using AbstractAlgebra using Groups using GroupRings using PropertyT using SCS solver(tol, iterations) = SCSSolver(linearsolver=SCS.Direct, eps=tol, max_iters=iterations, alpha=1.95, acceleration_lookback=1) include("../main.jl") using PropertyTGroups args = Dict("SAut" => 5, "upper-bound" => 10.0, "radius" => 2, "nosymmetry"=>false, "tol"=>1e-10, "iterations" =>200000, "repetitions"=>5) Gr = PropertyTGroups.PropertyTGroup(args) sett = PropertyT.Settings(Gr, args, solver(args["tol"], args["iterations"])) @show sett fullpath = PropertyT.fullpath(sett) isdir(fullpath) || mkpath(fullpath) # setup_logging(PropertyT.filename(fullpath, :fulllog), :fulllog) function (p::perm)(A::GroupRingElem) RG = parent(A) T = eltype(A.coeffs) result = zero(RG, T) for (idx, c) in enumerate(A.coeffs) if c!= zero(T) result[p(RG.basis[idx])] = c end end return result end function small_generating_set(RG::GroupRing{AutGroup{N}}, n) where N indexing = [(i,j) for i in 1:n for j in 1:n if i≠j] rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing] lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing] gen_set = RG.group.([rmuls; lmuls]) return [gen_set; inv.(gen_set)] end function computeX(RG::GroupRing{AutGroup{N}}) where N Tn = small_generating_set(RG, N-1) ℤ = Int64 Δn = length(Tn)*one(RG, ℤ) - RG(Tn, ℤ); Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0] @time X = sum(σ(Δn)*sum(τ(Δn) for τ ∈ Alt_N if τ ≠ σ) for σ in Alt_N); return X end function Sq(RG::GroupRing{AutGroup{N}}) where N T2 = small_generating_set(RG, 2) ℤ = Int64 Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ); Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0] elt = sum(σ(Δ₂)^2 for σ in Alt_N) return elt end function Adj(RG::GroupRing{AutGroup{N}}) where N T2 = small_generating_set(RG, 2) ℤ = Int64 Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ); Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0] adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]]) adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 1] @time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N); # return RG(elt.coeffs÷factorial(N-2)^2) return elt end function Op(RG::GroupRing{AutGroup{N}}) where N T2 = small_generating_set(RG, 2) ℤ = Int64 Δ₂ = length(T2)*one(RG, ℤ) - RG(T2, ℤ); Alt_N = [g for g in elements(PermutationGroup(N)) if parity(g) == 0] adj(σ::perm, τ::perm, i=1, j=2) = Set([σ[i], σ[j]]) ∩ Set([τ[i], τ[j]]) adj(σ::perm) = [τ for τ in Alt_N if length(adj(σ, τ)) == 0] @time elt = sum(σ(Δ₂)*sum(τ(Δ₂) for τ in adj(σ)) for σ in Alt_N); # return RG(elt.coeffs÷factorial(N-2)^2) return elt end const ELT_FILE = joinpath(dirname(PropertyT.filename(sett, :Δ)), "SqAdjOp_coeffs.jld") const WARMSTART_FILE = PropertyT.filename(sett, :warmstart) if isfile(PropertyT.filename(sett,:Δ)) && isfile(ELT_FILE) && isfile(PropertyT.filename(sett, :OrbitData)) # cached Δ = PropertyT.loadGRElem(PropertyT.filename(sett,:Δ), sett.G) RG = parent(Δ) orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData") sq_c, adj_c, op_c = load(ELT_FILE, "Sq", "Adj", "Op") # elt = ELT_FILE, sett.G) sq = GroupRingElem(sq_c, RG) adj = GroupRingElem(adj_c, RG) op = GroupRingElem(op_c, RG); else info("Compute Laplacian") Δ = PropertyT.Laplacian(sett.S, sett.radius) RG = parent(Δ) info("Compute Sq, Adj, Op") @time sq, adj, op = Sq(RG), Adj(RG), Op(RG) PropertyT.saveGRElem(PropertyT.filename(sett, :Δ), Δ) save(ELT_FILE, "Sq", sq.coeffs, "Adj", adj.coeffs, "Op", op.coeffs) info("Compute OrbitData") if !isfile(PropertyT.filename(sett, :OrbitData)) orbit_data = PropertyT.OrbitData(parent(Y), sett.autS) save(PropertyT.filename(sett, :OrbitData), "OrbitData", orbit_data) else orbit_data = load(PropertyT.filename(sett, :OrbitData), "OrbitData") end end; orbit_data = PropertyT.decimate(orbit_data); elt = adj+3op; SDP_problem, varλ, varP = PropertyT.SOS_problem(elt, Δ, orbit_data; upper_bound=sett.upper_bound) begin using SCS scs_solver = SCS.SCSSolver(linearsolver=SCS.Direct, eps=sett.tol, max_iters=args["iterations"], alpha=1.95, acceleration_lookback=1) JuMP.setsolver(SDP_problem, scs_solver) end λ = Ps = nothing ws = PropertyT.warmstart(sett) using ProgressMeter @showprogress "Running SDP optimization step... " for i in 1:args["repetitions"] # while true λ, Ps, ws = PropertyT.solve(PropertyT.filename(sett, :solverlog), SDP_problem, varλ, varP, ws); if all((!isnan).(ws[1])) save(WARMSTART_FILE, "warmstart", ws, "λ", λ, "Ps", Ps) save(WARMSTART_FILE[1:end-4]*"_$(now()).jld", "warmstart", ws, "λ", λ, "Ps", Ps) else warn("No valid solution was saved!") end end function check_SOS_precision(Q::Matrix, eoi::GroupRingElem) RG = parent(eoi) @time sos = PropertyT.compute_SOS(RG, Q); residue = eoi - sos return norm(residue, 1) end info("Reconstructing P...") @time P = PropertyT.reconstruct(Ps, orbit_data); save(PropertyT.filename(sett, :solution), "λ", λ, "P", P) addprocs(4) @everywhere using PropertyT @time const Q = real(sqrtm(P)); const EOI = elt - λ*Δ; @show λ - 2^3*check_SOS_precision(Q, EOI); using IntervalArithmetic Qint = PropertyT.augIdproj(Q); @assert all([zero(eltype(Q)) in sum(view(Qint, :, i)) for i in 1:size(Qint, 2)]) EOIint = GroupRingElem([@interval(c) for c in EOI.coeffs], parent(Δ)); b_int = check_SOS_precision(Qint, EOIint) @show @interval(λ) - 2^3*b_int;