mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-19 23:30:26 +01:00
99 lines
2.2 KiB
Julia
99 lines
2.2 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"))
|
|
include(joinpath(@__DIR__, "utils.jl"))
|
|
|
|
# const N = parsed_args["N"]
|
|
const HALFRADIUS = parsed_args["halfradius"]
|
|
const UPPER_BOUND = parsed_args["upper_bound"]
|
|
|
|
include(joinpath(@__DIR__, "./G₂_gens.jl"))
|
|
|
|
G, roots, Weyl = G₂_roots_weyl()
|
|
@info "Running Adj² - λ·Δ sum of squares decomposition for G₂"
|
|
|
|
@info "computing group algebra structure"
|
|
RG, S, sizes = @time PropertyT.group_algebra(G, halfradius = HALFRADIUS)
|
|
|
|
@info "computing WedderburnDecomposition"
|
|
wd = let Σ = Weyl, RG = RG
|
|
act = PropertyT.AlphabetPermutation{eltype(Σ),Int64}(
|
|
Dict(g => PermutationGroups.AP.perm(g) for g in Σ),
|
|
)
|
|
|
|
@time SW.WedderburnDecomposition(
|
|
Float64,
|
|
Σ,
|
|
act,
|
|
basis(RG),
|
|
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
|
|
semisimple = false,
|
|
)
|
|
end
|
|
@info wd
|
|
|
|
function desubscriptify(symbol::Symbol)
|
|
digits = [
|
|
Int(l) - 0x2080 for
|
|
l in reverse(string(symbol)) if 0 ≤ Int(l) - 0x2080 ≤ 9
|
|
]
|
|
res = 0
|
|
for (i, d) in enumerate(digits)
|
|
res += 10^(i - 1) * d
|
|
end
|
|
return res
|
|
end
|
|
|
|
function PropertyT.grading(g::MatrixGroups.MatrixElt, roots = roots)
|
|
id = desubscriptify(g.id)
|
|
return roots[id]
|
|
end
|
|
|
|
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
|
Δs = PropertyT.laplacians(
|
|
RG,
|
|
S,
|
|
x -> (gx = PropertyT.grading(x); Set([gx, -gx])),
|
|
)
|
|
|
|
elt = PropertyT.Adj(Δs)
|
|
@assert elt == Δ^2 - PropertyT.Sq(Δs)
|
|
unit = Δ
|
|
|
|
@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/G2/r=$HALFRADIUS/Adj-$(UPPER_BOUND)Δ",
|
|
optimizer = scs_optimizer(;
|
|
linear_solver = SCS.MKLDirectSolver,
|
|
eps = 1e-9,
|
|
max_iters = 100_000,
|
|
accel = 50,
|
|
alpha = 1.95,
|
|
),
|
|
data = (elt = elt, unit = unit, halfradius = HALFRADIUS),
|
|
)
|