  We consider the inverse problem of recovering the magnetic and potential term
of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds
with boundary from partial Dirichlet and Neumann data on suitable subsets of
the boundary. The uniqueness proof relies on proving a suitable Carleman
estimate for functions which vanish only on a part of boundary and constructing
complex geometric optics solutions which vanish on a part of the boundary.
