[Trilinos-Users] Concerning Matrix-Matrix product
Riccardo Rossi
rrossi at cimne.upc.edu
Wed Jun 2 12:26:46 MDT 2010
Hi all,
concerning the thread on Mat-Mat products, i also use
D * Minv * G
where Minv is diag and D has the "structure" of the transpose of G but
is not necessarily its transpose...
if in making the optimized product you may it sufficiently flexible to
take in account this case i would be very grateful
thank you
Riccardo
-
________________________________________________________________
Riccardo Rossi, Ph.D, Civil Engineer
member of the Kratos Group: kratos.cimne.upc.es
Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE)
Universidad Politécnica de Cataluña (UPC)
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On Wed, 2010-06-02 at 12:00 -0600,
trilinos-users-request at software.sandia.gov wrote:
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> Today's Topics:
>
> 1. EpetraExt MatrixMatrix (Kevin Long)
> 2. Re: EpetraExt MatrixMatrix (Heroux, Michael A)
> 3. Re: EpetraExt MatrixMatrix (Erik Boman)
> 4. Re: EpetraExt MatrixMatrix (Kurtis Nusbaum)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Tue, 1 Jun 2010 18:23:29 -0500
> From: "Kevin Long" <kevin.long at ttu.edu>
> Subject: [Trilinos-Users] EpetraExt MatrixMatrix
> To: "trilinos-users at software.sandia.gov"
> <trilinos-users at software.sandia.gov>, "Victoria Howle"
> <victoria.howle at ttu.edu>
> Message-ID: <201006011823.29336.kevin.long at ttu.edu>
> Content-Type: text/plain; charset=utf-8
>
>
> 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
>
>
>
>
>
> --
> ------------------------------------------------------
> Kevin Long
> Associate Professor
> Department of Mathematics and Statistics
> Texas Tech University
> Lubbock, TX
>
> "The end of fear is the beginning of wisdom"
> -- Bertrand Russell
> ------------------------------------------------------
>
>
>
> ------------------------------
>
> Message: 2
> Date: Wed, 2 Jun 2010 09:29:13 -0600
> From: "Heroux, Michael A" <maherou at sandia.gov>
> Subject: Re: [Trilinos-Users] EpetraExt MatrixMatrix
> To: Kevin Long <kevin.long at ttu.edu>,
> "trilinos-users at software.sandia.gov"
> <trilinos-users at software.sandia.gov>, Vicki Howle
> <victoria.howle at ttu.edu>
> Message-ID: <C82BE2F9.25C00%maherou at sandia.gov>
> Content-Type: text/plain; charset="us-ascii"
>
> 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
> >
> >
> >
> >
>
>
>
>
> ------------------------------
>
> Message: 3
> Date: Wed, 02 Jun 2010 09:35:48 -0600
> From: Erik Boman <egboman at sandia.gov>
> Subject: Re: [Trilinos-Users] EpetraExt MatrixMatrix
> To: Kevin Long <kevin.long at ttu.edu>
> Cc: Victoria Howle <victoria.howle at ttu.edu>,
> "trilinos-users at software.sandia.gov"
> <trilinos-users at software.sandia.gov>
> Message-ID: <1275492948.15283.124.camel at octopi.sandia.gov>
> Content-Type: text/plain
>
> 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
> >
> >
> >
> >
> >
>
>
>
> ------------------------------
>
> Message: 4
> Date: Wed, 2 Jun 2010 10:34:41 -0600
> From: "Kurtis Nusbaum" <klnusbaum at gmail.com>
> Subject: Re: [Trilinos-Users] EpetraExt MatrixMatrix
> To: "Heroux, Michael A" <maherou at sandia.gov>
> Cc: Kevin Long <kevin.long at ttu.edu>, Vicki Howle
> <victoria.howle at ttu.edu>, "trilinos-users at software.sandia.gov"
> <trilinos-users at software.sandia.gov>
> Message-ID:
> <AANLkTin4VCdQkAp1TBf7Hh9BhbPGU74FKkwxL6aYtzj1 at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Kevin,
> I'm currently in the preliminary stages of implementing the Mat-Mat multiply
> kernel in Tpetra. Right now I'm just trying to a get a basic, general
> Mat-Mat kernel working. Once I've got that working, I plan on starting to
> implement optimizations for specific cases. I've added this to my list of
> specific cases that I'm going to take a look at. I'll make it the first
> optimization I look at since it's the only one that's been explicitly
> requested thus far. I'll also try to keep you updated.
>
> -Kurtis
>
> On Wed, Jun 2, 2010 at 9:29 AM, Heroux, Michael A <maherou at sandia.gov>wrote:
>
> > 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
> > >
> > >
> > >
> > >
> >
> >
> > _______________________________________________
> > Trilinos-Users mailing list
> > Trilinos-Users at software.sandia.gov
> > http://software.sandia.gov/mailman/listinfo/trilinos-users
> >
> >
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