[petsc-dev] QR factorization of dense matrix

[Franck Houssen]

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)); 
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