Test the backward error, not the forward error

Author: YingboMa

test/runtests.jl

@@ -5,11 +5,10 @@ import LinearAlgebra
 baselu = LinearAlgebra.lu
 mylu = RecursiveFactorization.lu
 
-function testlu(MF, BF)
+function testlu(A, MF, BF)
     @test MF.info == BF.info
-    @test MF.L ≈ BF.L
-    @test MF.U ≈ BF.U
-    @test MF.P ≈ BF.P
+    @test MF.P == BF.P
+    @test MF.L*MF.U ≈ A[MF.p, :]
     nothing
 end
 
@@ -18,12 +17,12 @@ end
         A = rand(100, 100)
         MF = mylu(A, p)
         BF = baselu(A, p)
-        testlu(MF, BF)
+        testlu(A, MF, BF)
         for i in 1:100
             A[:, i] .= 0
             MF = mylu(A, p, check=false)
             BF = baselu(A, p, check=false)
-            testlu(MF, BF)
+            testlu(A, MF, BF)
         end
     end
 end