65 lines
1.5 KiB
Julia
65 lines
1.5 KiB
Julia
using JuMP
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import SCS: SCSSolver
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import Mosek: MosekSolver
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push!(LOAD_PATH, "./")
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using GroupAlgebras
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include("property(T).jl")
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const VERBOSE=true
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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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#solver = SCSSolver(eps=10.0^-TOL, max_iters=ITERATIONS, verbose=true);
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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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product_matrix = readdlm("SL₃Z.product_matrix", Int)
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L = readdlm("SL₃Z.Δ.coefficients")[:, 1]
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Δ = GroupAlgebraElement(L, product_matrix)
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# @show Δ
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A = readdlm("matrix.A.Mosek")
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κ = readdlm("kappa.Mosek")[1]
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# @show eigvals(A)
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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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SOS_EOI_fp_L₁, Ω_fp_dist = check_solution(κ, A_sqrt, Δ)
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κ_rational = rationalize(BigInt, κ;)
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A_sqrt_rational = rationalize(BigInt, A_sqrt)
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Δ_rational = rationalize(BigInt, Δ)
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SOS_EOI_rat_L₁, Ω_rat_dist = check_solution(κ_rational, A_sqrt_rational, Δ_rational)
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