numerical orthogonality

[nblinov]

Hello!

My goal is to compute some mode overlaps so I was wondering about the numerical precision with which I expect mode orthogonality to hold for a given tolerance in the ModeSolver object.
Specifically, suppose I try to compute the overalp (H1, H2^*), where H1 and H2 are field eigenmodes corresponding to different bands.
From some numerical experiments I see that this usually differs from zero by about ~ sqrt(tolerance), but it depends on the band choices and the k vector etc.

Is there a more formal error estimate for this numerical uncertainty? Basically I want a good criterium to decide whether a given integral over a product of modes is numerically negligible or not. I realize that this is probably strongly linked to the iterative eigenvalue solver used by MPB, so if that's discussed somewhere in the literature you could just point me there.

Thank you!