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https://github.com/kalmarek/PropertyT.jl.git
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update and reformat tests
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@ -1,9 +1,8 @@
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@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, twisted=true)
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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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@ -15,15 +14,15 @@
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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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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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@ -33,8 +32,10 @@
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@testset "SL(3,F₅)" begin
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N = 3
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G = MatrixGroups.SpecialLinearGroup{N}(SymbolicWedderburn.Characters.FiniteFields.GF{5})
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RG, S, sizes = PropertyT.group_algebra(G, halfradius=2, twisted=true)
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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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@ -46,15 +47,15 @@
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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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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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@ -62,12 +63,15 @@
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@test λ > 1
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m = PropertyT.sos_problem_dual(elt, unit)
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PropertyT.solve(m, 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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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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@ -76,7 +80,7 @@
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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, twisted=true)
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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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@ -88,53 +92,46 @@
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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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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 =
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PropertyT.sos_problem_primal(elt, upper_bound=ub)
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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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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 = PropertyT.certify_solution(
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elt,
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zero(elt),
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0.0,
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Q,
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halfradius=2,
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)
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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, twisted=true)
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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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@ -145,18 +142,18 @@
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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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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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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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@ -170,13 +167,13 @@
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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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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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@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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@ -186,18 +183,18 @@
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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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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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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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@ -210,13 +207,13 @@
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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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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 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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@ -1,9 +1,9 @@
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@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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RG, S, sizes = PropertyT.group_algebra(G, halfradius=2, twisted=true)
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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 = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
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Σ = PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
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@ -15,6 +15,7 @@
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basis(RG),
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StarAlgebras.Basis{UInt16}(@view 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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@ -27,14 +28,14 @@
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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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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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@ -47,7 +48,8 @@
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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, twisted=true)
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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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@ -62,6 +64,7 @@
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basis(RSL),
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StarAlgebras.Basis{UInt16}(@view 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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@ -71,8 +74,8 @@
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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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upper_bound = ub,
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augmented = false,
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)
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wdfl = SymbolicWedderburn.WedderburnDecomposition(
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@ -86,18 +89,18 @@
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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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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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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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@ -105,34 +108,34 @@
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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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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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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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real.(sqrt(JuMP.value.(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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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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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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@ -155,22 +158,23 @@
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basis(RSL),
