[petsc-users] Preconditioner for LSQR

[Jose E. Roman]

> El 1 mar 2022, a las 18:06, Lucas Banting <bantingl at myumanitoba.ca> escribió:
> 
> Thanks everyone, QR makes the most sense for my application. 
> 
> Jose, 
> Once I get R from BVOrthogonalize, how I should I solve the upper triangular system?
> Is the returned Mat R setup to be used in MatBackwardSolve?

MatBackwardSolve() would be the operation to use, but unfortunately it seems to be implemented only for SBAIJ matrices, not for dense matrices.

You will have to get the array with MatDenseGetArray()/MatDenseRestoreArray() and then call BLAStrsm_

The KSP/PC interface is more convenient.

Jose


> 
> Pierre, 
> I can reuse A for many iterations, but I cannot do a matmatsolve as I need the resulting solution to produce the next right hand side vector.
> 
> Thanks again,
> Lucas
> From: Jose E. Roman <jroman at dsic.upv.es>
> Sent: Tuesday, March 1, 2022 4:49 AM
> To: Pierre Jolivet <pierre at joliv.et>
> Cc: Lucas Banting <bantingl at myumanitoba.ca>; petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> Subject: Re: [petsc-users] Preconditioner for LSQR
>  
> Caution: This message was sent from outside the University of Manitoba.
> 
> 
> To use SLEPc's TSQR one would do something like this:
> 
>   ierr = BVCreateFromMat(A,&X);CHKERRQ(ierr);
>   ierr = BVSetFromOptions(X);CHKERRQ(ierr);
>   ierr = BVSetOrthogonalization(X,BV_ORTHOG_CGS,BV_ORTHOG_REFINE_IFNEEDED,PETSC_DEFAULT,BV_ORTHOG_BLOCK_TSQR);CHKERRQ(ierr);
>   ierr = BVOrthogonalize(X,R);CHKERRQ(ierr);
> 
> But then one would have to use BVDotVec() to obtain Q'*b and finally solve a triangular system with R.
> Jose
> 
> > El 1 mar 2022, a las 8:36, Pierre Jolivet <pierre at joliv.et> escribió:
> >
> > Hello Lucas,
> > In your sequence of systems, is A changing?
> > Are all right-hand sides available from the get-go?
> > In that case, you can solve everything in a block fashion and that’s how you could get real improvements.
> > Also, instead of PCCHOLESKY on A^T * A + KSPCG, you could use PCQR on A + KSPPREONLY, but this may not be needed, cf. Jed’s answer.
> >
> > Thanks,
> > Pierre
> >
> >> On 1 Mar 2022, at 12:54 AM, Lucas Banting <bantingl at myumanitoba.ca> wrote:
> >>
> >> Hello,
> >>
> >> I have an MPIDENSE matrix of size about 200,000 x 200, using KSPLSQR on my machine a solution takes about 15 s. I typically run with six to eight processors.
> >> I have to solve the system several times, typically 4-30, and was looking for recommendations on reusable preconditioners to use with KSPLSQR to increase speed.
> >>
> >> Would it make the most sense to use PCCHOLESKY on the smaller system A^T * A?
> >>
> >> Thanks,
> >> Lucas
> >