getindex(::Factorization) not type stable

[jiahao]

The current idiom for accessing components of a matrix Factorization object is by indexing. For example, eigfact(M)[:values] returns the eigenvalues of M after computing its spectral factorization, which is stored in an Eigen type. However, eigfact(M)[:values] returns a vector while eigfact(M)[:vectors] returns a matrix. The result is that getindex(::Eigen) is not type stable and static analysis cannot infer a concrete return type.

Consequently, linear algebra code building upon computed matrix factors must either make special effort to avoid the type instability, or break the abstraction of the Factorization object by directly accessing its fields, or else risk degraded performance if the lack of a concrete return type pollutes type inference downstream.

See

• Some type stability improvements to linalg julia#10863 where code in Base was rewritten to use direct field access instead of getindex
• Define svdvals(::SVD) julia#12747, where a type assertion was necessary to guarantee a concrete return type

and also this simple code illustrating the problem, annotated with the inferred types given by code_warntype:

function svdvals_in_ascending_order(A::Matrix{Float64})
    S = svdfact(A) #SVD{Float64,Float64,Matrix{Float64}}
    Σ = S[:S] #Union{Array{Float64,1},Array{Float64,2}}
    sort!(Σ, rev=false) #Any; method with kwarg is hard for Julia to analyze
end

It seems like we should think more about whether the getindex idiom makes sense when the Factorization object consists of heterogeneous fields. I vaguely recall this issue being raised before, but I couldn't find it on GitHub.

[andreasnoack]

Dup of #12