  We use europium doped single crystalline NaYF$_4$ nanorods for probing the
electric and magnetic contributions to the local density of optical states
(LDOS). Reciprocically, we determine intrinsic properties of the emitters
(oscillator strength, quantum yield) by comparing their measured and simulated
optical responses in front of a mirror. We first experimentally determine the
specifications of the nanoprobe (orientation and oscillator strength of the
electric and magnetic dipoles moments) and show significant orientation
sensitivity of the branching ratios associated with electric and magnetic
transitions. In a second part, we measure the modification of the LDOS in front
of a gold mirror in a Drexhage's experiment. We discuss the role of the
electric and magnetic LDOS on the basis of numerical simulations, taking into
account the orientation of the dipolar emitters. We demonstrate that they
behave like degenerated dipoles sensitive to polarized partial LDOS.
