Include what the public headers use

Several public headers include headers they do not use, such as
Eigen/Dense, while relying on transitive includes for symbols they do
use. This exposes users to dependencies they may come to rely on and
makes IWYU attribute symbols to unrelated headers. Remove the unused
includes, forward declare types used only through pointers and
references, and include the remaining dependencies directly.

Change-Id: Ic8d44bf4d3d3cc00f030199d7207e06e77e2397c