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.

Beginne damit, das gemeldete Verhalten von dsyev und dsyevx mit den angegebenen make-Optionen zu reproduzieren, wobei du den verlinkten GitHub Actions-Lauf und die Benchmark-Skripte verwendest. Vergleiche ihr Parallelverhalten mit dsyevd und dsyevr und ermittle anschließend, ob die Ursache in der Konfiguration oder in der Implementierung liegt. Als erledigt gilt die Aufgabe, wenn die Grundursache identifiziert und entweder eine validierte Behebung bereitgestellt oder eine dokumentierte Einschränkung angegeben wurde.