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Specialized default_blasmul! for Diagonal, Tridiagonal, and SymTridiagonal? #101

@jagot

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@jagot

Since

julia> Base.IndexStyle(Diagonal)
IndexCartesian()

julia> Base.IndexStyle(Tridiagonal)
IndexCartesian()

julia> Base.IndexStyle(SymTridiagonal)
IndexCartesian()

default_blasmul! will fallback to a dense algorithm: https://github.com/JuliaMatrices/ArrayLayouts.jl/blob/a5767f77a867758956c58078442bc61ca8c345c1/src/muladd.jl#L202-L221
which is suboptimal.

Would we like something like the following in ArrayLayouts.jl?:

for MT in [:Diagonal, :SymTridiagonal, :Tridiagonal]
    @eval begin
        ArrayLayouts.default_blasmul!(α, A::$MT, B::AbstractVector, β, C::AbstractVector) =
            mul!(C, A, B, α, β)
    end
end

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