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docs/src/tutorials/Noncommutative and Hermitian/chsh.jl
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,116 @@ | ||
| import QuantumStuff: trace_monoid, Monoids | ||
| using StarAlgebras | ||
|
|
||
| M, A, C = trace_monoid(2, 2, A=:A, C=:C) | ||
|
|
||
| RM = let M = M, A = A, C = C, level = 4 | ||
| A_l, sizesA = Monoids.wlmetric_ball(A, radius=level) | ||
| C_l, sizesC = Monoids.wlmetric_ball(C, radius=level) | ||
|
|
||
| # starAlg(M, 1, half = unique!([a*c for a in A_l for c in C_l])) | ||
|
|
||
| @time words, sizes = Monoids.wlmetric_ball( | ||
| unique!([a * c for a in A_l for c in C_l]); | ||
| radius=2, | ||
| ) | ||
| @info "Sizes of generated balls:" (A, C, combined) = (sizesA, sizesC, sizes) | ||
|
|
||
| b = @time StarAlgebras.FixedBasis(words, StarAlgebras.DiracMStructure(*), (UInt32(sizes[1]), UInt32(sizes[1]))) | ||
| StarAlgebra(M, b) | ||
| end | ||
|
|
||
| A = RM.(A) | ||
| C = RM.(C) | ||
| chsh = A[1] * C[1] + A[1] * C[2] + A[2] * C[1] - A[2] * C[2] | ||
|
|
||
| import StarAlgebras as SA | ||
| struct Full{B} <: SA.ImplicitBasis{B,B} end | ||
| Base.getindex(::Full{B}, b::B) where {B} = b | ||
| import MultivariateBases as MB | ||
| MB.implicit_basis(::SA.FixedBasis{B}) where {B} = Full{B}() | ||
| MB.algebra(b::Full{B}) where {B} = SA.StarAlgebra(M, b) | ||
| SA.mstructure(::Full) = SA.DiracMStructure(*) | ||
|
|
||
| b = basis(chsh) | ||
| import StarAlgebras as SA | ||
| f = SA.AlgebraElement( | ||
| SA.SparseCoefficients( | ||
| [b[k] for (k, _) in SA.nonzero_pairs(coeffs(chsh))], | ||
| [v for (_, v) in SA.nonzero_pairs(coeffs(chsh))], | ||
| ), | ||
| SA.StarAlgebra( | ||
| parent(chsh).object, | ||
| Full{eltype(b)}() | ||
| ), | ||
| ) | ||
| n = size(b.table, 1) | ||
| gram_basis = @time StarAlgebras.FixedBasis(b.elts[1:n], StarAlgebras.DiracMStructure(*)); | ||
| one(f) | ||
| SA.coeffs(f, b) | ||
| using SumOfSquares | ||
| function SumOfSquares._term_element(a, mono::Monoids.MonoidElement) | ||
| SA.AlgebraElement( | ||
| SA.SparseCoefficients((mono,), (a,)), | ||
| MB.algebra(Full{typeof(mono)}()), | ||
| ) | ||
| end | ||
|
|
||
| cone = SumOfSquares.WeightedSOSCone{MOI.PositiveSemidefiniteConeTriangle}( | ||
| b, | ||
| [gram_basis], | ||
| [one(f)], | ||
| ) | ||
| import SCS | ||
| scs = optimizer_with_attributes( | ||
| SCS.Optimizer, | ||
| "eps_abs" => 1e-9, | ||
| "eps_rel" => 1e-9, | ||
| "max_iters" => 1000, | ||
| ) | ||
|
|
||
| import Dualization | ||
| #model = Model(Dualization.dual_optimizer(scs)) | ||
| model = Model(scs) | ||
| SumOfSquares.Bridges.add_all_bridges(backend(model).optimizer, Float64) | ||
| MOI.Bridges.remove_bridge(backend(model).optimizer, SumOfSquares.Bridges.Constraint.ImageBridge{Float64}) | ||
| @variable(model, λ) | ||
| @objective(model, Min, λ) | ||
| @constraint(model, SA.coeffs(λ * one(f) - f, b) in cone); | ||
| optimize!(model) | ||
| solution_summary(model) | ||
| objective_value(model) ≈ 2√2 | ||
| function _add!(f, psd, model, F, S) | ||
| append!(psd, [ | ||
| f(MOI.get(model, MOI.ConstraintSet(), ci)) | ||
| for ci in MOI.get(model, MOI.ListOfConstraintIndices{F,S}()) | ||
| ], | ||
| ) | ||
| end | ||
