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?
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 <[email protected]> Sent: Tuesday, March 1, 2022 4:49 AM To: Pierre Jolivet <[email protected]> Cc: Lucas Banting <[email protected]>; [email protected] <[email protected]> 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 <[email protected]> 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 <[email protected]> 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 >
