mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-12-25 02:15:29 +01:00
246 lines
8.0 KiB
Julia
246 lines
8.0 KiB
Julia
@testset "Sq, Adj, Op" begin
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function isconstant_on_orbit(v, orb)
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isempty(orb) && return true
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k = v[first(orb)]
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return all(v[o] == k for o in orb)
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end
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@testset "unit tests" begin
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for N in [3,4]
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M = MatrixAlgebra(zz, N)
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@test PropertyT.EltaryMat(M, 1, 2) isa MatAlgElem
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e12 = PropertyT.EltaryMat(M, 1, 2)
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@test e12[1,2] == 1
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@test inv(e12)[1,2] == -1
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S = PropertyT.generating_set(M)
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@test e12 ∈ S
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@test length(PropertyT.generating_set(M)) == 2N*(N-1)
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@test all(inv(s) ∈ S for s in S)
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A = SAut(FreeGroup(N))
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@test length(PropertyT.generating_set(A)) == 4N*(N-1)
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S = PropertyT.generating_set(A)
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@test all(inv(s) ∈ S for s in S)
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end
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@test PropertyT.isopposite(perm"(1,2,3)(4)", perm"(1,4,2)")
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@test PropertyT.isadjacent(perm"(1,2,3)", perm"(1,2)(3)")
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@test !PropertyT.isopposite(perm"(1,2,3)", perm"(1,2)(3)")
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@test !PropertyT.isadjacent(perm"(1,4)", perm"(2,3)(4)")
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@test isconstant_on_orbit([1,1,1,2,2], [2,3])
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@test !isconstant_on_orbit([1,1,1,2,2], [2,3,4])
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end
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@testset "Sq, Adj, Op" begin
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N = 4
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M = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(M)
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Δ = PropertyT.Laplacian(S, 2)
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RG = parent(Δ)
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autS = WreathProduct(SymmetricGroup(2), SymmetricGroup(N))
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orbits = PropertyT.orbit_decomposition(autS, RG.basis)
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@test PropertyT.Sq(RG) isa GroupRingElem
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sq = PropertyT.Sq(RG)
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@test all(isconstant_on_orbit(sq, orb) for orb in orbits)
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@test PropertyT.Adj(RG) isa GroupRingElem
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adj = PropertyT.Adj(RG)
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@test all(isconstant_on_orbit(adj, orb) for orb in orbits)
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@test PropertyT.Op(RG) isa GroupRingElem
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op = PropertyT.Op(RG)
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@test all(isconstant_on_orbit(op, orb) for orb in orbits)
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sq, adj, op = PropertyT.SqAdjOp(RG, N)
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@test sq == PropertyT.Sq(RG)
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@test adj == PropertyT.Adj(RG)
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@test op == PropertyT.Op(RG)
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e = one(M)
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g = PropertyT.EltaryMat(M, 1,2)
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h = PropertyT.EltaryMat(M, 1,3)
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k = PropertyT.EltaryMat(M, 3,4)
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edges = N*(N-1)÷2
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@test sq[e] == 20*edges
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@test sq[g] == sq[h] == -8
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@test sq[g^2] == sq[h^2] == 1
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@test sq[g*h] == sq[h*g] == 0
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# @test adj[e] == ...
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@test adj[g] == adj[h] # == ...
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@test adj[g^2] == adj[h^2] == 0
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@test adj[g*h] == adj[h*g] # == ...
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# @test op[e] == ...
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@test op[g] == op[h] # == ...
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@test op[g^2] == op[h^2] == 0
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@test op[g*h] == op[h*g] == 0
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@test op[g*k] == op[k*g] # == ...
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@test op[h*k] == op[k*h] == 0
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end
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end
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@testset "1812.03456 examples" begin
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function SOS_residual(x::GroupRingElem, Q::Matrix)
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RG = parent(x)
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@time sos = PropertyT.compute_SOS(RG, Q);
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return x - sos
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end
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function check_positivity(elt, Δ, orbit_data, upper_bound, warm=nothing; with_solver=with_SCS(20_000, accel=10))
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SDP_problem, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=upper_bound)
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status, warm = PropertyT.solve(SDP_problem, with_solver, warm);
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Base.Libc.flush_cstdio()
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@info "Optimization status:" status
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λ = value(SDP_problem[:λ])
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Ps = [value.(P) for P in varP]
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Qs = real.(sqrt.(Ps));
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Q = PropertyT.reconstruct(Qs, orbit_data);
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b = SOS_residual(elt - λ*Δ, Q)
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return b, λ, warm
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end
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@testset "SL(3,Z)" begin
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N = 3
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halfradius = 2
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M = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(M)
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Δ = PropertyT.Laplacian(S, halfradius)
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RG = parent(Δ)
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orbit_data = PropertyT.OrbitData(RG, WreathProduct(SymmetricGroup(2), SymmetricGroup(N)))
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orbit_data = PropertyT.decimate(orbit_data);
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@testset "Sq₃ is SOS" begin
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elt = PropertyT.Sq(RG)
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UB = 0.05 # 0.105?
