  The localized-itinerant nature of Ce-4$f$ valence electrons in heavy fermion
compound CeIn$_{3}$ under pressure is studied thoroughly by means of the
combination of density functional theory and single-site dynamical mean-field
theory. The detailed evolutions of electronic structures of CeIn$_{3}$,
including total and partial density of states, momentum-resolved spectral
functions, and valence state histograms etc., are calculated in a wide pressure
range where the corresponding volume compression $V/V_0 \in [0.6,1.0]$ (here
$V_0$ is the experimental crystal volume) at $T \cong 116$ K. Upon increasing
pressure, two strong peaks associated with the Ce-$4f$ states emerge near the
Fermi level, and the $c$-$f$ hybridization and valence state fluctuation are
enhanced remarkably. Moreover, the kinetic and potential energies raise, while
the occupancy, total angular momentum, and low-energy scattering rate of the
Ce-$4f$ electrons decline with respect to pressure. All the physical
observables considered here exhibit prominent kinks or fluctuations in $V/V_0
\in [0.80,0.90]$, which are probably the desired fingerprints for the Ce-4$f$
localized-itinerant crossover.
