System of equations using metaprogramming

Question

I am trying to create a function that computes the residuals of a system of equations using metaprogramming.

This is what I have tried so far (toy example):

function syst!(x::Vector, ou::Vector)
    for i in 1:length(x)
        eval(parse("ou[$i] = x[$i]^2 + x[$i]"))
    end
    return ou
end

However, when I try to compute the function, Julia says that the variable x is not defined. But if I include a println(parse("ou[$i] = x[$i]^2 + x[$i]")) I get the code that would be "typed" in the body of the function (sorry if I'm not using the correct technical CS terms, I come from the "scientific culture").

Anyways, it seems that the parseed x lives in another scope. How can I bring that parsed x to the scope of the function so that it represents the x from the arguments of syst!?

Bonus: I have a system of 700 equations and they are amenable to be "typed" using metaprogramming, what's the best way/technique to create a function that computes the residuals of the system? Was I on the right track?

Answer 1

Stefan's comment is right; in this specific example there is no need for metaprogramming. However, if you wanted to generate many lines similar to ou[i] = x[i]^2 + x[i] but different in complicated ways, you could generate them with a macro. See http://docs.julialang.org/en/release-0.4/manual/metaprogramming/. Macros expand to generated code "in place" as if you had typed it yourself, so variables can refer to the surrounding scope.