# [petsc-users] Problem solving Ax=b with rectangular matrix A

Pierre Jolivet pierre at joliv.et
Wed Sep 21 05:20:27 CDT 2022

```Yes, but you need to use a KSP that handles rectangular Mat, such as KSPLSQR (-ksp_type lsqr).
PCLU does not handle rectangular Pmat. The only PC that handle rectangular Pmat are PCQR, PCNONE.
If you supply the normal equations as the Pmat for LSQR, then you can use “standard” PC.
You can have a look at https://petsc.org/main/src/ksp/ksp/tutorials/ex27.c.html <https://petsc.org/main/src/ksp/ksp/tutorials/ex27.c.html> that covers most of these cases.

Thanks,
Pierre

> On 21 Sep 2022, at 10:03 AM, fujisan <fujisan43 at gmail.com> wrote:
>
> I'm trying to solve Ax=b with a sparse rectangular matrix A (of size 33x17 in my test) using
> options '-ksp_type stcg -pc_type lu' on 1 or 2 cpus.
>
> And I always get an error saying "Incompatible vector local lengths" (see below).
>
> Here is the relevant lines of my code:
>
> program test
>     ...
>     ! Variable declarations
>
>     PetscCallA(PetscInitialize(PETSC_NULL_CHARACTER,ierr))
>
>     PetscCall(MatCreate(PETSC_COMM_WORLD,A,ierr))
>     PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,n,ierr))
>     PetscCall(MatSetType(A,MATMPIAIJ,ierr))
>     PetscCall(MatSetFromOptions(A,ierr))
>     PetscCall(MatSetUp(A,ierr))
>     PetscCall(MatGetOwnershipRange(A,istart,iend,ierr))
>
>     do irow=istart,iend-1
>         ... Reading from file ...
>         ...
>     enddo
>
>     PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
>     PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))
>
>     ! Creating vectors x and b
>     PetscCallA(MatCreateVecs(A,x,b,ierr))
>
>     ! Duplicating x in u.
>     PetscCallA(VecDuplicate(x,u,ierr))
>
>     ! u is used to calculate b
>     PetscCallA(VecSet(u,1.0,ierr))
>
>     PetscCallA(VecAssemblyBegin(u,ierr))
>     PetscCallA(VecAssemblyEnd(u,ierr))
>
>     ! Calculating Au = b
>     PetscCallA(MatMult(A,u,b,ierr)) ! A.u = b
>
>     PetscCallA(KSPSetType(ksp,KSPCG,ierr))
>
>     PetscCallA(KSPSetOperators(ksp,A,A,ierr))
>
>     PetscCallA(KSPSetFromOptions(ksp,ierr))
>
>     ! Solving Ax = b, x unknown
>     PetscCallA(KSPSolve(ksp,b,x,ierr))
>
>     PetscCallA(VecDestroy(x,ierr))
>     PetscCallA(VecDestroy(u,ierr))
>     PetscCallA(VecDestroy(b,ierr))
>     PetscCallA(MatDestroy(A,ierr))
>     PetscCallA(KSPDestroy(ksp,ierr))
>
>     call PetscFinalize(ierr)
> end program
>
> The code reads a sparse matrix from a binary file.
> I also output the sizes of matrix A and vectors b, x, u.
> They all seem consistent.
>
> What am I doing wrong?
> Is it possible to solve Ax=b with A rectangular?
>
> Have a nice day.
>
> Fuji
>
>  Matrix size : m=          33  n=          17  cpu size:            1
>  Size of matrix A  :           33          17
>  Size of vector b :           33
>  Size of vector x :           17
>  Size of vector u :           17
> [0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
> [0]PETSC ERROR: Arguments are incompatible
> [0]PETSC ERROR: Incompatible vector local lengths parameter # 1 local size 33 != parameter # 2 local size 17
> [0]PETSC ERROR: See https://petsc.org/release/faq/ <https://petsc.org/release/faq/> for trouble shooting.
> [0]PETSC ERROR: Petsc Development GIT revision: v3.17.4-1341-g91b2b62a00  GIT Date: 2022-09-15 19:26:07 +0000
> [0]PETSC ERROR: ./bin/solve on a x86_64 named master by fujisan Tue Sep 20 16:56:37 2022
> [0]PETSC ERROR: #1 VecCopy() at /data/softs/petsc/src/vec/vec/interface/vector.c:1607
> [0]PETSC ERROR: #2 KSPSolve_BiCG() at /data/softs/petsc/src/ksp/ksp/impls/bicg/bicg.c:40
> [0]PETSC ERROR: #3 KSPSolve_Private() at /data/softs/petsc/src/ksp/ksp/interface/itfunc.c:877
> [0]PETSC ERROR: #4 KSPSolve() at /data/softs/petsc/src/ksp/ksp/interface/itfunc.c:1048
> [0]PETSC ERROR: #5 solve.F90:218
> Abort(75) on node 0 (rank 0 in comm 16): application called MPI_Abort(MPI_COMM_SELF, 75) - process 0
>

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