kalmar/PropertyT.jl
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Abstract group-unspecific functions

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kalmar 2017-01-09 01:01:31 +01:00
parent 53dec056e0
commit 90ef2e2c8c
1 changed files with 65 additions and 5 deletions
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70
property(T).jl
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@ -11,6 +11,17 @@ function products{T<:Real}(S1::Array{Array{T,2},1}, S2::Array{Array{T,2},1})
return unique(result[2:end])
end
function generate_B₂_and_B₄(identity, S₁)
S₂ = products(S₁, S₁);
S₃ = products(S₁, S₂);
S₄ = products(S₂, S₂);
B₂ = unique(vcat([identity],S₁,S₂));
B₄ = unique(vcat(B₂, S₃, S₄));
@assert B₄[1:length(B₂)] == B₂
return B₂, B₄;
end
function read_GAP_raw_list(filename::String)
return eval(parse(String(read(filename))))
end
@ -71,10 +82,22 @@ function Laplacian(S::Array{Array{Float64,2},1},
return full(Laplacian_sparse(S,basis))
end
function create_SDP_problem(matrix_constraints,
Δ²::GroupAlgebraElement, Δ::GroupAlgebraElement)
function prepare_Laplacian_and_constraints{T}(S::Vector{Array{T,2}};)
identity = eye(S[1])
B₂, B₄ = generate_B₂_and_B₄(identity, S)
product_matrix, matrix_constraints = create_product_matrix(B₄,length(B₂));
L= Laplacian(S, B₄);
const Δ = GroupAlgebraElement(L, product_matrix)
return Δ, matrix_constraints
end
function create_SDP_problem(matrix_constraints, Δ::GroupAlgebraElement)
N = size(Δ.product_matrix,1)
@assert length(Δ) == length(Δ²)
const Δ² = Δ*Δ
@assert length(Δ) == length(matrix_constraints)
m = Model();
@variable(m, A[1:N, 1:N], SDP)
@ -88,7 +111,35 @@ function create_SDP_problem(matrix_constraints,
return m
end
function resulting_SOS{T<:Number}(sqrt_matrix::Array{T,2}, elt::GroupAlgebraElement{T})
function solve_for_property_T{T}(S₁::Vector{Array{T,2}}, solver; verbose=true)
Δ, matrix_constraints = prepare_Laplacian_and_constraints(S₁)
problem = create_SDP_problem(matrix_constraints, Δ);
@show solver
setsolver(problem, solver);
verbose && @show problem
solution_status = solve(problem);
verbose && @show solution_status
if solution_status != :Optimal
throw(ExceptionError("The solver did not solve the problem successfully!"))
else
κ = SL_3ZZ.objVal;
A = getvalue(getvariable(SL_3ZZ, :A));;
end
return κ, A
end
function EOI{T<:Number}(Δ::GroupAlgebraElement{T}, κ::T)
return Δ*Δ - κ*Δ
end
function resulting_SOS{T<:Number}(sqrt_matrix::Array{T,2},
elt::GroupAlgebraElement{T})
result = zeros(elt.coefficients)
zzz = zeros(elt.coefficients)
L = size(sqrt_matrix,2)
@ -106,10 +157,19 @@ function correct_to_augmentation_ideal{T<:Rational}(sqrt_matrix::Array{T,2})
for i in 1:l
col = view(sqrt_matrix,:,i)
sqrt_corrected[:,i] = col - sum(col)//l
# @assert sum(sqrt_corrected[:,i]) == 0
# @assert sum(sqrt_corrected[:,i]) == 0
end
return sqrt_corrected
end
function check_solution{T<:Number}(κ::T,
sqrt_matrix::Array{T,2},
Δ::GroupAlgebraElement{T})
eoi = EOI(Δ, κ)
result = resulting_SOS(sqrt_matrix, Δ)
return sum(abs.((result - eoi).coefficients)), sum(result.coefficients)
end
function rationalize{T<:Integer, S<:Real}(::Type{T},
X::AbstractArray{S}; tol::Real=eps(eltype(X)))