Add DirectLinearSolver support for length-1 vectors (#200)

* Add DirectLinearSolver support for length-1 vectors

* Fix test

* remove example from gallery

---------

Co-authored-by: mbouyges <maxime.bouyges@onera.fr>

Author: bmxam

src/settings.jl

@@ -19,7 +19,10 @@ Specify that linear systems `Ax = b` should be solved with a direct method.
 struct DirectLinearSolver <: AbstractSolver end
 
 function (solver::DirectLinearSolver)(
-    A::Union{AbstractMatrix,Factorization}, _Aᵀ, b::AbstractVector, x0::AbstractVector
+    A::Union{AbstractMatrix,Factorization,Number},
+    _Aᵀ,
+    b::AbstractVector,
+    x0::AbstractVector,
 )
     return A \ b
 end

test/systematic.jl

@@ -19,6 +19,23 @@ using TestItems
         test_implicit(scen)
         test_implicit(scen2)
     end
+
+    # Test for output vector of length 1
+    for (linear_solver, backends) in Iterators.product(
+        [DirectLinearSolver(), IterativeLinearSolver()],
+        [nothing, (; x=AutoForwardDiff(), y=AutoZygote())],
+    )
+        yield()
+        scen = Scenario(;
+            solver=x -> (sqrt.(x), nothing),
+            conditions=(x, y, z) -> y .^ 2 .- x,
+            x=[1.0],
+            implicit_kwargs=(; representation, linear_solver, backends),
+        )
+        scen2 = add_arg_mult(scen)
+        test_implicit(scen)
+        test_implicit(scen2)
+    end
 end;
 
 @testitem "Operator" setup = [TestUtils] begin