add tests for sparse arrays and sparse solvers

Author: jClugstor

test/forwarddiff_overloads.jl

@@ -1,6 +1,7 @@
 using LinearSolve
 using ForwardDiff
 using Test
+using SparseArrays
 
 function h(p)
     (A = [p[1] p[2]+1 p[2]^3;
@@ -48,6 +49,9 @@ new_A, new_b = h([ForwardDiff.Dual(5.0, 1.0, 0.0), ForwardDiff.Dual(5.0, 0.0, 1.
 cache.A = new_A
 cache.b = new_b
 
+@test cache.A == new_A
+@test cache.b == new_b
+
 x_p = solve!(cache)
 backslash_x_p = new_A \ new_b
 
@@ -61,7 +65,7 @@ cache = init(prob)
 
 new_A, _ = h([ForwardDiff.Dual(5.0, 1.0, 0.0), ForwardDiff.Dual(5.0, 0.0, 1.0)])
 cache.A = new_A
-@test cache.A = new_A
+@test cache.A == new_A
 
 x_p = solve!(cache)
 backslash_x_p = new_A \ b
@@ -139,3 +143,40 @@ end
 
 @test ≈(ForwardDiff.hessian(slash_f_hes, [5.0]),
     ForwardDiff.hessian(linprob_f_hes, [5.0]))
+
+
+# Test aliasing
+
+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
+
+linu = [ForwardDiff.Dual(0.0, 0.0, 0.0), ForwardDiff.Dual(0.0, 0.0, 0.0),
+    ForwardDiff.Dual(0.0, 0.0, 0.0)]
+cache.u = linu
+x_p = solve!(cache)
+backslash_x_p = new_A \ new_b
+
+@test linu == cache.u
+
+
+# Test Float Only solvers
+
+A, b = h([ForwardDiff.Dual(5.0, 1.0, 0.0), ForwardDiff.Dual(5.0, 0.0, 1.0)])
+
+prob = LinearProblem(sparse(A), sparse(b))
+overload_x_p = solve(prob, KLUFactorization())
+backslash_x_p = A \ b
+
+@test ≈(overload_x_p, backslash_x_p, rtol = 1e-9)
+
+A, b = h([ForwardDiff.Dual(5.0, 1.0, 0.0), ForwardDiff.Dual(5.0, 0.0, 1.0)])
+
+prob = LinearProblem(A, b)
+overload_x_p = solve(prob, UMFPACKFactorization())
+backslash_x_p = A \ b
+
+@test ≈(overload_x_p, backslash_x_p, rtol = 1e-9)