mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-19 15:25:29 +01:00
84 lines
2.0 KiB
Julia
84 lines
2.0 KiB
Julia
|
using LinearAlgebra
|
|||
|
|
using MKL_jll
|
|||
|
|
BLAS.set_num_threads(4)
|
|||
|
|
|
|||
|
|
ENV["OMP_NUM_THREADS"] = 4
|
|||
|
|
|
|||
|
|
using Groups
|
|||
|
|
import Groups.MatrixGroups
|
|||
|
|
|
|||
|
|
include(joinpath(@__DIR__, "../test/optimizers.jl"))
|
|||
|
|
using PropertyT
|
|||
|
|
|
|||
|
|
using PropertyT.SymbolicWedderburn
|
|||
|
|
using PropertyT.PermutationGroups
|
|||
|
|
using PropertyT.StarAlgebras
|
|||
|
|
|
|||
|
|
include(joinpath(@__DIR__, "argparse.jl"))
|
|||
|
|
include(joinpath(@__DIR__, "utils.jl"))
|
|||
|
|
|
|||
|
|
const N = parsed_args["N"]
|
|||
|
|
const HALFRADIUS = parsed_args["halfradius"]
|
|||
|
|
const UPPER_BOUND = parsed_args["upper_bound"]
|
|||
|
|
|
|||
|
|
const GENUS = 2N
|
|||
|
|
|
|||
|
|
G = MatrixGroups.SymplecticGroup{GENUS}(Int8)
|
|||
|
|
@info "Running Δ² - 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 SymbolicWedderburn.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)
|
|||
|
|
elt = Δ^2
|
|||
|
|
unit = Δ
|
|||
|
|
|
|||
|
|
@info "defining optimization problem"
|
|||
|
|
@time model, varP = PropertyT.sos_problem_primal(
|
|||
|
|
elt,
|
|||
|
|
unit,
|
|||
|
|
wd;
|
|||
|
|
upper_bound = UPPER_BOUND,
|
|||
|
|
augmented = true,
|
|||
|
|
show_progress = true,
|
|||
|
|
)
|
|||
|
|
|
|||
|
|
solve_in_loop(
|
|||
|
|
model,
|
|||
|
|
wd,
|
|||
|
|
varP;
|
|||
|
|
logdir = "./log/Sp($N,Z)/r=$HALFRADIUS/Δ²-$(UPPER_BOUND)Δ",
|
|||
|
|
optimizer = scs_optimizer(;
|
|||
|
|
linear_solver = SCS.MKLDirectSolver,
|
|||
|
|
eps = 1e-10,
|
|||
|
|
max_iters = 50_000,
|
|||
|
|
accel = 50,
|
|||
|
|
alpha = 1.95,
|
|||
|
|
),
|
|||
|
|
data = (elt = elt, unit = unit, halfradius = HALFRADIUS),
|
|||
|
|
)
|
|||
|
|
|
|||
|
|
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
|