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https://github.com/kalmarek/PropertyT.jl.git
synced 2024-12-25 02:15:29 +01:00
update tests and test spectral_gap directly
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@ -2,38 +2,50 @@
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@testset "SL(2,Z)" begin
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N = 2
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G = MatrixSpace(Nemo.ZZ, N,N)
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S = Groups.gens(G)
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S = [S; inv.(S)]
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G = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(G)
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rm("SL($N,Z)", recursive=true, force=true)
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sett = PropertyT.Settings("SL($N,Z)", G, S, solver(20000, accel=20); upper_bound=0.1)
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings("SL($N,Z)", G, S, with_SCS(20000, accel=20); upper_bound=0.1)
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PropertyT.print_summary(sett)
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λ = PropertyT.spectral_gap(sett)
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@test λ < 0.0
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@test PropertyT.interpret_results(sett, λ) == false
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end
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@testset "SL(3,Z)" begin
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N = 3
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G = MatrixSpace(Nemo.ZZ, N,N)
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S = Groups.gens(G)
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S = [S; inv.(S)]
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G = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(G)
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rm("SL($N,Z)", recursive=true, force=true)
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sett = PropertyT.Settings("SL($N,Z)", G, S, solver(1000, accel=20); upper_bound=0.1)
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@test PropertyT.check_property_T(sett) == true
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sett = PropertyT.Settings("SL($N,Z)", G, S, with_SCS(1000, accel=20); upper_bound=0.1)
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PropertyT.print_summary(sett)
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λ = PropertyT.spectral_gap(sett)
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@test λ > 0.0999
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@test PropertyT.interpret_results(sett, λ) == true
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@test PropertyT.check_property_T(sett) == true #second run should be fast
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end
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@testset "SAut(F₂)" begin
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N = 2
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G = SAut(FreeGroup(N))
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S = Groups.gens(G)
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S = [S; inv.(S)]
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S = PropertyT.generating_set(G)
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rm("SAut(F$N)", recursive=true, force=true)
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sett = PropertyT.Settings("SAut(F$N)", G, S, solver(20000);
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sett = PropertyT.Settings("SAut(F$N)", G, S, with_SCS(10000);
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upper_bound=0.15, warmstart=false)
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@test PropertyT.check_property_T(sett) == false
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PropertyT.print_summary(sett)
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λ = PropertyT.spectral_gap(sett)
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@test λ < 0.0
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@test PropertyT.interpret_results(sett, λ) == false
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end
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end
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@ -2,58 +2,85 @@
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@testset "oSL(3,Z)" begin
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N = 3
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G = MatrixSpace(Nemo.ZZ, N,N)
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S = Groups.gens(G)
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S = [S; inv.(S)]
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G = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(G)
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autS = WreathProduct(PermGroup(2), PermGroup(N))
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rm("oSL($N,Z)", recursive=true, force=true)
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, solver(2000, accel=20);
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upper_bound=0.27, warmstart=false)
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@test PropertyT.check_property_T(sett) == false
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#second run just checks the solution
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, solver(2000, accel=20);
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rm("oSL($N,Z)", recursive=true, force=true)
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(2000, accel=20);
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upper_bound=0.27, warmstart=false)
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PropertyT.print_summary(sett)
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λ = PropertyT.spectral_gap(sett)
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@test λ < 0.0
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@test PropertyT.interpret_results(sett, λ) == false
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# second run just checks the solution due to warmstart=false above
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@test λ == PropertyT.spectral_gap(sett)
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(2000, accel=20);
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upper_bound=0.27, warmstart=true)
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PropertyT.print_summary(sett)
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λ = PropertyT.spectral_gap(sett)
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@test λ > 0.269999
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@test PropertyT.interpret_results(sett, λ) == true
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# this should be very fast due to warmstarting:
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@test λ ≈ PropertyT.spectral_gap(sett) atol=1e-5
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@test PropertyT.check_property_T(sett) == true
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end
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@testset "oSL(4,Z)" begin
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N = 4
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G = MatrixSpace(Nemo.ZZ, N,N)
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S = Groups.gens(G)
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S = [S; inv.(S)]
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G = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(G)
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autS = WreathProduct(PermGroup(2), PermGroup(N))
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rm("oSL($N,Z)", recursive=true, force=true)
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, solver(2000, accel=20);
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upper_bound=1.3, warmstart=false)
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@test PropertyT.check_property_T(sett) == false
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#second run just checks the obtained solution
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, solver(5000, accel=20);
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rm("oSL($N,Z)", recursive=true, force=true)
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(2000, accel=20);
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upper_bound=1.3, warmstart=false)
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PropertyT.print_summary(sett)
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λ = PropertyT.spectral_gap(sett)
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@test λ < 0.0
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@test PropertyT.interpret_results(sett, λ) == false
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# second run just checks the solution due to warmstart=false above
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@test λ == PropertyT.spectral_gap(sett)
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, with_SCS(5000, accel=20);
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upper_bound=1.3, warmstart=true)
