mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-14 14:15:28 +01:00
Merge branch 'master' into enh/julia-v0.6
This commit is contained in:
commit
498a6700ec
@ -3,8 +3,7 @@ import Base: rationalize
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using IntervalArithmetic
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IntervalArithmetic.setrounding(Interval, :tight)
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IntervalArithmetic.setformat(sigfigs=10)
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IntervalArithmetic.setprecision(Interval, 53) # slightly faster than 256
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IntervalArithmetic.setformat(sigfigs=12)
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import IntervalArithmetic.±
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@ -15,131 +14,97 @@ end
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(±)(X::GroupRingElem, tol::Real) = GroupRingElem(X.coeffs ± tol, parent(X))
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function Base.rationalize{T<:Integer, S<:Real}(::Type{T},
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X::AbstractArray{S}; tol::Real=eps(eltype(X)))
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r(x) = rationalize(T, x, tol=tol)
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return r.(X)
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end
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ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol)
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EOI{T<:Number}(Δ::GroupRingElem{T}, λ::T) = Δ*Δ - λ*Δ
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function groupring_square(vect::AbstractVector, l, pm)
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zzz = zeros(eltype(vect), l)
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zzz[1:length(vect)] .= vect
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return GroupRings.mul!(similar(zzz), zzz, zzz, pm)
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return GroupRings.mul!(zzz, vect, vect, pm)
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end
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function compute_SOS(sqrt_matrix, elt::GroupRingElem)
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n = size(sqrt_matrix,2)
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l = length(elt.coeffs)
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pm = parent(elt).pm
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function compute_SOS(Q::AbstractArray, pm::Array{Int,2}, l::Int)
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result = zeros(eltype(sqrt_matrix), l)
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for i in 1:n
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result .+= groupring_square(view(sqrt_matrix,:,i), l, pm)
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end
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# @everywhere groupring_square = PropertyT.groupring_square
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#
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# result = @parallel (+) for i in 1:n
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# groupring_square(view(sqrt_matrix,:,i), length(elt.coeffs), parent(elt).pm)
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# result = zeros(eltype(Q), l)
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# r = similar(result)
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# for i in 1:size(Q,2)
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# print(" $i")
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# result += GroupRings.mul!(r, view(Q,:,i), view(Q,:,i), pm)
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# end
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return GroupRingElem(result, parent(elt))
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@everywhere groupring_square = PropertyT.groupring_square
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result = @parallel (+) for i in 1:size(Q,2)
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groupring_square(Q[:,i], l, pm)
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end
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println("")
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return result
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end
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function correct_to_augmentation_ideal{T<:Rational}(sqrt_matrix::Array{T,2})
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l = size(sqrt_matrix, 2)
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sqrt_corrected = Array{Interval{Float64}}(l,l)
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function compute_SOS(Q::AbstractArray, RG::GroupRing, l::Int)
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result = compute_SOS(Q, RG.pm, l)
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return GroupRingElem(result, RG)
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end
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function distance_to_cone{T<:Interval}(elt::GroupRingElem, Q::AbstractArray{T,2}, wlen::Int)
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SOS = compute_SOS(Q, parent(elt), length(elt.coeffs))
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SOS_diff = elt - SOS
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L1_dist)")
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dist = 2^(wlen-1)*eoi_SOS_L1_dist
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return dist
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end
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function distance_to_cone{T}(elt::GroupRingElem, Q::AbstractArray{T,2}, wlen::Int)
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SOS = compute_SOS(Q, parent(elt), length(elt.coeffs))
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SOS_diff = elt - SOS
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", ɛ_dist))")
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", eoi_SOS_L1_dist))")
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dist = 2^(wlen-1)*eoi_SOS_L1_dist
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return dist
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end
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function augIdproj{T, I<:AbstractInterval}(S::Type{I}, Q::AbstractArray{T,2})
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l = size(Q, 2)
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R = zeros(S, (l,l))
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Threads.@threads for j in 1:l
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col = sum(view(sqrt_matrix, :,j))//l
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col = sum(view(Q, :,j))/l
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for i in 1:l
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sqrt_corrected[i,j] = (Float64(sqrt_matrix[i,j]) - Float64(col)) ± eps(0.0)
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R[i,j] = Q[i,j] - col ± eps(0.0)
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end
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end
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return sqrt_corrected
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return R
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end
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function distance_to_cone{T<:Rational}(λ::T, sqrt_matrix::Array{T,2}, Δ::GroupRingElem{T}, wlen)
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SOS = compute_SOS(sqrt_matrix, Δ)
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SOS_diff = EOI(Δ, λ) - SOS
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "λ = $λ (≈$(@sprintf("%.10f", float(λ)))")
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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if ɛ_dist ≠ 0//1
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warn(logger, "The SOS is not in the augmentation ideal, numbers below are meaningless!")
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end
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) = $ɛ_dist")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ = $(@sprintf("%.10f", float(eoi_SOS_L1_dist)))")
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distance_to_cone = λ - 2^(wlen-1)*eoi_SOS_L1_dist
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return distance_to_cone
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end
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function distance_to_cone{T<:Rational, S<:Interval}(λ::T, sqrt_matrix::AbstractArray{S,2}, Δ::GroupRingElem{T}, wlen)
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SOS = compute_SOS(sqrt_matrix, Δ)
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info(logger, "ɛ(∑ξᵢ*ξᵢ) ∈ $(GroupRings.augmentation(SOS))")
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λ_int = @interval(λ)
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Δ_int = GroupRingElem([@interval(c) for c in Δ.coeffs], parent(Δ))
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SOS_diff = EOI(Δ_int, λ_int) - SOS
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "λ = $λ (≈≥$(@sprintf("%.10f",float(λ))))")
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ∈ $(ɛ_dist)")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(eoi_SOS_L1_dist)")
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distance_to_cone = λ - 2^(wlen-1)*eoi_SOS_L1_dist
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return distance_to_cone
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end
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function distance_to_cone(λ, sqrt_matrix::AbstractArray, Δ::GroupRingElem, wlen)
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SOS = compute_SOS(sqrt_matrix, Δ)
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SOS_diff = EOI(Δ, λ) - SOS
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eoi_SOS_L1_dist = norm(SOS_diff,1)
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info(logger, "λ = $λ")
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ɛ_dist = GroupRings.augmentation(SOS_diff)
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info(logger, "ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", ɛ_dist))")
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info(logger, "‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", eoi_SOS_L1_dist))")
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distance_to_cone = λ - 2^(wlen-1)*eoi_SOS_L1_dist
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return distance_to_cone
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end
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function rationalize_and_project{T}(Q::AbstractArray{T}, δ::T, logger)
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info(logger, "")
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info(logger, "Rationalizing with accuracy $δ")
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t = @timed Q_ℚ = ℚ(Q, δ)
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info(logger, timed_msg(t))
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info(logger, "Projecting columns of the rationalized Q to the augmentation ideal...")
