I calculate numerically eigenvalues and eigenvectors of some parametrically dependent operator $\hat{H}(R)$. So after representation of this operator in some basis set I have matrix $\mathbb{H}(R)$ which after diagonalization have a form $\mathbb{Z}(R) \mathbb{D}(R) \mathbb{Z}(R)^{-1}$ where $\mathbb{Z}(R)$ are obtained eigenvectors for some particular value of parameter $R$.
My problem is that I need to calculate derivative with respect to parameter $R$ of these eigenvectors. But as you probably know normalized eigenvectors are defined up to some sign, so $-\mathbb{Z}(R)$ also are eigenvectors of my operator. Unfortunately numerical libraries for diagonalization (such as LAPACK for example) produce eigevectors with this uncertainty, which make the numerical calculation of derivative $d \mathbb{Z}(R) / d R$ impossible.
Can some of you suggest more or less general way to adjust sign of eigenvectors on different points of parameter's grid? I know about some methods like adjusting sign of extreme points but they don't satisfy me.
Thanks in advance for you help!