Add test with rotations

Author: asterycs

test/JuliaTest.jl

@@ -170,6 +170,14 @@ end
         @test jgrad(Â, B̂, x̂) ≈ ForwardDiff.gradient(x -> f(Â, B̂, x), x̂)
     end
 
+    @testset "gradient of x' * sin.(A * x)" begin
+        f(A, x) = x' * sin.(A * x)
+
+        jgrad = eval(to_std(gradient(f(A, x), x); format = dc.JuliaFunc()))
+
+        @test jgrad(Â, x̂) ≈ ForwardDiff.gradient(x -> f(Â, x), x̂)
+    end
+
     @testset "jacobian of sin(A * x + y - z)" begin
         f(A, x, y, z) = sin.(A * x + y - z)
 
@@ -201,4 +209,12 @@ end
 
         @test jhess(x̂) ≈ ForwardDiff.hessian(x -> f(x), x̂)
     end
+
+    @testset "hessian of x' * sin.(A * x)" begin
+        f(A, x) = x' * sin.(A * x)
+
+        jhess = eval(to_std(hessian(f(A, x), x); format = dc.JuliaFunc()))
+
+        @test jhess(Â, x̂) ≈ ForwardDiff.hessian(x -> f(Â, x), x̂)
+    end
 end

test/StdStrTest.jl

@@ -55,6 +55,7 @@ using LinearAlgebra: tr, diag, diagm, norm
     @test to_std(gradient((x .^ 2 .* y)' * c, x)) == "2(x ⊙ y ⊙ c)"
     @test to_std(gradient(norm(A * x, 2), x)) == "1/2sum((xᵀAᵀ)²)⁻¹⸍²2AᵀAx"
     @test to_std(gradient(log.(A*x)' * x, x)) == "Aᵀdiagm(vec(1) ⊘ (Ax))x + log(Ax)" # TODO: Simplify diagm(quotient) * vec
+    @test to_std(gradient(x' * sin.(A * x), x)) == "Aᵀdiagm(cos(Ax))x + sin(Ax)"
 end
 
 @testset "test Jacobian in standard notation" begin
@@ -91,4 +92,6 @@ end
     @test to_std(hessian(2 * x' * x, x)) == "4I"
     @test to_std(hessian(sin(cos(x' * A * B' * x)), x)) ==
           "cos(cos(xᵀBAᵀx))((-1)sin(xᵀBAᵀx)(BAᵀ + ABᵀ) + (BAᵀx + ABᵀx)(-1)cos(xᵀBAᵀx)(xᵀABᵀ + xᵀBAᵀ)) + (-1)(-1)sin(xᵀBAᵀx)(BAᵀx + ABᵀx)sin(cos(xᵀBAᵀx))(-1)sin(xᵀBAᵀx)(xᵀABᵀ + xᵀBAᵀ)"
+    @test to_std(hessian(x' * sin.(A * x), x)) ==
+          "diagm(cos(Ax))A + Aᵀdiagm(cos(Ax)) + (-1)Aᵀdiagm(x ⊙ sin(Ax))A"
 end