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t = @timed Q_int = correct_to_augmentation_ideal(Q_ℚ)
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info(logger, timed_msg(t))
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function augIdproj{T}(Q::AbstractArray{T,2}, logger)
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info(logger, "Projecting columns of Q to the augmentation ideal...")
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@logtime logger Q = augIdproj(Interval{T}, Q)
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info(logger, "Checking that sum of every column contains 0.0... ")
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check = all([0.0 in sum(view(Q_int, :, i)) for i in 1:size(Q_int, 2)])
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check = all([0.0 in sum(view(Q, :, i)) for i in 1:size(Q, 2)])
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info(logger, (check? "They do." : "FAILED!"))
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@assert check
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return Q_int
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return Q
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end
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function check_distance_to_positive_cone(Δ::GroupRingElem, λ, Q, wlen;
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tol=1e-14, rational=false)
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function distance_to_positive_cone(Δ::GroupRingElem, λ, Q, wlen::Int)
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info(logger, "------------------------------------------------------------")
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info(logger, "")
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info(logger, "λ = $λ")
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info(logger, "Checking in floating-point arithmetic...")
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t = @timed fp_distance = distance_to_cone(λ, Q, Δ, wlen)
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info(logger, timed_msg(t))
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Δ²_λΔ = EOI(Δ, λ)
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@logtime logger fp_distance = λ - distance_to_cone(Δ²_λΔ, Q, wlen)
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info(logger, "Floating point distance (to positive cone) ≈ $(@sprintf("%.10f", fp_distance))")
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info(logger, "------------------------------------------------------------")
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@ -148,26 +113,16 @@ function check_distance_to_positive_cone(Δ::GroupRingElem, λ, Q, wlen;
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end
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info(logger, "")
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Q_ℚω_int = rationalize_and_project(Q, tol, logger)
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λ_ℚ = ℚ(λ, tol)
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Δ_ℚ = ℚ(Δ, tol)
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Q = augIdproj(Q, logger)
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info(logger, "Checking in interval arithmetic")
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λ = @interval(λ)
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Δ = GroupRingElem([@interval(c) for c in Δ.coeffs], parent(Δ))
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Δ²_λΔ = EOI(Δ, λ)
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t = @timed Interval_dist_to_ΣSq = distance_to_cone(λ_ℚ, Q_ℚω_int, Δ_ℚ, wlen)
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info(logger, timed_msg(t))
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@logtime logger Interval_dist_to_ΣSq = λ - distance_to_cone(Δ²_λΔ, Q, wlen)
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info(logger, "The Augmentation-projected actual distance (to positive cone) ∈ $(Interval_dist_to_ΣSq)")
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info(logger, "------------------------------------------------------------")
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if Interval_dist_to_ΣSq.lo ≤ 0 || !rational
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return Interval_dist_to_ΣSq
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else
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info(logger, "Checking Projected SOS decomposition in exact rational arithmetic...")
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t = @timed ℚ_dist_to_ΣSq = distance_to_cone(λ_ℚ, Q_ℚω, Δ_ℚ, wlen)
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info(logger, timed_msg(t))
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@assert isa(ℚ_dist_to_ΣSq, Rational)
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info(logger, "Augmentation-projected rational distance (to positive cone) ≥ $(Float64(trunc(ℚ_dist_to_ΣSq,8)))")
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info(logger, "------------------------------------------------------------")
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return ℚ_dist_to_ΣSq
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end
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return Interval_dist_to_ΣSq
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end
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@ -8,44 +8,50 @@ immutable Settings
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N::Int
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G::Group
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S::Vector
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AutS::Group
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autS::Group
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radius::Int
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solver::SCSSolver
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upper_bound::Float64
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tol::Float64
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end
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immutable OrbitData
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prefix(s::Settings) = s.name
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suffix(s::Settings) = "$(s.upper_bound)"
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prepath(s::Settings) = prefix(s)
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fullpath(s::Settings) = joinpath(prefix(s), suffix(s))
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immutable OrbitData{T<:AbstractArray{Float64, 2}, LapType <:AbstractVector{Float64}}
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name::String
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Us::Vector
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Us::Vector{T}
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Ps::Vector{Array{JuMP.Variable,2}}
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cnstr::Vector
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laplacian::Vector
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laplacianSq::Vector
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cnstr::Vector{SparseMatrixCSC{Float64, Int}}
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laplacian::LapType
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laplacianSq::LapType
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dims::Vector{Int}
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end
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function OrbitData(name::String)
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splap = load(joinpath(name, "delta.jld"), "Δ");
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pm = load(joinpath(name, "pm.jld"), "pm");
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cnstr = PropertyT.constraints_from_pm(pm);
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function OrbitData(sett::Settings)
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splap = load(joinpath(prepath(sett), "delta.jld"), "Δ");
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pm = load(joinpath(prepath(sett), "pm.jld"), "pm");
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cnstr = PropertyT.constraints(pm);
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splap² = similar(splap)
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splap² = GroupRings.mul!(splap², splap, splap, pm);
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# Uπs = load(joinpath(name, "U_pis.jld"), "Uπs");
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Uπs = load(joinpath(name, "U_pis.jld"), "spUπs");
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Uπs = load(joinpath(prepath(sett), "U_pis.jld"), "Uπs")
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Uπs = sparsify!.(Uπs, sett.tol, check=true, verbose=true)
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#dimensions of the corresponding πs:
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dims = load(joinpath(name, "U_pis.jld"), "dims")
