gp_dot_prod_cov() [4/6]

template<typename T_x , typename T_sigma >

Eigen::Matrix< return_type_t< T_x, T_sigma >, Eigen::Dynamic, Eigen::Dynamic > stan::math::gp_dot_prod_cov	(	const std::vector< T_x > &	x,
		const T_sigma &	sigma
	)

Returns a dot product covariance matrix.

A member of Stan's Gaussian Process Library.

\(k(x,x') = \sigma^2 + x \cdot x'\)

A dot product covariance matrix is the same covariance matrix as in bayesian regression with \(N(0,1)\) priors on regression coefficients and a \(N(0,\sigma^2)\) prior on the constant function. See Rasmussen and Williams et al 2006, Chapter 4.

Template Parameters

T_x	type of std::vector of double
T_sigma	type of sigma

Parameters

x	std::vector of elements that can be used in transpose and multiply This function assumes each element of x is the same size.
sigma	constant function that can be used in stan::math::square

Returns

dot product covariance matrix that is positive semi-definite

Exceptions

std::domain_error

if sigma < 0, nan, inf or x is nan or infinite

Definition at line 100 of file gp_dot_prod_cov.hpp.