Slow performance of function `dsyev` and `dsyevx` (not fully paralleled)

Hello developers!

I found that functions dsyev and dsyevx seems not fully paralleled, when

• compiled by gcc (11.4/12.3)
• AMD (16 cores @ Ryzen 7945HX of laptop / 2 cores @ EPYC 7763 of github action)
• make options TARGET=ZEN USE_64BITINT=1 DYNAMIC_ARCH=1 NO_CBLAS=0 NO_LAPACK=0 NO_LAPACKE=0 NO_AFFINITY=1 USE_OPENMP=1

Preliminary testing on Intel CPU may also show similar problem.

I'm not sure whether if it's the problem of make configurations, or OpenBLAS currently not fully implemented parallel version of dsyev and dsyevx.
Hope to hear any thoughts or advices, and thanks in advance!

I guess that dsyevr and dsyevd could be better replacements to dsyev. dsyevd is the fastest but consumes more memory, while dsyevr uses much smaller temporary memory.
So additionally, as a programmer not very familiar to low-level BLAS/LAPACK, I wonder that if it's common to use dsyevr and dsyevd as eigen-solvers, instead of dsyev? If so, this may not be such important issue.

Benchmark results (16 cores @ Ryzen 7945HX)

• CPU ratio refers to (CPU time) / (elapsed time)
• eigen problem of matrix of 2048 x 2048, eigenvectors required, filled with values from 1 -- 2048

Reproduction of this issue can be found in Github Action CI (2 physical cores @ EPYC 7763 of github action)(https://github.com/ajz34/issue_openblas_dsyev/actions/runs/9578584638/job/26409147609).

For scripts used in 16 cores @ Ryzen 7945HX, also see https://github.com/ajz34/issue_openblas_dsyev/tree/16-cores-Ryzen-7945HX.

Inizia riproducendo il comportamento segnalato di dsyev e dsyevx con le opzioni make fornite, utilizzando l’esecuzione GitHub Actions collegata e gli script di benchmark. Confronta il loro comportamento parallelo con dsyevd e dsyevr, quindi determina se la causa è nella configurazione o nell’implementazione. Il lavoro è completato quando la causa principale è stata identificata e viene fornita una correzione convalidata oppure viene documentata una limitazione.