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dims = load(joinpath(prepath(sett), "U_pis.jld"), "dims")
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m, P = init_model(Uπs);
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m, P = init_model(size(Uπs,1), [size(U,2) for U in Uπs]);
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orbits = load(joinpath(name, "orbits.jld"), "orbits");
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orbits = load(joinpath(prepath(sett), "orbits.jld"), "orbits");
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n = size(Uπs[1],1)
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orb_spcnstrm = [orbit_constraint(cnstr[collect(orb)], n) for orb in orbits]
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orb_splap = orbit_spvector(splap, orbits)
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orb_splap² = orbit_spvector(splap², orbits)
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orbData = OrbitData(name, Uπs, P, orb_spcnstrm, orb_splap, orb_splap², dims);
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orbData = OrbitData(fullpath(sett), Uπs, P, orb_spcnstrm, orb_splap, orb_splap², dims);
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# orbData = OrbitData(name, Uπs, P, orb_spcnstrm, splap, splap², dims);
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@ -89,19 +95,19 @@ function sparsify!{T}(M::AbstractArray{T}, eps=eps(T); check=false, verbose=fals
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info(logger, "Sparsified density:", rpad(densM, 20), " → ", rpad(dens(M),20))
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end
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return M
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return sparse(M)
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end
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sparsify{T}(U::AbstractArray{T}, tol=eps(T)) = sparsify!(deepcopy(U), tol)
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sparsify{T}(U::AbstractArray{T}, tol=eps(T); check=true, verbose=false) = sparsify!(deepcopy(U), tol, check=check, verbose=verbose)
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function init_orbit_data(logger, sett::Settings; radius=2)
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ex(fname) = isfile(joinpath(sett.name, fname))
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ex(fname) = isfile(joinpath(prepath(sett), fname))
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files_exists = ex.(["delta.jld", "pm.jld", "U_pis.jld", "orbits.jld"])
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files_exists = ex.(["delta.jld", "pm.jld", "U_pis.jld", "orbits.jld", "preps.jld"])
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if !all(files_exists)
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compute_orbit_data(logger, sett.name, sett.G, sett.S, sett.AutS, radius=radius)
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compute_orbit_data(logger, prepath(sett), sett.G, sett.S, sett.autS, radius=radius)
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end
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return 0
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@ -118,9 +124,9 @@ end
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A(data::OrbitData, π, t) = data.dims[π].*transform(data.Us[π], data.cnstr[t])
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function constrLHS(m::JuMP.Model, data::OrbitData, t)
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l = endof(data.Us)
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lhs = @expression(m, sum(vecdot(A(data, π, t), data.Ps[π]) for π in 1:l))
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return lhs
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l = endof(data.Us)
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lhs = @expression(m, sum(vecdot(A(data, π, t), data.Ps[π]) for π in 1:l))
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return lhs
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end
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function constrLHS(m::JuMP.Model, cnstr, Us, Ust, dims, vars, eps=100*eps(1.0))
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@ -154,36 +160,32 @@ function addconstraints!(m::JuMP.Model, data::OrbitData, l::Int=length(data.lapl
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println("")
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end
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function init_model(Uπs)
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m = JuMP.Model();
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l = size(Uπs,1)
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P = Vector{Array{JuMP.Variable,2}}(l)
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function init_model(n, sizes)
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m = JuMP.Model();
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P = Vector{Array{JuMP.Variable,2}}(n)
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for k in 1:l
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s = size(Uπs[k],2)
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P[k] = JuMP.@variable(m, [i=1:s, j=1:s])
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JuMP.@SDconstraint(m, P[k] >= 0.0)
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end
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for (k,s) in enumerate(sizes)
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P[k] = JuMP.@variable(m, [i=1:s, j=1:s])
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JuMP.@SDconstraint(m, P[k] >= 0.0)
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end
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JuMP.@variable(m, λ >= 0.0)
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JuMP.@objective(m, Max, λ)
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return m, P
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JuMP.@variable(m, λ >= 0.0)
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JuMP.@objective(m, Max, λ)
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return m, P
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end
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function create_SDP_problem(name::String; upper_bound=Inf)
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function create_SDP_problem(sett::Settings)
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||||
info(logger, "Loading orbit data....")
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t = @timed SDP_problem, orb_data = OrbitData(name);
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||||
info(logger, PropertyT.timed_msg(t))
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@logtime logger SDP_problem, orb_data = OrbitData(sett);
|
||||
|
||||
if upper_bound < Inf
|
||||
if sett.upper_bound < Inf
|
||||
λ = JuMP.getvariable(SDP_problem, :λ)
|
||||
JuMP.@constraint(SDP_problem, λ <= upper_bound)
|
||||
JuMP.@constraint(SDP_problem, λ <= sett.upper_bound)
|
||||
end
|
||||
|
||||
t = length(orb_data.laplacian)
|
||||
info(logger, "Adding $t constraints ... ")
|
||||
t = @timed addconstraints!(SDP_problem, orb_data)
|
||||
info(logger, PropertyT.timed_msg(t))
|
||||
@logtime logger addconstraints!(SDP_problem, orb_data)
|
||||
|
||||
return SDP_problem, orb_data
|
||||
end
|
||||
@ -201,28 +203,36 @@ function λandP(m::JuMP.Model, data::OrbitData, sett::Settings)
|
||||
|
||||
info(logger, "Reconstructing P...")
|
||||
|
||||
t = @timed preps = perm_reps(sett.G, sett.S, sett.AutS, sett.radius)
|
||||
info(logger, PropertyT.timed_msg(t))
|
||||
preps = load_preps(joinpath(prepath(sett), "preps.jld"), sett.autS)
|
||||
|
||||
t = @timed recP = reconstruct_sol(preps, data.Us, Ps, data.dims)
|
||||
info(logger, PropertyT.timed_msg(t))
|
||||
@logtime logger recP = reconstruct_sol(preps, data.Us, Ps, data.dims)
|
||||
|
||||
fname = PropertyT.λSDPfilenames(data.name)[2]
|
||||
fname = PropertyT.λSDPfilenames(fullpath(sett))[2]
|
||||
save(fname, "origP", Ps, "P", recP)
|
||||
return λ, recP
|
||||
end
|
||||
|
||||
function load_preps(fname::String, G::Nemo.Group)
|
||||
lded_preps = load(fname, "perms_d")
|
||||
permG = PermutationGroup(length(first(lded_preps)))
|
||||
@assert length(lded_preps) == order(G)
|
||||
return Dict(k=>permG(v) for (k,v) in zip(elements(G), lded_preps))
|
||||
end
|
||||
|
||||
function save_preps(fname::String, preps)
|
||||
autS = parent(first(keys(preps)))
|
||||
JLD.save(fname, "perms_d", [preps[elt].d for elt in elements(autS)])
|
||||
end
|
||||
|
||||
function check_property_T(sett::Settings)
|
||||
|
||||
init_orbit_data(logger, sett, radius=sett.radius)
|
||||
|
||||
fnames = PropertyT.λSDPfilenames(sett.name)
|
||||
|
||||
if all(isfile.(fnames))
|
||||
λ, P = PropertyT.λandP(sett.name)
|
||||
if all(isfile.(λSDPfilenames(fullpath(sett))))
|
||||
λ, P = PropertyT.λandP(fullpath(sett))
|
||||
else
|
||||
info(logger, "Creating SDP problem...")
