88 lines
2.5 KiB
Julia
88 lines
2.5 KiB
Julia
using JuMP
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import MathProgBase: AbstractMathProgSolver
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function create_product_matrix(basis, limit)
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product_matrix = zeros(Int, (limit,limit))
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basis_dict = Dict{Array, Int}(x => i
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for (i,x) in enumerate(basis))
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for i in 1:limit
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x_inv::eltype(basis) = inv(basis[i])
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for j in 1:limit
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w = x_inv*basis[j]
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product_matrix[i,j] = basis_dict[w]
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# index = findfirst(basis, w)
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# index ≠ 0 || throw(ArgumentError("Product is not supported on basis: $w"))
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# product_matrix[i,j] = index
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end
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end
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return product_matrix
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end
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function constraints_from_pm(pm, total_length)
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n = size(pm,1)
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constraints = constraints = [Array{Int,1}[] for x in 1:total_length]
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for j in 1:n
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Threads.@threads 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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constraints_from_pm(pm) = constraints_from_pm(pm, maximum(pm))
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function splaplacian_coeff(S, basis, n=length(basis))
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result = spzeros(n)
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result[1] = float(length(S))
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for s in S
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ind = findfirst(basis, s)
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result[ind] += -1.0
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end
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return result
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end
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function laplacian_coeff(S, basis)
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return full(splaplacian_coeff(S,basis))
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end
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function create_SDP_problem(matrix_constraints, Δ::GroupAlgebraElement; upper_bound=Inf)
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N = size(Δ.product_matrix,1)
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const Δ² = Δ*Δ
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@assert length(Δ) == length(matrix_constraints)
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m = JuMP.Model();
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JuMP.@variable(m, A[1:N, 1:N], SDP)
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JuMP.@SDconstraint(m, A >= 0)
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JuMP.@constraint(m, sum(A[i] for i in eachindex(A)) == 0)
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JuMP.@variable(m, κ >= 0.0)
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if upper_bound < Inf
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JuMP.@constraint(m, κ <= upper_bound)
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end
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JuMP.@objective(m, Max, κ)
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for (pairs, δ², δ) in zip(matrix_constraints, Δ².coefficients, Δ.coefficients)
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JuMP.@constraint(m, sum(A[i,j] for (i,j) in pairs) == δ² - κ*δ)
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end
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return m
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end
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function solve_SDP(SDP_problem, solver)
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@show SDP_problem
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@show solver
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JuMP.setsolver(SDP_problem, solver);
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# @time MathProgBase.writeproblem(SDP_problem, "/tmp/SDP_problem")
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solution_status = JuMP.solve(SDP_problem);
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if solution_status != :Optimal
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warn("The solver did not solve the problem successfully!")
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end
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@show solution_status
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κ = JuMP.getvalue(JuMP.getvariable(SDP_problem, :κ))
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A = JuMP.getvalue(JuMP.getvariable(SDP_problem, :A))
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return κ, A
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end
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