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StarAlgebras.Basis{UInt16}(@view 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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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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scs_optimizer(
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eps=1e-8,
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max_iters=20_000,
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accel=0,
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alpha=1.9,
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scs_optimizer(;
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eps = 1e-8,
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max_iters = 20_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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@ -178,7 +182,7 @@
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Q = @time let varP = varP
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Qs = map(varP) do P
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real.(sqrt(JuMP.value.(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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@ -187,8 +191,8 @@
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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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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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@ -21,8 +21,9 @@ using SparseArrays
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@testset "Sq, Adj, Op in SL(4,Z)" begin
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N = 4
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G = MatrixGroups.SpecialLinearGroup{N}(Int8)
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@info "running tests for" G
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RG, S, sizes = PropertyT.group_algebra(G, halfradius=2, twisted=true)
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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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@ -39,6 +40,7 @@ using SparseArrays
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basis(RG),
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StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[2]]),
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)
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@info wd
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ivs = SymbolicWedderburn.invariant_vectors(wd)
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sq, adj, op = PropertyT.SqAdjOp(RG, N)
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@ -82,7 +84,7 @@ using SparseArrays
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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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RG, S, sizes = PropertyT.group_algebra(G, halfradius=2, twisted=true)
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RG, S, sizes = PropertyT.group_algebra(G; halfradius = 2)
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sq, adj, op = PropertyT.SqAdjOp(RG, n)
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@test sq(one(G)) == 216
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@ -98,7 +100,8 @@ end
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n = 3
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G = MatrixGroups.SpecialLinearGroup{n}(Int8)
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RG, S, sizes = PropertyT.group_algebra(G, halfradius=2, twisted=true)
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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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Δ = RG(length(S)) - sum(RG(s) for s in S)
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@ -113,6 +116,7 @@ end
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basis(RG),
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StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[2]]),
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)
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@info wd
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sq, adj, op = PropertyT.SqAdjOp(RG, n)
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|
||||
@ -123,10 +127,10 @@ end
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
Δ,
|
||||
wd,
|
||||