|
||||
SDP_problem, orb_data = create_SDP_problem(sett.name, upper_bound=sett.upper_bound)
|
||||
SDP_problem, orb_data = create_SDP_problem(sett)
|
||||
JuMP.setsolver(SDP_problem, sett.solver)
|
||||
|
||||
λ, P = λandP(SDP_problem, orb_data, sett)
|
||||
@ -234,17 +244,16 @@ function check_property_T(sett::Settings)
|
||||
info(logger, "minimum(P) = $(minimum(P))")
|
||||
|
||||
if λ > 0
|
||||
pm_fname = joinpath(sett.name, "pm.jld")
|
||||
pm_fname, Δ_fname = pmΔfilenames(prepath(sett))
|
||||
RG = GroupRing(sett.G, load(pm_fname, "pm"))
|
||||
Δ_fname = joinpath(sett.name, "delta.jld")
|
||||
Δ = GroupRingElem(load(Δ_fname, "Δ")[:, 1], RG)
|
||||
|
||||
isapprox(eigvals(P), abs.(eigvals(P)), atol=sett.tol) ||
|
||||
warn("The solution matrix doesn't seem to be positive definite!")
|
||||
warn("The solution matrix doesn't seem to be positive definite!")
|
||||
# @assert P == Symmetric(P)
|
||||
Q = real(sqrtm(Symmetric(P)))
|
||||
@logtime logger Q = real(sqrtm(Symmetric(P)))
|
||||
|
||||
sgap = PropertyT.check_distance_to_positive_cone(Δ, λ, Q, 2*sett.radius, tol=sett.tol, rational=false)
|
||||
sgap = distance_to_positive_cone(Δ, λ, Q, 2*sett.radius)
|
||||
if isa(sgap, Interval)
|
||||
sgap = sgap.lo
|
||||
end
|
||||
|
||||
@ -10,7 +10,7 @@ mutable struct FFEltsIter{T<:Generic.FinField}
|
||||
all::Int
|
||||
field::T
|
||||
|
||||
function FFEltsIter{T}(F::T) where {T}
|
||||
function FFEltsIter{T}(F::T) where {T}
|
||||
return new(Int(characteristic(F)^degree(F)), F)
|
||||
end
|
||||
end
|
||||
@ -79,89 +79,61 @@ function orbit_spvector(vect::AbstractVector, orbits)
|
||||
return orb_vector
|
||||
end
|
||||
|
||||
function orbit_constraint(constraints::Vector{Vector{Vector{Int64}}}, n)
|
||||
function orbit_constraint(constraints::Vector{Vector{Tuple{Int,Int}}}, n)
|
||||
result = spzeros(n,n)
|
||||
for cnstr in constraints
|
||||
for p in cnstr
|
||||
result[p[2], p[1]] += 1.0
|
||||
result[p[2], p[1]] += 1.0/length(constraints)
|
||||
end
|
||||
end
|
||||
return 1/length(constraints)*result
|
||||
return result
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# Matrix- and C*-representations
|
||||
# Matrix-, Permutation- and C*-representations
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function matrix_repr(g::GroupElem, E, E_dict)
|
||||
rep_matrix = spzeros(Int, length(E), length(E))
|
||||
function matrix_repr(p::perm)
|
||||
N = parent(p).n
|
||||
return sparse(1:N, p.d, [1.0 for _ in 1:N])
|
||||
end
|
||||
|
||||
function matrix_reps{T<:GroupElem}(preps::Dict{T,perm})
|
||||
kk = collect(keys(preps))
|
||||
mreps = Vector{SparseMatrixCSC{Float64, Int}}(length(kk))
|
||||
Threads.@threads for i in 1:length(kk)
|
||||
mreps[i] = matrix_repr(preps[kk[i]])
|
||||
end
|
||||
return Dict(kk[i] => mreps[i] for i in 1:length(kk))
|
||||
end
|
||||
|
||||
function perm_repr(g::GroupElem, E::Vector, E_dict)
|
||||
p = Vector{Int}(length(E))
|
||||
for (i,elt) in enumerate(E)
|
||||
j = E_dict[g(elt)]
|
||||
rep_matrix[i,j] = 1
|
||||
p[i] = E_dict[g(elt)]
|
||||
end
|
||||
return rep_matrix
|
||||
return p
|
||||
end
|
||||
|
||||
function matrix_reps{T<:GroupElem}(G::Group, S::Vector{T}, AutS::Group, radius::Int)
|
||||
Id = (isa(G, Nemo.Ring) ? one(G) : G())
|
||||
E2, _ = Groups.generate_balls(S, Id, radius=radius)
|
||||
Edict = GroupRings.reverse_dict(E2)
|
||||
|
||||
elts = collect(elements(AutS))
|
||||
l = length(elts)
|
||||
mreps = Vector{SparseMatrixCSC{Int, Int}}(l)
|
||||
|
||||
Threads.@threads for i in 1:l
|
||||
mreps[i] = PropertyT.matrix_repr(elts[i], E2, Edict)
|
||||
end
|
||||
|
||||
mreps_dict = Dict(elts[i]=>mreps[i] for i in 1:l)
|
||||
|
||||
return mreps_dict
|
||||
end
|
||||
|
||||
function matrix_reps(G::Group, E2, E_dict)
|
||||
function perm_reps(G::Group, E::Vector, E_rdict=GroupRings.reverse_dict(E))
|
||||
elts = collect(elements(G))
|
||||
l = length(elts)
|
||||
mreps = Vector{SparseMatrixCSC{Int, Int}}(l)
|
||||
|
||||
Threads.@threads for i in 1:l
|
||||
mreps[i] = matrix_repr(elts[i], E2, E_dict)
|
||||
end
|
||||
|
||||
return Dict(elts[i]=>mreps[i] for i in 1:l)
|
||||
end
|
||||
|
||||
function perm_reps{T<:GroupElem}(G::Group, S::Vector{T}, AutS::Group, radius::Int)
|
||||
Id = (isa(G, Nemo.Ring) ? one(G) : G())
|
||||
E_R, _ = Groups.generate_balls(S, Id, radius=radius)
|
||||
Edict = GroupRings.reverse_dict(E_R)
|
||||
|
||||
