# DenseAxisArray in JuMP

**URL:** <https://discourse.julialang.org/t/denseaxisarray-in-jump/129258>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [May 23, 2025, 12:48am UTC](https://discourse.julialang.org/t/denseaxisarray-in-jump/129258 "2025-05-23T00:48:19Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [May 23, 2025, 12:48am UTC](https://discourse.julialang.org/t/denseaxisarray-in-jump/129258/1 "2025-05-23T00:48:19Z")

</div>

I wonder why is the `y` below so complicated, unlike `x`.

```julia
julia> using JuMP

julia> model = Model();

julia> @variable(model, x[1:3]); x
3-element Vector{VariableRef}:
 x[1]
 x[2]
 x[3]

julia> R = 1:3
1:3

julia> @variable(model, y[R]); y
1-dimensional DenseAxisArray{VariableRef,1,...} with index sets:
    Dimension 1, 1:3
And data, a 3-element Vector{VariableRef}:
 y[1]
 y[2]
 y[3]

julia> typeof(y)
JuMP.Containers.DenseAxisArray{VariableRef, 1, Tuple{UnitRange{Int64}}, Tuple{JuMP.Containers._AxisLookup{Tuple{Int64, Int64}}}}

```

Moreover, if I want an `x`-like outcome for `y`, what code should I write?  
Maybe something like `@variable(model, y[$R])`? (is there a correct style?)

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [May 23, 2025, 2:24am UTC](https://discourse.julialang.org/t/denseaxisarray-in-jump/129258/2 "2025-05-23T02:24:04Z")

</div>

See [Variables · JuMP](https://jump.dev/JuMP.jl/stable/manual/variables/#variable_forcing)

---

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [June 3, 2025, 7:37am UTC](https://discourse.julialang.org/t/denseaxisarray-in-jump/129258/3 "2025-06-03T07:37:29Z")

</div>

Reuse this topic to ask a new question—as follows—why can’t I do this

```julia
julia> using JuMP

julia> model = Model();

julia> c = @constraint(model, [i in [2]], 0 == 1);

julia> delete.(model, c)
1-dimensional DenseAxisArray{Nothing,1,...} with index sets:
    Dimension 1, [2]
And data, a 1-element Vector{Nothing}:
 nothing

julia> c .= @constraint(model, [i in [2]], 0 == 2) # `.=` reuses the container `c`
ERROR: DenseAxisArray does not support this operation.
Stacktrace:
  [1] error(s::String)
    @ Base .\error.jl:35
  [2] LinearIndices(::JuMP.Containers.DenseAxisArray{ConstraintRef{…}, 1, Tuple{…}, Tuple{…}})
    @ JuMP.Containers K:\judepot1115\packages\JuMP\RGIK3\src\Containers\DenseAxisArray.jl:304
  [3] copyto_unaliased!
    @ .\abstractarray.jl:1072 [inlined]
  [4] copyto!
    @ .\abstractarray.jl:1061 [inlined]
  [5] copyto!
    @ .\broadcast.jl:966 [inlined]
  [6] copyto!
    @ .\broadcast.jl:925 [inlined]
  [7] materialize!
    @ .\broadcast.jl:883 [inlined]
  [8] materialize!
    @ .\broadcast.jl:880 [inlined]
  [9] materialize!(dest::JuMP.Containers.DenseAxisArray{…}, x::JuMP.Containers.DenseAxisArray{…})
    @ Base.Broadcast .\broadcast.jl:876
 [10] top-level scope
    @ REPL[5]:1
Some type information was truncated. Use `show(err)` to see complete types.

```

---

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [June 3, 2025, 8:13am UTC](https://discourse.julialang.org/t/denseaxisarray-in-jump/129258/4 "2025-06-03T08:13:48Z")

</div>

(So this is perhaps the reason why we should only use normal Arrays in JuMP.)

And a further question is, is there a more efficient in-place method that refill a container with new constraints (without allocating new container)?

```julia
julia> c = @constraint(model, [i in 1:3], 0 == 1);

julia> delete.(model, c);

julia> c
3-element Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}, ScalarShape}}:
 InvalidConstraintRef
 InvalidConstraintRef
 InvalidConstraintRef

julia> c .= @constraint(model, [i in 1:3], 0 == 2) # What is the most efficient way to do this?
3-element Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}, ScalarShape}}:
 0 == 2
 0 == 2
 0 == 2

```

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [June 3, 2025, 8:32am UTC](https://discourse.julialang.org/t/denseaxisarray-in-jump/129258/5 "2025-06-03T08:32:41Z")

</div>

Why would you want to do that?

This is another Julia interface issue: the set of methods to implement to support all possible behaviors is not well defined. In this case, we’re just missing some methods. But I’m also not really sure I want to support this.

---

<div class="post-metadata">

**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [June 3, 2025, 8:35am UTC](https://discourse.julialang.org/t/denseaxisarray-in-jump/129258/6 "2025-06-03T08:35:46Z")

</div>

> [@odow](#):
>
> But I’m also not really sure I want to support this

I think needless. ~~Basic julia Array for containing variables and constraints are enough. We don’t need Dense or SparseAxisArray, they are hard to use~~ Although they are not supported well, they can be used sometimes with minor modification, e.g.

```julia
julia> model = JuMP.Model(); v = [4, 2];

julia> JuMP.@variable(model, x[s = 1:2, c = 1:v[s]]);

julia> x[2, :]
JuMP.Containers.SparseAxisArray{JuMP.VariableRef, 1, Tuple{Int64}} with 2 entries:
  [1] = x[2,1]
  [2] = x[2,2]

julia> ans' # ERROR: `Base.size` is not implemented

julia> [i for i in x[2, :]]
2-element Vector{JuMP.VariableRef}:
 x[2,1]
 x[2,2]

julia> ans'
1×2 adjoint(::Vector{JuMP.VariableRef}) with eltype JuMP.VariableRef:
 x[2,1] x[2,2]

```