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PropertyT.print_summary(sett)
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λ = PropertyT.spectral_gap(sett)
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@test λ > 1.2999
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@test PropertyT.interpret_results(sett, λ) == true
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# this should be very fast due to warmstarting:
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@test λ ≈ PropertyT.spectral_gap(sett) atol=1e-5
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@test PropertyT.check_property_T(sett) == true
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end
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@testset "SAut(F₃)" begin
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N = 3
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G = SAut(FreeGroup(N))
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S = Groups.gens(G)
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S = [S; inv.(S)]
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S = PropertyT.generating_set(G)
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autS = WreathProduct(PermGroup(2), PermGroup(N))
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rm("oSAut(F$N)", recursive=true, force=true)
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sett = PropertyT.Settings("SAut(F$N)", G, S, autS, solver(5000);
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sett = PropertyT.Settings("SAut(F$N)", G, S, autS, with_SCS(1000);
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upper_bound=0.15, warmstart=false)
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PropertyT.print_summary(sett)
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@test PropertyT.check_property_T(sett) == false
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end
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end
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@ -7,26 +7,25 @@
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@testset "unit tests" begin
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for N in [3,4]
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M = MatrixSpace(Nemo.ZZ, N,N)
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A = SAut(FreeGroup(N))
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@test length(PropertyT.generating_set(M)) == 2N*(N-1)
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M = MatrixAlgebra(zz, N)
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@test PropertyT.E(M, 1, 2) isa MatAlgElem
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e12 = PropertyT.E(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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N = 4
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M = MatrixSpace(Nemo.ZZ, N,N)
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S = PropertyT.generating_set(M)
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@test PropertyT.E(M, 1, 2) isa MatElem
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e12 = PropertyT.E(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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@test e12 ∈ S
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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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@ -40,7 +39,7 @@
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@testset "Sq, Adj, Op" begin
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N = 4
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M = MatrixSpace(Nemo.ZZ, N,N)
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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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@ -94,24 +93,17 @@ end
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@testset "1812.03456 examples" begin
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with_SCS = with_optimizer(SCS.Optimizer,
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linear_solver=SCS.Direct,
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eps=2e-10,
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max_iters=20000,
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alpha=1.5,
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acceleration_lookback=10,
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warm_start=true)
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function SOS_residual(x::GroupRingElem, Q::Matrix)
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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)
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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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@ -127,7 +119,7 @@ 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 = MatrixSpace(Nemo.ZZ, N,N)
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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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@ -139,6 +131,7 @@ end
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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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@ -151,6 +144,7 @@ end
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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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@ -162,6 +156,7 @@ end
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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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@ -171,7 +166,7 @@ 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 = MatrixSpace(Nemo.ZZ, N,N)
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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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@ -183,6 +178,7 @@ end
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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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@ -204,7 +200,9 @@ end
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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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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 certify positivity
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@ -215,6 +213,7 @@ end
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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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@ -1,5 +1,3 @@
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using PropertyT.GroupRings
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@testset "Correctness of HPC SOS computation" begin
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function prepare(G_name, λ, S_size)
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@ -1,24 +1,15 @@
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using AbstractAlgebra, Nemo, Groups, SCS
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using SparseArrays
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using JLD
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using PropertyT
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using Test
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using JuMP
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using LinearAlgebra, SparseArrays
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using AbstractAlgebra, Groups, GroupRings
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using PropertyT
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using JLD
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indexing(n) = [(i,j) for i in 1:n for j in (i+1):n]
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function Groups.gens(M::MatSpace)
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@assert ncols(M) == nrows(M)
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N = ncols(M)
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E(i,j) = begin g = M(1); g[i,j] = 1; g end
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S = [E(i,j) for (i,j) in indexing(N)]
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S = [S; transpose.(S)]
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return S
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end
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using JuMP, SCS
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solver(iters; accel=1) =
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with_SCS(iters; accel=1, eps=1e-10) =
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with_optimizer(SCS.Optimizer,
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linear_solver=SCS.Direct, max_iters=iters,
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acceleration_lookback=accel, eps=1e-10, warm_start=true)
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acceleration_lookback=accel, eps=eps, warm_start=true)
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include("1703.09680.jl")
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include("1712.07167.jl")
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