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def __pow__(self,other): |
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""" |
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Raises symbol self to the power of other. |
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""" |
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a=_matchShape([self,other]) |
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return Power_Symbol(a[0],a[1]) |
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|
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def __rpow__(self,other): |
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""" |
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Raises other to the symbol self. |
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""" |
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a=_matchShape([self,other]) |
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return Power_Symbol(a[1],a[0]) |
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|
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def __mul__(self,other): |
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""" |
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Multiplies other by symbol self. if _testForZero(other) 0 is returned. |
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""" |
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if _testForZero(other): |
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return 0 |
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else: |
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a=_matchShape([self,other]) |
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return Mult_Symbol(a[0],a[1]) |
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|
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def __rmul__(self,other): |
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""" |
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Multiplies other by symbol self. if _testSForZero(other) 0 is returned. |
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""" |
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return self*other |
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|
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def __getitem__(self,sl): |
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print sl |
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|
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class Float_Symbol(Symbol): |
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def __init__(self,name="symbol",shape=(),args=[]): |
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Symbol.__init__(self,dim=0,name="symbol",shape=(),args=[]) |
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|
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class ScalarSymbol(Symbol): |
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""" |
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A scalar symbol. |
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""" |
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def __init__(self,dim=3,name="scalar"): |
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""" |
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Creates a scalar symbol of spatial dimension dim. |
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""" |
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if hasattr(dim,"getDim"): |
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d=dim.getDim() |
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else: |
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d=dim |
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Symbol.__init__(self,shape=(),dim=d,name=name) |
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|
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class VectorSymbol(Symbol): |
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""" |
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A vector symbol. |
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""" |
