# JuMP non-rectangular variable container: more efficient representation?

**URL:** <https://discourse.julialang.org/t/jump-non-rectangular-variable-container-more-efficient-representation/82669>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, optimization\
**Created:** [June 13, 2022, 9:30am UTC](https://discourse.julialang.org/t/jump-non-rectangular-variable-container-more-efficient-representation/82669 "2022-06-13T09:30:12Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Shuhua](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/shuhua/32/27618_2.png) [@Shuhua](https://discourse.julialang.org/u/Shuhua)\
**Post date:** [June 13, 2022, 9:30am UTC](https://discourse.julialang.org/t/jump-non-rectangular-variable-container-more-efficient-representation/82669/1 "2022-06-13T09:30:12Z")

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Let’s consider a minimal case. I have three kinds of variables: `x` of length 50, `y` of length 80, `z` of length 100. The length actually represents the number of time steps. I know that after time 50, `x` is always zero, and `y` becomes zero after time 80. I want to collect them into an array-like container to facilitate subsequent operations, e.g., sum along dim 1. In reality, there are many more than three variables. Essentially, the container should be non-rectangular.

Currently I do it like this:

```julia
using JuMP
model = JuMP.Model()
@variable(model, v[1:3, 1:100])
fix.(v[1, 51:100], 0)
fix.(v[1, 81:100], 0)

```

However,

- More variables are created than necessary, though the extra variables are `fix`ed to zero. Will these fixed variables still be treated as variables or replaced by 0 in JuMP?
- Is it appropriate to use [`SparseAxisArray`](https://jump.dev/JuMP.jl/stable/manual/variables/#variable_sparseaxisarrays)? Can we apply common array operations like `sum` to it?
- Is there any suggestion to improve efficiency by reducing the number of unnecessary variables?

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<div class="post-metadata">

**Author:** ![metab0t](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/metab0t/32/15551_2.png) [@metab0t](https://discourse.julialang.org/u/metab0t)\
**Post date:** [June 13, 2022, 11:13am UTC](https://discourse.julialang.org/t/jump-non-rectangular-variable-container-more-efficient-representation/82669/2 "2022-06-13T11:13:18Z")

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1. IIRC `fix` will not replace variables with constant because converting it to a constant is an irreversible operation, you cannot set its upper bound or lower bound afterwards.
2. `SparseAxisArray` behaves like a `SparseArray`. It is also an `AbstractArray` so `sum` should work as usual, but common index operation of dense array cannot be used (like v[1, :]). You can access all indices via `eachindex(v)`. It is closer to a `Dict{Index, Value}` where `index` is a N dimensional tuple.  
[Containers · JuMP](https://jump.dev/JuMP.jl/stable/manual/containers/) gives a clear comparison.
3. Use `SparseAxisArray` if your variables are really sparse, otherwise using `DenseAxisArray` then fixing variables is more convenient.  
If creating variables is not your bottleneck, do not worry about it before profiling. Most solvers will eliminate fixed variables at the presolve step so it will impact the solution time significantly.