From a matrix of locations and covariance parameters of the form (variance, range, nugget), return the square matrix of all pairwise covariances.
matern35_isotropic(covparms, locs)d_matern35_isotropic(covparms, locs)
d_matern45_isotropic(covparms, locs)
A matrix with n rows and n columns, with the i,j entry
containing the covariance between observations at locs[i,] and
locs[j,].
A vector with covariance parameters in the form (variance, range, nugget)
A matrix with n rows and d columns.
Each row of locs is a point in R^d.
d_matern35_isotropic(): Derivatives of isotropic
matern covariance function with smoothness 3.5
d_matern45_isotropic(): Derivatives of isotropic
matern covariance function with smoothness 3.5
The covariance parameter vector is (variance, range, nugget) = \((\sigma^2,\alpha,\tau^2)\), and the covariance function is parameterized as $$ M(x,y) = \sigma^2 ( \sum_{j=0}^3 c_j || x - y ||^j/ \alpha^j ) exp( - || x - y ||/ \alpha )$$ where c_0 = 1, c_1 = 1, c_2 = 2/5, c_3 = 1/15. The nugget value \( \sigma^2 \tau^2 \) is added to the diagonal of the covariance matrix. NOTE: the nugget is \( \sigma^2 \tau^2 \), not \( \tau^2 \).