upper_bound=UB,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(accel=50, alpha=1.9)
|
||||
wd;
|
||||
upper_bound = UB,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(; accel = 50, alpha = 1.9),
|
||||
)
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test certified
|
||||
@ -140,10 +144,10 @@ end
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
Δ,
|
||||
wd,
|
||||
upper_bound=UB,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(accel=50, alpha=1.9)
|
||||
wd;
|
||||
upper_bound = UB,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(; accel = 50, alpha = 1.9),
|
||||
)
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test certified
|
||||
@ -152,10 +156,11 @@ end
|
||||
m, _ = PropertyT.sos_problem_primal(elt, wd)
|
||||
PropertyT.solve(
|
||||
m,
|
||||
scs_optimizer(max_iters=5000, accel=50, alpha=1.9)
|
||||
scs_optimizer(; max_iters = 5000, accel = 50, alpha = 1.9),
|
||||
)
|
||||
|
||||
@test JuMP.termination_status(m) in (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL, JuMP.ITERATION_LIMIT)
|
||||
@test JuMP.termination_status(m) in
|
||||
(JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL, JuMP.ITERATION_LIMIT)
|
||||
@test abs(JuMP.objective_value(m)) < 1e-3
|
||||
end
|
||||
|
||||
@ -168,10 +173,10 @@ end
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
Δ,
|
||||
wd,
|
||||
upper_bound=UB,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(accel=50, alpha=1.9)
|
||||
wd;
|
||||
upper_bound = UB,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(; accel = 50, alpha = 1.9),
|
||||
)
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test !certified
|
||||
@ -183,7 +188,8 @@ end
|
||||
n = 4
|
||||
|
||||
G = MatrixGroups.SpecialLinearGroup{n}(Int8)
|
||||
RG, S, sizes = PropertyT.group_algebra(G, halfradius=2, twisted=true)
|
||||
@info "running tests for" G
|
||||
RG, S, sizes = PropertyT.group_algebra(G; halfradius = 2)
|
||||
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
|
||||
@ -198,6 +204,7 @@ end
|
||||
basis(RG),
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[2]]),
|
||||
)
|
||||
@info wd
|
||||
|
||||
sq, adj, op = PropertyT.SqAdjOp(RG, n)
|
||||
|
||||
@ -208,10 +215,10 @@ end
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
Δ,
|
||||
wd,
|
||||
upper_bound=UB,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(accel=50, alpha=1.9)
|
||||
wd;
|
||||
upper_bound = UB,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(; accel = 50, alpha = 1.9),
|
||||
)
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test certified
|
||||
@ -225,10 +232,10 @@ end
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
Δ,
|
||||
wd,
|
||||
upper_bound=UB,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(accel=50, alpha=1.9)
|
||||
wd;
|
||||
upper_bound = UB,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(; accel = 50, alpha = 1.9),
|
||||
)
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test certified
|
||||
@ -242,10 +249,10 @@ end
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
Δ,
|
||||
wd,
|
||||
upper_bound=UB,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(accel=50, alpha=1.9)
|
||||
wd;
|
||||
upper_bound = UB,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(; accel = 50, alpha = 1.9),
|
||||
)
|
||||
@test status == JuMP.OPTIMAL
|
||||
@test !certified
|
||||
|
||||
168
test/Chevalley.jl
Normal file
168
test/Chevalley.jl
Normal file
@ -0,0 +1,168 @@
|
||||
countmap(v) = countmap(identity, v)
|
||||
function countmap(f, v)
|
||||
counts = Dict{eltype(f(first(v))),Int}()
|
||||
for x in v
|
||||
fx = f(x)
|
||||
counts[fx] = get!(counts, fx, 0) + 1
|
||||
end
|
||||
return counts
|
||||
end
|
||||
|
||||
@testset "classify_root_system" begin
|
||||
α = PropertyT.Roots.Root([1, -1, 0])
|
||||
β = PropertyT.Roots.Root([0, 1, -1])
|
||||
γ = PropertyT.Roots.Root([2, 0, 0])
|
||||
|
||||
@test PropertyT.Roots.classify_root_system(α, β, (false, false)) == :A₂
|
||||
@test PropertyT.Roots.classify_root_system(α, γ, (false, true)) == :C₂
|
||||
@test PropertyT.Roots.classify_root_system(β, γ, (false, true)) ==
|
||||
Symbol("A₁×C₁")
|
||||
end
|
||||
|
||||
@testset "Exceptional root systems" begin
|
||||
@testset "F4" begin
|
||||
F4 = let Σ = PermutationGroups.PermGroup(perm"(1,2,3,4)", perm"(1,2)")
|
||||
long = let x = (1.0, 1.0, 0.0, 0.0)
|
||||
PropertyT.Roots.Root.(
|
||||
union(
