exp,exponentialExponential covariance:
$$\sigma^2 \exp(-d/\rho)$$
exp2,exponential2,gaussianGaussian/double
exponential covariance:
$$\sigma^2 \exp(-(d/\rho)^2)$$
cubicCubic covariance:
$$\sigma^2 (1 - 7 (d/\rho)^2 + 8.75 (d/\rho)^3 -
3.5 (d/\rho)^5 + 0.75 (d/\rho)^7)$$
if \(d<\rho\).
sphericalSpherical covariance:
$$\sigma ^2(1 - 1.5(d/\rho) + 0.5 (d/\rho)^3)$$
if \(d<\rho\).
maternMatern covariance:
$$\frac{\sigma^2}{\Gamma(\nu) 2^{\nu-1}}
\left(\frac{d\sqrt{8\nu}}{\rho}\right)^\nu
K_\nu\left(\frac{d\sqrt{8\nu}}{\rho}\right)$$
cauchyCauchy covariance:
$$ \frac{\sigma^2}{(1 + (d/\rho)^2)^{\nu}}$$
iidIID covariance, i.e. zero matrix
since nugget is added afterwards. $$0$$