Sparse Ensemble Kalman Inversion

SparseInversion <: Process

A sparse ensemble Kalman Inversion process

Fields

• γ::AbstractFloat: upper limit of l1-norm

• threshold_value::AbstractFloat: threshold below which the norm of parameters is pruned to zero

• uc_idx::Union{Colon, AbstractVector}: indices of parameters included in the evaluation of l1-norm constraint

• reg::AbstractFloat: a small regularization value to enhance robustness of convex optimization

Constructors

SparseInversion(; γ, threshold_value, uc_idx, reg)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/SparseEnsembleKalmanInversion.jl:20.

SparseInversion(γ, threshold_value, uc_idx, reg)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/SparseEnsembleKalmanInversion.jl:21.

SparseInversion(γ; threshold_value, uc_idx, reg)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/SparseEnsembleKalmanInversion.jl:31.

 sparse_eki_update(
    ekp::EnsembleKalmanProcess{FT, IT, SparseInversion{FT}},
    u::AbstractMatrix{FT},
    g::AbstractMatrix{FT},
    y::AbstractMatrix{FT},
    obs_noise_cov::Union{AbstractMatrix{CT}, UniformScaling{CT}},
) where {FT <: Real, CT <: Real, IT}

Returns the sparse updated parameter vectors given their current values and the corresponding forward model evaluations, using the inversion algorithm from eqns. (3.7) and (3.14) of Schneider et al. (2021).

Localization is applied following Tong and Morzfeld (2022).

sparse_qp(
    ekp::EnsembleKalmanProcess{FT, IT, SparseInversion{FT}},
    v_j::Vector{FT},
    cov_vv_inv::AbstractMatrix{FT},
    H_u::SparseArrays.SparseMatrixCSC{FT},
    H_g::SparseArrays.SparseMatrixCSC{FT},
    y_j::Vector{FT};
    H_uc::SparseArrays.SparseMatrixCSC{FT} = H_u,
) where {FT, IT}

Solving quadratic programming problem with sparsity constraint.