mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-14 14:15:28 +01:00
80 lines
2.2 KiB
Julia
80 lines
2.2 KiB
Julia
using JuMP
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import SCS: SCSSolver
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import Mosek: MosekSolver
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workers_processes = addprocs()
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@everywhere push!(LOAD_PATH, "./")
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using GroupAlgebras
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@everywhere include("property(T).jl")
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function E(i::Int, j::Int, N::Int=3)
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@assert i≠j
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k = eye(N)
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k[i,j] = 1
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return k
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end
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function SL_3ZZ_generating_set()
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S = [E(1,2), E(1,3), E(2,3)];
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S = vcat(S, [x' for x in S]);
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S = vcat(S, [inv(x) for x in S]);
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return S
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end
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const ID = eye(3)
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const S₁ = SL_3ZZ_generating_set()
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const TOL=10.0^-7
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# const VERBOSE=true
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#solver = SCSSolver(eps=TOL, max_iters=ITERATIONS, verbose=VERBOSE);
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# solver = MosekSolver(MSK_DPAR_INTPNT_CO_TOL_REL_GAP=TOL,
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# # MSK_DPAR_INTPNT_CO_TOL_PFEAS=1e-15,
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# # MSK_DPAR_INTPNT_CO_TOL_DFEAS=1e-15,
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# # MSK_IPAR_PRESOLVE_USE=0,
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# QUIET=!VERBOSE)
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# κ, A = solve_for_property_T(S₁, solver, verbose=VERBOSE)
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const product_matrix = readdlm("SL3Z.product_matrix", Int)
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const L = readdlm("SL3Z.delta.coefficients")[:, 1]
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const Δ = GroupAlgebraElement(L, product_matrix)
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const A = readdlm("SL3Z.SDPmatrixA.Mosek")
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const κ = readdlm("SL3Z.kappa.Mosek")[1]
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@assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
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@assert A == Symmetric(A)
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const A_sqrt = real(sqrtm(A))
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const SOS_fp_diff, SOS_fp_L₁_distance = check_solution(κ, A_sqrt, Δ)
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@show SOS_fp_L₁_distance
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@show GroupAlgebras.ɛ(SOS_fp_diff)
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const κ_rational = rationalize(BigInt, κ, tol=TOL)
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const A_sqrt_rational = rationalize(BigInt, A_sqrt, tol=TOL)
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const Δ_rational = rationalize(BigInt, Δ, tol=TOL)
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const SOS_rational_diff, SOS_rat_L₁_distance = check_solution(κ_rational, A_sqrt_rational, Δ_rational)
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@assert isa(SOS_rat_L₁_distance, Rational{BigInt})
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@show float(SOS_rat_L₁_distance)
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@show float(GroupAlgebras.ɛ(SOS_rational_diff))
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const A_sqrt_augmented = correct_to_augmentation_ideal(A_sqrt_rational)
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const SOS_rational_aug_diff, SOS_aug_rat_L₁_distance = check_solution(κ_rational, A_sqrt_augmented, Δ_rational)
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@assert isa(SOS_aug_rat_L₁_distance, Rational{BigInt})
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@assert GroupAlgebras.ɛ(SOS_rational_aug_diff) == 0//1
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@show float(SOS_aug_rat_L₁_distance)
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@show float(κ_rational - 2^3*SOS_aug_rat_L₁_distance)
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rmprocs(workers_processes)
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