Finsberg/interpolate expression

[finsberg]

Summary

Merged in finsberg/interpolate_func_into_space to pick up its interpolation-matrix cache fixes, then found and fixed several additional bugs in the expression-interpolation support (ExprInterpolationBlock) and the Constant/Function overload types.

Bugs fixed

1. Constant controls were silently downcast to Function during arithmetic

Function._ad_mul, _ad_add, _ad_copy, and _ad_create_checkpoint all hardcoded construction of a plain overloaded Function when building a new instance (and _ad_create_checkpoint relied on dolfinx.fem.Function.copy(), which itself always returns a plain Function regardless of subclass). Since Constant is a Function subclass, any of these operations run on a Constant — which pyadjoint calls internally during Taylor tests and optimization — silently produced a plain Function instead, breaking with TypeError: Control value must be an OverloadedType object with the same type as the control.

Fixed by adding Function._ad_new_like(), which bypasses the constructor (type(self).__new__(type(self), V) + Function.__init__(r, V)) to build a new instance of the correct concrete subclass sharing the same function space, since Constant.__init__ takes a different signature (mesh, value) than Function.__init__ (function_space) and can't be called generically.

2. import dolfinx_adjoint required scifem even if unused

blocks/interpolation.py had a module-level import scifem, and scifem is only needed by ExprInterpolationBlock for assembling Jacobian/Hessian matrices of UFL expressions. Since __init__.py eagerly imports interpolate, this meant the whole package failed to import for anyone without scifem installed, even if they only use the linear Function→Function interpolation path (or nothing interpolation-related at all). scifem also wasn't declared as a dependency anywhere.

Fixed by making the scifem import lazy (only at the two call sites that actually need it, raising a friendly pip install scifem error if missing), and adding scifem as an explicit optional-dependency group in pyproject.toml.

3. ExprInterpolationBlock re-derived dependency indices it already had

Every adjoint/TLM/Hessian method reimplemented a custom identity-matching lookup (get_dependency_index) to find a dependency's position, even though pyadjoint already passes the correct index directly (idx, and relevant_dependencies as (idx, block_variable) tuples) — confirmed by reading pyadjoint's own Block.evaluate_adj/evaluate_hessian. This was extra, fragile complexity for no benefit, and it also masked a shape bug in a manually-driven test (test_expr_interpolation_adjoint_property was calling prepare_evaluate_adj with the wrong relevant_dependencies shape — a bare list instead of (idx, block_variable) tuples).

Simplified all the block's evaluate/prepare methods to trust the index pyadjoint provides directly. Kept get_dependency_index itself as a small public helper, since it's still legitimately needed for tests that drive the block manually outside of pyadjoint's tape, and fixed that test's relevant_dependencies shape to match pyadjoint's real contract.

4. Two Taylor tests were missing a required re-evaluation before computing derivatives

test_expr_interpolation_taylor_test_function/_constant computed Jh.derivative()/Jh.hessian() without first re-calling Jh(control), so the tape was left checkpointed at the last perturbed point from the preceding first-order Taylor test rather than at the true control value — causing the second-order convergence check to fail at rate ≈1 instead of ≈3. Fixed by adding the missing Jh(control) call, matching the pattern already used in the analogous Function→Function interpolation test.

Verification

Full test suite passes (58/58), ruff check/ruff format --check clean, mypy clean (aside from one pre-existing, unrelated error in compat.py). Each fix was independently reproduced against the pre-fix commit to confirm the bug was real, and re-verified after the fix — including simulating a scifem-free environment and testing Constant arithmetic directly.

AI assistance

I used Claude Code (Claude Sonnet 5 and Claude Opus 5) to help implement, test, and iterate on this feature, and to draft this PR description. I reviewed, tested, and take full responsibility for the final contribution.