Re: [eigen] banded matrices in Eigen

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

Hi Andreas,

yes, this SpecialMatrix page is pretty old now. Regarding band
storage, our goal is to support general band matrices as currently
supported by BandMatrix (arbitrary fixed or dynamic number of
sub/super diagonals, triangular, selfadjoint). As explain in the
previous email, the matrix operations and factorizations are still
missing though. More specific structures, like a symmetry wrt the
anti-antidiagonal, are not planed because they are too specific and
they unlikely offer real computational advantage beside a potentially
more compact storage.

gael


On Wed, Feb 6, 2013 at 4:50 PM, Andreas Keil <keil.andreas@xxxxxxxxx> wrote:
> On 2013-01-30 21:24, Deaglan O Halligan wrote:
>>
>> Hi,
>>
>> I'm a grad student working on Trilinos, a collection of algorithms for
>> large-scale scientific computation from Sandia Labs, and a related fluid
>> dynamics application code called Tramonto. We're implementing algorithms
>> that use David Bailey's qdlib data types, and this work led us to look at
>> Eigen for doing a few necessary dense computations. I'm currently working on
>> adding some Eigen code to Trilinos as a third-party-library (TPL).
>>
>> So far I've added Eigen's householderQR and PartialPivLU to Trilinos. I'm
>> also interested in adding the symmetric eigensolver and a banded LU
>> factorization. I tried using Eigen's unsupported Skyline module but ran into
>> problems, and I'm not sure what the status of that module is. I then
>> realized that there is a BandMatrix class that uses the banded storage
>> format, and there's been some mention on forum threads about more
>> functionality being added for the BandMatrix class. It seems like the
>> BandMatrix class is where future development will go on and I should ignore
>> the Skyline module? I'm very interested in knowing what the status of
>> BandMatrix is and how I can help with further development (in particular
>> implementing LU and products) if that's needed.
>>
>> Thanks,
>> Deaglan Halligan
>>
>
> Hi list,
>
> In a similar vein, I am very interested in multi-diagonal matrices and found
> this page which seems a little outdated:
> http://eigen.tuxfamily.org/index.php?title=SpecialMatrix
>
> More specifically, I would like to use a multi-diagonal matrix (one which
> only has entries in the diagonals numbered -C, -B, -A, 0, A, B, C with A, B,
> C > 0). And even more specifically, my matrices would be Laplacian-like,
> i.e. symmetric.
>
> Is there any way to represent such a matrix efficiently (by only storing the
> coefficients and the sub-/super-diagonal numbers) and to perform
> matrix-vector-products in a parallelized way? (A class with an interface
> similar to the matrix expression Eigen::Diagonal would go in this direction,
> I guess.)
>
> Thanks for any input,
> Andreas.
>
>