using LinearAlgebra
BLAS.set_num_threads(8)

ENV["OMP_NUM_THREADS"] = 1

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"]

const GENUS = 2N

G = MatrixGroups.SymplecticGroup{GENUS}(Int8)

RG, S, sizes =
    @time PropertyT.group_algebra(G, halfradius=HALFRADIUS, twisted=true)

wd = let RG = RG, N = N
    G = StarAlgebras.object(RG)
    P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
    Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
    # Σ = P
    act = PropertyT.action_by_conjugation(G, Σ)
    @info "Computing WedderburnDecomposition"

    wdfl = @time SymbolicWedderburn.WedderburnDecomposition(
        Float64,
        Σ,
        act,
        basis(RG),
        StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
    )
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 = Δ^2
elt = PropertyT.Adj(Δs, :C₂)
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/r=$HALFRADIUS/Sp($N,Z)/Adj_C₂-InfΔ",
    optimizer=cosmo_optimizer(
        eps=1e-10,
        max_iters=20_000,
        accel=50,
        alpha=1.95,
    ),
    data=(elt=elt, unit=unit, halfradius=HALFRADIUS)
)