gp_periodic_cov() [1/3]

template<typename T_x , typename T_sigma , typename T_l , typename T_p >

Eigen::Matrix< return_type_t< T_x, T_sigma, T_l, T_p >, Eigen::Dynamic, Eigen::Dynamic > stan::math::gp_periodic_cov ( const std::vector< T_x > &  x, const T_sigma &  sigma, const T_l &  l, const T_p &  p  )

inline

Returns a periodic covariance matrix $\mathbf{K}$ using the input $\mathbf{X}$.

The elements of $\mathbf{K}$ are defined as $\mathbf{K}_{ij} = k(\mathbf{X}_i,\mathbf{X}_j),$ where $\mathbf{X}_i$ is the $i$-th row of $\mathbf{X}$ and
$k(\mathbf{x},\mathbf{x}^\prime) = \sigma^2 \exp\left(-\frac{2\sin^2(\pi |\mathbf{x}-\mathbf{x}^\prime|/p)}{\ell^2}\right),$
where $\sigma^2$, $\ell$ and $p$ are the signal variance, length-scale and period.

Template Parameters

T_x	type of std::vector elements of x. T_x can be a scalar, an Eigen::Vector, or an Eigen::RowVector.
T_sigma	type of sigma
T_l	type of length-scale
T_p	type of period

Parameters

x	std::vector of input elements. This function assumes that all elements of x have the same size.
sigma	standard deviation of the signal
l	length-scale
p	period

Returns

periodic covariance matrix

Exceptions

std::domain_error

if sigma <= 0, l <= 0, p <= 0 or x is nan or infinite

Definition at line 47 of file gp_periodic_cov.hpp.