Re: [eigen] banded matrices in Eigen

[何震邦 <jdh8@xxxxxxxxxxxxxx>]

在 2013 二月 6 週三 16:50:48，Andreas Keil 寫道:
> 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 found this page which seems a little outdated: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.

Hi,

Maybe we can implement new methods from blas/BandTriangularSolver.h.

Thanks,
Chen-Pang He.