Result not correct for complex hermitian generalized eigen problem (ZHEGVD)

[ajz34]

Hi FLAME devs!

It seems that when using ZHEGVD ($\mathbf{A} \boldsymbol{x} = \lambda \mathbf{B} \boldsymbol{x}$ in this case, corresponds to itype=1) subroutine in flame, the result seems not correct.

Minimal reproducible example refers to ajz34/issue-flame-zhegvd.

Numerical statement

a
[ 0.4967141530112327+0.5425600435859647j -0.1382643011711847-0.4634176928124623j  0.6476885381006925-0.4657297535702569j
  1.5230298564080254+0.2419622715660341j -0.234153374723336 -1.913280244657798j  -0.2341369569491805-1.7249178325130328j
  1.5792128155073915-0.5622875292409727j  0.7674347291529088-1.0128311203344238j -0.4694743859349521+0.3142473325952739j]
b
[ 1.3576924170122822+0.j                 -0.323380017801413 -0.2376316036052268j  0.5414063362623477-0.5959408793491383j
 -0.323380017801413 +0.2376316036052268j  0.8979017216901242+0.j                  0.2665855013651873+0.2610192531743049j
  0.5414063362623477+0.5959408793491383j  0.2665855013651872-0.261019253174305j   1.6252107235389968+0.j                ]
eigh A x = lambda B x, eigenvalues:
[-2.484839662098958  -0.8894810223570818  2.891093919244652 ]

Reproduction of this issue

• Flame can be both compiled or distributed by APT:
  • reproduction github action that nightly FLAME is compiled: https://github.com/ajz34/issue-flame-zhegvd/actions/runs/16587783382/job/46916423552 , FLAME built by

    LIBS=-lblas ./configure --enable-dynamic-build --enable-lapack2flame

  • reproduction github action that distributed by APT: https://github.com/ajz34/issue-flame-zhegvd/actions/runs/16587783389/job/46916423545
• Main program for reproducing this issue: https://github.com/ajz34/issue-flame-zhegvd/blob/main/issue.cpp

Result from FLAME (seems not correct):

W: -1.99510617329178 -1.15859650658041 2.73917206915266 

Result from LAPACK (correct):

W: -2.48483966209896 -0.889481022357083 2.89109391924465 

Other status of this issue

• This issue affects complex[double], but seems not related to double (subroutine DSYGVD seems correct).
• This issue affects generalized eigen problem, but seems not related to non-generalized eigen problem (subroutine ZHEEVD seems correct).
• This problem was found when we are developing rust-based tensor toolkit RSTSR, and using BLIS/FLAME DeviceBLIS as backend
  • DeviceBLIS have error value on complex generalized hermitian eigen problem RESTGroup/rstsr#50
• By testing in RSTSR, some other subroutines that are commonly used (SVD, Cholesky, LU) and BLAS functions seems not affected, both double and complex[double].
• I have not checked whether float (single) and complex[float] is also affected.
• Building LAPACK with BLIS does not show erroneous results of ZHEGVD.
• AMD AOCL FLAME seems not show erroneous results of ZHEGVD.