PolyUtils module

Utilities for constructing interpolant-basis polynomial sum-of-squares models.

abstract type Domain{T<:Real}

Real domains for polynomial constraints.

dimension(dom)

Dimension of a domain.

degree(dom)

Degree of a polynomial constraints defining a domain.

sample(dom, npts)

Sample npts points from the interior of the domain.

weights(dom, pts)

Evaluations of the polynomial domain constraints at the points.

mutable struct EllipsoidDomain{T<:Real} <: Hypatia.PolyUtils.Domain{T<:Real}

Hyperellipse $(x-c)' Q (x-c) \leq 1$ with center c::Vector{T} and symmetric positive definite scaling/rotation matrix Q::AbstractMatrix{T}.

mutable struct BoxDomain{T<:Real} <: Hypatia.PolyUtils.Domain{T<:Real}

Hyperbox $x ∈ [l, u]$ with lower bounds l::Vector{T} and upper bounds u::Vector{T}.

mutable struct BallDomain{T<:Real} <: Hypatia.PolyUtils.Domain{T<:Real}

Euclidean hyperball $\lVert (x-c) \rVert_2 \leq r$ with center c::Vector{T} and positive radius r::T.

mutable struct FreeDomain{T<:Real} <: Hypatia.PolyUtils.Domain{T<:Real}

Real vectors $x ∈ ℝⁿ$ of dimension n::Int.

interpolate(
    dom,
    d;
    calc_V,
    get_quadr,
    sample,
    sample_factor
)

Compute interpolation data for a real weighted sum-of-squares conic constraint on a domain.

interpolate(
    R,
    halfdeg,
    n,
    gs,
    g_halfdegs;
    sample_factor,
    use_qr
)

Compute interpolation data for a complex weighted sum-of-squares conic constraint on a domain.