| function summary(model) | ||
| free = MOI.get(model, MOI.NumberOfVariables()) | ||
| psd = Int[] | ||
| F = MOI.VectorOfVariables | ||
| S = MOI.PositiveSemidefiniteConeTriangle | ||
| _add!(MOI.side_dimension, psd, model, F, S) | ||
| S = SCS.ScaledPSDCone | ||
| _add!(MOI.side_dimension, psd, model, F, S) | ||
| free -= sum(psd, init = 0) do d | ||
| div(d * (d + 1), 2) | ||
| end | ||
| F = MOI.VectorAffineFunction{Float64} | ||
| S = MOI.PositiveSemidefiniteConeTriangle | ||
| _add!(MOI.side_dimension, psd, model, F, S) | ||
| S = SCS.ScaledPSDCone | ||
| _add!(MOI.side_dimension, psd, model, F, S) | ||
| eq = Int[] | ||
| F = MOI.VectorAffineFunction{Float64} | ||
| S = MOI.Zeros | ||
| _add!(MOI.dimension, eq, model, F, S) | ||
| F = MOI.ScalarAffineFunction{Float64} | ||
| S = MOI.EqualTo{Float64} | ||
| _add!(MOI.dimension, eq, model, F, S) | ||
| return free, psd, sum(eq, init = 0) | ||
| end | ||
| summary(backend(model).optimizer.model) | ||
| summary(backend(model).optimizer.model.optimizer.dual_problem.dual_model.model) | ||
| print_active_bridges(model) |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,178 @@ | ||
| struct LagrangeBridge{T,M} <: MOI.Bridges.Variable.AbstractBridge | ||
| affine::Vector{MOI.ScalarAffineFunction{T}} | ||
| variables::Vector{Vector{MOI.VariableIndex}} | ||
| constraints::Vector{MOI.ConstraintIndex{MOI.VectorOfVariables}} | ||
| set::SOS.WeightedSOSCone{M} | ||
| end | ||
|
|
||
| function MOI.Bridges.Variable.bridge_constrained_variable( | ||
| ::Type{KernelBridge{T,M}}, | ||
| model::MOI.ModelLike, | ||
| set::SOS.WeightedSOSCone{M}, | ||
| ) where {T,M} | ||
| variables = Vector{MOI.VariableIndex}[] | ||
| constraints = MOI.ConstraintIndex{MOI.VectorOfVariables}[] | ||
| acc = zero( | ||
| MOI.ScalarAffineFunction{T}, | ||
| MB.algebra(MB.implicit_basis(set.basis)), | ||
| ) | ||
| for (gram_basis, weight) in zip(set.gram_bases, set.weights) | ||
| gram, vars, con = SOS.add_gram_matrix(model, M, gram_basis, T) | ||
| push!(variables, vars) | ||
| push!(constraints, con) | ||
| MA.operate!(SA.UnsafeAddMul(*), acc, gram, weight) | ||
| end | ||
| MA.operate!(SA.canonical, SA.coeffs(acc)) | ||
| return KernelBridge{T,M}( | ||
| SA.coeffs(acc, set.basis), | ||
| variables, | ||
| constraints, | ||
| set, | ||
| ) | ||
| end | ||
|
|
||
| function MOI.Bridges.Variable.supports_constrained_variable( | ||
| ::Type{<:KernelBridge}, | ||
| ::Type{<:SOS.WeightedSOSCone}, | ||
| ) | ||
| return true | ||
| end | ||
|
|
||
| function MOI.Bridges.added_constrained_variable_types( | ||
| ::Type{KernelBridge{T,M}}, | ||
| ) where {T,M} | ||
| return SOS.Bridges.Constraint.constrained_variable_types(M) | ||
| end | ||
|
|
||
| function MOI.Bridges.added_constraint_types(::Type{<:KernelBridge}) | ||
| return Tuple{Type,Type}[] | ||
| end | ||
|
|
||
| function MOI.Bridges.Variable.concrete_bridge_type( | ||
| ::Type{<:KernelBridge{T}}, | ||
| ::Type{<:SOS.WeightedSOSCone{M}}, | ||
| ) where {T,M} | ||
| return KernelBridge{T,M} | ||
| end | ||
|
|
||
| # Attributes, Bridge acting as a model | ||
| function MOI.get(bridge::KernelBridge, ::MOI.NumberOfVariables) | ||
| return sum(length, bridge.variables) | ||
