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PropertyT.jl
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cosmetics

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kalmar 2017-02-26 13:51:20 +01:00
parent 35f669595d
commit 068bfaf29f
1 changed files with 11 additions and 19 deletions
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property(T).jl
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@ -121,7 +121,7 @@ function correct_to_augmentation_ideal{T<:Rational}(sqrt_matrix::Array{T,2})
return sqrt_corrected return sqrt_corrected
end end
function check_solution(κ, sqrt_matrix, Δ; verbose=true, augmented=false) 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) result = compute_SOS(sqrt_matrix, Δ)
if augmented if augmented
@assert GroupAlgebras.ɛ(result) == 0//1 @assert GroupAlgebras.ɛ(result) == 0//1
@ -155,33 +155,25 @@ end;
ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol) ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol)
function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
κ::Float64, tol=10.0^-7, verbose=true)
A::Array{Float64,2};
tol=10.0^-7,
verbose=true)
@show maximum(A) isapprox(eigvals(A), abs(eigvals(A)), atol=tol) ||
if maximum(A) < 1e-2 warn("The solution matrix doesn't seem to be positive definite!")
warn("Solver might not solved the problem successfully and the positive solution is due to floating-point error, proceeding anyway...")
end
@assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
@assert A == Symmetric(A) @assert A == Symmetric(A)
A_sqrt = real(sqrtm(A)) A_sqrt = real(sqrtm(A))
println("")
println("")
println("Checking in floating-point arithmetic...") println("Checking in floating-point arithmetic...")
fp_distance = check_solution(κ, A_sqrt, Δ, verbose=VERBOSE) @time fp_distance = check_solution(κ, A_sqrt, Δ, verbose=verbose)
println("Distance to positive cone ≈ $(Float64(trunc(fp_distance,8)))") println("Distance to positive cone ≈ $(Float64(trunc(fp_distance,8)))")
println("-------------------------------------------------------------") println("-------------------------------------------------------------")
println("") println("")
println("Checking in rational arithmetic...") println("Checking in rational arithmetic...")
κ_ℚ = ℚ(trunc(κ,Int(abs(log10(tol)))), TOL) κ_ℚ = ℚ(trunc(κ,Int(abs(log10(tol)))), tol)
@assert κ - κ_ℚ ≥ 0 A_sqrt_ℚ, Δ_ℚ = ℚ(A_sqrt, tol), ℚ(Δ, tol)
A_sqrt_ℚ, Δ_ℚ = ℚ(A_sqrt, TOL), ℚ(Δ, TOL) @time ℚ_distance = check_solution(κ_ℚ, A_sqrt_ℚ, Δ_ℚ, verbose=verbose)
ℚ_distance = check_solution(κ_ℚ, A_sqrt_ℚ, Δ_ℚ, verbose=VERBOSE)
@assert isa(ℚ_distance, Rational) @assert isa(ℚ_distance, Rational)
println("Distance to positive cone ≈ $(Float64(trunc(ℚ_distance,8)))") println("Distance to positive cone ≈ $(Float64(trunc(ℚ_distance,8)))")
println("-------------------------------------------------------------") println("-------------------------------------------------------------")
@ -189,7 +181,7 @@ function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement,
println("Projecting columns of A_sqrt to the augmentation ideal...") println("Projecting columns of A_sqrt to the augmentation ideal...")
A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ) A_sqrt_ℚ_aug = correct_to_augmentation_ideal(A_sqrt_ℚ)
ℚ_dist_to_Σ² = check_solution(κ_ℚ, A_sqrt_ℚ_aug, Δ_ℚ, verbose=VERBOSE, augmented=true) @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) @assert isa(ℚ_dist_to_Σ², Rational)
s = (ℚ_dist_to_Σ² < 0? "≤": "≥") s = (ℚ_dist_to_Σ² < 0? "≤": "≥")
println("Distance to positive cone $s $(Float64(trunc(ℚ_dist_to_Σ²,8)))") println("Distance to positive cone $s $(Float64(trunc(ℚ_dist_to_Σ²,8)))")