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rework distance_to_cone
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@ -25,12 +25,12 @@ end
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EOI{T<:Number}(Δ::GroupRingElem{T}, λ::T) = Δ*Δ - λ*Δ
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function groupring_square(vect::AbstractVector, pm)
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function groupring_square(pm, vect::AbstractVector)
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zzz = zeros(eltype(vect), maximum(pm))
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return GroupRings.mul!(zzz, vect, vect, pm)
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end
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function compute_SOS(Q::AbstractArray, pm::Array{Int,2})
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function compute_SOS(pm::Array{I,2}, Q::AbstractArray) where I<:Integer
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# result = zeros(eltype(Q), maximum(pm))
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# r = similar(result)
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@ -42,28 +42,17 @@ function compute_SOS(Q::AbstractArray, pm::Array{Int,2})
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@everywhere groupring_square = PropertyT.groupring_square
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result = @parallel (+) for i in 1:size(Q,2)
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groupring_square(Q[:,i], pm)
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groupring_square(pm, Q[:,i])
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end
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return result
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end
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function compute_SOS(Q::AbstractArray, RG::GroupRing)
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result = compute_SOS(Q, RG.pm)
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return GroupRingElem(result, RG)
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function compute_SOS(RG::GroupRing, Q::AbstractArray)
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result = compute_SOS(RG.pm, Q)
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return RG(result)
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end
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function distances_to_cone(elt::GroupRingElem, wlen::Int)
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ɛ_dist = GroupRings.augmentation(elt)
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eoi_SOS_L1_dist = norm(elt,1)
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dist = 2^(wlen-1)*eoi_SOS_L1_dist
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return dist, ɛ_dist, eoi_SOS_L1_dist
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end
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function augIdproj{T, I<:AbstractInterval}(S::Type{I}, Q::AbstractArray{T,2})
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function augIdproj(Q::AbstractArray{T,2}) where {T<:Real}
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R = zeros(Interval{T}, size(Q))
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l = size(Q, 2)
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@ -89,56 +78,42 @@ function augIdproj(Q::AbstractArray{T,2}, logger) where {T<:Real}
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return Q
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end
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function distance_to_cone(elt::GroupRingElem, λ::T, Q::AbstractArray{T,2}, wlen::Int, logger) where {T<:AbstractFloat}
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function distance_to_cone(Δ::GroupRingElem, λ, Q; wlen::Int=4, logger=getlogger())
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info(logger, "------------------------------------------------------------")
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info(logger, "λ = $λ")
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info(logger, "Checking in floating-point arithmetic...")
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@logtime logger SOS_diff = elt - compute_SOS(Q, parent(elt), length(elt.coeffs))
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dist, ɛ_dist, eoi_SOS_L1_dist = distances_to_cone(SOS_diff, wlen)
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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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info(logger, "λ = $λ")
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@logtime logger sos = compute_SOS(parent(Δ), Q)
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residue = Δ^2-λ*Δ - sos
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", aug(residue)))")
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L1_norm = norm(residue,1)
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", L1_norm))")
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fp_distance = λ - dist
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distance = λ - 2^(wlen-1)*L1_norm
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info(logger, "Floating point distance (to positive cone) ≈")
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info(logger, "$(@sprintf("%.10f", fp_distance))")
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info(logger, "$(@sprintf("%.10f", distance))")
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info(logger, "")
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return fp_distance
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end
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function distance_to_cone(elt::GroupRingElem, λ::T, Q::AbstractArray{T,2}, wlen::Int, logger) where {T<:AbstractInterval}
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info(logger, "------------------------------------------------------------")
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info(logger, "λ = $λ")
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info(logger, "Checking in interval arithmetic...")
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@logtime logger SOS_diff = elt - compute_SOS(Q, parent(elt), length(elt.coeffs))
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dist, ɛ_dist, eoi_SOS_L1_dist = distances_to_cone(SOS_diff, wlen)
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info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L1_dist)")
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int_distance = λ - dist
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info(logger, "The Augmentation-projected actual distance (to positive cone) ∈")
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info(logger, "$(int_distance)")
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info(logger, "")
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return int_distance
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end
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function check_distance_to_cone(Δ::GroupRingElem, λ, Q, wlen::Int, logger)
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fp_distance = distance_to_cone(EOI(Δ, λ), λ, Q, wlen, logger)
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if fp_distance ≤ 0
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return fp_distance
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if distance ≤ 0
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return distance
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end
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λ = @interval(λ)
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Δ = GroupRingElem([@interval(c) for c in Δ.coeffs], parent(Δ))
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eoi = Δ^2 - λ*Δ
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Q = augIdproj(Q, logger)
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int_distance = distance_to_cone(EOI(Δ, λ), λ, Q, wlen, logger)
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info(logger, "------------------------------------------------------------")
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info(logger, "Checking in interval arithmetic...")
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info(logger, "λ ∈ $λ")
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@logtime logger sos = compute_SOS(parent(Δ), Q)
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residue = Δ^2-λ*Δ - sos
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info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(aug(residue))")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)")
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return int_distance.lo
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distance = λ - 2^(wlen-1)*L1_norm
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info(logger, "The Augmentation-projected distance (to positive cone) ∈")
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info(logger, "$(distance)")
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info(logger, "")
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return distance.lo
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end
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