# [petsc-users] forming a matrix from a set of vectors

Nicolas Pozin nicolas.pozin at inria.fr
Wed Aug 26 16:01:29 CDT 2015

```Yes, this is sequentially and yes again, d is stored as a AIJ matrix

----- Mail original -----
> De: "Barry Smith" <bsmith at mcs.anl.gov>
> À: "Nicolas Pozin" <nicolas.pozin at inria.fr>
> Cc: "Jed Brown" <jed at jedbrown.org>, petsc-users at mcs.anl.gov
> Envoyé: Mercredi 26 Août 2015 22:58:12
> Objet: Re: [petsc-users] forming a matrix from a set of vectors
>
>
>    Since A is tiny I am assuming you are doing this sequentially only?
>
>    Do you have d stored as a AIJ matrix or is transpose(d) stored as a AIJ
>    matrix?
>
>
>
>
> > On Aug 26, 2015, at 3:41 PM, Nicolas Pozin <nicolas.pozin at inria.fr> wrote:
> >
> > Actually I want to get the diagonal of the matrix : transpose(d)*A*d where
> > -d is a sparse matrix of size (n1,m1)
> > -A is a dense symetric matrix of size size (n1,n1)
> > with m1 very big compared to n1 (1 million against a few dozens).
> >
> > The problem is too big to allow the use of MatMatMult.
> > What I planned to do :
> > -compute the vectors Vi defined by transpose(d)*Ai where Ai is the i-th
> > column of A : quick since d is sparse and n1 is small
> > -deduce the matrix transpose(d)*A = [V1 ... Vn]
> > and then get the diagonal of transpose(d)*transpose([V1 ...Vn]) through
> > -transpose([V1 ...Vn]) and get its columns C1 ... Cn
> > -conclude on the i-th diagonal value which is the i-th component of
> > tranpose(d)*Ci
> >
> >
> >
> > ----- Mail original -----
> >> De: "Barry Smith" <bsmith at mcs.anl.gov>
> >> À: "Nicolas Pozin" <nicolas.pozin at inria.fr>
> >> Cc: "Jed Brown" <jed at jedbrown.org>, petsc-users at mcs.anl.gov
> >> Envoyé: Mercredi 26 Août 2015 22:21:04
> >> Objet: Re: [petsc-users] forming a matrix from a set of vectors
> >>
> >>
> >>> On Aug 26, 2015, at 3:06 PM, Nicolas Pozin <nicolas.pozin at inria.fr>
> >>> wrote:
> >>>
> >>> Thank you for this answer.
> >>>
> >>> What I want to do is to get the lines of this matrix and store them in
> >>> vectors.
> >>
> >>  If you want to treat the columns of the dense matrix as vectors then use
> >>  MatDenseGetArray() and call VecCreateMPIWithArray() with a pointer to the
> >>  first row of each column of the obtained array (PETSc dense matrices are
> >>  stored by column; same as for example LAPACK).
> >>
> >>  But if you explained more why you want to treat something sometimes as a
> >>  Mat (which is a linear operator on vectors) and sometimes as vectors we
> >>  might be able to suggest how to organize your code.
> >>
> >>   Barry
> >>
> >>>
> >>>
> >>> ----- Mail original -----
> >>>> De: "Jed Brown" <jed at jedbrown.org>
> >>>> À: "Nicolas Pozin" <nicolas.pozin at inria.fr>, petsc-users at mcs.anl.gov
> >>>> Envoyé: Mercredi 26 Août 2015 20:38:37
> >>>> Objet: Re: [petsc-users]  forming a matrix from a set of vectors
> >>>>
> >>>> Nicolas Pozin <nicolas.pozin at inria.fr> writes:
> >>>>> Given a set of vectors V1, V2,...,Vn, is there an efficient way to form
> >>>>> the
> >>>>> dense matrix [V1 V2 ... Vn]?
> >>>>
> >>>> What do you want to do with that matrix?  The vector representation is
> >>>> pretty flexible and the memory semantics are similar unless you store
> >>>> the dense matrix row-aligned (not the default).
> >>>>
> >>
> >>
>
>
```