|
||||
(x^g for g in Σ),
|
||||
((x .* (-1, 1, 1, 1))^g for g in Σ),
|
||||
((-1 .* x)^g for g in Σ),
|
||||
),
|
||||
)
|
||||
end
|
||||
|
||||
short = let x = (1.0, 0.0, 0.0, 0.0)
|
||||
PropertyT.Roots.Root.(
|
||||
union((x^g for g in Σ), ((-1 .* x)^g for g in Σ))
|
||||
)
|
||||
end
|
||||
|
||||
signs = collect(Iterators.product(fill([-1, +1], 4)...))
|
||||
halfs = let x = 1 / 2 .* (1.0, 1.0, 1.0, 1.0)
|
||||
PropertyT.Roots.Root.(union(x .* sgn for sgn in signs))
|
||||
end
|
||||
|
||||
union(long, short, halfs)
|
||||
end
|
||||
|
||||
@test length(F4) == 48
|
||||
|
||||
a = F4[1]
|
||||
@test isapprox(length(a), sqrt(2))
|
||||
b = F4[6]
|
||||
@test isapprox(length(b), sqrt(2))
|
||||
c = a + b
|
||||
@test isapprox(length(c), 2.0)
|
||||
@test PropertyT.Roots.classify_root_system(b, c, (false, true)) == :C₂
|
||||
|
||||
long = F4[findfirst(r -> length(r) == sqrt(2), F4)]
|
||||
short = F4[findfirst(r -> length(r) == 1.0, F4)]
|
||||
|
||||
subtypes = Set([:C₂, :A₂, Symbol("A₁×C₁")])
|
||||
|
||||
let Ω = F4, α = long
|
||||
counts = countmap([
|
||||
PropertyT.Roots.classify_sub_root_system(Ω, α, γ) for
|
||||
γ in Ω if !PropertyT.Roots.isproportional(α, γ)
|
||||
])
|
||||
@test Set(keys(counts)) == subtypes
|
||||
d, r = divrem(counts[:C₂], 6)
|
||||
@test r == 0 && d == 3
|
||||
|
||||
d, r = divrem(counts[:A₂], 4)
|
||||
@test r == 0 && d == 4
|
||||
end
|
||||
|
||||
let Ω = F4, α = short
|
||||
counts = countmap([
|
||||
PropertyT.Roots.classify_sub_root_system(Ω, α, γ) for
|
||||
γ in Ω if !PropertyT.Roots.isproportional(α, γ)
|
||||
])
|
||||
@test Set(keys(counts)) == subtypes
|
||||
d, r = divrem(counts[:C₂], 6)
|
||||
@test r == 0 && d == 3
|
||||
|
||||
d, r = divrem(counts[:A₂], 4)
|
||||
@test r == 0 && d == 4
|
||||
end
|
||||
end
|
||||
|
||||
@testset "E6-7-8 exceptional root systems" begin
|
||||
E8 =
|
||||
let Σ = PermutationGroups.PermGroup(
|
||||
perm"(1,2,3,4,5,6,7,8)",
|
||||
perm"(1,2)",
|
||||
)
|
||||
long = let x = (1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
|
||||
PropertyT.Roots.Root.(
|
||||
union(
|
||||
(x^g for g in Σ),
|
||||
((x .* (-1, 1, 1, 1, 1, 1, 1, 1))^g for g in Σ),
|
||||
((-1 .* x)^g for g in Σ),
|
||||
),
|
||||
)
|
||||
end
|
||||
|
||||
signs = collect(
|
||||
p for p in Iterators.product(fill([-1, +1], 8)...) if
|
||||
iseven(count(==(-1), p))
|
||||
)
|
||||
halfs = let x = 1 / 2 .* ntuple(i -> 1.0, 8)
|
||||
rts = unique(PropertyT.Roots.Root(x .* sgn) for sgn in signs)
|
||||
end
|
||||
|
||||
union(long, halfs)
|
||||
end
|
||||
|
||||
subtypes = Set([:A₂, Symbol("A₁×A₁")])
|
||||
|
||||
@testset "E8" begin
|
||||
@test length(E8) == 240
|
||||
@test all(r -> length(r) ≈ sqrt(2), E8)
|
||||
|
||||
let Ω = E8, α = first(Ω)
|
||||
counts = countmap([
|
||||
PropertyT.Roots.classify_sub_root_system(Ω, α, γ) for
|
||||
γ in Ω if !PropertyT.Roots.isproportional(α, γ)
|
||||
])
|
||||
@test Set(keys(counts)) == subtypes
|
||||
d, r = divrem(counts[:A₂], 4)
|
||||
@test r == 0 && d == 28
|
||||
end
|
||||
end
|
||||
@testset "E7" begin
|
||||
E7 = filter(r -> iszero(sum(r.coord)), E8)
|
||||
@test length(E7) == 126
|
||||
|
||||
let Ω = E7, α = first(Ω)
|
||||
counts = countmap([
|
||||
PropertyT.Roots.classify_sub_root_system(Ω, α, γ) for
|
||||
γ in Ω if !PropertyT.Roots.isproportional(α, γ)
|
||||
])
|
||||
@test Set(keys(counts)) == subtypes
|
||||
d, r = divrem(counts[:A₂], 4)
|
||||
@test r == 0 && d == 16
|
||||
end
|
||||
end
|
||||
|
||||
@testset "E6" begin
|
||||
E6 = filter(
|
||||
r -> r.coord[end] == r.coord[end-1] == r.coord[end-2],
|
||||
E8,
|
||||
)
|
||||
@test length(E6) == 72
|
||||
|
||||
let Ω = E6, α = first(Ω)
|
||||
counts = countmap([
|
||||
PropertyT.Roots.classify_sub_root_system(Ω, α, γ) for
|
||||
γ in Ω if !PropertyT.Roots.isproportional(α, γ)
|
||||
])
|
||||
@test Set(keys(counts)) == subtypes
|
||||
d, r = divrem(counts[:A₂], 4)
|
||||
@info d, r
|
||||
@test r == 0 && d == 10
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
@ -3,7 +3,7 @@ function test_action(basis, group, act)
|
||||
return @testset "action definition" begin
|
||||
@test all(basis) do b
|
||||
e = one(group)
|
||||
action(act, e, b) == b
|
||||
return action(act, e, b) == b
|
||||
end
|
||||
|
||||
a = let a = rand(basis)
|
||||
@ -30,12 +30,12 @@ function test_action(basis, group, act)
|
