  We present ab-initio calculations of effective magnetic exchange, $J$, as
well as Hubbard parameters ($t$, $U$ and $\delta \varepsilon$) as a function of
the local distribution of doping atoms for the high-$T_c$ superconducting $\rm
(Ca_xLa_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_3O_y$ family. We found that both the
exchange and the energies of the magnetic orbitals are strongly dependant on
the local dopant distribution, both through the induced modification of the
apical oxygen location and of the induced local electrostatic potential. The
$J$ real-space map, for a random distribution of dopants, positively compares
with observed STS gap inhomogeneity maps. Similarly, the orbital energy
fluctuations induce weak charge inhomogeneities on copper sites, that can be
positively compared with the observed LDOS inhomogeneities. These results
clearly support an extrinsic origin of both the gap inhomogeneities and LDOS.