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def __init__(self,dim=3,name="vector"): |
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""" |
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Creates a vector symbol of spatial dimension dim. |
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""" |
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if hasattr(dim,"getDim"): |
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d=dim.getDim() |
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else: |
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d=dim |
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Symbol.__init__(self,shape=(d,),dim=d,name=name) |
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|
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class TensorSymbol(Symbol): |
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""" |
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A tensor symbol. |
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""" |
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def __init__(self,dim=3,name="tensor"): |
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""" |
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Creates a tensor symbol of spatial dimension dim. |
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""" |
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if hasattr(dim,"getDim"): |
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d=dim.getDim() |
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else: |
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d=dim |
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Symbol.__init__(self,shape=(d,d),dim=d,name=name) |
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|
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class Tensor3Symbol(Symbol): |
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""" |
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A tensor order 3 symbol. |
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""" |
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def __init__(self,dim=3,name="tensor3"): |
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""" |
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Creates a tensor order 3 symbol of spatial dimension dim. |
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""" |
| 306 |
if hasattr(dim,"getDim"): |
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d=dim.getDim() |
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else: |
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d=dim |
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Symbol.__init__(self,shape=(d,d,d),dim=d,name=name) |
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|
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class Tensor4Symbol(Symbol): |
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""" |
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A tensor order 4 symbol. |
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""" |
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def __init__(self,dim=3,name="tensor4"): |
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""" |
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Creates a tensor order 4 symbol of spatial dimension dim. |
| 319 |
""" |
| 320 |
if hasattr(dim,"getDim"): |
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d=dim.getDim() |
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else: |
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d=dim |
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Symbol.__init__(self,shape=(d,d,d,d),dim=d,name=name) |
| 325 |
|
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class Add_Symbol(Symbol): |
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""" |
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Symbol representing the sum of two arguments. |
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""" |
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def __init__(self,arg0,arg1): |
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a=[arg0,arg1] |
