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PropertyT.jl/scripts/G₂_Adj.jl

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),
)