Glas List: Re: [glas] Skalar-Like concepts from GLAS and MTL

From: Peter Gottschling (pgottsch_at_[hidden])
Date: 2005-05-23 18:03:52

Hello Karl and Toon:

On May 23, 2005, at 4:20 PM, Toon Knapen wrote:

> Karl Meerbergen wrote:
>> Hello Peter,
>> * Perhaps it would be better not to talk about functors in the 
>> concepts. What we need in a Magma is some function op(x,y). This is a 
>> free function that can be implemented using a functor, but does not 
>> have to.
>
>
> But what 'op' actually is must be kept abstract. The actual name does 
> not matter. The 'op' is just of a type 'Op'. And Op is the type of a 
> function that takes 2 arguments (like in 'T (*Op)(const T&, const 
> T&)')
>
I just realized that there are different interpretations of the term 
functor. Stroustrup defines it in his book in section 18.4 as an object 
of a class with an application operator. I prefer the definition in the 
STL, which includes free functions as pointers 
(http://www.sgi.com/tech/stl/functors.html). So, we should make it 
clear that we use functor in its more general meaning.
>
>> * I would call the corresponding Group concept, OpGroup, because it 
>> has a function op. The mathematical concept group is not exactly a 
>> C++ concept and there are various ways to define those. AdditiveGroup 
>> is not an OpGroup (because it does not have a member op), but an 
>> addaptor can be created that maps it into an OpGroup.
>
>
 From my perspective, there is no essential difference between the 
mathematical definition of group and the concept, it is only 
syntactical not semantical.
>
> As I mention above. 'op' is just a function of type 'Op'. For the 
> additive-group this 'op' is just called 'plus' which is a function 
> that relies on the operator+.
>
>
>
>> * I am thinking one step ahead now: our goal is not develop software 
>> for scalar operations but for vector and matrix classes. From an 
>> OpGroup for scalars, an OpGroup for a vector can be created. The same 
>> free function op() can be used for op()'s on vectors. With the 
>> functors this is much more difficult.
>> * For an  OpRing, we need op1() and op2() ?
>
>
> This kind of 'making abstraction of what actually the two operators of 
> the Ring do' only serves in algorithms where we actually want to make 
> abstraction of the operation being performed. For instance an 
> algorithm like the multiplyAndSquare in section 5.3 of Peter's paper 
> (although the 'multiply' in the name of the function is maybe not a 
> good choise because it's up to the operator being passed what the 
> operator will actually do). In the case we want the algorithm makes 
> abstraction of actually what the operator does, we can indeed pas a 
> function/functor.
>
> I think it would be instructive to ask us the very practical 
> questions: how do we allow a matrix-matrix multiply and an 
> elemtwise-matrix multiply without clearly penalising one over the 
> other. This is a practical problem where we want to map both 
> operations to the operator* so how do we practically solve that. Or 
> same with the norm-function. Which norm (1-norm,2-norm,...) do we map 
> to the function called norm?
>
> _______________________________________________
> glas mailing list
> glas_at_[hidden]
> http://lists.boost.org/mailman/listinfo.cgi/glas
>
------------
Peter Gottschling
Research Associate
Open Systems Laboratory
Indiana University
215 Lindley Hall
Bloomington, IN 47405
Tel.: [phone]   Fax: [phone]
http://www.osl.iu.edu/~pgottsch