Clarification on gesv Function and GEMM Optimization

[Harishmcw]

Hello @martin-frbg,

I’m working on optimizing the gesv function in OpenBLAS and have a few questions:

• What is the primary role of the gesv function in OpenBLAS?
• Could you briefly outline the execution flow of gesv, particularly its interaction with GEMM and thread distribution?
• From ETL traces, GEMM appears to dominate the computational cost during gesv. Is this expected, and are there specific strategies to optimize GEMM in this context?
• Are there any specific configurations or build options that could improve multithreading and core utilization for gesv?

[martin-frbg]

The GESV implementation in OpenBLAS is imported unchanged from Reference-LAPACK, where it is basically a wrapper around GETRF/GETRS. As such, there is no "primary role" except to provide standard LAPACK functionality.

Please see the call graph for GESV in the online documentation of the reference implementation of LAPACK on netlib.org.

GETRF makes heavy use of GEMM and has been reimplemented and parallelized in OpenBLAS. I believe the only specific optimization possible would be to explore the multithreading strategy and the validity of the current problem size threshold for the switchover between single and multithreaded operation in GETRF/GETRS.