# How to define an array of variables in JuMP that has different lengths in different dimensions
**URL:** https://discourse.julialang.org/t/how-to-define-an-array-of-variables-in-jump-that-has-different-lengths-in-different-dimensions/89598
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [November 1, 2022, 4:48am UTC](https://discourse.julialang.org/t/how-to-define-an-array-of-variables-in-jump-that-has-different-lengths-in-different-dimensions/89598 "2022-11-01T04:48:25Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@Alex\_ricci](https://discourse.julialang.org/u/Alex_ricci)
#### Post date: [November 1, 2022, 4:48am UTC](https://discourse.julialang.org/t/how-to-define-an-array-of-variables-in-jump-that-has-different-lengths-in-different-dimensions/89598/1 "2022-11-01T04:48:25Z")
I have a parameter called z\_{t, w} with the size of 2 \times 2 which is a vector of vectors.
For example, z\_{1,1} and z\_{2,1} are
```julia
z[1,1] = [10 10 30 40 50]
z[2,1] = [20 30 40]
```
I want to define a variable y based on z. The first two indices of y and z are the same. However, y has one extra index which is defined based on the length corresponding z element.
since the `length(z[1,1]) = 5` and `length(z[2,1]) = 3`,
Therefore, we should have
```julia
y[1,1,:] =
y[1,1,1]
y[1,1,2]
y[1,1,3]
y[1,1,4]
y[1,1,5]
```
and
```julia
y[2,1,:] =
y[2,1,1]
y[2,1,2]
y[2,1,3]
```
Is it possible to define such a variable in Julia using the JuMP package?
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [November 1, 2022, 6:43am UTC](https://discourse.julialang.org/t/how-to-define-an-array-of-variables-in-jump-that-has-different-lengths-in-different-dimensions/89598/2 "2022-11-01T06:43:44Z")
```julia
@variable(model, y[i=1:2, j=1:2, k=1:length(z[i, j])])
```
Documentation: [Variables ยท JuMP](https://jump.dev/JuMP.jl/stable/manual/variables/#variable_sparseaxisarrays)