add really quick tests to be run first
tests run really fast, but compilation time is killing it...
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@ -1,20 +1,3 @@
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function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
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@time sos_problem =
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PropertyT.sos_problem_primal(elt, unit, upper_bound=upper_bound)
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status, _ = PropertyT.solve(sos_problem, optimizer)
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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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unit,
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JuMP.objective_value(sos_problem),
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Q,
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halfradius=halfradius,
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)
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return status, certified, λ_cert
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end
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@testset "1703.09680 Examples" begin
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@testset "SL(2,Z)" begin
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@ -1,27 +1,3 @@
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function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimizer)
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@assert aug(elt) == aug(unit) == 0
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@time sos_problem, Ps =
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PropertyT.sos_problem_primal(elt, unit, wd, upper_bound=upper_bound)
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@time status, _ = PropertyT.solve(sos_problem, optimizer)
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Q = let Ps = Ps
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Qs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
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PropertyT.reconstruct(Qs, wd)
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end
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λ = JuMP.value(sos_problem[:λ])
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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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)
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return status, certified, λ_cert
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end
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@testset "1712.07167 Examples" begin
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@testset "SAut(F₃)" begin
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@ -0,0 +1,41 @@
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function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
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@time sos_problem =
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PropertyT.sos_problem_primal(elt, unit, upper_bound=upper_bound)
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status, _ = PropertyT.solve(sos_problem, optimizer)
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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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unit,
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JuMP.objective_value(sos_problem),
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Q,
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halfradius=halfradius,
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)
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return status, certified, λ_cert
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end
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function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimizer)
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@assert aug(elt) == aug(unit) == 0
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@time sos_problem, Ps =
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PropertyT.sos_problem_primal(elt, unit, wd, upper_bound=upper_bound)
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@time status, _ = PropertyT.solve(sos_problem, optimizer)
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Q = let Ps = Ps
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Qs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
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PropertyT.reconstruct(Qs, wd)
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end
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λ = JuMP.value(sos_problem[:λ])
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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=halfradius
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)
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return status, certified, λ_cert
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end
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@ -0,0 +1,80 @@
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@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}(SymbolicWedderburn.Characters.FiniteFields.GF{p})
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RG, S, sizes = PropertyT.group_algebra(G, halfradius=3, twisted=true)
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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=cosmo_optimizer(
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eps=1e-7,
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max_iters=5_000,
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accel=50,
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alpha=1.95,
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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(m, 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=1.95,
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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) ≈ λ_cert atol = 1e-2
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end
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@testset "Wedderburn decomposition" begin
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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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act = PropertyT.action_by_conjugation(G, Σ)
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wd = 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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)
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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 > 5857 // 10000
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end
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end
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end
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@ -1,8 +1,6 @@
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using Test
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using LinearAlgebra
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using SparseArrays
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BLAS.set_num_threads(1)
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ENV["OMP_NUM_THREADS"] = 4
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using Groups
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using Groups.GroupsCore
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@ -14,15 +12,18 @@ using SymbolicWedderburn.StarAlgebras
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using SymbolicWedderburn.PermutationGroups
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include("optimizers.jl")
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include("check_positivity.jl")
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include("quick_tests.jl")
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@testset "PropertyT" begin
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if haskey(ENV, "FULL_TEST") || haskey(ENV, "CI")
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@testset "PropertyT" begin
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include("constratint_matrices.jl")
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include("actions.jl")
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include("constratint_matrices.jl")
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include("actions.jl")
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include("1703.09680.jl")
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include("1712.07167.jl")
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include("1812.03456.jl")
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include("1703.09680.jl")
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include("1712.07167.jl")
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include("1812.03456.jl")
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include("graded_adj.jl")
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include("graded_adj.jl")
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end
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end
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