Tests for MultivariateFun (#137)

Author: jishnub

test/MultivariateTest.jl

@@ -342,28 +342,42 @@ using Base: oneto
 
         @test F(1.5,1.5im) ≈ hankelh1(0,10abs(1.5im-1.5))
 
+        P = ProductFun((x,y)->x^2*y^3, Chebyshev() ⊗ Chebyshev())
+        @test (Derivative() * P)(0.1, 0.2) ≈ ProductFun((x,y)->2x*y^3)(0.1, 0.2)
+        @test (P * Derivative())(0.1, 0.2) ≈ ProductFun((x,y)->x^2*3y^2)(0.1, 0.2)
+
         P = ProductFun((x,y)->x*y, Chebyshev() ⊗ Chebyshev())
-        x = Fun(); y = x;
-        @test Evaluation(1) * P == x
-        @test Evaluation(-1) * P == -x
+        xf = Fun(); yf = xf;
+        xi, yi = 0.1, 0.2
+        x, y = xf(xi), yf(yi)
+        @test Evaluation(1) * P == xf
+        @test Evaluation(-1) * P == -xf
         D1 = Derivative(Chebyshev() ⊗ Chebyshev(), [1,0])
         D2 = Derivative(Chebyshev() ⊗ Chebyshev(), [0,1])
-        @test (D2 * P)(0.1, 0.2) ≈ x(0.1)
-        @test (D1 * P)(0.1, 0.2) ≈ y(0.2)
-        @test ((P * D1) * P)(0.1, 0.2) ≈ x(0.1) * (y(0.2))^2
-        @test ((P * D2) * P)(0.1, 0.2) ≈ (x(0.1))^2 * y(0.2)
-        @test ((I ⊗ Derivative()) * P)(0.1, 0.2) ≈ x(0.1)
-        @test ((Derivative() ⊗ I) * P)(0.1, 0.2) ≈ y(0.2)
+        @test (D2 * P)(xi, yi) ≈ x
+        @test (D1 * P)(xi, yi) ≈ y
+        @test ((P * D1) * P)(xi, yi) ≈ x * y^2
+        @test ((P * D2) * P)(xi, yi) ≈ x^2 * y
+        @test ((I ⊗ Derivative()) * P)(xi, yi) ≈ x
+        @test ((Derivative() ⊗ I) * P)(xi, yi) ≈ y
+
+        # distribute over plus operator
+        @test ((D1 + Multiplication(xf)⊗I) * P)(xi, yi) ≈ y +  x^2 * y
+        @test ((P * (D1 + Multiplication(xf)⊗I)) * P)(xi, yi) ≈ x * y^2 +  x^3 * y^2
+
+        A = (Multiplication(xf)⊗I) * Derivative(Chebyshev()^2, [0,1])
+        @test (A * P)(xi, yi) ≈ x^2
 
         # MultivariateFun methods
         f = invoke(*, Tuple{KroneckerOperator, ApproxFunBase.MultivariateFun},
                 Derivative() ⊗ I, P)
-        @test f(0.1, 0.2) ≈ y(0.2)
+        @test f(xi, yi) ≈ y
         O = invoke(*, Tuple{ApproxFunBase.MultivariateFun, KroneckerOperator},
                 P, Derivative() ⊗ I)
-        @test (O * Fun(P))(0.1, 0.2) ≈ x(0.1) * (y(0.2))^2
+        @test (O * Fun(P))(xi, yi) ≈ x * y^2
 
         @testset "chopping" begin
+            local P
             M = [0 0 0; 0 1 0; 0 0 1]
             P = ProductFun(M, Chebyshev() ⊗ Chebyshev(), chopping = true)
             @test coefficients(P) == M
@@ -377,6 +391,23 @@ using Base: oneto
             P = ProductFun(M, Chebyshev() ⊗ Chebyshev(), chopping = true)
             @test all(iszero, coefficients(P))
         end
+
+        @testset "KroneckerOperator" begin
+            local P
+            P = ProductFun((x,y)->x^2*y^3, Chebyshev() ⊗ Chebyshev())
+            A = Multiplication(xf)⊗I
+            a = (KroneckerOperator(A) * P)(xi, yi)
+            b = (A * P)(xi, yi)
+            @test a ≈ b
+            a = ((P * KroneckerOperator(A)) * P)(xi, yi)
+            b = ((P * A) * P)(xi, yi)
+            @test a ≈ b
+            # distribute a KroneckerOperator over a times operator
+            A = (Multiplication(xf)⊗I) * Derivative(Chebyshev()^2, [0,1])
+            a = ((P * A) * P)(xi, yi)
+            b = ((P * KroneckerOperator(A)) * P)(xi, yi)
+            @test a ≈ b
+        end
     end
 
     @testset "Functional*Fun" begin
@@ -395,4 +426,13 @@ using Base: oneto
         f=Fun((x,y)->[exp(x*cos(y)) cos(x*sin(y)); 2 1],ChebyshevInterval()^2)
         @test f(0.1,0.2) ≈ [exp(0.1*cos(0.2)) cos(0.1*sin(0.2));2 1]
     end
+
+    @testset "grad" begin
+        f = Fun((x,y)->x^2*y^3, Chebyshev()^2)
+        g = grad(f)
+        @test g == grad(space(f))*f == grad(domain(f)) * f
+        x = 0.1; y = 0.2
+        @test g[1](x, y) ≈ 2x*y^3
+        @test g[2](x, y) ≈ x^2*3y^2
+    end
 end