UFL.Interpolate() ValueError: Expecting the first argument to be primal.

[Alpha-Legion]

I'm trying to import external data to Firedrake.
I basically followed the method here: https://www.firedrakeproject.org/point-evaluation.html#primary-api
Then I wanted to interpolate point_data to CG1, but it reported the error in the title of this post.
The error is raised at ufl/core/interpolate.py line 40.
I searched the documentation of UFL, but got nothing.

[connorjward]

Please share a minimum failing example. This error is saying that your input to interpolate is somehow wrong but we have to see what you have in order to suggest a fix.

[leo-collins]

I don't get the error ValueError: Expecting the first argument to be primal. when running this, but I get a NotImplementedError: VertexOnlyMeshes don't have a working locate_cells_ref_coords_and_dists method because you're trying to interpolate from a VOM onto mesh which doesn't make sense.

@Alpha-Legion What are you trying to do mathematically? Also what firedrake version do you have installed?

[Alpha-Legion]

I think my Firedrake is the latest version (2025.10.2) because I installed it at the end of 2025.

Originally, I want to import a normal vector field of the surface (defined on vertices/faces of the mesh) and feed it to init_cell_orientations(). I first tried to feed the result interpolated to vom (i.e. the vector version of f_vom above) directly to init_cell_orientations(), but got an error:

Traceback (most recent call last):
  File "/mnt/d/Research/1_Projects/Helmholtz-Hodge_Decomposition/2025-04-18_Hodge_Theory_2D/Sphere/Sphere_HHD_inputs.py", line 30, in <module>
    mesh.init_cell_orientations(normal_verts_vom)
  File "petsc4py/PETSc/Log.pyx", line 250, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "petsc4py/PETSc/Log.pyx", line 251, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/mesh.py", line 2804, in init_cell_orientations
    f.interpolate(ufl.dot(expr, normal))
  File "petsc4py/PETSc/Log.pyx", line 250, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "petsc4py/PETSc/Log.pyx", line 251, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/function.py", line 388, in interpolate
    return assemble(interp, tensor=self, ad_block_tag=ad_block_tag)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "petsc4py/PETSc/Log.pyx", line 250, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "petsc4py/PETSc/Log.pyx", line 251, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/adjoint_utils/assembly.py", line 30, in wrapper
    output = assemble(form, *args, **kwargs)
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/assemble.py", line 148, in assemble
    return get_assembler(expr, *args, **kwargs).assemble(**assemble_kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/assemble.py", line 429, in assemble
    result = BaseFormAssembler.base_form_postorder_traversal(self._form, visitor, visited)
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/assemble.py", line 656, in base_form_postorder_traversal
    visited[e] = visitor(e, *(visited[arg] for arg in operands))
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/assemble.py", line 425, in visitor
    return self.base_form_assembly_visitor(e, t, bcs, *operands)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/assemble.py", line 622, in base_form_assembly_visitor
    interpolator = firedrake.Interpolator(expr, V, bcs=bcs, **interp_data)
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/l/venv-firedrake/lib/python3.12/site-packages/firedrake/interpolation.py", line 276, in __new__
    source_mesh = extract_unique_domain(operand) or target_mesh
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/l/venv-firedrake/lib/python3.12/site-packages/ufl/domain.py", line 428, in extract_unique_domain
    raise ValueError("Found multiple domains, cannot return just one.")
ValueError: Found multiple domains, cannot return just one.

So I guess I need to interpolate to the parent mesh before calling init_cell_orientations(). Then I did the thing described previously and got that error.

[connorjward]

I don't quite understand why you need a VoM here. Why isn't something like a DG0 or CG1 function defined on the original mesh sufficient?

[Alpha-Legion]

Because I looked at this: #3789 (reply in thread)
and this: #4078 (reply in thread)
I am not sure whether it is correct to interpolate to the original mesh nodes.
So I followed the instructions here https://www.firedrakeproject.org/point-evaluation.html#primary-api

Also, sometimes the external data are given on points that are not nodes.

I can not directly write to .dat.data because the order of vertices on which functions are defined is different from the order of external data.

[dham]

I think I see the cause of your confusion. Point evaluation is the other way around from what you are trying to do. It's the case where you have data in Firedrake and you'd like to know its value at a particular set of points.

Your circumstance, as I understand it, is that you know field values externally, and would like to interpolate them into a Firedrake Function. The recipe for that is here: https://www.firedrakeproject.org/interpolation.html#interpolation-from-external-data . That recipe tells you how to write to the correct entries in .dat.data

[Alpha-Legion]

Is there a solution to this issue?

[Alpha-Legion]

Yes, Firedrake provide an order, say order A. At the same time, any external data has its own order, which is the same as the order of vertices of input mesh, say order B. There needs a common rule that can be understood by both internal and external sides, equivalently, a mapping from the order A to order B (or B to A). This can only be provided by Firedrake, because only Firedrake contains this information.

[dham]

That approach requires full data model compatibility between Firedrake and the external data source, which is a huge undertaking. It's nowhere near as simple as input mesh vertex ordering (which is already hard for reasons explained by Connor), because the incoming data could be in a different function space that doesn't just have DoFs which are point evaluation at vertices.

In contrast, the data source knows its own mesh, and its own basis functions, so it has all the information it needs to evaluate its own fields at any point in the domain, which is all Firedrake is asking for.

[Alpha-Legion]

Maybe I have figured out how to do this, although I have no idea of the renumbering mechanism of Firedrake.
It's realized by modifying the input mesh file: change the coordinates of vertices of the input mesh to their line numbers:

1 1 1
2 2 2
.....

but leave the topology of the mesh unchanged. Import this mesh and read mesh.coordinates, which is expected to give the mapping.
Do you think this will work?

[dham]

I think that may well work in serial. I'm not convinced that it's necessarily safe in parallel because I don't know whether the graph partitioners that PETSc calls to do the parallel mesh decomposition take the mesh geometry into account.

[Alpha-Legion]

That approach requires full data model compatibility between Firedrake and the external data source, which is a huge undertaking. It's nowhere near as simple as input mesh vertex ordering (which is already hard for reasons explained by Connor), because the incoming data could be in a different function space that doesn't just have DoFs which are point evaluation at vertices.

In contrast, the data source knows its own mesh, and its own basis functions, so it has all the information it needs to evaluate its own fields at any point in the domain, which is all Firedrake is asking for.

If I'm not misunderstanding, you still mean that Firedrake asks for an interpolated function implemented externally (i.e. mydata in the "recipe"). But often, one only has a mesh with topology and geometry and data defined on vertices/barycenter of cells, and the data is not obtained from any basis. To interpolate from these data, it requires to build the mesh with basis. Basically, it's equivalent and parallel to what Firedrake does, but implemented externally. Right?