gpLib.WendlandKernel

class gpLib.WendlandKernel(mu: float = 1.0, k: int = 0, **kwargs)

Compactly-supported Wendland kernel.

Let \(t = \|x-x'\|/\ell_{0}\), \((1-t)_+ = \max(1-t,0)\) and \(\ell = k+1+\mu\).

\[\begin{split}k(t) = \begin{cases} (1-t)_+^{\ell}, & k = 0,\\[6pt] (1-t)_+^{\ell+1}\bigl[1 + (\ell+1)t\bigr], & k = 1,\\[6pt] (1-t)_+^{\ell+2}\!\Bigl[ 1 + (\ell+2)t + \tfrac13(\ell^{2}+4\ell+3)t^{2} \Bigr], & k = 2. \end{cases}\end{split}\]

Parameters:

• mu – Smoothness parameter \(\mu>0\).

• k – Order 0, 1 or 2 (see cases above).