add check_positivity.jl

Positivity_X/check_positivity.jl

@@ -0,0 +1,200 @@
+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;