Test Jacobians numerically

Author: asterycs

test/JuliaTest.jl

@@ -1,19 +1,39 @@
 using ForwardDiff
 
+using LinearAlgebra: diagm, I
+
 @testset "test Julia function" begin
-    @vector x
+    @matrix A B C
+    @vector x y
 
     x̂ = [
-        0.0552
+        0.055
         0.395
         0.821
-        0.558
-        0.048
-        0.144
-        0.519
-        0.376
-        0.264
-        0.001
+    ]
+
+    ŷ = [
+        0.442
+        0.630
+        0.176
+    ]
+
+    Â = [
+        0.023 0.136 0.181
+        0.443 0.132 0.576
+        0.786 0.198 0.583
+    ]
+
+    B̂ = [
+        0.570 0.987 0.124
+        0.855 0.400 0.196
+        0.111 0.469 0.406
+    ]
+
+    Ĉ = [
+        0.884 0.947 0.401
+        0.999 0.623 0.473
+        0.415 0.483 0.969
     ]
 
     @testset "gradient of x'*x" begin
@@ -33,4 +53,17 @@ using ForwardDiff
 
         @test jgrad(x̂) ≈ ForwardDiff.gradient(x -> cos(tr(x * x')), x̂)
     end
+
+    @testset "jacobian of sin(A * x + y)" begin
+        jgrad = eval(to_std(jacobian(sin(A * x + y), x); format = dc.Julia()))
+
+        @test jgrad(Â, x̂, ŷ) ≈ ForwardDiff.jacobian(x -> sin.(Â * x + ŷ), x̂)
+    end
+
+    @testset "jacobian of (A .* B) * C * x)' * x * x" begin
+        jgrad = eval(to_std(jacobian(((A .* B) * C * x)' * x * x, x); format = dc.Julia()))
+
+        @test jgrad(x̂, Ĉ, Â, B̂) ≈
+              ForwardDiff.jacobian(x -> ((Â .* B̂) * Ĉ * x)' * x * x, x̂)
+    end
 end