[petsc-dev] QR factorization of dense matrix

[Jose E. Roman]

Franck,

SLEPc has some support for this, but it is intended only for tall-skinny matrices, that is, when the number of columns is much smaller than rows. For an almost square matrix you should not use it.

Have a look at this
http://slepc.upv.es/documentation/current/docs/manualpages/BV/BVOrthogonalize.html
http://slepc.upv.es/documentation/current/docs/manualpages/BV/BVOrthogBlockType.html

You can see there are three methods. All of them have drawbacks:
GS: This is a Gram-Schmidt QR, computed column by column, so it is slower than the other two. However, it is robust.
CHOL: Cholesky QR, it is not numerically stable. In the future we will add Cholesky QR2.
TSQR: Unfortunately this is not implemented in parallel. I wanted to add the parallel version for 3.8, but didn't have time. It will be added soon.

You can use BVCreateFromMat() to create a BV object from a Mat.

Jose


> El 27 oct 2017, a las 18:39, Franck Houssen <franck.houssen at inria.fr> escribió:
> 
> I am looking for QR factorization of (sequential) dense matrix: is this available in PETSc ? I "just" need the diagonal of R (I do not need neither the full content of R, nor Q)
> 
> I found that (old !) thread https://lists.mcs.anl.gov/pipermail/petsc-users/2013-November/019577.html that says it could be implemented: has it been done ?
> As for a direct solve, the way to go is "KSPSetType(ksp, KSPPREONLY); PCSetType(pc, PCLU);", I was expecting something like "KSPSetType(ksp, KSPPREONLY); PCSetType(pc, PCQR);"... But it seems there is no PCQR available. Or is it possible to do that using "an iterative way" with a specific kind of KSP that triggers a Gram Schmidt orthogonalization in back-end ? (I have seen a KSPLSQR but could I get Q and R back ? As I understand this, I would say no: I would say the user can only get the solution)
> 
> Is it possible to QR a (sequential) dense matrix in PETSc ? If yes, what are the steps to follow ?
> 
> Franck
> 
> My understanding is that DGEQRF from lapack can do "more" than what I need, but, no sure to get if I can use it from PETSc through a KSP:
> >> git grep DGEQRF
> include/petscblaslapack_stdcall.h:#  define LAPACKgeqrf_ DGEQRF
> >> git grep LAPACKgeqrf_
> include/petscblaslapack.h:PETSC_EXTERN void LAPACKgeqrf_(PetscBLASInt*,PetscBLASInt*,PetscScalar*,PetscBLASInt*,PetscScalar*,PetscScalar*,PetscBLASInt*,PetscBLASInt*);
> include/petscblaslapack_mangle.h:#define LAPACKgeqrf_ PETSCBLAS(geqrf,GEQRF)
> include/petscblaslapack_stdcall.h:#  define LAPACKgeqrf_ SGEQRF
> include/petscblaslapack_stdcall.h:#  define LAPACKgeqrf_ DGEQRF
> include/petscblaslapack_stdcall.h:#  define LAPACKgeqrf_ CGEQRF
> include/petscblaslapack_stdcall.h:#  define LAPACKgeqrf_ ZGEQRF
> include/petscblaslapack_stdcall.h:PETSC_EXTERN void PETSC_STDCALL LAPACKgeqrf_(PetscBLASInt*,PetscBLASInt*,PetscScalar*,PetscBLASInt*,PetscScalar*,PetscScalar*,PetscBLASInt*,PetscBLASInt*);
> src/dm/dt/interface/dt.c:  PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&M,&N,A,&lda,tau,work,&ldwork,&info));
> src/dm/dt/interface/dtfv.c:  LAPACKgeqrf_(&M,&N,A,&lda,tau,work,&ldwork,&info);
> src/ksp/ksp/impls/gmres/agmres/agmres.c:  PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&lC, &KspSize, agmres->hh_origin, &ldH, agmres->tau, agmres->work, &lwork, &info));
> src/ksp/pc/impls/bddc/bddcprivate.c:      PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
> src/ksp/pc/impls/bddc/bddcprivate.c:          PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
> src/ksp/pc/impls/gamg/agg.c:      PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Mdata, &N, qqc, &LDA, TAU, WORK, &LWORK, &INFO));
> src/tao/leastsquares/impls/pounders/pounders.c:    PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasnp,&blasnplus1,mfqP->Q_tmp,&blasnpmax,mfqP->tau_tmp,mfqP->mwork,&blasmaxmn,&info));
> src/tao/leastsquares/impls/pounders/pounders.c:        PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&blasn,&blask,mfqP->Q,&blasnpmax,mfqP->tau,mfqP->mwork,&blasmaxmn,&info));