[petsc-users] create a block matrix from existing petsc matrices and/or vectors

[NENNIG Benoit]

Dear petsc users,

I have parallel matrix A (mpiaij) and I would like to create a matrix B like
B = [A v 
     wT 0 ]
where wT and v are vectors.
A is involved in eigenvalue computation (slepc4py) and B will be used by a direct solver.
Currently, the matrix A is built from a sparse scipy matrix thanks to A.createAIJ, but I would like to avoid to create B from scipy. I am looking for a more _petscic_ way to solve this problem.
 
I have read that it seems not possible to change a matrix structure after its assembly. However

- Is there a way to build directly in petsc this kind of block matrix B to reuse A ?
- Is there a way to convert the petsc matrix A into csr form and to create B as new petsc matrix ?
- Is there a way to copy a matrix into another one with a different structure ?
- ...

My second question is similar, suppose I have three matrices A1, A2, C resulting form coupled 2 FEM problems, what is the good way to create the coupled global system 
B = [A1 C
     CT A2]
to use it with direct solver.

Thanks a lot,

Benoit