76 lines
1.9 KiB
Julia
76 lines
1.9 KiB
Julia
using JuMP
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import MathProgBase: AbstractMathProgSolver
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function constraints(pm, total_length=maximum(pm))
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n = size(pm,1)
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constraints = [Vector{Tuple{Int,Int}}() for _ in 1:total_length]
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for j in 1:n
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for i in 1:n
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idx = pm[i,j]
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push!(constraints[idx], (i,j))
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end
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end
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return constraints
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end
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function splaplacian(RG::GroupRing, S, T::Type=Float64)
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result = RG(T)
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result[RG.group()] = T(length(S))
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for s in S
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result[s] -= one(T)
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end
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return result
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end
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function splaplacian{TT<:Ring}(RG::GroupRing{TT}, S, T::Type=Float64)
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result = RG(T)
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result[one(RG.group)] = T(length(S))
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for s in S
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result[s] -= one(T)
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end
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return result
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end
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function create_SDP_problem(Δ::GroupRingElem, matrix_constraints; upper_bound=Inf)
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N = size(parent(Δ).pm, 1)
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Δ² = Δ*Δ
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@assert length(Δ.coeffs) == length(matrix_constraints)
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m = JuMP.Model();
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JuMP.@variable(m, P[1:N, 1:N])
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JuMP.@SDconstraint(m, P >= 0)
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JuMP.@constraint(m, sum(P[i] for i in eachindex(P)) == 0)
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if upper_bound < Inf
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JuMP.@variable(m, 0.0 <= λ <= upper_bound)
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else
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JuMP.@variable(m, λ >= 0)
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end
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for (pairs, δ², δ) in zip(matrix_constraints, Δ².coeffs, Δ.coeffs)
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JuMP.@constraint(m, sum(P[i,j] for (i,j) in pairs) == δ² - λ*δ)
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end
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JuMP.@objective(m, Max, λ)
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return m, λ, P
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end
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function solve_SDP(SDP_problem)
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info(logger, Base.repr(SDP_problem))
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o = redirect_stdout(solver_logger.handlers["solver_log"].io)
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Base.Libc.flush_cstdio()
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@logtime logger solution_status = MathProgBase.optimize!(SDP_problem.internalModel)
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Base.Libc.flush_cstdio()
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redirect_stdout(o)
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if solution_status != :Optimal
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warn(logger, "The solver did not solve the problem successfully!")
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end
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info(logger, solution_status)
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return 0
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end
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