Radial
Gets the degree of polynomial augmentation required for this kernel, or -1 if no augmentation is needed.
Definition
Namespace: Numerics.NET.Curves
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.1.0
C#
For strictly positive definite (PD) kernels: -1 (no polynomial augmentation). For conditionally positive definite (CPD) kernels: the degree of the polynomial tail (typically 1 for affine polynomials: 1, x₁, x₂, ..., xₐ).
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.1.0
public int AugmentedPolynomialDegree { get; }Property Value
Int32For strictly positive definite (PD) kernels: -1 (no polynomial augmentation). For conditionally positive definite (CPD) kernels: the degree of the polynomial tail (typically 1 for affine polynomials: 1, x₁, x₂, ..., xₐ).
Remarks
Conditionally positive definite (CPD) kernels such as ThinPlate, Linear, Cubic, and Quintic require polynomial augmentation to ensure the interpolation system is well-posed and to guarantee exact reproduction of low-degree polynomials.
When this property returns a value ≥ 0, RBF interpolation automatically constructs an augmented system with polynomial constraints.
Strictly positive definite (PD) kernels such as Gaussian, Multiquadric, InverseMultiquadric, and InverseQuadratic do not require polynomial augmentation and return -1.