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just two simple distance_to_cone functions
for Numbers and for Intervals
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@ -60,55 +60,34 @@ function correct_to_augmentation_ideal{T<:Rational}(sqrt_matrix::Array{T,2})
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return sqrt_corrected
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end
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function distance_to_cone{T<:Rational}(λ::T, sqrt_matrix::Array{T,2}, Δ::GroupRingElem{T}, wlen)
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SOS = compute_SOS(sqrt_matrix, Δ)
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function distance_to_cone{S<:Interval}(elt::GroupRingElem, Q::AbstractArray{S,2}, wlen::Int)
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SOS = compute_SOS(Q, parent(elt), length(elt.coeffs))
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SOS_diff = elt - SOS
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SOS_diff = EOI(Δ, λ) - SOS
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
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info(logger, "λ = $λ (≈$(@sprintf("%.10f", float(λ)))")
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ɛ_dist = GroupRings.augmentation(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, numbers below are meaningless!")
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end
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) = $ɛ_dist")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ = $(@sprintf("%.10f", float(eoi_SOS_L1_dist)))")
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L1_dist)")
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distance_to_cone = λ - 2^(wlen-1)*eoi_SOS_L1_dist
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return distance_to_cone
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dist = 2^(wlen-1)*eoi_SOS_L1_dist
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return dist
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end
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function distance_to_cone{T<:Rational, S<:Interval}(λ::T, sqrt_matrix::AbstractArray{S,2}, Δ::GroupRingElem{T}, wlen)
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SOS = compute_SOS(sqrt_matrix, Δ)
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info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(GroupRings.augmentation(SOS))")
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λ_int = @interval(λ)
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Δ_int = GroupRingElem([@interval(c) for c in Δ.coeffs], parent(Δ))
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SOS_diff = EOI(Δ_int, λ_int) - SOS
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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function distance_to_cone{T}(elt::GroupRingElem, Q::AbstractArray{T,2}, wlen::Int)
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SOS = compute_SOS(Q, parent(elt), length(elt.coeffs))
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SOS_diff = elt - SOS
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info(logger, "λ = $λ (≈≥$(@sprintf("%.10f",float(λ))))")
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", ɛ_dist))")
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L1_dist)")
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", eoi_SOS_L1_dist))")
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distance_to_cone = λ - 2^(wlen-1)*eoi_SOS_L1_dist
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return distance_to_cone
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dist = 2^(wlen-1)*eoi_SOS_L1_dist
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return dist
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end
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function distance_to_cone(λ, sqrt_matrix::AbstractArray, Δ::GroupRingElem, wlen)
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SOS = compute_SOS(sqrt_matrix, Δ)
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SOS_diff = EOI(Δ, λ) - SOS
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "λ = $λ")
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", ɛ_dist))")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", eoi_SOS_L1_dist))")
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distance_to_cone = λ - 2^(wlen-1)*eoi_SOS_L1_dist
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return distance_to_cone
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end
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function rationalize_and_project{T}(Q::AbstractArray{T}, δ::T, logger)
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