[WIP] Add implementation of sparse EKI

[jinlong83]

This PR adds the option of sparse EKI to Ensemble Kalman Inversion process:

• Added the option of sparse EKI to EnsembleKalmanInversion.jl
• Added an example (LossMinimization/loss_minimization_sparse_eki.jl)

[odunbar]

Hi Jinlong, the way we have been adding different methods is by keeping them separated rather than using flags. As the sparsity preserving EKI is sufficiently different from EKI maybe we could do it in this case. (You can use the Sampler type as a guide (in EnsembleKalmanSampler.jl))

Could you create a new file SparseEnsembleKalmanInversion.jl and inside you can add

• a Type called SparseInversion which takes in all the "Sparse method only" parameters
• an update_ensemble(ekp::EnsembleKalmanProcess{FT, IT, SparseInversion{FT}}, ...) method where you put in the sparse update

We can call to chat more about this

[odunbar]

Note I got this to run by first

conda install -c conda-forge cvxopt

and then in the project base

julia --project
]
add CVXOPT

then in the example directory

julia --project loss_minimization_sparse.jl

[ilopezgp]

Is there a way to implement the Sparse EKI without PyCall? Python dependencies are a headache, and should be avoided if we can. This might be useful: https://jump.dev/Convex.jl/stable/

[jinlong83]

Is there a way to implement the Sparse EKI without PyCall? Python dependencies are a headache, and should be avoided if we can. This might be useful: https://jump.dev/Convex.jl/stable/

I have updated the implementation to avoid PyCall. It seems that Convex.jl is slightly less stable than CVXOPT, so I also updated the default settings of sparse EKI parameters in the example.

[odunbar]

I forgot to mention the unit tests. Your code is untested

Could you transfer the sparse example you created, and place it in the file test/EnsembleKalmanProcessModule/runtests.jl (remove all the literate comments etc)

inside you then add some@test statements - which are like fancy asserts. You can use the the EnsembleKalmanInversion testing done in the file as aguide, (and maybe add something to test the sparsity property?)

To checkthe testing offline you go to the base and do

julia --project
using Test
include("test/runtests.jl")

[odunbar]

Excellent addition. LGTM

Please add a check for the L^1 norm in the sparse eki loop.

If you could create a docs PR soon, that adds a page linking to your paper / what the sparsity means in this context etc. that would be awesome.

[ilopezgp]

After my Threads.@threads question has been addressed by someone more experienced with Julia, LGTM.

[jakebolewski]

bors r+

[bors]

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