# Multi-dimensional array of tuples

**URL:** <https://discourse.julialang.org/t/multi-dimensional-array-of-tuples/83288>\
**Category:** Optimization (Mathematical)\
**Tags:** question\
**Created:** [June 24, 2022, 2:31am UTC](https://discourse.julialang.org/t/multi-dimensional-array-of-tuples/83288 "2022-06-24T02:31:54Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![pqdmac](https://avatars.discourse-cdn.com/v4/letter/p/9f8e36/32.png) [@pqdmac](https://discourse.julialang.org/u/pqdmac)\
**Post date:** [June 24, 2022, 2:31am UTC](https://discourse.julialang.org/t/multi-dimensional-array-of-tuples/83288/1 "2022-06-24T02:31:54Z")

</div>

I am working in an combinatorial optimization problem (multiple vehicle routing with profits) where I have a binary variable ` x[i,j,p]` representing an edge ` (i,j)` traversed by a vehicle `p`. I would like to get a p-dimensional array of tuples ` (i,j)` regarding each path ‘p’ when ` value.(x[i,j,p])=1` . I am using JuMP package.  
To a better understanding: `1:n` is the set of nodes and `L` is a subset of `1:n`  
I am trying this block of code inside another loop because I am reoptimizing sevral times:

```julia
g1 = Tuple{Int,Int}[]
    g2 = Tuple{Int,Int}[]
    for p in 1:P
        if p == 1
            append!(g1, (i,j) for i in 1:n, j in 1:n if (i in L || j in L) && (value.(x[i, j, p]) >= a) && (i!=1 && j!=n))
        else
            append!(g2, (i,j) for i in 1:n, j in 1:n if (i in L || j in L) && (value.(x[i, j, p]) >= a) && (i!=1 && j!=n))
        end
    end

```

And I get, for example:

```julia
g1 = [(7, 11), (11, 16), (16, 22)]
g2 = [(8, 12), (12, 17)]

```

However, I would like to have something like this, if ` p=2` :

```julia
g = [[(7, 11), (11, 16), (16, 22)], [(8, 12), (12, 17)]]

```

and a more general and efficient code taking accounting different values of ` p` . I would appreciate if someone could help me with this.

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**Author:** ![jd-foster](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jd-foster/32/35824_2.png) [@jd-foster](https://discourse.julialang.org/u/jd-foster)\
**Post date:** [June 24, 2022, 3:34am UTC](https://discourse.julialang.org/t/multi-dimensional-array-of-tuples/83288/2 "2022-06-24T03:34:59Z")

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Welcome. A good start is often write things as a functions:

```julia
tuple_match(n,L,x,a,p) = [(i,j) for i in 2:n, j in 1:(n-1) if (i in L || j in L) && (value(x[i, j, p]) >= a)]

```

or a more general version would be

```julia
tuple_match(S1,S2,L,x,a,p) = [(i,j) for i in S1, j in S2 if (i in L || j in L) && (value(x[i, j, p]) >= a)]

```

where `S1 = 2:n` and `S2 = 1:(n-1)` etc. in your code.

Here I’m using [Comprehensions](https://docs.julialang.org/en/v1/manual/arrays/#man-comprehensions).

Then you could write, for given values of `n, L, x, a` ,

```julia
g = [tuple_match(n, L, x, a, p) for p in 1:P]

```

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<div class="post-metadata">

**Author:** ![pqdmac](https://avatars.discourse-cdn.com/v4/letter/p/9f8e36/32.png) [@pqdmac](https://discourse.julialang.org/u/pqdmac)\
**Post date:** [June 24, 2022, 7:26pm UTC](https://discourse.julialang.org/t/multi-dimensional-array-of-tuples/83288/3 "2022-06-24T19:26:30Z")

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Thank you so much, @jd-foster! It worked perfectly!