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PropertyT.jl
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Printing of messages

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kalmar 2017-03-14 16:40:53 +01:00
parent dba02c87ac
commit a328502773
1 changed files with 26 additions and 44 deletions
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70
src/checksolution.jl
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@ -45,25 +45,24 @@ function check_solution{T<:Number}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlge
result = compute_SOS(sqrt_matrix, Δ)
if augmented
epsilon = GroupAlgebras.ɛ(result)
if isa(epsilon, Interval)
@assert 0 in epsilon
elseif isa(epsilon, Rational)
@assert epsilon == 0//1
else
warn("Does checking for augmentation has meaning for $(typeof(epsilon))?")
end
@show epsilon
end
SOS_diff = EOI(Δ, κ) - result
SOS_diff = EOI(Δ, κ) - result
eoi_SOS_L₁_dist = norm(SOS_diff,1)
if verbose
@show κ
ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
@printf("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ≈ %.10f\n", ɛ_dist)
@printf("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ %.10f\n", eoi_SOS_L₁_dist)
if isa(ɛ_dist, Interval)
ɛ_dist = ɛ_dist.lo
L₁_dist = eoi_SOS_L₁_dist.lo
else
L₁_dist = eoi_SOS_L₁_dist
end
@printf("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ≈ %.10f\n", float(ɛ_dist))
@printf("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ≈ %.10f\n", float(L₁_dist))
end
distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
return distance_to_cone
end
@ -91,43 +90,27 @@ function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
warn("The solution matrix doesn't seem to be positive definite!")
@assert A == Symmetric(A)
A_sqrt = real(sqrtm(A))
# println("")
# println("Checking in floating-point arithmetic...")
# @time fp_distance = check_solution(κ, A_sqrt, Δ, verbose=verbose)
# println("Floating point distance (to positive cone) ≈ $(Float64(trunc(fp_distance,8)))")
# println("-------------------------------------------------------------")
# println("")
#
# if fp_distance ≤ 0
# return fp_distance
# end
println("Checking in interval arithmetic...")
A_sqrtᴵ = A_sqrt ± tol
κᴵ = κ ± tol
Δᴵ = Δ ± tol
@time Interval_distance = check_solution(κᴵ, A_sqrtᴵ, Δᴵ, verbose=verbose)
# @assert isa(ℚ_distance, Rational)
println("The actual distance (to positive cone) is contained in $Interval_distance")
println("-------------------------------------------------------------")
println("")
println("Checking in floating-point arithmetic...")
@time fp_distance = check_solution(κ, A_sqrt, Δ, verbose=verbose)
println("Floating point distance (to positive cone)\n ≈ $(Float64(trunc(fp_distance,8)))")
println("-------------------------------------------------------------")
println("")
if Interval_distance.lo ≤ 0
return Interval_distance.lo
end
println("Projecting columns of A_sqrt to the augmentation ideal...")
A_sqrt_ℚ = ℚ(A_sqrt, tol)
println("Projecting columns of rationalized A_sqrt to the augmentation ideal...")
δ = eps(κ)
A_sqrt_ℚ = ℚ(A_sqrt, δ)
A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
κ_ℚ = ℚ(κ, tol)
Δ_ℚ = ℚ(Δ, tol)
κ_ℚ = ℚ(κ, δ)
Δ_ℚ = ℚ(Δ, δ)
A_sqrt_ℚ_augᴵ = A_sqrt_ℚ_aug ± tol
κᴵ = κ_ℚ ± tol
Δᴵ = Δ_ℚ ± tol
println("Checking in interval arithmetic")
A_sqrt_ℚ_augᴵ = A_sqrt_ℚ_aug ± δ
κᴵ = κ_ℚ ± δ
Δᴵ = Δ_ℚ ± δ
@time Interval_dist_to_Σ² = check_solution(κᴵ, A_sqrt_ℚ_augᴵ, Δᴵ, verbose=verbose, augmented=true)
println("The Augmentation-projected actual distance (to positive cone) is contained in $Interval_dist_to_Σ²")
println("The Augmentation-projected actual distance (to positive cone) belongs to \n$Interval_dist_to_Σ²")
println("-------------------------------------------------------------")
println("")
@ -138,9 +121,8 @@ function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
println("Checking Projected SOS decomposition in exact rational arithmetic...")
@time ℚ_dist_to_Σ² = check_solution(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=verbose, augmented=true)
@assert isa(ℚ_dist_to_Σ², Rational)
println("Augmentation-projected rational distance (to positive cone) ≥ $(Float64(trunc(ℚ_dist_to_Σ²,8)))")
println("Augmentation-projected rational distance (to positive cone)\n ≥ $(Float64(trunc(ℚ_dist_to_Σ²,8)))")
println("-------------------------------------------------------------")
return ℚ_dist_to_Σ²
end
end