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https://github.com/kalmarek/PropertyT.jl.git
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221 lines
5.6 KiB
Julia
221 lines
5.6 KiB
Julia
@testset "1703.09680 Examples" begin
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@testset "SL(2,Z)" begin
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N = 2
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G = MatrixGroups.SpecialLinearGroup{N}(Int8)
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RG, S, sizes = PropertyT.group_algebra(G; halfradius = 2)
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Δ = let RG = RG, S = S
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RG(length(S)) - sum(RG(s) for s in S)
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end
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elt = Δ^2
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unit = Δ
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ub = 0.1
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status, certified, λ = check_positivity(
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elt,
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unit;
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upper_bound = ub,
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halfradius = 2,
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optimizer = scs_optimizer(;
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eps = 1e-10,
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max_iters = 5_000,
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accel = 50,
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alpha = 1.9,
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),
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)
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@test status == JuMP.ALMOST_OPTIMAL
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@test !certified
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@test λ < 0
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end
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@testset "SL(3,F₅)" begin
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N = 3
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G = MatrixGroups.SpecialLinearGroup{N}(
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SymbolicWedderburn.Characters.FiniteFields.GF{5},
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)
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RG, S, sizes = PropertyT.group_algebra(G; halfradius = 2)
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Δ = let RG = RG, S = S
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RG(length(S)) - sum(RG(s) for s in S)
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end
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elt = Δ^2
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unit = Δ
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ub = 1.01 # 1.5
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status, certified, λ = check_positivity(
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elt,
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unit;
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upper_bound = ub,
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halfradius = 2,
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optimizer = scs_optimizer(;
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eps = 1e-10,
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max_iters = 5_000,
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accel = 50,
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alpha = 1.9,
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),
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)
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@test status == JuMP.OPTIMAL
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@test certified
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@test λ > 1
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m = PropertyT.sos_problem_dual(elt, unit)
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PropertyT.solve(
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m,
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cosmo_optimizer(;
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eps = 1e-6,
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max_iters = 5_000,
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accel = 50,
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alpha = 1.9,
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),
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)
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@test JuMP.termination_status(m) in (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
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@test JuMP.objective_value(m) ≈ 1.5 atol = 1e-2
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end
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@testset "SAut(F₂)" begin
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N = 2
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G = SpecialAutomorphismGroup(FreeGroup(N))
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RG, S, sizes = PropertyT.group_algebra(G; halfradius = 2)
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Δ = let RG = RG, S = S
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RG(length(S)) - sum(RG(s) for s in S)
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end
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elt = Δ^2
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unit = Δ
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ub = 0.1
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status, certified, λ = check_positivity(
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elt,
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unit;
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upper_bound = ub,
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halfradius = 2,
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optimizer = scs_optimizer(;
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eps = 1e-10,
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max_iters = 5_000,
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accel = 50,
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alpha = 1.9,
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),
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)
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@test status == JuMP.ALMOST_OPTIMAL
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@test λ < 0
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@test !certified
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@time sos_problem = PropertyT.sos_problem_primal(elt; upper_bound = ub)
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status, _ = PropertyT.solve(
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sos_problem,
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cosmo_optimizer(;
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eps = 1e-7,
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max_iters = 10_000,
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accel = 0,
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alpha = 1.9,
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),
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)
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@test status == JuMP.OPTIMAL
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P = JuMP.value.(sos_problem[:P])
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Q = real.(sqrt(P))
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certified, λ_cert =
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PropertyT.certify_solution(elt, zero(elt), 0.0, Q; halfradius = 2)
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@test !certified
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@test λ_cert < 0
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end
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@testset "SL(3,Z) has (T)" begin
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n = 3
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SL = MatrixGroups.SpecialLinearGroup{n}(Int8)
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RSL, S, sizes = PropertyT.group_algebra(SL; halfradius = 2)
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Δ = RSL(length(S)) - sum(RSL(s) for s in S)
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@testset "basic formulation" begin
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elt = Δ^2
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unit = Δ
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ub = 0.1
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opt_problem = PropertyT.sos_problem_primal(
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elt,
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unit;
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upper_bound = ub,
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augmented = false,
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)
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status, _ = PropertyT.solve(
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opt_problem,
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cosmo_optimizer(;
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eps = 1e-10,
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max_iters = 10_000,
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accel = 0,
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alpha = 1.5,
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),
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)
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@test status == JuMP.OPTIMAL
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λ = JuMP.value(opt_problem[:λ])
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@test λ > 0.09
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Q = real.(sqrt(JuMP.value.(opt_problem[:P])))
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certified, λ_cert = PropertyT.certify_solution(
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elt,
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unit,
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λ,
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Q;
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halfradius = 2,
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augmented = false,
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)
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@test certified
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@test isapprox(λ_cert, λ, rtol = 1e-5)
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end
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@testset "augmented formulation" begin
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elt = Δ^2
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unit = Δ
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ub = 0.20001 # Inf
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opt_problem = PropertyT.sos_problem_primal(
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elt,
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unit;
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upper_bound = ub,
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augmented = true,
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)
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status, _ = PropertyT.solve(
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opt_problem,
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scs_optimizer(;
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eps = 1e-10,
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max_iters = 10_000,
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accel = -10,
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alpha = 1.5,
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),
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)
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@test status == JuMP.OPTIMAL
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λ = JuMP.value(opt_problem[:λ])
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Q = real.(sqrt(JuMP.value.(opt_problem[:P])))
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certified, λ_cert = PropertyT.certify_solution(
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elt,
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unit,
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λ,
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Q;
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halfradius = 2,
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augmented = true,
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)
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@test certified
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@test isapprox(λ_cert, λ, rtol = 1e-5)
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@test λ_cert > 2 // 10
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end
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end
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end
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