Change SVD.S::Vector{Tr} to SVD.S::AbstractVector{Tr}

Specific Domains
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1

I am developing a new package for Kronecker product matrices

A ⊗ B ⊗ ....

I want to support efficient factorizations for these type of matrices and want to use the types in LinearAlgebra.jl

Here follows the type definition of SVD in LinearAlgebra/src/svd.jl

struct SVD{T,Tr,M<:AbstractArray{T}} <: Factorization{T}
U::M
S::Vector{Tr}
Vt::M
function SVD{T,Tr,M}(U, S, Vt) where {T,Tr,M<:AbstractArray{T}}
require_one_based_indexing(U, S, Vt)
new{T,Tr,M}(U, S, Vt)
end
end

Storage of the singular values in a standard Vector is sub-optimal for an svd of Kronecker products. Can we make the following change?

S::Vector{Tr}

to

S::AbstractVector{Tr}
2

Maybe this could be done with Kronecker.jl.

3

In Kronecker.jl they decided to define their own Factorization types instead of using the parametric ones in LinearAlgebra.jl. I should probably open an issue at Issues · JuliaLang/julia · GitHub for this issue.

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4

You can not replace a concretely typed field with an abstractly typed field, that would kill performance. You could potentially make the vector type a type parameter, but I’m not sure if this would be considered a breaking change since it would change the type definition.

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