# Iterating through a continuous decision variable and retrieving its values

**URL:** <https://discourse.julialang.org/t/iterating-through-a-continuous-decision-variable-and-retrieving-its-values/124412>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [January 3, 2025, 2:04pm UTC](https://discourse.julialang.org/t/iterating-through-a-continuous-decision-variable-and-retrieving-its-values/124412 "2025-01-03T14:04:46Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![rolim.gustavo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rolim.gustavo/32/46941_2.png) [@rolim.gustavo](https://discourse.julialang.org/u/rolim.gustavo)\
**Post date:** [January 3, 2025, 2:04pm UTC](https://discourse.julialang.org/t/iterating-through-a-continuous-decision-variable-and-retrieving-its-values/124412/1 "2025-01-03T14:04:46Z")

</div>

Dear colleagues,

I am implementing a branch-and-check procedure in JuMP that requires to extract some variable values. For instance, I have to retrieve the values of decision variable X, that is defined as follows:

```julia
@variable(Master, 0 <= X[i in 1:m, j in 1:n+1, k in 1:n+1; j != k] <= 1)

```

After optimizing the Master model, this can be easily obtained:

```julia
XM = value.(Master[:X])

```

I pass XM as the argument of a function and i need to multiply its values by a certain amount :

```julia
function Master_Machine_Makespan(XM::JuMP.Containers.SparseAxisArray{Float64, 3, Tuple{Int64, Int64, Int64}},
    YM::Matrix{Float64}, m::Int8, n::Int16, p::Matrix{Int16}, s::Vector{Matrix{Int16}})
    #----- Calculate and return the makespan of each machine of the master problem

    rlx_Cmax = zeros(Float64, m)

    #----- Compute the sum of setup times of each machine

    for i in eachindex(XM)
        for j in eachindex(XM[i])
            for k in eachindex(XM[i][j])
                rlx_Cmax[i] += s[i][j, k] * XM[i][j][k]
            end
        end
    end

    return rlx_Cmax
end

```

If I use:

```julia
typeof(XM[i][j][k])

```

Julia returns me a variable of type Float64, however, I am getting the error message:  
LoadError: ArgumentError: invalid index: (1, 1, 2) of type Tuple{Int64, Int64, Int64}

Anyone knows a way to fix this? I would really appreciate your help 🙂

---

<div class="post-metadata">

**Author:** ![kellertuer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kellertuer/32/220707_2.png) [@kellertuer](https://discourse.julialang.org/u/kellertuer)\
**Post date:** [January 3, 2025, 2:23pm UTC](https://discourse.julialang.org/t/iterating-through-a-continuous-decision-variable-and-retrieving-its-values/124412/2 "2025-01-03T14:23:02Z")

</div>

Without running your example it might be a bit hard to narrow down. From the error message I would maybe assume that

```julia
for i in eachindex(XM)

```

already iterates over all three dimensions of `XM` in form of tuples? could you maybe `@show` or `println` the `I`, maybe for completeness also `j` and `k`?

Similar question, are `I,j,k` in the `typeof` the same as in the for loops or indices you choose yourself? or in other words: What is `typeof(XM)`?

---

<div class="post-metadata">

**Author:** ![rolim.gustavo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rolim.gustavo/32/46941_2.png) [@rolim.gustavo](https://discourse.julialang.org/u/rolim.gustavo)\
**Post date:** [January 3, 2025, 2:36pm UTC](https://discourse.julialang.org/t/iterating-through-a-continuous-decision-variable-and-retrieving-its-values/124412/3 "2025-01-03T14:36:05Z")

</div>

After running:

```julia
    for i in eachindex(XM)
        for j in eachindex(XM[i])
            for k in eachindex(XM[i][j])
                println("i: $i, j: $j, k: $k")
            end
        end
    end

```

I get something like this:

i: (1, 1, 2), j: 1, k: 1  
i: (1, 1, 3), j: 1, k: 1  
i: (1, 1, 4), j: 1, k: 1  
i: (1, 1, 5), j: 1, k: 1  
i: (1, 1, 6), j: 1, k: 1  
i: (1, 1, 7), j: 1, k: 1  
i: (1, 2, 1), j: 1, k: 1  
i: (1, 2, 3), j: 1, k: 1  
i: (1, 2, 4), j: 1, k: 1 (…)

It seems that `i` refers to Tuple indices and, perhaps, I do not need `j` and `k`. Typeof(XM) returns:

```julia
JuMP.Containers.SparseAxisArray{Float64, 3, Tuple{Int64, Int64, Int64}}

```

---

<div class="post-metadata">

**Author:** ![kellertuer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kellertuer/32/220707_2.png) [@kellertuer](https://discourse.julialang.org/u/kellertuer)\
**Post date:** [January 3, 2025, 3:05pm UTC](https://discourse.julialang.org/t/iterating-through-a-continuous-decision-variable-and-retrieving-its-values/124412/4 "2025-01-03T15:05:53Z")

</div>

I would guess then `XM[i...]` should work fine for addressing that one and you can have `j=i[2]` and `k=i[2]`?

The type indicates `XM` is a 3-dimensional array and then `i`already iterates over all enrties.

_edit:_ ah I See, in your original code `j,k` are always just `1` anyways since `XM[i]` is a number already, and for `k` the `[1]` the `j` does is maybe ignored? Without running the code myself this is a bit Moree guesswork that actual debugging, but I hope that helps.

---

<div class="post-metadata">

**Author:** ![rolim.gustavo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rolim.gustavo/32/46941_2.png) [@rolim.gustavo](https://discourse.julialang.org/u/rolim.gustavo)\
**Post date:** [January 3, 2025, 5:29pm UTC](https://discourse.julialang.org/t/iterating-through-a-continuous-decision-variable-and-retrieving-its-values/124412/5 "2025-01-03T17:29:45Z")

</div>

It seems that SparseAxisArray in Julia should be iterated using eachindex(). The following loop worked fine:

```julia
    for (i, j, k) in eachindex(XM)
        rlx_Cmax[i] += s[i][j, k] * XM[i, j, k]
    end

```

Best wishes,