Improve performance for det(F) where F is a LUfactor

[KristofferC]

I noticed that some of the vectorized operations in the determinants on LUFactors took a very long time. This devectorizes them for a significant speed up, especially for small matrices (600x speedup). These are used in the calculation of determinants for normal matrices so it is good to get them fast.

Benchmark code

function f(N, n)
    A = rand(n,n)
    F = lufact(A)
    @time for i = 1:N
        logabsdet(F)
    end
     @time for i = 1:N
        det(F)
    end
end

for elty in (Float64, Complex128)
    println("eltype $elty:")
    println("n = 4")
    f(10^5, 4)
    println("n = 100")
    f(10^5, 100)
end

Master

eltype Float64:
n = 4
  0.604570 seconds (2.50 M allocations: 505.066 MB, 5.28% gc time)
  0.579472 seconds (2.20 M allocations: 477.600 MB, 4.88% gc time)
n = 100
  0.886912 seconds (2.50 M allocations: 810.242 MB, 3.91% gc time)
  0.651776 seconds (2.20 M allocations: 553.894 MB, 4.27% gc time)
eltype Complex{Float64}:
n = 4
  0.603211 seconds (2.50 M allocations: 505.066 MB, 5.09% gc time)
  0.577971 seconds (2.20 M allocations: 477.600 MB, 4.83% gc time)
n = 100
  0.849031 seconds (2.50 M allocations: 810.242 MB, 3.81% gc time)
  0.650605 seconds (2.20 M allocations: 553.894 MB, 4.08% gc time)

PR

eltype Float64:
n = 4
  0.007293 seconds
  0.000908 seconds
n = 100
  0.173780 seconds
  0.011353 seconds
eltype Complex{Float64}:
n = 4
  0.007362 seconds
  0.000880 seconds
n = 100
  0.165616 seconds
  0.011188 seconds

[KristofferC]

I think AppVeyor needs a restart. Not sure what the errors on Travis are. Anyone?

[tkelman]

Bugs for everyone. Travis was one fatal: unable to connect to github.com: and one fatal: unable to access 'https://github.com/JuliaLang/JuliaDoc.git/': gnutls_handshake() failed: A TLS packet with unexpected length was received., and appveyor was appveyor/ci#353. Can you rebase and force push here?

[KristofferC]

Rebased and green now. From my point of view, this is good to go.

[andreasnoack]

Thanks.