using LinearAlgebra BLAS.set_num_threads(8) 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"] 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.perm(g) for g in Σ), ) @time SymbolicWedderburn.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, ) warm = nothing solve_in_loop( model, wd, varP; logdir = "./log/G2/r=$HALFRADIUS/Adj-InfΔ", optimizer = scs_optimizer(; eps = 1e-10, max_iters = 50_000, accel = 50, alpha = 1.95, ), data = (elt = elt, unit = unit, halfradius = HALFRADIUS), )