I'm looking for a LAPACK routine that does precisely what dlead4 does, that is, update the eigenvalues of a diagonal matrix by a rank-$1$ matrix. $$D + \rho z z^*$$The only difference is that $z z^*$ is not symmetric but Hermitian, i.e., complex in my case.Is there a routine that does this? I was unable to find it.As for the eigenvectors, there are references in dlead4 to dlaed3, dlaed9 that allow for the construction of eigenvectors. All these routines seem to be on a deeper level to be used in the more general eigensolvers. Ultimately, I would be surprised that there is no general solver for my problem in LAPACK.
LAPACK routine for eigenvalues/vectors of diagonal + rank 1 matrix
eigenvalues;eigensystem;lapack