MatSeqBAIJ: add MatProduct_AtB implementation (B of type MatSeqDense)

This MR optimize some MAT[SB]AIJ operations related to the diagonal

The longer term goal is to refactor some Mat_SeqXXX non-numeric code to make it easier to also implement it on GPUs. For example,

This MR optimize some MAT[SB]AIJ operations related to the diagonal

The longer term goal is to refactor some Mat_SeqXXX non-numeric code to make it easier to also implement it on GPUs. For example, MatGetDiagonal() and friends

This commit
- MatMarkDiagonal_SeqAIJ/ELL()
- now use change in mat->nonzerostate to determine if it needs to recheck the diagonal locations
- sets diagDense flag for a complete diagonal
- MatInvertDiagonal_SeqAIJ/ELL()
- now uses change in mat->state to determine if diagonal entries and inverses need to be recomputed
- name changed to MatInvertDiagonalForSOR_SeqAIJ/ELL() for code clarity
- Added MatInvertDiagonal_SeqAIJ_Inode() for use by MatSOR_SeqAIJ_Inode()
- now uses change in mat->state to determine if block diagonal entries and inverses need to be recomputed

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Updates to manual pages related to MatProductCreate()

Not for release

Change names of Mat_XXX product contexts to MatProductCtx_XXX for code maintainability

Update destroy callback of all MatProductCtx and MatShellSetMatProductOperation() to use PetscCtxDestroyFn

MATSOLVERSUPERLU_DIST: proper prefix for -pc_precision option

Implements MatGetDiagonal for CUDA to take place on device.

Reported-by: Pierre.LEDAC@cea.fr
Thanks-to: Junchao Zhang

Merge remote-tracking branch 'origin/release'

Minor fixes to MATXXXAIJCUSPARSE manual pages

Merge branch 'balay/fix-doc' into 'release'

doc: remove non-existing references

See merge request petsc/petsc!8748

Merge branch 'jolivet/fix-arrays' into 'release'

Fix error in MatTransposeMatMultSymbolic() in case of empty rows

See merge request petsc/petsc!8773

MatSetUp_(Seq|MPI)_Hash(): fix confusing -info message

[0] <mat:mpiaij> MatSetUp_MPI_Hash(): Using hash-based MatSetValues() for MATMPISBAIJ because no preallocation provided

checkbadSource: enforce proper style in makefiles

Merge remote-tracking branch 'origin/release'

MUMPS: remove the unneeded ;

MUMPS: remove nsol_loc introduced in 5.7 as we do not use it

It cause compilation errors with MUMPS-5.6 shipped by the recent Ubuntu LTS version

Reported-by: Josh Hope-Collins

Tiny improvements to MatSOR manual page

MatZeroEntries_SeqAIJCUSPARSE() was zeroing both the CPU and GPU array. Instead just zero the GPU array if it is available, save unneeded CPU operation.

Merge branch 'jczhang/2025-09-19/precision-mumps' into 'main'

Support different precisions with MUMPS

See merge request petsc/petsc!8715

Enable ScaLAPACK and MUMPS for other precisions

MUMPS: add multi-precision support

superlu_dist: revise to make use of the new enum PetscPrecision

Fix -Wshorten-64-to-32

Edit mpiaijkok.kokkos.cxx

Avoid extra allocation

Fix error in MatTransposeMatMultSymbolic() in case of empty rows

Reported-by: Vincent Robert <vincent.robert@cea.fr>

[381]PETSC ERROR: PETSc has generated inconsistent data
[381]PETSC ERROR: j 4 no

Fix error in MatTransposeMatMultSymbolic() in case of empty rows

Reported-by: Vincent Robert <vincent.robert@cea.fr>

[381]PETSC ERROR: PETSc has generated inconsistent data
[381]PETSC ERROR: j 4 not equal to expected number of sends 5
[381]PETSC ERROR: #1 PetscGatherMessageLengths2() at src/sys/utils/mpimesg.c:271
[381]PETSC ERROR: #2 MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ() at src/mat/impls/ai
j/mpi/mpimatmatmult.c:1867
[381]PETSC ERROR: #3 MatProductSymbolic_AtB_MPIAIJ_MPIAIJ() at src/mat/impls/aij/mpi
/mpimatmatmult.c:2071
[381]PETSC ERROR: #4 MatProductSymbolic() at src/mat/interface/matproduct.c:810
[381]PETSC ERROR: #5 MatProduct_Private() at src/mat/interface/matrix.c:10216
[381]PETSC ERROR: #6 MatTransposeMatMult() at src/mat/interface/matrix.c:10355

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