Are eigenvectors computed by the functionLAPACKE_zhpevd ( ) for a hermitian matrix guaranteed to be orthogonal ? If not, is there a way to orthogonalize them ?
Yes, the vectors must be orthogonal. Here it is an excerpt from the manual:
If jobz = 'V', then this array is overwritten by the unitary matrix Z which contains the eigenvectors of A. If
jobz = 'N', then z is not referenced.So, if in your case you don't observe this feature this may be a bug. But you also should keep in mind that Divide-and-Conquer method is not the best algorithm for matrices with multiple eivenvalues.