Add a function to check if square A is needed

src/NonlinearSolve.jl

@@ -88,10 +88,8 @@ import PrecompileTools
         for T in (Float32, Float64)
             prob = NonlinearProblem{false}((u, p) -> u .* u .- p, T(0.1), T(2))
 
-            # precompile_algs = (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
-            #     PseudoTransient(), GeneralBroyden(), GeneralKlement(), nothing)
-            # DON'T MERGE
-            precompile_algs = ()
+            precompile_algs = (NewtonRaphson(), TrustRegion(), LevenbergMarquardt(),
+                PseudoTransient(), GeneralBroyden(), GeneralKlement(), nothing)
 
             for alg in precompile_algs
                 solve(prob, alg, abstol = T(1e-2))

src/gaussnewton.jl

@@ -82,9 +82,7 @@ function SciMLBase.__init(prob::NonlinearLeastSquaresProblem{uType, iip}, alg_::
     alg = get_concrete_algorithm(alg_, prob)
     @unpack f, u0, p = prob
 
-    # Use QR if the user did not specify a linear solver
-    if alg.linsolve === nothing || alg.linsolve isa QRFactorization ||
-       alg.linsolve isa FastQRFactorization
+    if !needs_square_A(alg.linsolve) && !(u isa Number) && !(u isa StaticArray)
         linsolve_with_JᵀJ = Val(false)
     else
         linsolve_with_JᵀJ = Val(true)

src/levenberg.jl

@@ -164,9 +164,7 @@ function SciMLBase.__init(prob::Union{NonlinearProblem{uType, iip},
     u = alias_u0 ? u0 : deepcopy(u0)
     fu1 = evaluate_f(prob, u)
 
-    # Use QR if the user did not specify a linear solver
-    if (alg.linsolve === nothing || alg.linsolve isa QRFactorization ||
-        alg.linsolve isa FastQRFactorization) && !(u isa Number)
+    if !needs_square_A(alg.linsolve) && !(u isa Number) && !(u isa StaticArray)
         linsolve_with_JᵀJ = Val(false)
     else
         linsolve_with_JᵀJ = Val(true)

src/utils.jl

@@ -256,3 +256,30 @@ function _try_factorize_and_check_singular!(linsolve, X)
     return _issingular(X), false
 end
 _try_factorize_and_check_singular!(::Nothing, x) = _issingular(x), false
+
+# Needs Square Matrix
+"""
+    needs_square_A(alg)
+
+Returns `true` if the algorithm requires a square matrix.
+"""
+needs_square_A(::Nothing) = false
+function needs_square_A(alg)
+    try
+        A = [1.0 2.0;
+            3.0 4.0;
+            5.0 6.0]
+        b = ones(Float64, 3)
+        solve(LinearProblem(A, b), alg)
+        return false
+    catch err
+        return true
+    end
+end
+for alg in (:QRFactorization, :FastQRFactorization, NormalCholeskyFactorization,
+    NormalBunchKaufmanFactorization)
+    @eval needs_square_A(::$(alg)) = false
+end
+for kralg in (LinearSolve.Krylov.lsmr!, LinearSolve.Krylov.craigmr!)
+    @eval needs_square_A(::KrylovJL{$(typeof(kralg))}) = false
+end

test/23_test_problems.jl

@@ -59,13 +59,14 @@ end
 end
 
 @testset "LevenbergMarquardt 23 Test Problems" begin
-    alg_ops = (LevenbergMarquardt(; linsolve = NormalCholeskyFactorization()),
-        LevenbergMarquardt(; α_geodesic = 0.1, linsolve = NormalCholeskyFactorization()))
+    alg_ops = (LevenbergMarquardt(), LevenbergMarquardt(; α_geodesic = 0.1),
+        LevenbergMarquardt(; linsolve = CholeskyFactorization()))
 
     # dictionary with indices of test problems where method does not converge to small residual
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [3, 6, 11, 21]
-    broken_tests[alg_ops[2]] = [3, 6, 11, 21]
+    broken_tests[alg_ops[1]] = [3, 6, 17, 21]
+    broken_tests[alg_ops[2]] = [3, 6, 17, 21]
+    broken_tests[alg_ops[3]] = [6, 11, 21]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end

test/basictests.jl

@@ -352,7 +352,8 @@ end
             AutoSparseForwardDiff(), AutoSparseFiniteDiff(), AutoZygote(),
             AutoSparseZygote(), AutoSparseEnzyme()), u0 in (1.0, [1.0, 1.0])
         probN = NonlinearProblem(quadratic_f, u0, 2.0)
-        @test all(solve(probN, LevenbergMarquardt(; autodiff)).u .≈ sqrt(2.0))
+        @test all(solve(probN, LevenbergMarquardt(; autodiff); abstol = 1e-9,
+            reltol = 1e-9).u .≈ sqrt(2.0))
     end
 
     # Test that `LevenbergMarquardt` passes a test that `NewtonRaphson` fails on.
@@ -368,7 +369,7 @@ end
     @testset "Keyword Arguments" begin
         damping_initial = [0.5, 2.0, 5.0]
         damping_increase_factor = [1.5, 3.0, 10.0]
-        damping_decrease_factor = Float64[2, 5, 10]
+        damping_decrease_factor = Float64[2, 5, 12]
         finite_diff_step_geodesic = [0.02, 0.2, 0.3]
         α_geodesic = [0.6, 0.8, 0.9]
         b_uphill = Float64[0, 1, 2]
@@ -379,14 +380,14 @@ end
             min_damping_D)
         for options in list_of_options
             local probN, sol, alg
-            alg = LevenbergMarquardt(damping_initial = options[1],
+            alg = LevenbergMarquardt(; damping_initial = options[1],
                 damping_increase_factor = options[2],
                 damping_decrease_factor = options[3],
                 finite_diff_step_geodesic = options[4], α_geodesic = options[5],
                 b_uphill = options[6], min_damping_D = options[7])
 
             probN = NonlinearProblem{false}(quadratic_f, [1.0, 1.0], 2.0)
-            sol = solve(probN, alg, abstol = 1e-10)
+            sol = solve(probN, alg, abstol = 1e-12)
             @test all(abs.(quadratic_f(sol.u, 2.0)) .< 1e-10)
         end
     end