mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-19 07:20:28 +01:00
make augmented compute_sos fast
This commit is contained in:
parent
65286e09d2
commit
227e82d551
@ -5,80 +5,50 @@ function augment_columns!(Q::AbstractMatrix)
|
||||
return Q
|
||||
end
|
||||
|
||||
function _fma_SOS_thr!(
|
||||
result::AbstractVector{T},
|
||||
mstructure::AbstractMatrix{<:Integer},
|
||||
Q::AbstractMatrix{T},
|
||||
acc_matrix=zeros(T, size(mstructure)...),
|
||||
) where {T}
|
||||
function __sos_via_sqr!(
|
||||
res::StarAlgebras.AlgebraElement,
|
||||
P::AbstractMatrix;
|
||||
augmented::Bool
|
||||
)
|
||||
StarAlgebras.zero!(res)
|
||||
A = parent(res)
|
||||
b = basis(A)
|
||||
@assert size(A.mstructure) == size(P)
|
||||
e = b[one(b[1])]
|
||||
|
||||
s1, s2 = size(mstructure)
|
||||
|
||||
@inbounds for k = 1:s2
|
||||
let k = k, s1 = s1, s2 = s2, Q = Q, acc_matrix = acc_matrix
|
||||
Threads.@threads for j = 1:s2
|
||||
for i = 1:s1
|
||||
@inbounds acc_matrix[i, j] =
|
||||
muladd(Q[i, k], Q[j, k], acc_matrix[i, j])
|
||||
end
|
||||
for i in axes(A.mstructure, 1)
|
||||
x = StarAlgebras._istwisted(A.mstructure) ? StarAlgebras.star(b[i]) : b[i]
|
||||
for j in axes(A.mstructure, 2)
|
||||
p = P[i, j]
|
||||
xy = b[A.mstructure[i, j]]
|
||||
# either result += P[x,y]*(x*y)
|
||||
res[xy] += p
|
||||
if augmented
|
||||
# or result += P[x,y]*(1-x)*(1-y) == P[x,y]*(2-x-y+xy)
|
||||
y = b[j]
|
||||
res[e] += p
|
||||
res[x] -= p
|
||||
res[y] -= p
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
@inbounds for j = 1:s2
|
||||
for i = 1:s1
|
||||
result[mstructure[i, j]] += acc_matrix[i, j]
|
||||
end
|
||||
end
|
||||
|
||||
return result
|
||||
return res
|
||||
end
|
||||
|
||||
function _cnstr_sos!(res::StarAlgebras.AlgebraElement, Q::AbstractMatrix, cnstrs)
|
||||
function __sos_via_cnstr!(res::StarAlgebras.AlgebraElement, Q²::AbstractMatrix, cnstrs)
|
||||
StarAlgebras.zero!(res)
|
||||
Q² = Q' * Q
|
||||
for (g, A_g) in cnstrs
|
||||
res[g] = dot(A_g, Q²)
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
function _augmented_sos!(res::StarAlgebras.AlgebraElement, Q::AbstractMatrix)
|
||||
A = parent(res)
|
||||
StarAlgebras.zero!(res)
|
||||
Q² = Q' * Q
|
||||
|
||||
N = LinearAlgebra.checksquare(A.mstructure)
|
||||
augmented_basis = [A(1) - A(b) for b in @view basis(A)[1:N]]
|
||||
tmp = zero(res)
|
||||
|
||||
for (j, y) in enumerate(augmented_basis)
|
||||
for (i, x) in enumerate(augmented_basis)
|
||||
# res += Q²[i, j] * x * y
|
||||
|
||||
StarAlgebras.mul!(tmp, x, y)
|
||||
StarAlgebras.mul!(tmp, tmp, Q²[i, j])
|
||||
StarAlgebras.add!(res, res, tmp)
|
||||
end
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
function compute_sos(A::StarAlgebras.StarAlgebra, Q::AbstractMatrix; augmented::Bool)
|
||||
if augmented
|
||||
z = zeros(eltype(Q), length(basis(A)))
