  The Douglas--Rachford algorithm is a classical and very successful splitting
method for finding the zeros of the sums of monotone operators. When the
underlying operators are normal cone operators, the algorithm solves a convex
feasibility problem. In this paper, we provide a detailed study of the
Douglas--Rachford iterates and the corresponding {shadow sequence} when the
sets are affine subspaces that do not necessarily intersect. We prove strong
convergence of the shadows to the nearest generalized solution. Our results
extend recent work from the consistent to the inconsistent case. Various
examples are provided to illustrates the results.
