BUG: adjoint interpolation is missing complex conjugation

[jrmaddison]

Describe the bug
action(adjoint(interpolate(...)), ...) applies transpose interpolation, rather than adjoint interpolation.

Steps to Reproduce

import firedrake as fd
from firedrake.__future__ import interpolate

mesh = fd.UnitIntervalMesh(1)
space = fd.FunctionSpace(mesh, "DG", 0)

expr = interpolate(fd.Constant(1.0j) * fd.TestFunction(space), space)
u = fd.Cofunction(space.dual())
u.dat.data[:] = 1

v = fd.assemble(fd.action(fd.adjoint(expr), u))
print(f"{v.dat.data_ro=}")

displays (with complex Firedrake)

v.dat.data_ro=array([0.+1.j])

which is the complex conjugate of the expected value.

Expected behavior
The action of the adjoint should include the complex conjugation.

Error message
No error.

Environment:
Ubuntu 24.04, complex Firedrake built today.

Additional Info
The _interpolate methods of Interpolator subclasses accept a transpose argument, rather than e.g. adjoint or hermitian_transpose.

[connorjward]

Is this related to the complex failures in #3939?

[jrmaddison]

Is this related to the complex failures in #3939?

No, I'd just missed the conjs for complex.

[jrmaddison]

You can see the bug in the test_assemble_interp_adjoint_tensor test in #3939 if f1 is complex.