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https://github.com/kalmarek/PropertyT.jl.git
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replace all shows and printlns by info(logger,...
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@ -36,7 +36,7 @@ function ΔandSDPconstraints(name::String)
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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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info(logger, "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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@ -60,7 +60,7 @@ function κandA(name::String)
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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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info(logger, "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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@ -79,9 +79,11 @@ function timed_msg(t)
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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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info(logger, "Creating SDP problem...")
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t = @timed SDP_problem = create_SDP_problem(sdp_constraints, Δ; upper_bound=upper_bound)
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info(logger, timed_msg(t))
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info(logger, "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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@ -94,15 +96,19 @@ function κandA(name::String, sdp_constraints, Δ::GroupAlgebraElement, solver::
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end
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function check_property_T(name::String, ID, generate_B₄::Function;
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verbose=true, tol=1e-6, upper_bound=Inf)
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tol=1e-6, upper_bound=Inf)
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# solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=!verbose)
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solver = SCSSolver(eps=tol, max_iters=100000, verbose=verbose)
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if !isdir(name)
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mkdir(name)
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end
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@show name
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@show verbose
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@show tol
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add_handler(logger, DefaultHandler("./$name/full.log"), "full")
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add_handler(solver_logger, DefaultHandler("./$name/solver.log"), "solver")
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info(logger, "Group: $name")
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info(logger, "Precision: $tol")
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# solver = MosekSolver(INTPNT_CO_TOL_REL_GAP=tol, QUIET=false)
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solver = SCSSolver(eps=tol, max_iters=1000000, verbose=true)
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Δ, sdp_constraints = try
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ΔandSDPconstraints(name)
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@ -110,12 +116,13 @@ function check_property_T(name::String, ID, generate_B₄::Function;
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if isa(err, ArgumentError)
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ΔandSDPconstraints(name, ID, generate_B₄)
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else
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throw(err)
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error(logger, err)
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end
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end
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println("|S| = $(countnz(Δ.coefficients) -1)")
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@show length(Δ)
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@show size(Δ.product_matrix)
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info(logger, "|S| = $(countnz(Δ.coefficients) - 1)")
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info(logger, "length(Δ) = $(length(Δ))")
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info(logger, "size(Δ.product_matrix) = $(size(Δ.product_matrix))")
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κ, A = try
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κandA(name)
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@ -123,26 +130,26 @@ function check_property_T(name::String, ID, generate_B₄::Function;
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if isa(err, ArgumentError)
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κandA(name, sdp_constraints, Δ, solver; upper_bound=upper_bound)
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else
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throw(err)
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# throw(err)
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error(logger, err)
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end
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end
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@show κ
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@show sum(A)
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@show maximum(A)
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@show minimum(A)
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info(logger, "κ = $κ")
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info(logger, "sum(A) = $(sum(A))")
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info(logger, "maximum(A) = $(maximum(A))")
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info(logger, "minimum(A) = $(minimum(A))")
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if κ > 0
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true_kappa = check_distance_to_positive_cone(Δ, κ, A, tol=tol, verbose=verbose, rational=false)
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true_kappa = check_distance_to_positive_cone(Δ, κ, A, tol=tol, rational=false)
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true_kappa = Float64(trunc(true_kappa,12))
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if true_kappa > 0
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println("κ($name, S) ≥ $true_kappa: Group HAS property (T)!")
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info(logger, "κ($name, S) ≥ $true_kappa: Group HAS property (T)!")
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else
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println("κ($name, S) ≥ $true_kappa: Group may NOT HAVE property (T)!")
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info(logger, "κ($name, S) ≥ $true_kappa: Group may NOT HAVE property (T)!")
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end
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else
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println("κ($name, S) ≥ $κ < 0: Tells us nothing about property (T)")
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info(logger, "κ($name, S) ≥ $κ < 0: Tells us nothing about property (T)")
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end
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end
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@ -61,99 +61,94 @@ end
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ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol)
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function distance_to_cone{T<:Rational}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true, augmented=false)
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function distance_to_cone{T<:Rational}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T})
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SOS = compute_SOS(sqrt_matrix, Δ)
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if augmented
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epsilon = GroupAlgebras.ɛ(SOS)
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@show epsilon
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end
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SOS_diff = EOI(Δ, κ) - SOS
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eoi_SOS_L₁_dist = norm(SOS_diff,1)
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if verbose
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@show κ
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ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
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L₁_dist = eoi_SOS_L₁_dist
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@printf("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) = %.10f\n", float(ɛ_dist))
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@printf("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ = %.10f\n", float(L₁_dist))
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info(logger, "κ = $κ")
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ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
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if ɛ_dist ≠ 0//1
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warn(logger, "The SOS is not in the augmentation ideal, number below are meaningless!")
