# How to map JuMP VariableRef to NLPModelMeta indices?

**URL:** <https://discourse.julialang.org/t/how-to-map-jump-variableref-to-nlpmodelmeta-indices/38681>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [May 3, 2020, 3:38pm UTC](https://discourse.julialang.org/t/how-to-map-jump-variableref-to-nlpmodelmeta-indices/38681 "2020-05-03T15:38:54Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![nlaws](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nlaws/32/22205_2.png) [@nlaws](https://discourse.julialang.org/u/nlaws)\
**Post date:** [May 3, 2020, 3:38pm UTC](https://discourse.julialang.org/t/how-to-map-jump-variableref-to-nlpmodelmeta-indices/38681/1 "2020-05-03T15:38:54Z")

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I am developing a large scale bilevel problem (1M+ variables), and as a first step I am extracting the constraint coefficient matrix of the lower level linear program using NLPModelMeta (see [this post](https://discourse.julialang.org/t/how-do-i-extract-the-coefficients-and-rhss-of-all-constraints-in-a-jump-linear-program-need-for-kkt/38525)). Here is a simple example:

```julia
using JuMP
using NLPModels
using NLPModelsJuMP

model = Model()

@variable(model, x₂) # intentionally defining x₂ first
@variable(model, x₁ ≥ 0)

@objective(model, Min, 2x₁ + 4x₂)

@constraint(model, x₁ + 4x₂ ≥ 3)
@constraint(model, 3x₁ + 2x₂ == 14)

nlp = MathOptNLPModel(model)
x = zeros(nlp.meta.nvar)
A = Matrix(jac(nlp, x)
# ... more code deriving constraint coefficients and bounds vectors to create KKT conditions

```

```julia
julia> A
2×2 Array{Float64,2}:
 2.0 3.0
 4.0 1.0

```

In this example the entries of A and the constraints indicate that `x = [x₂; x₁] `, where `x₂` is in the first entry. From this I assume that `MathOptNLPModel` builds the meta data according to the order in which variables were added to the JuMP model (please correct me if I’m wrong!).

My question is this: **is there a way to track or map JuMP VariableRefs to the correct indices in the `MathOptNLPModel` meta data? (Other than tracking the order of variable definitions and their sizes).** For example, the meta data already includes helpful indices such as “indices of equality constraints” for `NLPModelMeta.jfix`. Is it possible to get the indices of `x₂`?

(Note that for this trivial example it is easy to determine which indices of the meta data map to the model variables. However, my case will contain millions of variables, some of them vectors of ~10,000 entries.)

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<div class="post-metadata">

**Author:** ![abelsiqueira](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/abelsiqueira/32/47269_2.png) [@abelsiqueira](https://discourse.julialang.org/u/abelsiqueira)\
**Post date:** [May 3, 2020, 7:47pm UTC](https://discourse.julialang.org/t/how-to-map-jump-variableref-to-nlpmodelmeta-indices/38681/2 "2020-05-03T19:47:01Z")

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I believe we follow the order of `all_variables(model)`. `all_variables` belong to either `JuMP` or `MOI`.  
@amontoison, can you confirm?

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<div class="post-metadata">

**Author:** ![amontoison](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/amontoison/32/218741_2.png) [@amontoison](https://discourse.julialang.org/u/amontoison)\
**Post date:** [May 4, 2020, 2:52am UTC](https://discourse.julialang.org/t/how-to-map-jump-variableref-to-nlpmodelmeta-indices/38681/3 "2020-05-04T02:52:07Z")

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Yes, you’re right Abel. @nlaws if you want to know the mapping between `VariableRefs` and indices in a `MathOptNLPModel` you just need that :  
`vr = all_variables(model)`  
`indices = [vr[i].index.value for i=1:length(vr)]`