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rework distance_to_cone

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kalmarek 2018-08-14 19:18:36 +02:00
parent f9180d5d68
commit ff8f5d45c2
1 changed files with 31 additions and 56 deletions
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87
src/CheckSolution.jl
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@ -25,12 +25,12 @@ end
EOI{T<:Number}(Δ::GroupRingElem{T}, λ::T) = Δ*Δ - λ*Δ EOI{T<:Number}(Δ::GroupRingElem{T}, λ::T) = Δ*Δ - λ*Δ
function groupring_square(vect::AbstractVector, pm) function groupring_square(pm, vect::AbstractVector)
zzz = zeros(eltype(vect), maximum(pm)) zzz = zeros(eltype(vect), maximum(pm))
return GroupRings.mul!(zzz, vect, vect, pm) return GroupRings.mul!(zzz, vect, vect, pm)
end end
function compute_SOS(Q::AbstractArray, pm::Array{Int,2}) function compute_SOS(pm::Array{I,2}, Q::AbstractArray) where I<:Integer
# result = zeros(eltype(Q), maximum(pm)) # result = zeros(eltype(Q), maximum(pm))
# r = similar(result) # r = similar(result)
@ -42,28 +42,17 @@ function compute_SOS(Q::AbstractArray, pm::Array{Int,2})
@everywhere groupring_square = PropertyT.groupring_square @everywhere groupring_square = PropertyT.groupring_square
result = @parallel (+) for i in 1:size(Q,2) result = @parallel (+) for i in 1:size(Q,2)
groupring_square(Q[:,i], pm) groupring_square(pm, Q[:,i])
end end
return result return result
end end
function compute_SOS(Q::AbstractArray, RG::GroupRing) function compute_SOS(RG::GroupRing, Q::AbstractArray)
result = compute_SOS(Q, RG.pm) result = compute_SOS(RG.pm, Q)
return GroupRingElem(result, RG) return RG(result)
end end
function distances_to_cone(elt::GroupRingElem, wlen::Int)
ɛ_dist = GroupRings.augmentation(elt)
eoi_SOS_L1_dist = norm(elt,1)
dist = 2^(wlen-1)*eoi_SOS_L1_dist
return dist, ɛ_dist, eoi_SOS_L1_dist
end
function augIdproj{T, I<:AbstractInterval}(S::Type{I}, Q::AbstractArray{T,2})
function augIdproj(Q::AbstractArray{T,2}) where {T<:Real} function augIdproj(Q::AbstractArray{T,2}) where {T<:Real}
R = zeros(Interval{T}, size(Q)) R = zeros(Interval{T}, size(Q))
l = size(Q, 2) l = size(Q, 2)
@ -89,56 +78,42 @@ function augIdproj(Q::AbstractArray{T,2}, logger) where {T<:Real}
return Q return Q
end end
function distance_to_cone(elt::GroupRingElem, λ::T, Q::AbstractArray{T,2}, wlen::Int, logger) where {T<:AbstractFloat} function distance_to_cone(Δ::GroupRingElem, λ, Q; wlen::Int=4, logger=getlogger())
info(logger, "------------------------------------------------------------") info(logger, "------------------------------------------------------------")
info(logger, "λ = $λ")
info(logger, "Checking in floating-point arithmetic...") info(logger, "Checking in floating-point arithmetic...")
@logtime logger SOS_diff = elt - compute_SOS(Q, parent(elt), length(elt.coeffs)) info(logger, "λ = $λ")
dist, ɛ_dist, eoi_SOS_L1_dist = distances_to_cone(SOS_diff, wlen) @logtime logger sos = compute_SOS(parent(Δ), Q)
info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", ɛ_dist))") residue = Δ^2-λ*Δ - sos
info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", eoi_SOS_L1_dist))") info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", aug(residue)))")
L1_norm = norm(residue,1)
info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", L1_norm))")
fp_distance = λ - dist distance = λ - 2^(wlen-1)*L1_norm
info(logger, "Floating point distance (to positive cone) ≈") info(logger, "Floating point distance (to positive cone) ≈")
info(logger, "$(@sprintf("%.10f", fp_distance))") info(logger, "$(@sprintf("%.10f", distance))")
info(logger, "") info(logger, "")
return fp_distance if distance ≤ 0
end return distance
function distance_to_cone(elt::GroupRingElem, λ::T, Q::AbstractArray{T,2}, wlen::Int, logger) where {T<:AbstractInterval}
info(logger, "------------------------------------------------------------")
info(logger, "λ = $λ")
info(logger, "Checking in interval arithmetic...")
@logtime logger SOS_diff = elt - compute_SOS(Q, parent(elt), length(elt.coeffs))
dist, ɛ_dist, eoi_SOS_L1_dist = distances_to_cone(SOS_diff, wlen)
info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L1_dist)")
int_distance = λ - dist
info(logger, "The Augmentation-projected actual distance (to positive cone) ∈")
info(logger, "$(int_distance)")
info(logger, "")
return int_distance
end
function check_distance_to_cone(Δ::GroupRingElem, λ, Q, wlen::Int, logger)
fp_distance = distance_to_cone(EOI(Δ, λ), λ, Q, wlen, logger)
if fp_distance ≤ 0
return fp_distance
end end
λ = @interval(λ) λ = @interval(λ)
Δ = GroupRingElem([@interval(c) for c in Δ.coeffs], parent(Δ)) eoi = Δ^2 - λ*Δ
Q = augIdproj(Q, logger) Q = augIdproj(Q, logger)
int_distance = distance_to_cone(EOI(Δ, λ), λ, Q, wlen, logger) info(logger, "------------------------------------------------------------")
info(logger, "Checking in interval arithmetic...")
info(logger, "λ ∈ $λ")
@logtime logger sos = compute_SOS(parent(Δ), Q)
residue = Δ^2-λ*Δ - sos
info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(aug(residue))")
info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)")
return int_distance.lo distance = λ - 2^(wlen-1)*L1_norm
info(logger, "The Augmentation-projected distance (to positive cone) ∈")
info(logger, "$(distance)")
info(logger, "")
return distance.lo
end end