[Trilinos-Users] EpetraExt MatrixMatrix
Erik Boman
egboman at sandia.gov
Wed Jun 2 09:35:48 MDT 2010
Kevin and Vicki,
I've done this before to form a Schur complement explicitly.
I used the LeftScale method in Epetra to form C1=D*B. This helps, but is
not a great solution since I then needed to store the scaled copy of B.
I don't know if anybody has implemented a more efficient solution.
Erik
On Tue, 2010-06-01 at 17:23 -0600, Kevin Long wrote:
> Hi,
>
> Vicki Howle and I have encountered a problem for which we want to compute
> explicitly (as an Epetra_CrsMatrix) the product B^T D B, where D is a
> diagonal matrix. We have B as an Epetra_CrsMatrix and diag(D) as an
> Epetra_Vector.
>
> We can do this easily enough by making an Epetra_CrsMatrix representation of
> D, then calling EpetraExt::MatrixMatrix::Multiply() twice, first to form
> C1=D*B, then again to form C= B^T C1. The second call can use
> transposeA=true so we don't need to form B^T.
>
> Alternatively, I could form C1=sqrt(D) B, then do C1^T C1. Again, not hard to
> write.
>
> However, neither approach takes advantage of the fact that D is diagonal,
> which means (a) I need to construct a whole Epetra_CrsMatrix for something
> that can really just be stored as a vector, and (b) inside
> MatrixMatrix::Multiply(), I'm doing needless work to find the graph of the
> product D B when I already know that D B and B will have the same graph.
>
> The operation B^T D B is a fairly common; any chance that someone will extend
> MatrixMatrix to provide an optimized multiply for that case? Or better yet,
> has anyone already written such code?
>
> Thanks,
>
> Kevin
>
>
>
>
>
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