# Help simplify this code? JuMP constraints

**URL:** <https://discourse.julialang.org/t/help-simplify-this-code-jump-constraints/100003>\
**Category:** New to Julia\
**Created:** [June 7, 2023, 1:51pm UTC](https://discourse.julialang.org/t/help-simplify-this-code-jump-constraints/100003 "2023-06-07T13:51:46Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![TheHardew](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thehardew/32/50603_2.png) [@TheHardew](https://discourse.julialang.org/u/TheHardew)\
**Post date:** [June 7, 2023, 1:51pm UTC](https://discourse.julialang.org/t/help-simplify-this-code-jump-constraints/100003/1 "2023-06-07T13:51:46Z")

</div>

```julia
for i in 1:Y, j in 1:X
	s = sum(x[max(1, i - 1):min(Y, i + 1), max(1, j - 1):min(X, j + 1)])
	s -= x[i, j]

	@constraint(model, 2a[i, j] <= s)
	@constraint(model, 5a[i, j] <= 8 - s)
	@constraint(model, 4b[i, j] <= s)
	@constraint(model, 4b[i, j] <= 8 - s)
	@constraint(model, 5c[i, j] <= s)
end

```

I’m using JuMP. I’m trying to make it so that:

- a[i,j] = 1 iff the sum of elements around x[i, j] (3x3, without it, up to 8 elements in total) is between 2-3.
- b[i, j] = 1 iff the sum = 4
- c[i, j] == 1 iff the sum \>= 5.

I don’t like how this code looks, but it was the cleanest I could think of.

`x[max(1, i - 1):min(Y, i + 1), max(1, j - 1):min(X, j + 1)]` selects the 3x3 submatrix of x around x[i, j].

Some ideas I had to simplify it were:

- Maybe there is some function to choose the submatrix without having to do the bound checking manually?
- Preferable, I tried to do a convolution:

```julia
mask = centered(ones(3, 3))
mask[0, 0] = 0
S = imfilter(x, mask, Fill(zero(VariableRef)))
#S = imfilter(x, mask, Fill(zero(AffExpr)))

```

But both of these convolutions fail:

```julia
ERROR: LoadError: ArgumentError: Cannot convert elements of border=Fill{AffExpr, 2}(0, (1, 1), (1, 1)) to eltype(inner)=VariableRef.
[...]
caused by: MethodError: Cannot `convert` an object of type AffExpr to an object of type VariableRef

```

Any ideas?  
Thanks