Correctness issues with SHermitianCompact

[lxvm]

I've been trying to use SHermitianCompact to speed up some interpolation and linear algebra, but I find it quite a difficult type to work with because it doesn't actually guarantee its values are Hermitian. The simplest example is multiplying a SHermitianCompact matrix by a complex number, which will generically result in a non-Hermitian matrix.

julia> using StaticArrays, LinearAlgebra

julia> y = rand(SHermitianCompact{3,Float64,6});

julia> x = rand(ComplexF64);

julia> norm(y*x - SMatrix(y)*x)
2.1996254891748803

julia> using Pkg

julia> Pkg.status("StaticArrays")
Status `/local/home/lxvm/projects/autobz/Project.toml`
  [90137ffa] StaticArrays v1.9.5

A summary of the problems I've encountered include:

• (As shown above) multiplication of a SHermitianCompact by a complex number should promote to a SMatrix
• The diagonal of a SHermitianCompact should always be real-valued, so that the ishermitian method, which is hard-coded to return true, is correct
• The issymmetric method should be true when the element type is real, and otherwise there should be a numerical check

I think I can correct all of the above without changing the storage layout of SHermitianCompact in a small PR. Do the proposed changes seem reasonable and am I missing any others?

[mateuszbaran]

Multiplication by complex numbers indeed looks bugged. A small PR with a fix would be appreciated 🙂 .

[lxvm]

This issue is resolved by #1264 and #1266