mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-14 14:15:28 +01:00
total rewrite with the aim of modularisation
This commit is contained in:
parent
c59ebe5086
commit
c5de9c206f
143
SL(3,Z).jl
143
SL(3,Z).jl
@ -1,79 +1,104 @@
|
||||
using JuMP
|
||||
import SCS: SCSSolver
|
||||
import Mosek: MosekSolver
|
||||
function SL₃ℤ_generatingset()
|
||||
|
||||
workers_processes = addprocs()
|
||||
function E(i::Int, j::Int, N::Int=3)
|
||||
@assert i≠j
|
||||
k = eye(N)
|
||||
k[i,j] = 1
|
||||
return k
|
||||
end
|
||||
|
||||
@everywhere push!(LOAD_PATH, "./")
|
||||
using GroupAlgebras
|
||||
@everywhere include("property(T).jl")
|
||||
|
||||
function E(i::Int, j::Int, N::Int=3)
|
||||
@assert i≠j
|
||||
k = eye(N)
|
||||
k[i,j] = 1
|
||||
return k
|
||||
end
|
||||
|
||||
function SL_3ZZ_generating_set()
|
||||
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
|
||||
|
||||
const ID = eye(3)
|
||||
function generate_B₂_and_B₄(B₁)
|
||||
B₂ = products(B₁, B₁);
|
||||
B₃ = products(B₁, B₂);
|
||||
B₄ = products(B₁, B₃);
|
||||
|
||||
const S₁ = SL_3ZZ_generating_set()
|
||||
@assert B₄[1:length(B₂)] == B₂
|
||||
return B₂, B₄;
|
||||
end
|
||||
|
||||
function prepare_Laplacian_and_constraints(S, identity)
|
||||
|
||||
B₂, B₄ = generate_B₂_and_B₄(vcat([identity], S))
|
||||
product_matrix = create_product_matrix(B₄,length(B₂));
|
||||
sdp_constraints = constraints_from_pm(product_matrix, length(B₄))
|
||||
L_coeff = splaplacian_coeff(S, B₄);
|
||||
|
||||
return GroupAlgebraElement(L_coeff, product_matrix), sdp_constraints
|
||||
end
|
||||
|
||||
function prepare_Δ_sdp_constraints(name::String;cached=true)
|
||||
f₁ = isfile("$name.product_matrix")
|
||||
f₂ = isfile("$name.delta.coefficients")
|
||||
if cached && f₁ && f₂
|
||||
println("Loading precomputed pm, Δ, sdp_constraints...")
|
||||
product_matrix = readdlm("$name.product_matrix", Int)
|
||||
L = readdlm("$name.delta.coefficients")[:, 1]
|
||||
Δ = GroupAlgebraElement(L, product_matrix)
|
||||
sdp_constraints = constraints_from_pm(product_matrix)
|
||||
else
|
||||
println("Computing pm, Δ, sdp_constraints...")