elts = collect(elements(AutS))
|
||||
l = length(elts)
|
||||
preps = Vector{Generic.perm}(l)
|
||||
|
||||
G = Nemo.PermutationGroup(length(E_R))
|
||||
permG = Nemo.PermutationGroup(length(E))
|
||||
|
||||
Threads.@threads for i in 1:l
|
||||
preps[i] = G(perm_repr(elts[i], E_R, Edict))
|
||||
preps[i] = permG(PropertyT.perm_repr(elts[i], E, E_rdict))
|
||||
end
|
||||
|
||||
preps_dict = Dict(elts[i]=>preps[i] for i in 1:l)
|
||||
|
||||
return preps_dict
|
||||
return Dict(elts[i]=>preps[i] for i in 1:l)
|
||||
end
|
||||
|
||||
function perm_repr(g::GroupElem, E, E_dict)
|
||||
l = length(E)
|
||||
p = Vector{Int}(l)
|
||||
for (i,elt) in enumerate(E)
|
||||
j = E_dict[g(elt)]
|
||||
p[i] = j
|
||||
end
|
||||
return p
|
||||
function perm_reps(S::Vector, autS::Group, radius::Int)
|
||||
E, _ = Groups.generate_balls(S, radius=radius)
|
||||
return perm_reps(autS, E)
|
||||
end
|
||||
|
||||
function reconstruct_sol{T<:GroupElem}(preps::Dict{T, Generic.perm},
|
||||
@ -189,22 +161,17 @@ function reconstruct_sol{T<:GroupElem}(preps::Dict{T, Generic.perm},
|
||||
end
|
||||
|
||||
function Cstar_repr(x::GroupRingElem{T}, mreps::Dict) where {T}
|
||||
nzindx = [i for i in eachindex(x.coeffs) if x[i] != zero(T)]
|
||||
RG = parent(x)
|
||||
res = sum(Float64(x[i]).*mreps[RG.basis[i]] for i in nzindx)
|
||||
|
||||
return res
|
||||
return sum(x[i].*mreps[parent(x).basis[i]] for i in findn(x.coeffs))
|
||||
end
|
||||
|
||||
function orthSVD(M::AbstractMatrix)
|
||||
M = full(M)
|
||||
fact = svdfact(M)
|
||||
singv = fact[:S]
|
||||
M_rank = sum(singv .> maximum(size(M))*eps(eltype(singv)))
|
||||
return fact[:U][:,1:M_rank]
|
||||
function orthSVD{T}(M::AbstractMatrix{T})
|
||||
M = full(M)
|
||||
fact = svdfact(M)
|
||||
M_rank = sum(fact[:S] .> maximum(size(M))*eps(T))
|
||||
return fact[:U][:,1:M_rank]
|
||||
end
|
||||
|
||||
function compute_orbit_data{T<:GroupElem}(logger, name::String, G::Nemo.Group, S::Vector{T}, AutS; radius=2)
|
||||
function compute_orbit_data{T<:GroupElem}(logger, name::String, G::Nemo.Group, S::Vector{T}, autS::Nemo.Group; radius=2)
|
||||
isdir(name) || mkdir(name)
|
||||
|
||||
info(logger, "Generating ball of radius $(2*radius)")
|
||||
@ -212,44 +179,46 @@ function compute_orbit_data{T<:GroupElem}(logger, name::String, G::Nemo.Group, S
|
||||
# TODO: Fix that by multiple dispatch?
|
||||
Id = (isa(G, Nemo.Ring) ? one(G) : G())
|
||||
|
||||
@time E4, sizes = Groups.generate_balls(S, Id, radius=2*radius);
|
||||
@logtime logger E_2R, sizes = Groups.generate_balls(S, Id, radius=2*radius);
|
||||
info(logger, "Balls of sizes $sizes.")
|
||||
info(logger, "Reverse dict")
|
||||
@time E_dict = GroupRings.reverse_dict(E4)
|
||||
@logtime logger E_rdict = GroupRings.reverse_dict(E_2R)
|
||||
|
||||
info(logger, "Product matrix")
|
||||
@time pm = GroupRings.create_pm(E4, E_dict, sizes[radius], twisted=true)
|
||||
RG = GroupRing(G, E4, E_dict, pm)
|
||||
@logtime logger pm = GroupRings.create_pm(E_2R, E_rdict, sizes[radius], twisted=true)
|
||||
RG = GroupRing(G, E_2R, E_rdict, pm)
|
||||
Δ = PropertyT.splaplacian(RG, S)
|
||||
@assert GroupRings.augmentation(Δ) == 0
|
||||
save(joinpath(name, "delta.jld"), "Δ", Δ.coeffs)
|
||||
save(joinpath(name, "pm.jld"), "pm", pm)
|
||||
|
||||
info(logger, "Decomposing E into orbits of $(AutS)")
|
||||
@time orbs = orbit_decomposition(AutS, E4, E_dict)
|
||||
@assert sum(length(o) for o in orbs) == length(E4)
|
||||
info(logger, "Decomposing E into orbits of $(autS)")
|
||||
@logtime logger orbs = orbit_decomposition(autS, E_2R, E_rdict)
|
||||
@assert sum(length(o) for o in orbs) == length(E_2R)
|
||||
info(logger, "E consists of $(length(orbs)) orbits!")
|
||||
save(joinpath(name, "orbits.jld"), "orbits", orbs)
|
||||
|
||||
info(logger, "Action matrices")
|
||||
@time AutS_mreps = matrix_reps(AutS, E4[1:sizes[radius]], E_dict)
|
||||
@logtime logger reps = perm_reps(autS, E_2R[1:sizes[radius]], E_rdict)
|
||||
save_preps(joinpath(name, "preps.jld"), reps)
|
||||
reps = matrix_reps(reps)
|
||||
|
||||
info(logger, "Projections")
|
||||
@time AutS_mps = rankOne_projections(AutS);
|
||||
@logtime logger autS_mps = rankOne_projections(autS);
|
||||
|
||||
@time π_E_projections = [Cstar_repr(p, AutS_mreps) for p in AutS_mps]
|
||||
@logtime logger π_E_projections = [Cstar_repr(p, reps) for p in autS_mps]
|
||||
|
||||
info(logger, "Uπs...")
