mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-25 16:50:27 +01:00
add 1812.03456 positivity tests in SL(n,Z)
This commit is contained in:
parent
6c906b05cb
commit
80e338f191
@ -91,3 +91,135 @@
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
@testset "1812.03456 examples" begin
|
||||
|
||||
with_SCS = with_optimizer(SCS.Optimizer,
|
||||
linear_solver=SCS.Direct,
|
||||
eps=2e-10,
|
||||
max_iters=20000,
|
||||
alpha=1.5,
|
||||
acceleration_lookback=10,
|
||||
warm_start=true)
|
||||
|
||||
function SOS_residual(x::GroupRingElem, Q::Matrix)
|
||||
RG = parent(x)
|
||||
@time sos = PropertyT.compute_SOS(RG, Q);
|
||||
return x - sos
|
||||
end
|
||||
|
||||
function check_positivity(elt, Δ, orbit_data, upper_bound, warm=nothing; with_solver=with_SCS)
|
||||
SDP_problem, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=upper_bound)
|
||||
|
||||
status, warm = PropertyT.solve(SDP_problem, with_solver, warm);
|
||||
@info "Optimization status:" status
|
||||
|
||||
λ = value(SDP_problem[:λ])
|
||||
Ps = [value.(P) for P in varP]
|
||||
|
||||
Qs = real.(sqrt.(Ps));
|
||||
Q = PropertyT.reconstruct(Qs, orbit_data);
|
||||
|
||||
b = SOS_residual(elt - λ*Δ, Q)
|
||||
return b, λ, warm
|
||||
end
|
||||
|
||||
@testset "SL(3,Z)" begin
|
||||
N = 3
|
||||
halfradius = 2
|
||||
M = MatrixSpace(Nemo.ZZ, N,N)
|
||||
S = PropertyT.generating_set(M)
|
||||
Δ = PropertyT.Laplacian(S, halfradius)
|
||||
RG = parent(Δ)
|
||||
orbit_data = PropertyT.OrbitData(RG, WreathProduct(PermGroup(2), PermGroup(N)))
|
||||
orbit_data = PropertyT.decimate(orbit_data);
|
||||
|
||||
@testset "Sq₃ is SOS" begin
|
||||
elt = PropertyT.Sq(RG)
|
||||
UB = 0.05 # 0.105?
|
||||
|
||||
residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
|
||||
@info "obtained λ and residual" λ norm(residual, 1)
|
||||
|
||||
@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
|
||||
|
||||
@test 2^2*norm(residual, 1) < λ/100
|
||||
end
|
||||
|
||||
@testset "Adj₃ is SOS" begin
|
||||
elt = PropertyT.Adj(RG)
|
||||
UB = 0.1 # 0.157?
|
||||
|
||||
residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
|
||||
@info "obtained λ and residual" λ norm(residual, 1)
|
||||
|
||||
@test 2^2*norm(residual, 1) < λ
|
||||
@test 2^2*norm(residual, 1) < λ/100
|
||||
end
|
||||
|
||||
@testset "Op₃ is empty, so can not be certified" begin
|
||||
elt = PropertyT.Op(RG)
|
||||
UB = Inf
|
||||
|
||||
residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
|
||||
@info "obtained λ and residual" λ norm(residual, 1)
|
||||
|
||||
@test 2^2*norm(residual, 1) > λ
|
||||
end
|
||||
end
|
||||
|
||||
@testset "SL(4,Z)" begin
|
||||
N = 4
|
||||
halfradius = 2
|
||||
M = MatrixSpace(Nemo.ZZ, N,N)
|
||||
S = PropertyT.generating_set(M)
|
||||
Δ = PropertyT.Laplacian(S, halfradius)
|
||||
RG = parent(Δ)
|
||||
orbit_data = PropertyT.OrbitData(RG, WreathProduct(PermGroup(2), PermGroup(N)))
|
||||
orbit_data = PropertyT.decimate(orbit_data);
|
||||
|
||||
@testset "Sq₄ is SOS" begin
|
||||
elt = PropertyT.Sq(RG)
|
||||
UB = 0.2 # 0.3172
|
||||
|
||||
residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
|
||||
@info "obtained λ and residual" λ norm(residual, 1)
|
||||
|
||||
@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
|
||||
@test 2^2*norm(residual, 1) < λ/100
|
||||
end
|
||||
|
||||
@testset "Adj₄ is SOS" begin
|
||||
elt = PropertyT.Adj(RG)
|
||||
UB = 0.3 # 0.5459?
|
||||
|
||||
residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
|
||||
@info "obtained λ and residual" λ norm(residual, 1)
|
||||
|
||||
@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
|
||||
@test 2^2*norm(residual, 1) < λ/100
|
||||
end
|
||||
|
||||
@testset "we can't cerify that Op₄ SOS" begin
|
||||
elt = PropertyT.Op(RG)
|
||||
UB = 2.0
|
||||
|
||||
residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
|
||||
@info "obtained λ and residual" λ norm(residual, 1)
|
||||
|
||||
@test 2^2*norm(residual, 1) > λ # i.e. we can certify positivity
|
||||
end
|
||||
|
||||
@testset "Adj₄ + Op₄ is SOS" begin
|
||||
elt = PropertyT.Adj(RG) + PropertyT.Op(RG)
|
||||
UB = 0.6 # 0.82005
|
||||
|
||||
residual, λ, _ = check_positivity(elt, Δ, orbit_data, UB)
|
||||
@info "obtained λ and residual" λ norm(residual, 1)
|
||||
|
||||
@test 2^2*norm(residual, 1) < λ # i.e. we can certify positivity
|
||||
@test 2^2*norm(residual, 1) < λ/100
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
|
Loading…
Reference in New Issue
Block a user