Re: [boost] Re: Standard Matrix interfaces

From: Tony Kirke (tkirke_at_[hidden])
Date: 2001-08-22 17:20:25

 Do we need to wait for MTL-3 or can we kickstart some kind of interface
definition first?
How do we proceed from here? (I'm a newcomer to this group/effort).
Thanks
Tony

> ----- Original Message -----
> From: "David Abrahams" <david.abrahams_at_[hidden]>
> To: <boost_at_[hidden]>
> Sent: Wednesday, August 22, 2001 8:48 AM
> Subject: Re: [boost] Re: Standard Matrix interfaces
>
>
> >
> > ----- Original Message -----
> > From: "Jeremy Siek" <jsiek_at_[hidden]>
> >
> >
> > > On Wed, 22 Aug 2001, David Abrahams wrote:
> > > david.>
> > > david.> > In libs/numberic/doc you will find
LinearAlgebraConcepts.html
> > which
> > > david.> > describes the high-level concepts for linear algebra
> operations.
> > > david.>
> > > david.> One thing I think is missing from this document is
> > > david.> InvertibleLinearOperator. Do you agree, or did you imagine
> > > david.> the role of that concept being filled in some other way?
> > >
> > > Hmm, I've always thought of creating an inverse as something an
> algorithm,
> > > or collection of algorithms, would do. That it would not just be a
> single
> > > "operation" that could be described in a concept. However, if we could
> fit
> > > taking an inverse into a nice interface that fits as an "operation"
> > > without sacrificing performance, that would be nice, so I'm open to
that
> > > approach.
> >
> > I agree that it's a design question. Here's the scenario I'm describing
in
> > more detail:
> >
> > A matrix is not a linear operator by itself; it's more of a container.
> > You could make any of several linear operators from a given matrix, e.g.
> by
> > sticking the matrix in a wrapper.
> > In particular, if the matrix describes a linear operator with an exact
> > inverse, you could make an InvertibleLinearOperator whose inverse_type
> > contains the matrix's LU factorization and uses the usual
> forward/backsolve
> > internally when the inverse is applied to a vector. Note that the
inverse
> is
> > NOT the inverse of the matrix (you can't efficiently index its
elements),
> > but it /is/ the inverse of the LinearOperator described by the matrix.
> Even
> > if the matrix is singular, you may be able to make an
> > ApproximatelyInvertibleLinearOperator (or something shorter ;0) from it,
> > whose inverse uses, say, GMRES when it is applied to a vector.
> >
> > I guess what I'm trying to emphasize here is that the factorization of a
> > matrix is useful as a LinearOperator but is not, by itself, a matrix in
> the
> > usual sense.
> >
> > > david.> I'd like to work with you on that (but perhaps after the
> > > david.> tmpw01 paper is polished ;-)).
> > >
> > > Yeah, I'm going to be a busy little bee. I've also got the final draft
> of
> > > the BGL book due on the 27th!
> >
> > Likewise, I'm sure!
> >
> > -Dave
> >
> >
> > Info: http://www.boost.org  Unsubscribe:
> <mailto:boost-unsubscribe_at_[hidden]>
> >
> > Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
> >
> >
>