||||
@test all([(g, h) for g in group for h in group]) do (g, h)
|
||||
x = action(act, h, action(act, g, a))
|
||||
y = action(act, g * h, a)
|
||||
x == y
|
||||
return x == y
|
||||
end
|
||||
|
||||
if act isa SymbolicWedderburn.ByPermutations
|
||||
@test all(basis) do b
|
||||
action(act, g, b) ∈ basis && action(act, h, b) ∈ basis
|
||||
return action(act, g, b) ∈ basis && action(act, h, b) ∈ basis
|
||||
end
|
||||
end
|
||||
end
|
||||
@ -44,21 +44,18 @@ end
|
||||
## Testing
|
||||
|
||||
@testset "Actions on SL(3,ℤ)" begin
|
||||
|
||||
n = 3
|
||||
|
||||
SL = MatrixGroups.SpecialLinearGroup{n}(Int8)
|
||||
RSL, S, sizes = PropertyT.group_algebra(SL, halfradius=2, twisted=true)
|
||||
RSL, S, sizes = PropertyT.group_algebra(SL; halfradius = 2)
|
||||
|
||||
@testset "Permutation action" begin
|
||||
|
||||
Γ = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
|
||||
ΓpA = PropertyT.action_by_conjugation(SL, Γ)
|
||||
|
||||
test_action(basis(RSL), Γ, ΓpA)
|
||||
|
||||
@testset "mps is successful" begin
|
||||
|
||||
charsΓ =
|
||||
SymbolicWedderburn.Character{
|
||||
Rational{Int},
|
||||
@ -66,9 +63,9 @@ end
|
||||
|
||||
RΓ = SymbolicWedderburn._group_algebra(Γ)
|
||||
|
||||
@time mps, simple =
|
||||
@time mps, ranks =
|
||||
SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
|
||||
@test all(simple)
|
||||
@test all(isone, ranks)
|
||||
end
|
||||
|
||||
@testset "Wedderburn decomposition" begin
|
||||
@ -77,17 +74,17 @@ end
|
||||
Γ,
|
||||
ΓpA,
|
||||
basis(RSL),
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSL)[1:sizes[2]])
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSL)[1:sizes[2]]),
|
||||
)
|
||||
|
||||
@test length(invariant_vectors(wd)) == 918
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [40, 23, 18]
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) ==
|
||||
[40, 23, 18]
|
||||
@test all(issimple, direct_summands(wd))
|
||||
end
|
||||
end
|
||||
|
||||
@testset "Wreath action" begin
|
||||
|
||||
Γ = let P = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
|
||||
PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
|
||||
end
|
||||
@ -97,7 +94,6 @@ end
|
||||
test_action(basis(RSL), Γ, ΓpA)
|
||||
|
||||
@testset "mps is successful" begin
|
||||
|
||||
charsΓ =
|
||||
SymbolicWedderburn.Character{
|
||||
Rational{Int},
|
||||
@ -105,9 +101,9 @@ end
|
||||
|
||||
RΓ = SymbolicWedderburn._group_algebra(Γ)
|
||||
|
||||
@time mps, simple =
|
||||
@time mps, ranks =
|
||||
SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
|
||||
@test all(simple)
|
||||
@test all(isone, ranks)
|
||||
end
|
||||
|
||||
@testset "Wedderburn decomposition" begin
|
||||
@ -116,32 +112,30 @@ end
|
||||
Γ,
|
||||
ΓpA,
|
||||
basis(RSL),
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSL)[1:sizes[2]])
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSL)[1:sizes[2]]),
|
||||
)
|
||||
|
||||
@test length(invariant_vectors(wd)) == 247
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [14, 9, 6, 14, 12]
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) ==
|
||||
[14, 9, 6, 14, 12]
|
||||
@test all(issimple, direct_summands(wd))
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
@testset "Actions on SAut(F4)" begin
|
||||
|
||||
n = 4
|
||||
|
||||
SAutFn = SpecialAutomorphismGroup(FreeGroup(n))
|
||||
RSAutFn, S, sizes = PropertyT.group_algebra(SAutFn, halfradius=1, twisted=true)
|
||||
RSAutFn, S, sizes = PropertyT.group_algebra(SAutFn; halfradius = 1)
|
||||
|
||||
@testset "Permutation action" begin
|
||||
|
||||
Γ = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
|
||||
ΓpA = PropertyT.action_by_conjugation(SAutFn, Γ)
|
||||
|
||||
test_action(basis(RSAutFn), Γ, ΓpA)
|
||||
|
||||
@testset "mps is successful" begin
|
||||
|
||||
charsΓ =
|
||||
SymbolicWedderburn.Character{
|
||||
Rational{Int},
|
||||
@ -149,9 +143,9 @@ end
|
||||
|
||||
RΓ = SymbolicWedderburn._group_algebra(Γ)
|
||||
|
||||
@time mps, simple =
|
||||
@time mps, ranks =
|
||||
SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
|
||||
@test all(simple)
|
||||
@test all(isone, ranks)
|
||||
end
|
||||
|
||||
@testset "Wedderburn decomposition" begin
|
||||
@ -160,17 +154,17 @@ end
|
||||
Γ,
|
||||
ΓpA,
|
||||
basis(RSAutFn),
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSAutFn)[1:sizes[1]])
