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rename distance_to_positive_cone → certify_SOS_decomposition

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and make it a bit more general
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kalmarek 2019-04-02 18:56:02 +02:00
parent 6fde981b32
commit bb42538ee5
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1 changed files with 24 additions and 19 deletions
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src/1712.07167.jl
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@ -156,25 +156,26 @@ end
#
###############################################################################
function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
function certify_SOS_decomposition(elt::GroupRingElem, orderunit::GroupRingElem,
λ::Number, Q::AbstractMatrix; R::Int=2)
separator = "-"^76
@info "$separator\nChecking in floating-point arithmetic..." λ
eoi = Δ^2-λ*Δ
eoi = elt - λ*orderunit
@info("Computing sum of squares decomposition...")
@time residual = eoi - compute_SOS(parent(eoi), augIdproj(Q))
L1_norm = norm(residual,1)
distance = λ - 2.0^(2ceil(log2(R)))*L1_norm
certified_λ = λ - 2.0^(2ceil(log2(R)))*L1_norm
info_strs = ["Numerical metrics of the obtained SOS:",
"ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(aug(residual))",
"‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(L1_norm)",
"Floating point distance (to positive cone) ≈"]
@info join(info_strs, "\n") distance
"ɛ(elt - λu - ∑ξᵢ*ξᵢ) ≈ $(aug(residual))",
"‖elt - λu - ∑ξᵢ*ξᵢ‖₁ ≈ $(L1_norm)",
"Floating point (NOT certified) λ ≈"]
@info join(info_strs, "\n") certified_λ
if distance ≤ 0
return distance
if certified_λ ≤ 0
return certified_λ
end
λ = @interval(λ)
@ -182,27 +183,31 @@ function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
"Checking in interval arithmetic...",
"λ ∈ $λ"]
@info(join(info_strs, "\n"))
eoi = Δ^2 - λ*Δ
eoi = elt - λ*orderunit
@info("Projecting columns of Q to the augmentation ideal...")
@time Q, check = augIdproj(Interval, Q)
result = (check ? "Correct." : "FAILED!")
@info "Checking that sum of every column contains 0.0..." result
@info "Checking that sum of every column contains 0.0..." check_augmented=check
check || @warn("The following numbers are meaningless!")
@info("Computing sum of squares decomposition...")
@time residual = eoi - compute_SOS(parent(eoi), Q)
L1_norm = norm(residual,1)
distance = λ - 2.0^(2ceil(log2(R)))*L1_norm
certified_λ = λ - 2.0^(2ceil(log2(R)))*L1_norm
info_strs = ["Numerical metrics of the obtained SOS:",
"ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ∈ $(aug(residual))",
"‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)",
"Interval distance (to positive cone) ∈"]
@info join(info_strs, "\n") distance
"ɛ(elt - λu - ∑ξᵢ*ξᵢ) ∈ $(aug(residual))",
"‖elt - λu - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)",
"Interval aritmetic (certified) λ ∈"]
@info join(info_strs, "\n") certified_λ
return distance.lo
return certified_λ.lo
end
function spectral_gap(Δ::GroupRingElem, λ::Number, Q::AbstractMatrix; R::Int=2)
@info "elt = Δ², u = Δ"
return certify_SOS_decomposition(Δ^2, Δ, λ, Q, R=R)
end
###############################################################################
@ -285,7 +290,7 @@ function spectral_gap(sett::Settings)
@warn "The solution matrix doesn't seem to be positive definite!"
@time Q = real(sqrt(Symmetric( (P.+ P')./2 )))
certified_sgap = distance_to_positive_cone(Δ, λ, Q, R=sett.radius)
certified_sgap = spectral_gap(Δ, λ, Q, R=sett.radius)
return certified_sgap
end