# JuMP abs in expression macro
**URL:** https://discourse.julialang.org/t/jump-abs-in-expression-macro/49196
**Category:** Optimization (Mathematical)
**Created:** [October 28, 2020, 6:22pm UTC](https://discourse.julialang.org/t/jump-abs-in-expression-macro/49196 "2020-10-28T18:22:26Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Paul\_McVay](https://discourse.julialang.org/u/Paul_McVay)
#### Post date: [October 28, 2020, 6:22pm UTC](https://discourse.julialang.org/t/jump-abs-in-expression-macro/49196/1 "2020-10-28T18:22:26Z")
I am hoping to extend the expression/objective JuMP macro to automatically introduce the necessary slack variable when using absolute values. I don’t have a lot of experience with JuMP internals and was hoping for some pointers. Essentially, if have two vectors `x` and `y` and I would like the to extend the macro so that
```julia
@expression m sum(abs.(x .- y))
```
becomes
```julia
@constraint m z .>= (x .- y)
@constraint m z .>= -(x .- y)
@expression m sum(z)
```
---
### Author:  [@joaquimg](https://discourse.julialang.org/u/joaquimg)
#### Post date: [October 28, 2020, 9:36pm UTC](https://discourse.julialang.org/t/jump-abs-in-expression-macro/49196/2 "2020-10-28T21:36:02Z")
Hi,
One big issue with that is that does not always work.
A simple case is:
```julia
model = Model()
@variable(model, -1 <= x <= 1)
@objective(model, Max, abs(x))
```
your `z` would go to infinity in this case.
You might want to consider converting:
`@constraint(model, λ >= norm(x,1))`
into its current JuMP form
`@constraint(model, [λ, x] in MOI.NormOneCone(1 + length(x)))`
Note that `λ` can be a scalar expression and `x` a vector expression.
The absolute value case requires `x` to be a scalar expression.
`@constraint(model, λ >= abs(x))`
would become the valid JuMP constraint:
`@constraint(model, [λ, x] in MOI.NormOneCone(2))`
---
### Author:  [@Paul\_McVay](https://discourse.julialang.org/u/Paul_McVay)
#### Post date: [October 29, 2020, 4:09pm UTC](https://discourse.julialang.org/t/jump-abs-in-expression-macro/49196/3 "2020-10-29T16:09:19Z")
That is certainly an excellent point. I was more trying to create a small solution I could use personally understanding the limitations than suggesting it be used widespread where everyone expects it to be correct in every instance.
I apologize for this next question. It might be better placed in the first steps area as it is more about how to write macros as I am not very good at it.
So my current attempt is to write the macro
```julia
macro sumAbs(m, ex, name)
slackVar = Symbol("slackVar", randstring(12))
return quote
@variable $m $slackVar[1:$(length(ex))]
@constraint $m $slackVar .>= $ex
@constraint $m $slackVar .>= -$ex
$name = @expression $m sum($slackVar)
end
end
```
It’s not quite working just yet. Surprisingly to me, it does work if you make `slackVar` a scalar and not an array (so just delete `[1:$(length(ex))]`). But I can’t figure out how to define it as an array in the macro.
Any help?
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 29, 2020, 6:08pm UTC](https://discourse.julialang.org/t/jump-abs-in-expression-macro/49196/4 "2020-10-29T18:08:48Z")
There’s no need to write a macro for this.
```nohighlight
function sumAbs(model, expr::Vector)
slack = @variable(model, [1:length(expr)], lower_bound = 0.0)
@constraint(model, slack .>= expr)
@constraint(model, slack .>= -expr)
return @expression(model, sum(slack))
end
model = Model()
@variable(model, x[1:3])
@variable(model, y[1:3])
ex = @expression(model, [a = 1:3], x[a] - y[a])
z = sumAbs(model, ex)
```
In general, you should almost never need to write a macro. They are difficult to write, and functions have the benefit of having typed arguments.