kalmar/PropertyT.jl
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multiple dispatch on distance_to_cone

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kalmar 2017-03-14 23:35:52 +01:00
parent 52a68e8429
commit f9fd7e63a7
2 changed files with 43 additions and 20 deletions
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2
src/PropertyT.jl
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@ -121,7 +121,7 @@ function check_property_T(name::String, ID, generate_B₄::Function;
if κ > 0
true_kappa = ℚ_distance_to_positive_cone(Δ, κ, A, tol=tol, verbose=verbose, rational=true)
true_kappa = check_distance_to_positive_cone(Δ, κ, A, tol=tol, verbose=verbose, rational=false)
true_kappa = Float64(trunc(true_kappa,12))
if true_kappa > 0
println("κ($name, S) ≥ $true_kappa: Group HAS property (T)!")

61
src/checksolution.jl
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@ -60,49 +60,75 @@ function Base.rationalize{T<:Integer, S<:Real}(::Type{T},
end
ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol)
function check_solution{T<:Number}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true, augmented=false)
result = compute_SOS(sqrt_matrix, Δ)
function distance_to_cone{T<:Rational}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true, augmented=false)
SOS = compute_SOS(sqrt_matrix, Δ)
if augmented
epsilon = GroupAlgebras.ɛ(result)
@show epsilon
end
SOS_diff = EOI(Δ, κ) - result
SOS_diff = EOI(Δ, κ) - SOS
eoi_SOS_L₁_dist = norm(SOS_diff,1)
if verbose
@show κ
ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
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))
L₁_dist = eoi_SOS_L₁_dist
@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
function distance_to_cone{T<:Rational, S<:Interval}(κ::T, sqrt_matrix::Array{S,2}, Δ::GroupAlgebraElement{T}; verbose=true)
SOS = compute_SOS(sqrt_matrix, Δ)
verbose && println("ɛ(∑ξᵢ*ξᵢ) ∈ $(GroupAlgebras.ɛ(SOS))")
SOS_diff = EOI(Δ, κ) - SOS
eoi_SOS_L₁_dist = norm(SOS_diff,1)
if verbose
@show κ
ɛ_dist = GroupAlgebras.ɛ(SOS_diff)
println("ɛ(Δ² - κΔ - ∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
println("‖Δ² - κΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L₁_dist)")
end
distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
return distance_to_cone
end
function distance_to_cone{T<:AbstractFloat}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true)
SOS = compute_SOS(sqrt_matrix, Δ)
function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
SOS_diff = EOI(Δ, κ) - SOS
eoi_SOS_L₁_dist = norm(SOS_diff,1)
if verbose
println("κ = $κ (≈$(float(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)
end
distance_to_cone = κ - 2^3*eoi_SOS_L₁_dist
return distance_to_cone
end
function check_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
tol=1e-7, verbose=true, rational=false)
isapprox(eigvals(A), abs(eigvals(A)), atol=tol) ||
warn("The solution matrix doesn't seem to be positive definite!")
@assert A == Symmetric(A)
A_sqrt = real(sqrtm(A))
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)))")
@time fp_distance = distance_to_cone(κ, A_sqrt, Δ, verbose=verbose)
println("Floating point distance (to positive cone)\n ≈ $(Float64(trunc(fp_distance,10)))")
println("-------------------------------------------------------------")
println("")
@ -115,17 +141,14 @@ function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
println("Checking in interval arithmetic")
A_sqrt_ℚ_augᴵ = A_sqrt_ℚ_aug ± δ
κᴵ = κ_ℚ ± δ
Δᴵ = Δ_ℚ ± δ
@time Interval_dist_to_Σ² = check_solution(κᴵ, A_sqrt_ℚ_augᴵ, Δᴵ, verbose=verbose, augmented=true)
@time Interval_dist_to_Σ² = distance_to_cone(κ_ℚ, A_sqrt_ℚ_augᴵ, Δ_ℚ, verbose=verbose)
println("The Augmentation-projected actual distance (to positive cone) belongs to \n$Interval_dist_to_Σ²")
println("-------------------------------------------------------------")
println("")
if Interval_dist_to_Σ².lo ≤ 0 || !rational
if Interval_dist_to_Σ².lo ≤ 0
return Interval_dist_to_Σ².lo
else
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)