1
0
mirror of https://github.com/kalmarek/PropertyT.jl.git synced 2024-11-14 14:15:28 +01:00

cosmetics

This commit is contained in:
kalmar 2017-02-26 13:51:20 +01:00
parent 35f669595d
commit 068bfaf29f

View File

@ -121,7 +121,7 @@ function correct_to_augmentation_ideal{T<:Rational}(sqrt_matrix::Array{T,2})
return sqrt_corrected
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)
if augmented
@assert GroupAlgebras.ɛ(result) == 0//1
@ -155,33 +155,25 @@ end;
(x, tol::Real) = rationalize(BigInt, x, tol=tol)
function _distance_to_positive_cone(Δ::GroupAlgebraElement,
κ::Float64,
A::Array{Float64,2};
tol=10.0^-7,
verbose=true)
function _distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
tol=10.0^-7, verbose=true)
@show maximum(A)
if maximum(A) < 1e-2
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)
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...")
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("-------------------------------------------------------------")
println("")
println("Checking in rational arithmetic...")
κ_ = (trunc(κ,Int(abs(log10(tol)))), TOL)
@assert κ - κ_ 0
A_sqrt_, Δ_ = (A_sqrt, TOL), (Δ, TOL)
_distance = check_solution(κ_, A_sqrt_, Δ_, verbose=VERBOSE)
κ_ = (trunc(κ,Int(abs(log10(tol)))), tol)
A_sqrt_, Δ_ = (A_sqrt, tol), (Δ, tol)
@time _distance = check_solution(κ_, A_sqrt_, Δ_, verbose=verbose)
@assert isa(_distance, Rational)
println("Distance to positive cone ≈ $(Float64(trunc(_distance,8)))")
println("-------------------------------------------------------------")
@ -189,7 +181,7 @@ function _distance_to_positive_cone(Δ::GroupAlgebraElement,
println("Projecting columns of A_sqrt to the augmentation ideal...")
A_sqrt__aug = correct_to_augmentation_ideal(A_sqrt_)
_dist_to_Σ² = check_solution(κ_, A_sqrt__aug, Δ_, verbose=VERBOSE, augmented=true)
@time _dist_to_Σ² = check_solution(κ_, A_sqrt__aug, Δ_, verbose=verbose, augmented=true)
@assert isa(_dist_to_Σ², Rational)
s = (_dist_to_Σ² < 0? "": "")
println("Distance to positive cone $s $(Float64(trunc(_dist_to_Σ²,8)))")