add tests for updating cache

Author: jClugstor

test/forwarddiff_overloads.jl

@@ -24,4 +24,18 @@ prob = LinearProblem(A, [6.0, 10.0, 25.0])
 _, b = h([ForwardDiff.Dual(5.0, 1.0, 0.0), ForwardDiff.Dual(5.0, 0.0, 1.0)])
 A = [5.0 6.0 125.0; 15.0 10.0 21.0; 25.0 45.0 5.0]
 prob = LinearProblem(A, b)
-@test ≈(solve(prob).u, A \ b, rtol = 1e-9)
+@test ≈(solve(prob).u, A \ b, rtol = 1e-9)
+
+A, b = h([ForwardDiff.Dual(10.0, 1.0, 0.0), ForwardDiff.Dual(10.0, 0.0, 1.0)])
+
+prob = LinearProblem(A, b)
+cache = init(prob)
+
+new_A, new_b = h([ForwardDiff.Dual(5.0, 1.0, 0.0), ForwardDiff.Dual(5.0, 0.0, 1.0)])
+cache.A = new_A
+cache.b = new_b
+
+x_p = solve!(cache)
+other_x_p = new_A \ new_b
+
+@test ≈(x_p, other_x_p, rtol = 1e-9)