Hi LAPACK team,
With LAPACK 3.4.1, we have run into a situation where DSYEV returns non-orthogonal eigenvectors. Please see the attached code for reproduction. The repro program computes the maximum difference between V**T * V (where V are the eigenvectors) and identity matrix of the same size. On my computer, the result is:
Maximum difference between V'*V and identity matrix is:
With LAPACK 3.3.1, there is no problem. The maximum difference is in the order of e-14.
It appears recent changes to ila[d,s,c,z]lr.f may have caused this issue. For example, I replaced the iladlr.f with the version from LAPACK 3.3.1, and then the issue is solved.