use @info, @warn without ()
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@ -84,13 +84,13 @@ end
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function computeλandP(sett::Naive, Δ::GroupRingElem;
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solverlog=tempname()*".log")
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@info("Creating SDP problem...")
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@info "Creating SDP problem..."
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SDP_problem = SOS_problem(Δ^2, Δ, upper_bound=sett.upper_bound)
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@info(Base.repr(SDP_problem))
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ws = warmstart(sett)
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@time status, ws = PropertyT.solve(solverlog, SDP_problem, sett.solver, ws)
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@info("Solver's status: $status")
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@info "Optimization has finished:" status
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P = value.(SDP_problem[:P])
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λ = value(SDP_problem[:λ])
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@ -112,14 +112,13 @@ function computeλandP(sett::Symmetrized, Δ::GroupRingElem;
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orbit_data = load(filename(sett, :OrbitData), "OrbitData")
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orbit_data = decimate(orbit_data)
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@info("Creating SDP problem...")
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@info "Creating SDP problem..."
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SDP_problem, varP = SOS_problem(Δ^2, Δ, orbit_data, upper_bound=sett.upper_bound)
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@info(Base.repr(SDP_problem))
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ws = warmstart(sett)
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@time status, ws = PropertyT.solve(solverlog, SDP_problem, sett.solver, ws)
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@info("Solver's status: $status")
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@info "Optimization has finished:" status
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λ = value(SDP_problem[:λ])
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Ps = [value.(P) for P in varP]
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@ -127,7 +126,7 @@ function computeλandP(sett::Symmetrized, Δ::GroupRingElem;
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save(filename(sett, :warmstart),
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"warmstart", (ws.primal, ws.dual, ws.slack), "Ps", Ps, "λ", λ)
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@info("Reconstructing P...")
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@info "Reconstructing P..."
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@time P = reconstruct(Ps, orbit_data)
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return λ, P
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@ -141,10 +140,7 @@ end
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function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
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separator = "-"^76
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info_strs = [separator,
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"Checking in floating-point arithmetic...",
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"λ = $λ"]
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@info(join(info_strs, "\n"))
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@info "$separator\nChecking in floating-point arithmetic..." λ
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eoi = Δ^2-λ*Δ
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@info("Computing sum of squares decomposition...")
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@ -153,12 +149,11 @@ function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
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L1_norm = norm(residual,1)
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distance = λ - 2.0^(2ceil(log2(R)))*L1_norm
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info_strs = ["Numerical metrics:",
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"ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(@sprintf("%.10f", aug(residual)))",
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"‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(@sprintf("%.10f", L1_norm))",
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"Floating point distance (to positive cone) ≈",
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"$(@sprintf("%.10f", distance))"]
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@info(join(info_strs, "\n"))
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info_strs = ["Numerical metrics of the obtained SOS:",
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"ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ≈ $(aug(residual))",
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"‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ≈ $(L1_norm)",
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"Floating point distance (to positive cone) ≈"]
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@info join(info_strs, "\n") distance
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if distance ≤ 0
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return distance
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@ -173,9 +168,8 @@ function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
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@info("Projecting columns of Q to the augmentation ideal...")
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@time Q, check = augIdproj(Interval, Q)
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info_strs = ["Checking that sum of every column contains 0.0...",
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(check ? "DONE!" : "FAILED!")]
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@info(join(info_strs, "\n"))
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result = (check ? "Correct." : "FAILED!")
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@info "Checking that sum of every column contains 0.0..." result
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check || @warn("The following numbers are meaningless!")
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@info("Computing sum of squares decomposition...")
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@ -184,13 +178,11 @@ function distance_to_positive_cone(Δ::GroupRingElem, λ, Q; R::Int=2)
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L1_norm = norm(residual,1)
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distance = λ - 2.0^(2ceil(log2(R)))*L1_norm
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info_strs = ["Numerical metrics:",
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info_strs = ["Numerical metrics of the obtained SOS:",
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"ɛ(Δ² - λΔ - ∑ξᵢ*ξᵢ) ∈ $(aug(residual))",
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"‖Δ² - λΔ - ∑ξᵢ*ξᵢ‖₁ ∈ $(L1_norm)",
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"Interval distance (to positive cone) ∈",
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"$(distance)",
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separator]
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@info(join(info_strs, "\n"))
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"Interval distance (to positive cone) ∈"]
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@info join(info_strs, "\n") distance
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return distance.lo
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end
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@ -220,21 +212,21 @@ function print_summary(sett::Settings)
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"Solvers options: "]
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append!(info_strs, [rpad(" $k", 30)* "→ \t$v" for (k,v) in sett.solver().options])
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push!(info_strs, separator)
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@info(join(info_strs, "\n"))
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@info join(info_strs, "\n")
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end
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function interpret_results(sett::Settings, sgap::Number)
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if sgap > 0
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Kazhdan_κ = Kazhdan(sgap, length(sett.S))
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if Kazhdan_κ > 0
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@info("κ($(sett.name), S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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@info "κ($(sett.name), S) ≥ $Kazhdan_κ: Group HAS property (T)!"
