using Random, NExOS, ProximalOperators, LinearAlgebra

Random.seed!(1234)

m = 10

n = 2*m

M = 1.0

k = convert(Int64, m*n/20)

r = convert(Int64,round(m*.35))

barA = randn(k, m*n)

b = randn(k)

Z0 = zeros(m,n);

f = LeastSquaresOverMatrix(barA, b, 1.0, iterative = true);

C = RankSet(M, r)

settings = Settings(μ_max = 2, μ_mult_fact = 0.5, verbose = false, freq = 500, γ_updt_rule = :safe)

problem = Problem(f, C, settings.β, Z0)

state_final = solve!(problem, settings)

f(state_final.x)

log10(state_final.fxd_pnt_gap) <= -4

log10(state_final.fsblt_gap) <= -4