90 lines
2.6 KiB
Julia
90 lines
2.6 KiB
Julia
@testset "Quick tests" begin
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@testset "SL(2,F₇)" begin
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N = 2
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p = 7
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halfradius = 3
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G = MatrixGroups.SpecialLinearGroup{N}(
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SW.Characters.FiniteFields.GF{p},
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)
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RG, S, sizes = PropertyT.group_algebra(G; halfradius = 3)
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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 = 0.58578# Inf# 1.5
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@testset "standard formulation" begin
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status, certified, λ_cert = 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-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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@test certified
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@test λ_cert > 5857 // 10000
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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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scs_optimizer(;
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eps = 1e-8,
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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 JuMP.termination_status(m) in
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(JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
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@test JuMP.objective_value(m) ≈
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PropertyT.IntervalArithmetic.mid(λ_cert) atol = 1e-2
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end
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@testset "Wedderburn decomposition" 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(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[halfradius]]),
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)
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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 = scs_optimizer(;
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eps = 1e-8,
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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 > 5857 // 10000
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end
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end
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end
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