def METHOD_NAME(matrices):
    A_dense, A_sparse, b = matrices
    sparse_cls = type(A_sparse)
    lu = splin.spilu(A_sparse)
    assert isinstance(lu.L, sparse_cls)
    assert isinstance(lu.U, sparse_cls)
    z = lu.solve(A_sparse.todense())
    assert_allclose(z, np.eye(len(b)), atol=1e-3)