mirror of
https://github.com/kalmarek/PropertyT.jl.git
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210 lines
5.7 KiB
Julia
210 lines
5.7 KiB
Julia
@testset "1712.07167 Examples" begin
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@testset "SAut(F₃)" begin
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N = 3
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G = SpecialAutomorphismGroup(FreeGroup(N))
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@info "running tests for" G
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RG, S, sizes = PropertyT.group_algebra(G; halfradius = 2)
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P = PG.PermGroup(PG.perm"(1,2)", PG.Perm(circshift(1:N, -1)))
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Σ = Groups.Constructions.WreathProduct(PG.PermGroup(PG.perm"(1,2)"), P)
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act = PropertyT.action_by_conjugation(G, Σ)
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wd = SW.WedderburnDecomposition(
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Float64,
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Σ,
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act,
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SA.basis(RG),
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SA.Basis{UInt16}(@view SA.basis(RG)[1:sizes[2]]),
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)
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@info wd
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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 = Inf
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status, certified, λ_cert = check_positivity(
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elt,
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unit,
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wd;
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upper_bound = ub,
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halfradius = 2,
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optimizer = cosmo_optimizer(;
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eps = 1e-7,
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max_iters = 10_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_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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@info "running tests for" SL
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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 "Wedderburn formulation" begin
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P = PG.PermGroup(PG.perm"(1,2)", PG.Perm(circshift(1:n, -1)))
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Σ = Groups.Constructions.WreathProduct(
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PG.PermGroup(PG.perm"(1,2)"),
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P,
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)
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act = PropertyT.action_by_conjugation(SL, Σ)
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wd = SW.WedderburnDecomposition(
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Rational{Int},
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Σ,
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act,
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SA.basis(RSL),
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SA.Basis{UInt16}(@view SA.basis(RSL)[1:sizes[2]]),
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)
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@info wd
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elt = Δ^2
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unit = Δ
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ub = 0.2801
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@test_throws ErrorException 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 = ub,
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augmented = false,
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)
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wdfl = SW.WedderburnDecomposition(
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Float64,
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Σ,
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act,
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SA.basis(RSL),
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SA.Basis{UInt16}(@view SA.basis(RSL)[1:sizes[2]]),
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)
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model, varP = PropertyT.sos_problem_primal(
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elt,
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unit,
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wdfl;
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upper_bound = ub,
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augmented = false,
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)
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status, warm = PropertyT.solve(
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model,
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cosmo_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 = 1.9,
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),
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)
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@test status == JuMP.OPTIMAL
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status, _ = 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 = 100,
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accel = -20,
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alpha = 1.2,
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),
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warm,
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)
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@test status == JuMP.OPTIMAL
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Q = @time let varP = varP
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Qs = map(varP) do P
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return real.(sqrt(JuMP.value.(P)))
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end
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PropertyT.reconstruct(Qs, wdfl)
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end
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λ = JuMP.value(model[:λ])
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sos = PropertyT.compute_sos(parent(elt), Q; augmented = false)
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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 λ_cert >= 28 // 100
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end
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@testset "augmented Wedderburn formulation" begin
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elt = Δ^2
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unit = Δ
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ub = Inf
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P = PG.PermGroup(PG.perm"(1,2)", PG.Perm(circshift(1:n, -1)))
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Σ = Groups.Constructions.WreathProduct(
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PG.PermGroup(PG.perm"(1,2)"),
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P,
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)
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act = PropertyT.action_by_conjugation(SL, Σ)
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wdfl = SW.WedderburnDecomposition(
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Float64,
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Σ,
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act,
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SA.basis(RSL),
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SA.Basis{UInt16}(@view SA.basis(RSL)[1:sizes[2]]),
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)
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@info wdfl
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opt_problem, varP = PropertyT.sos_problem_primal(
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elt,
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unit,
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wdfl;
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upper_bound = ub,
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# augmented = true # since both elt and unit are augmented
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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-8,
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max_iters = 20_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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Q = @time let varP = varP
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Qs = map(varP) do P
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return real.(sqrt(JuMP.value.(P)))
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end
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PropertyT.reconstruct(Qs, wdfl)
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end
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certified, λ_cert = PropertyT.certify_solution(
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elt,
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unit,
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JuMP.objective_value(opt_problem),
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Q;
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halfradius = 2,
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# augmented = true # since both elt and unit are augmented
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)
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@test certified
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@test λ_cert > 28 // 100
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end
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end
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end
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