Meaning of Function.assign(scalar)

[jrmaddison]

I have previously read u.assign(1.0) as 'set the Function u equal to the function equal to one'. This would only make sense for function spaces for which the function equal to one is a member -- e.g. this wouldn't make sense for a zero trace space, or for non scalar-valued spaces.

However I see e.g.

from firedrake import *

mesh = UnitSquareMesh(2, 2)
space = FunctionSpace(mesh, "RT", 1)
u = Function(space, name="u")

u.assign(1.0)
assert (u.dat.data_ro == 1.0).all()

runs without error, suggesting that u.assign(1.0) sets the degrees of freedom to one -- a different and basis dependent operation.

u.assign(Constant(1.0)) has the same behaviour.

Is this the intended behaviour, a bug, or am I using the assign method in an unexpected/invalid way?

[jrmaddison]

For comparison with legacy FEniCS

from fenics import *

mesh = UnitSquareMesh(2, 2)
space = FunctionSpace(mesh, "RT", 1)
u = Function(space, name="u")

u.assign(Constant((1.0, 1.0)))
print(f"{assemble(u[0] * dx)=}")

displays (approx) one. Using u.assign(Constant(1.0)) leads to an error.

[colinjcotter]

It’s really a question of whether it is necessary to anticipate every mistake the user makes and catch it with an error.

[jrmaddison]

I guess that's the third option.

[wence-]

.assign does dof-wise assignment of linear combinations of things in "compatible" spaces. So this is working as intended. In almost all cases you want to use .interpolate if you actually care about function spaces and the meaning of the value (if that is too slow, please open a bug)

[jrmaddison]

A more relevant example is

from firedrake import *

mesh = UnitSquareMesh(2, 2)
e = EnrichedElement(FiniteElement("Lagrange", mesh.ufl_cell(), 1),
                    FiniteElement("Bubble", mesh.ufl_cell(), 3))
space = FunctionSpace(mesh, e)

u = Function(space, name="u").assign(Constant(1.0))

print(f"{assemble(u * dx)=}")

with the result assemble(u * dx)=1.4499999999999995.

[wence-]

This is a long-standing consequence of EnrichedElement (it doesn't reorthonormalise the basis). If you want that, use NodalEnrichedElement

[jrmaddison]

I mean it's a continuous real scalar-valued case where dual basis evaluation is not point evaluation. dof assignment and function assignment both make sense here. It's not wrong, just not what I expected.

[wence-]

No, it's worse than that, interpolate into an enriched space like that will also give you 1.5

[wence-]

Because the EnrichedElement implementation only gives you a prime basis for which $\phi_i^*[\phi_j] = \delta_{ij}$ if the sum of the individual bases is direct.