|
||||
res = StarAlgebras.AlgebraElement(z, A)
|
||||
return _augmented_sos!(res, Q)
|
||||
cnstrs = constraints(basis(A), A.mstructure; augmented=true)
|
||||
return _cnstr_sos!(res, Q, cnstrs)
|
||||
else
|
||||
@assert size(A.mstructure) == size(Q)
|
||||
z = zeros(eltype(Q), length(basis(A)))
|
||||
|
||||
_fma_SOS_thr!(z, A.mstructure, Q)
|
||||
|
||||
return StarAlgebras.AlgebraElement(z, A)
|
||||
end
|
||||
Q² = Q' * Q
|
||||
res = StarAlgebras.AlgebraElement(zeros(eltype(Q²), length(basis(A))), A)
|
||||
res = __sos_via_sqr!(res, Q², augmented=augmented)
|
||||
return res
|
||||
end
|
||||
|
||||
function sufficient_λ(residual::StarAlgebras.AlgebraElement, λ; halfradius)
|
||||
@ -159,7 +129,7 @@ function certify_solution(
|
||||
true, compute_sos(parent(elt), Q_int, augmented=augmented)
|
||||
end
|
||||
|
||||
@info "Checking in $(eltype(sos_int)) arithmetic with" λ
|
||||
@info "Checking in $(eltype(sos_int)) arithmetic with" λ_int
|
||||
|
||||
λ_certified =
|
||||
sufficient_λ(elt, orderunit, λ_int, sos_int, halfradius=halfradius)
|
||||
|
||||
@ -6,37 +6,20 @@ function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimize
|
||||
@time status, _ = PropertyT.solve(sos_problem, optimizer)
|
||||
|
||||
Q = let Ps = Ps
|
||||
flPs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
|
||||
PropertyT.reconstruct(flPs, wd)
|
||||
Qs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
|
||||
PropertyT.reconstruct(Qs, wd)
|
||||
end
|
||||
|
||||
λ = JuMP.value(sos_problem[:λ])
|
||||
|
||||
sos = let RG = parent(elt), Q = Q
|
||||
z = zeros(eltype(Q), length(basis(RG)))
|
||||
res = AlgebraElement(z, RG)
|
||||
cnstrs = PropertyT.constraints(basis(RG), RG.mstructure, augmented=true)
|
||||
PropertyT._cnstr_sos!(res, Q, cnstrs)
|
||||
end
|
||||
|
||||
residual = elt - λ * unit - sos
|
||||
λ_fl = PropertyT.sufficient_λ(residual, λ, halfradius=2)
|
||||
|
||||
λ_fl < 0 && return status, false, λ_fl
|
||||
|
||||
sos = let RG = parent(elt), Q = [PropertyT.IntervalArithmetic.@interval(q) for q in Q]
|
||||
z = zeros(eltype(Q), length(basis(RG)))
|
||||
res = AlgebraElement(z, RG)
|
||||
cnstrs = PropertyT.constraints(basis(RG), RG.mstructure, augmented=true)
|
||||
PropertyT._cnstr_sos!(res, Q, cnstrs)
|
||||
end
|
||||
|
||||
λ_int = PropertyT.IntervalArithmetic.@interval(λ)
|
||||
|
||||
residual_int = elt - λ_int * unit - sos
|
||||
λ_int = PropertyT.sufficient_λ(residual_int, λ_int, halfradius=2)
|
||||
|
||||
return status, λ_int > 0, PropertyT.IntervalArithmetic.inf(λ_int)
|
||||
certified, λ_cert = PropertyT.certify_solution(
|
||||
elt,
|
||||
unit,
|
||||
λ,
|
||||
Q,
|
||||
halfradius=2
|
||||
)
|
||||
return status, certified, λ_cert
|
||||
end
|
||||
|
||||
@testset "1712.07167 Examples" begin
|
||||
|
||||
Loading…
Reference in New Issue
Block a user