folded.matern.covariance.1d evaluates the 1d folded Matern
covariance function over an interval \([0,L]\) under different
boundary conditions. For periodic boundary conditions
$$C_{\mathcal{P}}(h,m) = \sum_{k=-\infty}^{\infty} (C(h-m+2kL),$$
for Neumann boundary conditions
$$C_{\mathcal{N}}(h,m) = \sum_{k=-\infty}^{\infty}
(C(h-m+2kL)+C(h+m+2kL)),$$
and for Dirichlet boundary conditions:
$$C_{\mathcal{D}}(h,m) = \sum_{k=-\infty}^{\infty}
(C(h-m+2kL)-C(h+m+2kL)),$$
where \(C(\cdot)\) is the Matern covariance function:
$$C(h) = \frac{\sigma^2}{2^{\nu-1}\Gamma(\nu)}(\kappa h)^\nu
K_\nu(\kappa h).$$
We consider the truncation:
$$C_{{\mathcal{P}},N}(h,m) = \sum_{k=-N}^{N} C(h-m+2kL),
C_{\mathcal{N},N}(h,m) = \sum_{k=-\infty}^{\infty}
(C(h-m+2kL)+C(h+m+2kL)),$$
and
$$C_{\mathcal{D},N}(h,m) = \sum_{k=-N}^{N}
(C(h-m+2kL)-C(h+m+2kL)).$$