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return true
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end
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end
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info_strs = ["The certified lower bound on the spectral gap is negative:",
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"λ($(sett.name), S) ≥ 0.0 > $sgap",
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"This tells us nothing about property (T)"]
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@info(join(info_strs, "\n"))
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@info join(info_strs, "\n")
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return false
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end
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@ -242,11 +234,9 @@ function spectral_gap(sett::Settings)
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fp = PropertyT.fullpath(sett)
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isdir(fp) || mkpath(fp)
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if isfile(filename(sett,:Δ))
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# cached
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@info("Loading precomputed Δ...")
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@info "Loading precomputed Δ..."
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Δ = loadGRElem(filename(sett,:Δ), sett.G)
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else
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# compute
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@ -263,20 +253,20 @@ function spectral_gap(sett::Settings)
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save(filename(sett, :solution), "λ", λ, "P", P)
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if λ < 0
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@warn("Solver did not produce a valid solution!")
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@warn "Solver did not produce a valid solution!"
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end
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end
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info_strs = ["λ = $λ",
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info_strs = ["Numerical metrics of matrix solution:",
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"sum(P) = $(sum(P))",
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"maximum(P) = $(maximum(P))",
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"minimum(P) = $(minimum(P))"]
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@info(join(info_strs, "\n"))
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@info join(info_strs, "\n")
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isapprox(eigvals(P), abs.(eigvals(P))) ||
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@warn("The solution matrix doesn't seem to be positive definite!")
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@warn "The solution matrix doesn't seem to be positive definite!"
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@time Q = real(sqrt( (P.+ P')./2 ))
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@time Q = real(sqrt(Symmetric( (P.+ P')./2 )))
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certified_sgap = distance_to_positive_cone(Δ, λ, Q, R=sett.radius)
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return certified_sgap
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@ -33,11 +33,11 @@ function Laplacian(S::Vector{E}, radius) where E<:AbstractAlgebra.GroupElem
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end
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function Laplacian(S, Id, radius)
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@info("Generating metric ball of radius $(2radius)...")
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@info "Generating metric ball of radius" radius=2radius
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@time E_R, sizes = Groups.generate_balls(S, Id, radius=2radius)
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@info("Generated balls of sizes $sizes.")
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@info "Generated balls:" sizes
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@info("Creating product matrix...")
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@info "Creating product matrix..."
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rdict = GroupRings.reverse_dict(E_R)
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@time pm = GroupRings.create_pm(E_R, rdict, sizes[radius]; twisted=true)
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@ -12,19 +12,19 @@ struct OrbitData{T<:AbstractArray{Float64, 2}, GEl<:GroupElem, P<:perm}
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end
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function OrbitData(RG::GroupRing, autS::Group, verbose=true)
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verbose && @info("Decomposing basis of RG into orbits of $(autS)")
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verbose && @info "Decomposing basis of RG into orbits of" autS
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@time orbs = orbit_decomposition(autS, RG.basis, RG.basis_dict)
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@assert sum(length(o) for o in orbs) == length(RG.basis)
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verbose && @info("The action has $(length(orbs)) orbits")
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verbose && @info "The action has $(length(orbs)) orbits"
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verbose && @info("Finding projections in the Group Ring of $(autS)")
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verbose && @info "Finding projections in the Group Ring of" autS
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@time autS_mps = Projections.rankOne_projections(GroupRing(autS, collect(autS)))
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verbose && @info("Finding AutS-action matrix representation")
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verbose && @info "Finding AutS-action matrix representation"
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@time preps = perm_reps(autS, RG.basis[1:size(RG.pm,1)], RG.basis_dict)
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@time mreps = matrix_reps(preps)
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verbose && @info("Computing the projection matrices Uπs")
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verbose && @info "Computing the projection matrices Uπs"
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@time Uπs = [orthSVD(matrix_repr(p, mreps)) for p in autS_mps]
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multiplicities = size.(Uπs,2)
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@ -34,7 +34,7 @@ function OrbitData(RG::GroupRing, autS::Group, verbose=true)
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lpad("multiplicities", 14) * " =" * join(lpad.(multiplicities, 4), ""),
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lpad("dimensions", 14) * " =" * join(lpad.(dimensions, 4), "")
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]
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@info(join(info_strs, "\n"))
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@info join(info_strs, "\n")
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end
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@assert dot(multiplicities, dimensions) == size(RG.pm,1)
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@ -90,7 +90,7 @@ function SOS_problem(X::GroupRingElem, orderunit::GroupRingElem, data::OrbitData
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λ = JuMP.@variable(m, λ)
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end
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@info("Adding $(length(data.orbits)) constraints... ")
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@info "Adding $(length(data.orbits)) constraints..."
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@time addconstraints!(m, Ps, X, orderunit, data)
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JuMP.@objective(m, Max, λ)
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