| end | ||
|
|
||
| function MOI.get(bridge::KernelBridge, ::MOI.ListOfVariableIndices) | ||
| return reduce(vcat, bridge.variables) | ||
| end | ||
|
|
||
| function MOI.get( | ||
| bridge::KernelBridge, | ||
| ::MOI.NumberOfConstraints{MOI.VectorOfVariables,S}, | ||
| ) where {S<:MOI.AbstractVectorSet} | ||
| return count(bridge.constraints) do ci | ||
| return ci isa MOI.ConstraintIndex{MOI.VectorOfVariables,S} | ||
| end | ||
| end | ||
|
|
||
| function MOI.get( | ||
| bridge::KernelBridge, | ||
| ::MOI.ListOfConstraintIndices{MOI.VectorOfVariables,S}, | ||
| ) where {S} | ||
| return [ | ||
| ci for ci in bridge.constraints if | ||
| ci isa MOI.ConstraintIndex{MOI.VectorOfVariables,S} | ||
| ] | ||
| end | ||
|
|
||
| # Indices | ||
| function MOI.delete(model::MOI.ModelLike, bridge::KernelBridge) | ||
| for vars in bridge.variables | ||
| MOI.delete(model, vars) | ||
| end | ||
| return | ||
| end | ||
|
|
||
| # Attributes, Bridge acting as a constraint | ||
|
|
||
| function MOI.get(::MOI.ModelLike, ::MOI.ConstraintSet, bridge::KernelBridge) | ||
| return bridge.set | ||
| end | ||
|
|
||
| function MOI.get( | ||
| model::MOI.ModelLike, | ||
| attr::MOI.ConstraintPrimal, | ||
| bridge::KernelBridge, | ||
| ) | ||
| return [ | ||
| MOI.get( | ||
| model, | ||
| MOI.VariablePrimal(attr.result_index), | ||
| bridge, | ||
| MOI.Bridges.IndexInVector(i), | ||
| ) for i in eachindex(bridge.affine) | ||
| ] | ||
| end | ||
|
|
||
| function MOI.get( | ||
| model::MOI.ModelLike, | ||
| attr::MOI.VariablePrimal, | ||
| bridge::KernelBridge, | ||
| i::MOI.Bridges.IndexInVector, | ||
| ) | ||
| return MOI.Utilities.eval_variables(bridge.affine[i.value]) do vi | ||
| return MOI.get(model, MOI.VariablePrimal(attr.result_index), vi) | ||
| end | ||
| end | ||
|
|
||
| function MOI.get( | ||
| model::MOI.ModelLike, | ||
| attr::SOS.GramMatrixAttribute, | ||
| bridge::KernelBridge{T,M}, | ||
| ) where {T,M} | ||
| SOS.check_multiplier_index_bounds(attr, eachindex(bridge.constraints)) | ||
| return SOS.build_gram_matrix( | ||
| convert( | ||
| Vector{T}, | ||
| MOI.get( | ||
| model, | ||
| MOI.VariablePrimal(attr.result_index), | ||
| bridge.variables[attr.multiplier_index], | ||
| ), | ||
| ), | ||
| bridge.set.gram_bases[attr.multiplier_index], | ||
| M, | ||
| T, | ||
| ) | ||
| end | ||
|
|
||
| function MOI.get( | ||
| model::MOI.ModelLike, | ||
| attr::SOS.MomentMatrixAttribute, | ||
| bridge::KernelBridge{T,M}, | ||
| ) where {T,M} | ||
| SOS.check_multiplier_index_bounds(attr, eachindex(bridge.constraints)) | ||
| return SOS.build_moment_matrix( | ||
| convert( | ||
| Vector{T}, | ||
| MOI.get( | ||
| model, | ||
| MOI.ConstraintDual(attr.result_index), | ||
| bridge.constraints[attr.multiplier_index], | ||
| ), | ||
| ), | ||
| bridge.set.gram_bases[attr.multiplier_index], | ||
| ) | ||
| end | ||
|
|
||
| function MOI.Bridges.bridged_function( | ||
| bridge::KernelBridge, | ||
| i::MOI.Bridges.IndexInVector, | ||
| ) | ||
| return bridge.affine[i.value] | ||
| end | ||
|
|
||
| function MOI.Bridges.Variable.unbridged_map( | ||
| ::KernelBridge{T}, | ||
| ::Vector{MOI.VariableIndex}, | ||
| ) where {T} | ||
| return nothing | ||
| end |