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Ublas : |
From: Andrew Rieck (arieck_at_[hidden])
Date: 2005-07-11 20:14:13
The following:
#include <boost/enable_if.hpp>
would provide a very clean solution for selecting specializations based on
group/ring/field/etc properties.
In this case the above library relies on the SFINAE principle.
Kind regards,
Andrew
ublas-bounces_at_[hidden] wrote on 12/07/2005 09:29:46 AM:
> > The use of "abs" etc. in traits class may be worth, if you decide to
> > enable "contexts" in calls to ublas:
> >
> > May be this example is too "corner case" , but anyway :) .
> > Suppose that I have a "scalar" class C , which is internally
isomorphic
> > to 2x2 matrix.
>
> Your example reminds me of a few points I have raised before, which
> I re-state
> in a different context. If your C class is isomorphic to a 2x2 matrix,
let's
> make it a little more concrete and consider a 2x2 matrix of double.
>
> You want to use C as a scalar class with uBLAS. It would not be safe to
do
> this if:
> 1) uBLAS assumed that every non-zero element of class C has a
multiplicative
> inverse. See http://mathworld.wolfram.com/DivisionAlgebra.html
>
> Your class C would have to cope with elements of C which do not have an
> inverse. Maybe it would return a NaN result, or throw an exception when
asked
> for 1/c, where c is in C and c has no inverse. Then uBLAS would have to
cope
> with NaN (or an exception) as a result of 1/c.
>
> 2) uBLAS assumed that multiplication is commutative.
> See http://mathworld.wolfram.com/CommutativeRing.html
>
> If you hand uBLAS two scalars, a and b of type C, where a*b != b*a, then
you
> would want to be sure that there are no places in uBLAS which assume
that
> a*b == b*a.
>
> Then again, maybe either or both of these assumptions allow some
significant
> optimization somewhere in uBLAS. In this case, you would want uBLAS to
> provide some sort of ring_traits, such as is_division_ring<T>,
> is_commutative_ring<T>. Then uBLAS would be able to have different code
for
> the different cases, allowing both correct operation and optimization
where
> possible.
>
> The same ideas apply to the other field and ring axioms, although I
would
> personally draw the line at addition. AFAICT, it is reasonable to assume
that
> any scalar class K used with addition in uBLAS would be such that K
models an
> Abelian group under addition (possibly subject to IEEE arithmetic and
> rounding error).
>
> Maybe the best idea would be to assume that any scalar class K which is
used
> with the algebraic operations of uBLAS would be such that K models a
ring,
> and then supply ring_traits to cover the extra axioms between ring and
field.
> See http://mathworld.wolfram.com/Ring.html
> http://mathworld.wolfram.com/Field.html
> http://mathworld.wolfram.com/FieldAxioms.html
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