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Add documentation on performance and work-around for sparse variable creation #2126

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Dec 29, 2019
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Add documentation on performance and work-around for sparse variable creation #2126

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c2e84a5
Add note on performance when creating sparse variables.
hellemo Dec 27, 2019
f8ef6c9
Fix typo.
hellemo Dec 28, 2019
61e87a5
Updated based on PR comments.
hellemo Dec 28, 2019
ccb5f94
Fix alignment
mlubin Dec 29, 2019
e3b0071
Wording and formatting changes
mlubin Dec 29, 2019
fcc93f6
The example is not a doctest, remove jldoctest
mlubin Dec 29, 2019
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6 changes: 6 additions & 0 deletions docs/src/variables.md
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Expand Up @@ -387,6 +387,12 @@ JuMP.Containers.SparseAxisArray{VariableRef,1,Tuple{Int64}} with 2 entries:
[2] = x[2]
```

Note that with many indices and large amount of sparcity, variable construction may take more time than expected, as JuMP is effectively iterating over all indices and evaluating the conditional for each combination. The recommended work-around in such cases is to work directly with a list of tuples. For example:
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sparcity -> sparsity

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Please follow the 80-character limit used in the rest of the documentation.

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"is effectively iterating" is unnecessarily imprecise, just "iterates"


```jldoctest; setup=:(model=Model())
S = [(1,1,1),(10,10,10)]
@variable(model, x[S])
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Could you make an example with both approach and then show that e.g. one has quadratic complexity and the other one has linear complexity? For instance with a condition i == j and n elements for i and j, it will be quadratic complexity vs linear complexity

```
### [Forcing the container type](@id variable_forcing)

When creating a container of JuMP variables, JuMP will attempt to choose the
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