kalmar/PropertyT.jl
1
0
Fork 0
mirror of https://github.com/kalmarek/PropertyT.jl.git synced 2024-11-19 07:20:28 +01:00
Code Issues Releases Wiki Activity

rename distance_to_positive_cone → certify_SOS_decomposition

Browse Source 
and make it a bit more general
This commit is contained in:
kalmarek 2019-04-02 18:56:02 +02:00
parent 6fde981b32
commit bb42538ee5
No known key found for this signature in database
GPG Key ID: 8BF1A3855328FC15
1 changed files with 24 additions and 19 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

43
src/1712.07167.jl
View File

@ -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 separator = "-"^76
@info "$separator\nChecking in floating-point arithmetic..." λ @info "$separator\nChecking in floating-point arithmetic..." λ
eoi = Δ^2-λ*Δ eoi = elt - λ*orderunit
@info("Computing sum of squares decomposition...") @info("Computing sum of squares decomposition...")
@time residual = eoi - compute_SOS(parent(eoi), augIdproj(Q)) @time residual = eoi - compute_SOS(parent(eoi), augIdproj(Q))
L1_norm = norm(residual,1) 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:", info_strs = ["Numerical metrics of the obtained SOS:",
"ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(aug(residual))", "ɛ(elt - λu - ∑ξᵢ*ξᵢ) ≈ $(aug(residual))",
"‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(L1_norm)", "‖elt - λu - ∑ξᵢ*ξᵢ‖₁ ≈ $(L1_norm)",
"Floating point distance (to positive cone) ≈"] "Floating point (NOT certified) λ ≈"]
@info join(info_strs, "\n") distance @info join(info_strs, "\n") certified_λ
if distance ≤ 0 if certified_λ ≤ 0
return distance return certified_λ
end end
λ = @interval(λ) λ = @interval(λ)
@ -182,27 +183,31 @@ function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
"Checking in interval arithmetic...", "Checking in interval arithmetic...",
"λ ∈ $λ"] "λ ∈ $λ"]
@info(join(info_strs, "\n")) @info(join(info_strs, "\n"))
eoi = Δ^2 - λ*Δ eoi = elt - λ*orderunit
@info("Projecting columns of Q to the augmentation ideal...") @info("Projecting columns of Q to the augmentation ideal...")
@time Q, check = augIdproj(Interval, Q) @time Q, check = augIdproj(Interval, Q)
result = (check ? "Correct." : "FAILED!") @info "Checking that sum of every column contains 0.0..." check_augmented=check
@info "Checking that sum of every column contains 0.0..." result
check || @warn("The following numbers are meaningless!") check || @warn("The following numbers are meaningless!")
@info("Computing sum of squares decomposition...") @info("Computing sum of squares decomposition...")
@time residual = eoi - compute_SOS(parent(eoi), Q) @time residual = eoi - compute_SOS(parent(eoi), Q)
L1_norm = norm(residual,1) 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:", info_strs = ["Numerical metrics of the obtained SOS:",
"ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ∈ $(aug(residual))", "ɛ(elt - λu - ∑ξᵢ*ξᵢ) ∈ $(aug(residual))",
"‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)", "‖elt - λu - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)",
"Interval distance (to positive cone) ∈"] "Interval aritmetic (certified) λ ∈"]
@info join(info_strs, "\n") distance @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 end
############################################################################### ###############################################################################
@ -285,7 +290,7 @@ function spectral_gap(sett::Settings)
@warn "The solution matrix doesn't seem to be positive definite!" @warn "The solution matrix doesn't seem to be positive definite!"
@time Q = real(sqrt(Symmetric( (P.+ P')./2 ))) @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 return certified_sgap
end end