Fix size-1 StructuredMatrix's broadcast.

[N5N3]

1. size-1 StructuredMatrix should behave like scalar during broadcast. Thus their fzero should return the only element.

2. But for simple broadcast with only one StructuredMatrix, we can keep stability as the structure is "preserved" even for size-1 case. Thus count_structedmatrix is added to check that.

3. count_structedmatrix is fused to keep Bidiagonal stability.

fix JuliaLang/LinearAlgebra.jl#1063
replace #54067

[jishnub]

The impact of the type-instability is small on performance

julia> D = Diagonal(ones(10000));

julia> @btime $D .+ $D;
  7.359 μs (5 allocations: 78.22 KiB)

julia> @btime $D + $D;
  7.330 μs (3 allocations: 78.19 KiB)

but I wonder if this might lead to cascading type-instabilities downstream if one tries to store the result in a struct/array. The single-element structured matrix is a rather niche use case as such. I wonder if this should just be deprecated, with a suggestion to use a Matrix instead?

[N5N3]

The single-element structured matrix is a rather niche use case as such.

I agree the size-1 case has no realistic usage, but throwing for inputs which are valid for general fallback looks too broken.

but I wonder if this might lead to cascading type-instabilities downstream

I guess there's no need to worry too much for this.
The stability of StructuredMatrix's broadcast is also fragile on master, e.g.

julia> bad(T) = T .* 2
bad (generic function with 1 method)

julia> good(T) = T .* 2.
good (generic function with 1 method)

julia> T = Tridiagonal(1:1,1:2,1:1)
2×2 Tridiagonal{Int64, UnitRange{Int64}}:
 1  1
 1  2

julia> @code_warntype good(T)
MethodInstance for good(::Tridiagonal{Int64, UnitRange{Int64}})
  from good(T) @ Main REPL[2]:1
Arguments
  #self#::Core.Const(good)
  T::Tridiagonal{Int64, UnitRange{Int64}}
Body::Tridiagonal{Float64, Vector{Float64}}
1 ─ %1 = Main.:*::Core.Const(*)
│   %2 = Base.broadcasted(%1, T, 2.0)::Core.PartialStruct(Base.Broadcast.Broadcasted{LinearAlgebra.StructuredMatrixStyle{Tridiagonal}, Nothing, typeof(*), Tuple{Tridiagonal{Int64, UnitRange{Int64}}, Float64}}, Any[Core.Const(LinearAlgebra.StructuredMatrixStyle{Tridiagonal}()), Core.Const(*), Core.PartialStruct(Tuple{Tridiagonal{Int64, UnitRange{Int64}}, Float64}, Any[Tridiagonal{Int64, UnitRange{Int64}}, Core.Const(2.0)]), Nothing])
│   %3 = Base.materialize(%2)::Tridiagonal{Float64, Vector{Float64}}
└──      return %3


julia> @code_warntype bad(T)
MethodInstance for bad(::Tridiagonal{Int64, UnitRange{Int64}})
  from bad(T) @ Main REPL[1]:1
Arguments
  #self#::Core.Const(bad)
  T::Tridiagonal{Int64, UnitRange{Int64}}
Body::Union{Tridiagonal{Int64, Vector{Int64}}, Matrix{Int64}}
1 ─ %1 = Main.:*::Core.Const(*)
│   %2 = Base.broadcasted(%1, T, 2)::Core.PartialStruct(Base.Broadcast.Broadcasted{LinearAlgebra.StructuredMatrixStyle{Tridiagonal}, Nothing, typeof(*), Tuple{Tridiagonal{Int64, UnitRange{Int64}}, Int64}}, Any[Core.Const(LinearAlgebra.StructuredMatrixStyle{Tridiagonal}()), Core.Const(*), Core.PartialStruct(Tuple{Tridiagonal{Int64, UnitRange{Int64}}, Int64}, Any[Tridiagonal{Int64, UnitRange{Int64}}, Core.Const(2)]), Nothing])
│   %3 = Base.materialize(%2)::Union{Tridiagonal{Int64, Vector{Int64}}, Matrix{Int64}}
└──      return %3

Users can always use typeassert to restore stability where possible.

[jishnub]

I'm not really in favor of making this type-unstable to address a rarely encountered case, but I wonder what @mbauman might have to say on this