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

[Nicolas Pozin]

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).
> >> 
> 
>