97 lines
2.3 KiB
Julia
97 lines
2.3 KiB
Julia
using LinearAlgebra
|
||
BLAS.set_num_threads(4)
|
||
ENV["OMP_NUM_THREADS"] = 4
|
||
include(joinpath(@__DIR__, "../test/optimizers.jl"))
|
||
using SCS_MKL_jll
|
||
|
||
using Groups
|
||
import Groups.MatrixGroups
|
||
|
||
using PropertyT
|
||
|
||
import PropertyT.SW as SW
|
||
using PropertyT.PG
|
||
using PropertyT.SA
|
||
|
||
include(joinpath(@__DIR__, "argparse.jl"))
|
||
|
||
const N = parsed_args["N"]
|
||
const HALFRADIUS = parsed_args["halfradius"]
|
||
const UPPER_BOUND = parsed_args["upper_bound"]
|
||
|
||
G = MatrixGroups.SpecialLinearGroup{N}(Int8)
|
||
@info "Running Adj - λ·Δ sum of squares decomposition for " G
|
||
|
||
@info "computing group algebra structure"
|
||
RG, S, sizes = @time PropertyT.group_algebra(G, halfradius = HALFRADIUS)
|
||
|
||
@info "computing WedderburnDecomposition"
|
||
wd = let RG = RG, N = N
|
||
G = StarAlgebras.object(RG)
|
||
P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
|
||
Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
|
||
act = PropertyT.action_by_conjugation(G, Σ)
|
||
|
||
wdfl = @time SW.WedderburnDecomposition(
|
||
Float64,
|
||
Σ,
|
||
act,
|
||
basis(RG),
|
||
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
|
||
)
|
||
end
|
||
@info wd
|
||
|
||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||
Δs = let ψ = identity
|
||
PropertyT.laplacians(RG, S, x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])))
|
||
end
|
||
elt = PropertyT.Adj(Δs, :A₂)
|
||
unit = Δ
|
||
warm = nothing
|
||
|
||
@info "defining optimization problem"
|
||
@time model, varP = PropertyT.sos_problem_primal(
|
||
elt,
|
||
unit,
|
||
wd;
|
||
upper_bound = UPPER_BOUND,
|
||
augmented = true,
|
||
)
|
||
|
||
begin
|
||
@time status, warm = PropertyT.solve(
|
||
model,
|
||
scs_optimizer(;
|
||
eps = 1e-10,
|
||
max_iters = 20_000,
|
||
accel = 50,
|
||
alpha = 1.95,
|
||
),
|
||
warm,
|
||
)
|
||
|
||
@info "reconstructing the solution"
|
||
Q = let wd = wd, Ps = [JuMP.value.(P) for P in varP]
|
||
Qs = real.(sqrt.(Ps))
|
||
PropertyT.reconstruct(Qs, wd)
|
||
end
|
||
|
||
@info "certifying the solution"
|
||
@time certified, λ = PropertyT.certify_solution(
|
||
elt,
|
||
unit,
|
||
JuMP.objective_value(model),
|
||
Q;
|
||
halfradius = HALFRADIUS,
|
||
augmented = true,
|
||
)
|
||
end
|
||
|
||
if certified && λ > 0
|
||
Κ(λ, S) = round(sqrt(2λ / length(S)), Base.RoundDown; digits = 5)
|
||
@info "Certified result: $G has property (T):" N λ Κ(λ, S)
|
||
else
|
||
@info "Could NOT certify the result:" certified λ
|
||
end
|