  We numerically calculate Perelman's entropy for a variety of canonical
metrics on $\mathbb{CP}^{1}$-bundles over products of Fano K\"ahler-Einstein
manifolds. The metrics investigated are Einstein metrics, K\"ahler-Ricci
solitons and quasi-Einstein metrics. The calculation of the entropy allows a
rough picture of how the Ricci flow behaves on each of the manifolds in
question.
