Add test for ComponentArray type preservation with ForwardDiff

Added comprehensive tests to verify that ComponentArrays maintain their
structure when used with ForwardDiff in LinearSolve:

1. Direct test with Dual-valued ComponentArrays to verify structure preservation
2. Test gradient computation with ComponentArray RHS inside ForwardDiff

Tests cover the fix for issue SciML/DifferentialEquations.jl#1110 where
ComponentArrays were being converted to plain Vectors, causing TypeErrors.

Added ComponentArrays to test dependencies in Project.toml [extras] and [targets].

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: ChrisRackauckas

Project.toml

@@ -148,6 +148,7 @@ Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
 BlockDiagonals = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"
 CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
+ComponentArrays = "b0b7db55-8e73-11e8-0d91-e798b35f94b1"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
 FastAlmostBandedMatrices = "9d29842c-ecb8-4973-b1e9-a27b1157504e"
 FastLapackInterface = "29a986be-02c6-4525-aec4-84b980013641"
@@ -176,4 +177,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "Test", "IterativeSolvers", "InteractiveUtils", "KrylovKit", "KrylovPreconditioners", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "BlockDiagonals", "FiniteDiff", "BandedMatrices", "FastAlmostBandedMatrices", "StaticArrays", "AllocCheck", "StableRNGs", "Zygote", "RecursiveFactorization", "Sparspak", "CliqueTrees", "FastLapackInterface", "SparseArrays", "ExplicitImports"]
+test = ["Aqua", "Test", "IterativeSolvers", "InteractiveUtils", "KrylovKit", "KrylovPreconditioners", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "BlockDiagonals", "FiniteDiff", "BandedMatrices", "FastAlmostBandedMatrices", "StaticArrays", "AllocCheck", "StableRNGs", "Zygote", "RecursiveFactorization", "Sparspak", "CliqueTrees", "FastLapackInterface", "SparseArrays", "ExplicitImports", "ComponentArrays"]

test/forwarddiff_overloads.jl

@@ -2,6 +2,7 @@ using LinearSolve
 using ForwardDiff
 using Test
 using SparseArrays
+using ComponentArrays
 
 function h(p)
     (A = [p[1] p[2]+1 p[2]^3;
@@ -194,4 +195,43 @@ A, b = h([ForwardDiff.Dual(5.0, 1.0, 0.0), ForwardDiff.Dual(5.0, 0.0, 1.0)])
 prob = LinearProblem(A, b)
 @test init(prob, GenericLUFactorization()) isa LinearSolve.LinearCache
 
-@test init(prob) isa LinearSolve.LinearCache
+@test init(prob) isa LinearSolve.LinearCache
+
+# Test ComponentArray with ForwardDiff (Issue SciML/DifferentialEquations.jl#1110)
+# This tests that ArrayInterface.restructure preserves ComponentArray structure
+
+# Direct test: ComponentVector with Dual elements should preserve structure
+ca_dual = ComponentArray(
+    a = ForwardDiff.Dual(1.0, 1.0, 0.0),
+    b = ForwardDiff.Dual(2.0, 0.0, 1.0)
+)
+A_dual = [ca_dual.a 1.0; 1.0 ca_dual.b]
+b_dual = ComponentArray(x = ca_dual.a + 1, y = ca_dual.b * 2)
+
+prob_dual = LinearProblem(A_dual, b_dual)
+sol_dual = solve(prob_dual)
+
+# The solution should preserve ComponentArray type
+@test sol_dual.u isa ComponentVector
+@test hasproperty(sol_dual.u, :x)
+@test hasproperty(sol_dual.u, :y)
+
+# Test gradient computation with ComponentArray inside ForwardDiff
+function component_linsolve(p)
+    # Create a matrix that depends on p
+    A = [p[1] p[2]; p[2] p[1] + 5]
+    # Create a ComponentArray RHS that depends on p
+    b_vec = ComponentArray(x = p[1] + 1, y = p[2] * 2)
+    prob = LinearProblem(A, b_vec)
+    sol = solve(prob)
+    # Return sum of solution
+    return sum(sol.u)
+end
+
+p_test = [2.0, 3.0]
+# This will internally create Dual numbers and ComponentArrays with Dual elements
+grad = ForwardDiff.gradient(component_linsolve, p_test)
+@test grad isa Vector
+@test length(grad) == 2
+@test !any(isnan, grad)
+@test !any(isinf, grad)