[Trilinos-Users] EpetraExt MatrixMatrix

[Heroux, Michael A]

Kevin,

We (read summer intern) are developing a new Matrix-Matrix capability using
templates for support of Tpetra.  I will mention this Kurtis Nusbaum (the
intern).  There are no plans, AFAIK, to modify the existing Epetra versions.

I think the best we can do at this point is to form D1 = sqrt(D) (O(n) cost)
as you suggest, then explicitly scale B using the LeftScale() method (O(nz)
cost), the use the existing Matrix-Matrix multiply kernel.

Kurtis is on this list, so he is now aware.

Mike


On 6/1/10 6:23 PM, "Kevin Long" <kevin.long at ttu.edu> 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
> 
> 
> 
>