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSAutFn)[1:sizes[1]]),
|
||||
)
|
||||
|
||||
@test length(invariant_vectors(wd)) == 93
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [4, 8, 5, 4]
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) ==
|
||||
[4, 8, 5, 4]
|
||||
@test all(issimple, direct_summands(wd))
|
||||
end
|
||||
end
|
||||
|
||||
@testset "Wreath action" begin
|
||||
|
||||
Γ = let P = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
|
||||
PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
|
||||
end
|
||||
@ -180,7 +174,6 @@ end
|
||||
test_action(basis(RSAutFn), Γ, ΓpA)
|
||||
|
||||
@testset "mps is successful" begin
|
||||
|
||||
charsΓ =
|
||||
SymbolicWedderburn.Character{
|
||||
Rational{Int},
|
||||
@ -188,9 +181,9 @@ end
|
||||
|
||||
RΓ = SymbolicWedderburn._group_algebra(Γ)
|
||||
|
||||
@time mps, simple =
|
||||
@time mps, ranks =
|
||||
SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
|
||||
@test all(simple)
|
||||
@test all(isone, ranks)
|
||||
end
|
||||
|
||||
@testset "Wedderburn decomposition" begin
|
||||
@ -199,11 +192,12 @@ end
|
||||
Γ,
|
||||
ΓpA,
|
||||
basis(RSAutFn),
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSAutFn)[1:sizes[1]])
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RSAutFn)[1:sizes[1]]),
|
||||
)
|
||||
|
||||
@test length(invariant_vectors(wd)) == 18
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [1, 1, 2, 2, 1, 2, 2, 1]
|
||||
@test SymbolicWedderburn.size.(direct_summands(wd), 1) ==
|
||||
[1, 1, 2, 2, 1, 2, 2, 1]
|
||||
@test all(issimple, direct_summands(wd))
|
||||
end
|
||||
end
|
||||
|
||||
@ -1,6 +1,12 @@
|
||||
function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
|
||||
function check_positivity(
|
||||
elt,
|
||||
unit;
|
||||
upper_bound = Inf,
|
||||
halfradius = 2,
|
||||
optimizer,
|
||||
)
|
||||
@time sos_problem =
|
||||
PropertyT.sos_problem_primal(elt, unit, upper_bound=upper_bound)
|
||||
PropertyT.sos_problem_primal(elt, unit; upper_bound = upper_bound)
|
||||
|
||||
status, _ = PropertyT.solve(sos_problem, optimizer)
|
||||
P = JuMP.value.(sos_problem[:P])
|
||||
@ -9,16 +15,23 @@ function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
|
||||
elt,
|
||||
unit,
|
||||
JuMP.objective_value(sos_problem),
|
||||
Q,
|
||||
halfradius=halfradius,
|
||||
Q;
|
||||
halfradius = halfradius,
|
||||
)
|
||||
return status, certified, λ_cert
|
||||
end
|
||||
|
||||
function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimizer)
|
||||
function check_positivity(
|
||||
elt,
|
||||
unit,
|
||||
wd;
|
||||
upper_bound = Inf,
|
||||
halfradius = 2,
|
||||
optimizer,
|
||||
)
|
||||
@assert aug(elt) == aug(unit) == 0
|
||||
@time sos_problem, Ps =
|
||||
PropertyT.sos_problem_primal(elt, unit, wd, upper_bound=upper_bound)
|
||||
PropertyT.sos_problem_primal(elt, unit, wd; upper_bound = upper_bound)
|
||||
|
||||
@time status, _ = PropertyT.solve(sos_problem, optimizer)
|
||||
|
||||
@ -29,13 +42,7 @@ function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimize
|
||||
|
||||
λ = JuMP.value(sos_problem[:λ])
|
||||
|
||||
certified, λ_cert = PropertyT.certify_solution(
|
||||
elt,
|
||||
unit,
|
||||
λ,
|
||||
Q,
|
||||
halfradius=halfradius
|
||||
)
|
||||
certified, λ_cert =
|
||||
PropertyT.certify_solution(elt, unit, λ, Q; halfradius = halfradius)
|
||||
return status, certified, λ_cert
|
||||
end
|
||||
|
||||
|
||||
@ -1,10 +1,9 @@
|
||||
@testset "Adj via grading" begin
|
||||
|
||||
@testset "SL(n,Z) & Aut(F₄)" begin
|
||||
n = 4
|
||||
halfradius = 1
|
||||
SL = MatrixGroups.SpecialLinearGroup{n}(Int8)
|
||||
RSL, S, sizes = PropertyT.group_algebra(SL, halfradius=halfradius, twisted=true)
|
||||
RSL, S, sizes = PropertyT.group_algebra(SL; halfradius = halfradius)
|
||||
|
||||
Δ = RSL(length(S)) - sum(RSL(s) for s in S)
|
||||
|
||||
@ -22,10 +21,9 @@
|
||||
@test PropertyT.Adj(Δs, :A₂) == adj
|
||||
@test PropertyT.Adj(Δs, Symbol("A₁×A₁")) == op
|
||||
|
||||
|
||||
halfradius = 1
|
||||
G = SpecialAutomorphismGroup(FreeGroup(n))
|
||||
RG, S, sizes = PropertyT.group_algebra(G, halfradius=halfradius, twisted=true)
|
||||
RG, S, sizes = PropertyT.group_algebra(G; halfradius = halfradius)
|
||||
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
|
||||
@ -44,7 +42,6 @@
|
||||
@test PropertyT.Adj(Δs, Symbol("A₁×A₁")) == op
|
||||
end
|
||||
|
||||
|
||||
