Introduce PCFactorSetDefaultOrdering_Factor() to allow each factorization package
to indicate its preferered ordering, which may be external (its own) or one of PETSc.

This also affects factorizatio

Introduce PCFactorSetDefaultOrdering_Factor() to allow each factorization package
to indicate its preferered ordering, which may be external (its own) or one of PETSc.

This also affects factorization like dense PETsc where the ordering passed in by PETSc is ignored and not needed.

Also fixed options for MUMPS and SuiteSparse where users needed to pass a particular options database option
to the package (MUMP or KLU) indicating they should use the PETSc provided ordering. Now if the PETSc provided ordering is provided
these packages automatically use them without need a special option. This simplifies ordering usage for external packages

Commit-type: optimization, bug-fix, testing-fix, style-fix
/spend 6h

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Mat: fix GPU memory init in MatDenseSeqCUDA

Reported by: Victor Eijkhout <eijkhout@tacc.utexas.edu>

Fix compile warnings

CI: fix compile warnings when built with --with-debugging=0 COPTFLAGS=-O3

Fix -Wmaybe-uninitialized warnings

Refactor LAPACK factorization routines used by MatSeqDense

Correct MatSolveTranspose for recent changes in MatSeqDense

Add geqrf QR factorization for sequential dense matrices

Correct orthogonal matrix character code for complex numbers

Merge branch 'tisaac/feature-mat-permute-via-createsubmatrix' into 'main'

Make MatPermute call MatCreateSubMatrix as a fallback

See merge request petsc/petsc!3636

Merge branch 'jczhang/sf-change-api' into 'main'

Change some SF APIs mentioned in the ECP paper

See merge request petsc/petsc!3659

SF: add an MPI_Op argument to SFBcast

MatConvert(): specializations MPIDense <-> MPIAIJ

Short-circuit MatCreateMPIMatConcatenateSeqMat()

MatConvert_SeqDense_SeqAIJ(): check for square A

Make MatCreateSubMatrix_SeqDense match current interface of MatCreateSubMatrix and test permutation

CHKERRQ() -> CHKERRMPI()

Merge remote-tracking branch 'origin/release'

Add manual page for MATMPIDENSE.

Commit-type: docs

MATSEQDENSECUDA: add MatCopy support

MatDenseGetColumnVec: prevent from allocating needless GPU memory

MATAIJ: some fixes for device builds

CUDA: add a couple of missing Lazy initializations

Convert MPI error type to PETSc error with string message for all MPI calls

Now PETSc examples will ONLY return PETSc error codes and never MPI error codes directly so we can understand and post-pro

Convert MPI error type to PETSc error with string message for all MPI calls

Now PETSc examples will ONLY return PETSc error codes and never MPI error codes directly so we can understand and post-process their
errors better.

The test harness will now automatically retry tests that fail with MPI, this may help with Intel MPI that produces
seemingly random failures.

Commit-type: error-checking
/spend 30m

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Merge remote-tracking branch 'origin/release'

checkbadSource: apply rules to *.cu *.cpp sources, and expand CHKERRQ check to CHKERR(Q|MPI|CUDA|CUBLAS|CUSPARSE)