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residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
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Base.Libc.flush_cstdio()
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@info "obtained λ and residual" λ norm(residual, 1)
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@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
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@test 2^2*norm(residual, 1) < 2λ/100
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end
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@testset "Adj₃ is SOS" begin
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elt = PropertyT.Adj(RG)
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UB = 0.1 # 0.157?
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residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
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Base.Libc.flush_cstdio()
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@info "obtained λ and residual" λ norm(residual, 1)
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@test 2^2*norm(residual, 1) < λ
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@test 2^2*norm(residual, 1) < λ/100
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end
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@testset "Op₃ is empty, so can not be certified" begin
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elt = PropertyT.Op(RG)
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UB = Inf
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residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
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Base.Libc.flush_cstdio()
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@info "obtained λ and residual" λ norm(residual, 1)
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@test 2^2*norm(residual, 1) > λ
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end
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end
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@testset "SL(4,Z)" begin
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N = 4
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halfradius = 2
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M = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(M)
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Δ = PropertyT.Laplacian(S, halfradius)
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RG = parent(Δ)
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orbit_data = PropertyT.OrbitData(RG, WreathProduct(SymmetricGroup(2), SymmetricGroup(N)))
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orbit_data = PropertyT.decimate(orbit_data);
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@testset "Sq₄ is SOS" begin
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elt = PropertyT.Sq(RG)
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UB = 0.2 # 0.3172
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residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
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Base.Libc.flush_cstdio()
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@info "obtained λ and residual" λ norm(residual, 1)
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@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
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@test 2^2*norm(residual, 1) < λ/100
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end
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@testset "Adj₄ is SOS" begin
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elt = PropertyT.Adj(RG)
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UB = 0.3 # 0.5459?
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residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
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@info "obtained λ and residual" λ norm(residual, 1)
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@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
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@test 2^2*norm(residual, 1) < λ/100
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end
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@testset "we can't cerify that Op₄ SOS" begin
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elt = PropertyT.Op(RG)
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UB = 2.0
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residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB,
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with_solver=with_SCS(20_000, accel=10, eps=2e-10))
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Base.Libc.flush_cstdio()
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@info "obtained λ and residual" λ norm(residual, 1)
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@test 2^2*norm(residual, 1) > λ # i.e. we can't certify positivity
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end
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@testset "Adj₄ + Op₄ is SOS" begin
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elt = PropertyT.Adj(RG) + PropertyT.Op(RG)
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UB = 0.6 # 0.82005
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residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
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Base.Libc.flush_cstdio()
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@info "obtained λ and residual" λ norm(residual, 1)
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@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
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@test 2^2*norm(residual, 1) < λ/100
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end
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end
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# @testset "Adj₄ + 100 Op₄ ∈ ISAut(F₄) is SOS" begin
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# N = 4
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# halfradius = 2
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# M = SAut(FreeGroup(N))
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# S = PropertyT.generating_set(M)
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# Δ = PropertyT.Laplacian(S, halfradius)
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# RG = parent(Δ)
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# orbit_data = PropertyT.OrbitData(RG, WreathProduct(SymmetricGroup(2), SymmetricGroup(N)))
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# orbit_data = PropertyT.decimate(orbit_data);
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#
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# @time elt = PropertyT.Adj(RG) + 100PropertyT.Op(RG)
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# UB = 0.05
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#
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# warm = nothing
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#
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# residual, λ, warm = check_positivity(elt, Δ, orbit_data, UB, warm, with_solver=with_SCS(20_000, accel=10))
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# @info "obtained λ and residual" λ norm(residual, 1)
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#
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# @test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
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# @test 2^2*norm(residual, 1) < λ/100
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# end
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end
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