  A stochastic gravitational-wave (GW) background consists of a large number of
weak, independent and uncorrelated events of astrophysical or cosmological
origin. The GW power on the sky is assumed to contain anisotropies on top of an
isotropic component, i.e., the angular monopole. Complementary to the
LIGO--Virgo--KAGRA (LVK) searches, we develop an efficient analysis pipeline to
compute the maximum-likelihood anisotropic sky maps in stochastic backgrounds
directly in the sky pixel domain using data folded over one sidereal day. We
invert the full pixel-pixel correlation matrix in map-making of the GW sky, up
to an optimal eigenmode cutoff decided systematically using simulations. In
addition to modeled mapping, we implement a model-independent method to probe
spectral shapes of stochastic backgrounds. Using data from LIGO--Virgo's first
three observing runs, we obtain upper limits on anisotropies as well as the
isotropic monopole as a limiting case, consistent with the LVK results. We also
set constraints on the spectral shape of the stochastic background using this
novel model-independent method.
