kalmar/PropertyT.jl
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check_solution reports actual lower bound for kappa

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kalmar 2017-03-06 11:55:40 +01:00
parent b7cb142672
commit c6f3d15ef4
1 changed files with 13 additions and 6 deletions
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property(T).jl
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@ -145,7 +145,7 @@ function check_solution{T<:Number}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlge
println("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $L₁_dist") println("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $L₁_dist")
end end
distance_to_cone = 2^3*eoi_SOS_L₁_dist - κ distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
return distance_to_cone return distance_to_cone
end end
@ -169,25 +169,32 @@ function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
println("") println("")
println("Checking in floating-point arithmetic...") println("Checking in floating-point arithmetic...")
@time fp_distance = check_solution(κ, A_sqrt, Δ, verbose=verbose) @time fp_distance = check_solution(κ, A_sqrt, Δ, verbose=verbose)
println("Distance to positive cone ≈ $(Float64(trunc(fp_distance,8)))") println("Floating point distance (to positive cone) ≈ $(Float64(trunc(fp_distance,8)))")
println("-------------------------------------------------------------") println("-------------------------------------------------------------")
println("") println("")
if fp_distance ≤ 0
return fp_distance
end
println("Checking in rational arithmetic...") println("Checking in rational arithmetic...")
κ_ℚ = ℚ(trunc(κ,Int(abs(log10(tol)))), tol) κ_ℚ = ℚ(trunc(κ,Int(abs(log10(tol)))), tol)
A_sqrt_ℚ, Δ_ℚ = ℚ(A_sqrt, tol), ℚ(Δ, tol) A_sqrt_ℚ, Δ_ℚ = ℚ(A_sqrt, tol), ℚ(Δ, tol)
@time ℚ_distance = check_solution(κ_ℚ, A_sqrt_ℚ, Δ_ℚ, verbose=verbose) @time ℚ_distance = check_solution(κ_ℚ, A_sqrt_ℚ, Δ_ℚ, verbose=verbose)
@assert isa(ℚ_distance, Rational) @assert isa(ℚ_distance, Rational)
println("Distance to positive cone ≈ $(Float64(trunc(ℚ_distance,8)))") println("Rational distance (to positive cone) ≈ $(Float64(trunc(ℚ_distance,8)))")
println("-------------------------------------------------------------") println("-------------------------------------------------------------")
println("") println("")
if ℚ_distance ≤ 0
return ℚ_distance
end
println("Projecting columns of A_sqrt to the augmentation ideal...") println("Projecting columns of A_sqrt to the augmentation ideal...")
A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ) A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
@time ℚ_dist_to_Σ² = check_solution(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=verbose, augmented=true) @time ℚ_dist_to_Σ² = check_solution(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=verbose, augmented=true)
@assert isa(ℚ_dist_to_Σ², Rational) @assert isa(ℚ_dist_to_Σ², Rational)
s = (ℚ_dist_to_Σ² < 0? "≤": "≥") println("Augmentation-projected rational distance (to positive cone)")
println("Distance to positive cone $s $(Float64(trunc(ℚ_dist_to_Σ²,8)))") println("$(Float64(trunc(ℚ_dist_to_Σ²,8))) ≤ κ(G,S)")
println("-------------------------------------------------------------")
return ℚ_dist_to_Σ² return ℚ_dist_to_Σ²
end end