Include pivoting in LUL⁻¹

[MikaelSlevinsky]

It turns out not every square matrix has an LUL⁻¹ factorization unless you incorporate pivoting. Simple examples include some lower-triangular matrices. Now, symmetric pivoting is supported so that

julia> A = [3 0 0; 2 2 0; 4 5 1]
3×3 Matrix{Int64}:
 3  0  0
 2  2  0
 4  5  1

julia> F = lulinv(A)
LULinv{Float64, Matrix{Float64}, Vector{Int64}}
L factor:
3×3 Matrix{Float64}:
 1.0   0.0  0.0
 0.0   1.0  0.0
 0.0  -0.0  1.0
U factor:
3×3 Matrix{Float64}:
 1.0  5.0  4.0
 0.0  2.0  2.0
 0.0  0.0  3.0

julia> A[F.p,F.p] ≈ F.L*F.U/F.L
true

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.17%. Comparing base (d30ad01) to head (7275b86).
⚠️ Report is 3 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #75      +/-   ##
==========================================
+ Coverage   92.97%   93.17%   +0.20%     
==========================================
  Files          10       10              
  Lines        1494     1524      +30     
==========================================
+ Hits         1389     1420      +31     
+ Misses        105      104       -1     

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