[petsc-users] [Ext] Re: Question on SLEPc + computing SVD with a "matrix free" matrix

[Dave May]

On Thu 25. Jun 2020 at 08:23, Ernesto Prudencio via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Thank you, Jose.
>
> However, in the case of a "matrix free" matrix, the APIs on PETSc seem to
> allow just the implementation of A.v, not of A' . w
>
> One could create another "matrix free" matrix B which could make the role
> of computing z = B . w = A' . w. But how could one force the routine
> MatMultTranspose(A, w, z) to call the routine for B? Here I am assuming
> that MatMultTranspose(A, w, z) is the routine that SLEPc calls internally
> in its algorithms when the user sets for implicit transpose.
>
> I see two possibilities (for brain storming, since I don't know if such
> approaches would be acceptable for the PETSc team and/or the SLEPc team):
> 1) PETSc could add an entry for a second routine that computes [ A' . w ]
> when calling MatMFFDSetFunction()
>

MatMFFD is designed for providing the action of the jacobian associated
with a nonlinear problem F(x)=0. It uses F to provide a finite difference
approx of the action J w. It does not support actions J’ w.

You will need to create a MatShell and supply the methods for MatMult and
MatMultTranspose (as Jose suggested).

Thanks
Dave



2) SLEPc could add an entry for the routine for computing [ A' . w ] when
> the matrix A is "matrix free"
>
> Thanks again,
>
> Ernesto.
>
>
> Schlumberger-Private
>
> -----Original Message-----
> From: Jose E. Roman [mailto:jroman at dsic.upv.es]
> Sent: Thursday, June 25, 2020 1:01 AM
> To: Ernesto Prudencio <EPrudencio at slb.com>
> Cc: petsc-users at mcs.anl.gov
> Subject: [Ext] Re: [petsc-users] Question on SLEPc + computing SVD with a
> "matrix free" matrix
>
> Yes, you have to set it with SVDSetImplicitTranspose(), but then the
> matrix-free matrix should implement both "A.v" and "A'.v" operations.
> Jose
>
>
> > El 24 jun 2020, a las 23:25, Ernesto Prudencio via petsc-users <
> petsc-users at mcs.anl.gov> escribió:
> >
> > Hi,
> >
> > Is it possible to compute a SVD for a “matrix free” matrix?
> >
> > At first, it seems it would be ok with a MatCreateMFFD() and
> MatMFFDSetFunction(), because one could then provide the routine that
> computes “A . v” for any given v, which is an operation needed by SLEPc.
> However, one would also need to set up the SVD object in SLEPc with an
> implicit transpose. Would that be possible?
> >
> > Thanks in advance,
> >
> > Ernesto.
> >
> > Schlumberger-Private
>
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