performance of \(::UpperOrLowerTriangular{Float64}, ::Matrix{ComplexF64}) regression since v1.10

[songjhaha]

MWE:

using Random
using LinearAlgebra
Random.seed!(1234)
G = rand(2000, 2000);
Q = rand(2000, 2000);
Z = G + im * Q;
function f(A, b)
    
    F = lu(A; check=false)

    L, U, P = F
    y = L \ (b[P, :])
    return U \ y
end

@time f(G, Z);

In Julia 1.10

julia> @time f(G, Z);
  8.785467 seconds (13.07 k allocations: 275.582 MiB, 0.35% gc time, 0.25% compilation time)

In Julia 1.9

julia> @time f(G, Z);
  0.711327 seconds (18 allocations: 396.760 MiB, 1.92% gc time)

tracking to this fallback implement:

julia/stdlib/LinearAlgebra/src/triangular.jl

Line 1124 in 95f30e5

function generic_trimatdiv!(C::AbstractVecOrMat, uploc, isunitc, tfun::Function, A::AbstractMatrix, B::AbstractVecOrMat)

the LAPACK routine is not hit because eltype(C) !== eltype(A)

julia/stdlib/LinearAlgebra/src/triangular.jl

Line 830 in 95f30e5

generic_trimatdiv!(C::StridedVecOrMat{T}, uploc, isunitc, tfun::Function, A::StridedMatrix{T}, B::AbstractVecOrMat{T}) where {T<:BlasFloat} =