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end
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info(logger, "ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) = $ɛ_dist")
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info(logger, "‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ = $(@sprintf("%.10f", float(eoi_SOS_L₁_dist)))")
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distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
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return distance_to_cone
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end
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function distance_to_cone{T<:Rational, S<:Interval}(κ::T, sqrt_matrix::Array{S,2}, Δ::GroupAlgebraElement{T}; verbose=true)
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function distance_to_cone{T<:Rational, S<:Interval}(κ::T, sqrt_matrix::Array{S,2}, Δ::GroupAlgebraElement{T})
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SOS = compute_SOS(sqrt_matrix, Δ)
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verbose && println("ɛ(∑ξᵢ*ξᵢ) ∈ $(GroupAlgebras.ɛ(SOS))")
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info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(GroupAlgebras.ɛ(SOS))")
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SOS_diff = EOI(Δ, κ) - SOS
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eoi_SOS_L₁_dist = norm(SOS_diff,1)
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if verbose
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@show κ
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ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
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info(logger, "κ = $κ")
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ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
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info(logger, "ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
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info(logger, "‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L₁_dist)")
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println("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
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println("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L₁_dist)")
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end
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distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
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return distance_to_cone
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end
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function distance_to_cone{T<:AbstractFloat}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true)
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function distance_to_cone{T<:AbstractFloat}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T})
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SOS = compute_SOS(sqrt_matrix, Δ)
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SOS_diff = EOI(Δ, κ) - SOS
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eoi_SOS_L₁_dist = norm(SOS_diff,1)
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if verbose
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println("κ = $κ (≈$(float(κ)))")
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ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
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@printf("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ≈ %.10f\n", ɛ_dist)
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@printf("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ %.10f\n", eoi_SOS_L₁_dist)
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end
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info(logger, "κ = $κ (≈$(float(κ)))")
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ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
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info(logger, "ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f\n", ɛ_dist))")
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info(logger, "‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f\n", eoi_SOS_L₁_dist))")
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distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
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return distance_to_cone
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end
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function check_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
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tol=1e-7, verbose=true, rational=false)
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tol=1e-7, rational=false)
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isapprox(eigvals(A), abs(eigvals(A)), atol=tol) ||
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warn("The solution matrix doesn't seem to be positive definite!")
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@assert A == Symmetric(A)
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A_sqrt = real(sqrtm(A))
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println("-------------------------------------------------------------")
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println("")
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println("Checking in floating-point arithmetic...")
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@time fp_distance = distance_to_cone(κ, A_sqrt, Δ, verbose=verbose)
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println("Floating point distance (to positive cone)\n ≈ $(Float64(trunc(fp_distance,10)))")
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println("-------------------------------------------------------------")
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println("")
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info(logger, "-------------------------------------------------------------")
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info(logger, "")
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info(logger, "Checking in floating-point arithmetic...")
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@time fp_distance = distance_to_cone(κ, A_sqrt, Δ)
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info(logger, "Floating point distance (to positive cone)\n ≈ $(Float64(trunc(fp_distance,10)))")
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info(logger, "-------------------------------------------------------------")
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info(logger, "")
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println("Projecting columns of rationalized A_sqrt to the augmentation ideal...")
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info(logger, "Projecting columns of rationalized A_sqrt to the augmentation ideal...")
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δ = eps(κ)
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A_sqrt_ℚ = ℚ(A_sqrt, δ)
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A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
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κ_ℚ = ℚ(κ, δ)
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Δ_ℚ = ℚ(Δ, δ)
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println("Checking in interval arithmetic")
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info(logger, "Checking in interval arithmetic")
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A_sqrt_ℚ_augᴵ = A_sqrt_ℚ_aug ± δ
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@time Interval_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_augᴵ, Δ_ℚ, verbose=verbose)
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println("The Augmentation-projected actual distance (to positive cone) belongs to \n$Interval_dist_to_Σ²")
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println("-------------------------------------------------------------")
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println("")
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@time Interval_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_augᴵ, Δ_ℚ)
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info(logger, "The Augmentation-projected actual distance (to positive cone) belongs to \n$Interval_dist_to_Σ²")
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info(logger, "-------------------------------------------------------------")
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info(logger, "")
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if Interval_dist_to_Σ².lo ≤ 0
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return Interval_dist_to_Σ².lo
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else
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println("Checking Projected SOS decomposition in exact rational arithmetic...")
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@time ℚ_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=verbose, augmented=true)
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info(logger, "Checking Projected SOS decomposition in exact rational arithmetic...")
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@time ℚ_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, augmented=true)
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@assert isa(ℚ_dist_to_Σ², Rational)
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println("Augmentation-projected rational distance (to positive cone)\n ≥ $(Float64(trunc(ℚ_dist_to_Σ²,8)))")
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println("-------------------------------------------------------------")
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info(logger, "Augmentation-projected rational distance (to positive cone)\n ≥ $(Float64(trunc(ℚ_dist_to_Σ²,8)))")
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info(logger, "-------------------------------------------------------------")
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return ℚ_dist_to_Σ²
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end
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end
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@ -68,8 +68,8 @@ function create_SDP_problem(matrix_constraints, Δ::GroupAlgebraElement; upper_b
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end
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function solve_SDP(SDP_problem, solver)
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@show SDP_problem
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@show solver
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info(logger, Base.repr(m))
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info(logger, solver)
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JuMP.setsolver(SDP_problem, solver);
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# @time MathProgBase.writeproblem(SDP_problem, "/tmp/SDP_problem")
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@ -78,7 +78,7 @@ function solve_SDP(SDP_problem, solver)
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if solution_status != :Optimal
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warn("The solver did not solve the problem successfully!")
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end
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@show solution_status
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info(logger, solution_status)
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κ = JuMP.getvalue(JuMP.getvariable(SDP_problem, :κ))
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A = JuMP.getvalue(JuMP.getvariable(SDP_problem, :A))
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