|
||||
@time Uπs = orthSVD.(π_E_projections)
|
||||
@logtime logger Uπs = orthSVD.(π_E_projections)
|
||||
|
||||
multiplicities = size.(Uπs,2)
|
||||
info(logger, "multiplicities = $multiplicities")
|
||||
dimensions = [Int(p[AutS()]*Int(order(AutS))) for p in AutS_mps];
|
||||
dimensions = [Int(p[autS()]*Int(order(autS))) for p in autS_mps];
|
||||
info(logger, "dimensions = $dimensions")
|
||||
@assert dot(multiplicities, dimensions) == sizes[radius]
|
||||
|
||||
save(joinpath(name, "U_pis.jld"),
|
||||
"Uπs", Uπs,
|
||||
"spUπs", sparsify!.(deepcopy(Uπs), check=true, verbose=true),
|
||||
"dims", dimensions)
|
||||
return 0
|
||||
end
|
||||
|
||||
@ -4,7 +4,7 @@
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
abstract type AbstractCharacter <: Function end
|
||||
abstract type AbstractCharacter end
|
||||
|
||||
struct PermCharacter <: AbstractCharacter
|
||||
p::Generic.Partition
|
||||
@ -20,6 +20,8 @@ function (chi::PermCharacter)(g::Generic.perm)
|
||||
return Int(Nemo.Generic.MN1inner(R, p, 1, Nemo.Generic._charvalsTable))
|
||||
end
|
||||
|
||||
Nemo.isone(p::GroupElem) = p == parent(p)()
|
||||
|
||||
## NOTE: this works only for Z/2!!!!
|
||||
function (chi::DirectProdCharacter)(g::DirectProductGroupElem)
|
||||
return reduce(*, 1, ((-1)^isone(g.elts[j]) for j in 1:chi.i))
|
||||
@ -47,18 +49,17 @@ end
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function central_projection(RG::GroupRing, chi::AbstractCharacter,
|
||||
T::Type=Rational{Int})
|
||||
result = RG(T)
|
||||
result.coeffs = full(result.coeffs)
|
||||
dim = chi(RG.group())
|
||||
ord = Int(order(RG.group))
|
||||
function central_projection(RG::GroupRing, chi::AbstractCharacter, T::Type=Rational{Int})
|
||||
result = RG(T)
|
||||
result.coeffs = full(result.coeffs)
|
||||
dim = chi(RG.group())
|
||||
ord = Int(order(RG.group))
|
||||
|
||||
for g in RG.basis
|
||||
result[g] = convert(T, (dim//ord)*chi(g))
|
||||
end
|
||||
for g in RG.basis
|
||||
result[g] = convert(T, (dim//ord)*chi(g))
|
||||
end
|
||||
|
||||
return result
|
||||
return result
|
||||
end
|
||||
|
||||
function idempotents(RG::GroupRing{Generic.PermGroup}, T::Type=Rational{Int})
|
||||
@ -90,12 +91,10 @@ function idempotents(RG::GroupRing{Generic.PermGroup}, T::Type=Rational{Int})
|
||||
return unique(idems)
|
||||
end
|
||||
|
||||
function rankOne_projection(chi::PropertyT.PermCharacter, idems::Vector{S}) where {S<:GroupRingElem}
|
||||
function rankOne_projection(chi::PropertyT.PermCharacter, idems::Vector{T}) where {T<:GroupRingElem}
|
||||
|
||||
RG = parent(first(idems))
|
||||
|
||||
T = eltype(first(idems))
|
||||
|
||||
ids = [[one(RG, T)]; idems]
|
||||
|
||||
for (i,j,k) in Base.product(ids, ids, ids)
|
||||
@ -112,7 +111,7 @@ function rankOne_projection(chi::PropertyT.PermCharacter, idems::Vector{S}) wher
|
||||
throw("Couldn't find rank-one projection for $chi")
|
||||
end
|
||||
|
||||
function minimalprojections(G::Generic.PermGroup, T::Type=Rational{Int})
|
||||
function rankOne_projections(G::Generic.PermGroup, T::Type=Rational{Int})
|
||||
if G.n == 1
|
||||
return [one(GroupRing(G), T)]
|
||||
elseif G.n < 8
|
||||
@ -128,7 +127,7 @@ function minimalprojections(G::Generic.PermGroup, T::Type=Rational{Int})
|
||||
chars = [PropertyT.PermCharacter(p) for p in parts]
|
||||
min_projs = Vector{eltype(RGidems)}(l)
|
||||
|
||||
Threads.@threads for i in 1:l
|
||||
for i in 1:l
|
||||
chi = PropertyT.PermCharacter(parts[i])
|
||||
min_projs[i] = rankOne_projection(chi,RGidems)*central_projection(RG,chi)
|
||||
end
|
||||
@ -136,15 +135,11 @@ function minimalprojections(G::Generic.PermGroup, T::Type=Rational{Int})
|
||||
return min_projs
|
||||
end
|
||||
|
||||
function rankOne_projections(G::Generic.PermGroup, T::Type=Rational{Int})
|
||||
return minimalprojections(G, T)
|
||||
end
|
||||
|
||||
function rankOne_projections(BN::WreathProduct, T::Type=Rational{Int})
|
||||
|
||||
N = BN.P.n
|
||||
# projections as elements of the group rings RSₙ
|
||||
SNprojs_nc = [rankOne_projections(PermutationGroup(i), T) for i in 1:N]
|
||||
SNprojs_nc = [rankOne_projections(PermutationGroup(i)) for i in 1:N]
|
||||
|
||||
# embedding into group ring of BN
|
||||
RBN = GroupRing(BN)
|
||||
@ -163,7 +158,7 @@ function rankOne_projections(BN::WreathProduct, T::Type=Rational{Int})
|
||||
last_emb = g->BN(Nemo.Generic.emb!(BN.P(), g, range[i+1:end]))
|
||||
|
||||
Sk_first = [RBN(p, first_emb) for p in SNprojs_nc[i]]
|
||||
Sk_last = [RBN(p, last_emb ) for p in SNprojs_nc[N-i]]
|
||||
Sk_last = [RBN(p, last_emb) for p in SNprojs_nc[N-i]]
|
||||
|
||||
append!(all_projs,
|
||||
[Qs[i]*p1*p2 for (p1,p2) in Base.product(Sk_first,Sk_last)])
|
||||
@ -187,18 +182,18 @@ doc"""
|
||||
> forming 'products' by adding `op` (which is `*` by default).
