  We have investigated electronic structures of a room temperature diluted
magnetic semiconductor : Co-doped anatase $\rm TiO_{2}$. We have obtained the
half-metallic ground state in the local-spin-density approximation(LSDA) but
the insulating ground state in the LSDA+$U$+SO incorporating the spin-orbit
interaction. In the stoichiometric case, the low spin state of Co is realized
with the substantially large orbital moment. However, in the presence of oxygen
vacancies near Co, the spin state of Co becomes intermediate. The
ferromagnetisms in the metallic and insulating phases are accounted for by the
double-exchange-like and the superexchange mechanism, respectively. Further,
the magnetic ground states are obtained for Mn and Fe doped $\rm TiO_{2}$,
while the paramagnetic ground state for Ni-doped $\rm TiO_{2}$.
