# Dof ordering: VectorFunctionSpace sub(0) vs. FunctionSpace

**URL:** <https://fenicsproject.discourse.group/t/dof-ordering-vectorfunctionspace-sub-0-vs-functionspace/5733>\
**Category:** Uncategorized\
**Created:** [May 5, 2021, 12:12am UTC](https://fenicsproject.discourse.group/t/dof-ordering-vectorfunctionspace-sub-0-vs-functionspace/5733 "2021-05-05T00:12:29Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![NickAlger](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/nickalger/32/1832_2.png) [@NickAlger](https://fenicsproject.discourse.group/u/NickAlger)\
**Post date:** [May 5, 2021, 12:12am UTC](https://fenicsproject.discourse.group/t/dof-ordering-vectorfunctionspace-sub-0-vs-functionspace/5733/1 "2021-05-05T00:12:29Z")

</div>

Is the ordering of degrees of freedom (dofs) guaranteed to be consistent between a FunctionSpace, and one component of a VectorFunctionSpace (or TensorFunctionSpace) that uses the same finite element?

Empirically, I have found that the ordering is consistent (see code below). But is it safe to write code based on this assumption? Can I rely on the ordering to remain consistent on different computers, or different versions of fenics in the future?

```
import numpy as np
import dolfin as dl

mesh = dl.UnitSquareMesh(3, 3)
V_scalar = dl.FunctionSpace(mesh, 'CG', 2)
V_vector = dl.VectorFunctionSpace(mesh, 'CG', 2, dim=2)
V_tensor = dl.TensorFunctionSpace(mesh, 'CG', 2, shape=(2,2))

X_scalar = V_scalar.tabulate_dof_coordinates()
X_vector = V_vector.tabulate_dof_coordinates()
X_tensor = V_tensor.tabulate_dof_coordinates()

X_scalar0 = X_vector[V_vector.sub(0).dofmap().dofs(), :]
X_scalar1 = X_vector[V_vector.sub(1).dofmap().dofs(), :]

order_discrepancy_vector = np.linalg.norm(X_scalar0 - X_scalar)
order_discrepancy_vector += np.linalg.norm(X_scalar1 - X_scalar)
print('order_discrepancy_vector=', order_discrepancy_vector)

X_scalar00 = X_tensor[V_tensor.sub(0).dofmap().dofs(), :]
X_scalar01 = X_tensor[V_tensor.sub(1).dofmap().dofs(), :]
X_scalar10 = X_tensor[V_tensor.sub(2).dofmap().dofs(), :]
X_scalar11 = X_tensor[V_tensor.sub(3).dofmap().dofs(), :]

order_discrepancy_tensor = np.linalg.norm(X_scalar00 - X_scalar)
order_discrepancy_tensor += np.linalg.norm(X_scalar01 - X_scalar)
order_discrepancy_tensor += np.linalg.norm(X_scalar10 - X_scalar)
order_discrepancy_tensor += np.linalg.norm(X_scalar11 - X_scalar)
print('order_discrepancy_tensor=', order_discrepancy_tensor)

```

On my computer this prints out the following:

```
order_discrepancy_vector= 0.0
order_discrepancy_tensor= 0.0
```

---

<div class="post-metadata">

**Author:** ![kamensky](https://avatars.discourse-cdn.com/v4/letter/k/e95f7d/32.png) [@kamensky](https://fenicsproject.discourse.group/u/kamensky)\
**Post date:** [May 5, 2021, 1:41pm UTC](https://fenicsproject.discourse.group/t/dof-ordering-vectorfunctionspace-sub-0-vs-functionspace/5733/2 "2021-05-05T13:41:29Z")

</div>

I’ve written code using such assumptions before. I don’t think it’s part of any official, documented API, but, anecdotally, I’ve observed DoF ordering conventions to remain consistent across different versions, and my code from ~2018 still works. Since most new development is going into FEniCS-X now, I’d guess that “old” FEniCS is likely to remain very stable in the future.