Variable reference in a function created by a macro

Specific Domains Optimization (Mathematical)
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1

Hello,

I am trying to use IntervalConstraintProgramming & associated packages to solve a geometric feasibility problem. In order to be able to use functions in constraints, the ICP package provides a macro for function definitions.

For example, one such function looks like this (phi1 is going to be an interval):
@function calc_a3(phi1) = sqrt($a1^2 + $a2^2 - 2*$a1*$a2*cos(phi1));

I can go further and embed those functions in each other (both phis are intervals here):
@function calc_l2_phi2(phi1,phi2) = (
a3 = calc_a3(phi1);
cos(phi2) * a3
)

Constraint creation with these functions works like this:
@constraint $r - calc_a3(phi1) < 0

In Julia, you can refer to variables in functions from the scope the function was created in:
r = 5
get_r() = r

I want to achieve something similar using the @function macro (I could probably work around it, but it would make my life easier), but I have no clue about how quoting, AST parsing, etc works in macros, so I have tried the following at random (hoping that a Shakespeare sonnet comes out):

@function get_r() =
$r, :(r ), :($r)

but none of these could be ‘flattened’.

Any help is appreciated!

2

Please read Please read: make it easier to help you and provide a minimal working example with what you have tried and what you are trying to achieve.

1 Like
3

Well, I cannot provide a working example, but I can provide a stripped down one:

using ValidatedNumerics
r = 5
@function f1() = r

Out of the things I could come up with, :($r) provided the most interesting error message:

Currently unable to process expressions with ex.head=quote

According to the relevant passage of the docs, this is the one I feel should work.

4

“Working” in the sense that it creates the same error message.

It looks like parameters aren’t fully supported:
https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl/pull/142
https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl/issues/140
https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl/issues/113

5

Yes, this seems to be the case. Thank you!

6

Can you state in a mathematical (rather than julia) language exactly which problem you are trying to solve?

7

Hello David,

unfortunately my background is corporate, so I’d rather not share the full story with the public, but I attempted to describe it in a private message to you.

In the meantime I found out (I am kind of goofy) that the @function macro works well, as evidenced by being able to say

using ValidatedNumerics
a1 = 3
a2 = 5
@function calc_a3(phi1) = sqrt($a1^2 + $a2^2 - 2*$a1*$a2*cos(phi1));

Here, there is no problem with referring to outside scalars (not as parameters, mind you, just as constants, like in a closure). I got an error when I tried to do something along the lines of this (as an intermediate step):

r = 5
@function get_r(phi1) = $r

The reason for this is that it doesn’t typecheck, @functions to be used in @constraints must return intervals. The error message (MethodError: no method matching iterate(::Expr)) startled me a bit, and I ran to the forums immediately. Sorry for that!

8

I’m glad you got it working. The support for parameters is very flaky and seriously needs to be improved.

There is now a new interface via ModelingToolkit.jl. I hope that the docs for that will be available shortly.

1 Like