rdiv for LU decompositions

[tpapp]

Would it be possible to support rdiv for LU decompositions? Eg

using LinearAlgebra
z = lu(randn(3, 3))
ones(3) / z # currently fails

[tpapp]

Something like

(Base.:/)(v::AbstractVector, F::LinearAlgebra.Factorization) = F' \ v

could take care of this (waiting for comments before I make a PR). There is code for transpose-free special cases at the end of src/factorization.jl but I guess this was somehow missed.

Anyway, I will wait for comments then I will make a PR.

[mikmoore]

The issue with your example is one of dimensionality, nothing to do with LU:

julia> ones(3,1) / lu(randn(1,1)) # the original example with a properly sized matrix
3×1 Matrix{Float64}:
 1.0751243704964084
 1.0751243704964084
 1.0751243704964084

julia> ones(3) / lu(randn(1,1)) # we *could* make this work, but it's a footgun so I wouldn't
ERROR: MethodError: no method matching /(::Vector{Float64}, ::LU{Float64, Matrix{Float64}, Vector{Int64}})

julia> ones(3)' / lu(randn(3,3)) # what the original example probably intended
1×3 Matrix{Float64}:
 -0.164752  -1.00218  1.74342

If you were aware of this but want v / F to work anyway as F' \ v (rather than (F' \ v')'), I would strongly disagree with such a change. It would be marginally convenient alone in some niche cases but catastrophically wrong as part of a larger expression (hence my footgun concern). And note that lu(randn(3,3))' \ ones(3) (namely, transposing an LU) is already legal.