|
||||
ID = eye(Int, 3)
|
||||
S₁ = SL₃ℤ_generatingset()
|
||||
Δ, sdp_constraints = prepare_Laplacian_and_constraints(S₁, ID)
|
||||
writedlm("$name.delta.coefficients", Δ.coefficients)
|
||||
writedlm("$name.product_matrix", Δ.product_matrix)
|
||||
end
|
||||
return Δ, sdp_constraints
|
||||
end
|
||||
|
||||
|
||||
const TOL=10.0^-7
|
||||
# const VERBOSE=true
|
||||
#solver = SCSSolver(eps=TOL, max_iters=ITERATIONS, verbose=VERBOSE);
|
||||
# solver = MosekSolver(MSK_DPAR_INTPNT_CO_TOL_REL_GAP=TOL,
|
||||
# # MSK_DPAR_INTPNT_CO_TOL_PFEAS=1e-15,
|
||||
# # MSK_DPAR_INTPNT_CO_TOL_DFEAS=1e-15,
|
||||
# # MSK_IPAR_PRESOLVE_USE=0,
|
||||
# QUIET=!VERBOSE)
|
||||
function compute_κ_A(name::String, Δ, sdp_constraints;
|
||||
cached = true,
|
||||
tol = TOL,
|
||||
verbose = VERBOSE,
|
||||
solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=!verbose))
|
||||
# solver = SCSSolver(eps=TOL, max_iters=ITERATIONS, verbose=VERBOSE))
|
||||
|
||||
# κ, A = solve_for_property_T(S₁, solver, 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
|
||||
|
||||
|
||||
const product_matrix = readdlm("SL3Z.product_matrix", Int)
|
||||
const L = readdlm("SL3Z.delta.coefficients")[:, 1]
|
||||
const Δ = GroupAlgebraElement(L, product_matrix)
|
||||
workers_processes = addprocs()
|
||||
@everywhere push!(LOAD_PATH, "./")
|
||||
using GroupAlgebras
|
||||
@everywhere include("property(T).jl")
|
||||
|
||||
const A = readdlm("SL3Z.SDPmatrixA.Mosek")
|
||||
const κ = readdlm("SL3Z.kappa.Mosek")[1]
|
||||
const NAME = "SL3Z"
|
||||
const VERBOSE = true
|
||||
const TOL=1e-7
|
||||
const Δ, sdp_constraints = prepare_Δ_sdp_constraints(NAME)
|
||||
const κ, A = compute_κ_A(NAME, Δ, sdp_constraints)
|
||||
|
||||
@assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
|
||||
@assert A == Symmetric(A)
|
||||
if κ > 0
|
||||
@time T = ℚ_distance_to_positive_cone(Δ, κ, A, tol=TOL, verbose=VERBOSE)
|
||||
|
||||
const A_sqrt = real(sqrtm(A))
|
||||
if T < 0
|
||||
println("$NAME HAS property (T)!")
|
||||
else
|
||||
println("$NAME may NOT HAVE property (T)!")
|
||||
end
|
||||
|
||||
const SOS_fp_diff, SOS_fp_L₁_distance = check_solution(κ, A_sqrt, Δ)
|
||||
|
||||
@show SOS_fp_L₁_distance
|
||||
@show GroupAlgebras.ɛ(SOS_fp_diff)
|
||||
|
||||
const κ_rational = rationalize(BigInt, κ, tol=TOL)
|
||||
const A_sqrt_rational = rationalize(BigInt, A_sqrt, tol=TOL)
|
||||
const Δ_rational = rationalize(BigInt, Δ, tol=TOL)
|
||||
|
||||
const SOS_rational_diff, SOS_rat_L₁_distance = check_solution(κ_rational, A_sqrt_rational, Δ_rational)
|
||||
|
||||
@assert isa(SOS_rat_L₁_distance, Rational{BigInt})
|
||||
@show float(SOS_rat_L₁_distance)
|
||||
@show float(GroupAlgebras.ɛ(SOS_rational_diff))
|
||||
|
||||
const A_sqrt_augmented = correct_to_augmentation_ideal(A_sqrt_rational)
|
||||
|
||||
const SOS_rational_aug_diff, SOS_aug_rat_L₁_distance = check_solution(κ_rational, A_sqrt_augmented, Δ_rational)
|
||||
|
||||
@assert isa(SOS_aug_rat_L₁_distance, Rational{BigInt})
|
||||
@assert GroupAlgebras.ɛ(SOS_rational_aug_diff) == 0//1
|
||||
|
||||
@show float(SOS_aug_rat_L₁_distance)
|
||||
@show float(κ_rational - 2^3*SOS_aug_rat_L₁_distance)
|
||||
else
|
||||
println("$κ < 0: $NAME may NOT HAVE property (T)!")
|
||||
end
|
||||
|
||||
rmprocs(workers_processes)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user