endas.localization.taper.GaspariCohn

class endas.localization.taper.GaspariCohn

Bases: endas.localization.TaperFn

Gaspari-Cohn covariance tapering function.

The function is defined by

\[\begin{split}G(r) = \begin{cases} \mbox{if } 0 \leq r < 1 \mbox{: } & 1 - \frac{5}{3}r^2 + \frac{5}{8}r^3 + \frac{1}{2}r^4 - \frac{1}{4}r^5 \\ \mbox{if } 0 \leq r < 2 \mbox{: } & 4 - 5r + \frac{5}{3}r^2 + \frac{5}{8}r^3 - \frac{1}{2}r^4 + \frac{1}{12}r^5 - \frac{2}{3r} \\ \mbox{otherwise : } & 0 \end{cases}\end{split}\]

where \(r = \vert i-j \vert / L\) and i, j are the (indexes of) two state variables, L is the distance scale factor (the localization radius). Therefore, the support range of the tapering function is 2L.