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common interface for groups: pm&Delta, kappa&A, filenames
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@ -186,6 +186,78 @@ function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
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return ℚ_distance
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return ℚ_distance
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end
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end
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function pmΔfilenames(name::String)
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if !isdir(name)
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mkdir(name)
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end
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prefix = name
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pm_filename = joinpath(prefix, "product_matrix.jld")
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Δ_coeff_filename = joinpath(prefix, "delta.coefficients.jld")
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return pm_filename, Δ_coeff_filename
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end
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function κSDPfilenames(name::String)
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if !isdir(name)
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mkdir(name)
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end
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prefix = name
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κ_filename = joinpath(prefix, "kappa.jld")
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SDP_filename = joinpath(prefix, "SDPmatrixA.jld")
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return κ_filename, SDP_filename
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end
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function ΔandSDPconstraints(name::String)
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pm_fname, Δ_fname = pmΔfilenames(name)
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f₁ = isfile(pm_fname)
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f₂ = isfile(Δ_fname)
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if f₁ && f₂
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println("Loading precomputed pm, Δ, sdp_constraints...")
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product_matrix = load(pm_fname, "pm")
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L = load(Δ_fname, "Δ")[:, 1]
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Δ = GroupAlgebraElement(L, Array{Int,2}(product_matrix))
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sdp_constraints = constraints_from_pm(product_matrix)
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else
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throw(ArgumentError("You need to precompute pm and Δ to load it!"))
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end
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return Δ, sdp_constraints
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end
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function ΔandSDPconstraints(name::String, ID, generating_func::Function)
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pm_fname, Δ_fname = pmΔfilenames(name)
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Δ, sdp_constraints = ΔandSDPconstraints(ID, generating_func())
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save(pm_fname, "pm", Δ.product_matrix)
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save(Δ_fname, "Δ", Δ.coefficients)
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return Δ, sdp_constraints
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end
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function κandA(name::String)
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κ_fname, SDP_fname = κSDPfilenames(name)
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f₁ = isfile(κ_fname)
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f₂ = isfile(SDP_fname)
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if f₁ && f₂
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println("Loading precomputed κ, A...")
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κ = load(κ_fname, "κ")
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A = load(SDP_fname, "A")
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else
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throw(ArgumentError("You need to precompute κ and SDP matrix A to load it!"))
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end
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return κ, A
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end
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function κandA(name::String, sdp_constraints, Δ::GroupAlgebraElement, solver::AbstractMathProgSolver; upper_bound=Inf)
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println("Creating SDP problem...")
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@time SDP_problem = create_SDP_problem(sdp_constraints, Δ; upper_bound=upper_bound)
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println("Solving SDP problem maximizing κ...")
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κ, A = solve_SDP(SDP_problem, solver)
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κ_fname, A_fname = κSDPfilenames(name)
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if κ > 0
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save(κ_fname, "κ", κ)
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save(A_fname, "A", A)
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else
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throw(ErrorException("Solver $solver did not produce a valid solution!: κ = $κ"))
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end
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return κ, A
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end
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println("Projecting columns of A_sqrt to the augmentation ideal...")
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println("Projecting columns of A_sqrt to the augmentation ideal...")
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A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
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A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
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@time ℚ_dist_to_Σ² = check_solution(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=verbose, augmented=true)
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@time ℚ_dist_to_Σ² = check_solution(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=verbose, augmented=true)
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