99 lines
2.3 KiB
Julia
99 lines
2.3 KiB
Julia
using LinearAlgebra
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BLAS.set_num_threads(8)
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ENV["OMP_NUM_THREADS"] = 4
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using Groups
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import Groups.MatrixGroups
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include(joinpath(@__DIR__, "../test/optimizers.jl"))
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using PropertyT
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using PropertyT.SymbolicWedderburn
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using PropertyT.PermutationGroups
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using PropertyT.StarAlgebras
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include(joinpath(@__DIR__, "argparse.jl"))
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include(joinpath(@__DIR__, "utils.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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include(joinpath(@__DIR__, "./G₂_gens.jl"))
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G, roots, Weyl = G₂_roots_weyl()
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@info "Running Δ² - λ·Δ sum of squares decomposition for G₂"
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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 Σ = Weyl, RG = RG
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act = PropertyT.AlphabetPermutation{eltype(Σ),Int64}(
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Dict(g => PermutationGroups.perm(g) for g in Σ),
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)
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@time SymbolicWedderburn.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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semisimple = false,
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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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@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 = false,
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)
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warm = nothing
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status = JuMP.OPTIMIZE_NOT_CALLED
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certified, λ = false, nothing
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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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eps = 1e-10,
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max_iters = 20_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]
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Qs = real.(sqrt.(Ps))
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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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@time 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: G₂ 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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