@testset "Symplectic group" begin
|
||||
@testset "Sp2(ℤ)" begin
|
||||
genus = 2
|
||||
@ -52,7 +49,8 @@
|
||||
|
||||
SpN = MatrixGroups.SymplecticGroup{2genus}(Int8)
|
||||
|
||||
RSpN, S_sp, sizes_sp = PropertyT.group_algebra(SpN, halfradius=halfradius, twisted=true)
|
||||
RSpN, S_sp, sizes_sp =
|
||||
PropertyT.group_algebra(SpN; halfradius = halfradius)
|
||||
|
||||
Δ, Δs = let RG = RSpN, S = S_sp, ψ = identity
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
@ -73,7 +71,8 @@
|
||||
|
||||
SpN = MatrixGroups.SymplecticGroup{2genus}(Int8)
|
||||
|
||||
RSpN, S_sp, sizes_sp = PropertyT.group_algebra(SpN, halfradius=halfradius, twisted=true)
|
||||
RSpN, S_sp, sizes_sp =
|
||||
PropertyT.group_algebra(SpN; halfradius = halfradius)
|
||||
|
||||
Δ, Δs = let RG = RSpN, S = S_sp, ψ = identity
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
@ -86,9 +85,14 @@
|
||||
end
|
||||
|
||||
@testset "Adj numerics for genus=$genus" begin
|
||||
|
||||
all_subtypes = (
|
||||
:A₁, :C₁, Symbol("A₁×A₁"), Symbol("C₁×C₁"), Symbol("A₁×C₁"), :A₂, :C₂
|
||||
:A₁,
|
||||
:C₁,
|
||||
Symbol("A₁×A₁"),
|
||||
Symbol("C₁×C₁"),
|
||||
Symbol("A₁×C₁"),
|
||||
:A₂,
|
||||
:C₂,
|
||||
)
|
||||
|
||||
@test PropertyT.Adj(Δs, :A₂)[one(SpN)] == 384
|
||||
@ -101,8 +105,8 @@
|
||||
@test isinteger(PropertyT.Adj(Δs, subtype)[one(SpN)] / 16)
|
||||
end
|
||||
end
|
||||
@test sum(PropertyT.Adj(Δs, subtype) for subtype in all_subtypes) == Δ^2
|
||||
@test sum(PropertyT.Adj(Δs, subtype) for subtype in all_subtypes) ==
|
||||
Δ^2
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
@ -1,11 +1,12 @@
|
||||
@testset "Quick tests" begin
|
||||
|
||||
@testset "SL(2,F₇)" begin
|
||||
N = 2
|
||||
p = 7
|
||||
halfradius = 3
|
||||
G = MatrixGroups.SpecialLinearGroup{N}(SymbolicWedderburn.Characters.FiniteFields.GF{p})
|
||||
RG, S, sizes = PropertyT.group_algebra(G, halfradius=3, twisted=true)
|
||||
G = MatrixGroups.SpecialLinearGroup{N}(
|
||||
SymbolicWedderburn.Characters.FiniteFields.GF{p},
|
||||
)
|
||||
RG, S, sizes = PropertyT.group_algebra(G; halfradius = 3)
|
||||
|
||||
Δ = let RG = RG, S = S
|
||||
RG(length(S)) - sum(RG(s) for s in S)
|
||||
@ -18,15 +19,15 @@
|
||||
@testset "standard formulation" begin
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
unit,
|
||||
upper_bound=ub,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(
|
||||
eps=1e-7,
|
||||
max_iters=5_000,
|
||||
accel=50,
|
||||
alpha=1.95,
|
||||
)
|
||||
unit;
|
||||
upper_bound = ub,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(;
|
||||
eps = 1e-7,
|
||||
max_iters = 5_000,
|
||||
accel = 50,
|
||||
alpha = 1.95,
|
||||
),
|
||||
)
|
||||
|
||||
@test status == JuMP.OPTIMAL
|
||||
@ -34,14 +35,18 @@
|
||||
@test λ_cert > 5857 // 10000
|
||||
|
||||
m = PropertyT.sos_problem_dual(elt, unit)
|
||||
PropertyT.solve(m, cosmo_optimizer(
|
||||
eps=1e-7,
|
||||
max_iters=10_000,
|
||||
accel=50,
|
||||
alpha=1.95,
|
||||
))
|
||||
PropertyT.solve(
|
||||
m,
|
||||
cosmo_optimizer(;
|
||||
eps = 1e-7,
|
||||
max_iters = 10_000,
|
||||
accel = 50,
|
||||
alpha = 1.95,
|
||||
),
|
||||
)
|
||||
|
||||
@test JuMP.termination_status(m) in (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
|
||||
@test JuMP.termination_status(m) in
|
||||
(JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
|
||||
@test JuMP.objective_value(m) ≈ λ_cert atol = 1e-2
|
||||
end
|
||||
|
||||
@ -55,20 +60,22 @@
|
||||
Σ,
|
||||
act,
|
||||
basis(RG),
|
||||
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[halfradius]]),
|
||||
StarAlgebras.Basis{UInt16}(
|
||||
@view basis(RG)[1:sizes[halfradius]]
|
||||
),
|
||||
)
|
||||
|
||||
status, certified, λ_cert = check_positivity(
|
||||
elt,
|
||||
unit,
|
||||
wd,
|
||||
upper_bound=ub,
|
||||
halfradius=2,
|
||||
optimizer=cosmo_optimizer(
|
||||
eps=1e-7,
|
||||
max_iters=10_000,
|
||||
accel=50,
|
||||
alpha=1.9,
|
||||
wd;
|
||||
upper_bound = ub,
|
||||
halfradius = 2,
|
||||
optimizer = cosmo_optimizer(;
|
||||
eps = 1e-7,
|
||||
max_iters = 10_000,
|
||||
accel = 50,
|
||||
alpha = 1.9,
|
||||
),
|
||||
)
|
||||
|
||||
|
||||
@ -25,5 +25,6 @@ if haskey(ENV, "FULL_TEST") || haskey(ENV, "CI")
|
||||
include("1812.03456.jl")
|
||||
|
||||
include("graded_adj.jl")
|
||||
include("Chevalley.jl")
|
||||
end
|
||||
end
|
||||
|
||||
Loading…
Reference in New Issue
Block a user