mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-19 15:25:29 +01:00
123 lines
3.4 KiB
Julia
123 lines
3.4 KiB
Julia
using JLD
|
||
using JuMP
|
||
import SCS: SCSSolver
|
||
import Mosek: MosekSolver
|
||
|
||
using Groups
|
||
using ProgressMeter
|
||
|
||
|
||
function SL₃ℤ_generatingset()
|
||
|
||
function E(i::Int, j::Int, N::Int=3)
|
||
@assert i≠j
|
||
k = eye(N)
|
||
k[i,j] = 1
|
||
return k
|
||
end
|
||
|
||
S = [E(1,2), E(1,3), E(2,3)];
|
||
S = vcat(S, [x' for x in S]);
|
||
S = vcat(S, [inv(x) for x in S]);
|
||
return S
|
||
end
|
||
|
||
function prepare_Δ_sdp_constraints(identity, S)
|
||
@show length(S)
|
||
|
||
B₁ = vcat([identity], S)
|
||
B₂ = products(B₁, B₁);
|
||
B₃ = products(B₁, B₂);
|
||
B₄ = products(B₁, B₃);
|
||
@assert B₄[1:length(B₂)] == B₂
|
||
|
||
product_matrix = create_product_matrix(B₄,length(B₂));
|
||
sdp_constraints = constraints_from_pm(product_matrix, length(B₄))
|
||
L_coeff = splaplacian_coeff(S, B₂, length(B₄));
|
||
Δ = GroupAlgebraElement(L_coeff, product_matrix)
|
||
|
||
return Δ, sdp_constraints
|
||
end
|
||
|
||
function load_Δ_sdp_constraints(name::String;cached=true)
|
||
pm_filename = "$name.product_matrix.jld"
|
||
Δ_coeff_filename = "$name.delta.coefficients.jld"
|
||
f₁ = isfile(pm_filename)
|
||
f₂ = isfile(Δ_coeff_filename)
|
||
if cached && f₁ && f₂
|
||
println("Loading precomputed pm, Δ, sdp_constraints...")
|
||
product_matrix = load(pm_filename, "pm")
|
||
L = load(Δ_coeff_filename, "Δ")[:, 1]
|
||
Δ = GroupAlgebraElement(L, Array{Int,2}(product_matrix))
|
||
sdp_constraints = constraints_from_pm(product_matrix)
|
||
else
|
||
println("Computing pm, Δ, sdp_constraints...")
|
||
ID = eye(Int, 3)
|
||
S = SL₃ℤ_generatingset()
|
||
Δ, sdp_constraints = prepare_Δ_sdp_constraints(ID, S)
|
||
|
||
save(pm_filename, "pm", Δ.product_matrix)
|
||
save(Δ_coeff_filename, "Δ", Δ.coefficients)
|
||
|
||
end
|
||
return Δ, sdp_constraints
|
||
end
|
||
|
||
|
||
function compute_κ_A(name::String, Δ, sdp_constraints;
|
||
cached = true,
|
||
tol = 1e-7,
|
||
verbose = false,
|
||
# solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=!verbose))
|
||
solver = SCSSolver(eps=tol, max_iters=20000, cg_rate=3, verbose=verbose))
|
||
|
||
f₁ = isfile("$name.kappa")
|
||
f₂ = isfile("$name.SDPmatrixA")
|
||
|
||
if cached && f₁ && f₂
|
||
println("Loading precomputed κ, A...")
|
||
A = readdlm("$name.SDPmatrixA")
|
||
κ = readdlm("$name.kappa")[1]
|
||
else
|
||
println("Solving SDP problem maximizing κ...")
|
||
κ, A = solve_SDP(sdp_constraints, Δ, solver, verbose=verbose)
|
||
# writedlm("$name.kappa", kappa)
|
||
# writedlm("$name.SDPmatrixA", A)
|
||
end
|
||
return κ, A
|
||
end
|
||
|
||
function main()
|
||
const NAME = "SL3Z"
|
||
const VERBOSE = true
|
||
const TOL=1e-7
|
||
const Δ, sdp_constraints = load_Δ_sdp_constraints(NAME)
|
||
const κ, A = compute_κ_A(NAME, Δ, sdp_constraints, cached=false, verbose=VERBOSE)
|
||
|
||
if maximum(A) < 1e-2
|
||
warn("Solver might not solved the problem successfully and the positive solution is due to floating-point error, proceeding anyway...")
|
||
end
|
||
|
||
if κ > 0
|
||
@assert A == Symmetric(A)
|
||
const A_sqrt = real(sqrtm(A))
|
||
|
||
T = ℚ_distance_to_positive_cone(Δ, κ, A, tol=TOL, verbose=VERBOSE)
|
||
|
||
if T < 0
|
||
println("$NAME HAS property (T)!")
|
||
else
|
||
println("$NAME may NOT HAVE property (T)!")
|
||
end
|
||
|
||
else
|
||
println("$κ < 0: $NAME may NOT HAVE property (T)!")
|
||
end
|
||
end
|
||
|
||
@everywhere push!(LOAD_PATH, "./")
|
||
using GroupAlgebras
|
||
@everywhere include("property(T).jl")
|
||
|
||
main()
|