More robust derivative/gradient/jacobian

Author: YingboMa

src/direct.jl

@@ -8,7 +8,7 @@ A helper function for computing the derivative of an expression with respect to
 """
 function derivative(O, v; simplify = true)
     if O isa AbstractArray
-        Num[expand_derivatives(Differential(v)(value(o)), simplify) for o in O]
+        Num[Num(expand_derivatives(Differential(v)(value(o)), simplify)) for o in O]
     else
         Num(expand_derivatives(Differential(v)(value(O)), simplify))
     end
@@ -23,7 +23,7 @@ A helper function for computing the gradient of an expression with respect to
 an array of variable expressions.
 """
 function gradient(O, vars::AbstractVector; simplify = true)
-    Num[expand_derivatives(Differential(v)(value(O)),simplify) for v in vars]
+    Num[Num(expand_derivatives(Differential(v)(value(O)),simplify)) for v in vars]
 end
 
 """
@@ -35,7 +35,7 @@ A helper function for computing the Jacobian of an array of expressions with res
 an array of variable expressions.
 """
 function jacobian(ops::AbstractVector, vars::AbstractVector; simplify = true)
-    Num[expand_derivatives(Differential(value(v))(value(O)),simplify) for O in ops, v in vars]
+    Num[Num(expand_derivatives(Differential(value(v))(value(O)),simplify)) for O in ops, v in vars]
 end
 
 """
@@ -57,7 +57,7 @@ function sparsejacobian(ops::AbstractVector, vars::AbstractVector; simplify = tr
     exprs = Num[]
 
     for (i,j) in zip(I, J)
-        push!(exprs, expand_derivatives(Differential(vars[j])(ops[i]), simplify))
+        push!(exprs, Num(expand_derivatives(Differential(vars[j])(ops[i]), simplify)))
     end
     sparse(I,J, exprs, length(ops), length(vars))
 end