refactor inv to also work for lu

Author: lxvm

src/inv.jl

@@ -76,10 +76,11 @@ end
     if prod(S) ≤ 14*14
         quote
             @_inline_meta
-            LUp = lu(A)
-            LUp.U \ (LUp.L \ typeof(A)(I)[LUp.p,:])
+            inv(lu(A))
         end
     else
         :(@_inline_meta; similar_type(A)(inv(Matrix(A))))
     end
 end
+
+inv(LUp::LU) = LUp.U \ (LUp.L \ typeof(LUp.L.data)(I)[LUp.p,:])

test/inv.jl

@@ -97,6 +97,12 @@ end
     @test inv(A) ≈ inv(SA)
 end
 
+@testset "LU to inverse" for sz in (5, 8, 15), typ in (Float64, Complex{Float64})
+    A = rand(typ, sz, sz)
+    SA = SMatrix{sz,sz,typ}(A)
+    @test inv(lu(A)) ≈ inv(lu(SA))
+end
+
 #-------------------------------------------------------------------------------
 # More comprehensive but qualitative testing for inv() accuracy
 #=