101 lines
2.6 KiB
Julia
101 lines
2.6 KiB
Julia
using LinearAlgebra
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BLAS.set_num_threads(4)
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ENV["OMP_NUM_THREADS"] = 4
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include(joinpath(@__DIR__, "../test/optimizers.jl"))
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using SCS_MKL_jll
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using Groups
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import Groups.MatrixGroups
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using PropertyT
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import PropertyT.SW as SW
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using PropertyT.PG
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using PropertyT.SA
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include(joinpath(@__DIR__, "argparse.jl"))
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const N = parsed_args["N"]
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const HALFRADIUS = parsed_args["halfradius"]
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const UPPER_BOUND = parsed_args["upper_bound"]
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G = SpecialAutomorphismGroup(FreeGroup(N))
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@info "Running Δ² - λ·Δ sum of squares decomposition for " G
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@info "computing group algebra structure"
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RG, S, sizes = @time PropertyT.group_algebra(G, halfradius = HALFRADIUS)
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@info "computing WedderburnDecomposition"
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wd = let RG = RG, N = N
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G = StarAlgebras.object(RG)
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P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
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Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
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act = PropertyT.action_by_conjugation(G, Σ)
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wdfl = @time SW.WedderburnDecomposition(
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Float64,
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Σ,
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act,
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basis(RG),
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StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
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)
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end
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@info wd
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Δ = RG(length(S)) - sum(RG(s) for s in S)
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elt = Δ^2;
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unit = Δ;
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warm = nothing
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@info "defining optimization problem"
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@time model, varP = PropertyT.sos_problem_primal(
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elt,
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unit,
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wd;
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upper_bound = UPPER_BOUND,
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augmented = true,
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show_progress = true,
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)
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let status = JuMP.OPTIMIZE_NOT_CALLED, warm = warm, eps = 1e-10
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certified, λ = false, 0.0
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while status ≠ JuMP.OPTIMAL
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@time status, warm = PropertyT.solve(
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model,
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scs_optimizer(;
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linear_solver = SCS.MKLDirectSolver,
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eps = eps,
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max_iters = N * 10_000,
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accel = 50,
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alpha = 1.95,
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),
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warm,
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)
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@info "reconstructing the solution"
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Q = @time let wd = wd, Ps = [JuMP.value.(P) for P in varP], eps = 1e-10
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PropertyT.__droptol!.(Ps, 100eps)
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Qs = real.(sqrt.(Ps))
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PropertyT.__droptol!.(Qs, eps)
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PropertyT.reconstruct(Qs, wd)
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end
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@info "certifying the solution"
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certified, λ = PropertyT.certify_solution(
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elt,
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unit,
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JuMP.objective_value(model),
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Q;
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halfradius = HALFRADIUS,
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augmented = true,
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)
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end
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if certified && λ > 0
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Κ(λ, S) = round(sqrt(2λ / length(S)), Base.RoundDown; digits = 5)
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@info "Certified result: $G has property (T):" N λ Κ(λ, S)
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else
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@info "Could NOT certify the result:" certified λ
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end
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end
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