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Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
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def __str__(self): |
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return "(%s+%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
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def eval(self,argval): |
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a=self.getEvaluatedArguments(argval) |
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return a[0]+a[1] |
| 338 |
def _diff(self,arg): |
| 339 |
a=self.getDifferentiatedArguments(arg) |
| 340 |
return a[0]+a[1] |
| 341 |
|
| 342 |
class Mult_Symbol(Symbol): |
| 343 |
""" |
| 344 |
Symbol representing the product of two arguments. |
| 345 |
""" |
| 346 |
def __init__(self,arg0,arg1): |
| 347 |
a=[arg0,arg1] |
| 348 |
Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
| 349 |
def __str__(self): |
| 350 |
return "(%s*%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 351 |
def eval(self,argval): |
| 352 |
a=self.getEvaluatedArguments(argval) |
| 353 |
return a[0]*a[1] |
| 354 |
def _diff(self,arg): |
| 355 |
a=self.getDifferentiatedArguments(arg) |
| 356 |
return self.getArgument(1)*a[0]+self.getArgument(0)*a[1] |
| 357 |
|
| 358 |
class Div_Symbol(Symbol): |
| 359 |
""" |
| 360 |
Symbol representing the quotient of two arguments. |
| 361 |
""" |
| 362 |
def __init__(self,arg0,arg1): |
| 363 |
a=[arg0,arg1] |
| 364 |
Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
| 365 |
def __str__(self): |
| 366 |
return "(%s/%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 367 |
def eval(self,argval): |
| 368 |
a=self.getEvaluatedArguments(argval) |
| 369 |
return a[0]/a[1] |
| 370 |
def _diff(self,arg): |
| 371 |
a=self.getDifferentiatedArguments(arg) |
| 372 |
return (a[0]*self.getArgument(1)-self.getArgument(0)*a[1])/ \ |
| 373 |
(self.getArgument(1)*self.getArgument(1)) |
| 374 |
|
| 375 |
class Power_Symbol(Symbol): |
| 376 |
""" |
| 377 |
Symbol representing the power of the first argument to the power of the |
| 378 |
second argument. |
| 379 |
""" |
| 380 |
def __init__(self,arg0,arg1): |
| 381 |
a=[arg0,arg1] |
| 382 |
Symbol.__init__(self,dim=_extractDim(a),shape=_extractShape(a),args=a) |
| 383 |
def __str__(self): |
| 384 |
return "(%s**%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 385 |
def eval(self,argval): |
| 386 |
a=self.getEvaluatedArguments(argval) |
| 387 |
return a[0]**a[1] |
| 388 |
def _diff(self,arg): |
| 389 |
a=self.getDifferentiatedArguments(arg) |
| 390 |
return self*(a[1]*log(self.getArgument(0))+self.getArgument(1)/self.getArgument(0)*a[0]) |
| 391 |
|
| 392 |
class Abs_Symbol(Symbol): |
| 393 |
""" |
| 394 |
Symbol representing absolute value of its argument. |
| 395 |
""" |
| 396 |
def __init__(self,arg): |
| 397 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 398 |
def __str__(self): |
| 399 |
return "abs(%s)"%str(self.getArgument(0)) |
| 400 |
def eval(self,argval): |
| 401 |
return abs(self.getEvaluatedArguments(argval)[0]) |
| 402 |
def _diff(self,arg): |
| 403 |
return sign(self.getArgument(0))*self.getDifferentiatedArguments(arg)[0] |
| 404 |
|
| 405 |
#========================================================= |
| 406 |
# some little helpers |
| 407 |
#========================================================= |
| 408 |
def _testForZero(arg): |
| 409 |
""" |
| 410 |
Returns True is arg is considered to be zero. |
| 411 |
""" |
| 412 |
if isinstance(arg,int): |
| 413 |
return not arg>0 |
| 414 |
elif isinstance(arg,float): |
| 415 |
return not arg>0. |
| 416 |
elif isinstance(arg,numarray.NumArray): |
| 417 |
a=abs(arg) |
| 418 |
while isinstance(a,numarray.NumArray): a=numarray.sometrue(a) |
| 419 |
return not a>0 |
| 420 |
else: |
| 421 |
return False |
| 422 |
|
| 423 |
def _extractDim(args): |
| 424 |
dim=None |
| 425 |
for a in args: |
| 426 |
if hasattr(a,"getDim"): |
| 427 |
d=a.getDim() |
| 428 |
if dim==None: |
| 429 |
dim=d |
| 430 |
else: |
| 431 |
if dim!=d: raise ValueError,"inconsistent spatial dimension of arguments" |
| 432 |
if dim==None: |
| 433 |
raise ValueError,"cannot recover spatial dimension" |
