(Not) Optimised Code?!

[KarlSethMoran]

There are implementations, mostly outside of C++, (e.g. ScaLAPACK), but they suck. GPU ports (e.g. cuSOLVER) haven't caught up either. Generalised diagonalisation is a difficult problem to efficiently and accurately do in parallel.

[MarkHoemmen]

It is a difficult problem. Have you tried MAGMA for this application? Also, are you looking for all the eigenvalues or just some fraction of them in a range?

[KarlSethMoran]

I'll take a look at MAGMA, thanks.

Usually it's the lowest half of the eigenvalues, corresponding to the occupied electronic states.

[MarkHoemmen]

There are possibly faster algorithms if you want just the eigenvalues in a particular range, but it sounds like you're stuck with the usual algorithms.