Function.subfunctions annotation

[jrmaddison]

No description provided.

[jrmaddison]

Most use cases appear straightforward, although an efficient implementation requires #299 to be resolved.

The more difficult case is a NonlinearVariationalSolver using both an aliased Function and an alias, e.g.

solve(inner(X.subfunctions[0] + X[0] - Constant(2.0), test[0]) * dx + ...)

It's not obvious to me that this would necessarily be an error (maybe some low order fixed-point method might use this deliberately) -- but tlm_adjoint could at least detect it and raise an exception.

[jrmaddison]

The simplest approach is to record extra Equations within Equation._pre_process and Equation._post_process, corresponding to copy operations, and analogous to the pyadjoint FloatingType. This would add some extra inefficiencies:

• In checkpointing/replay, which would perform the extra copy.
• Due to the lack of partial operations, Support partial operations #299.

Some tests suggest that this should work, but:

• Patches need to be updated to always call Equation._pre_process.
• There seem to be non-trivial interactions with reference dropping, with non-obvious causes of reference leaks.