| 434 |
return dim |
| 435 |
|
| 436 |
def _identifyShape(arg): |
| 437 |
""" |
| 438 |
Identifies the shape of arg. |
| 439 |
""" |
| 440 |
if hasattr(arg,"getShape"): |
| 441 |
arg_shape=arg.getShape() |
| 442 |
elif hasattr(arg,"shape"): |
| 443 |
s=arg.shape |
| 444 |
if callable(s): |
| 445 |
arg_shape=s() |
| 446 |
else: |
| 447 |
arg_shape=s |
| 448 |
else: |
| 449 |
arg_shape=() |
| 450 |
return arg_shape |
| 451 |
|
| 452 |
def _extractShape(args): |
| 453 |
""" |
| 454 |
Extracts the common shape of the list of arguments args. |
| 455 |
""" |
| 456 |
shape=None |
| 457 |
for a in args: |
| 458 |
a_shape=_identifyShape(a) |
| 459 |
if shape==None: shape=a_shape |
| 460 |
if shape!=a_shape: raise ValueError,"inconsistent shape" |
| 461 |
if shape==None: |
| 462 |
raise ValueError,"cannot recover shape" |
| 463 |
return shape |
| 464 |
|
| 465 |
def _matchShape(args,shape=None): |
| 466 |
""" |
| 467 |
Returns the list of arguments args as object which have all the |
| 468 |
specified shape. |
| 469 |
|
| 470 |
If shape is not given the shape "largest" shape of args is used. |
| 471 |
""" |
| 472 |
# identify the list of shapes: |
| 473 |
arg_shapes=[] |
| 474 |
for a in args: arg_shapes.append(_identifyShape(a)) |
| 475 |
# get the largest shape (currently the longest shape): |
| 476 |
if shape==None: shape=max(arg_shapes) |
| 477 |
|
| 478 |
out=[] |
| 479 |
for i in range(len(args)): |
| 480 |
if shape==arg_shapes[i]: |
| 481 |
out.append(args[i]) |
| 482 |
else: |
| 483 |
if len(shape)==0: # then len(arg_shapes[i])>0 |
| 484 |
raise ValueError,"cannot adopt shape of %s to %s"%(str(args[i]),str(shape)) |
| 485 |
else: |
| 486 |
if len(arg_shapes[i])==0: |
| 487 |
out.append(outer(args[i],numarray.ones(shape))) |
| 488 |
else: |
| 489 |
raise ValueError,"cannot adopt shape of %s to %s"%(str(args[i]),str(shape)) |
| 490 |
return out |
| 491 |
|
| 492 |
class Exp_Symbol(Symbol): |
| 493 |
""" |
| 494 |
Symbol representing the power of the first argument to the power of the |
| 495 |
second argument. |
| 496 |
""" |
| 497 |
def __init__(self,arg): |
| 498 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 499 |
def __str__(self): |
| 500 |
return "exp(%s)"%str(self.getArgument(0)) |
| 501 |
def eval(self,argval): |
| 502 |
return exp(self.getEvaluatedArguments(argval)[0]) |
| 503 |
def _diff(self,arg): |
| 504 |
return self*self.getDifferentiatedArguments(arg)[0] |
| 505 |
|
| 506 |
class Sqrt_Symbol(Symbol): |
| 507 |
""" |
| 508 |
Symbol representing square root of argument. |
| 509 |
""" |
| 510 |
def __init__(self,arg): |
| 511 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 512 |
def __str__(self): |
| 513 |
return "sqrt(%s)"%str(self.getArgument(0)) |
| 514 |
def eval(self,argval): |
| 515 |
return sqrt(self.getEvaluatedArguments(argval)[0]) |
| 516 |
def _diff(self,arg): |
| 517 |
return (-0.5)/self*self.getDifferentiatedArguments(arg)[0] |
| 518 |
|
| 519 |
class Log_Symbol(Symbol): |
| 520 |
""" |
| 521 |
Symbol representing logarithm of the argument. |
| 522 |
""" |
| 523 |
def __init__(self,arg): |
| 524 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 525 |
def __str__(self): |
| 526 |
return "log(%s)"%str(self.getArgument(0)) |
| 527 |
def eval(self,argval): |
| 528 |
return log(self.getEvaluatedArguments(argval)[0]) |
| 529 |
def _diff(self,arg): |
| 530 |
return self.getDifferentiatedArguments(arg)[0]/self.getArgument(0) |
| 531 |
|
| 532 |
class Ln_Symbol(Symbol): |
| 533 |
""" |
| 534 |
Symbol representing natural logarithm of the argument. |
| 535 |
""" |
| 536 |
def __init__(self,arg): |
| 537 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 538 |
def __str__(self): |
| 539 |
return "ln(%s)"%str(self.getArgument(0)) |
| 540 |
def eval(self,argval): |
| 541 |
return ln(self.getEvaluatedArguments(argval)[0]) |
| 542 |
def _diff(self,arg): |
| 543 |
return self.getDifferentiatedArguments(arg)[0]/self.getArgument(0) |
| 544 |
|
| 545 |
class Sin_Symbol(Symbol): |
| 546 |
""" |
| 547 |
Symbol representing sin of the argument. |
| 548 |
""" |
| 549 |
def __init__(self,arg): |
