LU Factorization without partial pivoting

[mkkcbe]

Which function should I use in ScaLAPACK to do LU factorization without partial pivoting, unlike pdgetrf ? Can I use pddttrf ? Kindly advise.

Thanks,
-Kay.

[Julien Langou]

Hello,

(1) I am sure you know that LU factorization without partial pivoting is really unstable in general, if we assume some property on the matrix A (for example diagonal dominance), they we can prove that partial pivoting is not activated in practice and so we are better off with a special purposed algorithm that do not seek pivot, that do not switch pivot rows as well. In that case, we would use so called "block LU" and it's faster than "partitioned LU".

(2) PDDTRF is for tridiagonal diagonally dominant-like matrices. This is really special case.

(3) We do not have block LU in ScaLAPACK not in LAPACK.

(4) It is possible to hack PDGETRF and PDGETRS to remove the pivot search and the row swap (simply comment the line of codes). You should get some speedup by doing this but the "block LU" algorithm would be even faster. (Since that would communication optimal, as oppsoed to what I am describing.) It's not too hard to write Block LU in the ScaLAPACK framework ...

(5) Can you describe why you need this functionnality? This might motivate some further development. What is the size of the matrix?

Best wishes,
Julien.