Fix *(::AbstractJuMPScalar{<:Real}, ::Hermitian) to return Hermitian

[odow]

Closes #3694

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Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 98.35%. Comparing base (a9b5ff9) to head (9b0eaee).

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #3695 +/- ## ========================================== - Coverage 98.36% 98.35% -0.02% ========================================== Files 43 43 Lines 5699 5707 +8 ========================================== + Hits 5606 5613 +7 - Misses 93 94 +1 ```

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[araujoms]

Could you also do the Symmetric case? It's actually much easier because you don't need to test whether the scalar is real.

[odow]

This one we can fix in MA: https://github.com/jump-dev/MutableArithmetics.jl/pull/268

[araujoms]

I've just realized that with this definition of multiplication you are generating hidden undefs in the lower triangular, that is, you are relying on the bug JuliaLang/julia#52895 being fixed, which I think is only the case for Julia 1.11 onwards. So the following code will fail for all previous version of Julia:

using JuMP
prob = Model()
@variable(prob,x)
m = x*LinearAlgebra.Hermitian(randn(2,2))
m+m

[odow]

Perhaps we should close this then. The currently behavior is correct. The new PR would introduce the risk of incorrect behavior due to bugs in Base.

If JuMP generates a Matrix, you can always explicitly wrap it in Hermitian.

It's really hard to uniformly support all of LinearAlgebra, SparseArrays, MutableArithmetics, and JuMP.

[araujoms]

Or you could just return instead

LinearAlgebra.Hermitian(Matrix(LinearAlgebra.Hermitian(B, c)),c)

This gets rids of the undefs, so no bugs are possible, you keep the performance gain, and don't require the users to always rewrap everything in Hermitian.

[araujoms]

Thanks a lot for solving all of the problems I pointed out! I'm always amazed by how quick you and @blegat are.

[odow]

No problem. A lot of the problems are because you might be the only person actively using JuMP for complex Hermitian stuff... 😆

[araujoms]

Well, one might say only, but I'd rather say first. :wink:

There are also these guys, but they invented their own reformulation of the complex Hermitian PSD cone, so they are only using JuMP for the real one.

[odow]

There are also these guys

You might recognize an author

[araujoms]

Well, I know some of them personally, but there is one that I'm sure you do. :laughing: