Fix DFSane tests and Klement allocations

Author: avik-pal

src/nlsolve/klement.jl

@@ -44,10 +44,11 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
             # Singularity test
             if !issuccess(F_)
                 J = __init_identity_jacobian!!(J)
+                @bb copyto!(F, J)
                 if setindex_trait(J) === CanSetindex()
-                    lu!(J; check = false)
+                    F_ = lu!(F; check = false)
                 else
-                    J = lu(J; check = false)
+                    F_ = lu(F; check = false)
                 end
             end
         end
@@ -66,7 +67,7 @@ function SciMLBase.__solve(prob::NonlinearProblem, alg::SimpleKlement, args...;
         tc_sol !== nothing && return tc_sol
 
         @bb δx .*= -1
-        @bb J_cache .= J' .^ 2
+        @bb J_cache .= transpose(J) .^ 2
         @bb @. δx² = δx^2
         @bb d = J_cache × vec(δx²)
         @bb δx² = J × vec(δx)

test/basictests.jl

@@ -198,11 +198,11 @@ end
             res = benchmark_nlsolve_oop(quadratic_f, @SVector[1.0, 1.0], p)
 
             if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res)
-                @test_broken all(res .≈ sqrt(p))
+                @test_broken all(abs.(res) .≈ sqrt(p))
                 @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                     @SVector[1.0, 1.0], p).u[end], p)) ≈ 1 / (2 * sqrt(p))
             else
-                @test all(res .≈ sqrt(p))
+                @test all(abs.(res) .≈ sqrt(p))
                 @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                         @SVector[1.0, 1.0], p).u[end], p)), 1 / (2 * sqrt(p)))
             end
@@ -213,12 +213,12 @@ end
         for p in 1.0:0.1:100.0
             res = benchmark_nlsolve_oop(quadratic_f, 1.0, p)
 
-            if any(x -> isnan(x) || x <= 1e-5 || x >= 1e5, res)
-                @test_broken all(res .≈ sqrt(p))
+            if any(x -> isnan(x), res)
+                @test_broken abs(res.u) ≈ sqrt(p)
                 @test_broken abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                         1.0, p).u, p)) ≈ 1 / (2 * sqrt(p))
             else
-                @test all(res .≈ sqrt(p))
+                @test abs(res.u) ≈ sqrt(p)
                 @test isapprox(abs.(ForwardDiff.derivative(p -> benchmark_nlsolve_oop(quadratic_f,
                             1.0, p).u, p)), 1 / (2 * sqrt(p)))
             end