How to optimize simple matrix equation solving

General Usage Performance
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16

As a fix to that backsolve_hess! works on rows instread of columns, the following, quite ugly, but a bit faster code seems to improve it by another 10-20%:


function backsolve_hess!(H::AbstractMatrix{T}, rhs::AbstractArray{T}) where {T}
    # Make H UpperTriangular and apply givens to rhs
    n = size(H,1)
    Ht = H'
    rotations = LinearAlgebra.Givens{T}[]
    for i = n:-1:2
        Gi, r = givens(Ht, i, i-1, i)
        push!(rotations, Gi')
        rmul!(H, Gi')
    end
    # H is now upper triangular
    ldiv!(UpperTriangular(H), rhs)
    for i in n-1:-1:1
        lmul!(rotations[i], rhs)
    end
    return rhs
end

@btime testfast(H, λs, b) #48.689 ms (2017 allocations: 654.73 KiB)
@btime testfast2(H, λs, b) # 40.799 ms (9017 allocations: 8.65 MiB)

some work can probably be done on the allocations, and proper testing of this new code is probably needed.