Add generic fallback

Author: YingboMa

src/lu.jl

@@ -14,13 +14,17 @@ function lu!(A::AbstractMatrix{T}, ipiv::AbstractVector{<:Integer},
     info = Ref(zero(BlasInt))
     m, n = size(A)
     mnmin = min(m, n)
-    reckernel!(A, pivot, m, mnmin, ipiv, info, blocksize)
-    if m < n # fat matrix
-        # [AL AR]
-        AL = @view A[:, 1:m]
-        AR = @view A[:, m+1:n]
-        apply_permutation!(ipiv, AR)
-        ldiv!(UnitLowerTriangular(AL), AR)
+    if isconcretetype(T)
+        reckernel!(A, pivot, m, mnmin, ipiv, info, blocksize)
+        if m < n # fat matrix
+            # [AL AR]
+            AL = @view A[:, 1:m]
+            AR = @view A[:, m+1:n]
+            apply_permutation!(ipiv, AR)
+            ldiv!(UnitLowerTriangular(AL), AR)
+        end
+      else # generic fallback
+        _generic_lufact!(A, pivot, ipiv, info)
     end
     check && checknonsingular(info[])
     LU{T, typeof(A)}(A, ipiv, info[])

test/runtests.jl

@@ -12,12 +12,19 @@ function testlu(A, MF, BF)
 end
 
 @testset "Test LU factorization" begin
-    for p in (Val(true), Val(false)), T in (Float64, Float32, ComplexF64, ComplexF32)
-        A = rand(T, 50, 100)
+    for p in (Val(true), Val(false)), T in (Float64, Float32, ComplexF64, ComplexF32, Real)
+        siz = (50, 100)
+        if isconcretetype(T)
+            A = rand(T, siz...)
+        else
+            _A = rand(50, 100)
+            A  = Matrix{T}(undef, siz...)
+            copyto!(A, _A)
+        end
         MF = mylu(A, p)
         BF = baselu(A, p)
         testlu(A, MF, BF)
-        for i in 1:100
+        for i in 50:7:100 # test `MF.info`
             A[:, i] .= 0
             MF = mylu(A, p, check=false)
             BF = baselu(A, p, check=false)