| 550 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 551 |
def __str__(self): |
| 552 |
return "sin(%s)"%str(self.getArgument(0)) |
| 553 |
def eval(self,argval): |
| 554 |
return sin(self.getEvaluatedArguments(argval)[0]) |
| 555 |
def _diff(self,arg): |
| 556 |
return cos(self.getArgument(0))*self.getDifferentiatedArguments(arg)[0] |
| 557 |
|
| 558 |
class Cos_Symbol(Symbol): |
| 559 |
""" |
| 560 |
Symbol representing cos of the argument. |
| 561 |
""" |
| 562 |
def __init__(self,arg): |
| 563 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 564 |
def __str__(self): |
| 565 |
return "cos(%s)"%str(self.getArgument(0)) |
| 566 |
def eval(self,argval): |
| 567 |
return cos(self.getEvaluatedArguments(argval)[0]) |
| 568 |
def _diff(self,arg): |
| 569 |
return -sin(self.getArgument(0))*self.getDifferentiatedArguments(arg)[0] |
| 570 |
|
| 571 |
class Tan_Symbol(Symbol): |
| 572 |
""" |
| 573 |
Symbol representing tan of the argument. |
| 574 |
""" |
| 575 |
def __init__(self,arg): |
| 576 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 577 |
def __str__(self): |
| 578 |
return "tan(%s)"%str(self.getArgument(0)) |
| 579 |
def eval(self,argval): |
| 580 |
return tan(self.getEvaluatedArguments(argval)[0]) |
| 581 |
def _diff(self,arg): |
| 582 |
s=cos(self.getArgument(0)) |
| 583 |
return 1./(s*s)*self.getDifferentiatedArguments(arg)[0] |
| 584 |
|
| 585 |
class Sign_Symbol(Symbol): |
| 586 |
""" |
| 587 |
Symbol representing the sign of the argument. |
| 588 |
""" |
| 589 |
def __init__(self,arg): |
| 590 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 591 |
def __str__(self): |
| 592 |
return "sign(%s)"%str(self.getArgument(0)) |
| 593 |
def eval(self,argval): |
| 594 |
return sign(self.getEvaluatedArguments(argval)[0]) |
| 595 |
|
| 596 |
class Max_Symbol(Symbol): |
| 597 |
""" |
| 598 |
Symbol representing the maximum value of the argument. |
| 599 |
""" |
| 600 |
def __init__(self,arg): |
| 601 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 602 |
def __str__(self): |
| 603 |
return "maxval(%s)"%str(self.getArgument(0)) |
| 604 |
def eval(self,argval): |
| 605 |
return maxval(self.getEvaluatedArguments(argval)[0]) |
| 606 |
|
| 607 |
class Min_Symbol(Symbol): |
| 608 |
""" |
| 609 |
Symbol representing the minimum value of the argument. |
| 610 |
""" |
| 611 |
def __init__(self,arg): |
| 612 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 613 |
def __str__(self): |
| 614 |
return "minval(%s)"%str(self.getArgument(0)) |
| 615 |
def eval(self,argval): |
| 616 |
return minval(self.getEvaluatedArguments(argval)[0]) |
| 617 |
|
| 618 |
class WherePositive_Symbol(Symbol): |
| 619 |
""" |
| 620 |
Symbol representing the wherePositive function. |
| 621 |
""" |
| 622 |
def __init__(self,arg): |
| 623 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 624 |
def __str__(self): |
| 625 |
return "wherePositive(%s)"%str(self.getArgument(0)) |
| 626 |
def eval(self,argval): |
| 627 |
return wherePositive(self.getEvaluatedArguments(argval)[0]) |
| 628 |
|
| 629 |
class WhereNegative_Symbol(Symbol): |
| 630 |
""" |
| 631 |
Symbol representing the whereNegative function. |
| 632 |
""" |
| 633 |
def __init__(self,arg): |
| 634 |
Symbol.__init__(self,shape=arg.getShape(),dim=arg.getDim(),args=[arg]) |
| 635 |
def __str__(self): |
| 636 |
return "whereNegative(%s)"%str(self.getArgument(0)) |
| 637 |
def eval(self,argval): |
| 638 |
return whereNegative(self.getEvaluatedArguments(argval)[0]) |
| 639 |
|
| 640 |
class Outer_Symbol(Symbol): |
| 641 |
""" |
| 642 |
Symbol representing the outer product of its two arguments. |
| 643 |
""" |
| 644 |
def __init__(self,arg0,arg1): |
| 645 |
a=[arg0,arg1] |
| 646 |
s=tuple(list(_identifyShape(arg0))+list(_identifyShape(arg1))) |
| 647 |
Symbol.__init__(self,shape=s,dim=_extractDim(a),args=a) |
| 648 |
def __str__(self): |
| 649 |
return "outer(%s,%s)"%(str(self.getArgument(0)),str(self.getArgument(1))) |
| 650 |
def eval(self,argval): |
| 651 |
a=self.getEvaluatedArguments(argval) |
| 652 |
return outer(a[0],a[1]) |
| 653 |
def _diff(self,arg): |
| 654 |
a=self.getDifferentiatedArguments(arg) |
| 655 |
