95 lines
2.7 KiB
Julia
95 lines
2.7 KiB
Julia
using IntervalArithmetic
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IntervalArithmetic.setrounding(Interval, :tight)
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IntervalArithmetic.setformat(sigfigs=12)
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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(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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# for i in 1:size(Q,2)
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# print(" $i")
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# result += GroupRings.mul!(r, view(Q,:,i), view(Q,:,i), pm)
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# end
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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(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(RG::GroupRing, Q::AbstractArray)
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result = compute_SOS(RG.pm, Q)
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return GroupRingElem(result, RG)
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end
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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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Threads.@threads for j in 1:l
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col = sum(view(Q, :,j))/l
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for i in 1:size(Q, 1)
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R[i,j] = @interval(Q[i,j] - col)
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end
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end
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return R
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end
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function distance_to_cone(Δ::GroupRingElem, λ, Q; wlen::Int=4)
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info("------------------------------------------------------------")
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info("Checking in floating-point arithmetic...")
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info("λ = $λ")
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@time sos = compute_SOS(parent(Δ), Q)
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residue = Δ^2-λ*Δ - sos
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info("ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", aug(residue)))")
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L1_norm = norm(residue,1)
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info("‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", L1_norm))")
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distance = λ - 2^(wlen-1)*L1_norm
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info("Floating point distance (to positive cone) ≈")
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info("$(@sprintf("%.10f", distance))")
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info("")
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if distance ≤ 0
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return distance
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end
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info("------------------------------------------------------------")
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info("Checking in interval arithmetic...")
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info("λ ∈ $λ")
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λ = @interval(λ)
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eoi = Δ^2 - λ*Δ
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info("Projecting columns of Q to the augmentation ideal...")
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T = eltype(Q)
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@time Q = augIdproj(Q)
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info("Checking that sum of every column contains 0.0... ")
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check = all([zero(T) in sum(view(Q, :, i)) for i in 1:size(Q, 2)])
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info((check? "They do." : "FAILED!"))
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@assert check
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@time sos = compute_SOS(parent(Δ), Q)
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residue = Δ^2-λ*Δ - sos
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info("ɛ(∑ξᵢ*ξᵢ) ∈ $(aug(residue))")
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L1_norm = norm(residue,1)
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info("‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)")
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distance = λ - 2^(wlen-1)*L1_norm
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info("The Augmentation-projected distance (to positive cone) ∈")
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info("$(distance)")
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info("")
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return distance.lo
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end
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