Interpolation basis

abstract type AbstractInterpolationBasis end

nelements(B::AbstractInterpolationBasis) -> Integer

Return the number of elements in B.

to_expressions(B::AbstractInterpolationBasis) -> AbstractVector{Expression}

Return the elements of B converted to Expressions.

HC.evaluate(B::AbstractInterpolationBasis, samples::AbstractMatrix{<:Number})

TBW

struct MonomialBasis{Tv<:Integer,Ti<:Integer} <: AbstractInterpolationBasis
    mexps::Vector{SparseVector{Tv,Ti}}
    vars::Vector{Variable}
end

An AbstractInterpolationBasis that consists of monomials. Parametric type Tv defines the type of exponents in multiexponents, Ti defines the type of non-zero exponent indicies. See also SparseVector.

MonomialBasis{Tv<:Integer, Ti<:Integer}(; variables::Vector{Variable}, degree::Integer)
monomials(variables::Vector{Variable}, degree::Integer)

Examples

julia> @var x y z
(x, y, z)

julia> mons = MonomialBasis{Int8, Int16}(variables=[x,y,z], degree=2)
10-element MonomialBasis{Int8, Int16}
[1, x, y, z, x^2, y^2, z^2, x*y, x*z, y*z]

julia> samples = randn(ComplexF64, 3, 2)
3×2 Matrix{ComplexF64}:
  0.299344-0.238374im  -0.527805-0.360128im
 -0.114638+1.89994im    0.127791-0.846475im
  0.303708+1.24025im   0.0363844-0.264417im

julia> evaluate(mons, samples)
10×2 Matrix{ComplexF64}:
       1.0+0.0im              1.0+0.0im
  0.299344-0.238374im   -0.527805-0.360128im
 -0.114638+1.89994im     0.127791-0.846475im
  0.303708+1.24025im    0.0363844-0.264417im
 0.0327848-0.142712im    0.148886+0.380155im
  -3.59664-0.43561im    -0.700189-0.216343im
  -1.44598+0.753349im  -0.0685926-0.0192413im
  0.418581+0.596063im   -0.372288+0.400752im
  0.386557+0.298866im   -0.114428+0.126458im
  -2.39122+0.434849im   -0.219173-0.0645886im