Include information needed to compute permutations of dofs

[mscroggs]

Information about the number of co-located dofs on each entity is needed for FEniCS/ffcx#176.

Most likely, this information would need to be an unflattening map or the shape of the unflattened dof map.

[wence-]

Is this for VectorElement etc... Because for scalar nodal elements there won't be co-located dofs, no?

[garth-wells]

Yes.

[michalhabera]

My opinion is, that FIAT is poor in handling dual spaces. It correctly stores the shape of basis functions, but unfortunately unrolls (flattens) dual basis during dual set construction.

For example, RT element of degree 3 (on triangle) has 9 integral moment dofs on facets of shape (co-shape?)=() but 3 integral moment dofs on cell of shape=(spatial_dim, ).

[dham]

I think that the original question here misses the point. @mscroggs is trying to get Dolfin to recover lost information. Recovering lost information almost always indicates that the design is wrong. Instead of providing hints to the reconstruction process, FIAT elements need a method basis_permutation(entity, s) where entity is a cell entity and s is an encoding of a member of that cell's symmetry group. FIAT should then return the signed permutation of the basis. The information to construct this is by definition available at FIAT level (though someone has to do the legwork) and this saves Dolfin from having to recover it in a hacky way.

[mscroggs]

I've changed the title of this, as the entity block size is not constant (eg N2curl has different dof types on a face).