Add tensor_view function and show usage in 2D-1 benchmark example.

[jpthiele]

As discussed today I have written a generic function that takes vector and index as well as tensor rank and dimension to construct a matching view.

@pjaap FYI

[chmerdon]

Ok, nice. Some other examples where this might be useful are Examples 226, 270, 282 and 290.

[chmerdon]

Unfortunately, I see lots of allocations in the kernel of Example245 again when using the tensorviews. My guess is, that the compiler has difficulties to infer the return type of the tensorview? I get no allocations when I define a separate function for each rank case, e.g. scalar_view, vector_view, matrix_view.

[pjaap]

If think you look for LinearAlgebra.BLAS.gemv!('T', alpha, A, x, beta, y)? It does not to any allocations in my tests.

[jpthiele]

Unfortunately, I see lots of allocations in the kernel of Example245 again when using the tensorviews. My guess is, that the compiler has difficulties to infer the return type of the tensorview? I get no allocations when I define a separate function for each rank case, e.g. scalar_view, vector_view, matrix_view.

Julia seems to have a problem with either the rank 3 or the generic rank n version.
If I comment those out it all works fine and without allocations.

I will try to figure this out further, one idea we had was to use ::Val{1} to ::Val{3} and then ::Val{rank} for the generic case. The main caveat is that the function call then becomes tensor_view(input,i,::Val(2),dim but the documentation for value types discourages writing those as internal functions and wrapping them in a generic function that calls Val(rank).

[jpthiele]

Another thing we should discuss is where the documentation for the helper functions would fit best.
We should probably explain usage both in at least one example and the documentations for BilinearOperator and NonlinearOperator

[chmerdon]

Instead of Val{k} one could also define abstract types like TScalar, TVector, TMatrix, TRank3, TRank4 (all subtypes of <: TensorType) etc. and use them for dispatch. One could even put the dimensions into the type, i.e., use TVector{3} or TMatrix{2,2} and then use, e.g., tensorview(input, 3, TMatrix{2,2})...

Concerning the documentation, I agree. The NonlinearOperator already has an example at the end of the page for which one could add the new possibility. Another example for the BilinearOperator would be good, too. We will think about that when the rest is sorted out.

[j-fu]

Had similar situations where I worked with wrapper structs:

Enabled Sparspak for dual numbers by implementing tailored BLAS routines:

• https://github.com/PetrKryslUCSD/Sparspak.jl/blob/main/src/Utilities/GenericBlasLapackFragments.jl
• The problem here is that the Sparspak code uses incompletely allocated arrays (inherited from dirty fortran tricks)

Local kernel callback routines in VoronoiFVM:

• https://github.com/j-fu/VoronoiFVM.jl/blob/efced035d65304acf842e5c4c1a61ad17a17af84/src/vfvm_geometryitems.jl#L87

[jpthiele]

Added TensorDescription, updated tensor_view and added documentation for everything new.
@Da-Be-Ru FYI

[chmerdon]

looks good to me now, are we ready to merge?

[jpthiele]

From my point of view, yes