Question regarding PDGBTRF

[ashtonaut]

I have a banded matrix distributed across 6 processes in the block-column fashion required. When I call PDGBTRF, I get an INFO=1 error code on all 6 processes.

From Scalapack guide:

If INFO = K<=NPROCS, the submatrix stored on processor INFO and factored locally was not nonsingular, and the factorization was not completed

Is it a requirement of this routine that all local submatrices can be factorised individually? If it is, this may explain the error, as I think the first column block is not diagonally dominant, even though the global matrix as a whole will be.

Any help would be most appreciated.

Ashton Peters

[Stan Tomov]

Yes, it is a requirement that the blocks can be factored individually.
For example, the matrix
/ 1 1 | 0 0 \
| 1 1 | 1 0 |
| 0 1 | 2 0 |
\ 0 0 | 0 2 /
is non-singular, but if solved on 2 processors with
splitting as indicated, the method will fail since it
will try to factor (as a first step of the algorithm)
the singular block A(1:2,1:2).
The method implemented is described in
http://www.netlib.org/lapack/lawns/lawn125.ps
It should work for diagonally dominant nonsymmetric banded
matrices.