Add a test for the tutorial issue

Author: ChrisRackauckas

test/matrix.jl

@@ -160,6 +160,42 @@ end
     orig_w = copy(w)
     L(w, v, u, p, t, α, β)
     @test w ≈ α * (A * v) + β * orig_w
+
+    A = [-2.0  1  0  0  0
+      1 -2  1  0  0
+      0  1 -2  1  0
+      0  0  1 -2  1
+      0  0  0  1 -2]
+    v = [3.0,2.0,1.0,2.0,3.0]
+    opA = MatrixOperator(A)
+
+    function update_function!(B, u, p, t)
+        dt = p
+        B .= A .* u + dt*I
+    end
+
+    u = Array(1:1.0:5); p = 0.1; t = 0.0
+    opB = MatrixOperator(copy(A); update_func! = update_function!)
+
+    function Bfunc!(w,v,u,p,t)
+        dt = p
+        w[1] = -(2*u[1]-dt)*v[1] + v[2]*u[1]
+        for i in 2:4
+            w[i] = v[i-1]*u[i] - (2*u[i]-dt)*v[i] + v[i+1]*u[i]
+        end
+        w[5] = v[4]*u[5] - (2*u[5]-dt)*v[5]
+        nothing
+    end
+
+    function Bfunc!(v,u,p,t)
+        w = zeros(5)
+        Bfunc!(w,v,u,p,t)
+        w
+    end
+
+    mfopB = FunctionOperator(Bfunc!, zeros(5), zeros(5); u, p, t, isconstant=false)
+
+    @test iszero(opB(v, Array(2:1.0:6), 0.5, nothing) - mfopB(v, Array(2:1.0:6), 0.5, nothing))
 end
 
 @testset "DiagonalOperator update test" begin