Re: [eigen] [PATCH] Toeplitz matrix specialization

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

2009/1/29 Mauro Iazzi <mauro.iazzi@xxxxxxxxx>:
> Hi, I'm still thinking about that...
> Is there any new idea on how to handle this problem?
>
> On a side note, wouldn't it be nice if sparse matrices were in the same class?

Yes we had a quick discussion over IRC yesterday, and yes we evocated
the idea that these special matrices were often sparse and then they
should be designed with interaction also with Sparse in mind.

Here's the log:

[mer. janv. 28 2009] [18:23:03] <ggael> I'm thinking about the
SpecialMatrix mess with Special in {Diagonal, Tridigonal, Toeplitz,
Band}x{Normal,SelfAdjoint}.....
[mer. janv. 28 2009] [18:23:32] <bjacob> good that you're thinking
about that in such generality
[mer. janv. 28 2009] [18:23:35] <ggael> and I don't have an elegent
solution yet :(
[mer. janv. 28 2009] [18:24:24] <bjacob> i still am tempted by the
brutal solution of giving up having these as MatrixBase expressions...
[mer. janv. 28 2009] [18:25:14] <bjacob> they are as special as
SparseMatrix (many of them are actually sparse matrices)
[mer. janv. 28 2009] [18:25:28] <ggael> the main problem is the
explosion of combination.... (unless we give up about perf and keep
branching inside coeff())
[mer. janv. 28 2009] [18:26:04] <bjacob> that only is a problem if you
want to allow all sorts of operations seamlessly on these matrices
[mer. janv. 28 2009] [18:27:12] <bjacob> the problem goes away if we
only support these matrices as stupid containers for communicating
with algorithms (we'd still allow operator= on them to copy into a
MatrixBase, but that's all)
[mer. janv. 28 2009] [18:27:37] <bjacob> e.g. tridiagonalization would
return a TridiagonalMatrix that's just a struct with a few vectors
[mer. janv. 28 2009] [18:27:47] <bjacob> then you could do MatrixXd m = tridiag;
[mer. janv. 28 2009] [18:27:49] <ggael> yes, for Toeplitz this would make sense
[mer. janv. 28 2009] [18:28:49] <bjacob> i don't think there's much of
a use case for e.g. multiplying a tridiagonal matrix by a diagonal
matrix
[mer. janv. 28 2009] [18:29:05] <bjacob> so we only need to let each
special mat type interoperate with MatrixBase
[mer. janv. 28 2009] [18:29:16] <bjacob> but we don't need to let them
interoperate with each other
[mer. janv. 28 2009] [18:29:28] <bjacob> so O(n) stuff not O(n^2)
[mer. janv. 28 2009] [18:30:51] <ggael> ok, then that would be doable
without too much work
[mer. janv. 28 2009] [18:31:13] <bjacob> yep
[mer. janv. 28 2009] [18:31:50] <bjacob> something just occured to me
[mer. janv. 28 2009] [18:31:51] <ggael> also Toeplitz => special
module, too specific !
[mer. janv. 28 2009] [18:32:18] <bjacob> these special matrices would
be actually not closer to MatrixBase than SparseMatrixBase
[mer. janv. 28 2009] [18:32:43] <bjacob> we should probably right away
think of letting them be useful also for Sparse
[mer. janv. 28 2009] [18:33:58] <ggael> yes of course
[mer. janv. 28 2009] [18:34:31] <bjacob> i hope that what i just said
doesn't contradict your latest big commit (haven't looked yet)
[mer. janv. 28 2009] [18:36:27] <ggael> no, what my commit mainly did
is to add: DiagonalMatrix<Scalar,Size>, it currently inherits
MatrixBase but that can be changed later
[mer. janv. 28 2009] [18:37:14] <bjacob> ok