# Difficulty building JuMP SparseAxisArrays for network problems
**URL:** https://discourse.julialang.org/t/difficulty-building-jump-sparseaxisarrays-for-network-problems/27227
**Category:** Optimization (Mathematical)
**Created:** [August 6, 2019, 4:09pm UTC](https://discourse.julialang.org/t/difficulty-building-jump-sparseaxisarrays-for-network-problems/27227 "2019-08-06T16:09:10Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@pulsipher](https://discourse.julialang.org/u/pulsipher)
#### Post date: [August 6, 2019, 4:09pm UTC](https://discourse.julialang.org/t/difficulty-building-jump-sparseaxisarrays-for-network-problems/27227/1 "2019-08-06T16:09:10Z")
I am trying to model a network flow problem via JuMP and I am having difficulty building the flow variables with the correct indexing using `@variable`. For example, let’s suppose I have a network with 2 flow variables x\_{12} and x\_{32}. Thus, I would like to build a `VariableRef` container named `x` that can be indexed at `[1, 2]` and `[3, 2]`. In other words, I would like to do the following using `@variable`:
```julia
julia> @variable(model, x[some_input], container = SparseAxisArray)
JuMP.Containers.SparseAxisArray{VariableRef,2,Tuple{Int64, Int64}} with 2 entries:
[1, 2] = x[1, 2]
[3, 2] = x[3, 2]
```
Is this behavior possible to achieve with JuMP in its current state? The closest I have come using `@variable` is by doing the following:
```julia
julia> @variable(model, x[[(1, 2), (3, 2)]], container = SparseAxisArray)
JuMP.Containers.SparseAxisArray{VariableRef,2,Tuple{Any}} with 2 entries:
[(1, 2)] = x[(1, 2)]
[(3, 2)] = x[(3, 2)]
```
However, having the nested tuples would be nice to avoid. The only way I can figure out how to get the desired container is to define it manually by doing the following:
```julia
using JuMP
model = Model()
idxs = [(1, 2), (3, 2)]
ns = [string("x[", idxs[i][1], ", ", idxs[i][2], "]") for i = 1:2]
var_dict = Dict(idxs[i] => @variable(model, base_name = ns[i]) for i = 1:2)
x = JuMP.Containers.SparseAxisArray(var_dict)
```
```julia
JuMP.Containers.SparseAxisArray{VariableRef,2,Tuple{Int64,Int64}} with 2 entries:
[1, 2] = x[1, 2]
[3, 2] = x[3, 2]
```
Can this be done with `@variable`? Thanks!
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [August 6, 2019, 4:51pm UTC](https://discourse.julialang.org/t/difficulty-building-jump-sparseaxisarrays-for-network-problems/27227/2 "2019-08-06T16:51:32Z")
You can go:
```nohighlight
julia> model = Model();
julia> S = [(1, 2), (3, 2)]
2-element Array{Tuple{Int64,Int64},1}:
(1, 2)
(3, 2)
julia> N = 3
3
julia> @variable(model, x[i=1:N, j=1:N; (i, j) in S])
JuMP.Containers.SparseAxisArray{VariableRef,2,Tuple{Any,Any}} with 2 entries:
[1, 2] = x[1,2]
[3, 2] = x[3,2]
```
But notice that the key is `Tuple{Any, Any}`. In addition, if `N` is large, this may take a long time to build. In general, your second or third option is preferred.