|
||||
"""
|
||||
function products{T<:GroupElem}(X::AbstractVector{T}, Y::AbstractVector{T}, op=*)
|
||||
result = Vector{T}()
|
||||
seen = Set{T}()
|
||||
for x in X
|
||||
for y in Y
|
||||
z = op(x,y)
|
||||
if !in(z, seen)
|
||||
push!(seen, z)
|
||||
push!(result, z)
|
||||
end
|
||||
end
|
||||
end
|
||||
return result
|
||||
result = Vector{T}()
|
||||
seen = Set{T}()
|
||||
for x in X
|
||||
for y in Y
|
||||
z = op(x,y)
|
||||
if !in(z, seen)
|
||||
push!(seen, z)
|
||||
push!(result, z)
|
||||
end
|
||||
end
|
||||
end
|
||||
return result
|
||||
end
|
||||
|
||||
doc"""
|
||||
|
||||
124
src/PropertyT.jl
124
src/PropertyT.jl
@ -26,36 +26,69 @@ function setup_logging(name::String)
|
||||
return logger
|
||||
end
|
||||
|
||||
macro logtime(logger, ex)
|
||||
quote
|
||||
local stats = Base.gc_num()
|
||||
local elapsedtime = Base.time_ns()
|
||||
local val = $(esc(ex))
|
||||
elapsedtime = Base.time_ns() - elapsedtime
|
||||
local diff = Base.GC_Diff(Base.gc_num(), stats)
|
||||
local ts = time_string(elapsedtime, diff.allocd, diff.total_time,
|
||||
Base.gc_alloc_count(diff))
|
||||
esc(info(logger, ts))
|
||||
val
|
||||
end
|
||||
end
|
||||
|
||||
function time_string(elapsedtime, bytes, gctime, allocs)
|
||||
str = @sprintf("%10.6f seconds", elapsedtime/1e9)
|
||||
if bytes != 0 || allocs != 0
|
||||
bytes, mb = Base.prettyprint_getunits(bytes, length(Base._mem_units), Int64(1024))
|
||||
allocs, ma = Base.prettyprint_getunits(allocs, length(Base._cnt_units), Int64(1000))
|
||||
if ma == 1
|
||||
str*= @sprintf(" (%d%s allocation%s: ", allocs, Base._cnt_units[ma], allocs==1 ? "" : "s")
|
||||
else
|
||||
str*= @sprintf(" (%.2f%s allocations: ", allocs, Base._cnt_units[ma])
|
||||
end
|
||||
if mb == 1
|
||||
str*= @sprintf("%d %s%s", bytes, Base._mem_units[mb], bytes==1 ? "" : "s")
|
||||
else
|
||||
str*= @sprintf("%.3f %s", bytes, Base._mem_units[mb])
|
||||
end
|
||||
if gctime > 0
|
||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
||||
end
|
||||
str*=")"
|
||||
elseif gctime > 0
|
||||
str*= @sprintf(", %.2f%% gc time", 100*gctime/elapsedtime)
|
||||
end
|
||||
return str
|
||||
end
|
||||
|
||||
function exists(fname::String)
|
||||
return isfile(fname) || islink(fname)
|
||||
end
|
||||
|
||||
function pmΔfilenames(name::String)
|
||||
if !isdir(name)
|
||||
mkdir(name)
|
||||
end
|
||||
prefix = name
|
||||
pm_filename = joinpath(prefix, "pm.jld")
|
||||
Δ_coeff_filename = joinpath(prefix, "delta.jld")
|
||||
return pm_filename, Δ_coeff_filename
|
||||
function pmΔfilenames(prefix::String)
|
||||
isdir(prefix) || mkdir(prefix)
|
||||
pm_filename = joinpath(prefix, "pm.jld")
|
||||
Δ_coeff_filename = joinpath(prefix, "delta.jld")
|
||||
return pm_filename, Δ_coeff_filename
|
||||
end
|
||||
|
||||
function λSDPfilenames(name::String)
|
||||
if !isdir(name)
|
||||
mkdir(name)
|
||||
end
|
||||
prefix = name
|
||||
λ_filename = joinpath(prefix, "lambda.jld")
|
||||
SDP_filename = joinpath(prefix, "SDPmatrix.jld")
|
||||
return λ_filename, SDP_filename
|
||||
function λSDPfilenames(prefix::String)
|
||||
isdir(prefix) || mkdir(prefix)
|
||||
λ_filename = joinpath(prefix, "lambda.jld")
|
||||
SDP_filename = joinpath(prefix, "SDPmatrix.jld")
|
||||
return λ_filename, SDP_filename
|
||||
end
|
||||
|
||||
function ΔandSDPconstraints(name::String, G::Group)
|
||||
function ΔandSDPconstraints(prefix::String, G::Group)
|
||||
info(logger, "Loading precomputed pm, Δ, sdp_constraints...")
|
||||
pm_fname, Δ_fname = pmΔfilenames(name)
|
||||
pm_fname, Δ_fname = pmΔfilenames(prefix)
|
||||
|
||||
product_matrix = load(pm_fname, "pm")
|
||||
sdp_constraints = constraints_from_pm(product_matrix)
|
||||
sdp_constraints = constraints(product_matrix)
|
||||
|
||||
RG = GroupRing(G, product_matrix)
|
||||
Δ = GroupRingElem(load(Δ_fname, "Δ")[:, 1], RG)
|
||||
@ -73,46 +106,21 @@ function ΔandSDPconstraints{T<:GroupElem}(name::String, S::Vector{T}, Id::T; ra
|
||||
end
|
||||
|
||||
function ΔandSDPconstraints{T<:GroupElem}(S::Vector{T}, Id::T; radius::Int=2)
|
||||
B, sizes = Groups.generate_balls(S, Id, radius=2*radius)
|
||||
info(logger, "Generated balls of sizes $sizes")
|
||||
info(logger, "Generating balls of sizes $sizes")
|
||||
@logtime logger E_R, sizes = Groups.generate_balls(S, Id, radius=2*radius)
|
||||
|
||||
info(logger, "Creating product matrix...")
|
||||
t = @timed pm = GroupRings.create_pm(B, GroupRings.reverse_dict(B), sizes[radius]; twisted=true)
|
||||
info(logger, timed_msg(t))
|
||||
@logtime logger pm = GroupRings.create_pm(E_R, GroupRings.reverse_dict(E_R), sizes[radius]; twisted=true)
|
||||
|
||||
info(logger, "Creating sdp_constratints...")
