This package is based on the work in the following publication:
M. Korda, M. Laurent, V. Magron, and A. Steenkamp. Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks. Mathematical Programming, 2023. https://doi.org/10.1007/s10107-023-01993-x
This code models the problem of bounding the completely positive rank of a symmetric nonnegative matrix via moment hierarchies.
- Test.jl
- JuMP.jl
- MosekTools.jl
- LinearAlgebra.jl
- Graphs.jl
- Random.jl
- DataFrames.jl
- CSV.jl
- TypedPolynomials.jl
- MultivariateMoments.jl
- HomotopyContinuation.jl
# Define the matrix of interest.
M = [1.0 0.707107 0.0 0.0 0.447214
0.707107 1.0 0.408248 0.0 0.0
0.0 0.408248 1.0 0.288675 0.0
0.0 0.0 0.288675 1.0 0.223607
0.447214 0.0 0.0 0.223607 1.0]
# set the level of the hierarchy
lvl = 1
# choose which constraitns to inclued (see the publication)
cons = join(["G","dag","ddag","xx"][[1,2,4]],"")
# choose from the three main hierarchies (see the publication)
hier = ["id", "sp", "wsp"][2]
# Define the model and run the optimization
ξₜᶜᵖⁱᵈ , _ = cp_model.get_ξₜᶜᵖ(M,lvl,hier*cons);
# Inspect the resutls in the terminal mom_dir = assets_dir*"results\\lit\\t2\\moments\\"
mom_dir_list = [c for c in readdir(mom_dir) if contains(c,"id")]
mom_path = mom_dir*mom_dir_list[1]
df_id = matrix_IO.load_moments(mom_path)
include(src_dir*"extract_atoms.jl")
n_id, t_id, mom_vals_id = extract_atoms.proc_mom(df_id)
ext_atoms_id = extract_atoms.get_atoms(n_id, t_id, mom_vals_id, 1e-4, true)
cents_id, weights_id = extract_atoms.ext_centers_weights(ext_atoms_id)
A_ext_id = extract_atoms.recon_mat(cents_id, weights_id)