Simplify deduction of eltype in FunctionValues constructor

[KnutAM]

In #764, a potential simplification of the code linked below was discussed. Would be good to investigate, but this should also become simpler if Ferrite-FEM/Tensors.jl#188 is finalized. CC @termi-official

Ferrite.jl/src/FEValues/FunctionValues.jl

Lines 8 to 30 in 324bd4a

	# Helpers to get the correct types for FunctionValues for the given function and, if needed, geometric interpolations.
	struct SInterpolationDims{rdim,sdim} end
	struct VInterpolationDims{rdim,sdim,vdim} end
	function InterpolationDims(::ScalarInterpolation, ip_geo::VectorizedInterpolation{sdim}) where sdim
	return SInterpolationDims{getdim(ip_geo),sdim}()
	end
	function InterpolationDims(::VectorInterpolation{vdim}, ip_geo::VectorizedInterpolation{sdim}) where {vdim,sdim}
	return VInterpolationDims{getdim(ip_geo),sdim,vdim}()
	end
	typeof_N(::Type{T}, ::SInterpolationDims) where T = T
	typeof_N(::Type{T}, ::VInterpolationDims{<:Any,dim,dim}) where {T,dim} = Vec{dim,T}
	typeof_N(::Type{T}, ::VInterpolationDims{<:Any,<:Any,vdim}) where {T,vdim} = SVector{vdim,T} # Why not ::Vec here?
	typeof_dNdx(::Type{T}, ::SInterpolationDims{dim,dim}) where {T,dim} = Vec{dim,T}
	typeof_dNdx(::Type{T}, ::SInterpolationDims{<:Any,sdim}) where {T,sdim} = SVector{sdim,T} # Why not ::Vec here?
	typeof_dNdx(::Type{T}, ::VInterpolationDims{dim,dim,dim}) where {T,dim} = Tensor{2,dim,T}
	typeof_dNdx(::Type{T}, ::VInterpolationDims{<:Any,sdim,vdim}) where {T,sdim,vdim} = SMatrix{vdim,sdim,T} # If vdim=sdim!=rdim Tensor would be possible...
	typeof_dNdξ(::Type{T}, ::SInterpolationDims{dim,dim}) where {T,dim} = Vec{dim,T}
	typeof_dNdξ(::Type{T}, ::SInterpolationDims{rdim}) where {T,rdim} = SVector{rdim,T} # Why not ::Vec here?
	typeof_dNdξ(::Type{T}, ::VInterpolationDims{dim,dim,dim}) where {T,dim} = Tensor{2,dim,T}
	typeof_dNdξ(::Type{T}, ::VInterpolationDims{rdim,<:Any,vdim}) where {T,rdim,vdim} = SMatrix{vdim,rdim,T} # If vdim=rdim!=sdim Tensor would be possible...

[termi-official]

Why not ::Vec here?

The only reason here is literally that I did not want to mix Vec and SMatrix , because of missing support for mixed tensors. :)

[KnutAM]

I think for now that is ok, but I talked to @fredrikekre that before releasing 1.0 we should probably add a note in the docs since this will be a breaking change for users of embedded elements when the output changes from SArray to Tensor/MixedTensor.

E.g. in interface elements (#767 ), they currently return SArrays when they would in the future return Tensor.

[termi-official]

I am not sure if there are users for this feature, because it is not really exposed in the docs and I struggle with meshgen. But yes, we should mention the breaking change anyway.

[fredrikekre]

There is also the possibility of vdim > 3 which Tensors don't handle(?). I think it is nice if we stick to the same type for each "case" and don't mix Tensors/StaticArrays.

[KnutAM]

There is also the possibility of vdim > 3 which Tensors don't handle(?)

What is the application of this?
If a generalized Tensor for higher dimensions is needed, that would be easy to add support for using the macro in Ferrite-FEM/Tensors.jl#211.

I would find it better to have a flag on FEValues construction, e.g. returntype=SArray (default being e.g. AbstractTensor) for such special cases to be very explicit. I find that getting SArray for some combinations of dimensions and Tensor for others is confusing/unexpected.

[termi-official]

The change from SArray to MixedTensor should be non-breaking, because tensors are just SArrays with defined size + some ops, right?

[KnutAM]

The change from SArray to MixedTensor should be non-breaking, because tensors are just SArrays with defined size + some ops, right?

Not fully...

julia> at = rand(Tensor{2,3});

julia> as = rand(SMatrix{3,3});

julia> as * as
3×3 SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 1.70716  1.13599   1.33628
 1.84993  1.49189   1.3397
 1.42037  0.676446  1.24042

julia> at * at
ERROR: use `⋅` (`\cdot`) for single contraction and `⊡` (`\boxdot`) for double contraction instead of `*`
Stacktrace:
 [1] error(s::String)
   @ Base .\error.jl:35
 [2] *(S1::Tensor{2, 3, Float64, 9}, S2::Tensor{2, 3, Float64, 9})
   @ Tensors C:\Users\meyer\.julia\packages\Tensors\DZnYM\src\tensor_ops_errors.jl:3
 [3] top-level scope
   @ REPL[6]:1