return outer(a[0],self.getArgument(1))+outer(self.getArgument(0),a[1]) |
| 656 |
|
| 657 |
class Interpolated_Symbol(Symbol): |
| 658 |
""" |
| 659 |
Symbol representing the integral of the argument. |
| 660 |
""" |
| 661 |
def __init__(self,arg,where): |
| 662 |
Symbol.__init__(self,shape=_extractShape(arg),dim=_extractDim([arg]),args=[arg,where]) |
| 663 |
def __str__(self): |
| 664 |
return "interpolated(%s)"%(str(self.getArgument(0))) |
| 665 |
def eval(self,argval): |
| 666 |
a=self.getEvaluatedArguments(argval) |
| 667 |
return integrate(a[0],where=self.getArgument(1)) |
| 668 |
def _diff(self,arg): |
| 669 |
a=self.getDifferentiatedArguments(arg) |
| 670 |
return integrate(a[0],where=self.getArgument(1)) |
| 671 |
|
| 672 |
class Grad_Symbol(Symbol): |
| 673 |
""" |
| 674 |
Symbol representing the gradient of the argument. |
| 675 |
""" |
| 676 |
def __init__(self,arg,where=None): |
| 677 |
d=_extractDim([arg]) |
| 678 |
s=tuple(list(_identifyShape([arg])).append(d)) |
| 679 |
Symbol.__init__(self,shape=s,dim=_extractDim([arg]),args=[arg,where]) |
| 680 |
def __str__(self): |
| 681 |
return "grad(%s)"%(str(self.getArgument(0))) |
| 682 |
def eval(self,argval): |
| 683 |
a=self.getEvaluatedArguments(argval) |
| 684 |
return grad(a[0],where=self.getArgument(1)) |
| 685 |
def _diff(self,arg): |
| 686 |
a=self.getDifferentiatedArguments(arg) |
| 687 |
return grad(a[0],where=self.getArgument(1)) |
| 688 |
|
| 689 |
class Integral_Symbol(Float_Symbol): |
| 690 |
""" |
| 691 |
Symbol representing the integral of the argument. |
| 692 |
""" |
| 693 |
def __init__(self,arg,where=None): |
| 694 |
Float_Symbol.__init__(self,shape=_identifyShape([arg]),args=[arg,where]) |
| 695 |
def __str__(self): |
| 696 |
return "integral(%s)"%(str(self.getArgument(0))) |
| 697 |
def eval(self,argval): |
| 698 |
a=self.getEvaluatedArguments(argval) |
| 699 |
return integrate(a[0],where=self.getArgument(1)) |
| 700 |
def _diff(self,arg): |
| 701 |
a=self.getDifferentiatedArguments(arg) |
| 702 |
return integrate(a[0],where=self.getArgument(1)) |
| 703 |
|
| 704 |
# ============================================ |
| 705 |
# testing |
| 706 |
# ============================================ |
| 707 |
|
| 708 |
if __name__=="__main__": |
| 709 |
u=ScalarSymbol(dim=2,name="u") |
| 710 |
v=ScalarSymbol(dim=2,name="v") |
| 711 |
v=VectorSymbol(2,"v") |
| 712 |
u=VectorSymbol(2,"u") |
| 713 |
|
| 714 |
print u+5,(u+5).diff(u) |
| 715 |
print 5+u,(5+u).diff(u) |
| 716 |
print u+v,(u+v).diff(u) |
| 717 |
print v+u,(v+u).diff(u) |
| 718 |
|
| 719 |
print u*5,(u*5).diff(u) |
| 720 |
print 5*u,(5*u).diff(u) |
| 721 |
print u*v,(u*v).diff(u) |
| 722 |
print v*u,(v*u).diff(u) |
| 723 |
|
| 724 |
print u-5,(u-5).diff(u) |
| 725 |
print 5-u,(5-u).diff(u) |
| 726 |
print u-v,(u-v).diff(u) |
| 727 |
print v-u,(v-u).diff(u) |
| 728 |
|
| 729 |
print u/5,(u/5).diff(u) |
| 730 |
print 5/u,(5/u).diff(u) |
| 731 |
print u/v,(u/v).diff(u) |
| 732 |
print v/u,(v/u).diff(u) |
| 733 |
|
| 734 |
print u**5,(u**5).diff(u) |
| 735 |
print 5**u,(5**u).diff(u) |
| 736 |
print u**v,(u**v).diff(u) |
| 737 |
print v**u,(v**u).diff(u) |
| 738 |
|
| 739 |
print exp(u),exp(u).diff(u) |
| 740 |
print sqrt(u),sqrt(u).diff(u) |
| 741 |
print log(u),log(u).diff(u) |
| 742 |
print sin(u),sin(u).diff(u) |
| 743 |
print cos(u),cos(u).diff(u) |
| 744 |
print tan(u),tan(u).diff(u) |
| 745 |
print sign(u),sign(u).diff(u) |
| 746 |
print abs(u),abs(u).diff(u) |
| 747 |
print wherePositive(u),wherePositive(u).diff(u) |
| 748 |
print whereNegative(u),whereNegative(u).diff(u) |
| 749 |
print maxval(u),maxval(u).diff(u) |
| 750 |
print minval(u),minval(u).diff(u) |
| 751 |
|
| 752 |
g=grad(u) |
| 753 |
print diff(5*g,g) |
| 754 |
4*(g+transpose(g))/2+6*trace(g)*kronecker(3) |
| 755 |
|
| 756 |
# |
| 757 |
# $Log$ |
| 758 |
# Revision 1.2 2005/09/15 03:44:19 jgs |
| 759 |
# Merge of development branch dev-02 back to main trunk on 2005-09-15 |
| 760 |
# |
| 761 |
# Revision 1.1.2.1 2005/09/07 10:32:05 gross |
| 762 |
# Symbols removed from util and put into symmbols.py. |
| 763 |
# |
| 764 |
# |
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