|
||||
t = @timed sdp_constraints = PropertyT.constraints_from_pm(pm)
|
||||
info(logger, timed_msg(t))
|
||||
@logtime logger sdp_constraints = PropertyT.constraints(pm)
|
||||
|
||||
RG = GroupRing(parent(Id), B, pm)
|
||||
RG = GroupRing(parent(Id), E_R, pm)
|
||||
|
||||
Δ = splaplacian(RG, S, Id)
|
||||
Δ = splaplacian(RG, S)
|
||||
return Δ, sdp_constraints
|
||||
end
|
||||
|
||||
macro logtime(logger, ex)
|
||||
quote
|
||||
local stats = Base.gc_num()
|
||||
local elapsedtime = Base.time_ns()
|
||||
local val = $(esc(ex))
|
||||
elapsedtime = Base.time_ns() - elapsedtime
|
||||
local diff = Base.GC_Diff(Base.gc_num(), stats)
|
||||
local ts = time_string(elapsedtime, diff.allocd, diff.total_time,
|
||||
Base.gc_alloc_count(diff))
|
||||
esc(warn($(esc(logger)), ts))
|
||||
val
|
||||
end
|
||||
end
|
||||
|
||||
function timed_msg(t)
|
||||
elapsed = t[2]
|
||||
bytes_alloc = t[3]
|
||||
gc_time = t[4]
|
||||
gc_diff = t[5]
|
||||
|
||||
return "took: $elapsed s, allocated: $bytes_alloc bytes ($(gc_diff.poolalloc) allocations)."
|
||||
end
|
||||
|
||||
function λandP(name::String)
|
||||
λ_fname, SDP_fname = λSDPfilenames(name)
|
||||
f₁ = exists(λ_fname)
|
||||
@ -148,7 +156,7 @@ function λandP(name::String, SDP_problem::JuMP.Model, varλ, varP)
|
||||
save(λ_fname, "λ", λ)
|
||||
save(P_fname, "P", P)
|
||||
else
|
||||
throw(ErrorException("Solver $solver did not produce a valid solution!: λ = $λ"))
|
||||
throw(ErrorException("Solver did not produce a valid solution!: λ = $λ"))
|
||||
end
|
||||
return λ, P
|
||||
|
||||
@ -188,15 +196,10 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius)
|
||||
info(logger, "|R[G]|.pm = $(size(parent(Δ).pm))")
|
||||
|
||||
if all(exists.(λSDPfilenames(name)))
|
||||
# cached
|
||||
λ, P = λandP(name)
|
||||
else
|
||||
# compute
|
||||
info(logger, "Creating SDP problem...")
|
||||
|
||||
t = @timed SDP_problem, λ, P = create_SDP_problem(Δ, sdp_constraints, upper_bound=upper_bound)
|
||||
info(logger, timed_msg(t))
|
||||
|
||||
SDP_problem, λ, P = create_SDP_problem(Δ, sdp_constraints, upper_bound=upper_bound)
|
||||
JuMP.setsolver(SDP_problem, solver)
|
||||
|
||||
λ, P = λandP(name, SDP_problem, λ, P)
|
||||
@ -208,13 +211,16 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius)
|
||||
info(logger, "minimum(P) = $(minimum(P))")
|
||||
|
||||
if λ > 0
|
||||
pm_fname, Δ_fname = pmΔfilenames(name)
|
||||
RG = GroupRing(parent(first(S)), load(pm_fname, "pm"))
|
||||
Δ = GroupRingElem(load(Δ_fname, "Δ")[:, 1], RG)
|
||||
|
||||
isapprox(eigvals(P), abs(eigvals(P)), atol=tol) ||
|
||||
warn("The solution matrix doesn't seem to be positive definite!")
|
||||
# @assert P == Symmetric(P)
|
||||
Q = real(sqrtm(Symmetric(P)))
|
||||
@logtime logger Q = real(sqrtm(Symmetric(P)))
|
||||
|
||||
sgap = check_distance_to_positive_cone(Δ, λ, Q, 2*radius, tol=tol)
|
||||
sgap = distance_to_positive_cone(Δ, λ, Q, 2*radius)
|
||||
if isa(sgap, Interval)
|
||||
sgap = sgap.lo
|
||||
end
|
||||
|
||||
17
src/SDPs.jl
17
src/SDPs.jl
@ -1,30 +1,30 @@
|
||||
using JuMP
|
||||
import MathProgBase: AbstractMathProgSolver
|
||||
|
||||
function constraints_from_pm(pm, total_length=maximum(pm))
|
||||
function constraints(pm, total_length=maximum(pm))
|
||||
n = size(pm,1)
|
||||
constraints = [Array{Int,1}[] for x in 1:total_length]
|
||||
constraints = [Vector{Tuple{Int,Int}}() for _ in 1:total_length]
|
||||
for j in 1:n
|
||||
for i in 1:n
|
||||
idx = pm[i,j]
|
||||
push!(constraints[idx], [i,j])
|
||||
push!(constraints[idx], (i,j))
|
||||
end
|
||||
end
|
||||
return constraints
|
||||
end
|
||||
|
||||
function splaplacian{TT<:Group}(RG::GroupRing{TT}, S, Id=RG.group(), T::Type=Float64)
|
||||
function splaplacian(RG::GroupRing, S, T::Type=Float64)
|
||||
result = RG(T)
|
||||
result[Id] = T(length(S))
|
||||
result[RG.group()] = T(length(S))
|
||||
for s in S
|
||||
result[s] -= one(T)
|
||||
end
|
||||
return result
|
||||
end
|
||||
|
||||
function splaplacian{TT<:Ring}(RG::GroupRing{TT}, S, Id=one(RG.group), T::Type=Float64)
|
||||
function splaplacian{TT<:Ring}(RG::GroupRing{TT}, S, T::Type=Float64)
|
||||
result = RG(T)
|
||||
result[Id] = T(length(S))
|
||||
result[one(RG.group)] = T(length(S))
|
||||
for s in S
|
||||
result[s] -= one(T)
|
||||
end
|
||||
@ -61,8 +61,7 @@ function solve_SDP(SDP_problem)
|
||||
o = redirect_stdout(solver_logger.handlers["solver_log"].io)
|
||||
Base.Libc.flush_cstdio()
|
||||
|
||||
t = @timed solution_status = JuMP.solve(SDP_problem)
|
||||
info(logger, timed_msg(t))
|
||||
@logtime logger solution_status = JuMP.solve(SDP_problem)
|
||||
Base.Libc.flush_cstdio()
|
||||
|
||||
redirect_stdout(o)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user